Search NASA⌕ Search

SEARCH · Search NASA

Results for “Cloud shadow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

160 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.

Scruggs, T.↗
DOE OSTI2024

Shortwave Array Spectroradiometer-Hemispheric (SAS-He): design and evaluation

A novel ground-based radiometer, referred to as the Shortwave Array Spectroradiometer-Hemispheric (SAS-He), is introduced. This radiometer uses the shadow-band technique to report total irradiance and its direct and diffuse components frequently (every 30 s) with continuous spectral coverage (350–1700 nm) and moderate spectral (~2.5 nm ultraviolet–visible and ~6 nm shortwave-infrared) resolution. The SAS-He's performance is evaluated using integrated datasets collected over coastal regions during three field campaigns supported by the US Department of Energy's Atmospheric Radiation Measurement (ARM) program, namely the (1) Two-Column Aerosol Project (TCAP; Cape Cod, Massachusetts), (2) Tracking Aerosol Convection Interactions Experiment (TRACER; in and around Houston, Texas), and (3) Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE; La Jolla, California). We compare (i) aerosol optical depth (AOD) and total optical depth (TOD) derived from the direct irradiance, as well as (ii) the diffuse irradiance and direct-to-diffuse ratio (DDR) calculated from two components of the total irradiance. As part of the evaluation, both AOD and TOD derived from the SAS-He direct irradiance are compared to those provided by a collocated Cimel sunphotometer (CSPHOT) at five (380, 440, 500, 675, 870 nm) and two (1020, 1640 nm) wavelengths, respectively. Additionally, the SAS-He diffuse irradiance and DDR are contrasted with their counterparts offered by a collocated multifilter rotating shadowband radiometer (MFRSR) at six (415, 500, 615, 675, 870, 1625 nm) wavelengths. Overall, reasonable agreement is demonstrated between the compared products despite the challenging observational conditions associated with varying aerosol loadings and diverse types of aerosols and clouds. For example, the AOD- and TOD-related values of root mean square error remain within 0.021 at 380, 440, 500, 675, 870, 1020, and 1640 nm wavelengths during the three field campaigns.

47 OTHER INSTRUMENTATION↗
NASA NTRS1993

Cirrus microphysics observations made during FIRE 2: Small particles, high concentrations, and probe comparisons

Aircraft observations of cirrus cloud microphysics were made near Coffeyville, Kansas during Nov. and Dec. 1991. Cloud microphysics measurements were made using both a PMS 2DC probe and an ice particle replicator, both were mounted on the UND Citation aircraft. Intercomparison is made of the size, area, and ice mass spectra determined from these probes. The PMS 2DC undercounts particles for D less than 70 microns and the replicator oversizes particles for D greater than 150 microns, at least when column rosettes are encountered. High concentrations of particles with D less than 50 microns are noted in selected portions of the 22 Nov. 91 replicator data set. Relations between the maximum dimension of a crystal and its shadow area (known as area dimensional relationships) are computed from the PMS data. Area and mass dimensional relationships are used to give a simple analytical expression for computing the wavelength dependent absorption coefficient averaged over a size bin. Calculations based upon the replicator data show that crystals with D less than 50 microns contribute significantly to the solar extinction and infrared absorption coefficients during some time intervals.

Arnott, W. P.↗
NASA NTRS1991

The detection of X-rays from the hot interstellar medium of the Large Magellanic Cloud

A comprehensive reanalysis is presented of the Einstein IPC data base on the LMC, and a number of new algorithms are used to improve the reliability of the point source detection in this crowded region and to produce the first large-scale map of diffuse emission free from the effects of solar scattered X-rays and cosmic-ray particles. Algorithms described in detail include a technique to decontaminate fields containing solar scattered flux, a mechanism for obtaining a spectrum-weighted vignetting function, and a source excision and smoothing algorithm which results in a diffuse map of uniform statistical quality. A catalog of discrete X-rays sources in the direction of the LMC is presented which contains 33 new sources and eliminates a number of spurious and/or marginal directions from previous lists. A possible detection of the long-sought shadowing effect on the cosmic X-ray background produced by cold LMC gas is reported.

Wang, Q.↗
NASA NTRS2002

Interaction Between Surface Heat Budgets, Sea Surface Temperature and Deep Convection in the Tropical Western Pacific

The surface heat budgets, sea surface temperature (SST), clouds and winds in the tropical western Pacific are analyzed and compared for the periods April-June 1998 and 1999. The spring of 1998 is in the later phase of a strong El Nino, whereas the spring of 1999 is in a period of a La Nina. The surface shortwave (SW) and longwave (LW) radiative fluxes are retrieved from Japanese Geostationary Meteorological Satellite radiance measurements, while the surface turbulent fluxes (latent and sensible heat) are derived from SSM/I-Inferred surface air humidity and winds. The SST and sea-air temperature differences are taken from NCEP/NCAR reanalysis. Deep convection is inferred from the outgoing longwave radiation of NOAA's polar-orbiting satellites. The longitudinal shift in maximum SST, deep convection and winds during El Nino and La Nina have a large impact on the spatial distribution of surface heating. Changes in clouds between these two periods have a large impact on the monthly-mean radiative heating, exceeding 60 W m(exp -2) over large oceanic regions. Similarly, the differences in wind speeds and SST have a large impact on the latent cooling, exceeding 40 W m(exp -2) over large oceanic areas. However, the maximum impacts on radiative and latent heat fluxes occur in different regions. The regions of maximum impact on radiative fluxes coincide with the regions of maximum change in clouds, whereas regions of maximum impact on turbulent heat fluxes coincide with the regions of maximum change in trade winds. The time-evolution of SST in relation to that of surface heat fluxes and winds are investigated and compared between the two El Nino and La Nina periods. In regions where wind speeds (or wind stresses) are large, the change in SST agrees well with the change in the net surface heating, indicating a deep ocean mixed layer associated with strong trade winds. On the other hand, in regions where radiative fluxes are large, the change in SST does not agree well with the change in the net surface heating, indicating the importance of solar radiation penetrating through the bottom of the shadow ocean mixed layer.

Chou, Shu-Hsien↗
NASA NTRS2004

Accuracy Assessments and Validation of an Expanded UV Irradiance Database from Satellite Total Ozone Mapping Spectrometer (TOMS)

The TOMS UV irradiance database (1978 to 2000) has been expanded to include 5 new products (noon irradiance at 305, 310, 324, and 380 nm, and noon erythemal-weighted irradiance), in addition to the existing erythemal daily exposure, which permit direct Comparisons with ground-based measurements from UV spectrometers. Sensitivity studies are conducted to estimate uncertainties of the new TOMS UV irradiance data due to algorithm apriori assumptions. Comparisons with Brewer spectrometers as well as filter radiometers are used to review of the sources of known errors. Inability to distinguish between snow and cloud cover using only TOMS data results in large errors in estimating surface UV using snow climatology. A correction is suggested for the case when the regional snow albedo is known from an independent source. The summer-time positive bias between TOMS UV estimations and Brewer measurements can be seen at all wavelengths. This suggests the difference is not related to ozone absorption effects. We emphasize that uncertainty of boundary layer UV aerosol absorption properties remains a major source of error in modeling UV irradiance in clear sky conditions. Neglecting aerosol absorption by the present TOMS algorithm results in a positive summertime bias in clear-sky UV estimations over many locations. Due to high aerosol variability the bias is strongly site dependent. Data from UV-shadow-band radiometer and well-calibrated CIMEL sun-sky radiometer are used to quantify the bias at NASA/GSFC site in Greenbelt, MD. Recommendations are given to enable potential users to better account for local conditions by combining standard TOMS UV data with ancillary ground measurements.

Krotkov, N. A.↗
DOE OSTI2022

Moderate spectral resolution solar irradiance measurements, aerosol optical depth, and solar transmission, from 360 to 1070 nm, using the refurbished rotating shadow band spectroradiometer (RSS)

Abstract. This paper reports on a third-generation rotating shadow band spectroradiometer (RSS) used to measure global and diffuse horizontal plus direct normal irradiances and transmissions at 1002 wavelengths between 360 and 1070 nm. The prism-dispersed spectral data are from the Atmospheric Radiation Measurement (ARM) Southern Great Plains site in north-central Oklahoma (36.605∘ N, 97.486∘ W) and cover dates between August 2009 and February 2014. The refurbished RSS isolates the detector in a vacuum chamber with pressures near 10−7 torr. This prevents the deposition of outgassed vapors from the interior of the spectrometer shell on the cooled detector that affected the operation of the first commercial RSS. Methods for (1) ensuring the correct wavelength registration of the data and (2) deriving extraterrestrial responses over the entire spectrum, including throughout strong water vapor and oxygen bands, are described. The resulting data produced are archived as ARM data records and include cloud-screened aerosol optical depths, spectral irradiances and direct normal solar transmission, as well as normalized diffuse and global irradiances.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2006

Solar Heating of Suspended Particles and the Dynamics of Martian Dust Devils

The heat input to Martian dust devils due to solar warming of suspended particles is assessed based on a prior estimate of dust loading and from an analysis of shadows cast by dust devils in images taken from orbit. Estimated values for solar heating range from 0.12 to 0.57 W/m3 with associated temperature increases of 0.011 to 0.051(deg)C per second. These warming rates are comparable to the adiabatic cooling rate expected for a gas parcel rising on Mars with a vertical velocity of 10 m/s. Solar warming of suspended dust serves to maintain buoyancy in a rising dust plume and may be one cause for the large scale of dust devils observed on Mars.

radiation interaction↗
NASA NTRS2010

Anticipated Electrical Environment Within Permanently Shadowed Lunar Craters

Shadowed locations ncar the lunar poles arc almost certainly electrically complex regions. At these locations near the terminator, the local solar wind flows nearly tangential to the surface and interacts with large-scale topographic features such as mountains and deep large craters, In this work, we study the solar wind orographic effects from topographic obstructions along a rough lunar surface, On the leeward side of large obstructions, plasma voids are formed in the solar wind because of the absorption of plasma on the upstream surface of these obstacles, Solar wind plasma expands into such voids) producing an ambipolar potential that diverts ion flow into the void region. A surface potential is established on these leeward surfaces in order to balance the currents from the expansion-limited electron and ion populations, Wc find that there arc regions ncar the leeward wall of the craters and leeward mountain faces where solar wind ions cannot access the surface, leaving an electron-rich plasma previously identified as an "electron cloud." In this case, some new current is required to complete the closure for current balance at the surface, and we propose herein that lofted negatively charged dust is one possible (nonunique) compensating current source. Given models for both ambipolar and surface plasma processes, we consider the electrical environment around the large topographic features of the south pole (including Shoemaker crater and the highly varied terrain near Nobile crater), as derived from Goldstone radar data, We also apply our model to moving and stationary objects of differing compositions located on the surface and consider the impact of the deflected ion flow on possible hydrogen resources within the craters

Farrell, W. M.↗
NASA NTRS2017

Development of a High-Fidelity Simulation Environment for Shadow-Mode Assessments of Air Traffic Concepts

This paper describes the Shadow-Mode Assessment Using Realistic Technologies for the National Airspace System (SMART-NAS) Test Bed. The SMART-NAS Test Bed is an air traffic simulation platform being developed by the National Aeronautics and Space Administration (NASA). The SMART-NAS Test Bed's core purpose is to conduct high-fidelity, real-time, human-in-the-loop and automation-in-the-loop simulations of current and proposed future air traffic concepts for the United States' Next Generation Air Transportation System called NextGen. The setup, configuration, coordination, and execution of realtime, human-in-the-loop air traffic management simulations are complex, tedious, time intensive, and expensive. The SMART-NAS Test Bed framework is an alternative to the current approach and will provide services throughout the simulation workflow pipeline to help alleviate these shortcomings. The principle concepts to be simulated include advanced gate-to-gate, trajectory-based operations, widespread integration of novel aircraft such as unmanned vehicles, and real-time safety assurance technologies to enable autonomous operations. To make this possible, SNTB will utilize Web-based technologies, cloud resources, and real-time, scalable, communication middleware. This paper describes the SMART-NAS Test Bed's vision, purpose, its concept of use, and the potential benefits, key capabilities, high-level requirements, architecture, software design, and usage.

human-in-the-loop↗
NASA NTRS1995

Saturn's central flash from the 3 July 1989 occultation of 28 Sgr

We present observations of Saturn's central flash obtained from Palomar and McDonald Observatories during the 3 July 1989 occultation of 28 Sgr. As the star passed close to the geometric center of Saturn's shadow, the focusing of the incident starlight by the planet's atmosphere formed multiple stellar images along the limb which were detected in infrared images obtained at wavelengths of 3.9 (Palomar) and 2.1 microns (McDonald). These are the first reported observations of a central flash due to Saturn, and the first of any planet in which the signal flash from each stellar image could be determined separately, permitting a comparison of both intensity and position for each image with model predictions. Four separate flashes were observed from each observatory, corresponding to points on the limb where the starlight passed through the Cassini Division and the relatively transparent C Ring, with maximum brightness reaching 1-2% of the unocculted stellar intensity. The timing of the flashes is quite sensitive to the shape of Saturn's limb, which depends in turn on the planet's zonal gravity harmonics and on the zonal wind profile in the lower stratosphere, near the 2.5-mbar pressure level. The locations of the images along the limb, as well as the timing, shapes, and amplitudes of the individual flash light curves, are well matched by a smoothed model based on a tropospheric zonal wind profile obtained from tracking cloud features in Voyager images and the Saturn ring optical depth profile obtained from the Voyager Photopolarimeter experiment. The smoothing required to give the best match to the data exceeds that attributable to the finite angular extent of the occulted star and may be due to refractive scattering by turbulence or wave structure in Saturn's atmosphere. There is no evidence of significant atmospheric absorption at the observed wavelengths, which correspond to spectral regions of weak methane absorption.

Nicholson, Philip D.↗
NASA NTRS2024

Advanced Libya-4 radiometric and atmospheric characterization utilizing MODIS and VIIRS full-scan reflective solar band measurements

The NASA Clouds and the Earth's Radiant Energy System (CERES) project provides observed flux and cloud products to the climate science community. The CERES instruments, along with the MODIS and VIIRS imagers, are onboard the Terra, Aqua, NPP, and NOAA20 satellites. In order to produce seamless multi-platform integrated products, long-term sensor stability and inter-calibration are required. Inter-calibration between sensors within the same sun-synchronous orbit relies on Earth invariant targets because simultaneous nadir overpasses are not possible. To facilitate inter-calibration efforts, the CERES Imager and Geostationary Calibration Group (IGCG) has improved the Libya-4 target characterization. Improvements include full scan angle characterization to enable daily observations, clear-sky identification using individual scan angle dynamic spatial homogeneity thresholds, and atmospheric corrections. The water vapor correction was found to be effective across the full scan, whereas the ozone and aerosol corrections were less effective. The atmospheric-corrected normalized radiance temporal fluctuations are similar across scan angles, spectral bands, and between the MODIS and VIIRS imagers, suggesting that the fluctuations are a result of the natural variability of the Libya-4 surface reflectance. The Libya-4 surface variability is more than likely caused by changes in the prevailing winds that alter sand dune orientation and resulting shadows. The full-scan-imager atmosphere and angle corrected reflected solar band radiance trend standard errors are between 0.6% and 1.0%, and for near-nadir observations, are between 0.5% and 0.8%. The advanced characterization suggests that the Libya-4 short-term surface reflectance anomalies may need to be considered for imager stability monitoring and inter-calibration efforts.

Libya-4 Pseudo-invariant Calibration Site↗
NASA NTRS2004

Recent Results in ICESat Geolocation Parameter Calibration from Range Residual Analysis

The Ice, Cloud and land Elevation Satellite (ICESat), launched on January 12, 2003, carries the Geoscience Laser Altimeter System (GLAS), which has a primary measurement of short-pulse laser-ranging to the Earths surface at 1064 nm wavelength at a rate of 40 pulses per second. The instrument has collected (at the time of this writing) over 540 million observations of the Earth's surface including precise elevation measurements of the ice sheets, sea ice roughness and thickness, ocean and land surface elevations and surface reflectivity. The accurate geolocation of GLASs surface returns, the spots from which the laser energy reflects on the Earths surface, is a critical issue in the scientific application of these data. Pointing, ranging, timing and orbit errors must be compensated to accurately geolocate the laser altimeter surface returns. Towards this end, the laser range observations can be fully exploited in an integrated residual analysis to accurately calibrate these geolocation/instrument parameters. The ICESat laser altimeter data have been simultaneously processed as direct altimetry from ocean sweeps and around-the-world scans along with dynamic crossovers in order to calibrate pointing ranging and timing. The analysis has resolved complex time varying signal resulting from thermal variations of instrument pointing and boresite shadowing. The calibration methodology and current calibration results are discussed along with future efforts and current geolocation accuracies.

Luthcke, Scott B.↗
NASA NTRS2018

Earthshine as an Illumination Source at the Moon

Earthshine is the dominant source of natural illumination on the surface of the Moon during lunar night, and at some locations within permanently shadowed regions (PSRs) near the poles that never receive direct sunlight. As such, earthshine has the potential to enable the scientific investigation and exploration of conditions in areas of the Moon that are either temporarily or permanently hidden from the Sun. Earthshine has also been used to refer to Earthlight reflected from the lunar surface, but in this study we use it to refer specifically to Earthlight incident at the Moon. Under certain circumstances, the heat flux from earthshine could also influence the transport and cold-trapping of volatiles present in the very coldest areas within PSRs. In this study, Earth's spectral irradiance, as it would appear at the Moon in the solar reflectance band (0.3–3.0 µm) and at thermal emission wavelengths (3–50 µm), is examined with a suite of model image cubes and whole-disk spectra created using the Virtual Planetary Laboratory (VPL) three-dimensional (latitude, longitude and altitude) modeling capability. At the Moon, the broadband, hemispherical irradiance from Earth at full-phase is approximately 0.15 W m−2 with comparable contributions from solar reflectance and thermal emission; for context, this about 0.01% that of solar irradiance and has an equivalent temperature of around 40 K. Over the simulated timeframe, spanning two lunations, Earth's thermal irradiance shows very little net change (less than a few mW m−2 resulting from cloud variability and the south-to-north motion of the sub-observer latitude on Earth). In the solar band, Earth's diurnally averaged light curve at phase angles g ≤ 60° is well-fit using a Henyey–Greenstein integral phase function. At wavelengths longward of about 0.7 µm, near the well-known vegetation “red edge”, Earth's reflected solar radiance shows significant diurnal modulation as a result of the broad maximum in projected landmass at terrestrial longitudes between 60°W and 0°, as well as from the distribution of clouds. A simple formulation with adjustable coefficients is presented, condensed from the VPL model grid, for estimating Earth's hemispherical irradiance at the Moon as a function of wavelength, phase angle and sub-observer coordinates (terrestrial latitude and longitude). Uncertainties in any one prediction are estimated to be 10–12% at 0.3 µm, rising to >25% near 2.5 µm as a result of the increasing relative brightness and unpredictable influence of clouds. Although coefficient values are derived from a suite of spring equinox models, the approximation appears to be valid for all seasons, to within the stated uncertainties. It is demonstrated that earthshine is sufficiently bright to serve as a natural illumination source for optical measurements on a robotic lander/rover, allowing the identification of water ice mixed with regolith at the percent-level of fractional area.

Surface↗
NASA NTRS2022

Lunar Rover Localization Using Craters as Landmarks

Onboard localization capabilities for planetary rovers to date have used relative navigation, by integrating combinations of wheel odometry, visual odometry, and inertial measurements during each drive to track position relative to the start of each drive. At the end of each drive, a “ground-in-the-loop” (GITL) interaction is used to get a position update from human operators in a more global reference frame, such as a map frame defined by orbital reconnaissance imaging of a large region around the rover’s current position. For Mars rovers, this typically has involved downlinking imagery from the rover mast cameras and using interactive visualization tools on Earth to register such images to the orbital reconnaissance images. For safety purposes, rover mission operations typically specify “keep out zones”, which human operators recognize as being unsafe in the orbital images. Autonomous rover drives are limited in distance so that accumulated relative navigation error does not risk the possibility of the rover driving into a keep out zone. The allowable autonomous drive distance in this mode of operation depends on the distribution of keep out zones and the accuracy of relative navigation; in practice, drive limits of a few hundred meters between GITL cycles are to be expected. Several rover mission concepts have recently been studied that require much longer drives between GITL cycles, particularly for the Moon. This includes lunar rover mission concepts that involve (1) driving mostly in sunlight at low latitudes, (2) driving in permanently shadowed regions near the south pole, and (3) a mixture of day and night driving in mid-latitudes. These concepts include total traverse distance requirements of up to 1,800 km in 4 Earth years, with individual drives of several kilometers between stops for downlink. These concepts require greater autonomy to minimize GITL cycles to enable such large range; onboard global localization is a key element of such autonomy. Multiple techniques have been studied in the past for onboard rover global localization, including radio navigation aiding from an orbiter, recognizing horizon landmarks that are known in a regional elevation map, and correlating a local elevation map created onboard the rover with a regional elevation map. These techniques all have drawbacks, including requiring an expensive extra mission element (navigation orbiter), unavailability of sufficient regional elevation map data, or limited accuracy in resulting position estimates (e.g. a few hundred meters with horizon landmarks). For the Moon, the ubiquitous craters offer another possibility, which involves mapping craters from orbit, then recognizing crater landmarks with cameras and/or a lidar onboard the rover. This approach is applicable everywhere on the Moon, does not require high resolution stereo imaging from orbit as some other approaches do, and has potential to enable position knowledge with order of 10 m accuracy at all times. This paper will provide more detail on our technical approach to crater-based lunar rover localization and will present initial results on crater detection using 3-D point cloud data from onboard lidar or stereo cameras and using shading cues in monocular onboard imagery.

Ono, M.↗
NASA NTRS2010

Analysis of Snow Bidirectional Reflectance from ARCTAS Spring-2008 Campaign

The spring 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) experiment was one of major intensive field campaigns of the International Polar Year aimed at detailed characterization of atmospheric physical and chemical processes in the Arctic region. A part of this campaign was a unique snow bidirectional reflectance experiment on the NASA P-3B aircraft conducted on 7 and 15 April by the Cloud Absorption Radiometer (CAR) jointly with airborne Ames Airborne Tracking Sunphotometer (AATS) and ground-based Aerosol Robotic Network (AERONET) sunphotometers. The CAR data were atmospherically corrected to derive snow bidirectional reflectance at high 1 degree angular resolution in view zenith and azimuthal angles along with surface albedo. The derived albedo was generally in good agreement with ground albedo measurements collected on 15 April. The CAR snow bidirectional reflectance factor (BRF) was used to study the accuracy of analytical Ross-Thick Li-Sparse (RTLS), Modified Rahman-Pinty-Verstraete (MRPV) and Asymptotic Analytical Radiative Transfer (AART) BRF models. Except for the glint region (azimuthal angles phi less than 40 degrees), the best fit MRPV and RTLS models fit snow BRF to within 0.05. The plane-parallel radiative transfer (PPRT) solution was also analyzed with the models of spheres, spheroids, randomly oriented fractal crystals, and with a synthetic phase function. The latter merged the model of spheroids for the forward scattering angles with the fractal model in the backscattering direction. The PPRT solution with synthetic phase function provided the best fit to measured BRF in the full range of angles. Regardless of the snow grain shape, the PPRT model significantly over-/underestimated snow BRF in the glint/backscattering regions, respectively, which agrees with other studies. To improve agreement with experiment, we introduced a model of macroscopic snow surface roughness by averaging the PPRT solution over the slope distribution function and by adding a simple model of shadows. With macroscopic roughness described by two parameters, the AART model achieved an accuracy of about plus or minus 0.05 with a possible bias of plus or minus 0.03 in the spectral range 0.4-2.2 micrometers. This high accuracy holds at view zenith angles below 55-60 degrees covering the practically important range for remote sensing applications, and includes both glint and backscattering directions.

Lyapustin, A.↗