Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison

Abstract The land surface albedo is a key parameter influencing the climate near the ground. Therefore, it must be determined with sufficient accuracy. In this paper, a statistical inversion method is presented in support of the application of kernel-based Bi-directional Reflectance Distribution Function (BRDF) models for the calculation of the surface albedo. The method provides the best linear unbiased estimations (BLUE) of the BRDF model coefficients for an arbitrary number of available angular measurements. When the number of measurements exceeds the number of the estimated coefficients, the QR decomposition method is proposed to improve the ill-conditional features of the inversion matrix. In other cases, the singular value decomposition (SVD) method is suggested. The proposed inversion method is innovative in that it provides confidence intervals for each of the BRDF model coefficients with a prescribed significance expressed by a probability level. Five candidate kernel-driven BRDF models were used in the present simulation study: Li–Sparse, Roujean, Li–Sparse–Wanner, Li–Dense and Walthall. A ground-based reflectance measurement data set including 11 surface types forms the background for the inversion experiments. The results show a strong dependence on the solar zenith angle (SZA) and on the land cover type (LCT) for all candidate models. Owing to this, none model could be recommend in a general manner. The Li–Sparse and the Li–Sparse–Wanner models performed the best for the grass and wheat LCT, while the Roujean model appeared as a favorite for the pine and deciduous forests. The implementation of the confidence interval technique shows that the BRDF model coefficients can be retrieved with an uncertainty of 20–30%, and somewhat greater in the case of forest. The measured angular reflectance curves lie, as a rule, within the uncertainty bands related to the 5% significance level (95% probability). The corresponding albedo estimates can be characterized by an absolute uncertainty of 1–2% in the visible band and 5–10% in the near infrared band, or by 10–30% in relative terms. The reflectance measurements at low SZA values are preferable for BRDF model inversion for the grassland and crop, while medium range of SZA seems to provide more information on forest features. For the majority of LCT, the results of BRDF model inversion seem to be less reliable when considering multi-angular measurements for various SZA than for a single SZA.