Bidirectional Reflectance Model Research Articles

A simple analytical function for bidirectional reflectance

A simple bidirectional reflectance model based on physical scattering laws is developed to calculate the bidirectional reflectance of a wide variety of surfaces. Chandrasekhar's radiative transfer solution, obtained for the anisotropically scattering semi‐infinite medium, is used to compute the multiplescattered radiances. However, since the radiative transfer solution does not take architectural effects into consideration, we adopt Hapke's (1986) approach and add an empirical term to explain the hot‐spot phenomenon and use Cox and Munk's (1954) formulation to take into account the specular reflection. The physical parameters of the model are retrieved from bidirectional reflectance measurements. For each surface, only one set of model parameters is needed for application to all illumination and viewing geometries. The validity of the model is established by comparing the computed and measured reflectances for sets of viewing and illumination angles that were not included in the inversion algorithm. Good agreement is shown between the model‐computed and the observed reflectances for dense prairie vegetation canopies, a sparse desert scrub community, a plowed agricultural field, and an alkali flat.

On the design and validation of surface bidirectional reflectance and albedo models

Physically based mathematical models of the bidirectional reflectance of terrestrial surfaces are needed to compute the albedo of these surfaces. Such models are also necessary to interpret satellite remote sensing data in terms of the fundamental physical parameters of the soil and vegetation which control how radiation is reflected by these media. Since a wide variety of mathematical functions can be made to fit the observed reflectances, a clear and discriminating strategy must be thought out to validate the proposed models. Such a strategy consists in inverting the models against reflectance data, and comparing the retrieved values of the parameters to those obtained independently from field or laboratory measurements. In this article, we review the state-of-the-art in modeling the bidirectional reflectance of natural surfaces, describe how such models can be validated, and highlight the remaining challenges for the remote sensing community.

Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing

In the case where a vegetation cover can be regarded as a collection of individual, discrete plant crowns, the geometric-optical effects of the shadows that the crowns cast on the background and on one another strongly condition the brightness of the vegetation cover as seen from a given viewpoint in the hemisphere. An asymmetric hotspot, in which the shape of the hotspot is related to the shape of the plant crowns in the scene, is created. At large zenith angles illumination shadows will preferentially shadow the lower portions of adjacent crowns. Further, these shadows will be preferentially obscured since adjacent crowns will also tend to obscure the lower portions of other crowns. This effect produces a 'bowl-shaped' bidirectional reflectance distribution function (BRDF) in which the scene brightness increases at the function's edges. Formulas describing the hotspot and mutual-shadowing effects are derived, and examples that show how the shape of the BRDF is dependent on the shape of the crowns, their density, their brightness relative to the background, and the thickness of the layer throughout which the crown centers are distributed are presented. >

The 27–28 October 1986 FIRE IFO Cirrus Case Study: Cirrus Parameter Relationships Derived from Satellite and Lidar Data

Cirrus cloud radiative and physical characteristics are determined using a combination of ground-based aircraft, and satellite measurements taken as part of the FIRE Cirrus Intensive Field observations (IFO) during October and November 1986. Lidar backscatter data are used with rawinsonde data to define cloud base, center, and top heights and the corresponding temperature Coincident GOES 4-km visible (0.65 μm) and 8-km infrared window (11.5 μm) radiances are analyzed to determine cloud emittances and reflectances. Infrared optical depth is computed from the emittance results. Visible optical depth is derived from reflectance using a theoretical ice crystal scattering model and an empirical bidirectional reflectance model. No clouds with visible optical depths greater than 5 or infrared optical depths less than 0.1 were used in the analysis. Average cloud thickness ranged from 0.5 km to 8.0 km for the 71 scenes. Mean vertical beam emittances derived from cloud-center temperatures were 0.62 for all scenes compared to 0.33 for the cam study (27–28 October) reflecting the thinner clouds observed for the latter scenes. Relationships between cloud emittance, extinction coefficients, and temperature for the case study are very similar to those derived from earlier surface-based studies. The thicker clouds seen during the other IFO days yield different results. Emittances derived using cloud-top temperature were ratioed to those determined from cloud-center temperature. A nearly linear relationship between these ratios and cloud-center temperature holds promise for determining actual cloud-top temperatures and cloud thickness from visible and infrared radiance pairs. The mean ratio of the visible scattering optical depth to the infrared absorption optical depth was 2.13 for these data. This scattering efficiency ratio shows a significant dependence on cloud temperature. Values of mean scattering efficiency as high as 2.6 suggest the presence of small ice particles at temperatures below 230 K. The parameterization of visible reflectance in terms of cloud optical depth and clear-sky reflectance shows promise as a simplified method for interpreting visible satellite data reflected from cirrus clouds. Large uncertainties in the optical parameters due to cloud reflectance anisotropy and shading were found by analyzing data for various solar zenith angles and for simultaneous AVHRR data. Inhomogeneities in the cloud fields result in uneven cloud shading that apparently causes the occurrence of anomalously dark, cloudy pixels in the GOES data. These shading effects complicate the interpretation of the satellite data. The results highlight the need for additional study of cirrus cloud scattering processes and remote sensing techniques.

Photometric phase functions of common geologic minerals and applications to quantitative analysis of mineral mixture reflectance spectra

Hapke's model for bidirectional reflectance is used to calculate the mass fractional abundance of components in intimately mixed, particulate surfaces from laboratory reflectance spectra. Application of this model, simplified by the assumptions that all surfaces scatter light with the same constant phase function and the opposition surge is negligible, to binary mineral mixtures are summarized and compared with new results for ternary mixtures of olivine, enstatite, and anorthite. These experimental tests indicate that the simple model is accurate to within 7% for mixtures not containing low albedo components (<10% reflectance). However, several observed systematic deviations of the calculated mass fractions from the actual mass fractions suggest that the simple model may be improved by allowing for variable scattering between the minerals used. An empirical scattering function, based on the physically plausible scattering behavior that low albedo materials are backward scattering and high albedo, transparent materials are forward scattering, reduces the magnitude of the systematic deviations in mass fractions observed with the constant scattering model. To determine if the empirical scattering function is representative of the actual scattering behavior of particulate mineral surfaces, specific photometric parameters (single‐scattering albedo, single‐particle phase function) of five different mineral components (olivine, enstatite, anorthite, magnetite, hematite) and two mineral mixtures (90% olivine 10% magnetite, 25% olivine 75% magnetite) are derived from bidirectional reflectance spectra measured at 17 different viewing geometries between 0.5 and 1.6 μm. Mineral components were crushed and wet sieved with ethanol to a 45 to 75 μm particle size. All reflectance data are corrected for the non‐Lambertian scattering properties of halon. Analysis of the parameters of the single‐particle phase function indicate that each mineral defines a relatively unique suite of scattering parameters as a function of albedo. In particular, the silicates are forward scattering where the degree of forward scattering increases with albedo, magnetite is forward scattering but the degree of forward scattering decreases with albedo, and hematite is entirely backward scattering where the degree of backward scattering increases with albedo. It is apparent that the physical properties of the particles (roughness, transparency, shape) rather than albedo or chemical composition determine the gross scattering properties of the particulate surfaces studied here. The scattering parameters of the mixtures are similar to the parameters of the more abundant mineral in the mixture. The experimentally determined single‐scattering albedos are used to calculate the mass fractions of olivine and magnetite in these mixtures. These new fractions are much improved over the previous analyses and indicate that more detailed information regarding the geometric dependence of reflectance overcomes the systematic deficiencies of the simplified methods. In general, the simplified method is appropriate for mixtures not containing low albedo material using bidirectional reflectance measured at intermediate phase angles (20°–40°) and small emergence angles (near 0°). Abundance estimates using this approach are accurate to within 5–10% when information regarding the particle size of the surface components is available, and in a relative sense for surfaces of unknown particle size distributions. More precise abundance estimates can be derived if the scattering properties of the surface are well characterized and incorporated into the analysis.

Engineering model of surface specularity - Spacecraft design implications

Spacecraft thermal design relies on radiative transfer computer codes based on the concept of diffuse and specular components of surface hemispherical reflectance. This study describes an engineering model of bidirectional reflectance that leads to a simple two-parameter definition of specularity (ratio of specular component to hemispherical reflectance). The parameters are observable from bidirectional reflectance data for normal incidence and are the ratio of specular peak magnitude to uniform base magnitude (bimodal ratio) and the half-angle subtended by the specular peak. Normal directional reflectance is introduced as a scale factor. Directional variations of the peak bidirectional reflectance and the conical half-angle are postulated to allow separable, successive integrations over emergent and incident half-space to obtain approximate closed-form expressions for the diffuse and specular components of hemispherical reflectance and specularity. Numerical evaluation shows that specularity is a strong increasing function of both bimodal ratio and conical half-angle. Nomenclature A — area D = detector signal, Ref. 10 FJk = shape factor coupling Aj and Ak i' = directional radiation intensity / = bidirectional radiation intensity J = integral in specular solid angle, Eq. (13) N = bimodal ratio, peak bidirectional reflectance to base bidirectional reflectance, pmlp q'a — reflected irradiation at dA2 based on bimodal model q'a — reflected irradiation at dA2 based on diffuse

Determination of the clear-sky planetary albedo from AVHRR using a bi-directional reflectance model

Clear-sky planetary albedos are derived from NOAA-9 AVHRR data during 1986 over the U.S. Great Plains with several distinct surface types (shrubland, grassland, deciduous and coniferous forests). The cloud-free observations are selected using a combination of absolute threshold and spatial coherence cloud-screening procedures. The broadband albedo is approximated from the narrow-band visible and near-infrared albedos. Bi-directional reflectivity models are applied to account for the effect of Sun-target-sensor geometry. The corrected albedos are converted to daily means using a directional model to account for the dependence upon sun angle. The results indicate a significant reduction in variability of the observed albedos. The efficiency of the model application is demonstrated on two examples: 1) using time series of cloud-free observations over one target and 2) using one daily image of mapped data in July, 1986.

A simple bidirectional reflectance model for terrestrial surfaces

A simple bidirectional reflectance model is derived for terrestrial surfaces. This model uses photometric relationships together with data from the Nimbus 7 Earth Radiation Budget (ERB) Experiment. It is shown that the model provides a good description of bidirectional patterns derived from satellite observations for two classes of broad uniform surfaces, namely, land and desert. Dependency of the derived albedo model on solar zenith angle is also studied and compared with several observations made at the surface of the earth. Despite the simplicity of the approach the proposed bidirectional reflectance model might be useful for several applications in satellite remote sensing.

Cloud bidirectional reflectance functions: a comparison of experimental and theoretical results

A comparison of bidirectional reflectance models developed by radiative transfer theory calculations with empirical models developed from Nimbus 7 Earth Radiation Budget (ERB) measurements indicates good overall comparison, with rms differences of about 10 percent for solar zenith angles lower than 60 deg. The results of these comparisons demonstrate that the theoretical model provides a good description of the reflected radiance fields of clouds as seen by satellite. A cloud model based on Geosynchronous Operational Environmental Satellite (GOES) data was also compared with the Nimbus 7 general cloud model, and it is found that bidirectional models which compare well with the Nimbus 7 ERB results can be reproduced using GOES data.

Diurnal Variability of Regional Cloud and Clear-Sky Radiative Parameters Derived from GOES Data. Part III: November 1978 Radiative Parameters

Abstract The diurnal variability of the radiation emitted and reflected from the earth-atmosphere is investigated at the regional scale using November 1978 GOES-East visible and infrared data and GOES-derived cloud information. Narrowband GOES data are converted to broadband radiances using spectral calibration functions determined empirically from colocated Nimbus-7 ERB and GOES-East measurements over ocean, land and cloud surfaces. Shortwave radiances are used to estimate radiant exitances with bidirectional reflectance models derived from GOES and aircraft data for ocean, land and clouds. Average albedo over clear ocean and land changed by factors of 4.2 and 2.2, respectively, for a solar zenith angle range of 0 to 80°. Average cloud albedo changed by a factor of 1.8 for the same range of solar zenith angles, but varied considerably from region to region. Mean clear-sky longwave radiant exitance varied diurnally from 2 W m−2 over some ocean areas to 100 W m−2 in one high elevation desert area in the An...

Diurnal Variability of Regional Cloud and Clear-Sky Radiative Parameters Derived from GOES Data. Part I: Analysis Method

Abstract A hybrid bispectral threshold method (HBTM) is developed for hourly regional cloud and radiative parameters from geostationary satellite visible and infrared radiance data. The quantities derived with the HBTM include equivalent blackbody temperatures for clear skies, for the total cloud cover and for the cloud cover at three levels in the atmosphere; the total fractional cloud cover and the fractional cloud amounts at three altitudes; and the clear-sky and total cloud reflectance characteristics. Geostationary satellite data taken during November 1978 are analyzed. A minimum reflectance technique is used to determine clear-sky brightness. A visible bidirectional reflectance model is derived for clear ocean areas. Clear-sky radiative temperature is found with a bispectral clear radiance technique during daylight hours. An empirical model is derived to predict clear-sky temperature at night. A combination of previously published infrared threshold and bispectral techniques is used to determine the...

Reflected Solar Radiances from Regional Scale Scenes

Abstract A set of bi-directional reflectance models is presented for various atmospheric scene types. The models were composited from data collected from an aircraft platform in May-July 1979 during Summer MONEX. The space scale of the composited models is generally from 250 to 1000 km, which corresponds to the scale of interest in climate monitoring and modeling. Composite models for the following scene types are presented: the desert sands of the Saudi Arabian Empty Quarters, the Himalayan mountains, the Arabian Sea with the ever-present fair weather cumulus cloudiness, the semi-arid agricultural land surface of the Indian subcontinent under pre-monsoon conditions, broken middle and low level clouds over ocean, an altostratus cloud deck, and the broken pack-ice fields of Hudson Bay. Nearly all the models display a degree of anisotropy such that serious errors (10–100%) would result in the reflected flux density isotropically inferred from some of the reflected radiances. The features of many of the mode...

Target-reflectivity theory for coherent laser radars

The general target characterization for coherent laser radars is shown to be a two-frequency bistatic scattering-amplitude matrix. This matrix is used to develop target-signature expressions for pulsed imager and 3-D imager systems. The relationships between the scattering matrix and the more familiar bidirectional reflectance, diffuse reflectivity, and multiplicative target models are explored. Problems that may arise in test bed or reflectometer measurements of target reflectivity are discussed, and test bed calibration-plate measurement data are reported. The latter will indicate the viability of diffuse reflectivity for rough-surface targets.

Bidirectional Reflectance Simulation

To improve techniques in remote sensing data analyses, the authors composed a program by introducing the idea of bidirectional reflectance model developed by D.D. Egbert. By applying the program to the forest, the effectiveness of the bidirectional reflectance ratio simulation model was confirmed. The simulation experiment was done step by step: first laboratory experiments, then field experiments and finally experiments using aerophoto data.As a result, the authors found the forest reflectance characteristic was simulated by the spherical perturbation model. And in the experiment using aerophoto data, the bidirectional reflectance ratio could be estimated by the reformed model plus topographical data and surface structure data of forest.

Surface roughness effects on equilibrium temperature.

An analysis is presented for evaluation of equilibrium temperature distribution on radiatively adiabatic, adjoint planes which are uniformly irradiated by a collimated solar flux. The analysis employs a semigrey spectral model. Radiation properties for surface emitted radiation are obtained from the expressions of electromagnetic theory for smooth surfaces. Rough surface properties for solar radiation are given by the Beckmann bidirectional reflectance model. Numerical solutions to the governing equations yield equilibrium temperature distributions for a range of the influencing parameters. Surface roughness has little influence on equilibrium temperature for materials with high values for solar absorptance. However, for low or intermediate values of solar absorptance, roughness effects on the spatial distribution of reflected solar radiation can significantly alter equilibrium temperature particularly at surface elements where radiant interaction is small.