Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models.

PubMed

Garcia, Tanya P; Ma, Yanyuan

2017-10-01

We develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates. We assume the model error and covariate distributions are unspecified, and the measurement error distribution is a general parametric distribution with unknown variance-covariance. We construct root- n consistent, asymptotically normal and locally efficient estimators using the semiparametric efficient score. We do not estimate any unknown distribution or model error heteroskedasticity. Instead, we form the estimator under possibly incorrect working distribution models for the model error, error-prone covariate, or both. Empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error-prone covariates.

Evaluation of three lidar scanning strategies for turbulence measurements

NASA Astrophysics Data System (ADS)

Newman, J. F.; Klein, P. M.; Wharton, S.; Sathe, A.; Bonin, T. A.; Chilson, P. B.; Muschinski, A.

2015-11-01

Several errors occur when a traditional Doppler-beam swinging (DBS) or velocity-azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers. Results indicate that the six-beam strategy mitigates some of the errors caused by VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.

Evaluation of three lidar scanning strategies for turbulence measurements

NASA Astrophysics Data System (ADS)

Newman, Jennifer F.; Klein, Petra M.; Wharton, Sonia; Sathe, Ameya; Bonin, Timothy A.; Chilson, Phillip B.; Muschinski, Andreas

2016-05-01

Several errors occur when a traditional Doppler beam swinging (DBS) or velocity-azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar, and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers.Results indicate that the six-beam strategy mitigates some of the errors caused by VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

Triple collocation based merging of satellite soil moisture retrievals

USDA-ARS?s Scientific Manuscript database

We propose a method for merging soil moisture retrievals from space borne active and passive microwave instruments based on weighted averaging taking into account the error characteristics of the individual data sets. The merging scheme is parameterized using error variance estimates obtained from u...

The error structure of the SMAP single and dual channel soil moisture retrievals

USDA-ARS?s Scientific Manuscript database

Knowledge of the temporal error structure for remotely-sensed surface soil moisture retrievals can improve our ability to exploit them for hydrology and climate studies. This study employs a triple collocation type analysis to investigate both the total variance and temporal auto-correlation of erro...

Empirical State Error Covariance Matrix for Batch Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joe

2015-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

Evaluation of three lidar scanning strategies for turbulence measurements

DOE PAGES

Newman, Jennifer F.; Klein, Petra M.; Wharton, Sonia; ...

2016-05-03

Several errors occur when a traditional Doppler beam swinging (DBS) or velocity–azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar, and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers.Results indicate that the six-beam strategy mitigates some of the errors caused bymore » VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.« less

Evaluation of three lidar scanning strategies for turbulence measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Newman, Jennifer F.; Klein, Petra M.; Wharton, Sonia

Several errors occur when a traditional Doppler beam swinging (DBS) or velocity–azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar, and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers.Results indicate that the six-beam strategy mitigates some of the errors caused bymore » VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.« less

The effect of covariate mean differences on the standard error and confidence interval for the comparison of treatment means.

PubMed

Liu, Xiaofeng Steven

2011-05-01

The use of covariates is commonly believed to reduce the unexplained error variance and the standard error for the comparison of treatment means, but the reduction in the standard error is neither guaranteed nor uniform over different sample sizes. The covariate mean differences between the treatment conditions can inflate the standard error of the covariate-adjusted mean difference and can actually produce a larger standard error for the adjusted mean difference than that for the unadjusted mean difference. When the covariate observations are conceived of as randomly varying from one study to another, the covariate mean differences can be related to a Hotelling's T(2) . Using this Hotelling's T(2) statistic, one can always find a minimum sample size to achieve a high probability of reducing the standard error and confidence interval width for the adjusted mean difference. ©2010 The British Psychological Society.

An Empirical State Error Covariance Matrix Orbit Determination Example

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Accuracy and speed in computing the Chebyshev collocation derivative

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Solomonoff, Alex

1991-01-01

We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

An Empirical State Error Covariance Matrix for the Weighted Least Squares Estimation Method

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the un-certainty in the estimated states. By a reinterpretation of the equations involved in the weighted least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. This proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. Results based on the proposed technique will be presented for a simple, two observer, measurement error only problem.

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Estimation of genetic connectedness diagnostics based on prediction errors without the prediction error variance-covariance matrix.

PubMed

Holmes, John B; Dodds, Ken G; Lee, Michael A

2017-03-02

An important issue in genetic evaluation is the comparability of random effects (breeding values), particularly between pairs of animals in different contemporary groups. This is usually referred to as genetic connectedness. While various measures of connectedness have been proposed in the literature, there is general agreement that the most appropriate measure is some function of the prediction error variance-covariance matrix. However, obtaining the prediction error variance-covariance matrix is computationally demanding for large-scale genetic evaluations. Many alternative statistics have been proposed that avoid the computational cost of obtaining the prediction error variance-covariance matrix, such as counts of genetic links between contemporary groups, gene flow matrices, and functions of the variance-covariance matrix of estimated contemporary group fixed effects. In this paper, we show that a correction to the variance-covariance matrix of estimated contemporary group fixed effects will produce the exact prediction error variance-covariance matrix averaged by contemporary group for univariate models in the presence of single or multiple fixed effects and one random effect. We demonstrate the correction for a series of models and show that approximations to the prediction error matrix based solely on the variance-covariance matrix of estimated contemporary group fixed effects are inappropriate in certain circumstances. Our method allows for the calculation of a connectedness measure based on the prediction error variance-covariance matrix by calculating only the variance-covariance matrix of estimated fixed effects. Since the number of fixed effects in genetic evaluation is usually orders of magnitudes smaller than the number of random effect levels, the computational requirements for our method should be reduced.

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Adjoints and Low-rank Covariance Representation

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.

2000-01-01

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Temporal gravity field modeling based on least square collocation with short-arc approach

NASA Astrophysics Data System (ADS)

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

Bio-Optical Data Assimilation With Observational Error Covariance Derived From an Ensemble of Satellite Images

NASA Astrophysics Data System (ADS)

Shulman, Igor; Gould, Richard W.; Frolov, Sergey; McCarthy, Sean; Penta, Brad; Anderson, Stephanie; Sakalaukus, Peter

2018-03-01

An ensemble-based approach to specify observational error covariance in the data assimilation of satellite bio-optical properties is proposed. The observational error covariance is derived from statistical properties of the generated ensemble of satellite MODIS-Aqua chlorophyll (Chl) images. The proposed observational error covariance is used in the Optimal Interpolation scheme for the assimilation of MODIS-Aqua Chl observations. The forecast error covariance is specified in the subspace of the multivariate (bio-optical, physical) empirical orthogonal functions (EOFs) estimated from a month-long model run. The assimilation of surface MODIS-Aqua Chl improved surface and subsurface model Chl predictions. Comparisons with surface and subsurface water samples demonstrate that data assimilation run with the proposed observational error covariance has higher RMSE than the data assimilation run with "optimistic" assumption about observational errors (10% of the ensemble mean), but has smaller or comparable RMSE than data assimilation run with an assumption that observational errors equal to 35% of the ensemble mean (the target error for satellite data product for chlorophyll). Also, with the assimilation of the MODIS-Aqua Chl data, the RMSE between observed and model-predicted fractions of diatoms to the total phytoplankton is reduced by a factor of two in comparison to the nonassimilative run.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J.; Golberg, M.

1978-01-01

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Tangborn, Andrew; Auger, Ludovic

2003-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

Evaluation of a lower-powered analyzer and sampling system for eddy-covariance measurements of nitrous oxide fluxes

NASA Astrophysics Data System (ADS)

Brown, Shannon E.; Sargent, Steve; Wagner-Riddle, Claudia

2018-03-01

Nitrous oxide (N2O) fluxes measured using the eddy-covariance method capture the spatial and temporal heterogeneity of N2O emissions. Most closed-path trace-gas analyzers for eddy-covariance measurements have large-volume, multi-pass absorption cells that necessitate high flow rates for ample frequency response, thus requiring high-power sample pumps. Other sampling system components, including rain caps, filters, dryers, and tubing, can also degrade system frequency response. This field trial tested the performance of a closed-path eddy-covariance system for N2O flux measurements with improvements to use less power while maintaining the frequency response. The new system consists of a thermoelectrically cooled tunable diode laser absorption spectrometer configured to measure both N2O and carbon dioxide (CO2). The system features a relatively small, single-pass sample cell (200 mL) that provides good frequency response with a lower-powered pump ( ˜ 250 W). A new filterless intake removes particulates from the sample air stream with no additional mixing volume that could degrade frequency response. A single-tube dryer removes water vapour from the sample to avoid the need for density or spectroscopic corrections, while maintaining frequency response. This eddy-covariance system was collocated with a previous tunable diode laser absorption spectrometer model to compare N2O and CO2 flux measurements for two full growing seasons (May 2015 to October 2016) in a fertilized cornfield in Southern Ontario, Canada. Both spectrometers were placed outdoors at the base of the sampling tower, demonstrating ruggedness for a range of environmental conditions (minimum to maximum daily temperature range: -26.1 to 31.6 °C). The new system rarely required maintenance. An in situ frequency-response test demonstrated that the cutoff frequency of the new system was better than the old system (3.5 Hz compared to 2.30 Hz) and similar to that of a closed-path CO2 eddy-covariance system (4.05 Hz), using shorter tubing and no dryer, that was also collocated at the site. Values of the N2O fluxes were similar between the two spectrometer systems (slope = 1.01, r2 = 0.96); CO2 fluxes as measured by the short-tubed eddy-covariance system and the two spectrometer systems correlated well (slope = 1.03, r2 = 0.998). The new lower-powered tunable diode laser absorption spectrometer configuration with the filterless intake and single-tube dryer showed promise for deployment in remote areas.

Boundary conditions in Chebyshev and Legendre methods

NASA Technical Reports Server (NTRS)

Canuto, C.

1984-01-01

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

Position Error Covariance Matrix Validation and Correction

NASA Technical Reports Server (NTRS)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a New Proposal

ERIC Educational Resources Information Center

Tian, Wei; Cai, Li; Thissen, David; Xin, Tao

2013-01-01

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

Interpolation of Superconducting Gravity Observations Using Least-Squares Collocation Method

NASA Astrophysics Data System (ADS)

Habel, Branislav; Janak, Juraj

2014-05-01

A pre-processing of the gravity data measured by superconducting gravimeter involves removing of spikes, offsets and gaps. Their presence in observations can limit the data analysis and degrades the quality of obtained results. Short data gaps are filling by theoretical signal in order to get continuous records of gravity. It requires the accurate tidal model and eventually atmospheric pressure at the observed site. The poster presents a design of algorithm for interpolation of gravity observations with a sampling rate of 1 min. Novel approach is based on least-squares collocation which combines adjustment of trend parameters, filtering of noise and prediction. It allows the interpolation of missing data up to a few hours without necessity of any other information. Appropriate parameters for covariance function are found using a Bayes' theorem by modified optimization process. Accuracy of method is improved by the rejection of outliers before interpolation. For filling of longer gaps the collocation model is combined with theoretical tidal signal for the rigid Earth. Finally, the proposed method was tested on the superconducting gravity observations at several selected stations of Global Geodynamics Project. Testing demonstrates its reliability and offers results comparable with the standard approach implemented in ETERNA software package without necessity of an accurate tidal model.

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

NASA Technical Reports Server (NTRS)

Au, Andrew Y.; Brown, Richard D.; Welker, Jean E.

1991-01-01

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred.

Estimation of Covariance Matrix on Bi-Response Longitudinal Data Analysis with Penalized Spline Regression

NASA Astrophysics Data System (ADS)

Islamiyati, A.; Fatmawati; Chamidah, N.

2018-03-01

The correlation assumption of the longitudinal data with bi-response occurs on the measurement between the subjects of observation and the response. It causes the auto-correlation of error, and this can be overcome by using a covariance matrix. In this article, we estimate the covariance matrix based on the penalized spline regression model. Penalized spline involves knot points and smoothing parameters simultaneously in controlling the smoothness of the curve. Based on our simulation study, the estimated regression model of the weighted penalized spline with covariance matrix gives a smaller error value compared to the error of the model without covariance matrix.

Relative-Error-Covariance Algorithms

NASA Technical Reports Server (NTRS)

Bierman, Gerald J.; Wolff, Peter J.

1991-01-01

Two algorithms compute error covariance of difference between optimal estimates, based on data acquired during overlapping or disjoint intervals, of state of discrete linear system. Provides quantitative measure of mutual consistency or inconsistency of estimates of states. Relative-error-covariance concept applied, to determine degree of correlation between trajectories calculated from two overlapping sets of measurements and construct real-time test of consistency of state estimates based upon recently acquired data.

Predictive Simulations of Neuromuscular Coordination and Joint-Contact Loading in Human Gait.

PubMed

Lin, Yi-Chung; Walter, Jonathan P; Pandy, Marcus G

2018-04-18

We implemented direct collocation on a full-body neuromusculoskeletal model to calculate muscle forces, ground reaction forces and knee contact loading simultaneously for one cycle of human gait. A data-tracking collocation problem was solved for walking at the normal speed to establish the practicality of incorporating a 3D model of articular contact and a model of foot-ground interaction explicitly in a dynamic optimization simulation. The data-tracking solution then was used as an initial guess to solve predictive collocation problems, where novel patterns of movement were generated for walking at slow and fast speeds, independent of experimental data. The data-tracking solutions accurately reproduced joint motion, ground forces and knee contact loads measured for two total knee arthroplasty patients walking at their preferred speeds. RMS errors in joint kinematics were < 2.0° for rotations and < 0.3 cm for translations while errors in the model-computed ground-reaction and knee-contact forces were < 0.07 BW and < 0.4 BW, respectively. The predictive solutions were also consistent with joint kinematics, ground forces, knee contact loads and muscle activation patterns measured for slow and fast walking. The results demonstrate the feasibility of performing computationally-efficient, predictive, dynamic optimization simulations of movement using full-body, muscle-actuated models with realistic representations of joint function.

Simplification of the Kalman filter for meteorological data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1991-01-01

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Model selection for marginal regression analysis of longitudinal data with missing observations and covariate measurement error.

PubMed

Shen, Chung-Wei; Chen, Yi-Hau

2015-10-01

Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Non-linear matter power spectrum covariance matrix errors and cosmological parameter uncertainties

NASA Astrophysics Data System (ADS)

Blot, L.; Corasaniti, P. S.; Amendola, L.; Kitching, T. D.

2016-06-01

The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc-1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ˜10 per cent at k > 0.3 h Mpc-1. Over the entire range these reduce to about ˜5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc-1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters.

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Schiesser, Emil R.

1998-01-01

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

External quality-assurance results for the National Atmospheric Deposition Program/National Trends Network during 1991

USGS Publications Warehouse

Nilles, M.A.; Gordon, J.D.; Schroder, L.J.; Paulin, C.E.

1995-01-01

The U.S. Geological Survey used four programs in 1991 to provide external quality assurance for the National Atmospheric Deposition Program/National Trends Network (NADP/NTN). An intersite-comparison program was used to evaluate onsite pH and specific-conductance determinations. The effects of routine sample handling, processing, and shipping of wet-deposition samples on analyte determinations and an estimated precision of analyte values and concentrations were evaluated in the blind-audit program. Differences between analytical results and an estimate of the analytical precision of four laboratories routinely measuring wet deposition were determined by an interlaboratory-comparison program. Overall precision estimates for the precipitation-monitoring system were determined for selected sites by a collocated-sampler program. Results of the intersite-comparison program indicated that 93 and 86 percent of the site operators met the NADP/NTN accuracy goal for pH determinations during the two intersite-comparison studies completed during 1991. The results also indicated that 96 and 97 percent of the site operators met the NADP/NTN accuracy goal for specific-conductance determinations during the two 1991 studies. The effects of routine sample handling, processing, and shipping, determined in the blind-audit program indicated significant positive bias (a=.O 1) for calcium, magnesium, sodium, potassium, chloride, nitrate, and sulfate. Significant negative bias (or=.01) was determined for hydrogen ion and specific conductance. Only ammonium determinations were not biased. A Kruskal-Wallis test indicated that there were no significant (*3t=.01) differences in analytical results from the four laboratories participating in the interlaboratory-comparison program. Results from the collocated-sampler program indicated the median relative error for cation concentration and deposition exceeded eight percent at most sites, whereas the median relative error for sample volume, sulfate, and nitrate concentration at all sites was less than four percent. The median relative error for hydrogen ion concentration and deposition ranged from 4.6 to 18.3 percent at the four sites and as indicated in previous years of the study, was inversely proportional to the acidity of the precipitation at a given site. Overall, collocated-sampling error typically was five times that of laboratory error estimates for most analytes.

The use of a covariate reduces experimental error in nutrient digestion studies in growing pigs

USDA-ARS?s Scientific Manuscript database

Covariance analysis limits error, the degree of nuisance variation, and overparameterizing factors to accurately measure treatment effects. Data dealing with growth, carcass composition, and genetics often utilize covariates in data analysis. In contrast, nutritional studies typically do not. The ob...

Improved Stratospheric Temperature Retrievals for Climate Reanalysis

NASA Technical Reports Server (NTRS)

Rokke, L.; Joiner, J.

1999-01-01

The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.

Error Covariance Penalized Regression: A novel multivariate model combining penalized regression with multivariate error structure.

PubMed

Allegrini, Franco; Braga, Jez W B; Moreira, Alessandro C O; Olivieri, Alejandro C

2018-06-29

A new multivariate regression model, named Error Covariance Penalized Regression (ECPR) is presented. Following a penalized regression strategy, the proposed model incorporates information about the measurement error structure of the system, using the error covariance matrix (ECM) as a penalization term. Results are reported from both simulations and experimental data based on replicate mid and near infrared (MIR and NIR) spectral measurements. The results for ECPR are better under non-iid conditions when compared with traditional first-order multivariate methods such as ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLS). Copyright © 2018 Elsevier B.V. All rights reserved.

Adaptive framework to better characterize errors of apriori fluxes and observational residuals in a Bayesian setup for the urban flux inversions.

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Karion, A.; Mueller, K.; Gourdji, S.; Martin, C.; Whetstone, J. R.

2017-12-01

The National Institute of Standards and Technology (NIST) supports the North-East Corridor Baltimore Washington (NEC-B/W) project and Indianapolis Flux Experiment (INFLUX) aiming to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties. These projects employ different flux estimation methods including top-down inversion approaches. The traditional Bayesian inversion method estimates emission distributions by updating prior information using atmospheric observations of Green House Gases (GHG) coupled to an atmospheric and dispersion model. The magnitude of the update is dependent upon the observed enhancement along with the assumed errors such as those associated with prior information and the atmospheric transport and dispersion model. These errors are specified within the inversion covariance matrices. The assumed structure and magnitude of the specified errors can have large impact on the emission estimates from the inversion. The main objective of this work is to build a data-adaptive model for these covariances matrices. We construct a synthetic data experiment using a Kalman Filter inversion framework (Lopez et al., 2017) employing different configurations of transport and dispersion model and an assumed prior. Unlike previous traditional Bayesian approaches, we estimate posterior emissions using regularized sample covariance matrices associated with prior errors to investigate whether the structure of the matrices help to better recover our hypothetical true emissions. To incorporate transport model error, we use ensemble of transport models combined with space-time analytical covariance to construct a covariance that accounts for errors in space and time. A Kalman Filter is then run using these covariances along with Maximum Likelihood Estimates (MLE) of the involved parameters. Preliminary results indicate that specifying sptio-temporally varying errors in the error covariances can improve the flux estimates and uncertainties. We also demonstrate that differences between the modeled and observed meteorology can be used to predict uncertainties associated with atmospheric transport and dispersion modeling which can help improve the skill of an inversion at urban scales.

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Cohn, Stephen E.

1994-01-01

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Evaluation of Approaches to Deal with Low-Frequency Nuisance Covariates in Population Pharmacokinetic Analyses.

PubMed

Lagishetty, Chakradhar V; Duffull, Stephen B

2015-11-01

Clinical studies include occurrences of rare variables, like genotypes, which due to their frequency and strength render their effects difficult to estimate from a dataset. Variables that influence the estimated value of a model-based parameter are termed covariates. It is often difficult to determine if such an effect is significant, since type I error can be inflated when the covariate is rare. Their presence may have either an insubstantial effect on the parameters of interest, hence are ignorable, or conversely they may be influential and therefore non-ignorable. In the case that these covariate effects cannot be estimated due to power and are non-ignorable, then these are considered nuisance, in that they have to be considered but due to type 1 error are of limited interest. This study assesses methods of handling nuisance covariate effects. The specific objectives include (1) calibrating the frequency of a covariate that is associated with type 1 error inflation, (2) calibrating its strength that renders it non-ignorable and (3) evaluating methods for handling these non-ignorable covariates in a nonlinear mixed effects model setting. Type 1 error was determined for the Wald test. Methods considered for handling the nuisance covariate effects were case deletion, Box-Cox transformation and inclusion of a specific fixed effects parameter. Non-ignorable nuisance covariates were found to be effectively handled through addition of a fixed effect parameter.

Tests for detecting overdispersion in models with measurement error in covariates.

PubMed

Yang, Yingsi; Wong, Man Yu

2015-11-30

Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results. Copyright © 2015 John Wiley & Sons, Ltd.

Examination of various roles for covariance matrices in the development, evaluation, and application of nuclear data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, D.L.

The last decade has been a period of rapid development in the implementation of covariance-matrix methodology in nuclear data research. This paper offers some perspective on the progress which has been made, on some of the unresolved problems, and on the potential yet to be realized. These discussions address a variety of issues related to the development of nuclear data. Topics examined are: the importance of designing and conducting experiments so that error information is conveniently generated; the procedures for identifying error sources and quantifying their magnitudes and correlations; the combination of errors; the importance of consistent and well-characterized measurementmore » standards; the role of covariances in data parameterization (fitting); the estimation of covariances for values calculated from mathematical models; the identification of abnormalities in covariance matrices and the analysis of their consequences; the problems encountered in representing covariance information in evaluated files; the role of covariances in the weighting of diverse data sets; the comparison of various evaluations; the influence of primary-data covariance in the analysis of covariances for derived quantities (sensitivity); and the role of covariances in the merging of the diverse nuclear data information. 226 refs., 2 tabs.« less

Using SAS PROC CALIS to fit Level-1 error covariance structures of latent growth models.

PubMed

Ding, Cherng G; Jane, Ten-Der

2012-09-01

In the present article, we demonstrates the use of SAS PROC CALIS to fit various types of Level-1 error covariance structures of latent growth models (LGM). Advantages of the SEM approach, on which PROC CALIS is based, include the capabilities of modeling the change over time for latent constructs, measured by multiple indicators; embedding LGM into a larger latent variable model; incorporating measurement models for latent predictors; and better assessing model fit and the flexibility in specifying error covariance structures. The strength of PROC CALIS is always accompanied with technical coding work, which needs to be specifically addressed. We provide a tutorial on the SAS syntax for modeling the growth of a manifest variable and the growth of a latent construct, focusing the documentation on the specification of Level-1 error covariance structures. Illustrations are conducted with the data generated from two given latent growth models. The coding provided is helpful when the growth model has been well determined and the Level-1 error covariance structure is to be identified.

A Study on Mutil-Scale Background Error Covariances in 3D-Var Data Assimilation

NASA Astrophysics Data System (ADS)

Zhang, Xubin; Tan, Zhe-Min

2017-04-01

The construction of background error covariances is a key component of three-dimensional variational data assimilation. There are different scale background errors and interactions among them in the numerical weather Prediction. However, the influence of these errors and their interactions cannot be represented in the background error covariances statistics when estimated by the leading methods. So, it is necessary to construct background error covariances influenced by multi-scale interactions among errors. With the NMC method, this article firstly estimates the background error covariances at given model-resolution scales. And then the information of errors whose scales are larger and smaller than the given ones is introduced respectively, using different nesting techniques, to estimate the corresponding covariances. The comparisons of three background error covariances statistics influenced by information of errors at different scales reveal that, the background error variances enhance particularly at large scales and higher levels when introducing the information of larger-scale errors by the lateral boundary condition provided by a lower-resolution model. On the other hand, the variances reduce at medium scales at the higher levels, while those show slight improvement at lower levels in the nested domain, especially at medium and small scales, when introducing the information of smaller-scale errors by nesting a higher-resolution model. In addition, the introduction of information of larger- (smaller-) scale errors leads to larger (smaller) horizontal and vertical correlation scales of background errors. Considering the multivariate correlations, the Ekman coupling increases (decreases) with the information of larger- (smaller-) scale errors included, whereas the geostrophic coupling in free atmosphere weakens in both situations. The three covariances obtained in above work are used in a data assimilation and model forecast system respectively, and then the analysis-forecast cycles for a period of 1 month are conducted. Through the comparison of both analyses and forecasts from this system, it is found that the trends for variation in analysis increments with information of different scale errors introduced are consistent with those for variation in variances and correlations of background errors. In particular, introduction of smaller-scale errors leads to larger amplitude of analysis increments for winds at medium scales at the height of both high- and low- level jet. And analysis increments for both temperature and humidity are greater at the corresponding scales at middle and upper levels under this circumstance. These analysis increments improve the intensity of jet-convection system which includes jets at different levels and coupling between them associated with latent heat release, and these changes in analyses contribute to the better forecasts for winds and temperature in the corresponding areas. When smaller-scale errors are included, analysis increments for humidity enhance significantly at large scales at lower levels to moisten southern analyses. This humidification devotes to correcting dry bias there and eventually improves forecast skill of humidity. Moreover, inclusion of larger- (smaller-) scale errors is beneficial for forecast quality of heavy (light) precipitation at large (small) scales due to the amplification (diminution) of intensity and area in precipitation forecasts but tends to overestimate (underestimate) light (heavy) precipitation .

Estimating error cross-correlations in soil moisture data sets using extended collocation analysis

USDA-ARS?s Scientific Manuscript database

Consistent global soil moisture records are essential for studying the role of hydrologic processes within the larger earth system. Various studies have shown the benefit of assimilating satellite-based soil moisture data into water balance models or merging multi-source soil moisture retrievals int...

The potential of 2D Kalman filtering for soil moisture data assimilation

USDA-ARS?s Scientific Manuscript database

We examine the potential for parameterizing a two-dimensional (2D) land data assimilation system using spatial error auto-correlation statistics gleaned from a triple collocation analysis and the triplet of: (1) active microwave-, (2) passive microwave- and (3) land surface model-based surface soil ...

On the Likely Utility of Hybrid Weights Optimized for Variances in Hybrid Error Covariance Models

NASA Astrophysics Data System (ADS)

Satterfield, E.; Hodyss, D.; Kuhl, D.; Bishop, C. H.

2017-12-01

Because of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble covariance is equal to the true error covariance of a forecast. Previous work demonstrated how information about the distribution of true error variances given an ensemble sample variance can be revealed from an archive of (observation-minus-forecast, ensemble-variance) data pairs. Here, we derive a simple and intuitively compelling formula to obtain the mean of this distribution of true error variances given an ensemble sample variance from (observation-minus-forecast, ensemble-variance) data pairs produced by a single run of a data assimilation system. This formula takes the form of a Hybrid weighted average of the climatological forecast error variance and the ensemble sample variance. Here, we test the extent to which these readily obtainable weights can be used to rapidly optimize the covariance weights used in Hybrid data assimilation systems that employ weighted averages of static covariance models and flow-dependent ensemble based covariance models. Univariate data assimilation and multi-variate cycling ensemble data assimilation are considered. In both cases, it is found that our computationally efficient formula gives Hybrid weights that closely approximate the optimal weights found through the simple but computationally expensive process of testing every plausible combination of weights.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife

ERIC Educational Resources Information Center

Jennrich, Robert I.

2008-01-01

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the…

A Wavelet Based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Auger, Ludovic; Tangborn, Andrew; Atlas, Robert (Technical Monitor)

2002-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.

On-line estimation of error covariance parameters for atmospheric data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1995-01-01

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

A Systematic Approach for Identifying Level-1 Error Covariance Structures in Latent Growth Modeling

ERIC Educational Resources Information Center

Ding, Cherng G.; Jane, Ten-Der; Wu, Chiu-Hui; Lin, Hang-Rung; Shen, Chih-Kang

2017-01-01

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which,…

Statistics of the residual refraction errors in laser ranging data

NASA Technical Reports Server (NTRS)

Gardner, C. S.

1977-01-01

A theoretical model for the range error covariance was derived by assuming that the residual refraction errors are due entirely to errors in the meteorological data which are used to calculate the atmospheric correction. The properties of the covariance function are illustrated by evaluating the theoretical model for the special case of a dense network of weather stations uniformly distributed within a circle.

Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

PubMed

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

PubMed Central

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W.; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation. PMID:23844016

Estimated variability of National Atmospheric Deposition Program/Mercury Deposition Network measurements using collocated samplers

USGS Publications Warehouse

Wetherbee, G.A.; Gay, D.A.; Brunette, R.C.; Sweet, C.W.

2007-01-01

The National Atmospheric Deposition Program/Mercury Deposition Network (MDN) provides long-term, quality-assured records of mercury in wet deposition in the USA and Canada. Interpretation of spatial and temporal trends in the MDN data requires quantification of the variability of the MDN measurements. Variability is quantified for MDN data from collocated samplers at MDN sites in two states, one in Illinois and one in Washington. Median absolute differences in the collocated sampler data for total mercury concentration are approximately 11% of the median mercury concentration for all valid 1999-2004 MDN data. Median absolute differences are between 3.0% and 14% of the median MDN value for collector catch (sample volume) and between 6.0% and 15% of the median MDN value for mercury wet deposition. The overall measurement errors are sufficiently low to resolve between NADP/MDN measurements by ??2 ng??l-1 and ??2 ????m-2?? year-1, which are the contour intervals used to display the data on NADP isopleths maps for concentration and deposition, respectively. ?? Springer Science+Business Media B.V. 2007.

Advances in Time and Frequency Transfer From Dual-Frequency GPS Pseudorange and Carrier-Phase Observations

DTIC Science & Technology

2008-12-01

collocated independent time transfer techniques such as Two-Way Satellite Time and Frequency Transfer ( TWSTFT ) [10,11]. The issue of pseudorange errors...transfer methods, e.g. TWSTFT . There is a side benefit that far exceeds just meeting the objective we have set. The new model explicitly reveals, on

Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation.

PubMed

Manzhos, Sergei; Carrington, Tucker

2016-12-14

We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H 2 CO, we obtain a mean absolute error of less than 1 cm -1 ; with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm -1 .

Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation

NASA Astrophysics Data System (ADS)

Manzhos, Sergei; Carrington, Tucker

2016-12-01

We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H2CO, we obtain a mean absolute error of less than 1 cm-1; with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm-1.

Background Error Covariance Estimation using Information from a Single Model Trajectory with Application to Ocean Data Assimilation into the GEOS-5 Coupled Model

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Kovach, Robin M.; Vernieres, Guillaume; Koster, Randal D. (Editor)

2014-01-01

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele; Kovach, Robin M.; Vernieres, Guillaume

2014-01-01

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Asynchrony of wind and hydropower resources in Australia.

PubMed

Gunturu, Udaya Bhaskar; Hallgren, Willow

2017-08-18

Wind and hydropower together constitute nearly 80% of the renewable capacity in Australia and their resources are collocated. We show that wind and hydro generation capacity factors covary negatively at the interannual time scales. Thus, the technology diversity mitigates the variability of renewable power generation at the interannual scales. The asynchrony of wind and hydropower resources is explained by the differential impact of the two modes of the El Ni˜no Southern Oscillation - canonical and Modoki - on the wind and hydro resources. Also, the Modoki El Ni˜no and the Modoki La Ni˜na phases have greater impact. The seasonal impact patterns corroborate these results. As the proportion of wind power increases in Australia's energy mix, this negative covariation has implications for storage capacity of excess wind generation at short time scales and for generation system adequacy at the longer time scales.

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Kovach, Robin M.; Vernieres, Guillaume

2013-01-01

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

On the equivalence of spherical splines with least-squares collocation and Stokes's formula for regional geoid computation

NASA Astrophysics Data System (ADS)

Ophaug, Vegard; Gerlach, Christian

2017-11-01

This work is an investigation of three methods for regional geoid computation: Stokes's formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

PubMed

Murad, Havi; Kipnis, Victor; Freedman, Laurence S

2016-10-01

Assessing interactions in linear regression models when covariates have measurement error (ME) is complex.We previously described regression calibration (RC) methods that yield consistent estimators and standard errors for interaction coefficients of normally distributed covariates having classical ME. Here we extend normal based RC (NBRC) and linear RC (LRC) methods to a non-classical ME model, and describe more efficient versions that combine estimates from the main study and internal sub-study. We apply these methods to data from the Observing Protein and Energy Nutrition (OPEN) study. Using simulations we show that (i) for normally distributed covariates efficient NBRC and LRC were nearly unbiased and performed well with sub-study size ≥200; (ii) efficient NBRC had lower MSE than efficient LRC; (iii) the naïve test for a single interaction had type I error probability close to the nominal significance level, whereas efficient NBRC and LRC were slightly anti-conservative but more powerful; (iv) for markedly non-normal covariates, efficient LRC yielded less biased estimators with smaller variance than efficient NBRC. Our simulations suggest that it is preferable to use: (i) efficient NBRC for estimating and testing interaction effects of normally distributed covariates and (ii) efficient LRC for estimating and testing interactions for markedly non-normal covariates. © The Author(s) 2013.

Absorption of Solar Radiation by Clouds: Interpretations of Satellite, Surface, and Aircraft Measurements

NASA Technical Reports Server (NTRS)

Cess, R. D.; Zhang, M. H.; Zhou, Y.; Jing, X.; Dvortsov, V.

1996-01-01

To investigate the absorption of shortwave radiation by clouds, we have collocated satellite and surface measurements of shortwave radiation at several locations. Considerable effort has been directed toward understanding and minimizing sampling errors caused by the satellite measurements being instantaneous and over a grid that is much larger than the field of view of an upward facing surface pyranometer. The collocated data indicate that clouds absorb considerably more shortwave radiation than is predicted by theoretical models. This is consistent with the finding from both satellite and aircraft measurements that observed clouds are darker than model clouds. In the limit of thick clouds, observed top-of-the-atmosphere albedos do not exceed a value of 0.7, whereas in models the maximum albedo can be 0.8.

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

PubMed Central

Zucker, David M.; Spiegelman, Donna

2013-01-01

SUMMARY We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain ‘localized error’ condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer. PMID:18219700

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level.

PubMed

Moerbeek, Mirjam; van Schie, Sander

2016-07-11

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects. The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level. The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest. The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

Using Audit Information to Adjust Parameter Estimates for Data Errors in Clinical Trials

PubMed Central

Shepherd, Bryan E.; Shaw, Pamela A.; Dodd, Lori E.

2013-01-01

Background Audits are often performed to assess the quality of clinical trial data, but beyond detecting fraud or sloppiness, the audit data is generally ignored. In earlier work using data from a non-randomized study, Shepherd and Yu (2011) developed statistical methods to incorporate audit results into study estimates, and demonstrated that audit data could be used to eliminate bias. Purpose In this manuscript we examine the usefulness of audit-based error-correction methods in clinical trial settings where a continuous outcome is of primary interest. Methods We demonstrate the bias of multiple linear regression estimates in general settings with an outcome that may have errors and a set of covariates for which some may have errors and others, including treatment assignment, are recorded correctly for all subjects. We study this bias under different assumptions including independence between treatment assignment, covariates, and data errors (conceivable in a double-blinded randomized trial) and independence between treatment assignment and covariates but not data errors (possible in an unblinded randomized trial). We review moment-based estimators to incorporate the audit data and propose new multiple imputation estimators. The performance of estimators is studied in simulations. Results When treatment is randomized and unrelated to data errors, estimates of the treatment effect using the original error-prone data (i.e., ignoring the audit results) are unbiased. In this setting, both moment and multiple imputation estimators incorporating audit data are more variable than standard analyses using the original data. In contrast, in settings where treatment is randomized but correlated with data errors and in settings where treatment is not randomized, standard treatment effect estimates will be biased. And in all settings, parameter estimates for the original, error-prone covariates will be biased. Treatment and covariate effect estimates can be corrected by incorporating audit data using either the multiple imputation or moment-based approaches. Bias, precision, and coverage of confidence intervals improve as the audit size increases. Limitations The extent of bias and the performance of methods depend on the extent and nature of the error as well as the size of the audit. This work only considers methods for the linear model. Settings much different than those considered here need further study. Conclusions In randomized trials with continuous outcomes and treatment assignment independent of data errors, standard analyses of treatment effects will be unbiased and are recommended. However, if treatment assignment is correlated with data errors or other covariates, naive analyses may be biased. In these settings, and when covariate effects are of interest, approaches for incorporating audit results should be considered. PMID:22848072

Using Analysis of Covariance (ANCOVA) with Fallible Covariates

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Aguinis, Herman

2011-01-01

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…

Visual Typo Correction by Collocative Optimization: A Case Study on Merchandize Images.

PubMed

Wei, Xiao-Yong; Yang, Zhen-Qun; Ngo, Chong-Wah; Zhang, Wei

2014-02-01

Near-duplicate retrieval (NDR) in merchandize images is of great importance to a lot of online applications on e-Commerce websites. In those applications where the requirement of response time is critical, however, the conventional techniques developed for a general purpose NDR are limited, because expensive post-processing like spatial verification or hashing is usually employed to compromise the quantization errors among the visual words used for the images. In this paper, we argue that most of the errors are introduced because of the quantization process where the visual words are considered individually, which has ignored the contextual relations among words. We propose a "spelling or phrase correction" like process for NDR, which extends the concept of collocations to visual domain for modeling the contextual relations. Binary quadratic programming is used to enforce the contextual consistency of words selected for an image, so that the errors (typos) are eliminated and the quality of the quantization process is improved. The experimental results show that the proposed method can improve the efficiency of NDR by reducing vocabulary size by 1000% times, and under the scenario of merchandize image NDR, the expensive local interest point feature used in conventional approaches can be replaced by color-moment feature, which reduces the time cost by 9202% while maintaining comparable performance to the state-of-the-art methods.

Triangular covariance factorizations for. Ph.D. Thesis. - Calif. Univ.

NASA Technical Reports Server (NTRS)

Thornton, C. L.

1976-01-01

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Treating Sample Covariances for Use in Strongly Coupled Atmosphere-Ocean Data Assimilation

NASA Astrophysics Data System (ADS)

Smith, Polly J.; Lawless, Amos S.; Nichols, Nancy K.

2018-01-01

Strongly coupled data assimilation requires cross-domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill-conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere-ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state-space localization via the Schur product, effectively removes sample noise but can dampen small cross-correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.

Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem

NASA Astrophysics Data System (ADS)

Man, J.; Li, W.; Zeng, L.; Wu, L.

2015-12-01

The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the Polynomial Chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so called "cure of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF is even more computationally expensive than EnKF. Motivated by recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problem. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to alleviate the inconsistency between model parameters and states. The performance of RAPCKF is tested by unsaturated flow numerical cases. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.

Dynamic characterization of Galfenol

NASA Astrophysics Data System (ADS)

Scheidler, Justin J.; Asnani, Vivake M.; Deng, Zhangxian; Dapino, Marcelo J.

2015-04-01

A novel and precise characterization of the constitutive behavior of solid and laminated research-grade, polycrystalline Galfenol (Fe81:6Ga18:4) under under quasi-static (1 Hz) and dynamic (4 to 1000 Hz) stress loadings was recently conducted by the authors. This paper summarizes the characterization by focusing on the experimental design and the dynamic sensing response of the solid Galfenol specimen. Mechanical loads are applied using a high frequency load frame. The dynamic stress amplitude for minor and major loops is 2.88 and 31.4 MPa, respectively. Dynamic minor and major loops are measured for the bias condition resulting in maximum, quasi-static sensitivity. Three key sources of error in the dynamic measurements are accounted for: (1) electromagnetic noise in strain signals due to Galfenol's magnetic response, (2) error in load signals due to the inertial force of fixturing, and (3) time delays imposed by conditioning electronics. For dynamic characterization, strain error is kept below 1.2 % of full scale by wiring two collocated gauges in series (noise cancellation) and through lead wire weaving. Inertial force error is kept below 0.41 % by measuring the dynamic force in the specimen using a nearly collocated piezoelectric load washer. The phase response of all conditioning electronics is explicitly measured and corrected for. In general, as frequency increases, the sensing response becomes more linear due to an increase in eddy currents. The location of positive and negative saturation is the same at all frequencies. As frequency increases above about 100 Hz, the elbow in the strain versus stress response disappears as the active (soft) regime stiffens toward the passive (hard) regime.

Dynamic Characterization of Galfenol

NASA Technical Reports Server (NTRS)

Scheidler, Justin; Asnani, Vivake M.; Deng, Zhangxian; Dapino, Marcelo J.

2015-01-01

A novel and precise characterization of the constitutive behavior of solid and laminated research-grade, polycrystalline Galfenol (Fe81:6Ga18:4) under under quasi-static (1 Hz) and dynamic (4 to 1000 Hz) stress loadings was recently conducted by the authors. This paper summarizes the characterization by focusing on the experimental design and the dynamic sensing response of the solid Galfenol specimen. Mechanical loads are applied using a high frequency load frame. The dynamic stress amplitude for minor and major loops is 2.88 and 31.4 MPa, respectively. Dynamic minor and major loops are measured for the bias condition resulting in maximum, quasi-static sensitivity. Three key sources of error in the dynamic measurements are accounted for: (1) electromagnetic noise in strain signals due to Galfenol's magnetic response, (2) error in load signals due to the inertial force of fixturing, and (3) time delays imposed by conditioning electronics. For dynamic characterization, strain error is kept below 1.2 % of full scale by wiring two collocated gauges in series (noise cancellation) and through lead wire weaving. Inertial force error is kept below 0.41 % by measuring the dynamic force in the specimen using a nearly collocated piezoelectric load washer. The phase response of all conditioning electronics is explicitly measured and corrected for. In general, as frequency increases, the sensing response becomes more linear due to an increase in eddy currents. The location of positive and negative saturation is the same at all frequencies. As frequency increases above about 100 Hz, the elbow in the strain versus stress response disappears as the active (soft) regime stiffens toward the passive (hard) regime.

Eddy Covariance Measurements of the Sea-Spray Aerosol Flu

NASA Astrophysics Data System (ADS)

Brooks, I. M.; Norris, S. J.; Yelland, M. J.; Pascal, R. W.; Prytherch, J.

2015-12-01

Historically, almost all estimates of the sea-spray aerosol source flux have been inferred through various indirect methods. Direct estimates via eddy covariance have been attempted by only a handful of studies, most of which measured only the total number flux, or achieved rather coarse size segregation. Applying eddy covariance to the measurement of sea-spray fluxes is challenging: most instrumentation must be located in a laboratory space requiring long sample lines to an inlet collocated with a sonic anemometer; however, larger particles are easily lost to the walls of the sample line. Marine particle concentrations are generally low, requiring a high sample volume to achieve adequate statistics. The highly hygroscopic nature of sea salt means particles change size rapidly with fluctuations in relative humidity; this introduces an apparent bias in flux measurements if particles are sized at ambient humidity. The Compact Lightweight Aerosol Spectrometer Probe (CLASP) was developed specifically to make high rate measurements of aerosol size distributions for use in eddy covariance measurements, and the instrument and data processing and analysis techniques have been refined over the course of several projects. Here we will review some of the issues and limitations related to making eddy covariance measurements of the sea spray source flux over the open ocean, summarise some key results from the last decade, and present new results from a 3-year long ship-based measurement campaign as part of the WAGES project. Finally we will consider requirements for future progress.

GEOS-2 refraction program summary document. [ionospheric and tropospheric propagation errors in satellite tracking instruments

NASA Technical Reports Server (NTRS)

Mallinckrodt, A. J.

1977-01-01

Data from an extensive array of collocated instrumentation at the Wallops Island test facility were intercompared in order to (1) determine the practical achievable accuracy limitations of various tropospheric and ionospheric correction techniques; (2) examine the theoretical bases and derivation of improved refraction correction techniques; and (3) estimate internal systematic and random error levels of the various tracking stations. The GEOS 2 satellite was used as the target vehicle. Data were obtained regarding the ionospheric and tropospheric propagation errors, the theoretical and data analysis of which was documented in some 30 separate reports over the last 6 years. An overview of project results is presented.

Attitude and vibration control of a large flexible space-based antenna

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1982-01-01

Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE PAGES

Grout, Ray; Kolla, Hemanth; Minion, Michael; ...

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited tomore » recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual on the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehen- sive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Robustness of meta-analyses in finding gene × environment interactions

PubMed Central

Shi, Gang; Nehorai, Arye

2017-01-01

Meta-analyses that synthesize statistical evidence across studies have become important analytical tools for genetic studies. Inspired by the success of genome-wide association studies of the genetic main effect, researchers are searching for gene × environment interactions. Confounders are routinely included in the genome-wide gene × environment interaction analysis as covariates; however, this does not control for any confounding effects on the results if covariate × environment interactions are present. We carried out simulation studies to evaluate the robustness to the covariate × environment confounder for meta-regression and joint meta-analysis, which are two commonly used meta-analysis methods for testing the gene × environment interaction or the genetic main effect and interaction jointly. Here we show that meta-regression is robust to the covariate × environment confounder while joint meta-analysis is subject to the confounding effect with inflated type I error rates. Given vast sample sizes employed in genome-wide gene × environment interaction studies, non-significant covariate × environment interactions at the study level could substantially elevate the type I error rate at the consortium level. When covariate × environment confounders are present, type I errors can be controlled in joint meta-analysis by including the covariate × environment terms in the analysis at the study level. Alternatively, meta-regression can be applied, which is robust to potential covariate × environment confounders. PMID:28362796

Absorption of Solar Radiation by the Cloudy Atmosphere Interpretations of Collocated Aircraft Measurements

NASA Technical Reports Server (NTRS)

Valero, Francisco P. J.; Cess, Robert D.; Zhang, Minghua; Pope, Shelly K.; Bucholtz, Anthony; Bush, Brett; Vitko, John, Jr.

1997-01-01

As part of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), we have obtained and analyzed measurements made from collocated aircraft of the absorption of solar radiation within the atmospheric column between the two aircraft. The measurements were taken during October 1995 at the ARM site in Oklahoma. Relative to a theoretical radiative transfer model, we find no evidence for excess solar absorption in the clear atmosphere and significant evidence for its existence in the cloudy atmosphere. This excess cloud solar absorption appears to occur in both visible (0.224-0.68 microns) and near-infrared (0.68-3.30 microns) spectral regions, although not at 0.5 microns for the visible contribution, and it is shown to be true absorption rather than an artifact of sampling errors caused by measuring three-dimensional clouds.

An embedded formula of the Chebyshev collocation method for stiff problems

NASA Astrophysics Data System (ADS)

Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu

2017-12-01

In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.

Covariate Imbalance and Precision in Measuring Treatment Effects

ERIC Educational Resources Information Center

Liu, Xiaofeng Steven

2011-01-01

Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average…

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

A Kalman filter for a two-dimensional shallow-water model

NASA Technical Reports Server (NTRS)

Parrish, D. F.; Cohn, S. E.

1985-01-01

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Measurement error is often neglected in medical literature: a systematic review.

PubMed

Brakenhoff, Timo B; Mitroiu, Marian; Keogh, Ruth H; Moons, Karel G M; Groenwold, Rolf H H; van Smeden, Maarten

2018-06-01

In medical research, covariates (e.g., exposure and confounder variables) are often measured with error. While it is well accepted that this introduces bias and imprecision in exposure-outcome relations, it is unclear to what extent such issues are currently considered in research practice. The objective was to study common practices regarding covariate measurement error via a systematic review of general medicine and epidemiology literature. Original research published in 2016 in 12 high impact journals was full-text searched for phrases relating to measurement error. Reporting of measurement error and methods to investigate or correct for it were quantified and characterized. Two hundred and forty-seven (44%) of the 565 original research publications reported on the presence of measurement error. 83% of these 247 did so with respect to the exposure and/or confounder variables. Only 18 publications (7% of 247) used methods to investigate or correct for measurement error. Consequently, it is difficult for readers to judge the robustness of presented results to the existence of measurement error in the majority of publications in high impact journals. Our systematic review highlights the need for increased awareness about the possible impact of covariate measurement error. Additionally, guidance on the use of measurement error correction methods is necessary. Copyright © 2018 Elsevier Inc. All rights reserved.

Use of an OSSE to Evaluate Background Error Covariances Estimated by the 'NMC Method'

NASA Technical Reports Server (NTRS)

Errico, Ronald M.; Prive, Nikki C.; Gu, Wei

2014-01-01

The NMC method has proven utility for prescribing approximate background-error covariances required by variational data assimilation systems. Here, untunedNMCmethod estimates are compared with explicitly determined error covariances produced within an OSSE context by exploiting availability of the true simulated states. Such a comparison provides insights into what kind of rescaling is required to render the NMC method estimates usable. It is shown that rescaling of variances and directional correlation lengths depends greatly on both pressure and latitude. In particular, some scaling coefficients appropriate in the Tropics are the reciprocal of those in the Extratropics. Also, the degree of dynamic balance is grossly overestimated by the NMC method. These results agree with previous examinations of the NMC method which used ensembles as an alternative for estimating background-error statistics.

Modelling airborne gravity data by means of adapted Space-Wise approach

NASA Astrophysics Data System (ADS)

Sampietro, Daniele; Capponi, Martina; Hamdi Mansi, Ahmed; Gatti, Andrea

2017-04-01

Regional gravity field modelling by means of remove - restore procedure is nowadays widely applied to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.) in gravimetric geoid determination as well as in exploration geophysics. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are generally adopted. However due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc. airborne data are contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations both in the low and high frequency should be applied to recover valuable information. In this work, a procedure to predict a grid or a set of filtered along track gravity anomalies, by merging GGM and airborne dataset, is presented. The proposed algorithm, like the Space-Wise approach developed by Politecnico di Milano in the framework of GOCE data analysis, is based on a combination of along track Wiener filter and Least Squares Collocation adjustment and properly considers the different altitudes of the gravity observations. Among the main differences with respect to the satellite application of the Space-Wise approach there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data recovering the gravitational signal with a predicted accuracy of about 0.25 mGal.

The estimation error covariance matrix for the ideal state reconstructor with measurement noise

NASA Technical Reports Server (NTRS)

Polites, Michael E.

1988-01-01

A general expression is derived for the state estimation error covariance matrix for the Ideal State Reconstructor when the input measurements are corrupted by measurement noise. An example is presented which shows that the more measurements used in estimating the state at a given time, the better the estimator.

Modeling uncertainty of evapotranspiration measurements from multiple eddy covariance towers over a crop canopy

USDA-ARS?s Scientific Manuscript database

All measurements have random error associated with them. With fluxes in an eddy covariance system, measurement error can been modelled in several ways, often involving a statistical description of turbulence at its core. Using a field experiment with four towers, we generated four replicates of meas...

System identification for modeling for control of flexible structures

NASA Technical Reports Server (NTRS)

Mettler, Edward; Milman, Mark

1986-01-01

The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.

Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection

NASA Astrophysics Data System (ADS)

Langford, B.; Acton, W.; Ammann, C.; Valach, A.; Nemitz, E.

2015-10-01

All eddy-covariance flux measurements are associated with random uncertainties which are a combination of sampling error due to natural variability in turbulence and sensor noise. The former is the principal error for systems where the signal-to-noise ratio of the analyser is high, as is usually the case when measuring fluxes of heat, CO2 or H2O. Where signal is limited, which is often the case for measurements of other trace gases and aerosols, instrument uncertainties dominate. Here, we are applying a consistent approach based on auto- and cross-covariance functions to quantify the total random flux error and the random error due to instrument noise separately. As with previous approaches, the random error quantification assumes that the time lag between wind and concentration measurement is known. However, if combined with commonly used automated methods that identify the individual time lag by looking for the maximum in the cross-covariance function of the two entities, analyser noise additionally leads to a systematic bias in the fluxes. Combining data sets from several analysers and using simulations, we show that the method of time-lag determination becomes increasingly important as the magnitude of the instrument error approaches that of the sampling error. The flux bias can be particularly significant for disjunct data, whereas using a prescribed time lag eliminates these effects (provided the time lag does not fluctuate unduly over time). We also demonstrate that when sampling at higher elevations, where low frequency turbulence dominates and covariance peaks are broader, both the probability and magnitude of bias are magnified. We show that the statistical significance of noisy flux data can be increased (limit of detection can be decreased) by appropriate averaging of individual fluxes, but only if systematic biases are avoided by using a prescribed time lag. Finally, we make recommendations for the analysis and reporting of data with low signal-to-noise and their associated errors.

Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection

NASA Astrophysics Data System (ADS)

Langford, B.; Acton, W.; Ammann, C.; Valach, A.; Nemitz, E.

2015-03-01

All eddy-covariance flux measurements are associated with random uncertainties which are a combination of sampling error due to natural variability in turbulence and sensor noise. The former is the principal error for systems where the signal-to-noise ratio of the analyser is high, as is usually the case when measuring fluxes of heat, CO2 or H2O. Where signal is limited, which is often the case for measurements of other trace gases and aerosols, instrument uncertainties dominate. We are here applying a consistent approach based on auto- and cross-covariance functions to quantifying the total random flux error and the random error due to instrument noise separately. As with previous approaches, the random error quantification assumes that the time-lag between wind and concentration measurement is known. However, if combined with commonly used automated methods that identify the individual time-lag by looking for the maximum in the cross-covariance function of the two entities, analyser noise additionally leads to a systematic bias in the fluxes. Combining datasets from several analysers and using simulations we show that the method of time-lag determination becomes increasingly important as the magnitude of the instrument error approaches that of the sampling error. The flux bias can be particularly significant for disjunct data, whereas using a prescribed time-lag eliminates these effects (provided the time-lag does not fluctuate unduly over time). We also demonstrate that when sampling at higher elevations, where low frequency turbulence dominates and covariance peaks are broader, both the probability and magnitude of bias are magnified. We show that the statistical significance of noisy flux data can be increased (limit of detection can be decreased) by appropriate averaging of individual fluxes, but only if systematic biases are avoided by using a prescribed time-lag. Finally, we make recommendations for the analysis and reporting of data with low signal-to-noise and their associated errors.

Analysis of filter tuning techniques for sequential orbit determination

NASA Technical Reports Server (NTRS)

Lee, T.; Yee, C.; Oza, D.

1995-01-01

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models.

PubMed

Kyle, Ryan P; Moodie, Erica E M; Klein, Marina B; Abrahamowicz, Michał

2016-08-01

Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014. © The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Galaxy–galaxy lensing estimators and their covariance properties

DOE PAGES

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros; ...

2017-07-21

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy–galaxy lensing estimators and their covariance properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy-galaxy lensing estimators and their covariance properties

NASA Astrophysics Data System (ADS)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uroš; Slosar, Anže; Vazquez Gonzalez, Jose

2017-11-01

We study the covariance properties of real space correlation function estimators - primarily galaxy-shear correlations, or galaxy-galaxy lensing - using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.

Absorption of Solar Radiation by the Cloudy Atmosphere: Further Interpretations of Collocated Aircraft Measurements

NASA Technical Reports Server (NTRS)

Cess, R. D.; Zhang, Minghua; Valero, Francisco P. J.; Pope, Shelly K.; Bucholtz, Anthony; Bush, Brett; Zender, Charles S.

1998-01-01

We have extended the interpretations made in two prior studies of the aircraft shortwave radiation measurements that were obtained as part of the Atmospheric Radiation Measurements (ARM) Enhanced Shortwave Experiments (ARESE). These extended interpretations use the 500 nm (10 nm bandwidth) measurements to minimize sampling errors in the broadband measurements. It is indicated that the clouds present during this experiment absorb more shortwave radiation than predicted by clear skies and thus by theoretical models, that at least some (less than or equal to 20%) of this enhanced cloud absorption occurs at wavelengths less than 680 nm, and that the observed cloud absorption does not appear to be an artifact of sampling errors nor of instrument calibration errors.

Covariate Measurement Error Correction for Student Growth Percentiles Using the SIMEX Method

ERIC Educational Resources Information Center

Shang, Yi; VanIwaarden, Adam; Betebenner, Damian W.

2015-01-01

In this study, we examined the impact of covariate measurement error (ME) on the estimation of quantile regression and student growth percentiles (SGPs), and find that SGPs tend to be overestimated among students with higher prior achievement and underestimated among those with lower prior achievement, a problem we describe as ME endogeneity in…

On the use of the covariance matrix to fit correlated data

NASA Astrophysics Data System (ADS)

D'Agostini, G.

1994-07-01

Best fits to data which are affected by systematic uncertainties on the normalization factor have the tendency to produce curves lower than expected if the covariance matrix of the data points is used in the definition of the χ2. This paper shows that the effect is a direct consequence of the hypothesis used to estimate the empirical covariance matrix, namely the linearization on which the usual error propagation relies. The bias can become unacceptable if the normalization error is large, or a large number of data points are fitted.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

Assessing XCTD Fall Rate Errors using Concurrent XCTD and CTD Profiles in the Southern Ocean

NASA Astrophysics Data System (ADS)

Millar, J.; Gille, S. T.; Sprintall, J.; Frants, M.

2010-12-01

Refinements in the fall rate equation for XCTDs are not as well understood as those for XBTs, due in part to the paucity of concurrent and collocated XCTD and CTD profiles. During February and March 2010, the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES) conducted 31 collocated 1000-meter XCTD and CTD casts in the Drake Passage. These XCTD/CTD profile pairs are closely matched in space and time, with a mean distance between casts of 1.19 km and a mean lag time of 39 minutes. The profile pairs are well suited to address the XCTD fall rate problem specifically in higher latitude waters, where existing fall rate corrections have rarely been assessed. Many of these XCTD/CTD profile pairs reveal an observable depth offset in measurements of both temperature and conductivity. Here, the nature and extent of this depth offset is evaluated.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory, using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis publications is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

PubMed Central

Jacob, Benjamin G; Griffith, Daniel A; Muturi, Ephantus J; Caamano, Erick X; Githure, John I; Novak, Robert J

2009-01-01

Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix. Results By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with An. arabiensis aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled An. arabiensis aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat. Conclusion An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific An. arabiensis aquatic habitats based on larval/pupal productivity. PMID:19772590

Data assimilation for unsaturated flow models with restart adaptive probabilistic collocation based Kalman filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Man, Jun; Li, Weixuan; Zeng, Lingzao

2016-06-01

The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so-called "curse of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF could be even more computationally expensive than EnKF. Motivated by most recent developments in uncertainty quantification, we proposemore » a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to eliminate the inconsistency between model parameters and states. The performance of RAPCKF is tested with numerical cases of unsaturated flow models. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.« less

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

NASA Technical Reports Server (NTRS)

Tsaoussi, Lucia S.; Koblinsky, Chester J.

1994-01-01

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Analyzing average and conditional effects with multigroup multilevel structural equation models

PubMed Central

Mayer, Axel; Nagengast, Benjamin; Fletcher, John; Steyer, Rolf

2014-01-01

Conventionally, multilevel analysis of covariance (ML-ANCOVA) has been the recommended approach for analyzing treatment effects in quasi-experimental multilevel designs with treatment application at the cluster-level. In this paper, we introduce the generalized ML-ANCOVA with linear effect functions that identifies average and conditional treatment effects in the presence of treatment-covariate interactions. We show how the generalized ML-ANCOVA model can be estimated with multigroup multilevel structural equation models that offer considerable advantages compared to traditional ML-ANCOVA. The proposed model takes into account measurement error in the covariates, sampling error in contextual covariates, treatment-covariate interactions, and stochastic predictors. We illustrate the implementation of ML-ANCOVA with an example from educational effectiveness research where we estimate average and conditional effects of early transition to secondary schooling on reading comprehension. PMID:24795668

True covariance simulation of the EUVE update filter

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Harman, R. R.

1989-01-01

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Analysis of Covariance: Is It the Appropriate Model to Study Change?

ERIC Educational Resources Information Center

Marston, Paul T., Borich, Gary D.

The four main approaches to measuring treatment effects in schools; raw gain, residual gain, covariance, and true scores; were compared. A simulation study showed true score analysis produced a large number of Type-I errors. When corrected for this error, this method showed the least power of the four. This outcome was clearly the result of the…

Error analysis for spectral approximation of the Korteweg-De Vries equation

NASA Technical Reports Server (NTRS)

Maday, Y.; recent years.

1987-01-01

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

NASA Technical Reports Server (NTRS)

Menga, G.

1975-01-01

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

The Potential Observation Network Design with Mesoscale Ensemble Sensitivities in Complex Terrain

DTIC Science & Technology

2012-03-01

in synoptic storms , extratropical transition and developing hurricanes. Because they rely on lagged covariances from a finite-sized ensemble, they...diagnose predictors of forecast error in synoptic storms , extratropical transition and developing hurricanes. Because they rely on lagged covariances...sensitivities can be used successfully to diagnose predictors of forecast error in synoptic storms (Torn and Hakim 2008), extratropical transition (Torn and

Learning Collocations: Do the Number of Collocates, Position of the Node Word, and Synonymy Affect Learning?

ERIC Educational Resources Information Center

Webb, Stuart; Kagimoto, Eve

2011-01-01

This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates…

The collocated station Košetice - Kešín u Pacova, Czech Republic: an important research infrastructure in central Europe

NASA Astrophysics Data System (ADS)

Dvorska, Alice; Milan, Váňa; Vlastimil, Hanuš; Marian, Pavelka

2013-04-01

The collocated station Košetice - Křešín u Pacova, central Czech Republic, is a major research and monitoring infrastructure in the Czech Republic and central Europe. It consists of two basic components: the observatory Košetice run since 1988 by the Czech Hydrometeorological Institute and the atmospheric station (AS) Křešín u Pacova starting operation in 2013. The AS is built and run by CzechGlobe - Global Change Research Centre, Academy of Sciences of the Czech Republic and is situated 100 m far from the observatory. There are three research and monitoring activities at the collocated station providing data necessary for the research on climate and related changes. The AS Křešín u Pacova consists of a 250 m tall tower serving for ground-based and vertical gradient measurements of (i) concentrations of CO2, CO, CH4, total gaseous mercury and tropospheric ozone (continuously), (ii) elemental and organic carbon (semicontinuously), (iii) carbon and oxygen isotopes, radon, N2O, SF6 and other species (episodically), (iv) optical properties of atmospheric aerosols and (v) meteorological parameters and the boundary layer height. Further, eddy covariance measurements in the nearby agroecosystem provide data on CO2 and H2O fluxes between the atmosphere and the ecosystem. Finally, monitoring activities at the nearby small hydrological catchment Anenské povodí run under the GEOMON network enables studying local hydrological and biogeochemical cycles. These measurements are supported by the long-term monitoring of meteorological and air quality parameters at the observatory Košetice, that are representative for the central European background. The collocated station provides a big research opportunity and challenge due to (i) a broad spectra of monitored chemical species, meteorological, hydrological and other parameters, (ii) measurements in various environmental compartments and especially the atmosphere, (iii) provision of data suitable for conducting multidisciplinar research activities and (iv) participation in a number of international programmes and projects, i.e. ICOS (AS Křešín u Pacova), ACTRIS, ACCENT, CLRTAP/EMEP, GAW and ICP-IM (Košetice) and others. Finally, the collocated station has potential for a successful participation in the planned network of European superstations covering both climate and air quality issues, one of the key areas in the European Strategy Forum on Research Infrastructures (ESFRI) process. Acknowledgement: This work is supported by the CzechGlobe (CZ.1.05/1.1.00/02.0073) and CZ.1.07/2.4.00/31.0056 projects.

Covariance analysis for evaluating head trackers

NASA Astrophysics Data System (ADS)

Kang, Donghoon

2017-10-01

Existing methods for evaluating the performance of head trackers usually rely on publicly available face databases, which contain facial images and the ground truths of their corresponding head orientations. However, most of the existing publicly available face databases are constructed by assuming that a frontal head orientation can be determined by compelling the person under examination to look straight ahead at the camera on the first video frame. Since nobody can accurately direct one's head toward the camera, this assumption may be unrealistic. Rather than obtaining estimation errors, we present a method for computing the covariance of estimation error rotations to evaluate the reliability of head trackers. As an uncertainty measure of estimators, the Schatten 2-norm of a square root of error covariance (or the algebraic average of relative error angles) can be used. The merit of the proposed method is that it does not disturb the person under examination by asking him to direct his head toward certain directions. Experimental results using real data validate the usefulness of our method.

Accounting for response misclassification and covariate measurement error improves power and reduces bias in epidemiologic studies.

PubMed

Cheng, Dunlei; Branscum, Adam J; Stamey, James D

2010-07-01

To quantify the impact of ignoring misclassification of a response variable and measurement error in a covariate on statistical power, and to develop software for sample size and power analysis that accounts for these flaws in epidemiologic data. A Monte Carlo simulation-based procedure is developed to illustrate the differences in design requirements and inferences between analytic methods that properly account for misclassification and measurement error to those that do not in regression models for cross-sectional and cohort data. We found that failure to account for these flaws in epidemiologic data can lead to a substantial reduction in statistical power, over 25% in some cases. The proposed method substantially reduced bias by up to a ten-fold margin compared to naive estimates obtained by ignoring misclassification and mismeasurement. We recommend as routine practice that researchers account for errors in measurement of both response and covariate data when determining sample size, performing power calculations, or analyzing data from epidemiological studies. 2010 Elsevier Inc. All rights reserved.

Precipitation Estimation from the ARM Distributed Radar Network during the MC3E Campaign

DOE PAGES

Giangrande, Scott E.; Collis, Scott; Theisen, Adam K.; ...

2014-09-12

This study presents radar-based precipitation estimates collected during the two-month DOE ARM - NASA Midlatitude Continental Convective Clouds Experiment (MC3E). Emphasis is on the usefulness of radar observations from the C-band and X-band scanning ARM precipitation radars (CSAPR, XSAPR) for rainfall estimation products to distances within 100 km of the Oklahoma SGP facility. A dense collection of collocated ARM, NASA GPM and nearby surface Oklahoma Mesonet gauge records are consulted to evaluate potential ARM radar-based hourly rainfall products and campaign optimized methods over individual gauge and areal characterizations. Rainfall products are evaluated against the performance of the regional operational NWSmore » NEXRAD S-band radar polarimetric product. Results indicate that the ARM C-band system may achieve similar point and areal-gauge bias and root mean square (rms) error performance to the NEXRAD standard for the variety of MC3E deep convective events sampled when capitalizing on differential phase measurements. The best campaign rainfall performance was achieved when applying radar relations capitalizing on estimates of the specific attenuation from the CSAPR system. The ARM X-band systems only demonstrate solid capabilities as compared to NEXRAD standards for hourly point and areal rainfall accumulations under 10 mm. Here, all methods exhibit a factor of 1.5 to 2.5 reduction in rms errors for areal accumulations over a 15 km2 NASA dense network housing 16 sites having collocated bucket gauges, with the higher error reductions best associated with polarimetric methods.« less

Precipitation Estimation from the ARM Distributed Radar Network during the MC3E Campaign

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giangrande, Scott E.; Collis, Scott; Theisen, Adam K.

This study presents radar-based precipitation estimates collected during the two-month DOE ARM - NASA Midlatitude Continental Convective Clouds Experiment (MC3E). Emphasis is on the usefulness of radar observations from the C-band and X-band scanning ARM precipitation radars (CSAPR, XSAPR) for rainfall estimation products to distances within 100 km of the Oklahoma SGP facility. A dense collection of collocated ARM, NASA GPM and nearby surface Oklahoma Mesonet gauge records are consulted to evaluate potential ARM radar-based hourly rainfall products and campaign optimized methods over individual gauge and areal characterizations. Rainfall products are evaluated against the performance of the regional operational NWSmore » NEXRAD S-band radar polarimetric product. Results indicate that the ARM C-band system may achieve similar point and areal-gauge bias and root mean square (rms) error performance to the NEXRAD standard for the variety of MC3E deep convective events sampled when capitalizing on differential phase measurements. The best campaign rainfall performance was achieved when applying radar relations capitalizing on estimates of the specific attenuation from the CSAPR system. The ARM X-band systems only demonstrate solid capabilities as compared to NEXRAD standards for hourly point and areal rainfall accumulations under 10 mm. Here, all methods exhibit a factor of 1.5 to 2.5 reduction in rms errors for areal accumulations over a 15 km2 NASA dense network housing 16 sites having collocated bucket gauges, with the higher error reductions best associated with polarimetric methods.« less

Application Of Multi-grid Method On China Seas' Temperature Forecast

NASA Astrophysics Data System (ADS)

Li, W.; Xie, Y.; He, Z.; Liu, K.; Han, G.; Ma, J.; Li, D.

2006-12-01

Correlation scales have been used in traditional scheme of 3-dimensional variational (3D-Var) data assimilation to estimate the background error covariance for the numerical forecast and reanalysis of atmosphere and ocean for decades. However there are still some drawbacks of this scheme. First, the correlation scales are difficult to be determined accurately. Second, the positive definition of the first-guess error covariance matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. (2005) indicated that a traditional 3D-Var only corrects some certain wavelength errors and its accuracy depends on the accuracy of the first-guess covariance. And in general, short wavelength error can not be well corrected until long one is corrected and then inaccurate first-guess covariance may mistakenly take long wave error as short wave ones and result in erroneous analysis. For the purpose of quickly minimizing the errors of long and short waves successively, a new 3D-Var data assimilation scheme, called multi-grid data assimilation scheme, is proposed in this paper. By assimilating the shipboard SST and temperature profiles data into a numerical model of China Seas, we applied this scheme in two-month data assimilation and forecast experiment which ended in a favorable result. Comparing with the traditional scheme of 3D-Var, the new scheme has higher forecast accuracy and a lower forecast Root-Mean-Square (RMS) error. Furthermore, this scheme was applied to assimilate the SST of shipboard, AVHRR Pathfinder Version 5.0 SST and temperature profiles at the same time, and a ten-month forecast experiment on sea temperature of China Seas was carried out, in which a successful forecast result was obtained. Particularly, the new scheme is demonstrated a great numerical efficiency in these analyses.

An adaptive filter method for spacecraft using gravity assist

NASA Astrophysics Data System (ADS)

Ning, Xiaolin; Huang, Panpan; Fang, Jiancheng; Liu, Gang; Ge, Shuzhi Sam

2015-04-01

Celestial navigation (CeleNav) has been successfully used during gravity assist (GA) flyby for orbit determination in many deep space missions. Due to spacecraft attitude errors, ephemeris errors, the camera center-finding bias, and the frequency of the images before and after the GA flyby, the statistics of measurement noise cannot be accurately determined, and yet have time-varying characteristics, which may introduce large estimation error and even cause filter divergence. In this paper, an unscented Kalman filter (UKF) with adaptive measurement noise covariance, called ARUKF, is proposed to deal with this problem. ARUKF scales the measurement noise covariance according to the changes in innovation and residual sequences. Simulations demonstrate that ARUKF is robust to the inaccurate initial measurement noise covariance matrix and time-varying measurement noise. The impact factors in the ARUKF are also investigated.

Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts.

PubMed

Gosho, Masahiko; Hirakawa, Akihiro; Noma, Hisashi; Maruo, Kazushi; Sato, Yasunori

2017-10-01

In longitudinal clinical trials, some subjects will drop out before completing the trial, so their measurements towards the end of the trial are not obtained. Mixed-effects models for repeated measures (MMRM) analysis with "unstructured" (UN) covariance structure are increasingly common as a primary analysis for group comparisons in these trials. Furthermore, model-based covariance estimators have been routinely used for testing the group difference and estimating confidence intervals of the difference in the MMRM analysis using the UN covariance. However, using the MMRM analysis with the UN covariance could lead to convergence problems for numerical optimization, especially in trials with a small-sample size. Although the so-called sandwich covariance estimator is robust to misspecification of the covariance structure, its performance deteriorates in settings with small-sample size. We investigated the performance of the sandwich covariance estimator and covariance estimators adjusted for small-sample bias proposed by Kauermann and Carroll ( J Am Stat Assoc 2001; 96: 1387-1396) and Mancl and DeRouen ( Biometrics 2001; 57: 126-134) fitting simpler covariance structures through a simulation study. In terms of the type 1 error rate and coverage probability of confidence intervals, Mancl and DeRouen's covariance estimator with compound symmetry, first-order autoregressive (AR(1)), heterogeneous AR(1), and antedependence structures performed better than the original sandwich estimator and Kauermann and Carroll's estimator with these structures in the scenarios where the variance increased across visits. The performance based on Mancl and DeRouen's estimator with these structures was nearly equivalent to that based on the Kenward-Roger method for adjusting the standard errors and degrees of freedom with the UN structure. The model-based covariance estimator with the UN structure under unadjustment of the degrees of freedom, which is frequently used in applications, resulted in substantial inflation of the type 1 error rate. We recommend the use of Mancl and DeRouen's estimator in MMRM analysis if the number of subjects completing is ( n + 5) or less, where n is the number of planned visits. Otherwise, the use of Kenward and Roger's method with UN structure should be the best way.

Intra-urban spatial variability of surface ozone in Riverside, CA: viability and validation of low-cost sensors

NASA Astrophysics Data System (ADS)

Sadighi, Kira; Coffey, Evan; Polidori, Andrea; Feenstra, Brandon; Lv, Qin; Henze, Daven K.; Hannigan, Michael

2018-03-01

Sensor networks are being more widely used to characterize and understand compounds in the atmosphere like ozone (O3). This study employs a measurement tool, called the U-Pod, constructed at the University of Colorado Boulder, to investigate spatial and temporal variability of O3 in a 200 km2 area of Riverside County near Los Angeles, California. This tool contains low-cost sensors to collect ambient data at non-permanent locations. The U-Pods were calibrated using a pre-deployment field calibration technique; all the U-Pods were collocated with regulatory monitors. After collocation, the U-Pods were deployed in the area mentioned. A subset of pods was deployed at two local regulatory air quality monitoring stations providing validation for the collocation calibration method. Field validation of sensor O3 measurements to minute-resolution reference observations resulted in R2 and root mean squared errors (RMSEs) of 0.95-0.97 and 4.4-5.9 ppbv, respectively. Using the deployment data, ozone concentrations were observed to vary on this small spatial scale. In the analysis based on hourly binned data, the median R2 values between all possible U-Pod pairs varied from 0.52 to 0.86 for ozone during the deployment. The medians of absolute differences were calculated between all possible pod pairs, 21 pairs total. The median values of those median absolute differences for each hour of the day varied between 2.2 and 9.3 ppbv for the ozone deployment. Since median differences between U-Pod concentrations during deployment are larger than the respective root mean square error values, we can conclude that there is spatial variability in this criteria pollutant across the study area. This is important because it means that citizens may be exposed to more, or less, ozone than they would assume based on current regulatory monitoring.

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

NASA Technical Reports Server (NTRS)

Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.

2013-01-01

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

PubMed

Sztepanacz, Jacqueline L; Blows, Mark W

2017-07-01

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

Evaluating the design of an earth radiation budget instrument with system simulations. Part 2: Minimization of instantaneous sampling errors for CERES-I

NASA Technical Reports Server (NTRS)

Stowe, Larry; Hucek, Richard; Ardanuy, Philip; Joyce, Robert

1994-01-01

Much of the new record of broadband earth radiation budget satellite measurements to be obtained during the late 1990s and early twenty-first century will come from the dual-radiometer Clouds and Earth's Radiant Energy System Instrument (CERES-I) flown aboard sun-synchronous polar orbiters. Simulation studies conducted in this work for an early afternoon satellite orbit indicate that spatial root-mean-square (rms) sampling errors of instantaneous CERES-I shortwave flux estimates will range from about 8.5 to 14.0 W/m on a 2.5 deg latitude and longitude grid resolution. Rms errors in longwave flux estimates are only about 20% as large and range from 1.5 to 3.5 W/sq m. These results are based on an optimal cross-track scanner design that includes 50% footprint overlap to eliminate gaps in the top-of-the-atmosphere coverage, and a 'smallest' footprint size to increase the ratio in the number of observations lying within to the number of observations lying on grid area boundaries. Total instantaneous measurement error also depends on the variability of anisotropic reflectance and emission patterns and on retrieval methods used to generate target area fluxes. Three retrieval procedures from both CERES-I scanners (cross-track and rotating azimuth plane) are used. (1) The baseline Earth Radiaton Budget Experiment (ERBE) procedure, which assumes that errors due to the use of mean angular dependence models (ADMs) in the radiance-to-flux inversion process nearly cancel when averaged over grid areas. (2) To estimate N, instantaneous ADMs are estimated from the multiangular, collocated observations of the two scanners. These observed models replace the mean models in computation of satellite flux estimates. (3) The scene flux approach, conducts separate target-area retrievals for each ERBE scene category and combines their results using area weighting by scene type. The ERBE retrieval performs best when the simulated radiance field departs from the ERBE mean models by less than 10%. For larger perturbations, both the scene flux and collocation methods produce less error than the ERBE retrieval. The scene flux technique is preferable, however, because it involves fewer restrictive assumptions.

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

NASA Astrophysics Data System (ADS)

Behnabian, Behzad; Mashhadi Hossainali, Masoud; Malekzadeh, Ahad

2018-02-01

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.

The Use of Verb Noun Collocations in Writing Stories among Iranian EFL Learners

ERIC Educational Resources Information Center

Bazzaz, Fatemeh Ebrahimi; Samad, Arshad Abd

2011-01-01

An important aspect of native speakers' communicative competence is collocational competence which involves knowing which words usually come together and which do not. This paper investigates the possible relationship between knowledge of collocations and the use of verb noun collocation in writing stories because collocational knowledge…

Developing and Evaluating a Chinese Collocation Retrieval Tool for CFL Students and Teachers

ERIC Educational Resources Information Center

Chen, Howard Hao-Jan; Wu, Jian-Cheng; Yang, Christine Ting-Yu; Pan, Iting

2016-01-01

The development of collocational knowledge is important for foreign language learners; unfortunately, learners often have difficulties producing proper collocations in the target language. Among the various ways of collocation learning, the DDL (data-driven learning) approach encourages the independent learning of collocations and allows learners…

Bounding filter - A simple solution to lack of exact a priori statistics.

NASA Technical Reports Server (NTRS)

Nahi, N. E.; Weiss, I. M.

1972-01-01

Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.

Development of a multi-data assimilation scheme to integrate Bio-Argo floats data with ocean colour satellite data into the CMEMS MFC-Biogeochemistry

NASA Astrophysics Data System (ADS)

Cossarini, Gianpiero; D'Ortenzio, Fabrizio; Mariotti, Laura; Mignot, Alexandre; Salon, Stefano

2017-04-01

The Mediterranean Sea is a very promising site to develop and test the assimilation of Bio-Argo data since 1) the Bio-Argo network is one of the densest of the global ocean, and 2) a consolidate data assimilation framework of biogeochemical variables (3DVAR-BIO, presently based on assimilation of satellite-estimated surface chlorophyll data) already exists within the CMEMS biogeochemical model system for Mediterranean Sea. The MASSIMILI project, granted by the CMEMS Service Evolution initiative, is aimed to develop the assimilation of Bio-Argo Floats data into the CMEMS biogeochemical model system of the Mediterranean Sea, by means of an upgrade of the 3DVAR-BIO scheme. Specific developments of the 3DVAR-BIO scheme focus on the estimate of new operators of the variational decomposition of the background error covariance matrix and on the implementation of the new observation operator specifically for the Bio-Argo float vertical profile data. In particular, a new horizontal covariance operator for chlorophyll, nitrate and oxygen is based on 3D fields of horizontal correlation radius calculated from a long-term reanalysis simulation. A new vertical covariance operator is built on monthly and spatial varying EOF decomposition to account for the spatiotemporal variability of vertical structure of the three variables error covariance. Further, the observation error covariance is a key factor for an effective assimilation of the Bio-Argo data into the model dynamics. The sensitivities of assimilation to the different factors are estimated. First results of the implementation of the new 3DVAR-BIO scheme show the impact of Bio-Argo data on the 3D fields of chlorophyll, nitrate and oxygen. Tuning the length scale factors of horizontal covariance, analysing the sensitivity of the observation error covariance, introducing non-diagonal biogeochemical covariance operator and non-diagonal multi-platform operator (i.e. Bio-Argo and satellite) are crucial future steps for the success of the MASSIMILI project. In our contribute, we will discuss the recent and promising advancements this strategic project has been having in the past year and its potential for the whole operational biogeochemical modelling community.

Predicting the geographic distribution of a species from presence-only data subject to detection errors

USGS Publications Warehouse

Dorazio, Robert M.

2012-01-01

Several models have been developed to predict the geographic distribution of a species by combining measurements of covariates of occurrence at locations where the species is known to be present with measurements of the same covariates at other locations where species occurrence status (presence or absence) is unknown. In the absence of species detection errors, spatial point-process models and binary-regression models for case-augmented surveys provide consistent estimators of a species’ geographic distribution without prior knowledge of species prevalence. In addition, these regression models can be modified to produce estimators of species abundance that are asymptotically equivalent to those of the spatial point-process models. However, if species presence locations are subject to detection errors, neither class of models provides a consistent estimator of covariate effects unless the covariates of species abundance are distinct and independently distributed from the covariates of species detection probability. These analytical results are illustrated using simulation studies of data sets that contain a wide range of presence-only sample sizes. Analyses of presence-only data of three avian species observed in a survey of landbirds in western Montana and northern Idaho are compared with site-occupancy analyses of detections and nondetections of these species.

Covariance NMR Processing and Analysis for Protein Assignment.

PubMed

Harden, Bradley J; Frueh, Dominique P

2018-01-01

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

Corpus-Aided Business English Collocation Pedagogy: An Empirical Study in Chinese EFL Learners

ERIC Educational Resources Information Center

Chen, Lidan

2017-01-01

This study reports an empirical study of an explicit instruction of corpus-aided Business English collocations and verifies its effectiveness in improving learners' collocation awareness and learner autonomy, as a result of which is significant improvement of learners' collocation competence. An eight-week instruction in keywords' collocations,…

Perceptions on L2 Lexical Collocation Translation with a Focus on English-Arabic

ERIC Educational Resources Information Center

Alqaed, Mai Abdullah

2017-01-01

This paper aims to shed light on recent research concerning translating English-Arabic lexical collocations. It begins with a brief overview of English and Arabic lexical collocations with reference to specialized dictionaries. Research views on translating lexical collocations are presented, with the focus on English-Arabic collocations. These…

Assessment of 3D cloud radiative transfer effects applied to collocated A-Train data

NASA Astrophysics Data System (ADS)

Okata, M.; Nakajima, T.; Suzuki, K.; Toshiro, I.; Nakajima, T. Y.; Okamoto, H.

2017-12-01

This study investigates broadband radiative fluxes in the 3D cloud-laden atmospheres using a 3D radiative transfer (RT) model, MCstar, and the collocated A-Train cloud data. The 3D extinction coefficients are constructed by a newly devised Minimum cloud Information Deviation Profiling Method (MIDPM) that extrapolates CPR radar profiles at nadir into off-nadir regions within MODIS swath based on collocated information of MODIS-derived cloud properties and radar reflectivity profiles. The method is applied to low level maritime water clouds, for which the 3D-RT simulations are performed. The radiative fluxes thus simulated are compared to those obtained from CERES as a way to validate the MIDPM-constructed clouds and our 3D-RT simulations. The results show that the simulated SW flux agrees with CERES values within 8 - 50 Wm-2. One of the large biases occurred by cyclic boundary condition that was required to pose into our computational domain limited to 20km by 20km with 1km resolution. Another source of the bias also arises from the 1D assumption for cloud property retrievals particularly for thin clouds, which tend to be affected by spatial heterogeneity leading to overestimate of the cloud optical thickness. These 3D-RT simulations also serve to address another objective of this study, i.e. to characterize the "observed" specific 3D-RT effects by the cloud morphology. We extend the computational domain to 100km by 100km for this purpose. The 3D-RT effects are characterized by errors of existing 1D approximations to 3D radiation field. The errors are investigated in terms of their dependence on solar zenith angle (SZA) for the satellite-constructed real cloud cases, and we define two indices from the error tendencies. According to the indices, the 3D-RT effects are classified into three types which correspond to different simple three morphologies types, i.e. isolated cloud type, upper cloud-roughened type and lower cloud-roughened type. These 3D-RT effects linked to cloud morphologies are also visualized in the form of the RGB composite maps constructed from MODIS/Aqua three channels, which show cloud optical thickness and cloud height information. Such a classification offers a novel insight into 3D-RT effect in a manner that directly relates to cloud morphology.

Generalized Fisher matrices

NASA Astrophysics Data System (ADS)

Heavens, A. F.; Seikel, M.; Nord, B. D.; Aich, M.; Bouffanais, Y.; Bassett, B. A.; Hobson, M. P.

2014-12-01

The Fisher Information Matrix formalism (Fisher 1935) is extended to cases where the data are divided into two parts (X, Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary covariance. In the simplest case, (X, Y) represent data pairs of abscissa and ordinate, in which case the analysis deals with the case of data pairs with errors in both coordinates, but X can be any measured quantities on which Y depends. The analysis applies for arbitrary covariance, provided all errors are Gaussian, and provided the errors in X are small, both in comparison with the scale over which the expected signal Y changes, and with the width of the prior distribution. This generalizes the Fisher Matrix approach, which normally only considers errors in the `ordinate' Y. In this work, we include errors in X by marginalizing over latent variables, effectively employing a Bayesian hierarchical model, and deriving the Fisher Matrix for this more general case. The methods here also extend to likelihood surfaces which are not Gaussian in the parameter space, and so techniques such as DALI (Derivative Approximation for Likelihoods) can be generalized straightforwardly to include arbitrary Gaussian data error covariances. For simple mock data and theoretical models, we compare to Markov Chain Monte Carlo experiments, illustrating the method with cosmological supernova data. We also include the new method in the FISHER4CAST software.

Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure.

PubMed

Yung, Yiu-Fai; Browne, Michael W; Zhang, Wei

2015-02-01

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple-group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy-to-use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large. © 2014 The British Psychological Society.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction.

PubMed

Chen, Peng; Yang, Yixin; Wang, Yong; Ma, Yuanliang

2018-05-08

When sensor position errors exist, the performance of recently proposed interference-plus-noise covariance matrix (INCM)-based adaptive beamformers may be severely degraded. In this paper, we propose a weighted subspace fitting-based INCM reconstruction algorithm to overcome sensor displacement for linear arrays. By estimating the rough signal directions, we construct a novel possible mismatched steering vector (SV) set. We analyze the proximity of the signal subspace from the sample covariance matrix (SCM) and the space spanned by the possible mismatched SV set. After solving an iterative optimization problem, we reconstruct the INCM using the estimated sensor position errors. Then we estimate the SV of the desired signal by solving an optimization problem with the reconstructed INCM. The main advantage of the proposed algorithm is its robustness against SV mismatches dominated by unknown sensor position errors. Numerical examples show that even if the position errors are up to half of the assumed sensor spacing, the output signal-to-interference-plus-noise ratio is only reduced by 4 dB. Beam patterns plotted using experiment data show that the interference suppression capability of the proposed beamformer outperforms other tested beamformers.

Investigating ESL Learners' Lexical Collocations: The Acquisition of Verb + Noun Collocations by Japanese Learners of English

ERIC Educational Resources Information Center

Miyakoshi, Tomoko

2009-01-01

Although it is widely acknowledged that collocations play an important part in second language learning, especially at intermediate-advanced levels, learners' difficulties with collocations have not been investigated in much detail so far. The present study examines ESL learners' use of verb-noun collocations, such as "take notes," "place an…

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC.

PubMed

Inghelbrecht, Veronique; Verhaevert, Jo; van Hecke, Tanja; Rogier, Hendrik

2014-11-11

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case.

On using summary statistics from an external calibration sample to correct for covariate measurement error.

PubMed

Guo, Ying; Little, Roderick J; McConnell, Daniel S

2012-01-01

Covariate measurement error is common in epidemiologic studies. Current methods for correcting measurement error with information from external calibration samples are insufficient to provide valid adjusted inferences. We consider the problem of estimating the regression of an outcome Y on covariates X and Z, where Y and Z are observed, X is unobserved, but a variable W that measures X with error is observed. Information about measurement error is provided in an external calibration sample where data on X and W (but not Y and Z) are recorded. We describe a method that uses summary statistics from the calibration sample to create multiple imputations of the missing values of X in the regression sample, so that the regression coefficients of Y on X and Z and associated standard errors can be estimated using simple multiple imputation combining rules, yielding valid statistical inferences under the assumption of a multivariate normal distribution. The proposed method is shown by simulation to provide better inferences than existing methods, namely the naive method, classical calibration, and regression calibration, particularly for correction for bias and achieving nominal confidence levels. We also illustrate our method with an example using linear regression to examine the relation between serum reproductive hormone concentrations and bone mineral density loss in midlife women in the Michigan Bone Health and Metabolism Study. Existing methods fail to adjust appropriately for bias due to measurement error in the regression setting, particularly when measurement error is substantial. The proposed method corrects this deficiency.

Effects of Correlated Errors on the Analysis of Space Geodetic Data

NASA Technical Reports Server (NTRS)

Romero-Wolf, Andres; Jacobs, C. S.

2011-01-01

As thermal errors are reduced instrumental and troposphere correlated errors will increasingly become more important. Work in progress shows that troposphere covariance error models improve data analysis results. We expect to see stronger effects with higher data rates. Temperature modeling of delay errors may further reduce temporal correlations in the data.

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration.

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

Bayesian approaches for handling covariate measurement error are well established and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper, we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration, arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to regression calibration and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next, we describe the closely related maximum likelihood and multiple imputation approaches and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of regression calibration and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.

A study on characteristics of retrospective optimal interpolation with WRF testbed

NASA Astrophysics Data System (ADS)

Kim, S.; Noh, N.; Lim, G.

2012-12-01

This study presents the application of retrospective optimal interpolation (ROI) with Weather Research and Forecasting model (WRF). Song et al. (2009) suggest ROI method which is an optimal interpolation (OI) that gradually assimilates observations over the analysis window for variance-minimum estimate of an atmospheric state at the initial time of the analysis window. Song and Lim (2011) improve the method by incorporating eigen-decomposition and covariance inflation. ROI method assimilates the data at post analysis time using perturbation method (Errico and Raeder, 1999) without adjoint model. In this study, ROI method is applied to WRF model to validate the algorithm and to investigate the capability. The computational costs for ROI can be reduced due to the eigen-decomposition of background error covariance. Using the background error covariance in eigen-space, 1-profile assimilation experiment is performed. The difference between forecast errors with assimilation and without assimilation is obviously increased as time passed, which means the improvement of forecast error by assimilation. The characteristics and strength/weakness of ROI method are investigated by conducting the experiments with other data assimilation method.

Problems with small area surveys: lensing covariance of supernova distance measurements.

PubMed

Cooray, Asantha; Huterer, Dragan; Holz, Daniel E

2006-01-20

While luminosity distances from type Ia supernovae (SNe) are a powerful probe of cosmology, the accuracy with which these distances can be measured is limited by cosmic magnification due to gravitational lensing by the intervening large-scale structure. Spatial clustering of foreground mass leads to correlated errors in SNe distances. By including the full covariance matrix of SNe, we show that future wide-field surveys will remain largely unaffected by lensing correlations. However, "pencil beam" surveys, and those with narrow (but possibly long) fields of view, can be strongly affected. For a survey with 30 arcmin mean separation between SNe, lensing covariance leads to a approximately 45% increase in the expected errors in dark energy parameters.

Measuring continuous baseline covariate imbalances in clinical trial data

PubMed Central

Ciolino, Jody D.; Martin, Renee’ H.; Zhao, Wenle; Hill, Michael D.; Jauch, Edward C.; Palesch, Yuko Y.

2014-01-01

This paper presents and compares several methods of measuring continuous baseline covariate imbalance in clinical trial data. Simulations illustrate that though the t-test is an inappropriate method of assessing continuous baseline covariate imbalance, the test statistic itself is a robust measure in capturing imbalance in continuous covariate distributions. Guidelines to assess effects of imbalance on bias, type I error rate, and power for hypothesis test for treatment effect on continuous outcomes are presented, and the benefit of covariate-adjusted analysis (ANCOVA) is also illustrated. PMID:21865270

Spatio-temporal representativeness of ground-based downward solar radiation measurements

NASA Astrophysics Data System (ADS)

Schwarz, Matthias; Wild, Martin; Folini, Doris

2017-04-01

Surface solar radiation (SSR) is most directly observed with ground based pyranometer measurements. Besides measurement uncertainties, which arise from the pyranometer instrument itself, also errors attributed to the limited spatial representativeness of observations from single sites for their large-scale surrounding have to be taken into account when using such measurements for energy balance studies. In this study the spatial representativeness of 157 homogeneous European downward surface solar radiation time series from the Global Energy Balance Archive (GEBA) and the Baseline Surface Radiation Network (BSRN) were examined for the period 1983-2015 by using the high resolution (0.05°) surface solar radiation data set from the Satellite Application Facility on Climate Monitoring (CM-SAF SARAH) as a proxy for the spatiotemporal variability of SSR. By correlating deseasonalized monthly SSR time series form surface observations against single collocated satellite derived SSR time series, a mean spatial correlation pattern was calculated and validated against purely observational based patterns. Generally decreasing correlations with increasing distance from station, with high correlations (R2 = 0.7) in proximity to the observational sites (±0.5°), was found. When correlating surface observations against time series from spatially averaged satellite derived SSR data (and thereby simulating coarser and coarser grids), very high correspondence between sites and the collocated pixels has been found for pixel sizes up to several degrees. Moreover, special focus was put on the quantification of errors which arise in conjunction to spatial sampling when estimating the temporal variability and trends for a larger region from a single surface observation site. For 15-year trends on a 1° grid, errors due to spatial sampling in the order of half of the measurement uncertainty for monthly mean values were found.

Are Nonadjacent Collocations Processed Faster?

ERIC Educational Resources Information Center

Vilkaite, Laura

2016-01-01

Numerous studies have shown processing advantages for collocations, but they only investigated processing of adjacent collocations (e.g., "provide information"). However, in naturally occurring language, nonadjacent collocations ("provide" some of the "information") are equally, if not more frequent. This raises the…

The GEOS Ozone Data Assimilation System: Specification of Error Statistics

NASA Technical Reports Server (NTRS)

Stajner, Ivanka; Riishojgaard, Lars Peter; Rood, Richard B.

2000-01-01

A global three-dimensional ozone data assimilation system has been developed at the Data Assimilation Office of the NASA/Goddard Space Flight Center. The Total Ozone Mapping Spectrometer (TOMS) total ozone and the Solar Backscatter Ultraviolet (SBUV) or (SBUV/2) partial ozone profile observations are assimilated. The assimilation, into an off-line ozone transport model, is done using the global Physical-space Statistical Analysis Scheme (PSAS). This system became operational in December 1999. A detailed description of the statistical analysis scheme, and in particular, the forecast and observation error covariance models is given. A new global anisotropic horizontal forecast error correlation model accounts for a varying distribution of observations with latitude. Correlations are largest in the zonal direction in the tropics where data is sparse. Forecast error variance model is proportional to the ozone field. The forecast error covariance parameters were determined by maximum likelihood estimation. The error covariance models are validated using x squared statistics. The analyzed ozone fields in the winter 1992 are validated against independent observations from ozone sondes and HALOE. There is better than 10% agreement between mean Halogen Occultation Experiment (HALOE) and analysis fields between 70 and 0.2 hPa. The global root-mean-square (RMS) difference between TOMS observed and forecast values is less than 4%. The global RMS difference between SBUV observed and analyzed ozone between 50 and 3 hPa is less than 15%.

Experimental compliance calibration of the compact fracture toughness specimen

NASA Technical Reports Server (NTRS)

Fisher, D. M.; Buzzard, R. J.

1980-01-01

Compliances and stress intensity coefficients were determined over crack length to width ratios from 0.1 to 0.8. Displacements were measured at the load points, load line, and crack mouth. Special fixturing was devised to permit accurate measurement of load point displacement. The results are in agreement with the currently used results of boundary collocation analyses. The errors which occur in stress intensity coefficients or specimen energy input determinations made from load line displacement measurements rather than from load point measurements are emphasized.

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

NASA Technical Reports Server (NTRS)

Funaro, Daniele; Gottlieb, David

1989-01-01

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Multi-fidelity stochastic collocation method for computation of statistical moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu; Linebarger, Erin M., E-mail: aerinline@sci.utah.edu; Xiu, Dongbin, E-mail: xiu.16@osu.edu

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

Long Island Sound Coastal Observatory: Assessment of Above-Water Radiometric Measurement Uncertainties Using Collocated Multi and Hyper-Spectral Systems

DTIC Science & Technology

2011-10-14

Chi]. These as- sumptions are usually not valid in coastal waters. This can create significant errors in BRDF estima- tions in coastal zones [38,39...collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION. 1. REPORT...platform (LISCO) near Northport, New York, has been recently established to support validation of ocean color radiometry (OCR) satellite data. LISCO

Investigating the role of background and observation error correlations in improving a model forecast of forest carbon balance using four dimensional variational data assimilation.

NASA Astrophysics Data System (ADS)

Pinnington, Ewan; Casella, Eric; Dance, Sarah; Lawless, Amos; Morison, James; Nichols, Nancy; Wilkinson, Matthew; Quaife, Tristan

2016-04-01

Forest ecosystems play an important role in sequestering human emitted carbon-dioxide from the atmosphere and therefore greatly reduce the effect of anthropogenic induced climate change. For that reason understanding their response to climate change is of great importance. Efforts to implement variational data assimilation routines with functional ecology models and land surface models have been limited, with sequential and Markov chain Monte Carlo data assimilation methods being prevalent. When data assimilation has been used with models of carbon balance, background "prior" errors and observation errors have largely been treated as independent and uncorrelated. Correlations between background errors have long been known to be a key aspect of data assimilation in numerical weather prediction. More recently, it has been shown that accounting for correlated observation errors in the assimilation algorithm can considerably improve data assimilation results and forecasts. In this paper we implement a 4D-Var scheme with a simple model of forest carbon balance, for joint parameter and state estimation and assimilate daily observations of Net Ecosystem CO2 Exchange (NEE) taken at the Alice Holt forest CO2 flux site in Hampshire, UK. We then investigate the effect of specifying correlations between parameter and state variables in background error statistics and the effect of specifying correlations in time between observation error statistics. The idea of including these correlations in time is new and has not been previously explored in carbon balance model data assimilation. In data assimilation, background and observation error statistics are often described by the background error covariance matrix and the observation error covariance matrix. We outline novel methods for creating correlated versions of these matrices, using a set of previously postulated dynamical constraints to include correlations in the background error statistics and a Gaussian correlation function to include time correlations in the observation error statistics. The methods used in this paper will allow the inclusion of time correlations between many different observation types in the assimilation algorithm, meaning that previously neglected information can be accounted for. In our experiments we compared the results using our new correlated background and observation error covariance matrices and those using diagonal covariance matrices. We found that using the new correlated matrices reduced the root mean square error in the 14 year forecast of daily NEE by 44 % decreasing from 4.22 g C m-2 day-1 to 2.38 g C m-2 day-1.

SEPARABLE FACTOR ANALYSIS WITH APPLICATIONS TO MORTALITY DATA

PubMed Central

Fosdick, Bailey K.; Hoff, Peter D.

2014-01-01

Human mortality data sets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution or an error model that allows for dependence along at most one or two dimensions of the data array. However, failing to account for other dependencies can lead to inefficient estimates of regression parameters, inaccurate standard errors and poor predictions. An alternative to assuming independent errors is to allow for dependence along each dimension of the array using a separable covariance model. However, the number of parameters in this model increases rapidly with the dimensions of the array and, for many arrays, maximum likelihood estimates of the covariance parameters do not exist. In this paper, we propose a submodel of the separable covariance model that estimates the covariance matrix for each dimension as having factor analytic structure. This model can be viewed as an extension of factor analysis to array-valued data, as it uses a factor model to estimate the covariance along each dimension of the array. We discuss properties of this model as they relate to ordinary factor analysis, describe maximum likelihood and Bayesian estimation methods, and provide a likelihood ratio testing procedure for selecting the factor model ranks. We apply this methodology to the analysis of data from the Human Mortality Database, and show in a cross-validation experiment how it outperforms simpler methods. Additionally, we use this model to impute mortality rates for countries that have no mortality data for several years. Unlike other approaches, our methodology is able to estimate similarities between the mortality rates of countries, time periods and sexes, and use this information to assist with the imputations. PMID:25489353

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

NASA Technical Reports Server (NTRS)

Borovikov, Anna; Rienecker, Michele M.; Keppenne, Christian; Johnson, Gregory C.

2004-01-01

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

The precision of wet atmospheric deposition data from national atmospheric deposition program/national trends network sites determined with collocated samplers

USGS Publications Warehouse

Nilles, M.A.; Gordon, J.D.; Schroder, L.J.

1994-01-01

A collocated, wet-deposition sampler program has been operated since October 1988 by the U.S. Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments at four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database. Sampling precision was determined from the absolute value of differences in the analytical results for the paired samples in terms of median relative and absolute difference. The median relative difference for Mg2+, Na+, K+ and NH4+ concentration and deposition was quite variable between sites and exceeded 10% at most sites. Relative error for analytes whose concentrations typically approached laboratory method detection limits were greater than for analytes that did not typically approach detection limits. The median relative difference for SO42- and NO3- concentration, specific conductance, and sample volume at all sites was less than 7%. Precision for H+ concentration and deposition ranged from less than 10% at sites with typically high levels of H+ concentration to greater than 30% at sites with low H+ concentration. Median difference for analyte concentration and deposition was typically 1.5-2-times greater for samples collected during the winter than during other seasons at two northern sites. Likewise, the median relative difference in sample volume for winter samples was more than double the annual median relative difference at the two northern sites. Bias accounted for less than 25% of the collocated variability in analyte concentration and deposition from weekly collocated precipitation samples at most sites.A collocated, wet-deposition sampler program has been operated since OCtober 1988 by the U.S Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database.

Space-Wise approach for airborne gravity data modelling

NASA Astrophysics Data System (ADS)

Sampietro, D.; Capponi, M.; Mansi, A. H.; Gatti, A.; Marchetti, P.; Sansò, F.

2017-05-01

Regional gravity field modelling by means of remove-compute-restore procedure is nowadays widely applied in different contexts: it is the most used technique for regional gravimetric geoid determination, and it is also used in exploration geophysics to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.), which are useful to understand and map geological structures in a specific region. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are usually adopted. However, due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc., airborne data are usually contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations in both the low and high frequencies should be applied to recover valuable information. In this work, a software to filter and grid raw airborne observations is presented: the proposed solution consists in a combination of an along-track Wiener filter and a classical Least Squares Collocation technique. Basically, the proposed procedure is an adaptation to airborne gravimetry of the Space-Wise approach, developed by Politecnico di Milano to process data coming from the ESA satellite mission GOCE. Among the main differences with respect to the satellite application of this approach, there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. The presented solution is suited for airborne data analysis in order to be able to quickly filter and grid gravity observations in an easy way. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data retrieving the gravitational signal with a predicted accuracy of about 0.4 mGal.

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2015-01-01

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude

NASA Technical Reports Server (NTRS)

Sedlak, J.

1994-01-01

Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.

Generalized Linear Covariance Analysis

NASA Technical Reports Server (NTRS)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Collocations: A Neglected Variable in EFL.

ERIC Educational Resources Information Center

Farghal, Mohammed; Obiedat, Hussein

1995-01-01

Addresses the issue of collocations as an important and neglected variable in English-as-a-Foreign-Language classes. Two questionnaires, in English and Arabic, involving common collocations relating to food, color, and weather were administered to English majors and English language teachers. Results show both groups deficient in collocations. (36…

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2010 CFR

2010-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2014 CFR

2014-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2011 CFR

2011-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2013 CFR

2013-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas

Code of Federal Regulations, 2012 CFR

2012-10-01

... Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION... the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal Communications Commission, the National Conference of State Historic...

Dynamic Tasking of Networked Sensors Using Covariance Information

DTIC Science & Technology

2010-09-01

has been created under an effort called TASMAN (Tasking Autonomous Sensors in a Multiple Application Network). One of the first studies utilizing this...environment was focused on a novel resource management approach, namely covariance-based tasking. Under this scheme, the state error covariance of...resident space objects (RSO), sensor characteristics, and sensor- target geometry were used to determine the effectiveness of future observations in

Constant covariance in local vertical coordinates for near-circular orbits

NASA Technical Reports Server (NTRS)

Shepperd, Stanley W.

1991-01-01

A method is presented for devising a covariance matrix that either remains constant or grows in keeping with the presence of a period error in a rotating local-vertical coordinate system. The solution presented may prove useful in the initialization of simulation covariance matrices for near-circular-orbit problems. Use is made of the Clohessy-Wiltshire equations and the travelling-ellipse formulation.

Regionalized PM2.5 Community Multiscale Air Quality model performance evaluation across a continuous spatiotemporal domain.

PubMed

Reyes, Jeanette M; Xu, Yadong; Vizuete, William; Serre, Marc L

2017-01-01

The regulatory Community Multiscale Air Quality (CMAQ) model is a means to understanding the sources, concentrations and regulatory attainment of air pollutants within a model's domain. Substantial resources are allocated to the evaluation of model performance. The Regionalized Air quality Model Performance (RAMP) method introduced here explores novel ways of visualizing and evaluating CMAQ model performance and errors for daily Particulate Matter ≤ 2.5 micrometers (PM2.5) concentrations across the continental United States. The RAMP method performs a non-homogenous, non-linear, non-homoscedastic model performance evaluation at each CMAQ grid. This work demonstrates that CMAQ model performance, for a well-documented 2001 regulatory episode, is non-homogeneous across space/time. The RAMP correction of systematic errors outperforms other model evaluation methods as demonstrated by a 22.1% reduction in Mean Square Error compared to a constant domain wide correction. The RAMP method is able to accurately reproduce simulated performance with a correlation of r = 76.1%. Most of the error coming from CMAQ is random error with only a minority of error being systematic. Areas of high systematic error are collocated with areas of high random error, implying both error types originate from similar sources. Therefore, addressing underlying causes of systematic error will have the added benefit of also addressing underlying causes of random error.

Examining Second Language Receptive Knowledge of Collocation and Factors That Affect Learning

ERIC Educational Resources Information Center

Nguyen, Thi My Hang; Webb, Stuart

2017-01-01

This study investigated Vietnamese EFL learners' knowledge of verb-noun and adjective-noun collocations at the first three 1,000 word frequency levels, and the extent to which five factors (node word frequency, collocation frequency, mutual information score, congruency, and part of speech) predicted receptive knowledge of collocation. Knowledge…

Treatment of systematic errors in land data assimilation systems

NASA Astrophysics Data System (ADS)

Crow, W. T.; Yilmaz, M.

2012-12-01

Data assimilation systems are generally designed to minimize the influence of random error on the estimation of system states. Yet, experience with land data assimilation systems has also revealed the presence of large systematic differences between model-derived and remotely-sensed estimates of land surface states. Such differences are commonly resolved prior to data assimilation through implementation of a pre-processing rescaling step whereby observations are scaled (or non-linearly transformed) to somehow "match" comparable predictions made by an assimilation model. While the rationale for removing systematic differences in means (i.e., bias) between models and observations is well-established, relatively little theoretical guidance is currently available to determine the appropriate treatment of higher-order moments during rescaling. This talk presents a simple analytical argument to define an optimal linear-rescaling strategy for observations prior to their assimilation into a land surface model. While a technique based on triple collocation theory is shown to replicate this optimal strategy, commonly-applied rescaling techniques (e.g., so called "least-squares regression" and "variance matching" approaches) are shown to represent only sub-optimal approximations to it. Since the triple collocation approach is likely infeasible in many real-world circumstances, general advice for deciding between various feasible (yet sub-optimal) rescaling approaches will be presented with an emphasis of the implications of this work for the case of directly assimilating satellite radiances. While the bulk of the analysis will deal with linear rescaling techniques, its extension to nonlinear cases will also be discussed.

Collocation and Galerkin Time-Stepping Methods

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2011-01-01

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

The Infinitesimal Jackknife with Exploratory Factor Analysis

ERIC Educational Resources Information Center

Zhang, Guangjian; Preacher, Kristopher J.; Jennrich, Robert I.

2012-01-01

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both…

Quantifying the quality of precipitation data from different sources

NASA Astrophysics Data System (ADS)

Leijnse, Hidde; Wauben, Wiel; Overeem, Aart; de Haij, Marijn

2015-04-01

There is an increasing demand for high-resolution rainfall data. The current manual and automatic networks of climate and meteorological stations provide high quality rainfall data, but they cannot provide the high spatial and temporal resolution required for many applications. This can only partly be solved by using remotely sensed data. It is therefore necessary to consider third-party data, such as rain gauges operated by amateurs and rainfall intensities from commercial cellular communication links. The quality of such third-party data is highly variable and generally lower than that of dedicated networks. Often, such data quality information is missing for third party data. In order to be able to use data from various sources it is vital that quantitative knowledge of the data quality is available. This holds for all data sources, including the rain gauges in the reference networks of climate and meteorological stations. Data quality information is generally either not available or very limited for third-party data sources. For most dedicated climate meteorological networks, this information is only available for the sensor in laboratory conditions. In many cases, however, a significant part of the measurement errors and uncertainties is determined by the siting and maintenance of the sensor, for which generally only qualitative information is available. Furthermore sensors may have limitations under specific conditions. We aim to quantify data quality for different data sources by performing analyses on collocated data sets. Here we present an intercomparison of two years of precipitation data from six different sources (manual rain gauge, automatic rain gauge, present weather sensor, weather radar, commercial cellular communication links, and Meteosat) at three different locations in the Netherlands. We use auxiliary meteorological data to determine if the quality is influenced by other variables (e.g. the temperature influencing the evaporation from the rain gauge). We use three techniques to compare the data sets: 1) direct comparison; 2) triple collocation (see Stoffelen, 1998); and 3) comparison of statistics. Stoffelen, A. (1998). Toward the true near-surface wind speed: Error modeling and calibration using triple collocation. Journal of Geophysical Research: Oceans (1978-2012), 103(C4), 7755-7766.

Collocation mismatch uncertainties in satellite aerosol retrieval validation

NASA Astrophysics Data System (ADS)

Virtanen, Timo H.; Kolmonen, Pekka; Sogacheva, Larisa; Rodríguez, Edith; Saponaro, Giulia; de Leeuw, Gerrit

2018-02-01

Satellite-based aerosol products are routinely validated against ground-based reference data, usually obtained from sun photometer networks such as AERONET (AEROsol RObotic NETwork). In a typical validation exercise a spatial sample of the instantaneous satellite data is compared against a temporal sample of the point-like ground-based data. The observations do not correspond to exactly the same column of the atmosphere at the same time, and the representativeness of the reference data depends on the spatiotemporal variability of the aerosol properties in the samples. The associated uncertainty is known as the collocation mismatch uncertainty (CMU). The validation results depend on the sampling parameters. While small samples involve less variability, they are more sensitive to the inevitable noise in the measurement data. In this paper we study systematically the effect of the sampling parameters in the validation of AATSR (Advanced Along-Track Scanning Radiometer) aerosol optical depth (AOD) product against AERONET data and the associated collocation mismatch uncertainty. To this end, we study the spatial AOD variability in the satellite data, compare it against the corresponding values obtained from densely located AERONET sites, and assess the possible reasons for observed differences. We find that the spatial AOD variability in the satellite data is approximately 2 times larger than in the ground-based data, and the spatial variability correlates only weakly with that of AERONET for short distances. We interpreted that only half of the variability in the satellite data is due to the natural variability in the AOD, and the rest is noise due to retrieval errors. However, for larger distances (˜ 0.5°) the correlation is improved as the noise is averaged out, and the day-to-day changes in regional AOD variability are well captured. Furthermore, we assess the usefulness of the spatial variability of the satellite AOD data as an estimate of CMU by comparing the retrieval errors to the total uncertainty estimates including the CMU in the validation. We find that accounting for CMU increases the fraction of consistent observations.

Accounting for baseline differences and measurement error in the analysis of change over time.

PubMed

Braun, Julia; Held, Leonhard; Ledergerber, Bruno

2014-01-15

If change over time is compared in several groups, it is important to take into account baseline values so that the comparison is carried out under the same preconditions. As the observed baseline measurements are distorted by measurement error, it may not be sufficient to include them as covariate. By fitting a longitudinal mixed-effects model to all data including the baseline observations and subsequently calculating the expected change conditional on the underlying baseline value, a solution to this problem has been provided recently so that groups with the same baseline characteristics can be compared. In this article, we present an extended approach where a broader set of models can be used. Specifically, it is possible to include any desired set of interactions between the time variable and the other covariates, and also, time-dependent covariates can be included. Additionally, we extend the method to adjust for baseline measurement error of other time-varying covariates. We apply the methodology to data from the Swiss HIV Cohort Study to address the question if a joint infection with HIV-1 and hepatitis C virus leads to a slower increase of CD4 lymphocyte counts over time after the start of antiretroviral therapy. Copyright © 2013 John Wiley & Sons, Ltd.

Natural abundance deuterium and 18-oxygen effects on the precision of the doubly labeled water method

NASA Technical Reports Server (NTRS)

Horvitz, M. A.; Schoeller, D. A.

2001-01-01

The doubly labeled water method for measuring total energy expenditure is subject to error from natural variations in the background 2H and 18O in body water. There is disagreement as to whether the variations in background abundances of the two stable isotopes covary and what relative doses of 2H and 18O minimize the impact of variation on the precision of the method. We have performed two studies to investigate the amount and covariance of the background variations. These were a study of urine collected weekly from eight subjects who remained in the Madison, WI locale for 6 wk and frequent urine samples from 14 subjects during round-trip travel to a locale > or = 500 miles from Madison, WI. Background variation in excess of analytical error was detected in six of the eight nontravelers, and covariance was demonstrated in four subjects. Background variation was detected in all 14 travelers, and covariance was demonstrated in 11 subjects. The median slopes of the regression lines of delta2H vs. delta18O were 6 and 7, respectively. Modeling indicated that 2H and 18O doses yielding a 6:1 ratio of final enrichments should minimize this error introduced to the doubly labeled water method.

Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-05-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Natural abundance deuterium and 18-oxygen effects on the precision of the doubly labeled water method.

PubMed

Horvitz, M A; Schoeller, D A

2001-06-01

The doubly labeled water method for measuring total energy expenditure is subject to error from natural variations in the background 2H and 18O in body water. There is disagreement as to whether the variations in background abundances of the two stable isotopes covary and what relative doses of 2H and 18O minimize the impact of variation on the precision of the method. We have performed two studies to investigate the amount and covariance of the background variations. These were a study of urine collected weekly from eight subjects who remained in the Madison, WI locale for 6 wk and frequent urine samples from 14 subjects during round-trip travel to a locale > or = 500 miles from Madison, WI. Background variation in excess of analytical error was detected in six of the eight nontravelers, and covariance was demonstrated in four subjects. Background variation was detected in all 14 travelers, and covariance was demonstrated in 11 subjects. The median slopes of the regression lines of delta2H vs. delta18O were 6 and 7, respectively. Modeling indicated that 2H and 18O doses yielding a 6:1 ratio of final enrichments should minimize this error introduced to the doubly labeled water method.

Trajectory prediction for ballistic missiles based on boost-phase LOS measurements

NASA Astrophysics Data System (ADS)

Yeddanapudi, Murali; Bar-Shalom, Yaakov

1997-10-01

This paper addresses the problem of the estimation of the trajectory of a tactical ballistic missile using line of sight (LOS) measurements from one or more passive sensors (typically satellites). The major difficulties of this problem include: the estimation of the unknown time of launch, incorporation of (inaccurate) target thrust profiles to model the target dynamics during the boost phase and an overall ill-conditioning of the estimation problem due to poor observability of the target motion via the LOS measurements. We present a robust estimation procedure based on the Levenberg-Marquardt algorithm that provides both the target state estimate and error covariance taking into consideration the complications mentioned above. An important consideration in the defense against tactical ballistic missiles is the determination of the target position and error covariance at the acquisition range of a surveillance radar in the vicinity of the impact point. We present a systematic procedure to propagate the target state and covariance to a nominal time, when it is within the detection range of a surveillance radar to obtain a cueing volume. Mont Carlo simulation studies on typical single and two sensor scenarios indicate that the proposed algorithms are accurate in terms of the estimates and the estimator calculated covariances are consistent with the errors.

Rigorous covariance propagation of geoid errors to geodetic MDT estimates

NASA Astrophysics Data System (ADS)

Pail, R.; Albertella, A.; Fecher, T.; Savcenko, R.

2012-04-01

The mean dynamic topography (MDT) is defined as the difference between the mean sea surface (MSS) derived from satellite altimetry, averaged over several years, and the static geoid. Assuming geostrophic conditions, from the MDT the ocean surface velocities as important component of global ocean circulation can be derived from it. Due to the availability of GOCE gravity field models, for the very first time MDT can now be derived solely from satellite observations (altimetry and gravity) down to spatial length-scales of 100 km and even below. Global gravity field models, parameterized in terms of spherical harmonic coefficients, are complemented by the full variance-covariance matrix (VCM). Therefore, for the geoid component a realistic statistical error estimate is available, while the error description of the altimetric component is still an open issue and is, if at all, attacked empirically. In this study we make the attempt to perform, based on the full gravity VCM, rigorous error propagation to derived geostrophic surface velocities, thus also considering all correlations. For the definition of the static geoid we use the third release of the time-wise GOCE model, as well as the satellite-only combination model GOCO03S. In detail, we will investigate the velocity errors resulting from the geoid component in dependence of the harmonic degree, and the impact of using/no using covariances on the MDT errors and its correlations. When deriving an MDT, it is spectrally filtered to a certain maximum degree, which is usually driven by the signal content of the geoid model, by applying isotropic or non-isotropic filters. Since this filtering is acting also on the geoid component, the consistent integration of this filter process into the covariance propagation shall be performed, and its impact shall be quantified. The study will be performed for MDT estimates in specific test areas of particular oceanographic interest.

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Nazirov, R. R.; Elyasberg, P. E.

1980-01-01

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

English Learners' Knowledge of Prepositions: Collocational Knowledge or Knowledge Based on Meaning?

ERIC Educational Resources Information Center

Mueller, Charles M.

2011-01-01

Second language (L2) learners' successful performance in an L2 can be partly attributed to their knowledge of collocations. In some cases, this knowledge is accompanied by knowledge of the semantic and/or grammatical patterns that motivate the collocation. At other times, collocational knowledge may serve a compensatory role. To determine the…

47 CFR 51.321 - Methods of obtaining interconnection and access to unbundled elements under section 251 of the Act.

Code of Federal Regulations, 2010 CFR

2010-10-01

... elements include, but are not limited to: (1) Physical collocation and virtual collocation at the premises... seeking a particular collocation arrangement, either physical or virtual, is entitled to a presumption... incumbent LEC shall be required to provide virtual collocation, except at points where the incumbent LEC...

Frequency of Input and L2 Collocational Processing: A Comparison of Congruent and Incongruent Collocations

ERIC Educational Resources Information Center

Wolter, Brent; Gyllstad, Henrik

2013-01-01

This study investigated the influence of frequency effects on the processing of congruent (i.e., having an equivalent first language [L1] construction) collocations and incongruent (i.e., not having an equivalent L1 construction) collocations in a second language (L2). An acceptability judgment task was administered to native and advanced…

Corpus-Based versus Traditional Learning of Collocations

ERIC Educational Resources Information Center

Daskalovska, Nina

2015-01-01

One of the aspects of knowing a word is the knowledge of which words it is usually used with. Since knowledge of collocations is essential for appropriate and fluent use of language, learning collocations should have a central place in the study of vocabulary. There are different opinions about the best ways of learning collocations. This study…

Collocations in Corpus-Based Language Learning Research: Identifying, Comparing, and Interpreting the Evidence

ERIC Educational Resources Information Center

Gablasova, Dana; Brezina, Vaclav; McEnery, Tony

2017-01-01

This article focuses on the use of collocations in language learning research (LLR). Collocations, as units of formulaic language, are becoming prominent in our understanding of language learning and use; however, while the number of corpus-based LLR studies of collocations is growing, there is still a need for a deeper understanding of factors…

A new method for determining the optimal lagged ensemble

PubMed Central

DelSole, T.; Tippett, M. K.; Pegion, K.

2017-01-01

Abstract We propose a general methodology for determining the lagged ensemble that minimizes the mean square forecast error. The MSE of a lagged ensemble is shown to depend only on a quantity called the cross‐lead error covariance matrix, which can be estimated from a short hindcast data set and parameterized in terms of analytic functions of time. The resulting parameterization allows the skill of forecasts to be evaluated for an arbitrary ensemble size and initialization frequency. Remarkably, the parameterization also can estimate the MSE of a burst ensemble simply by taking the limit of an infinitely small interval between initialization times. This methodology is applied to forecasts of the Madden Julian Oscillation (MJO) from version 2 of the Climate Forecast System version 2 (CFSv2). For leads greater than a week, little improvement is found in the MJO forecast skill when ensembles larger than 5 days are used or initializations greater than 4 times per day. We find that if the initialization frequency is too infrequent, important structures of the lagged error covariance matrix are lost. Lastly, we demonstrate that the forecast error at leads ≥10 days can be reduced by optimally weighting the lagged ensemble members. The weights are shown to depend only on the cross‐lead error covariance matrix. While the methodology developed here is applied to CFSv2, the technique can be easily adapted to other forecast systems. PMID:28580050

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

NASA Technical Reports Server (NTRS)

Boussalis, Dhemetrios; Bayard, David S.

2013-01-01

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

NASA Technical Reports Server (NTRS)

Ghrist, Richard W.; Plakalovic, Dragan

2012-01-01

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

Robust Mean and Covariance Structure Analysis through Iteratively Reweighted Least Squares.

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Bentler, Peter M.

2000-01-01

Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)

The Error Structure of the SMAP Single and Dual Channel Soil Moisture Retrievals

NASA Astrophysics Data System (ADS)

Dong, Jianzhi; Crow, Wade T.; Bindlish, Rajat

2018-01-01

Knowledge of the temporal error structure for remotely sensed surface soil moisture retrievals can improve our ability to exploit them for hydrologic and climate studies. This study employs a triple collocation analysis to investigate both the total variance and temporal autocorrelation of errors in Soil Moisture Active and Passive (SMAP) products generated from two separate soil moisture retrieval algorithms, the vertically polarized brightness temperature-based single-channel algorithm (SCA-V, the current baseline SMAP algorithm) and the dual-channel algorithm (DCA). A key assumption made in SCA-V is that real-time vegetation opacity can be accurately captured using only a climatology for vegetation opacity. Results demonstrate that while SCA-V generally outperforms DCA, SCA-V can produce larger total errors when this assumption is significantly violated by interannual variability in vegetation health and biomass. Furthermore, larger autocorrelated errors in SCA-V retrievals are found in areas with relatively large vegetation opacity deviations from climatological expectations. This implies that a significant portion of the autocorrelated error in SCA-V is attributable to the violation of its vegetation opacity climatology assumption and suggests that utilizing a real (as opposed to climatological) vegetation opacity time series in the SCA-V algorithm would reduce the magnitude of autocorrelated soil moisture retrieval errors.

Quantifying Adventitious Error in a Covariance Structure as a Random Effect

PubMed Central

Wu, Hao; Browne, Michael W.

2017-01-01

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the RMSEA. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. PMID:25813463

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

PubMed

Shin, Jaehyun; Zhong, Yongmin; Oetomo, Denny; Gu, Chengfan

2018-05-21

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

Linear time-dependent reference intervals where there is measurement error in the time variable-a parametric approach.

PubMed

Gillard, Jonathan

2015-12-01

This article re-examines parametric methods for the calculation of time specific reference intervals where there is measurement error present in the time covariate. Previous published work has commonly been based on the standard ordinary least squares approach, weighted where appropriate. In fact, this is an incorrect method when there are measurement errors present, and in this article, we show that the use of this approach may, in certain cases, lead to referral patterns that may vary with different values of the covariate. Thus, it would not be the case that all patients are treated equally; some subjects would be more likely to be referred than others, hence violating the principle of equal treatment required by the International Federation for Clinical Chemistry. We show, by using measurement error models, that reference intervals are produced that satisfy the requirement for equal treatment for all subjects. © The Author(s) 2011.

A Study on the Phenomenon of Collocations: Methodology of Teaching English and German Collocations to Russian Students

ERIC Educational Resources Information Center

Varlamova, Elena V.; Naciscione, Anita; Tulusina, Elena A.

2016-01-01

Relevance of the issue stated in the article is determined by the fact that there is a lack of research devoted to the methods of teaching English and German collocations. The aim of our work is to determine methods of teaching English and German collocations to Russian university students studying foreign languages through experimental testing.…

Uncertainty Propagation in OMFIT

NASA Astrophysics Data System (ADS)

Smith, Sterling; Meneghini, Orso; Sung, Choongki

2017-10-01

A rigorous comparison of power balance fluxes and turbulent model fluxes requires the propagation of uncertainties in the kinetic profiles and their derivatives. Making extensive use of the python uncertainties package, the OMFIT framework has been used to propagate covariant uncertainties to provide an uncertainty in the power balance calculation from the ONETWO code, as well as through the turbulent fluxes calculated by the TGLF code. The covariant uncertainties arise from fitting 1D (constant on flux surface) density and temperature profiles and associated random errors with parameterized functions such as a modified tanh. The power balance and model fluxes can then be compared with quantification of the uncertainties. No effort is made at propagating systematic errors. A case study will be shown for the effects of resonant magnetic perturbations on the kinetic profiles and fluxes at the top of the pedestal. A separate attempt at modeling the random errors with Monte Carlo sampling will be compared to the method of propagating the fitting function parameter covariant uncertainties. Work supported by US DOE under DE-FC02-04ER54698, DE-FG2-95ER-54309, DE-SC 0012656.

Are Low-order Covariance Estimates Useful in Error Analyses?

NASA Astrophysics Data System (ADS)

Baker, D. F.; Schimel, D.

2005-12-01

Atmospheric trace gas inversions, using modeled atmospheric transport to infer surface sources and sinks from measured concentrations, are most commonly done using least-squares techniques that return not only an estimate of the state (the surface fluxes) but also the covariance matrix describing the uncertainty in that estimate. Besides allowing one to place error bars around the estimate, the covariance matrix may be used in simulation studies to learn what uncertainties would be expected from various hypothetical observing strategies. This error analysis capability is routinely used in designing instrumentation, measurement campaigns, and satellite observing strategies. For example, Rayner, et al (2002) examined the ability of satellite-based column-integrated CO2 measurements to constrain monthly-average CO2 fluxes for about 100 emission regions using this approach. Exact solutions for both state vector and covariance matrix become computationally infeasible, however, when the surface fluxes are solved at finer resolution (e.g., daily in time, under 500 km in space). It is precisely at these finer scales, however, that one would hope to be able to estimate fluxes using high-density satellite measurements. Non-exact estimation methods such as variational data assimilation or the ensemble Kalman filter could be used, but they achieve their computational savings by obtaining an only approximate state estimate and a low-order approximation of the true covariance. One would like to be able to use this covariance matrix to do the same sort of error analyses as are done with the full-rank covariance, but is it correct to do so? Here we compare uncertainties and `information content' derived from full-rank covariance matrices obtained from a direct, batch least squares inversion to those from the incomplete-rank covariance matrices given by a variational data assimilation approach solved with a variable metric minimization technique (the Broyden-Fletcher- Goldfarb-Shanno algorithm). Two cases are examined: a toy problem in which CO2 fluxes for 3 latitude bands are estimated for only 2 time steps per year, and for the monthly fluxes for 22 regions across 1988-2003 solved for in the TransCom3 interannual flux inversion of Baker, et al (2005). The usefulness of the uncertainty estimates will be assessed as a function of the number of minimization steps used in the variational approach; this will help determine whether they will also be useful in the high-resolution cases that we would most like to apply the non-exact methods to. Baker, D.F., et al., TransCom3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988-2003, Glob. Biogeochem. Cycles, doi:10.1029/2004GB002439, 2005, in press. Rayner, P.J., R.M. Law, D.M. O'Brien, T.M. Butler, and A.C. Dilley, Global observations of the carbon budget, 3, Initial assessment of the impact of satellite orbit, scan geometry, and cloud on measuring CO2 from space, J. Geophys. Res., 107(D21), 4557, doi:10.1029/2001JD000618, 2002.

Sensitivity of Fit Indices to Misspecification in Growth Curve Models

ERIC Educational Resources Information Center

Wu, Wei; West, Stephen G.

2010-01-01

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

A Practical Methodology for Quantifying Random and Systematic Components of Unexplained Variance in a Wind Tunnel

NASA Technical Reports Server (NTRS)

Deloach, Richard; Obara, Clifford J.; Goodman, Wesley L.

2012-01-01

This paper documents a check standard wind tunnel test conducted in the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3M TCT) that was designed and analyzed using the Modern Design of Experiments (MDOE). The test designed to partition the unexplained variance of typical wind tunnel data samples into two constituent components, one attributable to ordinary random error, and one attributable to systematic error induced by covariate effects. Covariate effects in wind tunnel testing are discussed, with examples. The impact of systematic (non-random) unexplained variance on the statistical independence of sequential measurements is reviewed. The corresponding correlation among experimental errors is discussed, as is the impact of such correlation on experimental results generally. The specific experiment documented herein was organized as a formal test for the presence of unexplained variance in representative samples of wind tunnel data, in order to quantify the frequency with which such systematic error was detected, and its magnitude relative to ordinary random error. Levels of systematic and random error reported here are representative of those quantified in other facilities, as cited in the references.

47 CFR 69.121 - Connection charges for expanded interconnection.

Code of Federal Regulations, 2010 CFR

2010-10-01

... separations. (2) Charges for subelements associated with physical collocation or virtual collocation, other... of the virtual collocation equipment described in § 64.1401(e)(1) of this chapter, may reasonably...

Neural networks: further insights into error function, generalized weights and others

PubMed Central

2016-01-01

The article is a continuum of a previous one providing further insights into the structure of neural network (NN). Key concepts of NN including activation function, error function, learning rate and generalized weights are introduced. NN topology can be visualized with generic plot() function by passing a “nn” class object. Generalized weights assist interpretation of NN model with respect to the independent effect of individual input variables. A large variance of generalized weights for a covariate indicates non-linearity of its independent effect. If generalized weights of a covariate are approximately zero, the covariate is considered to have no effect on outcome. Finally, prediction of new observations can be performed using compute() function. Make sure that the feature variables passed to the compute() function are in the same order to that in the training NN. PMID:27668220

Radial orbit error reduction and sea surface topography determination using satellite altimetry

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Comparison of Flow-Dependent and Static Error Correlation Models in the DAO Ozone Data Assimilation System

NASA Technical Reports Server (NTRS)

Wargan, K.; Stajner, I.; Pawson, S.

2003-01-01

In a data assimilation system the forecast error covariance matrix governs the way in which the data information is spread throughout the model grid. Implementation of a correct method of assigning covariances is expected to have an impact on the analysis results. The simplest models assume that correlations are constant in time and isotropic or nearly isotropic. In such models the analysis depends on the dynamics only through assumed error standard deviations. In applications to atmospheric tracer data assimilation this may lead to inaccuracies, especially in regions with strong wind shears or high gradient of potential vorticity, as well as in areas where no data are available. In order to overcome this problem we have developed a flow-dependent covariance model that is based on short term evolution of error correlations. The presentation compares performance of a static and a flow-dependent model applied to a global three- dimensional ozone data assimilation system developed at NASA s Data Assimilation Office. We will present some results of validation against WMO balloon-borne sondes and the Polar Ozone and Aerosol Measurement (POAM) III instrument. Experiments show that allowing forecast error correlations to evolve with the flow results in positive impact on assimilated ozone within the regions where data were not assimilated, particularly at high latitudes in both hemispheres and in the troposphere. We will also discuss statistical characteristics of both models; in particular we will argue that including evolution of error correlations leads to stronger internal consistency of a data assimilation ,

Improving lidar turbulence estimates for wind energy

NASA Astrophysics Data System (ADS)

Newman, J. F.; Clifton, A.; Churchfield, M. J.; Klein, P.

2016-09-01

Remote sensing devices (e.g., lidars) are quickly becoming a cost-effective and reliable alternative to meteorological towers for wind energy applications. Although lidars can measure mean wind speeds accurately, these devices measure different values of turbulence intensity (TI) than an instrument on a tower. In response to these issues, a lidar TI error reduction model was recently developed for commercially available lidars. The TI error model first applies physics-based corrections to the lidar measurements, then uses machine-learning techniques to further reduce errors in lidar TI estimates. The model was tested at two sites in the Southern Plains where vertically profiling lidars were collocated with meteorological towers. Results indicate that the model works well under stable conditions but cannot fully mitigate the effects of variance contamination under unstable conditions. To understand how variance contamination affects lidar TI estimates, a new set of equations was derived in previous work to characterize the actual variance measured by a lidar. Terms in these equations were quantified using a lidar simulator and modeled wind field, and the new equations were then implemented into the TI error model.

Improving Lidar Turbulence Estimates for Wind Energy: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Newman, Jennifer; Clifton, Andrew; Churchfield, Matthew

2016-10-01

Remote sensing devices (e.g., lidars) are quickly becoming a cost-effective and reliable alternative to meteorological towers for wind energy applications. Although lidars can measure mean wind speeds accurately, these devices measure different values of turbulence intensity (TI) than an instrument on a tower. In response to these issues, a lidar TI error reduction model was recently developed for commercially available lidars. The TI error model first applies physics-based corrections to the lidar measurements, then uses machine-learning techniques to further reduce errors in lidar TI estimates. The model was tested at two sites in the Southern Plains where vertically profiling lidarsmore » were collocated with meteorological towers. Results indicate that the model works well under stable conditions but cannot fully mitigate the effects of variance contamination under unstable conditions. To understand how variance contamination affects lidar TI estimates, a new set of equations was derived in previous work to characterize the actual variance measured by a lidar. Terms in these equations were quantified using a lidar simulator and modeled wind field, and the new equations were then implemented into the TI error model.« less

Improving Lidar Turbulence Estimates for Wind Energy

DOE PAGES

Newman, Jennifer F.; Clifton, Andrew; Churchfield, Matthew J.; ...

2016-10-03

Remote sensing devices (e.g., lidars) are quickly becoming a cost-effective and reliable alternative to meteorological towers for wind energy applications. Although lidars can measure mean wind speeds accurately, these devices measure different values of turbulence intensity (TI) than an instrument on a tower. In response to these issues, a lidar TI error reduction model was recently developed for commercially available lidars. The TI error model first applies physics-based corrections to the lidar measurements, then uses machine-learning techniques to further reduce errors in lidar TI estimates. The model was tested at two sites in the Southern Plains where vertically profiling lidarsmore » were collocated with meteorological towers. Results indicate that the model works well under stable conditions but cannot fully mitigate the effects of variance contamination under unstable conditions. To understand how variance contamination affects lidar TI estimates, a new set of equations was derived in previous work to characterize the actual variance measured by a lidar. Terms in these equations were quantified using a lidar simulator and modeled wind field, and the new equations were then implemented into the TI error model.« less

Predicting ambient aerosol thermal-optical reflectance measurements from infrared spectra: elemental carbon

NASA Astrophysics Data System (ADS)

Dillner, A. M.; Takahama, S.

2015-10-01

Elemental carbon (EC) is an important constituent of atmospheric particulate matter because it absorbs solar radiation influencing climate and visibility and it adversely affects human health. The EC measured by thermal methods such as thermal-optical reflectance (TOR) is operationally defined as the carbon that volatilizes from quartz filter samples at elevated temperatures in the presence of oxygen. Here, methods are presented to accurately predict TOR EC using Fourier transform infrared (FT-IR) absorbance spectra from atmospheric particulate matter collected on polytetrafluoroethylene (PTFE or Teflon) filters. This method is similar to the procedure developed for OC in prior work (Dillner and Takahama, 2015). Transmittance FT-IR analysis is rapid, inexpensive and nondestructive to the PTFE filter samples which are routinely collected for mass and elemental analysis in monitoring networks. FT-IR absorbance spectra are obtained from 794 filter samples from seven Interagency Monitoring of PROtected Visual Environment (IMPROVE) sites collected during 2011. Partial least squares regression is used to calibrate sample FT-IR absorbance spectra to collocated TOR EC measurements. The FT-IR spectra are divided into calibration and test sets. Two calibrations are developed: one developed from uniform distribution of samples across the EC mass range (Uniform EC) and one developed from a uniform distribution of Low EC mass samples (EC < 2.4 μg, Low Uniform EC). A hybrid approach which applies the Low EC calibration to Low EC samples and the Uniform EC calibration to all other samples is used to produce predictions for Low EC samples that have mean error on par with parallel TOR EC samples in the same mass range and an estimate of the minimum detection limit (MDL) that is on par with TOR EC MDL. For all samples, this hybrid approach leads to precise and accurate TOR EC predictions by FT-IR as indicated by high coefficient of determination (R2; 0.96), no bias (0.00 μg m-3, a concentration value based on the nominal IMPROVE sample volume of 32.8 m3), low error (0.03 μg m-3) and reasonable normalized error (21 %). These performance metrics can be achieved with various degrees of spectral pretreatment (e.g., including or excluding substrate contributions to the absorbances) and are comparable in precision and accuracy to collocated TOR measurements. Only the normalized error is higher for the FT-IR EC measurements than for collocated TOR. FT-IR spectra are also divided into calibration and test sets by the ratios OC/EC and ammonium/EC to determine the impact of OC and ammonium on EC prediction. We conclude that FT-IR analysis with partial least squares regression is a robust method for accurately predicting TOR EC in IMPROVE network samples, providing complementary information to TOR OC predictions (Dillner and Takahama, 2015) and the organic functional group composition and organic matter estimated previously from the same set of sample spectra (Ruthenburg et al., 2014).

Predicting ambient aerosol Thermal Optical Reflectance (TOR) measurements from infrared spectra: elemental carbon

NASA Astrophysics Data System (ADS)

Dillner, A. M.; Takahama, S.

2015-06-01

Elemental carbon (EC) is an important constituent of atmospheric particulate matter because it absorbs solar radiation influencing climate and visibility and it adversely affects human health. The EC measured by thermal methods such as Thermal-Optical Reflectance (TOR) is operationally defined as the carbon that volatilizes from quartz filter samples at elevated temperatures in the presence of oxygen. Here, methods are presented to accurately predict TOR EC using Fourier Transform Infrared (FT-IR) absorbance spectra from atmospheric particulate matter collected on polytetrafluoroethylene (PTFE or Teflon) filters. This method is similar to the procedure tested and developed for OC in prior work (Dillner and Takahama, 2015). Transmittance FT-IR analysis is rapid, inexpensive, and non-destructive to the PTFE filter samples which are routinely collected for mass and elemental analysis in monitoring networks. FT-IR absorbance spectra are obtained from 794 filter samples from seven Interagency Monitoring of PROtected Visual Environment (IMPROVE) sites collected during 2011. Partial least squares regression is used to calibrate sample FT-IR absorbance spectra to collocated TOR EC measurements. The FTIR spectra are divided into calibration and test sets. Two calibrations are developed, one which is developed from uniform distribution of samples across the EC mass range (Uniform EC) and one developed from a~uniform distribution of low EC mass samples (EC < 2.4 μg, Low Uniform EC). A hybrid approach which applies the low EC calibration to low EC samples and the Uniform EC calibration to all other samples is used to produces predictions for low EC samples that have mean error on par with parallel TOR EC samples in the same mass range and an estimate of the minimum detection limit (MDL) that is on par with TOR EC MDL. For all samples, this hybrid approach leads to precise and accurate TOR EC predictions by FT-IR as indicated by high coefficient of variation (R2; 0.96), no bias (0.00 μg m-3, concentration value based on the nominal IMPROVE sample volume of 32.8 m-3), low error (0.03 μg m-3) and reasonable normalized error (21 %). These performance metrics can be achieved with various degrees of spectral pretreatment (e.g., including or excluding substrate contributions to the absorbances) and are comparable in precision and accuracy to collocated TOR measurements. Only the normalized error is higher for the FT-IR EC measurements than for collocated TOR. FT-IR spectra are also divided into calibration and test sets by the ratios OC/EC and ammonium/EC to determine the impact of OC and ammonium on EC prediction. We conclude that FT-IR analysis with partial least squares regression is a robust method for accurately predicting TOR EC in IMPROVE network samples; providing complementary information to TOR OC predictions (Dillner and Takahama, 2015) and the organic functional group composition and organic matter (OM) estimated previously from the same set of sample spectra (Ruthenburg et al., 2014).

Tropospheric profiles of wet refractivity and humidity from the combination of remote sensing data sets and measurements on the ground

NASA Astrophysics Data System (ADS)

Hurter, F.; Maier, O.

2013-11-01

We reconstruct atmospheric wet refractivity profiles for the western part of Switzerland with a least-squares collocation approach from data sets of (a) zenith path delays that are a byproduct of the GPS (global positioning system) processing, (b) ground meteorological measurements, (c) wet refractivity profiles from radio occultations whose tangent points lie within the study area, and (d) radiosonde measurements. Wet refractivity is a parameter partly describing the propagation of electromagnetic waves and depends on the atmospheric parameters temperature and water vapour pressure. In addition, we have measurements of a lower V-band microwave radiometer at Payerne. It delivers temperature profiles at high temporal resolution, especially in the range from ground to 3000 m a.g.l., though vertical information content decreases with height. The temperature profiles together with the collocated wet refractivity profiles provide near-continuous dew point temperature or relative humidity profiles at Payerne for the study period from 2009 to 2011. In the validation of the humidity profiles, we adopt a two-step procedure. We first investigate the reconstruction quality of the wet refractivity profiles at the location of Payerne by comparing them to wet refractivity profiles computed from radiosonde profiles available for that location. We also assess the individual contributions of the data sets to the reconstruction quality and demonstrate a clear benefit from the data combination. Secondly, the accuracy of the conversion from wet refractivity to dew point temperature and relative humidity profiles with the radiometer temperature profiles is examined, comparing them also to radiosonde profiles. For the least-squares collocation solution combining GPS and ground meteorological measurements, we achieve the following error figures with respect to the radiosonde reference: maximum median offset of relative refractivity error is -16% and quartiles are 5% to 40% for the lower troposphere. We further added 189 radio occultations that met our requirements. They mostly improved the accuracy in the upper troposphere. Maximum median offsets have decreased from 120% relative error to 44% at 8 km height. Dew point temperature profiles after the conversion with radiometer temperatures compare to radiosonde profiles as to: absolute dew point temperature errors in the lower troposphere have a maximum median offset of -2 K and maximum quartiles of 4.5 K. For relative humidity, we get a maximum mean offset of 7.3%, with standard deviations of 12-20%. The methodology presented allows us to reconstruct humidity profiles at any location where temperature profiles, but no atmospheric humidity measurements other than from GPS are available. Additional data sets of wet refractivity are shown to be easily integrated into the framework and strongly aid the reconstruction. Since the used data sets are all operational and available in near-realtime, we envisage the methodology of this paper to be a tool for nowcasting of clouds and rain and to understand processes in the boundary layer and at its top.

Designing Measurement Studies under Budget Constraints: Controlling Error of Measurement and Power.

ERIC Educational Resources Information Center

Marcoulides, George A.

1995-01-01

A methodology is presented for minimizing the mean error variance-covariance component in studies with resource constraints. The method is illustrated using a one-facet multivariate design. Extensions to other designs are discussed. (SLD)

Selecting a Separable Parametric Spatiotemporal Covariance Structure for Longitudinal Imaging Data

PubMed Central

George, Brandon; Aban, Inmaculada

2014-01-01

Longitudinal imaging studies allow great insight into how the structure and function of a subject’s internal anatomy changes over time. Unfortunately, the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation: the temporal from the repeated measures, and the spatial from the outcomes of interest being observed at multiple points in a patients body. We propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data. The model makes use of spatial (exponential, spherical, and Matérn) and temporal (compound symmetric, autoregressive-1, Toeplitz, and unstructured) parametric correlation functions. A simulation study, inspired by a longitudinal cardiac imaging study on mitral regurgitation patients, compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on Type I and II error rates for inference on fixed effects when the specified model is incorrect. Information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures. Misspecification of the covariance structure was found to have the ability to inflate the Type I error or have an overly conservative test size, which corresponded to decreased power. An example with clinical data is given illustrating how the covariance structure procedure can be done in practice, as well as how covariance structure choice can change inferences about fixed effects. PMID:25293361

Reprint of "Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency".

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-08-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

An improved error assessment for the GEM-T1 gravitational model

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Marsh, J. G.; Klosko, S. M.; Pavlis, E. C.; Patel, G. B.; Chinn, D. S.; Wagner, C. A.

1988-01-01

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Assessment of meteorological uncertainties as they apply to the ASCENDS mission

NASA Astrophysics Data System (ADS)

Snell, H. E.; Zaccheo, S.; Chase, A.; Eluszkiewicz, J.; Ott, L. E.; Pawson, S.

2011-12-01

Many environment-oriented remote sensing and modeling applications require precise knowledge of the atmospheric state (temperature, pressure, water vapor, surface pressure, etc.) on a fine spatial grid with a comprehensive understanding of the associated errors. Coincident atmospheric state measurements may be obtained via co-located remote sensing instruments or by extracting these data from ancillary models. The appropriate technique for a given application depends upon the required accuracy. State-of-the-art mesoscale/regional numerical weather prediction (NWP) models operate on spatial scales of a few kilometers resolution, and global scale NWP models operate on scales of tens of kilometers. Remote sensing measurements may be made on spatial scale comparable to the measurement of interest. These measurements normally require a separate sensor, which increases the overall size, weight, power and complexity of the satellite payload. Thus, a comprehensive understanding of the errors associated with each of these approaches is a critical part of the design/characterization of a remote-sensing system whose measurement accuracy depends on knowledge of the atmospheric state. One of the requirements as part of the overall ASCENDS (Active Sensing of CO2 Emissions over Nights, Days, and Seasons) mission development is to develop a consistent set of atmospheric state variables (vertical temperature and water vapor profiles, and surface pressure) for use in helping to constrain overall retrieval error budget. If the error budget requires tighter uncertainties on ancillary atmospheric parameters than can be provided by NWP models and analyses, additional sensors may be required to reduce the overall measurement error and meet mission requirements. To this end we have used NWP models and reanalysis information to generate a set of atmospheric profiles which contain reasonable variability. This data consists of a "truth" set and a companion "measured" set of profiles. The truth set contains climatologically-relevant profiles of pressure, temperature and humidity with an accompanying surface pressure. The measured set consists of some number of instances of the truth set which have been perturbed to represent realistic measurement uncertainty for the truth profile using measurement error covariance matrices. The primary focus has been to develop matrices derived using information about the profile retrieval accuracy as documented for on-orbit sensor systems including AIRS, AMSU, ATMS, and CrIS. Surface pressure variability and uncertainty was derived from globally-compiled station pressure information. We generated an additional measurement set of profiles which represent the overall error within NWP models. These profile sets will allow for comprehensive trade studies for sensor system design and provide a basis for setting measurement requirements for co-located temperature, humidity sounders, determine the utility of NWP data to either replace or supplement collocated measurements, and to assess the overall end-to-end system performance of the sensor system. In this presentation we discuss the process by which we created these data sets and show their utility in performing trade studies for sensor system concepts and designs.

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Computing the Deflection of the Vertical for Improving Aerial Surveys: A Comparison between EGM2008 and ITALGEO05 Estimates.

PubMed

Barzaghi, Riccardo; Carrion, Daniela; Pepe, Massimiliano; Prezioso, Giuseppina

2016-07-26

Recent studies on the influence of the anomalous gravity field in GNSS/INS applications have shown that neglecting the impact of the deflection of vertical in aerial surveys induces horizontal and vertical errors in the measurement of an object that is part of the observed scene; these errors can vary from a few tens of centimetres to over one meter. The works reported in the literature refer to vertical deflection values based on global geopotential model estimates. In this paper we compared this approach with the one based on local gravity data and collocation methods. In particular, denoted by ξ and η, the two mutually-perpendicular components of the deflection of the vertical vector (in the north and east directions, respectively), their values were computed by collocation in the framework of the Remove-Compute-Restore technique, applied to the gravity database used for estimating the ITALGEO05 geoid. Following this approach, these values have been computed at different altitudes that are relevant in aerial surveys. The (ξ, η) values were then also estimated using the high degree EGM2008 global geopotential model and compared with those obtained in the previous computation. The analysis of the differences between the two estimates has shown that the (ξ, η) global geopotential model estimate can be reliably used in aerial navigation applications that require the use of sensors connected to a GNSS/INS system only above a given height (e.g., 3000 m in this paper) that must be defined by simulations.

Computing the Deflection of the Vertical for Improving Aerial Surveys: A Comparison between EGM2008 and ITALGEO05 Estimates

PubMed Central

Barzaghi, Riccardo; Carrion, Daniela; Pepe, Massimiliano; Prezioso, Giuseppina

2016-01-01

Recent studies on the influence of the anomalous gravity field in GNSS/INS applications have shown that neglecting the impact of the deflection of vertical in aerial surveys induces horizontal and vertical errors in the measurement of an object that is part of the observed scene; these errors can vary from a few tens of centimetres to over one meter. The works reported in the literature refer to vertical deflection values based on global geopotential model estimates. In this paper we compared this approach with the one based on local gravity data and collocation methods. In particular, denoted by ξ and η, the two mutually-perpendicular components of the deflection of the vertical vector (in the north and east directions, respectively), their values were computed by collocation in the framework of the Remove-Compute-Restore technique, applied to the gravity database used for estimating the ITALGEO05 geoid. Following this approach, these values have been computed at different altitudes that are relevant in aerial surveys. The (ξ, η) values were then also estimated using the high degree EGM2008 global geopotential model and compared with those obtained in the previous computation. The analysis of the differences between the two estimates has shown that the (ξ, η) global geopotential model estimate can be reliably used in aerial navigation applications that require the use of sensors connected to a GNSS/INS system only above a given height (e.g., 3000 m in this paper) that must be defined by simulations. PMID:27472333

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Adaptive Error Estimation in Linearized Ocean General Circulation Models

NASA Technical Reports Server (NTRS)

Chechelnitsky, Michael Y.

1999-01-01

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Use of Two-Part Regression Calibration Model to Correct for Measurement Error in Episodically Consumed Foods in a Single-Replicate Study Design: EPIC Case Study

PubMed Central

Agogo, George O.; van der Voet, Hilko; Veer, Pieter van’t; Ferrari, Pietro; Leenders, Max; Muller, David C.; Sánchez-Cantalejo, Emilio; Bamia, Christina; Braaten, Tonje; Knüppel, Sven; Johansson, Ingegerd; van Eeuwijk, Fred A.; Boshuizen, Hendriek

2014-01-01

In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model. PMID:25402487

Kalman Filter for Spinning Spacecraft Attitude Estimation

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Sedlak, Joseph E.

2008-01-01

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Estimation of geopotential differences over intercontinental locations using satellite and terrestrial measurements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Pavlis, Nikolaos K.

1991-01-01

An error analysis study was conducted in order to assess the current accuracies and the future anticipated improvements in the estimation of geopotential differences over intercontinental locations. An observation/estimation scheme was proposed and studied, whereby gravity disturbance measurements on the Earth's surface, in caps surrounding the estimation points, are combined with corresponding data in caps directly over these points at the altitude of a low orbiting satellite, for the estimation of the geopotential difference between the terrestrial stations. The mathematical modeling required to relate the primary observables to the parameters to be estimated, was studied for the terrestrial data and the data at altitude. Emphasis was placed on the examination of systematic effects and on the corresponding reductions that need to be applied to the measurements to avoid systematic errors. The error estimation for the geopotential differences was performed using both truncation theory and least squares collocation with ring averages, in case observations on the Earth's surface only are used. The error analysis indicated that with the currently available global geopotential model OSU89B and with gravity disturbance data in 2 deg caps surrounding the estimation points, the error of the geopotential difference arising from errors in the reference model and the cap data is about 23 kgal cm, for 30 deg station separation.

A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems

DOE PAGES

Yadav, Vineet; Michalak, Anna M.; Ray, Jaideep; ...

2016-10-27

We study independent verification and quantification of fossil fuel (FF) emissions that constitutes a considerable scientific challenge. By coupling atmospheric observations of CO 2 with models of atmospheric transport, inverse models offer the possibility of overcoming this challenge. However, disaggregating the biospheric and FF flux components of terrestrial fluxes from CO 2 concentration measurements has proven to be difficult, due to observational and modeling limitations. In this study, we propose a statistical inverse modeling scheme for disaggregating winter time fluxes on the basis of their unique error covariances and covariates, where these covariances and covariates are representative of the underlyingmore » processes affecting FF and biospheric fluxes. The application of the method is demonstrated with one synthetic and two real data prototypical inversions by using in situ CO 2 measurements over North America. Also, inversions are performed only for the month of January, as predominance of biospheric CO 2 signal relative to FF CO 2 signal and observational limitations preclude disaggregation of the fluxes in other months. The quality of disaggregation is assessed primarily through examination of a posteriori covariance between disaggregated FF and biospheric fluxes at regional scales. Findings indicate that the proposed method is able to robustly disaggregate fluxes regionally at monthly temporal resolution with a posteriori cross covariance lower than 0.15 µmol m -2 s -1 between FF and biospheric fluxes. Error covariance models and covariates based on temporally varying FF inventory data provide a more robust disaggregation over static proxies (e.g., nightlight intensity and population density). However, the synthetic data case study shows that disaggregation is possible even in absence of detailed temporally varying FF inventory data.« less

Isogeometric Collocation for Elastostatics and Explicit Dynamics

DTIC Science & Technology

2012-01-25

ICES REPORT 12-07 January 2012 Isogeometric collocation for elastostatics and explicit dynamics by F. Auricchio, L. Beirao da Veiga , T.J.R. Hughes, A...Auricchio, L. Beirao da Veiga , T.J.R. Hughes, A. Reali, G. Sangalli, Isogeometric collocation for elastostatics and explicit dynamics, ICES REPORT 12-07...Isogeometric collocation for elastostatics and explicit dynamics F. Auricchio a,c, L. Beirão da Veiga b,c, T.J.R. Hughes d, A. Reali a,c,∗, G

Estimation and filtering techniques for high-accuracy GPS applications

NASA Technical Reports Server (NTRS)

Lichten, S. M.

1989-01-01

Techniques for determination of very precise orbits for satellites of the Global Positioning System (GPS) are currently being studied and demonstrated. These techniques can be used to make cm-accurate measurements of station locations relative to the geocenter, monitor earth orientation over timescales of hours, and provide tropospheric and clock delay calibrations during observations made with deep space radio antennas at sites where the GPS receivers have been collocated. For high-earth orbiters, meter-level knowledge of position will be available from GPS, while at low altitudes, sub-decimeter accuracy will be possible. Estimation of satellite orbits and other parameters such as ground station positions is carried out with a multi-satellite batch sequential pseudo-epoch state process noise filter. Both square-root information filtering (SRIF) and UD-factorized covariance filtering formulations are implemented in the software.

Application of Improved 5th-Cubature Kalman Filter in Initial Strapdown Inertial Navigation System Alignment for Large Misalignment Angles.

PubMed

Wang, Wei; Chen, Xiyuan

2018-02-23

In view of the fact the accuracy of the third-degree Cubature Kalman Filter (CKF) used for initial alignment under large misalignment angle conditions is insufficient, an improved fifth-degree CKF algorithm is proposed in this paper. In order to make full use of the innovation on filtering, the innovation covariance matrix is calculated recursively by an innovative sequence with an exponent fading factor. Then a new adaptive error covariance matrix scaling algorithm is proposed. The Singular Value Decomposition (SVD) method is used for improving the numerical stability of the fifth-degree CKF in this paper. In order to avoid the overshoot caused by excessive scaling of error covariance matrix during the convergence stage, the scaling scheme is terminated when the gradient of azimuth reaches the maximum. The experimental results show that the improved algorithm has better alignment accuracy with large misalignment angles than the traditional algorithm.

Regression dilution in the proportional hazards model.

PubMed

Hughes, M D

1993-12-01

The problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model. The naive approach to parameter estimation is considered whereby observed covariate values are used, inappropriately, in the usual analysis instead of the underlying covariate values. A relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed. With high censorship, adjustment of the naive estimate by the factor 1 + lambda, where lambda is the ratio of within-person variability about an underlying mean level to the variability of these levels in the population sampled, removes the bias. As censorship increases, the adjustment required increases and when there is no censorship is markedly higher than 1 + lambda and depends also on the true risk relationship.

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

Kernel Equating Under the Non-Equivalent Groups With Covariates Design

PubMed Central

Bränberg, Kenny

2015-01-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests. PMID:29881012

Multilevel Models for Intensive Longitudinal Data with Heterogeneous Autoregressive Errors: The Effect of Misspecification and Correction with Cholesky Transformation

PubMed Central

Jahng, Seungmin; Wood, Phillip K.

2017-01-01

Intensive longitudinal studies, such as ecological momentary assessment studies using electronic diaries, are gaining popularity across many areas of psychology. Multilevel models (MLMs) are most widely used analytical tools for intensive longitudinal data (ILD). Although ILD often have individually distinct patterns of serial correlation of measures over time, inferences of the fixed effects, and random components in MLMs are made under the assumption that all variance and autocovariance components are homogenous across individuals. In the present study, we introduced a multilevel model with Cholesky transformation to model ILD with individually heterogeneous covariance structure. In addition, the performance of the transformation method and the effects of misspecification of heterogeneous covariance structure were investigated through a Monte Carlo simulation. We found that, if individually heterogeneous covariances are incorrectly assumed as homogenous independent or homogenous autoregressive, MLMs produce highly biased estimates of the variance of random intercepts and the standard errors of the fixed intercept and the fixed effect of a level 2 covariate when the average autocorrelation is high. For intensive longitudinal data with individual specific residual covariance, the suggested transformation method showed lower bias in those estimates than the misspecified models when the number of repeated observations within individuals is 50 or more. PMID:28286490

Kernel Equating Under the Non-Equivalent Groups With Covariates Design.

PubMed

Wiberg, Marie; Bränberg, Kenny

2015-07-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests.

Mean gravity anomalies and sea surface heights derived from GEOS-3 altimeter data

NASA Technical Reports Server (NTRS)

Rapp, R. H.

1978-01-01

Approximately 2000 GEOS-3 altimeter arcs were analyzed to improve knowledge of the geoid and gravity field. An adjustment procedure was used to fit the sea surface heights (geoid undulations) in an adjustment process that incorporated cross-over constraints. The error model used for the fit was a one or two parameter model which was designed to remove altimeter bias and orbit error. The undulations on the adjusted arcs were used to produce geoid maps in 20 regions. The adjusted data was used to derive 301 5 degree equal area anomalies and 9995 1 x 1 degree anomalies in areas where the altimeter data was most dense, using least squares collocation techniques. Also emphasized was the ability of the altimeter data to imply rapid anomaly changes of up to 240 mgals in adjacent 1 x 1 degree blocks.

Accounting for spatial correlation errors in the assimilation of GRACE into hydrological models through localization

NASA Astrophysics Data System (ADS)

Khaki, M.; Schumacher, M.; Forootan, E.; Kuhn, M.; Awange, J. L.; van Dijk, A. I. J. M.

2017-10-01

Assimilation of terrestrial water storage (TWS) information from the Gravity Recovery And Climate Experiment (GRACE) satellite mission can provide significant improvements in hydrological modelling. However, the rather coarse spatial resolution of GRACE TWS and its spatially correlated errors pose considerable challenges for achieving realistic assimilation results. Consequently, successful data assimilation depends on rigorous modelling of the full error covariance matrix of the GRACE TWS estimates, as well as realistic error behavior for hydrological model simulations. In this study, we assess the application of local analysis (LA) to maximize the contribution of GRACE TWS in hydrological data assimilation. For this, we assimilate GRACE TWS into the World-Wide Water Resources Assessment system (W3RA) over the Australian continent while applying LA and accounting for existing spatial correlations using the full error covariance matrix. GRACE TWS data is applied with different spatial resolutions including 1° to 5° grids, as well as basin averages. The ensemble-based sequential filtering technique of the Square Root Analysis (SQRA) is applied to assimilate TWS data into W3RA. For each spatial scale, the performance of the data assimilation is assessed through comparison with independent in-situ ground water and soil moisture observations. Overall, the results demonstrate that LA is able to stabilize the inversion process (within the implementation of the SQRA filter) leading to less errors for all spatial scales considered with an average RMSE improvement of 54% (e.g., 52.23 mm down to 26.80 mm) for all the cases with respect to groundwater in-situ measurements. Validating the assimilated results with groundwater observations indicates that LA leads to 13% better (in terms of RMSE) assimilation results compared to the cases with Gaussian errors assumptions. This highlights the great potential of LA and the use of the full error covariance matrix of GRACE TWS estimates for improved data assimilation results.

Effects of error covariance structure on estimation of model averaging weights and predictive performance

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Meyer, Philip D.; Curtis, Gary P.; Shi, Xiaoqing; Niu, Xu-Feng; Yabusaki, Steve B.

2013-01-01

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, CE, of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, Cek, of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown Cek from the residuals during model calibration. The inferred Cek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using Cekresolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using Cek obtained from the iterative two-stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies.

Bayesian inversions of a dynamic vegetation model at four European grassland sites

NASA Astrophysics Data System (ADS)

Minet, J.; Laloy, E.; Tychon, B.; Francois, L.

2015-05-01

Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a priori or jointly inferred together with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root mean square errors (RMSEs) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19, 1.04 to 1.56 g C m-2 day-1 and 0.50 to 1.28 mm day-1, respectively. For the calibration period, using a homoscedastic eddy covariance residual error model resulted in a better agreement between measured and modelled data than using a heteroscedastic residual error model. However, a model validation experiment showed that CARAIB models calibrated considering heteroscedastic residual errors perform better. Posterior parameter distributions derived from using a heteroscedastic model of the residuals thus appear to be more robust. This is the case even though the classical linear heteroscedastic error model assumed herein did not fully remove heteroscedasticity of the GPP residuals. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides the residual error treatment, differences between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics.

Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters

NASA Astrophysics Data System (ADS)

Friedrich, Oliver; Eifler, Tim

2018-01-01

Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. Analytically computed covariances are noise-free and hence straightforward to invert; however, the model approximations might be insufficient for the statistical precision of future cosmological data. Estimating covariances from numerical simulations improves on these approximations, but the sample covariance estimator is inherently noisy, which introduces uncertainties in the error bars on cosmological parameters and also additional scatter in their best-fitting values. For future surveys, reducing both effects to an acceptable level requires an unfeasibly large number of simulations. In this paper we describe a way to expand the precision matrix around a covariance model and show how to estimate the leading order terms of this expansion from simulations. This is especially powerful if the covariance matrix is the sum of two contributions, C = A+B, where A is well understood analytically and can be turned off in simulations (e.g. shape noise for cosmic shear) to yield a direct estimate of B. We test our method in mock experiments resembling tomographic weak lensing data vectors from the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST). For DES we find that 400 N-body simulations are sufficient to achieve negligible statistical uncertainties on parameter constraints. For LSST this is achieved with 2400 simulations. The standard covariance estimator would require >105 simulations to reach a similar precision. We extend our analysis to a DES multiprobe case finding a similar performance.

Estimating restricted mean treatment effects with stacked survival models

PubMed Central

Wey, Andrew; Vock, David M.; Connett, John; Rudser, Kyle

2016-01-01

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is estimating a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution, and then marginalizing over the covariate distribution. Since the estimator for the restricted mean difference is defined by the estimator for the covariate-adjusted survival distribution, it is natural to expect that a better estimator of the covariate-adjusted survival distribution is associated with a better estimator of the restricted mean difference. We therefore propose estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric, semi-parametric, and non-parametric models, stacked survival models can robustly estimate a covariate-adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that better performance of the covariate-adjusted survival distribution often leads to better mean-squared error of the restricted mean difference although there are notable exceptions. In addition, we demonstrate that the proposed estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. Finally, the proposed estimator is illustrated with data from the United Network for Organ Sharing to evaluate post-lung transplant survival between large and small-volume centers. PMID:26934835

Filter Tuning Using the Chi-Squared Statistic

NASA Technical Reports Server (NTRS)

Lilly-Salkowski, Tyler

2017-01-01

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

NASA Technical Reports Server (NTRS)

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Collocation and Pattern Recognition Effects on System Failure Remediation

NASA Technical Reports Server (NTRS)

Trujillo, Anna C.; Press, Hayes N.

2007-01-01

Previous research found that operators prefer to have status, alerts, and controls located on the same screen. Unfortunately, that research was done with displays that were not designed specifically for collocation. In this experiment, twelve subjects evaluated two displays specifically designed for collocating system information against a baseline that consisted of dial status displays, a separate alert area, and a controls panel. These displays differed in the amount of collocation, pattern matching, and parameter movement compared to display size. During the data runs, subjects kept a randomly moving target centered on a display using a left-handed joystick and they scanned system displays to find a problem in order to correct it using the provided checklist. Results indicate that large parameter movement aided detection and then pattern recognition is needed for diagnosis but the collocated displays centralized all the information subjects needed, which reduced workload. Therefore, the collocated display with large parameter movement may be an acceptable display after familiarization because of the possible pattern recognition developed with training and its use.

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

NASA Technical Reports Server (NTRS)

Sedlak, Joseph E.; Harman, Richard

2004-01-01

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Spacecraft methods and structures with enhanced attitude control that facilitates gyroscope substitutions

NASA Technical Reports Server (NTRS)

Li, Rongsheng (Inventor); Kurland, Jeffrey A. (Inventor); Dawson, Alec M. (Inventor); Wu, Yeong-Wei A. (Inventor); Uetrecht, David S. (Inventor)

2004-01-01

Methods and structures are provided that enhance attitude control during gyroscope substitutions by insuring that a spacecraft's attitude control system does not drive its absolute-attitude sensors out of their capture ranges. In a method embodiment, an operational process-noise covariance Q of a Kalman filter is temporarily replaced with a substantially greater interim process-noise covariance Q. This replacement increases the weight given to the most recent attitude measurements and hastens the reduction of attitude errors and gyroscope bias errors. The error effect of the substituted gyroscopes is reduced and the absolute-attitude sensors are not driven out of their capture range. In another method embodiment, this replacement is preceded by the temporary replacement of an operational measurement-noise variance R with a substantially larger interim measurement-noise variance R to reduce transients during the gyroscope substitutions.

Orbit/attitude estimation with LANDSAT Landmark data

NASA Technical Reports Server (NTRS)

Hall, D. L.; Waligora, S.

1979-01-01

The use of LANDSAT landmark data for orbit/attitude and camera bias estimation was studied. The preliminary results of these investigations are presented. The Goddard Trajectory Determination System (GTDS) error analysis capability was used to perform error analysis studies. A number of questions were addressed including parameter observability and sensitivity, effects on the solve-for parameter errors of data span, density, and distribution an a priori covariance weighting. The use of the GTDS differential correction capability with acutal landmark data was examined. The rms line and element observation residuals were studied as a function of the solve-for parameter set, a priori covariance weighting, force model, attitude model and data characteristics. Sample results are presented. Finally, verfication and preliminary system evaluation of the LANDSAT NAVPAK system for sequential (extended Kalman Filter) estimation of orbit, and camera bias parameters is given.

[On-orbit radiometric calibration accuracy of FY-3A MERSI thermal infrared channel].

PubMed

Xu, Na; Hu, Xiu-qing; Chen, Lin; Zhang, Yong; Hu, Ju-yang; Sun, Ling

2014-12-01

Accurate satellite radiance measurements are significant for data assimilations and quantitative retrieval applications. In the present paper, radiometric calibration accuracy of FungYun-3A (FY-3A) Medium Resolution Spectral Imager (MERSI) thermal infrared (TIR) channel was evaluated based on simultaneous nadir observation (SNO) intercalibration method. Hyperspectral and high-quality measurements of METOP-A/IASI were used as reference. Assessment uncertainty from intercalibration method was also investigated by examining the relation between BT bias against four main collocation factors, i. e. observation time difference, view geometric difference related to zenith angles and azimuth angles, and scene spatial homogeneity. It was indicated that the BT bias is evenly distributed across the collocation variables with no significant linear relationship in MERSI IR channel. Among the four collocation factors, the scene spatial homogeneity may be the most important factor with the uncertainty less than 2% of BT bias. Statistical analysis of monitoring biases during one and a half years indicates that the brightness temperature measured by MERSI is much warmer than that of IASI. The annual mean bias (MERSI-IASI) in 2012 is (3.18±0.34) K. Monthly averaged BT biases show a little seasonal variation character, and fluctuation range is less than 0.8 K. To further verify the reliability, our evaluation result was also compared with the synchronous experiment results at Dunhuang and Qinghai Lake sites, which showed excellent agreement. Preliminary analysis indicates that there are two reasons leading to the warm bias. One is the overestimation of blackbody emissivity, and the other is probably the incorrect spectral respond function which has shifted to window spectral. Considering the variation character of BT biases, SRF error seems to be the dominant factor.

Multilevel Multidimensional Item Response Model with a Multilevel Latent Covariate

ERIC Educational Resources Information Center

Cho, Sun-Joo; Bottge, Brian A.

2015-01-01

In a pretest-posttest cluster-randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores that ignores measurement error in the…

Performance of Modified Test Statistics in Covariance and Correlation Structure Analysis under Conditions of Multivariate Nonnormality.

ERIC Educational Resources Information Center

Fouladi, Rachel T.

2000-01-01

Provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and details Monte Carlo simulation results on Type I and Type II error control. Demonstrates through the simulation that robustness and nonrobustness of structure analysis techniques vary as a…

Space shuttle navigation analysis. Volume 2: Baseline system navigation

NASA Technical Reports Server (NTRS)

Jones, H. L.; Luders, G.; Matchett, G. A.; Rains, R. G.

1980-01-01

Studies related to the baseline navigation system for the orbiter are presented. The baseline navigation system studies include a covariance analysis of the Inertial Measurement Unit calibration and alignment procedures, postflight IMU error recovery for the approach and landing phases, on-orbit calibration of IMU instrument biases, and a covariance analysis of entry and prelaunch navigation system performance.

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

NASA Technical Reports Server (NTRS)

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

[Spatio-Temporal Bioelectrical Brain Activity Organization during Reading Syntagmatic and Paradigmatic Collocations by Students with Different Foreign Language Proficiency].

PubMed

Sokolova, L V; Cherkasova, A S

2015-01-01

Texts or words/pseudowords are often used as stimuli for human verbal activity research. Our study pays attention to decoding processes of grammatical constructions consisted of two-three words--collocations. Russian and English collocation sets without any narrative were presented to Russian-speaking students with different English language skill. Stimulus material had two types of collocations: paradigmatic and syntagmatic. 30 students (average age--20.4 ± 0.22) took part in the study, they were divided into two equal groups depending on their English language skill (linguists/nonlinguists). During reading brain bioelectrical activity of cortex has been registered from 12 electrodes in alfa-, beta-, theta-bands. Coherent function reflecting cooperation of different cortical areas during reading collocations has been analyzed. Increase of interhemispheric and diagonal connections while reading collocations in different languages in the group of students with low knowledge of foreign language testifies of importance of functional cooperation between the hemispheres. It has been found out that brain bioelectrical activity of students with good foreign language knowledge during reading of all collocation types in Russian and English is characterized by economization of nervous substrate resources compared to nonlinguists. Selective activation of certain cortical areas has also been observed (depending on the grammatical construction type) in nonlinguists group that is probably related to special decoding system which processes presented stimuli. Reading Russian paradigmatic constructions by nonlinguists entailed increase between left cortical areas, reading of English syntagmatic collocations--between right ones.

Selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data.

PubMed

George, Brandon; Aban, Inmaculada

2015-01-15

Longitudinal imaging studies allow great insight into how the structure and function of a subject's internal anatomy changes over time. Unfortunately, the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation: the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patient's body. We propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data. The model makes use of spatial (exponential, spherical, and Matérn) and temporal (compound symmetric, autoregressive-1, Toeplitz, and unstructured) parametric correlation functions. A simulation study, inspired by a longitudinal cardiac imaging study on mitral regurgitation patients, compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on types I and II error rates for inference on fixed effects when the specified model is incorrect. Information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures. Misspecification of the covariance structure was found to have the ability to inflate the type I error or have an overly conservative test size, which corresponded to decreased power. An example with clinical data is given illustrating how the covariance structure procedure can be performed in practice, as well as how covariance structure choice can change inferences about fixed effects. Copyright © 2014 John Wiley & Sons, Ltd.

Are your covariates under control? How normalization can re-introduce covariate effects.

PubMed

Pain, Oliver; Dudbridge, Frank; Ronald, Angelica

2018-04-30

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. When covariates are included in the analysis, a common approach is to first adjust for the covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested in which rank-based INT was applied to the dependent variable before regressing covariates. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates, increasing type-I errors and reducing power. On the other hand, when rank-based INT was applied prior to controlling for covariate effects, residuals were normally distributed and linearly uncorrelated with covariates. This latter approach is therefore recommended in situations were normality of the dependent variable is required.

Learning L2 Collocations Incidentally from Reading

ERIC Educational Resources Information Center

Pellicer-Sánchez, Ana

2017-01-01

Previous studies have shown that intentional learning through explicit instruction is effective for the acquisition of collocations in a second language (L2) (e.g. Peters, 2014, 2015), but relatively little is known about the effectiveness of incidental approaches for the acquisition of L2 collocations. The present study examined the incidental…

Incidental Learning of Collocation

ERIC Educational Resources Information Center

Webb, Stuart; Newton, Jonathan; Chang, Anna

2013-01-01

This study investigated the effects of repetition on the learning of collocation. Taiwanese university students learning English as a foreign language simultaneously read and listened to one of four versions of a modified graded reader that included different numbers of encounters (1, 5, 10, and 15 encounters) with a set of 18 target collocations.…

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Code of Federal Regulations, 2011 CFR

2011-10-01

... accessible by both the incumbent LEC and the collocating telecommunications carrier, at which the fiber optic... technically feasible, the incumbent LEC shall provide the connection using copper, dark fiber, lit fiber, or... that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems...

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Code of Federal Regulations, 2010 CFR

2010-10-01

... accessible by both the incumbent LEC and the collocating telecommunications carrier, at which the fiber optic... technically feasible, the incumbent LEC shall provide the connection using copper, dark fiber, lit fiber, or... that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems...

Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

NASA Astrophysics Data System (ADS)

Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo

2014-04-01

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

Usability Study of Two Collocated Prototype System Displays

NASA Technical Reports Server (NTRS)

Trujillo, Anna C.

2007-01-01

Currently, most of the displays in control rooms can be categorized as status screens, alerts/procedures screens (or paper), or control screens (where the state of a component is changed by the operator). The primary focus of this line of research is to determine which pieces of information (status, alerts/procedures, and control) should be collocated. Two collocated displays were tested for ease of understanding in an automated desktop survey. This usability study was conducted as a prelude to a larger human-in-the-loop experiment in order to verify that the 2 new collocated displays were easy to learn and usable. The results indicate that while the DC display was preferred and yielded better performance than the MDO display, both collocated displays can be easily learned and used.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances.

PubMed

Gil, Manuel

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

PubMed Central

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error. PMID:25279263

Bayesian inversions of a dynamic vegetation model in four European grassland sites

NASA Astrophysics Data System (ADS)

Minet, J.; Laloy, E.; Tychon, B.; François, L.

2015-01-01

Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB dynamic vegetation model (DVM) with ten unknown parameters, using the DREAM(ZS) Markov chain Monte Carlo (MCMC) sampler. We compare model inversions considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a~priori or jointly inferred with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root-mean-square error (RMSE) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19 g C m-2 day-1, 1.04 to 1.56 g C m-2 day-1, and 0.50 to 1.28 mm day-1, respectively. In validation, mismatches between measured and simulated data are larger, but still with Nash-Sutcliffe efficiency scores above 0.5 for three out of the four sites. Although measurement errors associated with eddy covariance data are known to be heteroscedastic, we showed that assuming a classical linear heteroscedastic model of the residual errors in the inversion do not fully remove heteroscedasticity. Since the employed heteroscedastic error model allows for larger deviations between simulated and measured data as the magnitude of the measured data increases, this error model expectedly lead to poorer data fitting compared to inversions considering a constant variance of the residual errors. Furthermore, sampling the residual error variances along with model parameters results in overall similar model parameter posterior distributions as those obtained by fixing these variances beforehand, while slightly improving model performance. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides model behaviour, difference between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics. Lastly, the possibility of finding a common set of parameters among the four experimental sites is discussed.

New method for propagating the square root covariance matrix in triangular form. [using Kalman-Bucy filter

NASA Technical Reports Server (NTRS)

Choe, C. Y.; Tapley, B. D.

1975-01-01

A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Application of a single-objective, hybrid genetic algorithm approach to pharmacokinetic model building.

PubMed

Sherer, Eric A; Sale, Mark E; Pollock, Bruce G; Belani, Chandra P; Egorin, Merrill J; Ivy, Percy S; Lieberman, Jeffrey A; Manuck, Stephen B; Marder, Stephen R; Muldoon, Matthew F; Scher, Howard I; Solit, David B; Bies, Robert R

2012-08-01

A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q₁ = 4.9 % and q₃ = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data.

An algorithm for propagating the square-root covariance matrix in triangular form

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1976-01-01

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Design and Implementation of a Parallel Multivariate Ensemble Kalman Filter for the Poseidon Ocean General Circulation Model

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Koblinsky, Chester (Technical Monitor)

2001-01-01

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been implemented for the Poseidon ocean circulation model and tested with a Pacific Basin model configuration. There are about two million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are calculated from the phase-space distribution of the ensemble. Each processing element (PE) collects elements of a matrix measurement functional from nearby PEs. To avoid the introduction of spurious long-range covariances associated with finite ensemble sizes, the background-error covariances are given compact support by means of a Hadamard (element by element) product with a three-dimensional canonical correlation function. The methodology and the MvEnKF configuration are discussed. It is shown that the regionalization of the background covariances; has a negligible impact on the quality of the analyses. The parallel algorithm is very efficient for large numbers of observations but does not scale well beyond 100 PEs at the current model resolution. On a platform with distributed memory, memory rather than speed is the limiting factor.

Adaptive feedforward control of non-minimum phase structural systems

NASA Astrophysics Data System (ADS)

Vipperman, J. S.; Burdisso, R. A.

1995-06-01

Adaptive feedforward control algorithms have been effectively applied to stationary disturbance rejection. For structural systems, the ideal feedforward compensator is a recursive filter which is a function of the transfer functions between the disturbance and control inputs and the error sensor output. Unfortunately, most control configurations result in a non-minimum phase control path; even a collocated control actuator and error sensor will not necessarily produce a minimum phase control path in the discrete domain. Therefore, the common practice is to choose a suitable approximation of the ideal compensator. In particular, all-zero finite impulse response (FIR) filters are desirable because of their inherent stability for adaptive control approaches. However, for highly resonant systems, large order filters are required for broadband applications. In this work, a control configuration is investigated for controlling non-minimum phase lightly damped structural systems. The control approach uses low order FIR filters as feedforward compensators in a configuration that has one more control actuator than error sensors. The performance of the controller was experimentally evaluated on a simply supported plate under white noise excitation for a two-input, one-output (2I1O) system. The results show excellent error signal reduction, attesting to the effectiveness of the method.

Not Just "Small Potatoes": Knowledge of the Idiomatic Meanings of Collocations

ERIC Educational Resources Information Center

Macis, Marijana; Schmitt, Norbert

2017-01-01

This study investigated learner knowledge of the figurative meanings of 30 collocations that can be both literal and figurative. One hundred and seven Chilean Spanish-speaking university students of English were asked to complete a meaning-recall collocation test in which the target items were embedded in non-defining sentences. Results showed…

Teaching and Learning Collocation in Adult Second and Foreign Language Learning

ERIC Educational Resources Information Center

Boers, Frank; Webb, Stuart

2018-01-01

Perhaps the greatest challenge to creating a research timeline on teaching and learning collocation is deciding how wide to cast the net in the search for relevant publications. For one thing, the term "collocation" does not have the same meaning for all (applied) linguists and practitioners (Barfield & Gyllstad 2009) (see timeline).…

Supporting Collocation Learning with a Digital Library

ERIC Educational Resources Information Center

Wu, Shaoqun; Franken, Margaret; Witten, Ian H.

2010-01-01

Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on…

Cross-Linguistic Influence: Its Impact on L2 English Collocation Production

ERIC Educational Resources Information Center

Phoocharoensil, Supakorn

2013-01-01

This research study investigated the influence of learners' mother tongue on their acquisition of English collocations. Having drawn the linguistic data from two groups of Thai EFL learners differing in English proficiency level, the researcher found that the native language (L1) plays a significant role in the participants' collocation learning…

Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations

ERIC Educational Resources Information Center

Liu, Dilin

2010-01-01

Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,…

English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information

ERIC Educational Resources Information Center

Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji

2012-01-01

We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…

Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks

ERIC Educational Resources Information Center

Menon, Sujatha; Mukundan, Jayakaran

2012-01-01

This paper analyses the discourse of science through the study of collocational patterns of high frequency noun keywords in science textbooks used by upper secondary students in Malaysia. Research has shown that one of the areas of difficulty in science discourse concerns lexis, especially that of collocations. This paper describes a corpus-based…

The Effect of Grouping and Presenting Collocations on Retention

ERIC Educational Resources Information Center

Akpinar, Kadriye Dilek; Bardakçi, Mehmet

2015-01-01

The aim of this study is two-fold. Firstly, it attempts to determine the role of presenting collocations by organizing them based on (i) the keyword, (ii) topic related and (iii) grammatical aspect on retention of collocations. Secondly, it investigates the relationship between participants' general English proficiency and the presentation types…

Temi firthiani di linguistica applicata: "Restricted Languages" e "Collocation" (Firthian Themes in Applied Linguistics: "Restricted Languages" and "Collocation")

ERIC Educational Resources Information Center

Leonardi, Magda

1977-01-01

Discusses the importance of two Firthian themes for language teaching. The first theme, "Restricted Languages," concerns the "microlanguages" of every language (e.g., literary language, scientific, etc.). The second theme, "Collocation," shows that equivalent words in two languages rarely have the same position in…

Corpora and Collocations in Chinese-English Dictionaries for Chinese Users

ERIC Educational Resources Information Center

Xia, Lixin

2015-01-01

The paper identifies the major problems of the Chinese-English dictionary in representing collocational information after an extensive survey of nine dictionaries popular among Chinese users. It is found that the Chinese-English dictionary only provides the collocation types of "v+n" and "v+n," but completely ignores those of…

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

Hubness of strategic planning and sociality influences depressive mood and anxiety in College Population.

PubMed

Yun, Je-Yeon; Choi, Yoobin; Kwon, Yoonhee; Lee, Hwa Young; Choi, Soo-Hee; Jang, Joon Hwan

2017-12-19

Depressive mood and anxiety can reduce cognitive performance. Conversely, the presence of a biased cognitive tendency may serve as a trigger for depressive mood-anxiety. Previous studies have largely focused on group-wise correlations between clinical-neurocognitive variables. Using network analyses for intra-individual covariance, we sought to decipher the most influential clinical-neurocognitive hub in the differential severity of depressive-anxiety symptoms in a college population. Ninety college students were evaluated for depressive-anxiety symptoms, Minnesota multiphasic personality inventory-2(MMPI-2), and neuro-cognition. Weighted and undirected version of the intra-individual covariance networks, comprised of 18 clinical-neurocognitive variables satisfied small-worldness and modular organization in the sparsity range of K = 0.20-0.21. Furthermore, betweenness centrality of perseverative error for the Wisconsin card sorting test was reduced in more depressive individuals; higher anxiety was related to the increased betweenness centrality of MMPI-2 clinical scale 0(Si). Elevated edge-betweenness centrality of covariance between the MMPI-2 clinical scale 7(Pt) versus commission error of the continuous performance test predicted more anxiety higher than depressive mood. With intra-individual covariance network of clinical-neurocognitive variables, this study demonstrated critical drivers of depressive mood[attenuated influence of strategic planning] or anxiety[domination of social introversion/extroversion, in addition to the influence of compulsivity-impulsivity covariance as a shortcut component among various clinical-neurocognitive features].

Covariance Matrix Estimation for Massive MIMO

NASA Astrophysics Data System (ADS)

Upadhya, Karthik; Vorobyov, Sergiy A.

2018-04-01

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

The Vertical Error Characteristics of GOES-derived Winds: Description and Impact on Numerical Weather Prediction

NASA Technical Reports Server (NTRS)

Rao, P. Anil; Velden, Christopher S.; Braun, Scott A.; Einaudi, Franco (Technical Monitor)

2001-01-01

Errors in the height assignment of some satellite-derived winds exist because the satellites sense radiation emitted from a finite layer of the atmosphere rather than a specific level. Potential problems in data assimilation may arise because the motion of a measured layer is often represented by a single-level value. In this research, cloud and water vapor motion winds that are derived from the Geostationary Operational Environmental Satellites (GOES winds) are compared to collocated rawinsonde observations (RAOBs). An important aspect of this work is that in addition to comparisons at each assigned height, the GOES winds are compared to the entire profile of the collocated RAOB data to determine the vertical error characteristics of the GOES winds. The impact of these results on numerical weather prediction is then investigated. The comparisons at individual vector height assignments indicate that the error of the GOES winds range from approx. 3 to 10 m/s and generally increase with height. However, if taken as a percentage of the total wind speed, accuracy is better at upper levels. As expected, comparisons with the entire profile of the collocated RAOBs indicate that clear-air water vapor winds represent deeper layers than do either infrared or water vapor cloud-tracked winds. This is because in cloud-free regions the signal from water vapor features may result from emittance over a thicker layer. To further investigate characteristics of the clear-air water vapor winds, they are stratified into two categories that are dependent on the depth of the layer represented by the vector. It is found that if the vertical gradient of moisture is smooth and uniform from near the height assignment upwards, the clear-air water vapor wind tends to represent a relatively deep layer. The information from the comparisons is then used in numerical model simulations of two separate events to determine the forecast impacts. Four simulations are performed for each case: 1) A control simulation that assimilates no satellite wind data, 2) assimilation of all GOES winds according to their assigned single level height, 3) assimilation of all GOES winds spread over multiple levels, and 4) assimilation of all GOES winds spread over multiple levels, but with variations in the vertical influence of clear-air water vapor winds based on the moisture profile in the model. In the first case, a strong mid-latitude cyclone is present and the use of the satellite data results in improved storm tracks during the initial approx. 36 h forecast period. This is because the satellite data improves the analysis of the environment into which the storm progresses. Statistics for mean wind vector and height differences show that, with the exception of the height field at later times in the first case, the use of GOES winds improves the simulation with time. The simulation results suggest that it is beneficial to spread the GOES wind information over multiple levels, particularly when the moisture profile is used to define the vertical influence.

Validation of MODIS aerosol optical depth product over China using CARSNET measurements

NASA Astrophysics Data System (ADS)

Xie, Yong; Zhang, Yan; Xiong, Xiaoxiong; Qu, John J.; Che, Huizheng

2011-10-01

This study evaluates Moderate Resolution Imaging Spectroradiometer (MODIS) Aerosol Optical Depth (AOD) retrievals with ground measurements collected by the China Aerosol Remote Sensing NETwork (CARSNET). In current stage, the MODIS Collection 5 (C5) AODs are retrieved by two distinct algorithms: the Dark Target (DT) and the Deep Blue (DB). The CARSNET AODs are derived with measurements of Cimel Electronique CE-318, the same instrument deployed by the AEROsol Robotic Network (AEROENT). The collocation is performed by matching each MODIS AOD pixel (10 × 10 km 2) to CARSNET AOD mean within 7.5 min of satellite overpass. Four-year comparisons (2005-2008) of MODIS/CARSNET at ten sites show the performance of MODIS AOD retrieval is highly dependent on the underlying land surface. The MODIS DT AODs are on average lower than the CARSNET AODs by 6-30% over forest and grassland areas, but can be higher by up to 54% over urban area and 95% over desert-like area. More than 50% of the MODIS DT AODs fall within the expected error envelope over forest and grassland areas. The MODIS DT tends to overestimate for small AOD at urban area. At high vegetated area it underestimates for small AOD and overestimates for large AOD. Generally, its quality reduces with the decreasing AOD value. The MODIS DB is capable of retrieving AOD over desert but with a significant underestimation at CARSNET sites. The best retrieval of the MODIS DB is over grassland area with about 70% retrievals within the expected error. The uncertainties of MODIS AOD retrieval from spatial-temporal collocation and instrument calibration are discussed briefly.

The search for causal inferences: using propensity scores post hoc to reduce estimation error with nonexperimental research.

PubMed

Tumlinson, Samuel E; Sass, Daniel A; Cano, Stephanie M

2014-03-01

While experimental designs are regarded as the gold standard for establishing causal relationships, such designs are usually impractical owing to common methodological limitations. The objective of this article is to illustrate how propensity score matching (PSM) and using propensity scores (PS) as a covariate are viable alternatives to reduce estimation error when experimental designs cannot be implemented. To mimic common pediatric research practices, data from 140 simulated participants were used to resemble an experimental and nonexperimental design that assessed the effect of treatment status on participant weight loss for diabetes. Pretreatment participant characteristics (age, gender, physical activity, etc.) were then used to generate PS for use in the various statistical approaches. Results demonstrate how PSM and using the PS as a covariate can be used to reduce estimation error and improve statistical inferences. References for issues related to the implementation of these procedures are provided to assist researchers.

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

NASA Technical Reports Server (NTRS)

Melbourne, William G.

1986-01-01

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

NASA Astrophysics Data System (ADS)

Shirasaki, Masato; Takada, Masahiro; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma

2017-09-01

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogues. Using the mock catalogue to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the 'jackknife' (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be ∼10 per cent after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogues nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.

Quantifying Carbon Flux Estimation Errors

NASA Astrophysics Data System (ADS)

Wesloh, D.

2017-12-01

Atmospheric Bayesian inversions have been used to estimate surface carbon dioxide (CO2) fluxes from global to sub-continental scales using atmospheric mixing ratio measurements. These inversions use an atmospheric transport model, coupled to a set of fluxes, in order to simulate mixing ratios that can then be compared to the observations. The comparison is then used to update the fluxes to better match the observations in a manner consistent with the uncertainties prescribed for each. However, inversion studies disagree with each other at continental scales, prompting further investigations to examine the causes of these differences. Inter-comparison studies have shown that the errors resulting from atmospheric transport inaccuracies are comparable to those from the errors in the prior fluxes. However, not as much effort has gone into studying the origins of the errors induced by errors in the transport as by errors in the prior distribution. This study uses a mesoscale transport model to evaluate the effects of representation errors in the observations and of incorrect descriptions of the transport. To obtain realizations of these errors, we performed an Observing System Simulation Experiments (OSSEs), with the transport model used for the inversion operating at two resolutions, one typical of a global inversion and the other of a mesoscale, and with various prior flux distributions to. Transport error covariances are inferred from an ensemble of perturbed mesoscale simulations while flux error covariances are computed using prescribed distributions and magnitudes. We examine how these errors can be diagnosed in the inversion process using aircraft, ground-based, and satellite observations of meteorological variables and CO2.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Conflict Probability Estimation for Free Flight

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Erzberger, Heinz

1996-01-01

The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.

Using aggregate data to estimate the standard error of a treatment-covariate interaction in an individual patient data meta-analysis.

PubMed

Kovalchik, Stephanie A; Cumberland, William G

2012-05-01

Subgroup analyses are important to medical research because they shed light on the heterogeneity of treatment effectts. A treatment-covariate interaction in an individual patient data (IPD) meta-analysis is the most reliable means to estimate how a subgroup factor modifies a treatment's effectiveness. However, owing to the challenges in collecting participant data, an approach based on aggregate data might be the only option. In these circumstances, it would be useful to assess the relative efficiency and power loss of a subgroup analysis without patient-level data. We present methods that use aggregate data to estimate the standard error of an IPD meta-analysis' treatment-covariate interaction for regression models of a continuous or dichotomous patient outcome. Numerical studies indicate that the estimators have good accuracy. An application to a previously published meta-regression illustrates the practical utility of the methodology. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Application of Improved 5th-Cubature Kalman Filter in Initial Strapdown Inertial Navigation System Alignment for Large Misalignment Angles

PubMed Central

Wang, Wei; Chen, Xiyuan

2018-01-01

In view of the fact the accuracy of the third-degree Cubature Kalman Filter (CKF) used for initial alignment under large misalignment angle conditions is insufficient, an improved fifth-degree CKF algorithm is proposed in this paper. In order to make full use of the innovation on filtering, the innovation covariance matrix is calculated recursively by an innovative sequence with an exponent fading factor. Then a new adaptive error covariance matrix scaling algorithm is proposed. The Singular Value Decomposition (SVD) method is used for improving the numerical stability of the fifth-degree CKF in this paper. In order to avoid the overshoot caused by excessive scaling of error covariance matrix during the convergence stage, the scaling scheme is terminated when the gradient of azimuth reaches the maximum. The experimental results show that the improved algorithm has better alignment accuracy with large misalignment angles than the traditional algorithm. PMID:29473912

On the Effect of Gender and Years of Instruction on Iranian EFL Learners' Collocational Competence

ERIC Educational Resources Information Center

Ganji, Mansoor

2012-01-01

This study investigates the Iranian EFL learners' Knowledge of Lexical Collocation at three academic levels: freshmen, sophomores, and juniors. The participants were forty three English majors doing their B.A. in English Translation studies in Chabahar Maritime University. They took a 50-item fill-in-the-blank test of lexical collocations. The…

Iranian Pre-University Student's Retention of Collocations: Implicit Exposure or Explicit Instruction

ERIC Educational Resources Information Center

Gheisari, Nouzar; Yousofi, Nouroldin

2016-01-01

The effectiveness of different teaching methods of collocational expressions in ESL/EFL contexts of education has been a point of debate for more than two decades, with some believing in explicit and the others in implicit instruction of collocations. In this regard, the present study aimed at finding about which kind of instruction is more…

Formulaic Language and Collocations in German Essays: From Corpus-Driven Data to Corpus-Based Materials

ERIC Educational Resources Information Center

Krummes, Cedric; Ensslin, Astrid

2015-01-01

Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…

Symmetrical and Asymmetrical Scaffolding of L2 Collocations in the Context of Concordancing

ERIC Educational Resources Information Center

Rezaee, Abbas Ali; Marefat, Hamideh; Saeedakhtar, Afsaneh

2015-01-01

Collocational competence is recognized to be integral to native-like L2 performance, and concordancing can be of assistance in gaining this competence. This study reports on an investigation into the effect of symmetrical and asymmetrical scaffolding on the collocational competence of Iranian intermediate learners of English in the context of…

Profiling the Collocation Use in ELT Textbooks and Learner Writing

ERIC Educational Resources Information Center

Tsai, Kuei-Ju

2015-01-01

The present study investigates the collocational profiles of (1) three series of graded textbooks for English as a foreign language (EFL) commonly used in Taiwan, (2) the written productions of EFL learners, and (3) the written productions of native speakers (NS) of English. These texts were examined against a purpose-built collocation list. Based…

Learning and Teaching L2 Collocations: Insights from Research

ERIC Educational Resources Information Center

Szudarski, Pawel

2017-01-01

The aim of this article is to present and summarize the main research findings in the area of learning and teaching second language (L2) collocations. Being a large part of naturally occurring language, collocations and other types of multiword units (e.g., idioms, phrasal verbs, lexical bundles) have been identified as important aspects of L2…

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

NASA Technical Reports Server (NTRS)

Fukumori, I.

1995-01-01

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study.

PubMed

Chou, C P; Bentler, P M; Satorra, A

1991-11-01

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele; Borovikov, Anna Y.; Suarez, Max

1999-01-01

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Mesh refinement strategy for optimal control problems

NASA Astrophysics Data System (ADS)

Paiva, L. T.; Fontes, F. A. C. C.

2013-10-01

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

OD Covariance in Conjunction Assessment: Introduction and Issues

NASA Technical Reports Server (NTRS)

Hejduk, M. D.; Duncan, M.

2015-01-01

Primary and secondary covariances combined and projected into conjunction plane (plane perpendicular to relative velocity vector at TCA) Primary placed on x-axis at (miss distance, 0) and represented by circle of radius equal to sum of both spacecraft circumscribing radiiZ-axis perpendicular to x-axis in conjunction plane Pc is portion of combined error ellipsoid that falls within the hard-body radius circle

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

Bootstrap-based methods for estimating standard errors in Cox's regression analyses of clustered event times.

PubMed

Xiao, Yongling; Abrahamowicz, Michal

2010-03-30

We propose two bootstrap-based methods to correct the standard errors (SEs) from Cox's model for within-cluster correlation of right-censored event times. The cluster-bootstrap method resamples, with replacement, only the clusters, whereas the two-step bootstrap method resamples (i) the clusters, and (ii) individuals within each selected cluster, with replacement. In simulations, we evaluate both methods and compare them with the existing robust variance estimator and the shared gamma frailty model, which are available in statistical software packages. We simulate clustered event time data, with latent cluster-level random effects, which are ignored in the conventional Cox's model. For cluster-level covariates, both proposed bootstrap methods yield accurate SEs, and type I error rates, and acceptable coverage rates, regardless of the true random effects distribution, and avoid serious variance under-estimation by conventional Cox-based standard errors. However, the two-step bootstrap method over-estimates the variance for individual-level covariates. We also apply the proposed bootstrap methods to obtain confidence bands around flexible estimates of time-dependent effects in a real-life analysis of cluster event times.

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

NASA Astrophysics Data System (ADS)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

NASA Technical Reports Server (NTRS)

Koch, D. W.

1975-01-01

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

The Challenge of English Language Collocation Learning in an ES/FL Environment: PRC Students in Singapore

ERIC Educational Resources Information Center

Ying, Yang

2015-01-01

This study aimed to seek an in-depth understanding about English collocation learning and the development of learner autonomy through investigating a group of English as a Second Language (ESL) learners' perspectives and practices in their learning of English collocations using an AWARE approach. A group of 20 PRC students learning English in…

An Automatic Collocation Writing Assistant for Taiwanese EFL Learners: A Case of Corpus-Based NLP Technology

ERIC Educational Resources Information Center

Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin

2008-01-01

Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation…

First and Second Generation New York City Bilinguals: What Is the Role of Input in Their Collocational Knowledge of English and Spanish?

ERIC Educational Resources Information Center

Heidrick, Ingrid T.

2017-01-01

This study compares monolinguals and different kinds of bilinguals with respect to their knowledge of the type of lexical phenomenon known as collocation. Collocations are word combinations that speakers use recurrently, forming the basis of conventionalized lexical patterns that are shared by a linguistic community. Examples of collocations…

A wavelet approach to binary blackholes with asynchronous multitasking

NASA Astrophysics Data System (ADS)

Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo

2016-03-01

Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kristiansen, J.I.; Balliny, N.; Saxov, S.

Some available information on thermal conductivity of earth materials from the Scandinavian area is collected. The mean conductivities as reported from individual localities are grouped in crystalline and sedimentary rocks. Mean results are displayed in histograms and localities are mapped. The collocation of conductivity information contains new results of granites and sedimentary rocks from Sweden and of limestones and clays from Danish borings. The new values are presented as histograms of individual measurements and given as mean values with standard errors of mean. The crystalline rocks range from about 2 to about 4 W/ (m K), and the sedimentary rocksmore » range from about 0.8 to about 6 W/ (m K).« less

Improved characterisation of measurement errors in electrical resistivity tomography (ERT) surveys

NASA Astrophysics Data System (ADS)

Tso, C. H. M.; Binley, A. M.; Kuras, O.; Graham, J.

2016-12-01

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe a statistical model of data errors before inversion. Wrongly prescribed error levels can lead to over- or under-fitting of data, yet commonly used models of measurement error are relatively simplistic. With the heightening interests in uncertainty estimation across hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide more reliable estimates of uncertainty. We have analysed two time-lapse electrical resistivity tomography (ERT) datasets; one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24h timeframe, while the other is a year-long cross-borehole survey at a UK nuclear site with over 50,000 daily measurements. Our study included the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and covariance analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used. This agrees with reported speculation in previous literature that ERT errors could be somewhat correlated. Based on these findings, we develop a new error model that allows grouping based on electrode number in additional to fitting a linear model to transfer resistance. The new model fits the observed measurement errors better and shows superior inversion and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the number of the four electrodes used to make each measurement. The new model can be readily applied to the diagonal data weighting matrix commonly used in classical inversion methods, as well as to the data covariance matrix in the Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites.

Performance of FFT methods in local gravity field modelling

NASA Technical Reports Server (NTRS)

Forsberg, Rene; Solheim, Dag

1989-01-01

Fast Fourier transform (FFT) methods provide a fast and efficient means of processing large amounts of gravity or geoid data in local gravity field modelling. The FFT methods, however, has a number of theoretical and practical limitations, especially the use of flat-earth approximation, and the requirements for gridded data. In spite of this the method often yields excellent results in practice when compared to other more rigorous (and computationally expensive) methods, such as least-squares collocation. The good performance of the FFT methods illustrate that the theoretical approximations are offset by the capability of taking into account more data in larger areas, especially important for geoid predictions. For best results good data gridding algorithms are essential. In practice truncated collocation approaches may be used. For large areas at high latitudes the gridding must be done using suitable map projections such as UTM, to avoid trivial errors caused by the meridian convergence. The FFT methods are compared to ground truth data in New Mexico (xi, eta from delta g), Scandinavia (N from delta g, the geoid fits to 15 cm over 2000 km), and areas of the Atlantic (delta g from satellite altimetry using Wiener filtering). In all cases the FFT methods yields results comparable or superior to other methods.

Collocational Links in the L2 Mental Lexicon and the Influence of L1 Intralexical Knowledge

ERIC Educational Resources Information Center

Wolter, Brent; Gyllstad, Henrik

2011-01-01

This article assesses the influence of L1 intralexical knowledge on the formation of L2 intralexical collocations. Two tests, a primed lexical decision task (LDT) and a test of receptive collocational knowledge, were administered to a group of non-native speakers (NNSs) (L1 Swedish), with native speakers (NSs) of English serving as controls on the…

A Corpus-Driven Design of a Test for Assessing the ESL Collocational Competence of University Students

ERIC Educational Resources Information Center

Jaen, Maria Moreno

2007-01-01

This paper reports an assessment of the collocational competence of students of English Linguistics at the University of Granada. This was carried out to meet a two-fold purpose. On the one hand, we aimed to establish a solid corpus-driven approach based upon a systematic and reliable framework for the evaluation of collocational competence in…

Coincidence and covariance data acquisition in photoelectron and -ion spectroscopy. II. Analysis and applications

NASA Astrophysics Data System (ADS)

Mikosch, Jochen; Patchkovskii, Serguei

2013-10-01

We use an analytical theory of noisy Poisson processes, developed in the preceding companion publication, to compare coincidence and covariance measurement approaches in photoelectron and -ion spectroscopy. For non-unit detection efficiencies, coincidence data acquisition (DAQ) suffers from false coincidences. The rate of false coincidences grows quadratically with the rate of elementary ionization events. To minimize false coincidences for rare event outcomes, very low event rates may hence be required. Coincidence measurements exhibit high tolerance to noise introduced by unstable experimental conditions. Covariance DAQ on the other hand is free of systematic errors as long as stable experimental conditions are maintained. In the presence of noise, all channels in a covariance measurement become correlated. Under favourable conditions, covariance DAQ may allow orders of magnitude reduction in measurement times. Finally, we use experimental data for strong-field ionization of 1,3-butadiene to illustrate how fluctuations in experimental conditions can contaminate a covariance measurement, and how such contamination can be detected.

A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series.

ERIC Educational Resources Information Center

Molenaar, Peter C. M.; Nesselroade, John R.

1998-01-01

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

Association between split selection instability and predictive error in survival trees.

PubMed

Radespiel-Tröger, M; Gefeller, O; Rabenstein, T; Hothorn, T

2006-01-01

To evaluate split selection instability in six survival tree algorithms and its relationship with predictive error by means of a bootstrap study. We study the following algorithms: logrank statistic with multivariate p-value adjustment without pruning (LR), Kaplan-Meier distance of survival curves (KM), martingale residuals (MR), Poisson regression for censored data (PR), within-node impurity (WI), and exponential log-likelihood loss (XL). With the exception of LR, initial trees are pruned by using split-complexity, and final trees are selected by means of cross-validation. We employ a real dataset from a clinical study of patients with gallbladder stones. The predictive error is evaluated using the integrated Brier score for censored data. The relationship between split selection instability and predictive error is evaluated by means of box-percentile plots, covariate and cutpoint selection entropy, and cutpoint selection coefficients of variation, respectively, in the root node. We found a positive association between covariate selection instability and predictive error in the root node. LR yields the lowest predictive error, while KM and MR yield the highest predictive error. The predictive error of survival trees is related to split selection instability. Based on the low predictive error of LR, we recommend the use of this algorithm for the construction of survival trees. Unpruned survival trees with multivariate p-value adjustment can perform equally well compared to pruned trees. The analysis of split selection instability can be used to communicate the results of tree-based analyses to clinicians and to support the application of survival trees.

Information matrix estimation procedures for cognitive diagnostic models.

PubMed

Liu, Yanlou; Xin, Tao; Andersson, Björn; Tian, Wei

2018-03-06

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance. © 2018 The British Psychological Society.

Estimating the Uncertainty In Diameter Growth Model Predictions and Its Effects On The Uncertainty of Annual Inventory Estimates

Treesearch

Ronald E. McRoberts; Veronica C. Lessard

2001-01-01

Uncertainty in diameter growth predictions is attributed to three general sources: measurement error or sampling variability in predictor variables, parameter covariances, and residual or unexplained variation around model expectations. Using measurement error and sampling variability distributions obtained from the literature and Monte Carlo simulation methods, the...

Weighted linear regression using D2H and D2 as the independent variables

Treesearch

Hans T. Schreuder; Michael S. Williams

1998-01-01

Several error structures for weighted regression equations used for predicting volume were examined for 2 large data sets of felled and standing loblolly pine trees (Pinus taeda L.). The generally accepted model with variance of error proportional to the value of the covariate squared ( D2H = diameter squared times height or D...

A New Test of Linear Hypotheses in OLS Regression under Heteroscedasticity of Unknown Form

ERIC Educational Resources Information Center

Cai, Li; Hayes, Andrew F.

2008-01-01

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

Spectral analysis of GEOS-3 altimeter data and frequency domain collocation. [to estimate gravity anomalies

NASA Technical Reports Server (NTRS)

Eren, K.

1980-01-01

The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.

Spatio-Temporal EEG Models for Brain Interfaces

PubMed Central

Gonzalez-Navarro, P.; Moghadamfalahi, M.; Akcakaya, M.; Erdogmus, D.

2016-01-01

Multichannel electroencephalography (EEG) is widely used in non-invasive brain computer interfaces (BCIs) for user intent inference. EEG can be assumed to be a Gaussian process with unknown mean and autocovariance, and the estimation of parameters is required for BCI inference. However, the relatively high dimensionality of the EEG feature vectors with respect to the number of labeled observations lead to rank deficient covariance matrix estimates. In this manuscript, to overcome ill-conditioned covariance estimation, we propose a structure for the covariance matrices of the multichannel EEG signals. Specifically, we assume that these covariances can be modeled as a Kronecker product of temporal and spatial covariances. Our results over the experimental data collected from the users of a letter-by-letter typing BCI show that with less number of parameter estimations, the system can achieve higher classification accuracies compared to a method that uses full unstructured covariance estimation. Moreover, in order to illustrate that the proposed Kronecker product structure could enable shortening the BCI calibration data collection sessions, using Cramer-Rao bound analysis on simulated data, we demonstrate that a model with structured covariance matrices will achieve the same estimation error as a model with no covariance structure using fewer labeled EEG observations. PMID:27713590

Extraction of wind and temperature information from hybrid 4D-Var assimilation of stratospheric ozone using NAVGEM

NASA Astrophysics Data System (ADS)

Allen, Douglas R.; Hoppel, Karl W.; Kuhl, David D.

2018-03-01

Extraction of wind and temperature information from stratospheric ozone assimilation is examined within the context of the Navy Global Environmental Model (NAVGEM) hybrid 4-D variational assimilation (4D-Var) data assimilation (DA) system. Ozone can improve the wind and temperature through two different DA mechanisms: (1) through the flow-of-the-day ensemble background error covariance that is blended together with the static background error covariance and (2) via the ozone continuity equation in the tangent linear model and adjoint used for minimizing the cost function. All experiments assimilate actual conventional data in order to maintain a similar realistic troposphere. In the stratosphere, the experiments assimilate simulated ozone and/or radiance observations in various combinations. The simulated observations are constructed for a case study based on a 16-day cycling truth experiment (TE), which is an analysis with no stratospheric observations. The impact of ozone on the analysis is evaluated by comparing the experiments to the TE for the last 6 days, allowing for a 10-day spin-up. Ozone assimilation benefits the wind and temperature when data are of sufficient quality and frequency. For example, assimilation of perfect (no applied error) global hourly ozone data constrains the stratospheric wind and temperature to within ˜ 2 m s-1 and ˜ 1 K. This demonstrates that there is dynamical information in the ozone distribution that can potentially be used to improve the stratosphere. This is particularly important for the tropics, where radiance observations have difficulty constraining wind due to breakdown of geostrophic balance. Global ozone assimilation provides the largest benefit when the hybrid blending coefficient is an intermediate value (0.5 was used in this study), rather than 0.0 (no ensemble background error covariance) or 1.0 (no static background error covariance), which is consistent with other hybrid DA studies. When perfect global ozone is assimilated in addition to radiance observations, wind and temperature error decreases of up to ˜ 3 m s-1 and ˜ 1 K occur in the tropical upper stratosphere. Assimilation of noisy global ozone (2 % errors applied) results in error reductions of ˜ 1 m s-1 and ˜ 0.5 K in the tropics and slightly increased temperature errors in the Northern Hemisphere polar region. Reduction of the ozone sampling frequency also reduces the benefit of ozone throughout the stratosphere, with noisy polar-orbiting data having only minor impacts on wind and temperature when assimilated with radiances. An examination of ensemble cross-correlations between ozone and other variables shows that a single ozone observation behaves like a potential vorticity (PV) charge, or a monopole of PV, with rotation about a vertical axis and vertically oriented temperature dipole. Further understanding of this relationship may help in designing observation systems that would optimize the impact of ozone on the dynamics.

Accounting for the measurement error of spectroscopically inferred soil carbon data for improved precision of spatial predictions.

PubMed

Somarathna, P D S N; Minasny, Budiman; Malone, Brendan P; Stockmann, Uta; McBratney, Alex B

2018-08-01

Spatial modelling of environmental data commonly only considers spatial variability as the single source of uncertainty. In reality however, the measurement errors should also be accounted for. In recent years, infrared spectroscopy has been shown to offer low cost, yet invaluable information needed for digital soil mapping at meaningful spatial scales for land management. However, spectrally inferred soil carbon data are known to be less accurate compared to laboratory analysed measurements. This study establishes a methodology to filter out the measurement error variability by incorporating the measurement error variance in the spatial covariance structure of the model. The study was carried out in the Lower Hunter Valley, New South Wales, Australia where a combination of laboratory measured, and vis-NIR and MIR inferred topsoil and subsoil soil carbon data are available. We investigated the applicability of residual maximum likelihood (REML) and Markov Chain Monte Carlo (MCMC) simulation methods to generate parameters of the Matérn covariance function directly from the data in the presence of measurement error. The results revealed that the measurement error can be effectively filtered-out through the proposed technique. When the measurement error was filtered from the data, the prediction variance almost halved, which ultimately yielded a greater certainty in spatial predictions of soil carbon. Further, the MCMC technique was successfully used to define the posterior distribution of measurement error. This is an important outcome, as the MCMC technique can be used to estimate the measurement error if it is not explicitly quantified. Although this study dealt with soil carbon data, this method is amenable for filtering the measurement error of any kind of continuous spatial environmental data. Copyright © 2018 Elsevier B.V. All rights reserved.

Spatial-temporal-covariance-based modeling, analysis, and simulation of aero-optics wavefront aberrations.

PubMed

Vogel, Curtis R; Tyler, Glenn A; Wittich, Donald J

2014-07-01

We introduce a framework for modeling, analysis, and simulation of aero-optics wavefront aberrations that is based on spatial-temporal covariance matrices extracted from wavefront sensor measurements. Within this framework, we present a quasi-homogeneous structure function to analyze nonhomogeneous, mildly anisotropic spatial random processes, and we use this structure function to show that phase aberrations arising in aero-optics are, for an important range of operating parameters, locally Kolmogorov. This strongly suggests that the d5/3 power law for adaptive optics (AO) deformable mirror fitting error, where d denotes actuator separation, holds for certain important aero-optics scenarios. This framework also allows us to compute bounds on AO servo lag error and predictive control error. In addition, it provides us with the means to accurately simulate AO systems for the mitigation of aero-effects, and it may provide insight into underlying physical processes associated with turbulent flow. The techniques introduced here are demonstrated using data obtained from the Airborne Aero-Optics Laboratory.

Bias and heteroscedastic memory error in self-reported health behavior: an investigation using covariance structure analysis

PubMed Central

Kupek, Emil

2002-01-01

Background Frequent use of self-reports for investigating recent and past behavior in medical research requires statistical techniques capable of analyzing complex sources of bias associated with this methodology. In particular, although decreasing accuracy of recalling more distant past events is commonplace, the bias due to differential in memory errors resulting from it has rarely been modeled statistically. Methods Covariance structure analysis was used to estimate the recall error of self-reported number of sexual partners for past periods of varying duration and its implication for the bias. Results Results indicated increasing levels of inaccuracy for reports about more distant past. Considerable positive bias was found for a small fraction of respondents who reported ten or more partners in the last year, last two years and last five years. This is consistent with the effect of heteroscedastic random error where the majority of partners had been acquired in the more distant past and therefore were recalled less accurately than the partners acquired more recently to the time of interviewing. Conclusions Memory errors of this type depend on the salience of the events recalled and are likely to be present in many areas of health research based on self-reported behavior. PMID:12435276

Filter Tuning Using the Chi-Squared Statistic

NASA Technical Reports Server (NTRS)

Lilly-Salkowski, Tyler B.

2017-01-01

This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The goal of the process is to characterize the filter performance in the metric of covariance realism. The Chi-squared statistic is the value calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance. The process of tuning an Extended Kalman Filter (EKF) for Aqua and Aura support is described, including examination of the measurement errors of available observation types, and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-squared statistic, calculated from EKF solutions, are assessed.

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1994-01-01

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

On-Line Identification of Simulation Examples for Forgetting Methods to Track Time Varying Parameters Using the Alternative Covariance Matrix in Matlab

NASA Astrophysics Data System (ADS)

Vachálek, Ján

2011-12-01

The paper compares the abilities of forgetting methods to track time varying parameters of two different simulated models with different types of excitation. The observed parameters in the simulations are the integral sum of the Euclidean norm, deviation of the parameter estimates from their true values and a selected band prediction error count. As supplementary information, we observe the eigenvalues of the covariance matrix. In the paper we used a modified method of Regularized Exponential Forgetting with Alternative Covariance Matrix (REFACM) along with Directional Forgetting (DF) and three standard regularized methods.

A note on variance estimation in random effects meta-regression.

PubMed

Sidik, Kurex; Jonkman, Jeffrey N

2005-01-01

For random effects meta-regression inference, variance estimation for the parameter estimates is discussed. Because estimated weights are used for meta-regression analysis in practice, the assumed or estimated covariance matrix used in meta-regression is not strictly correct, due to possible errors in estimating the weights. Therefore, this note investigates the use of a robust variance estimation approach for obtaining variances of the parameter estimates in random effects meta-regression inference. This method treats the assumed covariance matrix of the effect measure variables as a working covariance matrix. Using an example of meta-analysis data from clinical trials of a vaccine, the robust variance estimation approach is illustrated in comparison with two other methods of variance estimation. A simulation study is presented, comparing the three methods of variance estimation in terms of bias and coverage probability. We find that, despite the seeming suitability of the robust estimator for random effects meta-regression, the improved variance estimator of Knapp and Hartung (2003) yields the best performance among the three estimators, and thus may provide the best protection against errors in the estimated weights.

Assimilation of surface NO2 and O3 observations into the SILAM chemistry transport model

NASA Astrophysics Data System (ADS)

Vira, J.; Sofiev, M.

2014-08-01

This paper describes assimilation of trace gas observations into the chemistry transport model SILAM using the 3D-Var method. Assimilation results for year 2012 are presented for the prominent photochemical pollutants ozone (O3) and nitrogen dioxide (NO2). Both species are covered by the Airbase observation database, which provides the observational dataset used in this study. Attention is paid to the background and observation error covariance matrices, which are obtained primarily by iterative application of a posteriori diagnostics. The diagnostics are computed separately for two months representing summer and winter conditions, and further disaggregated by time of day. This allows deriving background and observation error covariance definitions which include both seasonal and diurnal variation. The consistency of the obtained covariance matrices is verified using χ2 diagnostics. The analysis scores are computed for a control set of observation stations withheld from assimilation. Compared to a free-running model simulation, the correlation coefficient for daily maximum values is improved from 0.8 to 0.9 for O3 and from 0.53 to 0.63 for NO2.

A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing

PubMed Central

2018-01-01

Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in the case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, in particular, the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating quickly and reliably the covariance matrix dependent on just a few comprehensible and easily-obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a priori knowledge of the specific measurement noise. By means of extensive simulations, the performance and robustness of the new model in comparison to existing approaches is shown. PMID:29673205

A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix.

PubMed

Westgate, Philip M

2013-07-20

Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference. Copyright © 2012 John Wiley & Sons, Ltd.

ILIAD Testing; and a Kalman Filter for 3-D Pose Estimation

NASA Technical Reports Server (NTRS)

Richardson, A. O.

1996-01-01

This report presents the results of a two-part project. The first part presents results of performance assessment tests on an Internet Library Information Assembly Data Base (ILIAD). It was found that ILLAD performed best when queries were short (one-to-three keywords), and were made up of rare, unambiguous words. In such cases as many as 64% of the typically 25 returned documents were found to be relevant. It was also found that a query format that was not so rigid with respect to spelling errors and punctuation marks would be more user-friendly. The second part of the report shows the design of a Kalman Filter for estimating motion parameters of a three dimensional object from sequences of noisy data derived from two-dimensional pictures. Given six measured deviation values represendng X, Y, Z, pitch, yaw, and roll, twelve parameters were estimated comprising the six deviations and their time rate of change. Values for the state transiton matrix, the observation matrix, the system noise covariance matrix, and the observation noise covariance matrix were determined. A simple way of initilizing the error covariance matrix was pointed out.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Coherent Uncertainty Analysis of Aerosol Measurements from Multiple Satellite Sensors

NASA Technical Reports Server (NTRS)

Petrenko, M.; Ichoku, C.

2013-01-01

Aerosol retrievals from multiple spaceborne sensors, including MODIS (on Terra and Aqua), MISR, OMI, POLDER, CALIOP, and SeaWiFS altogether, a total of 11 different aerosol products were comparatively analyzed using data collocated with ground-based aerosol observations from the Aerosol Robotic Network (AERONET) stations within the Multi-sensor Aerosol Products Sampling System (MAPSS, http://giovanni.gsfc.nasa.gov/mapss/ and http://giovanni.gsfc.nasa.gov/aerostat/). The analysis was performed by comparing quality-screened satellite aerosol optical depth or thickness (AOD or AOT) retrievals during 2006-2010 to available collocated AERONET measurements globally, regionally, and seasonally, and deriving a number of statistical measures of accuracy. We used a robust statistical approach to detect and remove possible outliers in the collocated data that can bias the results of the analysis. Overall, the proportion of outliers in each of the quality-screened AOD products was within 12%. Squared correlation coefficient (R2) values of the satellite AOD retrievals relative to AERONET exceeded 0.6, with R2 for most of the products exceeding 0.7 over land and 0.8 over ocean. Root mean square error (RMSE) values for most of the AOD products were within 0.15 over land and 0.09 over ocean. We have been able to generate global maps showing regions where the different products present advantages over the others, as well as the relative performance of each product over different landcover types. It was observed that while MODIS, MISR, and SeaWiFS provide accurate retrievals over most of the landcover types, multi-angle capabilities make MISR the only sensor to retrieve reliable AOD over barren and snow / ice surfaces. Likewise, active sensing enables CALIOP to retrieve aerosol properties over bright-surface shrublands more accurately than the other sensors, while POLDER, which is the only one of the sensors capable of measuring polarized aerosols, outperforms other sensors in certain smoke-dominated regions, including broadleaf evergreens in Brazil and South-East Asia.

EvolQG - An R package for evolutionary quantitative genetics

PubMed Central

Melo, Diogo; Garcia, Guilherme; Hubbe, Alex; Assis, Ana Paula; Marroig, Gabriel

2016-01-01

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \\textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification. PMID:27785352

A model-data comparison of gross primary productivity: Results from the North American Carbon Program site synthesis

Treesearch

Kevin Schaefer; Christopher R. Schwalm; Chris Williams; M. Altaf Arain; Alan Barr; Jing M. Chen; Kenneth J. Davis; Dimitre Dimitrov; Timothy W. Hilton; David Y. Hollinger; Elyn Humphreys; Benjamin Poulter; Brett M. Raczka; Andrew D. Richardson; Alok Sahoo; Peter Thornton; Rodrigo Vargas; Hans Verbeeck; Ryan Anderson; Ian Baker; T. Andrew Black; Paul Bolstad; Jiquan Chen; Peter S. Curtis; Ankur R. Desai; Michael Dietze; Danilo Dragoni; Christopher Gough; Robert F. Grant; Lianhong Gu; Atul Jain; Chris Kucharik; Beverly Law; Shuguang Liu; Erandathie Lokipitiya; Hank A. Margolis; Roser Matamala; J. Harry McCaughey; Russ Monson; J. William Munger; Walter Oechel; Changhui Peng; David T. Price; Dan Ricciuto; William J. Riley; Nigel Roulet; Hanqin Tian; Christina Tonitto; Margaret Torn; Ensheng Weng; Xiaolu Zhou

2012-01-01

Accurately simulating gross primary productivity (GPP) in terrestrial ecosystem models is critical because errors in simulated GPP propagate through the model to introduce additional errors in simulated biomass and other fluxes. We evaluated simulated, daily average GPP from 26 models against estimated GPP at 39 eddy covariance flux tower sites across the United States...

Merging Multi-model CMIP5/PMIP3 Past-1000 Ensemble Simulations with Tree Ring Proxy Data by Optimal Interpolation Approach

NASA Astrophysics Data System (ADS)

Chen, Xin; Luo, Yong; Xing, Pei; Nie, Suping; Tian, Qinhua

2015-04-01

Two sets of gridded annual mean surface air temperature in past millennia over the Northern Hemisphere was constructed employing optimal interpolation (OI) method so as to merge the tree ring proxy records with the simulations from CMIP5 (the fifth phase of the Climate Model Intercomparison Project). Both the uncertainties in proxy reconstruction and model simulations can be taken into account applying OI algorithm. For better preservation of physical coordinated features and spatial-temporal completeness of climate variability in 7 copies of model results, we perform the Empirical Orthogonal Functions (EOF) analysis to truncate the ensemble mean field as the first guess (background field) for OI. 681 temperature sensitive tree-ring chronologies are collected and screened from International Tree Ring Data Bank (ITRDB) and Past Global Changes (PAGES-2k) project. Firstly, two methods (variance matching and linear regression) are employed to calibrate the tree ring chronologies with instrumental data (CRUTEM4v) individually. In addition, we also remove the bias of both the background field and proxy records relative to instrumental dataset. Secondly, time-varying background error covariance matrix (B) and static "observation" error covariance matrix (R) are calculated for OI frame. In our scheme, matrix B was calculated locally, and "observation" error covariance are partially considered in R matrix (the covariance value between the pairs of tree ring sites that are very close to each other would be counted), which is different from the traditional assumption that R matrix should be diagonal. Comparing our results, it turns out that regional averaged series are not sensitive to the selection for calibration methods. The Quantile-Quantile plots indicate regional climatologies based on both methods are tend to be more agreeable with regional reconstruction of PAGES-2k in 20th century warming period than in little ice age (LIA). Lager volcanic cooling response over Asia and Europe in context of recent millennium are detected in our datasets than that revealed in regional reconstruction from PAGES-2k network. Verification experiments have showed that the merging approach really reconcile the proxy data and model ensemble simulations in an optimal way (with smaller errors than both of them). Further research is needed to improve the error estimation on them.

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

An Application of Linear Covariance Analysis to the Design of Responsive Near-Rendezvous Missions

DTIC Science & Technology

2007-06-01

accurately before making large ma- neuvers. A fifth type of error is maneuver knowledge error (MKER). This error accounts for how well a spacecraft is able...utilized due in a large part to the cost of designing and launching spacecraft , in a market where currently there are not many options for launching...is then ordered to fire its thrusters to increase its orbital altitude to 800 km. Before the maneuver the spacecraft is moving with some velocity, V

Error Characterisation and Merging of Active and Passive Microwave Soil Moisture Data Sets

NASA Astrophysics Data System (ADS)

Wagner, Wolfgang; Gruber, Alexander; de Jeu, Richard; Parinussa, Robert; Chung, Daniel; Dorigo, Wouter; Reimer, Christoph; Kidd, Richard

2015-04-01

As part of the Climate Change Initiative (CCI) programme of the European Space Agency (ESA) a data fusion system has been developed which is capable of ingesting surface soil moisture data derived from active and passive microwave sensors (ASCAT, AMSR-E, etc.) flown on different satellite platforms and merging them to create long and consistent time series of soil moisture suitable for use in climate change studies. The so-created soil moisture data records (latest version: ESA CCI SM v02.1 released on 5/12/2014) are freely available and can be obtained from http://www.esa-soilmoisture-cci.org/. As described by Wagner et al. (2012) the principle steps of the data fusion process are: 1) error characterisation, 2) matching to account for data set specific biases, and 3) merging. In this presentation we present the current data fusion process and discuss how new error characterisation methods, such as the increasingly popular triple collocation method as discussed for example by Zwieback et al. (2012) may be used to improve it. The main benefit of an improved error characterisation would be a more reliable identification of the best performing microwave soil moisture retrieval(s) for each grid point and each point in time. In case that two or more satellite data sets provides useful information, the estimated errors can be used to define the weights with which each satellite data set are merged, i.e. the lower its error the higher its weight. This is expected to bring a significant improvement over the current data fusion scheme which is not yet based on quantitative estimates of the retrieval errors but on a proxy measure, namely the vegetation optical depth (Dorigo et al., 2015): over areas with low vegetation passive soil moisture retrievals are used, while over areas with moderate vegetation density active retrievals are used. In transition areas, where both products correlate well, both products are being used in a synergistic way: on time steps where only one of the products is available, the estimate of the respective product is used, while on days where both active and passive sensors provide an estimate, their observations are averaged. REFERENCES Dorigo, W.A., A. Gruber, R. de Jeu, W. Wagner, T. Stacke, A. Löw, C. Albergel, L. Brocca, D. Chung, R. Parinussa, R. Kidd (2015) Evaluation of the ESA CCI soil moisture product using ground-based observations, Remote Sensing of Environment, in press. Wagner, W., W. Dorigo, R. de Jeu, D. Fernandez, J. Benveniste, E. Haas, M. Ertl (2012) Fusion of active and passive microwave observations to create an Essential Climate Variable data record on soil moisture, ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS Annals), Volume I-7, XXII ISPRS Congress, Melbourne, Australia, 25 August-1 September 2012, 315-321. Zwieback, S., K. Scipal, W. Dorigo, W. Wagner (2012) Structural and statistical properties of the collocation technique for error characterization, Nonlinear Processes in Geophysics, 19, 69-80.

Cervicocephalic kinesthetic sensibility in young and middle-aged adults with or without a history of mild neck pain.

PubMed

Teng, C-C; Chai, H; Lai, D-M; Wang, S-F

2007-02-01

Previous research has shown that there is no significant relationship between the degree of structural degeneration of the cervical spine and neck pain. We therefore sought to investigate the potential role of sensory dysfunction in chronic neck pain. Cervicocephalic kinesthetic sensibility, expressed by how accurately an individual can reposition the head, was studied in three groups of individuals, a control group of 20 asymptomatic young adults and two groups of middle-aged adults (20 subjects in each group) with or without a history of mild neck pain. An ultrasound-based three-dimensional coordinate measuring system was used to measure the position of the head and to test the accuracy of repositioning. Constant error (indicating that the subject overshot or undershot the intended position) and root mean square errors (representing total errors of accuracy and variability) were measured during repositioning of the head to the neutral head position (Head-to-NHP) and repositioning of the head to the target (Head-to-Target) in three cardinal planes (sagittal, transverse, and frontal). Analysis of covariance (ANCOVA) was used to test the group effect, with age used as a covariate. The constant errors during repositioning from a flexed position and from an extended position to the NHP were significantly greater in the middle-aged subjects than in the control group (beta=0.30 and beta=0.60, respectively; P<0.05 for both). In addition, the root mean square errors during repositioning from a flexed or extended position to the NHP were greater in the middle-aged subjects than in the control group (beta=0.27 and beta=0.49, respectively; P<0.05 for both). The root mean square errors also increased during Head-to-Target in left rotation (beta=0.24;P<0.05), but there was no difference in the constant errors or root mean square errors during Head-to-NHP repositioning from other target positions (P>0.05). The results indicate that, after controlling for age as a covariate, there was no group effect. Thus, age appears to have a profound effect on an individual's ability to accurately reposition the head toward the neutral position in the sagittal plane and repositioning the head toward left rotation. A history of mild chronic neck pain alone had no significant effect on cervicocephalic kinesthetic sensibility.

Real-time prediction and gating of respiratory motion in 3D space using extended Kalman filters and Gaussian process regression network

NASA Astrophysics Data System (ADS)

Bukhari, W.; Hong, S.-M.

2016-03-01

The prediction as well as the gating of respiratory motion have received much attention over the last two decades for reducing the targeting error of the radiation treatment beam due to respiratory motion. In this article, we present a real-time algorithm for predicting respiratory motion in 3D space and realizing a gating function without pre-specifying a particular phase of the patient’s breathing cycle. The algorithm, named EKF-GPRN+ , first employs an extended Kalman filter (EKF) independently along each coordinate to predict the respiratory motion and then uses a Gaussian process regression network (GPRN) to correct the prediction error of the EKF in 3D space. The GPRN is a nonparametric Bayesian algorithm for modeling input-dependent correlations between the output variables in multi-output regression. Inference in GPRN is intractable and we employ variational inference with mean field approximation to compute an approximate predictive mean and predictive covariance matrix. The approximate predictive mean is used to correct the prediction error of the EKF. The trace of the approximate predictive covariance matrix is utilized to capture the uncertainty in EKF-GPRN+ prediction error and systematically identify breathing points with a higher probability of large prediction error in advance. This identification enables us to pause the treatment beam over such instances. EKF-GPRN+ implements a gating function by using simple calculations based on the trace of the predictive covariance matrix. Extensive numerical experiments are performed based on a large database of 304 respiratory motion traces to evaluate EKF-GPRN+ . The experimental results show that the EKF-GPRN+ algorithm reduces the patient-wise prediction error to 38%, 40% and 40% in root-mean-square, compared to no prediction, at lookahead lengths of 192 ms, 384 ms and 576 ms, respectively. The EKF-GPRN+ algorithm can further reduce the prediction error by employing the gating function, albeit at the cost of reduced duty cycle. The error reduction allows the clinical target volume to planning target volume (CTV-PTV) margin to be reduced, leading to decreased normal-tissue toxicity and possible dose escalation. The CTV-PTV margin is also evaluated to quantify clinical benefits of EKF-GPRN+ prediction.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Note: Rotaphone, a new self-calibrated six-degree-of-freedom seismic sensor

USGS Publications Warehouse

Brokešová, Johana; Málek, Jiří; Evans, John R.

2012-01-01

We have developed and tested (calibration, linearity, and cross-axis errors) a new six-degree-of-freedom mechanical seismic sensor for collocated measurements of three translational and three rotational ground motion velocity components. The device consists of standard geophones arranged in parallel pairs to detect spatial gradients. The instrument operates in a high-frequency range (above the natural frequency of the geophones, 4.5 Hz). Its theoretical sensitivity limit in this range is 10(-9) m/s in ground velocity and 10(-9) rad/s in rotation rate. Small size and weight, and easy installation and maintenance make the instrument useful for local-earthquake recording and seismic prospecting.

Orbit error characteristic and distribution of TLE using CHAMP orbit data

NASA Astrophysics Data System (ADS)

Xu, Xiao-li; Xiong, Yong-qing

2018-02-01

Space object orbital covariance data is required for collision risk assessments, but publicly accessible two line element (TLE) data does not provide orbital error information. This paper compared historical TLE data and GPS precision ephemerides of CHAMP to assess TLE orbit accuracy from 2002 to 2008, inclusive. TLE error spatial variations with longitude and latitude were calculated to analyze error characteristics and distribution. The results indicate that TLE orbit data are systematically biased from the limited SGP4 model. The biases can reach the level of kilometers, and the sign and magnitude are correlate significantly with longitude.

Spectral Approaches to Learning Predictive Representations

DTIC Science & Technology

2012-09-01

conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed...to the mean to form an initial prediction of x̂(ht). Similarly, Equation 2.3b can be interpreted as using the dynamics matrix A and error covarianceQ...in the sense of Lyapunov if its dynamics matrix A is. Thus, the Lyapunov criterion can be interpreted as holding for an LDS if, for a given covariance

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter. Pt. 2; Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics

NASA Technical Reports Server (NTRS)

Menard, Richard; Chang, Lang-Ping

1998-01-01

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Resampling-based Methods in Single and Multiple Testing for Equality of Covariance/Correlation Matrices

PubMed Central

Yang, Yang; DeGruttola, Victor

2016-01-01

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients. PMID:22740584

Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices.

PubMed

Yang, Yang; DeGruttola, Victor

2012-06-22

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Complementary nonparametric analysis of covariance for logistic regression in a randomized clinical trial setting.

PubMed

Tangen, C M; Koch, G G

1999-03-01

In the randomized clinical trial setting, controlling for covariates is expected to produce variance reduction for the treatment parameter estimate and to adjust for random imbalances of covariates between the treatment groups. However, for the logistic regression model, variance reduction is not obviously obtained. This can lead to concerns about the assumptions of the logistic model. We introduce a complementary nonparametric method for covariate adjustment. It provides results that are usually compatible with expectations for analysis of covariance. The only assumptions required are based on randomization and sampling arguments. The resulting treatment parameter is a (unconditional) population average log-odds ratio that has been adjusted for random imbalance of covariates. Data from a randomized clinical trial are used to compare results from the traditional maximum likelihood logistic method with those from the nonparametric logistic method. We examine treatment parameter estimates, corresponding standard errors, and significance levels in models with and without covariate adjustment. In addition, we discuss differences between unconditional population average treatment parameters and conditional subpopulation average treatment parameters. Additional features of the nonparametric method, including stratified (multicenter) and multivariate (multivisit) analyses, are illustrated. Extensions of this methodology to the proportional odds model are also made.

A stochastic multiple imputation algorithm for missing covariate data in tree-structured survival analysis.

PubMed

Wallace, Meredith L; Anderson, Stewart J; Mazumdar, Sati

2010-12-20

Missing covariate data present a challenge to tree-structured methodology due to the fact that a single tree model, as opposed to an estimated parameter value, may be desired for use in a clinical setting. To address this problem, we suggest a multiple imputation algorithm that adds draws of stochastic error to a tree-based single imputation method presented by Conversano and Siciliano (Technical Report, University of Naples, 2003). Unlike previously proposed techniques for accommodating missing covariate data in tree-structured analyses, our methodology allows the modeling of complex and nonlinear covariate structures while still resulting in a single tree model. We perform a simulation study to evaluate our stochastic multiple imputation algorithm when covariate data are missing at random and compare it to other currently used methods. Our algorithm is advantageous for identifying the true underlying covariate structure when complex data and larger percentages of missing covariate observations are present. It is competitive with other current methods with respect to prediction accuracy. To illustrate our algorithm, we create a tree-structured survival model for predicting time to treatment response in older, depressed adults. Copyright © 2010 John Wiley & Sons, Ltd.

The Impact of Ocean Data Assimilation on Seasonal-to-Interannual Forecasts: A Case Study of the 2006 El Nino Event

NASA Technical Reports Server (NTRS)

Yang, Shu-Chih; Rienecker, Michele; Keppenne, Christian

2010-01-01

This study investigates the impact of four different ocean analyses on coupled forecasts of the 2006 El Nino event. Forecasts initialized in June 2006 using ocean analyses from an assimilation that uses flow-dependent background error covariances are compared with those using static error covariances that are not flow dependent. The flow-dependent error covariances reflect the error structures related to the background ENSO instability and are generated by the coupled breeding method. The ocean analyses used in this study result from the assimilation of temperature and salinity, with the salinity data available from Argo floats. Of the analyses, the one using information from the coupled bred vectors (BV) replicates the observed equatorial long wave propagation best and exhibits more warming features leading to the 2006 El Nino event. The forecasts initialized from the BV-based analysis agree best with the observations in terms of the growth of the warm anomaly through two warming phases. This better performance is related to the impact of the salinity analysis on the state evolution in the equatorial thermocline. The early warming is traced back to salinity differences in the upper ocean of the equatorial central Pacific, while the second warming, corresponding to the mature phase, is associated with the effect of the salinity assimilation on the depth of the thermocline in the western equatorial Pacific. The series of forecast experiments conducted here show that the structure of the salinity in the initial conditions is important to the forecasts of the extension of the warm pool and the evolution of the 2006 El Ni o event.

Impact of variational assimilation using multivariate background error covariances on the simulation of monsoon depressions over India

NASA Astrophysics Data System (ADS)

Dhanya, M.; Chandrasekar, A.

2016-02-01

The background error covariance structure influences a variational data assimilation system immensely. The simulation of a weather phenomenon like monsoon depression can hence be influenced by the background correlation information used in the analysis formulation. The Weather Research and Forecasting Model Data assimilation (WRFDA) system includes an option for formulating multivariate background correlations for its three-dimensional variational (3DVar) system (cv6 option). The impact of using such a formulation in the simulation of three monsoon depressions over India is investigated in this study. Analysis and forecast fields generated using this option are compared with those obtained using the default formulation for regional background error correlations (cv5) in WRFDA and with a base run without any assimilation. The model rainfall forecasts are compared with rainfall observations from the Tropical Rainfall Measurement Mission (TRMM) and the other model forecast fields are compared with a high-resolution analysis as well as with European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis. The results of the study indicate that inclusion of additional correlation information in background error statistics has a moderate impact on the vertical profiles of relative humidity, moisture convergence, horizontal divergence and the temperature structure at the depression centre at the analysis time of the cv5/cv6 sensitivity experiments. Moderate improvements are seen in two of the three depressions investigated in this study. An improved thermodynamic and moisture structure at the initial time is expected to provide for improved rainfall simulation. The results of the study indicate that the skill scores of accumulated rainfall are somewhat better for the cv6 option as compared to the cv5 option for at least two of the three depression cases studied, especially at the higher threshold levels. Considering the importance of utilising improved flow-dependent correlation structures for efficient data assimilation, the need for more studies on the impact of background error covariances is obvious.

Skylab water balance error analysis

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1977-01-01

Estimates of the precision of the net water balance were obtained for the entire Skylab preflight and inflight phases as well as for the first two weeks of flight. Quantitative estimates of both total sampling errors and instrumentation errors were obtained. It was shown that measurement error is minimal in comparison to biological variability and little can be gained from improvement in analytical accuracy. In addition, a propagation of error analysis demonstrated that total water balance error could be accounted for almost entirely by the errors associated with body mass changes. Errors due to interaction between terms in the water balance equation (covariances) represented less than 10% of the total error. Overall, the analysis provides evidence that daily measurements of body water changes obtained from the indirect balance technique are reasonable, precise, and relaible. The method is not biased toward net retention or loss.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

A multi-pixel InSAR time series analysis method: Simultaneous estimation of atmospheric noise, orbital errors and deformation

NASA Astrophysics Data System (ADS)

Jolivet, R.; Simons, M.

2016-12-01

InSAR time series analysis allows reconstruction of ground deformation with meter-scale spatial resolution and high temporal sampling. For instance, the ESA Sentinel-1 Constellation is capable of providing 6-day temporal sampling, thereby opening a new window on the spatio-temporal behavior of tectonic processes. However, due to computational limitations, most time series methods rely on a pixel-by-pixel approach. This limitation is a concern because (1) accounting for orbital errors requires referencing all interferograms to a common set of pixels before reconstruction of the time series and (2) spatially correlated atmospheric noise due to tropospheric turbulence is ignored. Decomposing interferograms into statistically independent wavelets will mitigate issues of correlated noise, but prior estimation of orbital uncertainties will still be required. Here, we explore a method that considers all pixels simultaneously when solving for the spatio-temporal evolution of interferometric phase Our method is based on a massively parallel implementation of a conjugate direction solver. We consider an interferogram as the sum of the phase difference between 2 SAR acquisitions and the corresponding orbital errors. In addition, we fit the temporal evolution with a physically parameterized function while accounting for spatially correlated noise in the data covariance. We assume noise is isotropic for any given InSAR pair with a covariance described by an exponential function that decays with increasing separation distance between pixels. We regularize our solution in space using a similar exponential function as model covariance. Given the problem size, we avoid matrix multiplications of the full covariances by computing convolutions in the Fourier domain. We first solve the unregularized least squares problem using the LSQR algorithm to approach the final solution, then run our conjugate direction solver to account for data and model covariances. We present synthetic tests showing the efficiency of our method. We then reconstruct a 20-year continuous time series covering Northern Chile. Without input from any additional GNSS data, we recover the secular deformation rate, seasonal oscillations and the deformation fields from the 2005 Mw 7.8 Tarapaca and 2007 Mw 7.7 Tocopilla earthquakes.

Meta-STEPP: subpopulation treatment effect pattern plot for individual patient data meta-analysis.

PubMed

Wang, Xin Victoria; Cole, Bernard; Bonetti, Marco; Gelber, Richard D

2016-09-20

We have developed a method, called Meta-STEPP (subpopulation treatment effect pattern plot for meta-analysis), to explore treatment effect heterogeneity across covariate values in the meta-analysis setting for time-to-event data when the covariate of interest is continuous. Meta-STEPP forms overlapping subpopulations from individual patient data containing similar numbers of events with increasing covariate values, estimates subpopulation treatment effects using standard fixed-effects meta-analysis methodology, displays the estimated subpopulation treatment effect as a function of the covariate values, and provides a statistical test to detect possibly complex treatment-covariate interactions. Simulation studies show that this test has adequate type-I error rate recovery as well as power when reasonable window sizes are chosen. When applied to eight breast cancer trials, Meta-STEPP suggests that chemotherapy is less effective for tumors with high estrogen receptor expression compared with those with low expression. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A cautionary note on the use of the Analysis of Covariance (ANCOVA) in classification designs with and without within-subject factors

PubMed Central

Schneider, Bruce A.; Avivi-Reich, Meital; Mozuraitis, Mindaugas

2015-01-01

A number of statistical textbooks recommend using an analysis of covariance (ANCOVA) to control for the effects of extraneous factors that might influence the dependent measure of interest. However, it is not generally recognized that serious problems of interpretation can arise when the design contains comparisons of participants sampled from different populations (classification designs). Designs that include a comparison of younger and older adults, or a comparison of musicians and non-musicians are examples of classification designs. In such cases, estimates of differences among groups can be contaminated by differences in the covariate population means across groups. A second problem of interpretation will arise if the experimenter fails to center the covariate measures (subtracting the mean covariate score from each covariate score) whenever the design contains within-subject factors. Unless the covariate measures on the participants are centered, estimates of within-subject factors are distorted, and significant increases in Type I error rates, and/or losses in power can occur when evaluating the effects of within-subject factors. This paper: (1) alerts potential users of ANCOVA of the need to center the covariate measures when the design contains within-subject factors, and (2) indicates how they can avoid biases when one cannot assume that the expected value of the covariate measure is the same for all of the groups in a classification design. PMID:25954230

Analysis of Modified SMI Method for Adaptive Array Weight Control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dilsavor, Ronald Louis

1989-01-01

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Comparing Parameter Estimation Techniques for an Electrical Power Transformer Oil Temperature Prediction Model

NASA Technical Reports Server (NTRS)

Morris, A. Terry

1999-01-01

This paper examines various sources of error in MIT's improved top oil temperature rise over ambient temperature model and estimation process. The sources of error are the current parameter estimation technique, quantization noise, and post-processing of the transformer data. Results from this paper will show that an output error parameter estimation technique should be selected to replace the current least squares estimation technique. The output error technique obtained accurate predictions of transformer behavior, revealed the best error covariance, obtained consistent parameter estimates, and provided for valid and sensible parameters. This paper will also show that the output error technique should be used to minimize errors attributed to post-processing (decimation) of the transformer data. Models used in this paper are validated using data from a large transformer in service.

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Statistical learning from nonrecurrent experience with discrete input variables and recursive-error-minimization equations

NASA Astrophysics Data System (ADS)

Carter, Jeffrey R.; Simon, Wayne E.

1990-08-01

Neural networks are trained using Recursive Error Minimization (REM) equations to perform statistical classification. Using REM equations with continuous input variables reduces the required number of training experiences by factors of one to two orders of magnitude over standard back propagation. Replacing the continuous input variables with discrete binary representations reduces the number of connections by a factor proportional to the number of variables reducing the required number of experiences by another order of magnitude. Undesirable effects of using recurrent experience to train neural networks for statistical classification problems are demonstrated and nonrecurrent experience used to avoid these undesirable effects. 1. THE 1-41 PROBLEM The statistical classification problem which we address is is that of assigning points in ddimensional space to one of two classes. The first class has a covariance matrix of I (the identity matrix) the covariance matrix of the second class is 41. For this reason the problem is known as the 1-41 problem. Both classes have equal probability of occurrence and samples from both classes may appear anywhere throughout the ddimensional space. Most samples near the origin of the coordinate system will be from the first class while most samples away from the origin will be from the second class. Since the two classes completely overlap it is impossible to have a classifier with zero error. The minimum possible error is known as the Bayes error and

Scout trajectory error propagation computer program

NASA Technical Reports Server (NTRS)

Myler, T. R.

1982-01-01

Since 1969, flight experience has been used as the basis for predicting Scout orbital accuracy. The data used for calculating the accuracy consists of errors in the trajectory parameters (altitude, velocity, etc.) at stage burnout as observed on Scout flights. Approximately 50 sets of errors are used in Monte Carlo analysis to generate error statistics in the trajectory parameters. A covariance matrix is formed which may be propagated in time. The mechanization of this process resulted in computer program Scout Trajectory Error Propagation (STEP) and is described herein. Computer program STEP may be used in conjunction with the Statistical Orbital Analysis Routine to generate accuracy in the orbit parameters (apogee, perigee, inclination, etc.) based upon flight experience.

Systematic Error Study for ALICE charged-jet v2 Measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinz, M.; Soltz, R.

We study the treatment of systematic errors in the determination of v 2 for charged jets in √ sNN = 2:76 TeV Pb-Pb collisions by the ALICE Collaboration. Working with the reported values and errors for the 0-5% centrality data we evaluate the Χ 2 according to the formulas given for the statistical and systematic errors, where the latter are separated into correlated and shape contributions. We reproduce both the Χ 2 and p-values relative to a null (zero) result. We then re-cast the systematic errors into an equivalent co-variance matrix and obtain identical results, demonstrating that the two methodsmore » are equivalent.« less

Fitting dynamic models to the Geosat sea level observations in the tropical Pacific Ocean. I - A free wave model

NASA Technical Reports Server (NTRS)

Fu, Lee-Lueng; Vazquez, Jorge; Perigaud, Claire

1991-01-01

Free, equatorially trapped sinusoidal wave solutions to a linear model on an equatorial beta plane are used to fit the Geosat altimetric sea level observations in the tropical Pacific Ocean. The Kalman filter technique is used to estimate the wave amplitude and phase from the data. The estimation is performed at each time step by combining the model forecast with the observation in an optimal fashion utilizing the respective error covariances. The model error covariance is determined such that the performance of the model forecast is optimized. It is found that the dominant observed features can be described qualitatively by basin-scale Kelvin waves and the first meridional-mode Rossby waves. Quantitatively, however, only 23 percent of the signal variance can be accounted for by this simple model.

A mesoscale hybrid data assimilation system based on the JMA nonhydrostatic model

NASA Astrophysics Data System (ADS)

Ito, K.; Kunii, M.; Kawabata, T. T.; Saito, K. K.; Duc, L. L.

2015-12-01

This work evaluates the potential of a hybrid ensemble Kalman filter and four-dimensional variational (4D-Var) data assimilation system for predicting severe weather events from a deterministic point of view. This hybrid system is an adjoint-based 4D-Var system using a background error covariance matrix constructed from the mixture of a so-called NMC method and perturbations in a local ensemble transform Kalman filter data assimilation system, both of which are based on the Japan Meteorological Agency nonhydrostatic model. To construct the background error covariance matrix, we investigated two types of schemes. One is a spatial localization scheme and the other is neighboring ensemble approach, which regards the result at a horizontally spatially shifted point in each ensemble member as that obtained from a different realization of ensemble simulation. An assimilation of a pseudo single-observation located to the north of a tropical cyclone (TC) yielded an analysis increment of wind and temperature physically consistent with what is expected for a mature TC in both hybrid systems, whereas an analysis increment in a 4D-Var system using a static background error covariance distorted a structure of the mature TC. Real data assimilation experiments applied to 4 TCs and 3 local heavy rainfall events showed that hybrid systems and EnKF provided better initial conditions than the NMC-based 4D-Var, both for predicting the intensity and track forecast of TCs and for the location and amount of local heavy rainfall events.

Node-to-node field calibration of wireless distributed air pollution sensor network.

PubMed

Kizel, Fadi; Etzion, Yael; Shafran-Nathan, Rakefet; Levy, Ilan; Fishbain, Barak; Bartonova, Alena; Broday, David M

2018-02-01

Low-cost air quality sensors offer high-resolution spatiotemporal measurements that can be used for air resources management and exposure estimation. Yet, such sensors require frequent calibration to provide reliable data, since even after a laboratory calibration they might not report correct values when they are deployed in the field, due to interference with other pollutants, as a result of sensitivity to environmental conditions and due to sensor aging and drift. Field calibration has been suggested as a means for overcoming these limitations, with the common strategy involving periodical collocations of the sensors at an air quality monitoring station. However, the cost and complexity involved in relocating numerous sensor nodes back and forth, and the loss of data during the repeated calibration periods make this strategy inefficient. This work examines an alternative approach, a node-to-node (N2N) calibration, where only one sensor in each chain is directly calibrated against the reference measurements and the rest of the sensors are calibrated sequentially one against the other while they are deployed and collocated in pairs. The calibration can be performed multiple times as a routine procedure. This procedure minimizes the total number of sensor relocations, and enables calibration while simultaneously collecting data at the deployment sites. We studied N2N chain calibration and the propagation of the calibration error analytically, computationally and experimentally. The in-situ N2N calibration is shown to be generic and applicable for different pollutants, sensing technologies, sensor platforms, chain lengths, and sensor order within the chain. In particular, we show that chain calibration of three nodes, each calibrated for a week, propagate calibration errors that are similar to those found in direct field calibration. Hence, N2N calibration is shown to be suitable for calibration of distributed sensor networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Analysis and application of minimum variance discrete time system identification

NASA Technical Reports Server (NTRS)

Kaufman, H.; Kotob, S.

1975-01-01

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

NASA Technical Reports Server (NTRS)

McKinley, David P.

2006-01-01

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

Improving Lidar Turbulence Estimates for Wind Energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Newman, Jennifer F.; Clifton, Andrew; Churchfield, Matthew J.

2016-10-06

Remote sensing devices (e.g., lidars) are quickly becoming a cost-effective and reliable alternative to meteorological towers for wind energy applications. Although lidars can measure mean wind speeds accurately, these devices measure different values of turbulence intensity (TI) than an instrument on a tower. In response to these issues, a lidar TI error reduction model was recently developed for commercially available lidars. The TI error model first applies physics-based corrections to the lidar measurements, then uses machine-learning techniques to further reduce errors in lidar TI estimates. The model was tested at two sites in the Southern Plains where vertically profiling lidarsmore » were collocated with meteorological towers. This presentation primarily focuses on the physics-based corrections, which include corrections for instrument noise, volume averaging, and variance contamination. As different factors affect TI under different stability conditions, the combination of physical corrections applied in L-TERRA changes depending on the atmospheric stability during each 10-minute time period. This stability-dependent version of L-TERRA performed well at both sites, reducing TI error and bringing lidar TI estimates closer to estimates from instruments on towers. However, there is still scatter evident in the lidar TI estimates, indicating that there are physics that are not being captured in the current version of L-TERRA. Two options are discussed for modeling the remainder of the TI error physics in L-TERRA: machine learning and lidar simulations. Lidar simulations appear to be a better approach, as they can help improve understanding of atmospheric effects on TI error and do not require a large training data set.« less

Adult myeloid leukaemia and radon exposure: a Bayesian model for a case-control study with error in covariates.

PubMed

Toti, Simona; Biggeri, Annibale; Forastiere, Francesco

2005-06-30

The possible association between radon exposure in dwellings and adult myeloid leukaemia had been explored in an Italian province by a case-control study. A total of 44 cases and 211 controls were selected from death certificates file. No association had been found in the original study (OR = 0.58 for > 185 vs 80 < or = Bq/cm). Here we reanalyse the data taking into account the measurement error of radon concentration and the presence of missing data. A Bayesian hierarchical model with error in covariates is proposed which allows appropriate imputation of missing values. The general conclusion of no evidence of association with radon does not change, but a negative association is not observed anymore (OR = 0.99 for > 185 vs 80 < or = Bq/cm). After adjusting for residential house radon and gamma radiation, and for the multilevel data structure, geological features of the soil is associated with adult myeloid leukaemia risk (OR = 2.14, 95 per cent Cr.I. 1.0-5.5). Copyright 2005 John Wiley & Sons, Ltd.

Performance analysis of an integrated GPS/inertial attitude determination system. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Wendy I.

1994-01-01

The performance of an integrated GPS/inertial attitude determination system is investigated using a linear covariance analysis. The principles of GPS interferometry are reviewed, and the major error sources of both interferometers and gyroscopes are discussed and modeled. A new figure of merit, attitude dilution of precision (ADOP), is defined for two possible GPS attitude determination methods, namely single difference and double difference interferometry. Based on this figure of merit, a satellite selection scheme is proposed. The performance of the integrated GPS/inertial attitude determination system is determined using a linear covariance analysis. Based on this analysis, it is concluded that the baseline errors (i.e., knowledge of the GPS interferometer baseline relative to the vehicle coordinate system) are the limiting factor in system performance. By reducing baseline errors, it should be possible to use lower quality gyroscopes without significantly reducing performance. For the cases considered, single difference interferometry is only marginally better than double difference interferometry. Finally, the performance of the system is found to be relatively insensitive to the satellite selection technique.

Water, Energy, and Carbon with Artificial Neural Networks (WECANN): A statistically-based estimate of global surface turbulent fluxes and gross primary productivity using solar-induced fluorescence.

PubMed

Alemohammad, Seyed Hamed; Fang, Bin; Konings, Alexandra G; Aires, Filipe; Green, Julia K; Kolassa, Jana; Miralles, Diego; Prigent, Catherine; Gentine, Pierre

2017-01-01

A new global estimate of surface turbulent fluxes, latent heat flux (LE) and sensible heat flux (H), and gross primary production (GPP) is developed using a machine learning approach informed by novel remotely sensed Solar-Induced Fluorescence (SIF) and other radiative and meteorological variables. This is the first study to jointly retrieve LE, H and GPP using SIF observations. The approach uses an artificial neural network (ANN) with a target dataset generated from three independent data sources, weighted based on triple collocation (TC) algorithm. The new retrieval, named Water, Energy, and Carbon with Artificial Neural Networks (WECANN), provides estimates of LE, H and GPP from 2007 to 2015 at 1° × 1° spatial resolution and on monthly time resolution. The quality of ANN training is assessed using the target data, and the WECANN retrievals are evaluated using eddy covariance tower estimates from FLUXNET network across various climates and conditions. When compared to eddy covariance estimates, WECANN typically outperforms other products, particularly for sensible and latent heat fluxes. Analysing WECANN retrievals across three extreme drought and heatwave events demonstrates the capability of the retrievals in capturing the extent of these events. Uncertainty estimates of the retrievals are analysed and the inter-annual variability in average global and regional fluxes show the impact of distinct climatic events - such as the 2015 El Niño - on surface turbulent fluxes and GPP.

Water, Energy, and Carbon with Artificial Neural Networks (WECANN): a statistically based estimate of global surface turbulent fluxes and gross primary productivity using solar-induced fluorescence

NASA Astrophysics Data System (ADS)

Hamed Alemohammad, Seyed; Fang, Bin; Konings, Alexandra G.; Aires, Filipe; Green, Julia K.; Kolassa, Jana; Miralles, Diego; Prigent, Catherine; Gentine, Pierre

2017-09-01

A new global estimate of surface turbulent fluxes, latent heat flux (LE) and sensible heat flux (H), and gross primary production (GPP) is developed using a machine learning approach informed by novel remotely sensed solar-induced fluorescence (SIF) and other radiative and meteorological variables. This is the first study to jointly retrieve LE, H, and GPP using SIF observations. The approach uses an artificial neural network (ANN) with a target dataset generated from three independent data sources, weighted based on a triple collocation (TC) algorithm. The new retrieval, named Water, Energy, and Carbon with Artificial Neural Networks (WECANN), provides estimates of LE, H, and GPP from 2007 to 2015 at 1° × 1° spatial resolution and at monthly time resolution. The quality of ANN training is assessed using the target data, and the WECANN retrievals are evaluated using eddy covariance tower estimates from the FLUXNET network across various climates and conditions. When compared to eddy covariance estimates, WECANN typically outperforms other products, particularly for sensible and latent heat fluxes. Analyzing WECANN retrievals across three extreme drought and heat wave events demonstrates the capability of the retrievals to capture the extent of these events. Uncertainty estimates of the retrievals are analyzed and the interannual variability in average global and regional fluxes shows the impact of distinct climatic events - such as the 2015 El Niño - on surface turbulent fluxes and GPP.

Replica approach to mean-variance portfolio optimization

NASA Astrophysics Data System (ADS)

Varga-Haszonits, Istvan; Caccioli, Fabio; Kondor, Imre

2016-12-01

We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for r  =  N/T  <  1, where N is the dimension of the portfolio and T the length of the time series used to estimate the covariance matrix. At the critical point r  =  1 a phase transition is taking place. The out of sample estimation error blows up at this point as 1/(1  -  r), independently of the covariance matrix or the expected return, displaying the universality not only of the critical exponent, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.

Assimilation of surface NO2 and O3 observations into the SILAM chemistry transport model

NASA Astrophysics Data System (ADS)

Vira, J.; Sofiev, M.

2015-02-01

This paper describes the assimilation of trace gas observations into the chemistry transport model SILAM (System for Integrated modeLling of Atmospheric coMposition) using the 3D-Var method. Assimilation results for the year 2012 are presented for the prominent photochemical pollutants ozone (O3) and nitrogen dioxide (NO2). Both species are covered by the AirBase observation database, which provides the observational data set used in this study. Attention was paid to the background and observation error covariance matrices, which were obtained primarily by the iterative application of a posteriori diagnostics. The diagnostics were computed separately for 2 months representing summer and winter conditions, and further disaggregated by time of day. This enabled the derivation of background and observation error covariance definitions, which included both seasonal and diurnal variation. The consistency of the obtained covariance matrices was verified using χ2 diagnostics. The analysis scores were computed for a control set of observation stations withheld from assimilation. Compared to a free-running model simulation, the correlation coefficient for daily maximum values was improved from 0.8 to 0.9 for O3 and from 0.53 to 0.63 for NO2.

Adaptive error covariances estimation methods for ensemble Kalman filters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhen, Yicun, E-mail: zhen@math.psu.edu; Harlim, John, E-mail: jharlim@psu.edu

2015-08-01

This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for usingmore » information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.« less

Pairwise registration of TLS point clouds using covariance descriptors and a non-cooperative game

NASA Astrophysics Data System (ADS)

Zai, Dawei; Li, Jonathan; Guo, Yulan; Cheng, Ming; Huang, Pengdi; Cao, Xiaofei; Wang, Cheng

2017-12-01

It is challenging to automatically register TLS point clouds with noise, outliers and varying overlap. In this paper, we propose a new method for pairwise registration of TLS point clouds. We first generate covariance matrix descriptors with an adaptive neighborhood size from point clouds to find candidate correspondences, we then construct a non-cooperative game to isolate mutual compatible correspondences, which are considered as true positives. The method was tested on three models acquired by two different TLS systems. Experimental results demonstrate that our proposed adaptive covariance (ACOV) descriptor is invariant to rigid transformation and robust to noise and varying resolutions. The average registration errors achieved on three models are 0.46 cm, 0.32 cm and 1.73 cm, respectively. The computational times cost on these models are about 288 s, 184 s and 903 s, respectively. Besides, our registration framework using ACOV descriptors and a game theoretic method is superior to the state-of-the-art methods in terms of both registration error and computational time. The experiment on a large outdoor scene further demonstrates the feasibility and effectiveness of our proposed pairwise registration framework.

A Multipixel Time Series Analysis Method Accounting for Ground Motion, Atmospheric Noise, and Orbital Errors

NASA Astrophysics Data System (ADS)

Jolivet, R.; Simons, M.

2018-02-01

Interferometric synthetic aperture radar time series methods aim to reconstruct time-dependent ground displacements over large areas from sets of interferograms in order to detect transient, periodic, or small-amplitude deformation. Because of computational limitations, most existing methods consider each pixel independently, ignoring important spatial covariances between observations. We describe a framework to reconstruct time series of ground deformation while considering all pixels simultaneously, allowing us to account for spatial covariances, imprecise orbits, and residual atmospheric perturbations. We describe spatial covariances by an exponential decay function dependent of pixel-to-pixel distance. We approximate the impact of imprecise orbit information and residual long-wavelength atmosphere as a low-order polynomial function. Tests on synthetic data illustrate the importance of incorporating full covariances between pixels in order to avoid biased parameter reconstruction. An example of application to the northern Chilean subduction zone highlights the potential of this method.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part 1; Method and Uncertainties

NASA Technical Reports Server (NTRS)

Olson, William S.; Kummerow, Christian D.; Yang, Song; Petty, Grant W.; Tao, Wei-Kuo; Bell, Thomas L.; Braun, Scott A.; Wang, Yansen; Lang, Stephen E.; Johnson, Daniel E.

2004-01-01

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating/drying profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and non-convective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud resolving model simulations, and from the Bayesian formulation itself. Synthetic rain rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in instantaneous rain rate estimates at 0.5 deg resolution range from approximately 50% at 1 mm/h to 20% at 14 mm/h. These errors represent about 70-90% of the mean random deviation between collocated passive microwave and spaceborne radar rain rate estimates. The cumulative algorithm error in TMI estimates at monthly, 2.5 deg resolution is relatively small (less than 6% at 5 mm/day) compared to the random error due to infrequent satellite temporal sampling (8-35% at the same rain rate).

Glucose control and medication adherence among veterans with diabetes and serious mental illness: does collocation of primary care and mental health care matter?

PubMed

Long, Judith A; Wang, Andrew; Medvedeva, Elina L; Eisen, Susan V; Gordon, Adam J; Kreyenbuhl, Julie; Marcus, Steven C

2014-08-01

Persons with serious mental illness (SMI) may benefit from collocation of medical and mental health healthcare professionals and services in attending to their chronic comorbid medical conditions. We evaluated and compared glucose control and diabetes medication adherence among patients with SMI who received collocated care to those not receiving collocated care (which we call usual care). We performed a cross-sectional, observational cohort study of 363 veteran patients with type 2 diabetes and SMI who received care from one of three Veterans Affairs medical facilities: two sites that provided both collocated and usual care and one site that provided only usual care. Through a survey, laboratory tests, and medical records, we assessed patient characteristics, glucose control as measured by a current HbA1c, and adherence to diabetes medication as measured by the medication possession ration (MPR) and self-report. In the sample, the mean HbA1c was 7.4% (57 mmol/mol), the mean MPR was 80%, and 51% reported perfect adherence to their diabetes medications. In both unadjusted and adjusted analyses, there were no differences in glucose control and medication adherence by collocation of care. Patients seen in collocated care tended to have better HbA1c levels (β = -0.149; P = 0.393) and MPR values (β = 0.34; P = 0.132) and worse self-reported adherence (odds ratio 0.71; P = 0.143), but these were not statistically significant. In a population of veterans with comorbid diabetes and SMI, patients on average had good glucose control and medication adherence regardless of where they received primary care. © 2014 by the American Diabetes Association. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered.

Model dependence and its effect on ensemble projections in CMIP5

NASA Astrophysics Data System (ADS)

Abramowitz, G.; Bishop, C.

2013-12-01

Conceptually, the notion of model dependence within climate model ensembles is relatively simple - modelling groups share a literature base, parametrisations, data sets and even model code - the potential for dependence in sampling different climate futures is clear. How though can this conceptual problem inform a practical solution that demonstrably improves the ensemble mean and ensemble variance as an estimate of system uncertainty? While some research has already focused on error correlation or error covariance as a candidate to improve ensemble mean estimates, a complete definition of independence must at least implicitly subscribe to an ensemble interpretation paradigm, such as the 'truth-plus-error', 'indistinguishable', or more recently 'replicate Earth' paradigm. Using a definition of model dependence based on error covariance within the replicate Earth paradigm, this presentation will show that accounting for dependence in surface air temperature gives cooler projections in CMIP5 - by as much as 20% globally in some RCPs - although results differ significantly for each RCP, especially regionally. The fact that the change afforded by accounting for dependence across different RCPs is different is not an inconsistent result. Different numbers of submissions to each RCP by different modelling groups mean that differences in projections from different RCPs are not entirely about RCP forcing conditions - they also reflect different sampling strategies.

Impact of Flow-Dependent Error Correlations and Tropospheric Chemistry on Assimilated Ozone

NASA Technical Reports Server (NTRS)

Wargan, K.; Stajner, I.; Hayashi, H.; Pawson, S.; Jones, D. B. A.

2003-01-01

The presentation compares different versions of a global three-dimensional ozone data assimilation system developed at NASA's Data Assimilation Office. The Solar Backscatter Ultraviolet/2 (SBUV/2) total and partial ozone column retrievals are the sole data assimilated in all of the experiments presented. We study the impact of changing the forecast error covariance model from a version assuming static correlations with a one that captures a short-term Lagrangian evolution of those correlations. This is further combined with a study of the impact of neglecting the tropospheric ozone production, loss and dry deposition rates, which are obtained from the Harvard GEOS-CHEM model. We compare statistical characteristics of the assimilated data and the results of validation against independent observations, obtained from WMO balloon-borne sondes and the Polar Ozone and Aerosol Measurement (POAM) III instrument. Experiments show that allowing forecast error correlations to evolve with the flow results in positive impact on assimilated ozone within the regions where data were not assimilated, particularly at high latitudes in both hemispheres. On the other hand, the main sensitivity to tropospheric chemistry is in the Tropics and sub-Tropics. The best agreement between the assimilated ozone and the in-situ sonde data is in the experiment using both flow-dependent error covariances and tropospheric chemistry.

On the Stability of Collocated Controllers in the Presence or Uncertain Nonlinearities and Other Perils

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1985-01-01

Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.

Understanding a reference-free impedance method using collocated piezoelectric transducers

NASA Astrophysics Data System (ADS)

Kim, Eun Jin; Kim, Min Koo; Sohn, Hoon; Park, Hyun Woo

2010-03-01

A new concept of a reference-free impedance method, which does not require direct comparison with a baseline impedance signal, is proposed for damage detection in a plate-like structure. A single pair of piezoelectric (PZT) wafers collocated on both surfaces of a plate are utilized for extracting electro-mechanical signatures (EMS) associated with mode conversion due to damage. A numerical simulation is conducted to investigate the EMS of collocated PZT wafers in the frequency domain at the presence of damage through spectral element analysis. Then, the EMS due to mode conversion induced by damage are extracted using the signal decomposition technique based on the polarization characteristics of the collocated PZT wafers. The effects of the size and the location of damage on the decomposed EMS are investigated as well. Finally, the applicability of the decomposed EMS to the reference-free damage diagnosis is discussed.

Stochastic collocation using Kronrod-Patterson-Hermite quadrature with moderate delay for subsurface flow and transport

NASA Astrophysics Data System (ADS)

Liao, Q.; Tchelepi, H.; Zhang, D.

2015-12-01

Uncertainty quantification aims at characterizing the impact of input parameters on the output responses and plays an important role in many areas including subsurface flow and transport. In this study, a sparse grid collocation approach, which uses a nested Kronrod-Patterson-Hermite quadrature rule with moderate delay for Gaussian random parameters, is proposed to quantify the uncertainty of model solutions. The conventional stochastic collocation method serves as a promising non-intrusive approach and has drawn a great deal of interests. The collocation points are usually chosen to be Gauss-Hermite quadrature nodes, which are naturally unnested. The Kronrod-Patterson-Hermite nodes are shown to be more efficient than the Gauss-Hermite nodes due to nestedness. We propose a Kronrod-Patterson-Hermite rule with moderate delay to further improve the performance. Our study demonstrates the effectiveness of the proposed method for uncertainty quantification through subsurface flow and transport examples.

Double-adjustment in propensity score matching analysis: choosing a threshold for considering residual imbalance.

PubMed

Nguyen, Tri-Long; Collins, Gary S; Spence, Jessica; Daurès, Jean-Pierre; Devereaux, P J; Landais, Paul; Le Manach, Yannick

2017-04-28

Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. However, it is not always possible to include all covariates in adjustment. We aimed to find the optimal imbalance threshold for entering covariates into regression. We conducted a series of Monte Carlo simulations on virtual populations of 5,000 subjects. We performed PS 1:1 nearest-neighbor matching on each sample. We calculated standardized mean differences across groups to detect any remaining imbalance in the matched samples. We examined 25 thresholds (from 0.01 to 0.25, stepwise 0.01) for considering residual imbalance. The treatment effect was estimated using logistic regression that contained only those covariates considered to be unbalanced by these thresholds. We showed that regression adjustment could dramatically remove residual confounding bias when it included all of the covariates with a standardized difference greater than 0.10. The additional benefit was negligible when we also adjusted for covariates with less imbalance. We found that the mean squared error of the estimates was minimized under the same conditions. If covariate balance is not achieved, we recommend reiterating PS modeling until standardized differences below 0.10 are achieved on most covariates. In case of remaining imbalance, a double adjustment might be worth considering.

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere

NASA Astrophysics Data System (ADS)

Blakely, Christopher D.

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.

Robust Covariate-Adjusted Log-Rank Statistics and Corresponding Sample Size Formula for Recurrent Events Data

PubMed Central

Song, Rui; Kosorok, Michael R.; Cai, Jianwen

2009-01-01

Summary Recurrent events data are frequently encountered in clinical trials. This article develops robust covariate-adjusted log-rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula. The proposed log-rank tests are robust with respect to different data-generating processes and are adjusted for predictive covariates. It reduces to the Kong and Slud (1997, Biometrika 84, 847–862) setting in the case of a single event. The sample size formula is derived based on the asymptotic normality of the covariate-adjusted log-rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context. When the effect size is small and the baseline covariates do not contain significant information about event times, it reduces to the same form as that of Schoenfeld (1983, Biometrics 39, 499–503) for cases of a single event or independent event times within a subject. We carry out simulations to study the control of type I error and the comparison of powers between several methods in finite samples. The proposed sample size formula is illustrated using data from an rhDNase study. PMID:18162107

Recent Progresses of Microwave Marine Remote Sensing

NASA Astrophysics Data System (ADS)

Yang, Jingsong; Ren, Lin; Zheng, Gang; Wang, He; He, Shuangyan; Wang, Juan; Li, Xiaohui

2016-08-01

It is presented in this paper the recent progresses of Dragon 3 Program (ID. 10412) in the field of microwave marine remote sensing including (1) ocean surface wind fields from full polarization synthetic aperture radars (SAR), (2) joint retrieval of directional ocean wave spectra from SAR and wave spectrometer, (3) error analysis on ENVISAT ASAR wave mode significant wave height (SWH) retrievals using triple collocation model, (4) typhoon observation from SAR and optical sensors, (5) ocean internal wave observation from SAR and optical sensors, (6) ocean eddy observation from SAR and optical sensors, (7) retrieval models of water vapor and wet tropospheric path delay for the HY-2A calibration microwave radiometer, (8) calibration of SWH from HY-2A satellite altimeter.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Generalized Background Error covariance matrix model (GEN_BE v2.0)

NASA Astrophysics Data System (ADS)

Descombes, G.; Auligné, T.; Vandenberghe, F.; Barker, D. M.

2014-07-01

The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model to allow for a simpler, flexible, robust, and community-oriented framework that gathers methods used by meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks and showing some of the new features on data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to involve new control variables. While the generation of the background errors statistics code has been first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily extended to other domains of science and be chosen as a testbed for diagnostic and new modeling of B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Generalized background error covariance matrix model (GEN_BE v2.0)

NASA Astrophysics Data System (ADS)

Descombes, G.; Auligné, T.; Vandenberghe, F.; Barker, D. M.; Barré, J.

2015-03-01

The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Statistics of the epoch of reionization 21-cm signal - I. Power spectrum error-covariance

NASA Astrophysics Data System (ADS)

Mondal, Rajesh; Bharadwaj, Somnath; Majumdar, Suman

2016-02-01

The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum P(k). We have used a large ensemble of seminumerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix {C}ij. Our analytical model shows that {C}ij has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of P(k). The other is the trispectrum of the signal. Using the simulated 21-cm Signal Ensemble, an ensemble of the Randomized Signal and Ensembles of Gaussian Random Ensembles we have quantified the effect of the trispectrum on the error variance {C}II. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 ≤ k ≤ 1.0 Mpc-1, and can be even ˜200 times larger at k ˜ 5 Mpc-1. We also establish that the off-diagonal terms of {C}ij have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different k modes are not independent. We find a strong correlation between the errors at large k values (≥0.5 Mpc-1), and a weak correlation between the smallest and largest k values. There is also a small anticorrelation between the errors in the smallest and intermediate k values. These results are relevant for the k range that will be probed by the current and upcoming EoR 21-cm experiments.

Assessing the Impact of Pre-gpm Microwave Precipitation Observations in the Goddard WRF Ensemble Data Assimilation System

NASA Technical Reports Server (NTRS)

Chambon, Philippe; Zhang, Sara Q.; Hou, Arthur Y.; Zupanski, Milija; Cheung, Samson

2013-01-01

The forthcoming Global Precipitation Measurement (GPM) Mission will provide next generation precipitation observations from a constellation of satellites. Since precipitation by nature has large variability and low predictability at cloud-resolving scales, the impact of precipitation data on the skills of mesoscale numerical weather prediction (NWP) is largely affected by the characterization of background and observation errors and the representation of nonlinear cloud/precipitation physics in an NWP data assimilation system. We present a data impact study on the assimilation of precipitation-affected microwave (MW) radiances from a pre-GPM satellite constellation using the Goddard WRF Ensemble Data Assimilation System (Goddard WRF-EDAS). A series of assimilation experiments are carried out in a Weather Research Forecast (WRF) model domain of 9 km resolution in western Europe. Sensitivities to observation error specifications, background error covariance estimated from ensemble forecasts with different ensemble sizes, and MW channel selections are examined through single-observation assimilation experiments. An empirical bias correction for precipitation-affected MW radiances is developed based on the statistics of radiance innovations in rainy areas. The data impact is assessed by full data assimilation cycling experiments for a storm event that occurred in France in September 2010. Results show that the assimilation of MW precipitation observations from a satellite constellation mimicking GPM has a positive impact on the accumulated rain forecasts verified with surface radar rain estimates. The case-study on a convective storm also reveals that the accuracy of ensemble-based background error covariance is limited by sampling errors and model errors such as precipitation displacement and unresolved convective scale instability.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

On the anomaly of velocity-pressure decoupling in collocated mesh solutions

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Vanoverbeke, Thomas

1991-01-01

The use of various pressure correction algorithms originally developed for fully staggered meshes can yield a velocity-pressure decoupled solution for collocated meshes. The mechanism that causes velocity-pressure decoupling is identified. It is shown that the use of a partial differential equation for the incremental pressure eliminates such a mechanism and yields a velocity-pressure coupled solution. Example flows considered are a three dimensional lid-driven cavity flow and a laminar flow through a 90 deg bend square duct. Numerical results obtained using the collocated mesh are in good agreement with the measured data and other numerical results.

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

Testing a single regression coefficient in high dimensional linear models

PubMed Central

Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2017-01-01

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively. PMID:28663668

Testing a single regression coefficient in high dimensional linear models.

PubMed

Lan, Wei; Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2016-11-01

In linear regression models with high dimensional data, the classical z -test (or t -test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z -test to assess the significance of each covariate. Based on the p -value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

DTIC Science & Technology

2016-11-16

determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable...pro- ceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a...design of statistical estimators (i.e. sensors) as their respective inverses act as lower bounds to the (co)variances of the subject estimator, a property

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

NASA Technical Reports Server (NTRS)

Kumar, Sujay V.; Dong, Jiarul; Peters-Lidard, Christa D.; Mocko, David; Gomez, Breogan

2017-01-01

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

Precise Orbit Determination for GEOSAT Follow-On Using Satellite Laser Ranging Data and Intermission Altimeter Crossovers

NASA Technical Reports Server (NTRS)

Lemoine, Frank G.; Rowlands, David D.; Luthcke, Scott B.; Zelensky, Nikita P.; Chinn, Douglas S.; Pavlis, Despina E.; Marr, Gregory

2001-01-01

The US Navy's GEOSAT Follow-On Spacecraft was launched on February 10, 1998 with the primary objective of the mission to map the oceans using a radar altimeter. Following an extensive set of calibration campaigns in 1999 and 2000, the US Navy formally accepted delivery of the satellite on November 29, 2000. Satellite laser ranging (SLR) and Doppler (Tranet-style) beacons track the spacecraft. Although limited amounts of GPS data were obtained, the primary mode of tracking remains satellite laser ranging. The GFO altimeter measurements are highly precise, with orbit error the largest component in the error budget. We have tuned the non-conservative force model for GFO and the gravity model using SLR, Doppler and altimeter crossover data sampled over one year. Gravity covariance projections to 70x70 show the radial orbit error on GEOSAT was reduced from 2.6 cm in EGM96 to 1.3 cm with the addition of SLR, GFO/GFO and TOPEX/GFO crossover data. Evaluation of the gravity fields using SLR and crossover data support the covariance projections and also show a dramatic reduction in geographically-correlated error for the tuned fields. In this paper, we report on progress in orbit determination for GFO using GFO/GFO and TOPEX/GFO altimeter crossovers. We will discuss improvements in satellite force modeling and orbit determination strategy, which allows reduction in GFO radial orbit error from 10-15 cm to better than 5 cm.

Semiparametric Bayesian analysis of gene-environment interactions with error in measurement of environmental covariates and missing genetic data.

PubMed

Lobach, Iryna; Mallick, Bani; Carroll, Raymond J

2011-01-01

Case-control studies are widely used to detect gene-environment interactions in the etiology of complex diseases. Many variables that are of interest to biomedical researchers are difficult to measure on an individual level, e.g. nutrient intake, cigarette smoking exposure, long-term toxic exposure. Measurement error causes bias in parameter estimates, thus masking key features of data and leading to loss of power and spurious/masked associations. We develop a Bayesian methodology for analysis of case-control studies for the case when measurement error is present in an environmental covariate and the genetic variable has missing data. This approach offers several advantages. It allows prior information to enter the model to make estimation and inference more precise. The environmental covariates measured exactly are modeled completely nonparametrically. Further, information about the probability of disease can be incorporated in the estimation procedure to improve quality of parameter estimates, what cannot be done in conventional case-control studies. A unique feature of the procedure under investigation is that the analysis is based on a pseudo-likelihood function therefore conventional Bayesian techniques may not be technically correct. We propose an approach using Markov Chain Monte Carlo sampling as well as a computationally simple method based on an asymptotic posterior distribution. Simulation experiments demonstrated that our method produced parameter estimates that are nearly unbiased even for small sample sizes. An application of our method is illustrated using a population-based case-control study of the association between calcium intake with the risk of colorectal adenoma development.

Bayesian operational modal analysis with asynchronous data, Part II: Posterior uncertainty

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

A Bayesian modal identification method has been proposed in the companion paper that allows the most probable values of modal parameters to be determined using asynchronous ambient vibration data. This paper investigates the identification uncertainty of modal parameters in terms of their posterior covariance matrix. Computational issues are addressed. Analytical expressions are derived to allow the posterior covariance matrix to be evaluated accurately and efficiently. Synthetic, laboratory and field data examples are presented to verify the consistency, investigate potential modelling error and demonstrate practical applications.

Evaluating Remotely-Sensed Surface Soil Moisture Estimates Using Triple Collocation

USDA-ARS?s Scientific Manuscript database

Recent work has demonstrated the potential of enhancing remotely-sensed surface soil moisture validation activities through the application of triple collocation techniques which compare time series of three mutually independent geophysical variable estimates in order to acquire the root-mean-square...

Accuracy limitations of hyperbolic multilateration systems

DOT National Transportation Integrated Search

1973-03-22

The report is an analysis of the accuracy limitations of hyperbolic multilateration systems. A central result is a demonstration that the inverse of the covariance matrix for positional errors corresponds to the moment of inertia matrix of a simple m...

Observations of geographically correlated orbit errors for TOPEX/Poseidon using the global positioning system

NASA Technical Reports Server (NTRS)

Christensen, E. J.; Haines, B. J.; Mccoll, K. C.; Nerem, R. S.

1994-01-01

We have compared Global Positioning System (GPS)-based dynamic and reduced-dynamic TOPEX/Poseidon orbits over three 10-day repeat cycles of the ground-track. The results suggest that the prelaunch joint gravity model (JGM-1) introduces geographically correlated errors (GCEs) which have a strong meridional dependence. The global distribution and magnitude of these GCEs are consistent with a prelaunch covariance analysis, with estimated and predicted global rms error statistics of 2.3 and 2.4 cm rms, respectively. Repeating the analysis with the post-launch joint gravity model (JGM-2) suggests that a portion of the meridional dependence observed in JGM-1 still remains, with global rms error of 1.2 cm.

A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

NASA Technical Reports Server (NTRS)

Carpenter, Russell; Lee, Taesul

2008-01-01

Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

UTLS water vapour from SCIAMACHY limb measurementsV3.01 (2002-2012).

PubMed

Weigel, K; Rozanov, A; Azam, F; Bramstedt, K; Damadeo, R; Eichmann, K-U; Gebhardt, C; Hurst, D; Kraemer, M; Lossow, S; Read, W; Spelten, N; Stiller, G P; Walker, K A; Weber, M; Bovensmann, H; Burrows, J P

2016-01-01

The SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) aboard the Envisat satellite provided measurements from August 2002 until April 2012. SCIAMACHY measured the scattered or direct sunlight using different observation geometries. The limb viewing geometry allows the retrieval of water vapour at about 10-25 km height from the near-infrared spectral range (1353-1410 nm). These data cover the upper troposphere and lower stratosphere (UTLS), a region in the atmosphere which is of special interest for a variety of dynamical and chemical processes as well as for the radiative forcing. Here, the latest data version of water vapour (V3.01) from SCIAMACHY limb measurements is presented and validated by comparisons with data sets from other satellite and in situ measurements. Considering retrieval tests and the results of these comparisons, the V3.01 data are reliable from about 11 to 23 km and the best results are found in the middle of the profiles between about 14 and 20 km. Above 20 km in the extra tropics V3.01 is drier than all other data sets. Additionally, for altitudes above about 19 km, the vertical resolution of the retrieved profile is not sufficient to resolve signals with a short vertical structure like the tape recorder. Below 14 km, SCIAMACHY water vapour V3.01 is wetter than most collocated data sets, but the high variability of water vapour in the troposphere complicates the comparison. For 14-20 km height, the expected errors from the retrieval and simulations and the mean differences to collocated data sets are usually smaller than 10 % when the resolution of the SCIAMACHY data is taken into account. In general, the temporal changes agree well with collocated data sets except for the Northern Hemisphere extratropical stratosphere, where larger differences are observed. This indicates a possible drift in V3.01 most probably caused by the incomplete treatment of volcanic aerosols in the retrieval. In all other regions a good temporal stability is shown. In the tropical stratosphere an increase in water vapour is found between 2002 and 2012, which is in agreement with other satellite data sets for overlapping time periods.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

USGS Publications Warehouse

Langbein, John O.

2017-01-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fα">1/fα1/fα with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi:10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

NASA Technical Reports Server (NTRS)

Keppenne, Christian; Vernieres, Guillaume; Rienecker, Michele; Jacob, Jossy; Kovach, Robin

2011-01-01

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

NASA Astrophysics Data System (ADS)

Langbein, John

2017-08-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

A 10-Year Comparison of Water Levels Measured with a Geodetic GPS Receiver Versus a Conventional Tide Gauge

NASA Technical Reports Server (NTRS)

Larson, Kristine M.; Ray, Richard D.; Williams, Simon D. P.

2017-01-01

A standard geodetic GPS receiver and a conventional Aquatrak tide gauge, collocated at Friday Harbor, Washington, are used to assess the quality of 10 years of water levels estimated from GPS sea surface reflections.The GPS results are improved by accounting for (tidal) motion of the reflecting sea surface and for signal propagation delay by the troposphere. The RMS error of individual GPS water level estimates is about 12 cm. Lower water levels are measured slightly more accurately than higher water levels. Forming daily mean sea levels reduces the RMS difference with the tide gauge data to approximately 2 cm. For monthly means, the RMS difference is 1.3 cm. The GPS elevations, of course, can be automatically placed into a well-defined terrestrial reference frame. Ocean tide coefficients, determined from both the GPS and tide gauge data, are in good agreement, with absolute differences below 1 cm for all constituents save K1 and S1. The latter constituent is especially anomalous, probably owing to daily temperature-induced errors in the Aquatrak tide gauge

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials

PubMed Central

Diaz-Ordaz, Karla; Bartlett, Jonathan W

2016-01-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group. PMID:27177885

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

PubMed

Hossain, Anower; Diaz-Ordaz, Karla; Bartlett, Jonathan W

2017-06-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group.

Further Evaluation of Covariate Analysis using Empirical Bayes Estimates in Population Pharmacokinetics: the Perception of Shrinkage and Likelihood Ratio Test.

PubMed

Xu, Xu Steven; Yuan, Min; Yang, Haitao; Feng, Yan; Xu, Jinfeng; Pinheiro, Jose

2017-01-01

Covariate analysis based on population pharmacokinetics (PPK) is used to identify clinically relevant factors. The likelihood ratio test (LRT) based on nonlinear mixed effect model fits is currently recommended for covariate identification, whereas individual empirical Bayesian estimates (EBEs) are considered unreliable due to the presence of shrinkage. The objectives of this research were to investigate the type I error for LRT and EBE approaches, to confirm the similarity of power between the LRT and EBE approaches from a previous report and to explore the influence of shrinkage on LRT and EBE inferences. Using an oral one-compartment PK model with a single covariate impacting on clearance, we conducted a wide range of simulations according to a two-way factorial design. The results revealed that the EBE-based regression not only provided almost identical power for detecting a covariate effect, but also controlled the false positive rate better than the LRT approach. Shrinkage of EBEs is likely not the root cause for decrease in power or inflated false positive rate although the size of the covariate effect tends to be underestimated at high shrinkage. In summary, contrary to the current recommendations, EBEs may be a better choice for statistical tests in PPK covariate analysis compared to LRT. We proposed a three-step covariate modeling approach for population PK analysis to utilize the advantages of EBEs while overcoming their shortcomings, which allows not only markedly reducing the run time for population PK analysis, but also providing more accurate covariate tests.

Cloud radiative properties and aerosol - cloud interaction

NASA Astrophysics Data System (ADS)

Viviana Vladutescu, Daniela; Gross, Barry; Li, Clement; Han, Zaw

2015-04-01

The presented research discusses different techniques for improvement of cloud properties measurements and analysis. The need for these measurements and analysis arises from the high errors noticed in existing methods that are currently used in retrieving cloud properties and implicitly cloud radiative forcing. The properties investigated are cloud fraction (cf) and cloud optical thickness (COT) measured with a suite of collocated remote sensing instruments. The novel approach makes use of a ground based "poor man's camera" to detect cloud and sky radiation in red, green, and blue with a high spatial resolution of 30 mm at 1km. The surface-based high resolution photography provides a new and interesting view of clouds. As the cloud fraction cannot be uniquely defined or measured, it depends on threshold and resolution. However as resolution decreases, cloud fraction tends to increase if the threshold is below the mean, and vice versa. Additionally cloud fractal dimension also depends on threshold. Therefore these findings raise concerns over the ability to characterize clouds by cloud fraction or fractal dimension. Our analysis indicate that Principal Component analysis may lead to a robust means of quantifying cloud contribution to radiance. The cloud images are analyzed in conjunction with a collocated CIMEL sky radiometer, Microwave Radiometer and LIDAR to determine homogeneity and heterogeneity. Additionally, MFRSR measurements are used to determine the cloud radiative properties as a validation tool to the results obtained from the other instruments and methods. The cloud properties to be further studied are aerosol- cloud interaction, cloud particle radii, and vertical homogeneity.

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Multiple Imputation of a Randomly Censored Covariate Improves Logistic Regression Analysis.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2016-01-01

Randomly censored covariates arise frequently in epidemiologic studies. The most commonly used methods, including complete case and single imputation or substitution, suffer from inefficiency and bias. They make strong parametric assumptions or they consider limit of detection censoring only. We employ multiple imputation, in conjunction with semi-parametric modeling of the censored covariate, to overcome these shortcomings and to facilitate robust estimation. We develop a multiple imputation approach for randomly censored covariates within the framework of a logistic regression model. We use the non-parametric estimate of the covariate distribution or the semiparametric Cox model estimate in the presence of additional covariates in the model. We evaluate this procedure in simulations, and compare its operating characteristics to those from the complete case analysis and a survival regression approach. We apply the procedures to an Alzheimer's study of the association between amyloid positivity and maternal age of onset of dementia. Multiple imputation achieves lower standard errors and higher power than the complete case approach under heavy and moderate censoring and is comparable under light censoring. The survival regression approach achieves the highest power among all procedures, but does not produce interpretable estimates of association. Multiple imputation offers a favorable alternative to complete case analysis and ad hoc substitution methods in the presence of randomly censored covariates within the framework of logistic regression.

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part 1; Improved Method and Uncertainties

NASA Technical Reports Server (NTRS)

Olson, William S.; Kummerow, Christian D.; Yang, Song; Petty, Grant W.; Tao, Wei-Kuo; Bell, Thomas L.; Braun, Scott A.; Wang, Yansen; Lang, Stephen E.; Johnson, Daniel E.;

Stochastic modeling for time series InSAR: with emphasis on atmospheric effects

NASA Astrophysics Data System (ADS)

Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai

2018-02-01

Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Some spectral approximation of one-dimensional fourth-order problems

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Maday, Yvon

1989-01-01

Some spectral type collocation method well suited for the approximation of fourth-order systems are proposed. The model problem is the biharmonic equation, in one and two dimensions when the boundary conditions are periodic in one direction. It is proved that the standard Gauss-Lobatto nodes are not the best choice for the collocation points. Then, a new set of nodes related to some generalized Gauss type quadrature formulas is proposed. Also provided is a complete analysis of these formulas including some new issues about the asymptotic behavior of the weights and we apply these results to the analysis of the collocation method.

Simplified Estimation and Testing in Unbalanced Repeated Measures Designs.

PubMed

Spiess, Martin; Jordan, Pascal; Wendt, Mike

2018-05-07

In this paper we propose a simple estimator for unbalanced repeated measures design models where each unit is observed at least once in each cell of the experimental design. The estimator does not require a model of the error covariance structure. Thus, circularity of the error covariance matrix and estimation of correlation parameters and variances are not necessary. Together with a weak assumption about the reason for the varying number of observations, the proposed estimator and its variance estimator are unbiased. As an alternative to confidence intervals based on the normality assumption, a bias-corrected and accelerated bootstrap technique is considered. We also propose the naive percentile bootstrap for Wald-type tests where the standard Wald test may break down when the number of observations is small relative to the number of parameters to be estimated. In a simulation study we illustrate the properties of the estimator and the bootstrap techniques to calculate confidence intervals and conduct hypothesis tests in small and large samples under normality and non-normality of the errors. The results imply that the simple estimator is only slightly less efficient than an estimator that correctly assumes a block structure of the error correlation matrix, a special case of which is an equi-correlation matrix. Application of the estimator and the bootstrap technique is illustrated using data from a task switch experiment based on an experimental within design with 32 cells and 33 participants.

Precision, Reliability, and Effect Size of Slope Variance in Latent Growth Curve Models: Implications for Statistical Power Analysis

PubMed Central

Brandmaier, Andreas M.; von Oertzen, Timo; Ghisletta, Paolo; Lindenberger, Ulman; Hertzog, Christopher

2018-01-01

Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the latent intercept and its covariance with the latent slope. We derive a new reliability index for LGCM slope variance—effective curve reliability (ECR)—by scaling slope variance against effective error. ECR is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study's sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs. PMID:29755377

A fast Monte Carlo EM algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with AGC

PubMed Central

Kang, Le; Carter, Randy; Darcy, Kathleen; Kauderer, James; Liao, Shu-Yuan

2013-01-01

In this article we use a latent class model (LCM) with prevalence modeled as a function of covariates to assess diagnostic test accuracy in situations where the true disease status is not observed, but observations on three or more conditionally independent diagnostic tests are available. A fast Monte Carlo EM (MCEM) algorithm with binary (disease) diagnostic data is implemented to estimate parameters of interest; namely, sensitivity, specificity, and prevalence of the disease as a function of covariates. To obtain standard errors for confidence interval construction of estimated parameters, the missing information principle is applied to adjust information matrix estimates. We compare the adjusted information matrix based standard error estimates with the bootstrap standard error estimates both obtained using the fast MCEM algorithm through an extensive Monte Carlo study. Simulation demonstrates that the adjusted information matrix approach estimates the standard error similarly with the bootstrap methods under certain scenarios. The bootstrap percentile intervals have satisfactory coverage probabilities. We then apply the LCM analysis to a real data set of 122 subjects from a Gynecologic Oncology Group (GOG) study of significant cervical lesion (S-CL) diagnosis in women with atypical glandular cells of undetermined significance (AGC) to compare the diagnostic accuracy of a histology-based evaluation, a CA-IX biomarker-based test and a human papillomavirus (HPV) DNA test. PMID:24163493

Asteroid approach covariance analysis for the Clementine mission

NASA Technical Reports Server (NTRS)

Ionasescu, Rodica; Sonnabend, David

1993-01-01

The Clementine mission is designed to test Strategic Defense Initiative Organization (SDIO) technology, the Brilliant Pebbles and Brilliant Eyes sensors, by mapping the moon surface and flying by the asteroid Geographos. The capability of two of the instruments available on board the spacecraft, the lidar (laser radar) and the UV/Visible camera is used in the covariance analysis to obtain the spacecraft delivery uncertainties at the asteroid. These uncertainties are due primarily to asteroid ephemeris uncertainties. On board optical navigation reduces the uncertainty in the knowledge of the spacecraft position in the direction perpendicular to the incoming asymptote to a one-sigma value of under 1 km, at the closest approach distance of 100 km. The uncertainty in the knowledge of the encounter time is about 0.1 seconds for a flyby velocity of 10.85 km/s. The magnitude of these uncertainties is due largely to Center Finding Errors (CFE). These systematic errors represent the accuracy expected in locating the center of the asteroid in the optical navigation images, in the absence of a topographic model for the asteroid. The direction of the incoming asymptote cannot be estimated accurately until minutes before the asteroid flyby, and correcting for it would require autonomous navigation. Orbit determination errors dominate over maneuver execution errors, and the final delivery accuracy attained is basically the orbit determination uncertainty before the final maneuver.

Recent advances in (soil moisture) triple collocation analysis

USDA-ARS?s Scientific Manuscript database

To date, triple collocation (TC) analysis is one of the most important methods for the global scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method....

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

A Comparative Usage-Based Approach to the Reduction of the Spanish and Portuguese Preposition "Para"

ERIC Educational Resources Information Center

Gradoville, Michael Stephen

2013-01-01

This study examines the frequency effect of two-word collocations involving "para" "to," "for" (e.g. "fui para," "para que") on the reduction of "para" to "pa" (in Spanish) and "pra" (in Portuguese). Collocation frequency effects demonstrate that language speakers…

BAO from Angular Clustering: Optimization and Mitigation of Theoretical Systematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crocce, M.; et al.

We study the theoretical systematics and optimize the methodology in Baryon Acoustic Oscillations (BAO) detections using the angular correlation function with tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The MLE method yields the least bias in the fit results (bias/spreadmore » $$\\sim 0.02$$) and the error bar derived is the closest to the Gaussian results (1% from 68% Gaussian expectation). When there is mismatch between the template and the data either due to incorrect fiducial cosmology or photo-$z$ error, the MLE again gives the least-biased results. The BAO angular shift that is estimated based on the sound horizon and the angular diameter distance agree with the numerical fit. Various analysis choices are further tested: the number of redshift bins, cross-correlations, and angular binning. We propose two methods to correct the mock covariance when the final sample properties are slightly different from those used to create the mock. We show that the sample changes can be accommodated with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because the number of free parameters is substantially reduced [$p$ parameters versus $p(p+1)/2$ from direct measurement].« less

Effects of Increasing Drag on Conjunction Assessment

NASA Technical Reports Server (NTRS)

Frigm, Ryan Clayton; McKinley, David P.

2010-01-01

Conjunction Assessment Risk Analysis relies heavily on the computation of the Probability of Collision (Pc) and the understanding of the sensitivity of this calculation to the position errors as defined by the covariance. In Low Earth Orbit (LEO), covariance is predominantly driven by perturbations due to atmospheric drag. This paper describes the effects of increasing atmospheric drag through Solar Cycle 24 on Pc calculations. The process of determining these effects is found through analyzing solar flux predictions on Energy Dissipation Rate (EDR), historical relationship between EDR and covariance, and the sensitivity of Pc to covariance. It is discovered that while all LEO satellites will be affected by the increase in solar activity, the relative effect is more significant in the LEO regime around 700 kilometers in altitude compared to 400 kilometers. Furthermore, it is shown that higher Pc values can be expected at larger close approach miss distances. Understanding these counter-intuitive results is important to setting Owner/Operator expectations concerning conjunctions as solar maximum approaches.

Modeling of correlated data with informative cluster sizes: An evaluation of joint modeling and within-cluster resampling approaches.

PubMed

Zhang, Bo; Liu, Wei; Zhang, Zhiwei; Qu, Yanping; Chen, Zhen; Albert, Paul S

2017-08-01

Joint modeling and within-cluster resampling are two approaches that are used for analyzing correlated data with informative cluster sizes. Motivated by a developmental toxicity study, we examined the performances and validity of these two approaches in testing covariate effects in generalized linear mixed-effects models. We show that the joint modeling approach is robust to the misspecification of cluster size models in terms of Type I and Type II errors when the corresponding covariates are not included in the random effects structure; otherwise, statistical tests may be affected. We also evaluate the performance of the within-cluster resampling procedure and thoroughly investigate the validity of it in modeling correlated data with informative cluster sizes. We show that within-cluster resampling is a valid alternative to joint modeling for cluster-specific covariates, but it is invalid for time-dependent covariates. The two methods are applied to a developmental toxicity study that investigated the effect of exposure to diethylene glycol dimethyl ether.

Evaluating Light Rain Drop Size Estimates from Multiwavelength Micropulse Lidar Network Profiling

NASA Technical Reports Server (NTRS)

Lolli, Simone; Welton, Ellsworth J.; Campbell, James R.

2013-01-01

This paper investigates multiwavelength retrievals of median equivolumetric drop diameter D(sub 0) suitable for drizzle and light rain, through collocated 355-/527-nm Micropulse Lidar Network (MPLNET) observations collected during precipitation occurring 9 May 2012 at the Goddard Space Flight Center (GSFC) project site. By applying a previously developed retrieval technique for infrared bands, the method exploits the differential backscatter by liquid water at 355 and 527 nm for water drops larger than approximately 50 micrometers. In the absence of molecular and aerosol scattering and neglecting any transmission losses, the ratio of the backscattering profiles at the two wavelengths (355 and 527 nm), measured from light rain below the cloud melting layer, can be described as a color ratio, which is directly related to D(sub 0). The uncertainty associated with this method is related to the unknown shape of the drop size spectrum and to the measurement error. Molecular and aerosol scattering contributions and relative transmission losses due to the various atmospheric constituents should be evaluated to derive D(sub 0) from the observed color ratio profiles. This process is responsible for increasing the uncertainty in the retrieval. Multiple scattering, especially for UV lidar, is another source of error, but it exhibits lower overall uncertainty with respect to other identified error sources. It is found that the total error upper limit on D(sub 0) approaches 50%. The impact of this retrieval for long-term MPLNET monitoring and its global data archive is discussed.

Multiple Flux Footprints, Flux Divergences and Boundary Layer Mixing Ratios: Studies of Ecosystem-Atmosphere CO2 Exchange Using the WLEF Tall Tower.

NASA Astrophysics Data System (ADS)

Davis, K. J.; Bakwin, P. S.; Yi, C.; Cook, B. D.; Wang, W.; Denning, A. S.; Teclaw, R.; Isebrands, J. G.

2001-05-01

Long-term, tower-based measurements using the eddy-covariance method have revealed a wealth of detail about the temporal dynamics of netecosystem-atmosphere exchange (NEE) of CO2. The data also provide a measure of the annual net CO2 exchange. The area represented by these flux measurements, however, is limited, and doubts remain about possible systematic errors that may bias the annual net exchange measurements. Flux and mixing ratio measurements conducted at the WLEF tall tower as part of the Chequamegon Ecosystem-Atmosphere Study (ChEAS) allow for unique assessment of the uncertainties in NEE of CO2. The synergy between flux and mixing ratio observations shows the potential for comparing inverse and eddy-covariance methods of estimating NEE of CO2. Such comparisons may strengthen confidence in both results and begin to bridge the huge gap in spatial scales (at least 3 orders of magnitude) between continental or hemispheric scale inverse studies and kilometer-scale eddy covariance flux measurements. Data from WLEF and Willow Creek, another ChEAS tower, are used to estimate random and systematic errors in NEE of CO2. Random uncertainty in seasonal exchange rates and the annual integrated NEE, including both turbulent sampling errors and variability in enviromental conditions, is small. Systematic errors are identified by examining changes in flux as a function of atmospheric stability and wind direction, and by comparing the multiple level flux measurements on the WLEF tower. Nighttime drainage is modest but evident. Systematic horizontal advection occurs during the morning turbulence transition. The potential total systematic error appears to be larger than random uncertainty, but still modest. The total systematic error, however, is difficult to assess. It appears that the WLEF region ecosystems were a small net sink of CO2 in 1997. It is clear that the summer uptake rate at WLEF is much smaller than that at most deciduous forest sites, including the nearby Willow Creek site. The WLEF tower also allows us to study the potential for monitoring continental CO2 mixing ratios from tower sites. Despite concerns about the proximity to ecosystem sources and sinks, it is clear that boundary layer CO2 mixing ratios can be monitored using typical surface layer towers. Seasonal and annual land-ocean mixing ratio gradients are readily detectable, providing the motivation for a flux-tower based mixing ratio observation network that could greatly improve the accuracy of inversion-based estimates of NEE of CO2, and enable inversions to be applied on smaller temporal and spatial scales. Results from the WLEF tower illustrate the degree to which local flux measurements represent interannual, seasonal and synoptic CO2 mixing ratio trends. This coherence between fluxes and mixing ratios serves to "regionalize" the eddy-covariance based local NEE observations.

Reports 10, The Yugoslav Serbo-Croatian-English Contrastive Project.

ERIC Educational Resources Information Center

Filipovic, Rudolf

The tenth volume in this series contains five articles dealing with various aspects of Serbo-Croatian-English contrastive analysis. They are: "The Infinitive as Subject in English and Serbo-Croatian," by Ljiljana Bibovic; "The Contrastive Analysis of Collocations: Collocational Ranges of "Make" and "Take" with Nouns and Their Serbo-Croatian…

No Silver Bullet: L2 Collocation Instruction in an Advanced Spanish Classroom

ERIC Educational Resources Information Center

Jensen, Eric Carl

2017-01-01

Many contemporary second language (L2) instructional materials feature collocation exercises; however, few studies have verified their effectiveness (Boers, Demecheleer, Coxhead, & Webb, 2014) or whether these exercises can be utilized for target languages beyond English (Higueras García, 2017). This study addresses these issues by…

Assessing Team Learning in Technology-Mediated Collaboration: An Experimental Study

ERIC Educational Resources Information Center

Andres, Hayward P.; Akan, Obasi H.

2010-01-01

This study examined the effects of collaboration mode (collocated versus non-collocated videoconferencing-mediated) on team learning and team interaction quality in a team-based problem solving context. Situated learning theory and the theory of affordances are used to provide a framework that describes how technology-mediated collaboration…

Collocation in Regional Development--The Peel Education and TAFE Response.

ERIC Educational Resources Information Center

Goff, Malcolm H.; Nevard, Jennifer

The collocation of services in regional Western Australia (WA) is an important strand of WA's regional development policy. The initiative is intended to foster working relationships among stakeholder groups with a view toward ensuring that regional WA communities have access to quality services. Clustering compatible services in smaller…

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Code of Federal Regulations, 2012 CFR

2012-10-01

... unbundled network element if and only if the primary purpose and function of the equipment, as the... nondiscriminatory access to that unbundled network element, including any of its features, functions, or... must be a logical nexus between the additional functions the equipment would perform and the...

Testing ESL Learners' Knowledge of Collocations.

ERIC Educational Resources Information Center

Bonk, William J.

This study reports on the development, administration, and analysis of a test of collocational knowledge for English-as-a-Second-Language (ESL) learners of a wide range of proficiency levels. Through native speaker item validation and pilot testing, three subtests were developed and administered to 98 ESL learners of low-intermediate to advanced…

Improving control and estimation for distributed parameter systems utilizing mobile actuator-sensor network.

PubMed

Mu, Wenying; Cui, Baotong; Li, Wen; Jiang, Zhengxian

2014-07-01

This paper proposes a scheme for non-collocated moving actuating and sensing devices which is unitized for improving performance in distributed parameter systems. By Lyapunov stability theorem, each moving actuator/sensor agent velocity is obtained. To enhance state estimation of a spatially distributes process, two kinds of filters with consensus terms which penalize the disagreement of the estimates are considered. Both filters can result in the well-posedness of the collective dynamics of state errors and can converge to the plant state. Numerical simulations demonstrate that the effectiveness of such a moving actuator-sensor network in enhancing system performance and the consensus filters converge faster to the plant state when consensus terms are included. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Localization of short-range acoustic and seismic wideband sources: Algorithms and experiments

NASA Astrophysics Data System (ADS)

Stafsudd, J. Z.; Asgari, S.; Hudson, R.; Yao, K.; Taciroglu, E.

2008-04-01

We consider the determination of the location (source localization) of a disturbance source which emits acoustic and/or seismic signals. We devise an enhanced approximate maximum-likelihood (AML) algorithm to process data collected at acoustic sensors (microphones) belonging to an array of, non-collocated but otherwise identical, sensors. The approximate maximum-likelihood algorithm exploits the time-delay-of-arrival of acoustic signals at different sensors, and yields the source location. For processing the seismic signals, we investigate two distinct algorithms, both of which process data collected at a single measurement station comprising a triaxial accelerometer, to determine direction-of-arrival. The direction-of-arrivals determined at each sensor station are then combined using a weighted least-squares approach for source localization. The first of the direction-of-arrival estimation algorithms is based on the spectral decomposition of the covariance matrix, while the second is based on surface wave analysis. Both of the seismic source localization algorithms have their roots in seismology; and covariance matrix analysis had been successfully employed in applications where the source and the sensors (array) are typically separated by planetary distances (i.e., hundreds to thousands of kilometers). Here, we focus on very-short distances (e.g., less than one hundred meters) instead, with an outlook to applications in multi-modal surveillance, including target detection, tracking, and zone intrusion. We demonstrate the utility of the aforementioned algorithms through a series of open-field tests wherein we successfully localize wideband acoustic and/or seismic sources. We also investigate a basic strategy for fusion of results yielded by acoustic and seismic arrays.

Water, Energy, and Carbon with Artificial Neural Networks (WECANN): a statistically based estimate of global surface turbulent fluxes and gross primary productivity using solar-induced fluorescence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alemohammad, Seyed Hamed; Fang, Bin; Konings, Alexandra G.

A new global estimate of surface turbulent fluxes, latent heat flux (LE) and sensible heat flux ( H), and gross primary production (GPP) is developed using a machine learning approach informed by novel remotely sensed solar-induced fluorescence (SIF) and other radiative and meteorological variables. This is the first study to jointly retrieve LE, H, and GPP using SIF observations. The approach uses an artificial neural network (ANN) with a target dataset generated from three independent data sources, weighted based on a triple collocation (TC) algorithm. The new retrieval, named Water, Energy, and Carbon with Artificial Neural Networks (WECANN), provides estimatesmore » of LE, H, and GPP from 2007 to 2015 at 1° × 1° spatial resolution and at monthly time resolution. The quality of ANN training is assessed using the target data, and the WECANN retrievals are evaluated using eddy covariance tower estimates from the FLUXNET network across various climates and conditions. When compared to eddy covariance estimates, WECANN typically outperforms other products, particularly for sensible and latent heat fluxes. Analyzing WECANN retrievals across three extreme drought and heat wave events demonstrates the capability of the retrievals to capture the extent of these events. Uncertainty estimates of the retrievals are analyzed and the interannual variability in average global and regional fluxes shows the impact of distinct climatic events – such as the 2015 El Niño – on surface turbulent fluxes and GPP.« less

Water, Energy, and Carbon with Artificial Neural Networks (WECANN): a statistically based estimate of global surface turbulent fluxes and gross primary productivity using solar-induced fluorescence

DOE PAGES

Alemohammad, Seyed Hamed; Fang, Bin; Konings, Alexandra G.; ...

2017-09-20

A new global estimate of surface turbulent fluxes, latent heat flux (LE) and sensible heat flux ( H), and gross primary production (GPP) is developed using a machine learning approach informed by novel remotely sensed solar-induced fluorescence (SIF) and other radiative and meteorological variables. This is the first study to jointly retrieve LE, H, and GPP using SIF observations. The approach uses an artificial neural network (ANN) with a target dataset generated from three independent data sources, weighted based on a triple collocation (TC) algorithm. The new retrieval, named Water, Energy, and Carbon with Artificial Neural Networks (WECANN), provides estimatesmore » of LE, H, and GPP from 2007 to 2015 at 1° × 1° spatial resolution and at monthly time resolution. The quality of ANN training is assessed using the target data, and the WECANN retrievals are evaluated using eddy covariance tower estimates from the FLUXNET network across various climates and conditions. When compared to eddy covariance estimates, WECANN typically outperforms other products, particularly for sensible and latent heat fluxes. Analyzing WECANN retrievals across three extreme drought and heat wave events demonstrates the capability of the retrievals to capture the extent of these events. Uncertainty estimates of the retrievals are analyzed and the interannual variability in average global and regional fluxes shows the impact of distinct climatic events – such as the 2015 El Niño – on surface turbulent fluxes and GPP.« less

Eddy Covariance Method: Overview of General Guidelines and Conventional Workflow

NASA Astrophysics Data System (ADS)

Burba, G. G.; Anderson, D. J.; Amen, J. L.

2007-12-01

Atmospheric flux measurements are widely used to estimate water, heat, carbon dioxide and trace gas exchange between the ecosystem and the atmosphere. The Eddy Covariance method is one of the most direct, defensible ways to measure and calculate turbulent fluxes within the atmospheric boundary layer. However, the method is mathematically complex, and requires significant care to set up and process data. These reasons may be why the method is currently used predominantly by micrometeorologists. Modern instruments and software can potentially expand the use of this method beyond micrometeorology and prove valuable for plant physiology, hydrology, biology, ecology, entomology, and other non-micrometeorological areas of research. The main challenge of the method for a non-expert is the complexity of system design, implementation, and processing of the large volume of data. In the past several years, efforts of the flux networks (e.g., FluxNet, Ameriflux, CarboEurope, Fluxnet-Canada, Asiaflux, etc.) have led to noticeable progress in unification of the terminology and general standardization of processing steps. The methodology itself, however, is difficult to unify, because various experimental sites and different purposes of studies dictate different treatments, and site-, measurement- and purpose-specific approaches. Here we present an overview of theory and typical workflow of the Eddy Covariance method in a format specifically designed to (i) familiarize a non-expert with general principles, requirements, applications, and processing steps of the conventional Eddy Covariance technique, (ii) to assist in further understanding the method through more advanced references such as textbooks, network guidelines and journal papers, (iii) to help technicians, students and new researchers in the field deployment of the Eddy Covariance method, and (iv) to assist in its use beyond micrometeorology. The overview is based, to a large degree, on the frequently asked questions received from new users of the Eddy Covariance method and relevant instrumentation, and employs non-technical language to be of practical use to those new to this field. Information is provided on theory of the method (including state of methodology, basic derivations, practical formulations, major assumptions and sources of errors, error treatment, and use in non- traditional terrains), practical workflow (e.g., experimental design, implementation, data processing, and quality control), alternative methods and applications, and the most frequently overlooked details of the measurements. References and access to an extended 141-page Eddy Covariance Guideline in three electronic formats are also provided.

Application of the ORCHIDEE global vegetation model to evaluate biomass and soil carbon stocks of Qinghai-Tibetan grasslands

NASA Astrophysics Data System (ADS)

Tan, Kun; Ciais, Philippe; Piao, Shilong; Wu, Xiaopu; Tang, Yanhong; Vuichard, Nicolas; Liang, Shuang; Fang, Jingyun

2010-03-01

The cold grasslands of the Qinghai-Tibetan Plateau form a globally significant biome, which represents 6% of the world's grasslands and 44% of China's grasslands. Yet little is known about carbon cycling in this biome. In this study, we calibrated and applied a process-based ecosystem model called Organizing Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) to estimate the C fluxes and stocks of these grasslands. First, the parameterizations of ORCHIDEE were improved and calibrated against multiple time-scale and spatial-scale observations of (1) eddy-covariance fluxes of CO2 above one alpine meadow site; (2) soil temperature collocated with 30 meteorological stations; (3) satellite leaf area index (LAI) data collocated with the meteorological stations; and (4) soil organic carbon (SOC) density profiles from China's Second National Soil Survey. The extensive SOC survey data were used to extrapolate local fluxes to the entire grassland biome. After calibration, we show that ORCHIDEE can successfully capture the seasonal variation of net ecosystem exchange (NEE), as well as the LAI and SOC spatial distribution. We applied the calibrated model to estimate 0.3 Pg C yr-1 (1 Pg = 1015 g) of total annual net primary productivity (NPP), 0.4 Pg C of vegetation total biomass (aboveground and belowground), and 12 Pg C of SOC stocks for Qinghai-Tibetan grasslands covering an area of 1.4 × 106 km2. The mean annual NPP, vegetation biomass, and soil carbon stocks decrease from the southeast to the northwest, along with precipitation gradients. Our results also suggest that in response to an increase of temperature by 2°C, approximately 10% of current SOC stocks in Qinghai-Tibetan grasslands could be lost, even though NPP increases by about 9%. This result implies that Qinghai-Tibetan grasslands may be a vulnerable component of the terrestrial carbon cycle to future climate warming.

Matching on the Disease Risk Score in Comparative Effectiveness Research of New Treatments

PubMed Central

Wyss, Richard; Ellis, Alan R.; Brookhart, M. Alan; Funk, Michele Jonsson; Girman, Cynthia J.; Simpson, Ross J.; Stürmer, Til

2016-01-01

Purpose We use simulations and an empirical example to evaluate the performance of disease risk score (DRS) matching compared with propensity score (PS) matching when controlling large numbers of covariates in settings involving newly introduced treatments. Methods We simulated a dichotomous treatment, a dichotomous outcome, and 100 baseline covariates that included both continuous and dichotomous random variables. For the empirical example, we evaluated the comparative effectiveness of dabigatran versus warfarin in preventing combined ischemic stroke and all-cause mortality. We matched treatment groups on a historically estimated DRS and again on the PS. We controlled for a high-dimensional set of covariates using 20% and 1% samples of Medicare claims data from October 2010 through December 2012. Results In simulations, matching on the DRS versus the PS generally yielded matches for more treated individuals and improved precision of the effect estimate. For the empirical example, PS and DRS matching in the 20% sample resulted in similar hazard ratios (0.88 and 0.87) and standard errors (0.04 for both methods). In the 1% sample, PS matching resulted in matches for only 92.0% of the treated population and a hazard ratio and standard error of 0.89 and 0.19, respectively, while DRS matching resulted in matches for 98.5% and a hazard ratio and standard error of 0.85 and 0.16, respectively. Conclusions When PS distributions are separated, DRS matching can improve the precision of effect estimates and allow researchers to evaluate the treatment effect in a larger proportion of the treated population. However, accurately modeling the DRS can be challenging compared with the PS. PMID:26112690