On the Derivation of Geometric Optical Kernels for Directional Thermal Radiation

Abstract

The derivation of widely used geometric optical (GO) kernels in bidirectional reflectance distribution function models, that is, LiSparseReciprocal kernel (KGOLSR) and LiDenseReciprocal kernel, was based on two important assumptions: (1) The shaded components are perfect black and (2) the contributions of two sunlit components are identical. Different from the bidirectional reflectance, thermal radiation directionality effect mainly results from component temperature differences, suggesting the above assumptions are not applicable in most situations. Therefore, this study derived GO kernels for thermal radiation based on temperature differences rather than illumination differences. Specifically, four GO kernels, that is, KGO4 with considering sunlit/shaded vegetation and sunlit/shaded soil, KGO3 with considering sunlit/shaded soil and vegetation, KGO2 with considering vegetation and soil, and KGOg only considering the hottest sunlit soil, have been developed. By using a comprehensive simulated data set, their performances have been thoroughly evaluated and the comparison with KGOLSR has also been analyzed in depth. Results showed that (1) KGO4 had the highest accuracy and KGO3 was the second; in the case of only two available angles, KGOg performed best. (2) Variables such as component temperature, component emissivity, solar zenith angle, and the percentage of tree crown cover mainly affected the comparison result between KGOLSR and KGO2; KGOLSR would have a better performance for a scene with a stronger vegetation effect. Moreover, the best values of two structure characteristics, that is, the crown shape parameter b/r and relative height h/b, for these five kernels have been determined, which can provide instruction for practical application.