Improving the Asymptotic Radiative Transfer Model to Better Characterize the Pure Snow Hyperspectral Bidirectional Reflectance

Abstract

The asymptotic radiative transfer (ART) model has been widely used in snow remote sensing. However, the anisotropic effects of snow reflectance challenge this model because of its underestimation in the forward-scattering direction. To exhibit these strong scattering properties of the snow surface, a microfacet specular kernel has been supplemented with the ART model (hereinafter named the ARTS model). In this study, we propose a method of multiplying by a correction term for improving the ART model (hereinafter named the ARTF model). We validate the performance of the ARTF model using various data sources. Our results demonstrate that: 1) the ARTF model has higher accuracy in characterizing snow bidirectional signatures, with <inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> and root mean square error (RMSE) values in the ranges from 0.722 to 0.990 and 0.007 to 0.041, respectively, than the ART (<inline-formula> <tex-math notation="LaTeX">$R^{2} =0.507$ </tex-math></inline-formula>&#x2013;0.802 and RMSE &#x003D; 0.038&#x2013;0.088) and ARTS (<inline-formula> <tex-math notation="LaTeX">$R^{2} =0.686$ </tex-math></inline-formula>&#x2013;0.962 and RMSE &#x003D; 0.021&#x2013;0.044) models, especially in the long-wave near-infrared region and 2) the ARTF model can effectively represent snow hyperspectral reflectance, while the ART and ARTS models significantly underestimate snow reflectance in the visible and shortwave near-infrared region. The <inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> values of these three models reach &#x007E;0.99, and the RMSE values of the ARTF model range from 0.012 to 0.024, which are smaller than those of the ART (RMSE &#x003D; 0.021&#x2013;0.061) and ARTS (RMSE &#x003D; 0.021&#x2013;0.049) models. These results demonstrate that the ARTF model is better than the ART and ARTS models for characterizing snow hyperspectral bidirectional reflectance.