Multiplicity of solutions of the inverse problem for determining optical atmospheric parameters from remote observations

Abstract

Global climate change observed during the last two decades of the 20th century has attracted the attention of the world's scientific community. The non-uniqueness of atmospheric aerosols and the impact of clouds on warming (or cooling) of the atmosphere-underlying surface system need more detailed modelling to elucidate the optical properties of the atmosphere and surface. In multi-angle remote sensing, inverse problem retrieval using radiances over only one pixel presents a fundamental difficulty involving the multiplicity of solutions. In particular, it was found that different analytical approaches for the retrieval of optical parameters give a multiplicity of solutions, even in the simplest case of the slab homogeneous model and the standard scheme of illumination of the clear atmosphere. The phase function was approximated with one parameter functions. Only four parameters of the homogeneous atmosphere are retrieved in our simple variant. The found effect does not link with the low information content of observational data in respect to the desired parameters. It is not a result of the ill-posed inverse problem, insofar as it concerns properties of integral functionals in customary comprehension and calls for strong variations of vertical profiles of parameters. It seems that the effect of solution multiplicity is a direct consequence of radiation field non-linear dependence on atmospheric and surface parameters that leads to closely coinciding radiation fields forming with essentially different combinations of optical parameters.

Acknowledgements

The study was supported by Russian Foundation for Basic Research, Grants No. 05-05-64653-а.