Dominant wave directions and significant wave heights from synthetic aperture radar imagery of the ocean

We show that quasi-linear theory accounts for dominant wave directions observed in synthetic aperture radar (SAR) imagery of the ocean for range-to-velocity (R/V) ratios up to 70 s. We also show that when used in combination with Alpers and Hasselmann's [1982] model of signal-to-noise ratios in SAR imagery, this theory yields significant wave heights in good agreement with those actually observed. We have found that the apparent dominant wave direction in SAR imagery taken at a 45° incidence angle can differ from the true wave direction by as much as 40° under certain conditions. To understand such differences, we simulated SAR image spectra using quasi-linear theory, a surface wave spectrum measured by a buoy but with a variable angular spread, coherence times calculated from line-of-sight velocity spreads, and modulation transfer functions based on a functional form developed from Bragg scattering theory and data obtained during the SAR X Band Ocean Nonlinearities-Forschungsplatform Nordsee (SAXON-FPN) experiment. We carried out these simulations for a 45° incidence angle, L, C, and X bands, both horizontal/horizontal (HH) and vertical/vertical (VV) polarization, three different flight altitudes, and a variety of flight directions to compare the predicted apparent wave directions with those observed in the SAR imagery collected during SAXON-FPN. The difference between the SAR-derived dominant wave direction and the one measured by the buoy could be predicted well as a function of the true wave direction relative to the flight direction. The parameters of the quasi-linear theory that produced the best fit to the directional data differed somewhat from those measured by tower-based radars during SAXON-FPN, however. Significant wave heights obtained using the parameters that best fit the directional data were in good agreement with those measured by the buoy. The SAR-derived wave heights were consistently higher than the measured ones, however, unless the full system bandwidth was used in determining the clutter level, that is, unless bandwidth reductions due to azimuthal presumming and multilook averaging were removed. Finally, the prediction and observation of spectral splitting in SAR spectra of azimuthally traveling waves are also reported.