Theoretical study of the small slope approximation for ocean polarimetric thermal emission

Analytical models for ocean surface polarimetric thermal emission based on the small perturbation method (SPM) have shown success in matching brightness temperature azimuthal variations from aircraft based measurements. It has also been shown that use of the small perturbation method for calculation of surface emissivity results in a series in surface slope, not surface height, so that the method remains accurate for large height surface emission even when it fails for the corresponding scattering calculations. This paper presents a detailed analysis of the SPM/small slope approximation (SPM/SSA) for ocean surface polarimetric thermal emission, and investigates the extent to which varying ocean surface length scales contribute to brightness temperature zeroth and second azimuthal harmonics. It is found that ocean waves of lengths both comparable to and much greater than the electromagnetic wavelength can contribute to these harmonics, depending on the extent to which the ocean surface spectral model places asymmetry in these length scales. In addition, the SPM/SSA is approximated for the contributions of both very long and very short ocean length scales compared to the electromagnetic wavelength, and it is found that both long and short wave contributions can be expressed in simple equations involving either standard or modified ocean surface slope variances.