Two-scale polarimetric emissivity model: Efficiency improvements and comparisons with data

The two-scale model provides a framework for explaining the polarization and angular dependence of the microwave radiation emitted from the ocean surface. In this model the surface is viewed as a collection of randomly oriented facets. The emissivity of each facet is calculated using the small perturbation method (SPM), and that of the entire surface is obtained by integrating the local emissivity over all possible surface slopes, weighted by the probability of encountering these slopes. Since each SPM calculation involves a double integral, the model requires in principle the evaluation of a fourdimensional integral. This paper explores two methods for reducing the computational time required by the two-scale model. In one version, the azimuthal dependence of the local emissivity is represented by a truncated Fourier series and slope integral is computed numerically. In the second version the slope integral is carried out analytically, after expanding the integrand as a Taylor series in the surface slope. Hydrodynamic modulation effects are included in order to explain the upwind-downwind asymmetry of the emissivity. The calculated emissivities from the two versions of the model are compared with each other and with airborne and spaceborne measurements.