Abstract
BRDF defines anisotropy of the surface reflection. It is required to specify the boundary condition for radiative transfer (RT) modeling used in aerosol retrievals, cloud retrievals, atmospheric modeling and other applications. Ground based measurements of reflected radiance draw increasing attention as a source of information about anisotropy of surface reflection. Derivation of BRDF from surface radiance requires atmospheric correction. This study develops a new method of retrieving BRDF on its whole domain making it immediately suitable for further atmospheric RT modeling applications. The method is based on the integral equation relating surface reflected radiance, BRDF and solutions of two auxiliary atmosphere-only RT problems. The method requires kernel-based BRDF. The weights of the kernels are obtained with a quickly converging iterative procedure. RT modeling has to be done only one time before the start of iterative process.
Highlights
Radiation reflected from the Earth’s surface presents a valuable source of information about surface properties that can be formalized in the bi-directional reflection distribution function (BRDF)
If a plane-parallel atmosphere of total optical thickness τt and underlain with a surface given by BRDF (μ1, μ2, φ1 − φ2) (please note that both μ1 and μ2 are positive here in accordance with bottom boundary condition used in Radkevich [14], see Equation (3) there) is illuminated on its top with monodirectional light making polar angle θ0 with the vertical axis pointed to the surface, μ0 = cos(θ0), radiance of light reflected by the surface and propagating in direction (arccos(−μ), φ) at the surface level is given by the equation [13]
Though the origin of this noise is beyond the scope of this paper, its presence in the solution makes it a valuable opportunity to check robustness of BRDF retrievals by the iterative process described above
Summary
Radiation reflected from the Earth’s surface presents a valuable source of information about surface properties that can be formalized in the bi-directional reflection distribution function (BRDF). Ground based measurements of reflected radiance draw high attention as a source of information about anisotropy of surface reflection [1,2,3,4,5,6,7] in the past years, along with development of measurement techniques [8]. Atmospheric correction has to be done to derive BRDF from surface radiance, so retrieval methods were developed [9,10]. The retrieval methods are based on a comparison of the measured and computed reflected radiance at the ground level. If yet another evaluation of the radiance is needed, a full radiative transfer problem has to be solved anew for the estimate of BRDF. The accuracy of that approximation was found high in Lyapustin and Knyazikhin [11]
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