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NASA NTRS2023

New Mie Scattering Diffuse Targets Development and Characterization

Earth science remote sensing observations require the detection and measurement of light originating from bright targets, such as clouds, and darker targets, such as an open ocean. This requirement drives the need to design, develop, and characterize improved calibration targets in support of current and future NASA instruments. New diffuse targets to be used as spectral albedo calibration standards were developed and characterized. The new targets based on fused silica or/and pressed and sintered Polytetrafluoroethylene (PTFE) were developed to be Earth scene specific. The various reflectance levels are achieved by modifying the material parameters, thickness, and surface finish. The new targets were characterized in laboratory and simulated space environments. We acquired high accuracy reflectance and transmittance data using a precision optical scatterometer and spectrophotometer located in the NASA Goddard Space Flight Center (GSFC) Diffuser Calibration Lab. The Total hemispherical reflectance (THR) and Bidirectional Reflectance Distribution Function (BRDF) were measured over the range of solar incident and scattered elevation and azimuthal angles typically realized on orbit by remote sensing instruments. We intend to space certify the new calibration targets after concluding on-orbit testing on the International Space Stations (ISS) scheduled for the second half of 2023.

Georgi Georgiev↗
NASA NTRS1994

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Schluessel, G.↗
NASA NTRS1985

Bidirectional Reflectance Modeling of Non-homogeneous Plant Canopies

The objective of this research is to develop a 3-dimensional radiative transfer model for predicting the bidirectional reflectance distribution function (BRDF) for heterogeneous vegetation canopies. The model (named BIGAR) considers the angular distribution of leaves, leaf area index, the location and size of individual subcanopies such as widely spaced rows or trees, spectral and directional properties of leaves, multiple scattering, solar position and sky condition, and characteristics of the soil. The model relates canopy biophysical attributes to down-looking radiation measurements for nadir and off-nadir viewing angles. Therefore, inversion of this model, which is difficult but practical should provide surface biophysical pattern; a fundamental goal of remote sensing. Such a model also will help to evaluate atmospheric limitations to satellite remote sensing by providing a good surface boundary condition for many different kinds of canopies. Furthermore, this model can relate estimates of nadir reflectance, which is approximated by most satellites, to hemispherical reflectance, which is necessary in the energy budget of vegetated surfaces.

Norman, J. M.↗
NASA NTRS2017

Direct Radiative Effect of Aerosols Based on PARASOL and OMI Satellite Observations

Accurate portrayal of the aerosol characteristics is crucial to determine aerosol contribution to the Earth's radiation budget. We employ novel satellite retrievals to make a new measurement-based estimate of the shortwave direct radiative effect of aerosols (DREA), both over land and ocean. Global satellite measurements of aerosol optical depth, single-scattering albedo (SSA), and phase function from PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) are used in synergy with OMI (Ozone Monitoring Instrument) SSA. Aerosol information is combined with land-surface bidirectional reflectance distribution function and cloud characteristics from MODIS (Moderate Resolution Imaging Spectroradiometer) satellite products. Eventual gaps in observations are filled with the state-of-the-art global aerosol model ECHAM5-HAM2. It is found that our estimate of DREA is largely insensitive to model choice. Radiative transfer calculations show that DREA at top-of-atmosphere is −4.6 +/- 1.5 W/sq m for cloud-free and −2.1 +/- 0.7 W/sq m for all-sky conditions, during year 2006. These fluxes are consistent with, albeit generally less negative over ocean than, former assessments. Unlike previous studies, our estimate is constrained by retrievals of global coverage SSA, which may justify different DREA values. Remarkable consistency is found in comparison with DREA based on CERES (Clouds and the Earth's Radiant Energy System) and MODIS observations.

Globalsatellite measurements↗
NASA NTRSDate not supplied

Development of An Improved BRDF Hotspot Model and its Use in VLIDORT to Study the Impact of Atmospheric Scattering on Hotspot Directional Signatures in the Atmosphere

The term “hotspot” refers to the sharp increase of reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick-LiSparse-Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan- Bréon but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately. To improve its use in atmospheric radiative transfer (RT) model simulations, in this paper we have developed a modified version based on the Maignan-Bréon’s hotspot BRDF model that converge much faster numerically, making it more practical for use in RT models that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures. Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), we found that reasonable TOA hotspot accuracy can be obtained with just 23 Fourier terms for clear atmospheres, and 63 Fourier terms for atmospheres with aerosol scattering. One advantage of this modified model is that the new hotspot model agrees very well with the original RossThick model away the hotspot region, making it is very convenient to use in the condition with and without hotspot in applications. This model can calculate the amplitude of hot spot accurately, and has been added in the most recent version of VLIDORT. However, there are some difference of this modified model with the original model for scattering angle close the hot spot, and it may not be appropriate for those who need an exact representation of the hot spot angular signature close to hot spot.

Xiaozhen (Shawn) Xiong↗
NASA NTRS1981

Bidirectional reflectance spectroscopy. II - Experiments and observations

Aspects of the theoretical bidirectional reflectance expression derived by Hapke (1981) are studied experimentally, and it is shown that the expression describes satisfactorily the measured angular scattering and spectral properties of a cobalt glass powder in which the two properties vary greatly with wavelength. The theoretical reflectance function also describes measured distributions of intensity across the surfaces of planets, except near the sunlit limb, where the macroscopic roughness influences the brightness.

Hapke, B.↗
NASA NTRS2020

The AERONET Version 3 Aerosol Retrieval Algorithm, Associated Uncertainties and Comparisons to Version 2

The Aerosol Robotic Network (AERONET) Version 3 (V3) aerosol retrieval algorithm is described, which is based on the Version 2 (V2) algorithm with numerous updates. Comparisons of V3 aerosol retrievals to those of V2 are presented, along with a new approach to estimate uncertainties in many of the retrieved aerosol parameters. Changes in the V3 aerosol retrieval algorithm include (1) a new polarized radiative transfer code (RTC), which replaced the scalar RTC of V2, (2) detailed characterization of gas absorption by adding NO2 and H2O to specify total gas absorption in the atmospheric column, specification of vertical profiles of all the atmospheric species, (3) new bidirectional reflectance distribution function (BRDF) parameters for land sites adopted from the MODIS BRDF/Albedo product, (4) a new version of the extraterrestrial solar flux spectrum, and (5) a new temperature correction procedure of both direct Sun and sky radiance measurements. The potential effect of each change in V3 on single scattering albedo (SSA) retrievals was analyzed. The operational almucantar retrievals of V2 versus V3 were compared for four AERONET sites: GSFC, Mezaira, Mongu, and Kanpur. Analysis showed very good agreement in retrieved parameters of the size distributions. Comparisons of SSA retrievals for dust aerosols (Mezaira) showed a good agreement in 440 nm SSA, while for longer wavelengths V3 SSAs are systematically higher than those of V2, with the largest mean difference at 675 nm due to cumulative effects of both extraterrestrial solar flux and BRDF changes. For non-dust aerosols, the largest SSA deviation is at 675 nm due to differences in extraterrestrial solar flux spectrums used in each version. Further, the SSA 675 nm mean differences are very different for weakly (GSFC) and strongly (Mongu) absorbing aerosols, which is explained by the lower sensitivity to a bias in aerosol scattering optical depth by less absorbing aerosols. A new hybrid (HYB) sky radiance measurement scan is introduced and discussed. The HYB combines features of scans in two different planes to maximize the range of scattering angles and achieve scan symmetry, thereby allowing for cloud screening and spatial averaging, which is an advantage over the principal plane scan that lacks robust symmetry. We show that due to an extended range of scattering angles, HYB SSA retrievals for dust aerosols exhibit smaller variability with solar zenith angles (SZAs) than those of almucantar (ALM), which allows extension of HYB SSA retrievals to SZAs less than 50∘ to as small as 25∘. The comparison of SSA retrievals from closely time-matched HYB and ALM scans in the 50 to 75∘ SZA range showed good agreement with the differences below ∼0.005. We also present an approach to estimate retrieval uncertainties which utilizes the variability in retrieved parameters generated by perturbing both measurements and auxiliary input parameters as a proxy for retrieval uncertainty. The perturbations in measurements and auxiliary inputs are assumed as estimated biases in aerosol optical depth (AOD), radiometric calibration of sky radiances combined with solar spectral irradiance, and surface reflectance. For each set of Level 2 Sun/sky radiometer observations, 27 inputs corresponding to 27 combinations of biases were produced and separately inverted to generate the following statistics of the inversion results: average, standard deviation, minimum and maximum values. From these statistics, standard deviation (labeled U27) is used as a proxy for estimated uncertainty, and a lookup table (LUT) approach was implemented to reduce the computational time. The U27 climatological LUT was generated from the entire AERONET almucantar (1993–2018) and hybrid (2014–2018) scan databases by binning U27s in AOD (440 nm), Angström exponent (AE, 440–870 nm), and SSA (440, 675, 870, 1020 nm). Using this LUT approach, the uncertainty estimates U27 for each individual V3 Level 2 retrieval can be obtained by interpolation using the corresponding measured and inverted combination of AOD, AE, and SSA.

Aliaksandr Siniuk↗
NASA NTRS2000

Sensitivity of Cirrus Bidirectional Reflectance at MODIS Bands to Vertical Inhomogeneity of Ice Crystal Habits and Size Distribution

A common assumption in satellite imager-based cirrus retrieval algorithms is that the radiative properties of a cirrus cloud may be represented by those associated with a specific ice crystal shape (or habit) and a single particle size distribution. However, observations of cirrus clouds have shown that the shapes and sizes of ice crystals may vary substantially with height within the clouds. In this study we investigate the sensitivity of the top-of-atmosphere bidirectional reflectances at two MODIS bands centered at 0.65 micron and 2.11 micron to the cirrus models assumed to be either a single homogeneous layer or three distinct but contiguous, layers. First, we define the single- and three-layer cirrus cloud models with respect to ice crystal habit and size distribution on the basis of in situ replicator data acquired during the First ISCCP Regional Experiment (FIRE-II), held in Kansas during the fall of 1991. Subsequently, fundamental light scattering and radiative transfer theory is employed to determine the single scattering and the bulk radiative properties of the cirrus cloud. Regarding the radiative transfer computations, we present a discrete form of the adding/doubling principle by introducing a direct transmission function, which is computationally straightforward and efficient an improvement over previous methods. For the 0.65 micron band, at which absorption by ice is negligible, there is little difference between the bidirectional reflectances calculated for the one- and three-layer cirrus models, suggesting that the vertical inhomogeneity effect is relatively unimportant. At the 2.11 micron band, the bidirectional reflectances computed for both optically thin (tau = 1) and thick (tau = 10) cirrus clouds show significant differences between the results for the one- and three-layer models. The reflectances computed for the three-layer cirrus model are substantially larger than those computed for the single-layer cirrus. Finally, we find that cloud reflectance is very sensitive to the optical properties of the small crystals that predominate in the top layer of the three-layer cirrus model. It is critical to define the most realistic geometric shape for the small "quasi-spherical" ice crystals in the top layer for obtaining reliable single-scattering parameters and bulk radiative properties of cirrus.

Yang, P.↗
NASA NTRS2016

GOCI Yonsei Aerosol Retrieval (YAER) Algorithm and Validation During the DRAGON-NE Asia 2012 Campaign

The Geostationary Ocean Color Imager (GOCI) onboard the Communication, Ocean, and Meteorological Satellite (COMS) is the first multi-channel ocean color imager in geostationary orbit. Hourly GOCI top-of-atmosphere radiance has been available for the retrieval of aerosol optical properties over East Asia since March 2011. This study presents improvements made to the GOCI Yonsei Aerosol Retrieval (YAER) algorithm together with validation results during the Distributed Regional Aerosol Gridded Observation Networks - Northeast Asia 2012 campaign (DRAGONNE Asia 2012 campaign). The evaluation during the spring season over East Asia is important because of high aerosol concentrations and diverse types of Asian dust and haze. Optical properties of aerosol are retrieved from the GOCI YAER algorithm including aerosol optical depth (AOD) at 550 nm, fine-mode fraction (FMF) at 550 nm, single-scattering albedo (SSA) at 440 nm, Angstrom exponent (AE) between 440 and 860 nm, and aerosol type. The aerosol models are created based on a global analysis of the Aerosol Robotic Networks (AERONET) inversion data, and covers a broad range of size distribution and absorptivity, including nonspherical dust properties. The Cox-Munk ocean bidirectional reflectance distribution function (BRDF) model is used over ocean, and an improved minimum reflectance technique is used over land. Because turbid water is persistent over the Yellow Sea, the land algorithm is used for such cases. The aerosol products are evaluated against AERONET observations and MODIS Collection 6 aerosol products retrieved from Dark Target (DT) and Deep Blue (DB) algorithms during the DRAGON-NE Asia 2012 campaign conducted from March to May 2012. Comparison of AOD from GOCI and AERONET resulted in a Pearson correlation coefficient of 0.881 and a linear regression equation with GOCI AOD = 1.083 x AERONET AOD - 0.042. The correlation between GOCI and MODIS AODs is higher over ocean than land. GOCI AOD shows better agreement with MODIS DB than MODIS DT. The other GOCI YAER products (AE, FMF, and SSA) show lower correlation with AERONET than AOD, but still show some skills for qualitative use.

Choi, Myungje↗
NASA NTRS2008

Laboratory-Based Bidirectional Reflectance Distribution Functions of Radiometric Tarps

Laboratory-based bidirectional reflectance distribution functions of radiometric tarp samples used in the vicarious calibration of Earth remote sensing satellite instruments are presented in this paper. The results illustrate the BRDF dependence on the orientation of the tarps weft and warp threads. The study was performed using the GSFC scatterometer at incident zenith angles of 0 deg, 10 deg, and 30 deg; scatter zenith angles from 0 deg. to 60 deg.; and scatter azimuth angles of 0 deg., 45 deg., 90 deg., 135 deg. and 180 deg. The wavelengths were 485nm, 550nm, 633nm and 800nm. The tarp's weft and warp dependence on BRDF is well defined at all measurement geometries and wavelengths. The BRDF difference can be as high as 8% at 0o incident angle and 12% at 30 deg. incident angle. The fitted BRDF data shows a very small discrepancy from the measured ones. New data on the forward and backscatter properties of radiometric tarps are reported. The backward scatter is well pronounced for the white samples. The black sample has well pronounced forward scatter. The provided BRDF characterization of radiometric tarps is an excellent reference for anyone interested in using tarps for radiometric calibrations. The results are NIST traceable.

Georgiev, Georgi T.↗
NASA NTRS2019

Highly Absorptive Pupil Mask Fabricated with Black Silicon

Many of NASA’s direct imaging of exoplanet missions and projects require fabricated coronagraph masks to control scattering and diffraction of light. The designed, patterned mask intended for the coronagraphic testbeds are highly absorptive in the visible range on non-metallic regions. In this work, we employed the cryogenic etching process to fabricate black silicon (BSi) to achieve a high aspect ratio (HAR) structures with higher etch rate than conventional reactive ion etching (REI). Recent bidirectional reflectance distribution function (BRDF) measurements of uniformly etched BSi on silicon wafer show highly diffusive BSi with a specular reflective component in the orders of seven magnitudes lower than the total hemispherical reflectance when the polarized or non-polarized incident beam is used.

black-silicon↗
NASA NTRS2019

Highly Absorptive Pupil Mask Fabricated with Black Silicon

Many of NASA’s direct imaging of exoplanet missions and projects require fabricated coronagraph masks to control scattering and diffraction of light. The designed, patterned mask intended for the coronagraphic testbeds are highly absorptive in the visible range on non-metallic regions. In this work, we employed the cryogenic etching process to fabricate black silicon (BSi) to achieve a high aspect ratio (HAR) structures with higher etch rate than conventional reactive ion etching (REI). Recent bidirectional reflectance distribution function (BRDF) measurements of uniformly etched BSi on silicon wafer show highly diffusive BSi with a specular reflective component in the orders of seven magnitudes lower than the total hemispherical reflectance when the polarized or non-polarized incident beam is used.

BRDF↗
NASA NTRS1989

Cirrus optical depth retrieval from satellite-measured bidirectional reflectance

In the framework of investigating the relationship between the visible optical depth and microphysics of cirrus clouds, the doubling scheme for radiative transfer in cirrus cloudy atmospheres, as developed by Takano and Liou (1988), has been used to compute the bidirectional reflectances at the top of the atmosphere. Reflectance data taken at about the same time from GOES and AVHRR over Waussau, as well as particle distributions observed during the FIRE IFO carried out in Wisconsin (1986) were the basis of the experiment. For the cirrus microphysical model, hexagonal ice crystals and area-equivalent ice spheres are considered. The single scattering phase functions for randomly oriented hexagonal columns and area-equivalent ice spheres are computed from geometric optics and Mie theory, respectively.

Takano, Y.↗
NASA NTRS2012

Initial On-Orbit Radiometric Calibration of the Suomi NPP VIIRS Reflective Solar Bands

The on-orbit radiometric response calibration of the VISible/Near InfraRed (VISNIR) and the Short-Wave InfraRed (SWIR) bands of the Visible/Infrared Imager/Radiometer Suite (VIIRS) aboard the Suomi National Polar-orbiting Partnership (NPP) satellite is carried out through a Solar Diffuser (SD). The transmittance of the SD screen and the SD's Bidirectional Reflectance Distribution Function (BRDF) are measured before launch and tabulated, allowing the VIIRS sensor aperture spectral radiance to be accurately determined. The radiometric response of a detector is described by a quadratic polynomial of the detector?s digital number (dn). The coefficients were determined before launch. Once on orbit, the coefficients are assumed to change by a common factor: the F-factor. The radiance scattered from the SD allows the determination of the F-factor. In this Proceeding, we describe the methodology and the associated algorithms in the determination of the F-factors and discuss the results.

Lei, Ning↗
NASA NTRS1987

Bidirectional reflectance spectroscopy

An analytical model is developed for the opposition effects (heiligenshein) in the case of light scattering from a semi-infinite, particulate medium with particles that are large relative to the wavelength. The effect is common for natural materials, and comprises a bright surge in light diffusively reflected from a surface at near zero phase. A generalized expression is devised for the extinction coefficient of a particulate medium. Models are developed for step function and hyperbolic tangent distributions of light scattered from a stratified medium and exhibiting the opposition effect. A maximum brightness amplitude increase of 0.753 is projected for the effect. Greater values must have other causes. To illustrate the theory it is fitted to observations of the Moon, an asteroid, and a satellite of Uranus; Europa is also discussed.

Hapke, Bruce↗
NASA NTRSDate not supplied

Development of the Ames Global Hyperspectral Synthetic Dataset

This study develops the surface BRDF (bidirectional reflectance distribution function) product of the Ames Global Hyperspectral Synthetic Dataset (AGHSD), based on the corresponding MODIS products, to support the NASA Surface Biology and Geology mission development. A main challenge in deriving a hyperspectral dataset from the multi-band satellite products is how to identify a succinct yet robust algorithm that allow us to infer BRDF at unobserved wavelengths based on the few observed bands. Using the theories of radiative transfer in vegetation canopies, we arrive at a simple equation that accurately approximates hyperspectral surface BRDF as the weighted sum of components from the soil and the vegetation. Each of the components is modeled by the product of the spectrally-dependent optical properties of a surface element (the spectra of the soil surface reflectance, the leaf single albedo, or the canopy scattering coefficient) and a spectrally-independent bidirectional scattering function. The optical properties of the soil and the vegetation can be obtained from existing spectral libraries or model simulations. The bidirectional scattering functions are represented by the Ross-Thick-Li-Sparse BRDF model, where the linear coefficients are estimated with regression analysis from the multi-band MODIS data. We validate the algorithm with simulations by Monte Carlo Ray Tracing model experiments, and the results are highly consistent with the theoretic derivation. We apply the algorithm to generate the AGHSD BRDF product at 1km and 8-day resolutions for the year of 2019. The results are biogeochemically and physically coherent and consistent, and thus serve the goal to support the science and application development of the SBG community.

Hyperspectral↗
NASA NTRSDate not supplied

Verification of TROPOMI NO2 Product Using OMI NO2 algorithm

We evaluated S5P TROPOspheric Monitoring Instrument (TROPOMI) operational nitrogen dioxide (NO2) product by comparing with the NO2 retrievals from Ozone Monitoring Instrument (OMI) onboard NASA’s Aura satellite. We compared spatially matched NO2 vertical column density (VCD) data from OMI and TROPOMI to identify any discrepancies between the two operational products. We also applied OMI Air-Mass Factor (AMF) algorithm to TROPOMI Slant Column Density (SCD) data (v02.03.01) aiming to create long-term merged NO2 Earth Science Data Record (https://disc.gsfc.nasa.gov/datasets/TROPOMI_MINDS_NO2_1.1/summary ). The algorithm (version 4.0) uses new Geometry-dependent Lambertian Equivalent surface Reflectivity (GLER) product available for each TROPOMI pixel. GLER is pre-calculated using the vector linearized discrete ordinate radiative transfer (VLIDORT) model, which uses as input high-resolution bidirectional reflectance distribution function (BRDF) information from NASA's Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) over land and the wind-dependent Cox–Munk wave-facet slope distribution over water, the latter with a contribution from the water-leaving radiance based on MODIS gap-filled in-water chlorophyll-a data. The GLER data, combined with consistently retrieved cloud parameters, provide improved information for the calculation of the scattering weight profiles. Additional AMF improvements result from using high resolution (0.25o latitude x 0.25o longitude) a priori NO2 profile shapes and other auxiliary information from the Global Modeling Initiative (GMI) Replay simulation sampled using S5P orbital simulator. Our TROPOMI_MINDS_NO2 algorithm employs the stratosphere-troposphere separation scheme, de-striping, and surface snow/ice treatment consistently with the latest OMI NO2 re-processing (version 4). We evaluate the TROPOMI_MINDS_NO2 product by comparing with the S5P operational NO2 product as well as with independent NO2 observations from ground-based Pandora and aircraft observations. Our results indicate that the new TROPOMI_MINDS_NO2 retrievals are generally higher than the S5P operational NO2 product over polluted regions and show improved agreement with independent validation data.

TROPOMI↗
NASA NTRS1994

Asymmetry parameters of the phase function for densely packed scattering grains

Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionally of the inverse scattering problem.

Mishchenko, Michael I.↗