Nonlinearities and reverse travelling energy observed in wavenumber-frequency spectra of X-band ocean backscatter

Wavenumber-frequency spectra of microwave backscatter from the sea surface occasionally show harmonics of the expected linear gravity wave dispersion in both backscattered power (AM) and Doppler velocity (FM) modulations. Harmonics are confined to the peak wave direction, and the ratio of fundamental to second harmonic energy in the velocity modulation indicates increasing nonlinearity with wavenumber, peaking at a wavenumber consistent with observed wave group modulations. Under higher sea state conditions where whitecapping was evident, spectra show weak reverse travelling waves-opposite to the dominant wave direction. Space-time filtering of the image data suggests breaking events are a source for these waves