Classification, decomposition and modeling of polarimetric SAR data has received a great deal of attention in the recent literature. The objective behind these efforts is to better understand the scattering mechanisms which give rise to the polarimetric signatures seen in SAR image data. In this paper, a new approach is described, which involves the fit of a combination of three simple scattering mechanisms to the polarimetric SAR observations. The mechanisms are volume scatter from a cloud of randomly oriented dipoles, even-bounce scatter from a pair of orthogonal surfaces with different dielectric constants and Bragg scatter from a moderately rough surface. This composite scattering model is used to describe the polarimetric backscatter from naturally occurring scatterers. Results are presented of application of this new algorithm to different types of scene, including multi-frequency polarimetric SAR images of a tropical rain forest, a boreal forest, a pine forest, geologic targets, urban areas and agricultural fields. Fitting the model to polarimetric SAR data of the tropical rain forest for example, allows clear discrimination between flooded and non-flooded forest. The model can be used to estimate the overall contribution from each of the three basic scattering mechanisms for each SAR image pixel.