Lumme, K.; Bowell, E.
The multiple-scattering theory of K. Lumme and E. Bowell (1981) was criticized by B. Hapke by stating, in particular, that energy is not conserved. It is shown that Hapke's treatment is, in this respect, inferior to that of Lumme and Bowell, and itself violates the principal concepts of radiative transfer theory. Hapke's additinal claim that, in Lumme and Bowell's work, the reflectance tends to zero at the limb is also refuted. Comment is made on the deduction of surface physical properties by modeling photometric observations.
Pang, K.; Ajello, J. M.; Lumme, K.; Bowell, E.
The Lumme-Bowell (1981) theory has been used to interpret the integrated phase curves of Callisto and Ganymede, and it is noted that while the theory explains the brightness angles of these satellites up to about 80 deg solar phase angle, the observed brightness drops off at larger angles more rapidly than predicted. It is suggested that this discrepancy is due to the fact that single regolith particles must have phase functions which are much more elongated in the forward or backward scattering directions than is allowed for by the Lumme-Bowell theory. The hemispheric asymmetry in Callisto's surface texture can be explained by invoking the formation of an ice film on the trailing side, consistent with Voyager detailed photometry and thermometry of Callisto.
Karttunen, H.; Bowell, E.
Light curves and phase curves have been computed for various asteroid models using the Lumme-Bowell (1981) scattering law. The effects of the scattering parameters on light curves were found to be almost negligible for homogeneous surfaces. The effects on phase curves were more distinct, but changing any of the scattering parameters affects the phase curves in a very similar way, making it impossible to find a unique set of parameter values corresponding to a given phase curve. Light curve amplitudes, on the other hand, depend very strongly on body shape. At least in the case of a triaxial ellipsoid it is possible to determine the axial ratios. Some observed irregularities of light curves can also be modelled easily, but the uniqueness of such models is far from obvious.
Zhang, Hao; Voss, Kenneth J.
To understand the connection between single-particle optics and the optics of a closely packed surface, controlled laboratory measurements of bidirectional reflectance distribution functions on layers of polymer and glass spheres are carried out. The measurements are compared with predictions from five radiative-transfer models; the Hapke's models, the Lumme-Bowell model, the BRF algorithm of Mishchenko et al., and the discrete ordinate radiative transfer. It is found that models of strict numerical radiative-transfer equations (RTEs) predict measurements well in some regions but have errors in both forward-and backward-scattering directions. The improved Hapke's model, although it has an anisotropic multiple-scattering term, still produces considerable errors compared with the strict RTE. The difference can be attributed to the exclusion of a diffraction contribution in the Hapke model.
Peltoniemi, J. I.; Lumme, K.; Irvine, W. M.
Analysis of disk resolved images of Phobos obtained by the Phobos 2 spacecraft makes it possible to study the surface scattering law and albedo variations. Low phase angle images reveal variations in local geometric albedo about 10 percent, with a correlation length of about 1 km. The scattering law is reasonably well matched by the recently proposed LPI (Lumme et al., 1990) model, which makes it possible to deduce a small scale (1 mm) surface roughness (0.5), defined here as the rms tangent of the local surface normal relative to the mean surface normal in the Duxbury (1991) model of Phobos. This value is very close to what has been found for Mercury and the moon.
Peltoniemi, J I; Lumme, K; Irvine, W M
Analysis of disk resolved images of Phobos obtained by the Phobos 2 spacecraft allows us to study the surface scattering law and albedo variations. From low phase angle images we find variations in local geometric albedo approximately 10%, with a correlation length approximately 1km. The scattering law is reasonably well matched by the recent proposed LPI (Lumme et al. 1990a) model, which allows us to deduce a small scale (approximately 1 mm) surface roughness (approximately 0.5), defined here as the rms. tangent of the local surface normal relative to the mean surface normal in the Duxbury (1991) model of Phobos. This value is very close to what has been found for Mercury and the Moon. PMID:11538497
James, P. B.; Malolepszy, K. M.; Martin, L. J.
Published observational data on the seasonal recession of the south polar cap on Mars (covering the period 1903-1977) are compiled in tables and graphs and analyzed statistically. The basic data set (photographic observations obtained at Lowell Observatory) of Fischbacher et al. (1960) and James and Lumme (1982) and the reduction procedures described by Baum and Martin (1973) are employed, and Viking data from 1977 are used for comparison; the early onset (relative to the mean) of the 1956 recession is characterized in detail. A list of photographically documented large dust storms is provided, and it is suggested that in years with early spring storms, recession may be slower than in years without such storms.
The role of the Indian and Pacific sea surface temperature (SST) variability in the intraseasonal and interannual variability of the Indian summer monsoon rainfall is examined by performing a set of regionally coupled experiments with the Climate Forecast System (CFS), the latest and operational coupled general circulation model (CGCM) developed at the National Centers for Environmental Prediction (NCEP). The intraseasonal and interannual variability are studied by isolating oscillatory and persistent signals, respectively, from the unfiltered daily rainfall anomalies using multi-channel singular spectrum analysis (MSSA). This technique identifies nonlinear oscillations, its variance and period without preconditioning the data with a filter and also helps to separate the intraseasonal and low frequency climate signals from the daily variability. It is found that, although the model has large amount of daily variance in rainfall, the combined variance of coherently propagating intraseasonal oscillations is only about 7% while the corresponding number in the observations is 11%. The model has three intraseasonal oscillations with periods around 106, 57 and 30 days. The 106-day mode has a characteristic large-scale pattern extending from the Arabian Sea to the West Pacific with northward and eastward propagations. These features are similar to the northeastward propagating 45-day mode found in the observations except for the longer period. The 57-day mode is more dominant in the region, 60°E-100°E and is strictly northward-propagating. The 30-day mode appears to be equivalent to the northwestward propagating oscillation in the observations. The dominant low frequency persistent signal in the region is due to the El Nino-Southern Oscillation (ENSO). The ENSO-related rainfall anomalies, however fail to penetrate into the Extended Indian Monsoon Rainfall (EIMR) region, and therefore, the ENSO-monsoon relationship in the model is weak. Regionally coupled simulations of
Controlled laboratory BRDF and transmission measurements on layers of polymer and glass spheres have been carried out to investigate the connection between single particle optics and the optics of a packed surface. The measurements show that despite being closely packed, significant features of single scattering, such as the rainbow peaks, are preserved even in aggregated sphere layers. The measurements have been compared to 5 radiative transfer model predictions: the Hapke's model and its improved version, the Lumme-Bowell model, Mishchenko et al.'s BRF algorithm and DISORT. It has been found that strict numerical RTE models predict the measurements well in some regions, but have errors in both forward and backward scattering directions. The discrepancies have been attributed to the non-ideal factors such as internal inhomogeneity and surface roughness and may be corrected using Lumme-Bowell's roughness correction factor for oblique incident light. The inadequacy of the semi-empirical models can be partly attributed to the exclusion of a diffraction contribution in the models. In-situ BRDF measurements on submerged sediments with grain sizes ranging from 300 mum to over 1000 mum have been carried out. For normally illuminated small grain size samples the BRDF was nearly Lambertian, but samples with larger grain sizes are less Lambertian, with the BRDF decreasing with increasing view angles. Under oblique incident angles the samples become increasingly non-Lambertian; the dominant feature in the BRDF is enhanced backscattering. An empirical model is presented for each sediment type which represents the data within the standard deviation of the sample variation. This model is well behaved at angles out to 90°, and thus can be incorporated into the radiative transfer models to improve the light field predictions in shallow water. The BRDF of both dry and wet ooid sand layers with different particle size distributions and layer thicknesses on a reflecting mirror have
Morozhenko, Alexandr; Vidmachenko, Anatolij; Kostogryz, Nadiia
Typically, to analyze the data of the phase dependence of brightness atmosphereless celestial bodies one use some modification of the shadow mechanism involving the coherent mechanism. There are several modification of B.Hapke  model divided into two groups by the number of unknown parameters: the first one with 4 parameters [3,4] and the second one with up to 10 unknown parameters  providing a good agreement of observations and calculations in several wavelengths. However, they are complicated by analysing of the colorindex C(α) dependence and photometric contrast of details with phase K(α) and on the disk (μ o = cos i). We have got good agreement between observed and calculated values of C(α) = U(α)-I(α), K(α), K(muo) for Moon and Mars with a minimum number of unknown parameters . We used an empirical dependence of single scattering albedo (ω) and particle semi-transparency(æ): æ = (1-ω)n. Assuming that [χ (0°)/χ(5°)] = χ (5°)/χ (0°)], where χ(α) is scattering function, using the phase dependence of brightness and opposition effect in a single wavelength, we have defined ω,χ(α),g (particle packing factor), and the first term expansion of χ(α) in a series of Legendre polynomials x1. Good agreement between calculated and observed data of C(α) = U(α)-I(α) for the light and dark parts of the lunar surface and the integral disk reached at n ~ 0,25, g = 0,4 (porosity 0,91), x1 = -0,93, ω = 0,137 at λ = 359nm and 0,394 at λ = 1064nm;, for Mars with n ~ 0,25,g = 0,6 (porosity 0,84), x1 ~ 0, ω = 0,210 at λ = 359nm and ω = 0,784 at λ = 730nm. 1. Bowell E., Hapke B., Domingue D., Lumme K., et al. Applications of photometric models to asteroids, in Asteroids II. Tucson: Univ. Arizona Press. p.524-556. (1989) 2. Hapke B. A theoretical function for the lunar surface, J.Geophys.Res. 68, No.15., 4571-4586(1963). 3. Irwine W. M., The shadowing effect in diffuse reflection, J.Geophys.Res. 71,No.12, 2931-2937(1966). 4. Morozhenko A. V
Muinonen, K.; Wilkman, O.; Wang, X.; Cellino, A.
The rotational period, pole orientation, and convex three-dimensional shape of an asteroid can be derived from photometric lightcurves observed in a number of apparitions with varying illumination and observation geometries (e.g., Kaasalainen et al. 2001, Torppa et al. 2008, Durech et al. 2009). It is customary to estimate the rotational period with a simplified shape model and a small number of trial pole orientations. Once the period is available, the pole orientation can be refined with a general convex shape model represented by the spherical harmonics expansion for the Gaussian surface density. Once the Gaussian surface density is available, the actual convex shape is constructed as a solution of the Minkowski problem. We focus on the initial derivation of the rotational period and pole orientation with the help of the Lommel-Seeliger ellipsoid (LS-ellipsoid), a triaxial ellipsoid with a Lommel-Seeliger surface scattering law. The disk-integrated photometric brightness for the LS-ellipsoid is available in a closed form (Muinonen and Lumme, in preparation), warranting efficient direct computation of lightcurves. With modern computers and the LS-ellipsoid, the rotation period, pole orientation, and ellipsoidal shape can be derived, in principle, simultaneously (see Cellino et al., present meeting). However, here we choose to proceed systematically as follows. First, the rotation period is scanned systematically across its relevant range with a resolution of P_0^2/2T dictated by a tentative period estimate P_0 and the time interval spanned by the photometric data T. This is typically carried out for a small number of pole orientations distributed uniformly on a unit sphere. For each pole orientation, the ellipsoid pole orientation, rotational phase, and axial ratios are optimized with the help of the Nelder-Mead downhill simplex method. Although the shape optimization can suffer from getting stuck in local minima, overall, the rotation period is fairly accurately