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Effective exploitation of polarimetric SAR interferometry data over vegetated areas requires the use of a vegetation model of sufficient complexity to capture the underlying scattering processes. The standard Treuhaft model (randomly oriented vegetation + ground) makes a number of assumptions that may not be true in general. This paper presents a two-layer extended model that allows canopy attenuation to be a function of polarization, does not require the canopy to extend all the way to the ground, and allows the ground to be sloped. It is shown that many cases exist in which the two models predict similar coherence region shapes for significantly different structural parameters. It is argued that a minimum of two baselines is required for robust model selection and inversion.