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NASA NTRS1984

Bidirectional reflectance spectroscopy. III - Correction for macroscopic roughness

A mathematically rigorous formalism is derived by which an arbitrary photometric function for the bidirectional reflectance of a smooth surface may be corrected to include effects of general macroscopic roughness. The correction involves only one arbitrary parameter, the mean slope angle, and is applicable to surfaces of any albedo. Using physically reasonable assumptions and mathematical approximations, the correction expressions are evaluated analytically to second order in the mean slope angle. The correction is applied to the bidirectional-reflectance function of Hapke (1981). Expressions for both the differential and integral brightnesses are obtained. Photometric profiles on hypothetical smooth and rough planets of low and high albedo are shown to illustrate the effects of macroscopic roughness. The theory is applied to observations of Mercury and predicts the integral phase function, the apparent polar darkening, and the lack of limb brightness surge on the planet. The roughness-corrected bidirectional-reflectance function is sufficiently simple that it can be conveniently evaluated on a programmable hand-held calculator.

Hapke, B.↗
NASA NTRS1992

Simulation of space measurements of vegetation canopy bidirectional reflectance factors

A vegetation canopy receives both monodirectional and scattered radiation which is then reflected back into the atmosphere according to its bidirectional reflectance distribution function (BRDF). Remote measurements are typically the angular and spectral distributions of radiations exiting the atmosphere. The evaluation of vegetation canopy bidirectional reflectance factors requires a numerical solution of the canopy radiative transfer equation. A horizontally homogeneous vegetation canopy, of finite physical depth, filled densely with small leaves and bounded by a flat Lambertian ground surface is considered. The canopy is illuminated spatially uniformly by monodirectional radiation. The scattered intensity distribution emerging at the top of the canopy in all directions in the upper hemisphere is evaluated. The magnitude, sign and angular distribution of atmospheric effects are wavelength specific and depend on the composition of the atmosphere. The net atmospheric effect is positive (negative) at the red (near-infrared) wavelength due to strong scattering (absorption) in the atmosphere. The angular distribution of these effects is bowl-shaped. Thus, off-nadir remote observations, especially at shorter wavelengths, are most affected by atmospheric perturbations.

Myneni, R. B.↗
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 NTRS2017

Laser Pulse Bidirectional Reflectance from CALIPSO Mission

In this Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) study, we present a simple way of determining laser pulse bidirectional reflectance over snow/ice surface using the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) 532 nanometer polarization channels' measurements. The saturated laser pulse returns from snow and ice surfaces are recovered based on surface tail information. The method overview and initial assessment of the method performance will be presented. The retrieved snow surface bidirectional reflectance is compared with reflectance from both CALIOP cloud cover regions and Moderate Resolution Imaging Spectroradiometer (Earth Observing System (EOS)) (MODIS) Bi-directional Reflectance Distribution Function (BRDF) / Albedo model parameters. The comparisons show that the snow surface bidirectional reflectance over Antarctica for saturation region are generally reliable with a mean value of about 0.90 plus or minus 0.10, while the mean surface reflectance from cloud cover region is about 0.84 plus or minus 0.13 and the calculated MODIS reflectance at 555 nanometers from the BRDF / Albedo model with near nadir illumination and viewing angles is about 0.96 plus or minus 0.04. The comparisons here demonstrate that the snow surface reflectance underneath the cloud with cloud optical depth of about 1 is significantly lower than that for a clear sky condition.

Lu, Xiaomei↗
NASA NTRS1990

Modelling planetary bidirectional reflectance over land

Simulations of the bidirectional reflectance distribution functions at the top of the atmosphere (TOA) over land surfaces were performed and compared with observations derived from Nimbus-7. The two methods produce similar patterns even though the model computations were performed under the assumptions of a Lambertian surface. These results raise a question regarding the need to account for surface anisotropy in simulations intended for the interpretation of low-resolution satellite observations.

Pinker, R. T.↗
NASA NTRS1992

Prediction and measurement of soil bidirectional reflectance

The present model for soil bidirectional reflectance distribution functions in the visible and reflective IR ranges is based on a representation of soil surfaces by a collection of opaque spheres atop a Lambertian horizontal surface. The model is not sensitive to increases in the sphere area index beyond a value of 0.4. Observed soil reflectance factor data for a tilled field are noted to be consistent with those predicted by the model's expression of soil reflectance as a function of the horizontal area obscured by a sphere, the amount of surface in shadow, and relative brightness of a sphere, and the fraction of diffuse illumination.

Irons, James R.↗
NASA NTRS2010

The Effect of Incident Light Polarization on Vegetation Bidirectional Reflectance Factor

The Laboratory-based Bidirectional Reflectance Factor (BRF) polarization study of vegetation is presented in this paper. The BRF was measured using a short-arc Xenon lamp/monochromator assembly producing an incoherent, tunable light source with a well-defined spectral bandpass at visible and near-infrared wavelengths of interest at 470 nm and 870 nm and coherent light source at 1.656 microns. All vegetation samples were measured using P and S linearly polarized incident light over a range of incident and scatter angles. By comparing these results, we quantitatively examine how the BRF of the samples depends on the polarization of the incident light. The differences are significant, depend strongly on the incident and scatter angles, and can be as high as 120% at 67 deg incident and 470nm. The global nature of Earth's processes requires consistent long-term calibration of all instruments involved in data retrieval. The BRF defines the reflection characteristics of Earth surface. It provides the reflectance of a target in a specific direction as a function of illumination and viewing geometry. The BRF is a function of wavelength and reflects the structural and optical properties of the surface. Various space and airborne radiometric and imaging remote sensing instruments are used in the remote sensing characterization of vegetation canopies and soils, oceans, or especially large pollution sources. The satellite data is validated through comparison with airborne, ground-based and laboratory-based data in an effort to fully understand the vegetation canopy reflectance, The Sun's light is assumed to be unpolarized at the top of the atmosphere; however it becomes polarized to some degree due to atmospheric effects by the time it reaches the vegetation canopy. Although there are numerous atmospheric correction models, laboratory data is needed for model verification and improvement.

Georgiev, Georgi T.↗
NASA NTRS1987

Quantitative abundance estimates from bidirectional reflectance measurements

A simplified approach for estimating mineral abundances in mineral mixtures from bidirectional reflectance measurements is presented. Fundamental to this approach is a priori information concerning reflectance spectra of the individual minerals and an estimate of the particle sizes of the components. Simplified equations for bidirectional reflectance are used to linearize the systematics of spectral mixing. The method was used to determine the relative proportions of olivine, magnetite, enstatite, and anorthite in a mixture; the mass fractions of mixture components were calculated on the basis of known particle diameters. The results indicate that for materials without strongly adsorbing components, the accuracy of abundance determinations is better than 5 percent.

Mustard, John F.↗
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.↗
NASA NTRS1986

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. Leaf bidirectional reflectance and transmittance distribution functions were measured for corn and soybean leaves. The measurements clearly show that leaves are complex scatterers and considerable specular reflectance is possible. Because of the character of leaf reflectance, true leaf reflectance is larger than the nadir reflectances that are normally used to represent leaves. A 3-dimensional reflectance model, named BIGAR (Bidirectional General Array Model), was developed and compared with measurements from corn and soybean. The model is based on the concept that heterogeneous canopies can be described by a combination of many subcanopies, which contain all the foliage, and these subcanopy envelopes can be characterized by ellipsoids of various sizes and shapes. The model/measurement comparison results indicate that this relatively simple model captures the essential character of row crop BRDF's. Finally, two soil BDRF models were developed: one represents soil particles as rectangular blocks and the other represents soil particles as spheres. The sphere model was found to be superior.

Norman, John M.↗
NASA NTRS1991

Surface albedo from bidirectional reflectance

The validity of integrating over discrete wavelength bands is examined to estimate total shortwave bidirectional reflectance of vegetated and bare soil surfaces. Methods for estimating albedo from multiple angle, discrete wavelength band radiometer measurements are studied. These methods include a numerical integration technique and the integration of an empirically derived equation for bidirectional reflectance. It is concluded that shortwave albedos estimated through both techniques agree favorably with the independent pyranometer measurements. Absolute rms errors are found to be 0.5 percent or less for both grass sod and bare soil surfaces.

Ranson, K. J.↗
NASA NTRS2012

Assessment of a Bidirectional Reflectance Distribution Correction of Above-Water and Satellite Water-Leaving Radiance in Coastal Waters

Water-leaving radiances, retrieved from in situ or satellite measurements, need to be corrected for the bidirectional properties of the measured light in order to standardize the data and make them comparable with each other. The current operational algorithm for the correction of bidirectional effects from the satellite ocean color data is optimized for typical oceanic waters. However, versions of bidirectional reflectance correction algorithms specifically tuned for typical coastal waters and other case 2 conditions are particularly needed to improve the overall quality of those data. In order to analyze the bidirectional reflectance distribution function (BRDF) of case 2 waters, a dataset of typical remote sensing reflectances was generated through radiative transfer simulations for a large range of viewing and illumination geometries. Based on this simulated dataset, a case 2 water focused remote sensing reflectance model is proposed to correct above-water and satellite water-leaving radiance data for bidirectional effects. The proposed model is first validated with a one year time series of in situ above-water measurements acquired by collocated multispectral and hyperspectral radiometers, which have different viewing geometries installed at the Long Island Sound Coastal Observatory (LISCO). Match-ups and intercomparisons performed on these concurrent measurements show that the proposed algorithm outperforms the algorithm currently in use at all wavelengths, with average improvement of 2.4% over the spectral range. LISCO's time series data have also been used to evaluate improvements in match-up comparisons of Moderate Resolution Imaging Spectroradiometer satellite data when the proposed BRDF correction is used in lieu of the current algorithm. It is shown that the discrepancies between coincident in-situ sea-based and satellite data decreased by 3.15% with the use of the proposed algorithm.

LISCO(LONG ISLAND SOUND COASTAL OBSERVATORY)↗
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.↗
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.↗