Remote sensing of land, water, and atmosphere: the role of forward modeling as a data analysis tool

Forward modeling represents an emulation technique providing a numerical approximation of a physical process. Forward modeling is often applied to find a solution for problems where no direct inversion techniques are available. Typical examples are the determination of physical quantities that can only be found based on comparisons with successively refined models. Classical forward modeling often relies on learned guesses and practical experience. An overview will be given where this technique can be used profitably as a data analysis tool in remote sensing. We will show typical application areas such as imaging observations of land and water surfaces with optical and microwave instruments and compare the approaches with atmospheric retrieval techniques of a limb sounding instrument. Bridging the gap between practical experience and theoretical concepts, maximum likelihood calculations allow the assessment of forward modeling with respect to the accuracy of information extraction. Information theoretical bounds can be derived from the Cramer-Rao bound and the Kullbach-Liebler divergence. As a result, a maximum likelihood estimation can be defined and be interpreted as fitting the observed likelihood to its true value. This allows a determination of the attainable accuracy of the process to be modelled.