A theoretical study of sea surface up/down wind brightness temperature differences

The small slope approximation (SSA) for polarimetric thermal emission from a rough surface is applied to study the up/down wind difference of sea surface brightness temperatures. A complete third-order theory is used, with results expressed in terms of an integral over the sea surface bispectrum. An approximation is developed to obtain emission contributions for surface length scales much larger than the electromagnetic wavelength and in this limit, the up/down wind brightness temperature difference is determined entirely by a combination of third moments of surface slope. Polarization dependencies in this limit however do not match those obtained from the Jet Propulsion Laboratory (JPL) WindRAD empirical model. Another approximation is derived to capture up/down wind emission asymmetry due to short waves which are modulated by longer waves. In this case, an integral of emission "weighting functions" over a pair of "reduced" bispectra is obtained, and examination of the weighting functions shows the importance of surface length scales comparable to the electromagnetic wavelength. The polarization dependencies of these weighting functions illustrate the possibility of matching the WindRAD model, but the absence of an effective hydrodynamic model for short gravity-capillary wave modulation by longer waves limits detailed comparisons.