Emissivity Calculations for two-dimensional ocean Surfaces with the improved Integral Equation Model IEM2M

The Integral Equation Model (IEM) was developed originally by Fung and Pan (1986). The assumptions inherent to the model were amended in later publications but there were several important points that remained unclear and that propagated across all subsequent versions of the model. One of the authors of this paper proposed an improved IEM, called IEM2M (Alvarez-Perez, 2001), which removed these unnecessary assumptions and unified the small perturbation model (SPM) and the Kirchhoff approximation (KA) for bistatic scattering. This model was first criticized by Fung (2002) but later adopted by him and co-workers in 2003 and renamed as AIEM (advanced IEM). In contrast to other versions of IEM, IEM2M (integral equation model for second-order multiple scattering) is fully consistent with the SPM. This limit arises naturally from the second-order scattering terms when they produce an extra first-order contribution due to the local non-flatness, and therefore non-Kirchhoff character, of the surface. A central role in the IEM2M is played by a rigorous use of the Weyl representation of the retarded Green function through a homogeneous medium as well as a more physically based selection of the Fresnel coefficients. A further assessment of the model is its implementation for the problem of emissivity calculation. The difference between emissivity from a flat surface and a rough sea-like surface is very small and therefore demands an accurate description of the scattering coefficient, which must be integrated for all angles. Whereas an accuracy of 25% or 1 dB is sufficient for active remote sensing, passive remote sensing calculations require that energy conservation has to be typically within 0.3% error, which is the order of the aforementioned difference for flat and rough, sea-like surface emissivities.