Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using polder BRDF measurements. II. Comparison of several inversion techniques and uncertainty in albedo estimates

Abstract This paper develops a concept related to the significant information extracted from the bidirectional reflectance distribution function (BRDF) of the terrestrial targets. The main issues are: the choice of the BRDF model, the solution to the inverse problem, and the accuracy assessment of estimated albedo. The present concept is based on the fact that the exact solution to the inverse problem belongs to a statistically significant region centered on the least squares solution (LSS). Nonetheless, LSS may be useless if the matrix inversion yields an ill-posed problem. It is then recommended to seek an alternative solution, which will yield a similar confidence interval but will be more physically sound. A list of 15 kernels entering in a basic model is examined by means of factor analysis performed in vector space, which is spanned at all known kernels. The application is carried out with synthetic angular data generated for the SEVIRI/MSG observing system. Models are evaluated based on statistical results—minimum of squared sum of residuals (SSR) and maximum of explained variance—after adjustment on reflectance data corresponding to a wide set of land cover types. Since the matrix of the model is almost singular, we identified an optimal subset model consisting of eight kernels, which has higher conditioned index and falls within the 95% confidence interval. It was found that the reflectance predicted by multi-kernel model is consistent with measurements. The idea in opting for a multi-kernel approach comes from the necessity to perform a higher angular resolution for the BRDF retrieval. Inversion experiments confirmed an advantage of the composite model over conventional three-parameter models in accuracy assessment of reflectance and albedo in the case of uniform and restricted angular samplings. Three methods are considered: statistical inversion (provided by the LSS), ridge regression and statistical regularization. The two latter are advised to solve the ill-conditioned inverse problem. Statistical regularization uses a priori statistical information. The inversion numerical experiment with SEVIRI/MSG angular geometry shows that only ridge regression provides a reasonable solution when a composite model is used. In addition, ridge regression and statistical regularization methods provide physically acceptable solutions in terms of BRDF and albedo predictability, even for three-parameter models. It is advised that LSS be implemented only at the middle of the summer season in the Northern Hemisphere. Otherwise, the use of ridge regression and statistical regularization is recommended to retrieve BRDF and albedo at other time periods in extra-tropical latitudes.

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