The Description and Application of BRDF Based on Shape Vectors for Typical Landcovers
Authors: Yang Jian , Huang Jiapeng , Fan Hongdong , Duan Junbo , Ma Xianwei 
Published: September 2022

As the inherent attribute of land cover, anisotropy leads to the heterogeneity of directional reflection; meanwhile, it creates the opportunity for retrieving characteristics of land surface based on multi-angle observations. BRDF (Bidirectional Reflectance Distribution Function) is the theoretical expression of anisotropy and describes the reflectance in terms of incident-view geometry. Prior BRDF knowledge is used to achieve the multi-angle retrieval for earth observation systems with a narrow FOV (Field of View). Shape indicators are a feasible way to capture the characteristics of BRDF or to build an a priori database of BRDF. However, existing shape indicators based on the ratio of reflectance or the weight of scattering effects are too rough to describe the BRDF’s shape. Thus, it is necessary to propose new shape vectors to satisfy the demand. We selected six typical land covers from MODIS-MCD12 on the homogeneous underlayers as the study sites in North America. The daily BRDF is retrieved by MODIS-BRDF parameters and the RossThick-LiSparseR model. When the SZA (Solar Zenith Angle) is set at 45°, seven directions (−70°, −45°, −20°, 0°, 20°, 45°, and 70°) including edge spot, zenith spot, hot spot and approximate dark spot of the BRDF principal plane were selected to construct two vectors by the change rate of reflectance and angle formulation: Partial Anisotropic Vector (PAV) and Angular Effect Vector (AEV). Then, we assessed the effectiveness of PAV and AEV compared with ANIX (Anisotropic Index), ANIF (Anisotropic Factor) and AFX (Anisotropic Flat Index) by two typical BRDF shapes. The representativeness of PAV and AEV for the original BRDF was also assessed by cosine similarity and error transfer function. Lastly, the application of hot spot components in AEV for land cover classification, the monitoring of land cover in mining areas and the adjustment effect by NDVI (Normalized Difference Vegetation Index) were investigated. The results show that (1) the shape vectors have good representativeness compared with original BRDF. The representativeness of PAV assessed by cosine similarity is 0.980, 0.979 and 0.969, and the representativeness of AEV assessed by error transfer function is 0.987, 0.991 and 0.994 in the three MODIS broadbands of Near Infrared (NIR, 0.7–5.0 µm), Short Wave (SW, 0.3–5.0 µm) and Visible (VIS, 0.3–0.7 µm). (2) Some components of shape vectors have high correlation with AFX. The correlation coefficient between hot spot components in AEV and AFX is 0.936, 0.945 and 0.863, respectively, in NIR, SW and VIS bands. (3) The shape vectors show potentiality for land cover classification and the monitoring of land cover in mining areas. The correlation coefficients of hot spot components in AEV for MODIS-pixels with the same types (0.557, 0.561, 0.527) are significantly higher than MODIS-pixels with various types (0.069, 0.055, 0.051) in NIR, SW and VIS bands. The coefficients of variation for hot spot components are significantly higher after land reclamation (0.0071, 0.0099) than before land reclamation (0.0020, 0.0028). (4) The correlation between NDVI and the BRDF shapes is poor in three MODIS broad bands. The correlation coefficients between NDVI and the BRDF shapes in three temporal scales of annual, seasonal and monthly phases are only 0.134, 0.063 and 0.038 (NIR), 0.199, 0.185 and 0.165 (SW), and 0.323, 0.320 and 0.337 (VIS), on average.