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NASA NTRS2022

The Simulation and Subseasonal Forecasting of Hydrological Variables: Insights from a Simple Water Balance Model

Past work has shown that a land surface model’s (LSM’s) implicit (not explicitly coded) relationships between soil moisture and both evapotranspiration (ET) and runoff largely determine the LSM’s hydrological behavior. Here we estimate the relationships that appear to be operating in the real world and compare them to those of the LSM component of a state-of-the-art Earth system model (ESM). The two sets of relationships are determined by calibrating them within a simple water balance model (WBM): once using stream gauge observations from small, unregulated rivers over the eastern half of the U.S., and once using the runoffs generated by the LSM as part of a state-of-the-art atmospheric reanalysis. Hydrological simulations and subseasonal hydrological forecasts performed with the two calibrated versions of the WBM provide two key results. First, the version calibrated to the LSM-generated runoffs does successfully reproduce, to first order, the hydrological behavior of the full LSM within its ESM environment. Second, of the two WBM versions, the one calibrated to the observations reproduces more accurately a broad collection of fully independent streamflow observations as well as a similarly broad collection of in-situ soil moisture measurements. Taken together, the two results suggest that the observations-calibrated ET and runoff efficiency functions do successfully represent, at least to some degree, soil moisture controls over hydrological variability in Nature and can serve as potentially useful targets for further LSM development.

Water Balance Model↗
NASA NTRS1999

The MECA Payload as a Dust Analysis Laboratory on the MSP 2001 Lander

In a companion abstract, the "Mars Environmental Compatibility Assessment" (MECA) payload for Mars Surveyor Program 2001 (MSP 2001) is described in terms of its capabilities for addressing exobiology on Mars. Here we describe how the same payload elements perform in terms of gathering data about surface dust on the planet. An understanding of the origin and properties of dust is important to both human exploration and planetary geology. The MECA instrument is specifically designed for soil/dust investigations: it is a multifunctional laboratory equipped to assess particulate properties with wet chemistry, camera imagery, optical microscopy (potentially with LTV fluorescence capability), atomic force microscopy (AFM; potentially with mineral-discrimination capabilities), electrometry, active & passive external materials-test panels, mineral hardness testing, and electrostatic & magnetic materials testing. Additionally, evaluation of soil chemical and physical properties as a function of depth down to about 50 cm will be facilitated by the Lander/MECA robot arm on which the camera (RAC) and electrometer are mounted. Types of data being sought for the dust include: (1) general textural and grain-size characterization of the soil as a whole --for example, is the soil essentially dust with other components or is it a clast-supported material in which dust resides only in the clast interstices, (2) size frequency distribution for dust particles in the range 0.01 to 10.00 microns, (3) particle-shape distribution of the soil components and of the fine dust fraction in particular, (4) soil fabric such as grain clustering into clods, aggregates, and cemented/indurated grain amalgamations, as well as related porosity, cohesiveness, and other mechanical soil properties, (5) cohesive relationship that dust has to certain types of rocks and minerals as a clue to which soil materials may be prime hosts for dust "piggybacking", (6) particle, aggregate, and bulk soil electrostatic properties, (7) particle hardness, (8) particle magnetic properties, (9) bulk dust geochemistry (solubility, reactivity, ionic and mineral species). All of these quantities are needed in order for the human exploration program to make assessments of hazards on Mars, and to better enable the production on earth, of soil/dust simulants that can act as realistic test materials in terms of those properties that render dust a contaminant.Such properties include the small grain size that enables penetration of space-suit joints, mechanical interfaces and bearings, seals, etc., and presents difficulty for filtration systems. Size also plays a critical role in the potential for lung disease in long-term habitats. The properties of grain shape and hardness are important parameters in determining the abrasiveness of dust as it enters mechanical systems, or bombards helmet visors and habitat windows in dust-laden winds. Adhesive electrostatic and magnetic properties of dust will be prime causes of contamination of space suits and equipment. Contamination causes mechanical malfunction, tracking of dirt into habitats, "piggybacking" of toxins on dust into habitats, changes in albedo and efficiency of solar arrays and heat exchangers, and changes in electrical conductivity of suit surfaces and other materials that may have specific safety requirements regarding electrical conductivity. Other potentially hazardous properties of dust include the possibility of high solubility of some component grains (rendering them reactive), and toxicity of some materials --grains of superoxidants and heavy metals (there is always the slim, but not inconceivable possibility of biogenic components such as spores). Because Mars has no active surface aqueous regime, volcanic emissions, meteoritic debris, weathering products, and photochemical products of Mars have nowhere to go except reside in the surface; there are few mechanical or chemical (buffering) processes to remove the accumulation of eons. From a planetology perspective, there are many enigmatic issues relating to dust and the aeolian regime in general. MECA will be able to address many questions in this area. For example, if MECA determines a particular particle size distribution (size and sorting values), it will be possible to make inferences about the origin of the dust - - is it all aeolian, or a more primitive residue of weathering, volcanic emissions, and meteoritic gardening? Trenching with the Lander/MECA robot arm will enable local stratigraphy to be determined in terms of depositional rates, amounts and cyclicity in dust storms and/or local aeolian transport. Grain shape will betray the origin of the dust fragments as being the product of recent or ancient weathering, or the comminution products of aeolian transport --the dust-silt ratio might be a measure of aeolian comminution energy. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS1999

The MECA Payload as an Exobiology Laboratory on the MSP 2001 Lander

The "Mars Environmental Compatibility Assessment" (MECA) payload for Mars Surveyor Project 2001 (MSP 2001) is comprised of a multifunctional laboratory equipped to assess martian soil properties with wet chemistry, camera imagery, optical microscopy (potentially with UV fluorescence capability), atomic force microscopy (AFM; potentially with mineral-discrimination capabilities), electrometry, active & passive external materials-test panels, mineral hardness testing, and electrostatic and magnetic materials testing. Additionally, evaluation of soil chemical and physical properties as a function of depth down to -50 cm will be facilitated by the Lander/MECA robot arm on which the camera (RAC) and electrometer are mounted. MECA was designed as a NASA Human Exploration and Development of Space (HEDS) payload for determining the properties of martian soil that may be detrimental to human exploration. It is, however, well equipped to address exobiology questions in the following areas: (1)Geochemical clues to Aqueous Mineralogy and Oxidant formation; (2) Soil structures and microfabrics as indicators of water-volatiles migration; (3) Minerals and rocks as clues to ancient hydrology; (4) Grain textures as indicators of aqueous activity and weathering. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS2002

Implementation of the NCAR Community Land Model (CLM) in the NASA/NCAR finite-volume Global Climate Model (fvGCM)

In this study, the NCAR CLM version 2.0 land-surface model was integrated into the NASA/NCAR fvGCM. The CLM was developed collaboratively by an open interagency/university group of scientists and based on well-proven physical parameterizations and numerical schemes that combine the best features of BATS, NCAR-LSM, and IAP94. The CLM design is a one-dimensional point model with 1 vegetation layer, along with sub-grid scale tiles. The features of the CLM include 10-uneven soil layers with water, ice, and temperature states in each soil layer, and five snow layers, with water flow, refreezing, compaction, and aging allowed. In addition, the CLM utilizes two-stream canopy radiative transfer, the Bonan lake model and topographic enhanced streamflow based on TOPMODEL. The DAO fvGCM uses a genuinely conservative Flux-Form Semi-Lagrangian transport algorithm along with terrain- following Lagrangian control-volume vertical coordinates. The physical parameterizations are based on the NCAR Community Atmosphere Model (CAM-2). For our purposes, the fvGCM was run at 2 deg x 2.5 deg horizontal resolution with 55 vertical levels. The 10-year climate from the fvGCM with CLM2 was intercompared with the climate from fvGCM with LSM, ECMWF and NCEP. We concluded that the incorporation of CLM2 did not significantly impact the fvGCM climate from that of LSM. The most striking difference was the warm bias in the CLM2 surface skin temperature over desert regions. We determined that the warm bias can be partially attributed to the value of the drag coefficient for the soil under the canopy, which was too small resulting in a decoupling between the ground surface and the canopy. We also discovered that the canopy interception was high compared to observations in the Amazon region. A number of experiments were then performed focused on implementing model improvements. In order to correct the warm bias, the drag coefficient for the soil under the canopy was considered a function of LAI (Leaf Area Index). Analysis of the results revealed that there was a substantial impact, and the warm and dry bias in the CLM2 was significantly reduced. For the interception scheme, the canopy throughfall was increased to allow for more infiltration of precipitation into the soil, resulting in increased low-level moisture and a decrease in the interception loss ratio (canopy evaporation to precipitation).

Radakovich, Jon D.↗
NASA NTRS1993

Lunar phase function effects on spectral ratios used for resource assessment

Groundbased telescopic CCD images of 36 selected locations on the moon were obtained in five 'standard' bandpasses at 12 phase angles ranging from -78 deg to +75 deg to measure phase function effects on the ratio values used to quantify the abundance of TiO2 and qualitatively indicate soil maturity. Consistent with previous studies, we find that the moon is 'bluer' at small phase angles, but that the effect on the ratio values for TiO2 abundance for the phase angles of our data is on the order of the measurement uncertainties throughout the range of abundances found in the mare. The effect is more significant as seen from orbiting spacecraft over a range of selenographic latitude. Spectral ratio images (400/560 and 400/730 nm) were used to map the abundance of TiO2 using the empirical relation found by Charlette et al from analysis of returned lunar soils. Additionally, the 950/560 and 950/730 nm image ratios were used to define the regions of mature mare soil in which the relation is valid. Although the phase function dependence on wavelength was investigated and quantified for small areas and the integrated disc, the effect specifically on TiO2 mapping was not rigorously determined. For consistency and convenience in observing the whole lunar front side, our mapping utilized images taken -15 deg less than alpha less than 15 deg when the moon was fully illuminated from earth; however, this includes the strong opposition peak.

Larson, S. M.↗
NASA NTRS2003

Ultrasonic/Sonic Mechanisms for Drilling and Coring

Two apparatuses now under development are intended to perform a variety of deep-drilling, coring, and sensing functions for subsurface exploration of rock and soil. These are modified versions of the apparatuses described in Ultrasonic/Sonic Drill/Corers With Integrated Sensors (NPO-20856), NASA Tech Briefs, Vol. 25, No. 1 (January 2001), page 38. In comparison with the drilling equipment traditionally used in such exploration, these apparatuses weigh less and consume less power. Moreover, unlike traditional drills and corers, these apparatuses function without need for large externally applied axial forces.

Bar-Cohen, Yoseph↗
NASA NTRS1985

Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces

A simple equation has been developed for describing the bidirectional reflectance of some vegetative canopies and bare soil surfaces. The equation describes directional reflectance as a function of zenith and azimuth view angles and solar azimuth angle. The equation works for simulated and field measured red and IR reflectance under clear sky conditions. Hemispherical reflectance can be calculated as a function of the simple equation coefficients by integrating the equation over the hemisphere of view angles. A single equation for estimating soil bidirectional reflectance was obtained using the relationships between solar zenith angles and the simple equation coefficients for medium and rough soil distributions. The equation has many useful applications such as providing a lower level boundary condition in complex plant canopy models and providing an additional tool for studying bidirectional effects on pointable sensors.

Walthall, C. L.↗
NASA NTRS1980

Calculations of the spectral nature of the microwave emission from soils

The brightness temperatures for a set of soil profiles observed at USDA facilities in Arizona and Georgia were calculated at the wavelengths of 2.8, 6, 11, 21, and 49 cm using a coherent radiative transfer model. The soil moisture sampling depth is found to be a function of wavelength and is in the range 0.06 to 0.1 of a wavelength. The thermal sampling depth also depends on wavelength and is approximately equal to one wavelength at dry soil condition and 0.1 - 0.5 wavelengths at wet soil conditions. Calculated values of emissivity show strong diurnal variations when the soils are wet, while there is little diurnal change when the soil is dry. The soil moistures within the four depth intervals of 0-2, 0-5, 0-9, and 0-15 cm were parameterized as function of the calculated emissivity and brightness temperature. Best-fit parameters and correlation coefficients are presented for five wavelengths. Interrelationships among the effective temperature, surface temperature, and emissivity are displayed.

Mo, T.↗
NASA NTRS1990

Functional relation among subpixel canopy cover, ground shadow, and illuminated ground at large sampling scales

The functional relation among subpixel canopy cover, illuminated soil, and shadowed soil, which progressively develops with increasing pixel size, is investigated for Poisson distributed plants using a geometric canopy simulation model. An analytical relation among cover components is shown to be applicable when the scale of the pixel is much larger than the scale of the plant and ground shadow. The analysis is facilitated through the use of a nondimensional solar-geometric similarity parameter, eta, equal to the ratio of the area of one plant canopy to its associated ground shadow area, as viewed from nadir. A sampling scale ratio, defined as the ratio of the area of the pixel to the mean area of a single plant shadow, is tested as a quantitative criterion to evaluate when the functional relation among subpixel components occurs. The results of a remote sensing experiment over a natural conifer landscape provide preliminary confirmation of the theoretical analysis.

Jasinski, Michael F.↗
NASA NTRS2012

Arctic Tundra Vegetation Functional Types Based on Photosynthetic Physiology and Optical Properties

Climate change in tundra regions may alter vegetation species composition and ecosystem carbon balance. Remote sensing provides critical tools for monitoring these changes as optical signals provide a way to scale from plot measurements to regional patterns. Gas exchange measurements of pure patches of key vegetation functional types (lichens, mosses, and vascular plants) in sedge tundra at Barrow AK, show three significantly different values of light use efficiency (LUE) with values of 0.013+/-0.001, 0.0018+/-0.0002, and 0.0012 0.0001 mol C/mol absorbed quanta for vascular plants, mosses and lichens, respectively. Further, discriminant analysis of patch reflectance identifies five spectral bands that can separate each vegetation functional type as well as nongreen material (bare soil, standing water, and dead leaves). These results were tested along a 100 m transect where midsummer spectral reflectance and vegetation coverage were measured at one meter intervals. Area-averaged canopy LUE estimated from coverage fractions of the three functional types varied widely, even over short distances. Patch-level statistical discriminant functions applied to in situ hyperspectral reflectance successfully unmixed cover fractions of the vegetation functional types. These functions, developed from the tram data, were applied to 30 m spatial resolution Earth Observing-1 Hyperion imaging spectrometer data to examine regional variability in distribution of the vegetation functional types and from those distributions, the variability of LUE. Across the landscape, there was a fivefold variation in tundra LUE that was correlated to a spectral vegetation index developed to detect vegetation chlorophyll content.

Huemmrich, Karl F.↗
NASA NTRS2013

Arctic Tundra Vegetation Functional Types Based on Photosynthetic Physiology and Optical Properties

Non-vascular plants (lichens and mosses) are significant components of tundra landscapes and may respond to climate change differently from vascular plants affecting ecosystem carbon balance. Remote sensing provides critical tools for monitoring plant cover types, as optical signals provide a way to scale from plot measurements to regional estimates of biophysical properties, for which spatial-temporal patterns may be analyzed. Gas exchange measurements were collected for pure patches of key vegetation functional types (lichens, mosses, and vascular plants) in sedge tundra at Barrow, AK. These functional types were found to have three significantly different values of light use efficiency (LUE) with values of 0.013 plus or minus 0.0002, 0.0018 plus or minus 0.0002, and 0.0012 plus or minus 0.0001 mol C mol (exp -1) absorbed quanta for vascular plants, mosses and lichens, respectively. Discriminant analysis of the spectra reflectance of these patches identified five spectral bands that separated each of these vegetation functional types as well as nongreen material (bare soil, standing water, and dead leaves). These results were tested along a 100 m transect where midsummer spectral reflectance and vegetation coverage were measured at one meter intervals. Along the transect, area-averaged canopy LUE estimated from coverage fractions of the three functional types varied widely, even over short distances. The patch-level statistical discriminant functions applied to in situ hyperspectral reflectance data collected along the transect successfully unmixed cover fractions of the vegetation functional types. The unmixing functions, developed from the transect data, were applied to 30 m spatial resolution Earth Observing-1 Hyperion imaging spectrometer data to examine variability in distribution of the vegetation functional types for an area near Barrow, AK. Spatial variability of LUE was derived from the observed functional type distributions. Across this landscape, a fivefold variation in tundra LUE was observed. LUE calculated from the functional type cover fractions was also correlated to a spectral vegetation index developed to detect vegetation chlorophyll content. The concurrence of these alternate methods suggest that hyperspectral remote sensing can distinguish functionally distinct vegetation types and can be used to develop regional estimates of photosynthetic LUE in tundra landscapes.

VEGETATION↗
NASA NTRS1972

Spectral reflectance and emittance of Apollo 11 and 12 lunar material.

The thermal radiation properties of Apollo 11 and 12 fines (soils) are reviewed and presented as a function of wavelength, angle of illumination, and bulk density. The spectral directional reflectance is presented for wavelengths from 0.6 to 2 microns and for angles of illumination of 10, 20, 30, 45, and 60 deg. The normal emittance is presented for wavelengths from 2.5 to 14.5 microns. The solar albedo and total normal emittance as a function of temperature were calculated from the spectral values. The solar albedo for Apollo 11 fines is 0.099 whereas for Apollo 12 fines is approximately 0.119 for angles of illumination of 10 deg and a density of 1600 kg cu m.

Birkebak, R. C.↗
NASA NTRS1973

Optical properties of Apollo 12 moon samples.

We present the photometric phase function, color, normal albedo, polarimetric phase function, and spectrophotometry of the Apollo 12 soil. With a few minor exceptions, the optical properties of the Apollo 12 soil are very similar to those of the Apollo 11 soil and of lunar mare surfaces.

O'Leary, B.↗
NASA NTRS1993

The opposition effect of the moon - The contribution of coherent backscatter

The opposition effect, the sharp surge in brightness of an astronomical object observed near zero phase angle, which has been known for more than a century, has generally been explained by shadow hiding. The reflectances of several Apollo lunar soil samples have been measured as a function of phase angle in linearly and circularly polarized light. All samples exhibited a decrease in the linear polarization ratio and an increase in the circular polarization ratio in the opposition peak. This provides unequivocal proof that most of the lunar opposition effect is caused by coherent backscatter, not shadow hiding. This result has major implications for the interpretation of photometric observations of bodies in the solar system, including the Earth.

Hapke, Bruce W.↗
NASA NTRS2007

RadSTAR L-Band Imaging Scatterometer: Performance Assessment

RadSTAR is an instrument development program aimed at combining a radiometer and a scatterometer system into a highly compact configuration that uses a single, electronically scanned antenna to provide co-located and simultaneous measurements of emission and backscatter for airborne and spaceborne applications [I]. The program was designed to map soil moisture and ocean salinity, both important components of the water cycle, and to map sea ice density and thickness, an important factor in ocean-atmosphere heat exchange in Polar Regions. The accuracy in estimation of these and a number of other Earth science parameters can be greatly enhanced by providing the co-aligned radar/radiometer microwave measurements. For instance, radiometer estimates of soil moisture from soil emission are affected by emission from vegetation, and from the roughness of the surface. Complementary measurements using the scatterometer can be used to evaluate the vegetation and surface roughness effects. Hence, the combined observations can provide an improved estimate. As with soil moisture, the ocean salinity is a function of the microwave emission from the sea surface temperature (SST) and sea roughness. There, the addition of radar backscatter measurements of sea roughness enables the correction of the emissivity and provide more accurate estimates of ocean salinity. Similar arguments can be made for other important Earth science parameters. This paper discusses the RadSTAR program, the radar system design, calibration, and digital beamforming techniques, and presents preliminary analysis of the data collected during the test flights. The data sets obtained during the flights and during the radar calibration in the anechoic chamber are also employed to asses the performance of the radar. The paper also discusses the Digital Beamforming Synthetic Aperture Radar (DBSAR) processor, a real-time processor recently developed for the LIS instrument which enables beam synthesis, fine resolutions, and large swaths.

Rincon, Rafael↗
NASA NTRS2008

Martian Dust Simulator

The Martian Dust Simulator (MDS) was designed to investigate the contamination effects of Martian soil and rock on the performance and function of flight-like microvalves and flight-like filters located within the Sample Analysis at Mars (SAM) instrument suite. The SAM instrument suite, which houses over fifty percent of the science payload, is located on-board the Mars exploration rover. The mission objective of the Mars Science Laboratory Rover is to determine the past, present, and future habitability of Mars. It will serve as a robot geologist, traveling the Mars surface for a period of one Martian year (equivalent to two earth years). The microvalves were designed as a conduit to control the flow of Martian gas to the science instruments. If exposed to particle sizes greater than half a micron, both the science instruments and science equipment, including forty-seven microvalves, could experience performance degradation. As a result, filters were used at various gas inlets to protect flight hardware from particulate degradation. Additionally, the filters serve as the only interface between the Martian environment and the mechanisms within SAM. The MDS operates at 7 Torr (0.135 psi) with a gas flow rate of 0 to 20 m/s. Iron (III) Oxide was the only dust particle specimen used, although several others were initially considered (i.e. JSC-Mars-1, Corundum Powder (Al2O3), Hydrated Sulfate, and Belville (Basalt)). The overarching goal of the MDS is to demonstrate that the Mars exploration program is adequately designed and prepared for the Martian mission environment.

Zuray, Monica↗
NASA NTRS2008

A Vegetation Correction Methodology for Time Series Based Soil Moisture Retrieval From C-band Radar Observations

A methodology is presented to correct backscatter (sigma(sup 0)) observations for the effect of vegetation. The proposed methodology is based on the concept that the ratio of the surface scattering over the total amount of scattering (sigma(sup 0)(sub soil)/sigma(sup 0)) is only affected by the vegetation and can be described as a function of the vegetation water content. Backscatter observations sigma(sup 0) from the soil are not influenced by vegetation. Under bare soil conditions (sigma(sup 0)(sub soil)/sigma(sup 0)) equals 1. Under low to moderate biomass and soil moisture conditions, vegetation affects the observed sigma(sup 0) through absorption of the surface scattering and contribution of direct scattering by the vegetation itself. Therefore, the contribution of the surface scattering is smaller than the observed total amount of scattering and decreases as the biomass increases. For dense canopies scattering interactions between the soil surface and vegetation elements (e.g. leaves and stems) also become significant. Because these higher order scattering mechanisms are influenced by the soil surface, an increase in (sigma(sup 0)(sub soil)/sigma(sup 0)) may be observed as the biomass increases under densely vegetated conditions. This methodology is applied within the framework of time series based approach for the retrieval of soil moisture. The data set used for this investigation has been collected during a campaign conducted at USDA's Optimizing Production Inputs for Economic and Environmental Enhancement OPE-3) experimental site in Beltsville, Maryland (USA). This campaign took place during the corn growth cycle from May 10th to 0ctober 2nd, 2002. In this period the corn crops reached a vegetation water content of 5.1 kg m(exp -2) at peak biomass and a soil moisture range varying between 0.00 to 0.26 cubic cm/cubic cm. One of the deployed microwave instruments operated was a multi-frequency (C-band (4.75 GHz) and L-band (1.6 GHz)) quad-polarized (HH, HV, VV, VH) radar which was mounted on a 20 meter long boom. In the OPE-3 field campaign, radar observations were collected once a week at nominal times of 8 am, 10 am, 12 noon and 2 pm. During each data run the radar acquired sixty independent measurements within an azimuth of 120 degrees from a boom height of 12.2 m and at three different incidence angles (15,35, and 55 degrees). The sixty observations were averaged to provide one backscatter value for the study area and its accuracy is estimated to be 51.0 dB. For this investigation the C-band observations have been used. Application of the proposed methodology to the selected data set showed a well-defined relationship between (sigma(sup 0)(sub soil)/sigma(sup 0)) and the vegetation water content. It is found that this relationship can be described with two experimentally determined parameters, which depend on the sensing configuration (e.g. incidence angle and polarization). Through application of the proposed vegetation correction methodology and the obtained parameterizations, the soil moisture retrieval accuracy within the framework of a time series based approach is improved from 0.033 to 0.032 cubic cm/cubic cm, from 0.049 to 0.033 cubic cm/cubic cm and from 0.079 to 0.047 cubic cm/cubic cm for incidence angles of 15,35 and 55 degrees, respectively. Improvement in soil moisture retrieval due to vegetation correction is greater at larger incidence angles (due to the increased path length and larger vegetation effects on the surface signal at the larger angles).

Joseph, Alicia T.↗
NASA NTRS1999

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

Mishchenko, Michael I.↗