On utilization ofa priori knowledge in inversion of remote sensing models

Abstract

Satellite remote sensing deals with a complex system coupling atmosphere and surface. Any physical model with reasonable precision needs several to tens of parameters. Without a priori knowledge of these parameters, Proposition 3 of Verstraete et al. requires the number of independent observations to be greater than the number of unknown parameters. This requirement can hardly be satisfied even in the coming EOS era. As Tarantola pointed out, the inversion problems in geoscience are always underdetermined in some sense. In order to make good use of every kind of a priori knowledge for effectively extracting information from remote sensing observations, the right question to set is as follows:Given an imperfect model and a certain amount ofa priori information on model parameters, in which sense should one modify thea priori information, given the actual observation with noise?A priori knowledge of physical parameters can be presented in different ways such as physical limits, global statistical means and variance fora certain landcover type, or previous statistics and temporal variation of a specific target. When sucha priori knowledge can be expressed as joint probability density. Bayessian theorem can be used in the inversion to obtain posterior probability densities of parameters using newly acquired observations. There is no prerequirement on how many independent observations must be made, and the knowledge gained merely depends on the information content of the new observations. Some specific problems about knowledge accumulation and renewal are also discussed.