Theoretical study of ocean up/down wind brightness temperature differences with the small slope approximation

The second order small perturbation method (SPM) for polarimetric thermal emission from ocean surfaces has been found to produce good agreement with measured second harmonic (up/cross wind) azimuthal variations in brightness temperatures. The SPM formulation for emission has also been shown to be equivalent to a small slope approximation (SSA) so that emission from large height surfaces is calculated accurately as long as surface slopes remain small. Studies of first harmonic (up/down wind) azimuthal variations require a third order SSA and a description of the sea surface bispectrum. In this paper, the basic formulation of first harmonic contributions under the SSA is reviewed, and the theory is validated for simple asymmetric pyramidal surfaces through comparison with a numerical emission model. The SSA equations are also simplified for surfaces which contain only length scales large compared to the electromagnetic wavelength; it shown in this limit that the up/down wind brightness temperature difference depends only on the third moment of surface slopes