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 (K GOLSR ) 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, K GO4 with considering sunlit/shaded vegetation and sunlit/shaded soil, K GO3 with considering sunlit/shaded soil and vegetation, K GO2 with considering vegetation and soil, and K GOg 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 K GOLSR has also been analyzed in depth. Results showed that (1) K GO4 had the highest accuracy and K GO3 was the second; in the case of only two available angles, K GOg 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 K GOLSR and K GO2 ; K GOLSR 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. Plain Language SummaryLand surface temperature is a key variable for a variety of geoscientific studies. However, because of the heterogeneity of land surface, this important parameter has a significant angular effect. Previous studies mainly learned from directional reflectance models. Therefore, in this study, we developed four geometric optical kernels for correcting directional effect of land surface temperature from the inherent characteristic of thermal radiation. These new kernels not only own clearer physical meaning but also have higher accuracies. Moreover, we also determined the best values of two structure characteristics to provide instruction for practical application.

Satellite Remote Sensing of Global Land Surface Temperature: Definition, Methods, Products, and Applications

“…The kernel‐driven model assumes that the LST angular effect is a linear combination of different kernels, which can be formulated as follows: $$$A{E}_{LST}\left({\theta }_{v},{\theta }_{s},\varphi \right)={f}_{iso}\cdot 1+{f}_{geo}\cdot {K}_{geo}\left({\theta }_{v},{\theta }_{s},\varphi \right)+{f}_{vol}\cdot {K}_{vol}\left({\theta }_{v},{\theta }_{s},\varphi \right)$$$ where AE LST is the angular effect of LST, which can be expressed by LST (X. Liu et al., 2021), and the LST difference (Duffour et al., 2016) or LST ratio (Vinnikov et al., 2012) between the observed direction and reference direction; 1, K geo , and K vol are the isotropic kernel, geometric‐optical (GO) kernel, and volume scattering kernel, respectively; these kernels are mathematical functions of observation angles, solar angles, and canopy structural parameters, representing component fractions or fraction differences (Wanner et al., 1995); f iso , f geo , and f vol are kernel coefficients, corresponding to different component temperature or temperature differences (X. Liu, Tang, Li, Zhang, & Shang, 2020); θ v , θ s , and φ are VZA, SZA, and relative azimuth angle, respectively.…”

Development of Kernel-Driven Models With Fixed Hotspot Width Under a General Modeling Framework in the Thermal Infrared Domain

“…A potentially valuable work is determining the best kerneldriven model containing a hotspot kernel with fixed width. Based on component temperature differences rather than their illumination differences, Liu et al [28] derivate four new GO kernels with clearer physical meaning. These four kernels respectively describe the temperature differences between sunlit/shaded vegetation/soil components, sunlit/shaded soil and vegetation components, sunlit soil and other components, and vegetation and soil components.…”

“…Specifically, from sparse to dense, LAI and FVC are 1 and 0.13, 2 and 0.32, and 4 and 0.57, respectively. In order to consider all cases of component temperature differences, the same scheme as Liu et al [28] has been used to generate 36 component temperature profiles (Fig. 1).…”

“…where fiso, fHotspot and fBasesahpe refer to corresponding coefficients. Liu et al [28] simplified the modified geometric projected (MGP) model, which also assumes that TOC radiance is the sum of four component radiances weighted by their area fractions, from the perspective of temperature differences. As a result, four GO kernels for directional thermal radiation have been proposed.…”

“…Though KLiDenseR further consider the temperature difference between sunlit and shaded vegetations, it assume that these two temperature differences are identical to reduce the number of coefficients. This approximation is unreasonable for most cases, which leads to a worse performance of K LiDenseR than K GOg [28].…”