Optimization of Numerical Inversion in Photopolarimetric Remote Sensing

Abstract

Remote sensing is one primary tool for studying the interactions of solar radiation with the atmosphere and surface and their influence on the Earth radiation balance. During the past three decades the radiation measured from satellite, aircraft and ground have been employed successfully for characterizing radiative properties of land, ocean, atmospheric gases, aerosols, clouds, etc. One of the challenges in implementing remote sensing is the development of a reliable inversion procedure required for deriving information about the atmospheric or surface component interaction with the measured radiation. The inversion is particularly crucial and demanding for interpreting high complexity measurements where many unknowns should be derived simultaneously. Therefore the deployment of remote-sensing sensors of the next generation with diverse observational capabilities inevitably would be coupled with significant investments into inverse-algorithm development. Numerous publications offer a wide diversity of inversion methodologies suggesting somewhat different inversion methods. Such uncertainty in methodological guidance leads to excessive dependence of inversion algorithms on the personalized input and preferences of the developer. This study is an attempt to outline unified principles addressing such important aspects of inversion optimization as accounting for errors in the data used, inverting multi-source data with different levels of accuracy, accounting for a priori and ancillary information, estimating retrieval errors, clarifying potential of employing different mathematical inverse operations (e.g. comparing iterative versus matrix inversion), accelerating iterative convergence, etc. The described concept uses the principles of statistical estimation and suggests a generalized multi-term least-square-type formulation that complementarily unites advantages of a variety of practical inversion approaches, such as Phillips-Tikhonov-Twomey constrained inversion, Kalman filters, Gauss-Newton and Levenberg-Marquardt iterations, etc. The proposed methodology has resulted from the multi-year efforts of developing inversion algorithms for retrieving comprehensive aerosol properties from ground-based remote sensing observations.