The definition of remotely sensed reflectance quantities suitable for rugged terrain

The anisotropic scattering behavior of land surface is characterized by its bidirectional reflectance-distribution function (BRDF). However, a physically consistent BRDF definition is still lacking for heterogeneous and rugged terrain that accounts for approximately 24% of Earth's land surface. In this study, we revisited current BRDF definitions and updated them for rugged terrain with few dependent parameters: illumination and viewing geometries, terrain shadows, effective areas of illumination and observation, and anisotropic reflectance properties of subpixel-scale slopes. Furthermore, the bidirectional reflectance factor (BRF), hemispherical-directional reflectance factor (HDRF), directional-hemispheric reflectance (DHR), and bi-hemispherical reflectance (BHR) were proposed within the current physical framework of reflectance quantities. These reflectance quantities have been adopted by the 3-D Discrete Anisotropic Radiative Transfer (DART) model to provide the simulations of remote sensing images. To highlight the importance of a proper usage of such reflectance terms, we used DART simulations to present the topographic effects on these reflectance quantities. Finally, the other issues with respect to surface BRDF/BRF, such as spatial scale of rugged terrain, characterization of anisotropic reflectance of micro-scale surfaces, derivative reflectance quantities, topographic parameters, wavelength dependence and reciprocity, and future perspective were discussed.