Comparison of actual and simulated synthetic aperture radar image spectra of ocean waves

We have simulated synthetic aperture radar (SAR) image spectra of ocean waves, which were focused for stationary scenes using three popular formulations of SAR ocean imaging theory: the time-dependent, velocity-bunching, and quasi-linear models. All three models require functional forms for surface wave spectra, modulation transfer functions, and correlation times; these were obtained from data taken during the SAR and X Band Ocean Nonlinearities (SAXON)-Forschungsplatform Nordsee (FPN) experiment of November 1990. These measurements were made on and near the German research platform Nordsee during the same period of time that SAR images of ocean waves at X, C, and L bands were obtained by aircraft near the tower. We compare the results of our simulations to the actual SAR spectra for a variety of integration times, range-to-velocity ratios (R/V), and azimuth angles. We find that all three models reproduce the observed image spectra well when integration times are small and R/V ratios are low to moderate. Some adjustments of the parameters measured on the tower are occasionally necessary in order to produce this agreement, but in most cases these adjustments are small and within measurement errors; in all cases the same parameters suffice for all models. However, we reproduce a result previously obtained by Bruning et al. [1994] that measured modulated transfer functions do not properly account for imagery of range-traveling waves propagating downwind. We also find that our calculated velocity spreads seem to be too large to reproduce the observations when the significant wave height is above about 1.5 m and R/V is appreciable. For long integration times and high R/V ratios, the velocity-bunching model smears the spectrum more than the time-dependent model and more than the observations. We find that the velocity-bunching formulation is viable up to an integration time that is a function of R/V; for lower ratios, velocity bunching is viable up to longer integration times, and we offer an explanation of why this is so. Finally, we find that for large R/V ratios the quasi-linear model fails to produce the low-frequency components observed in actual image spectra and produced by velocity-bunching and time-dependent models.