On the nonlinear integral transform of an ocean wave spectrum into an along‐track interferometric synthetic aperture radar image spectrum

Abstract

We present a new nonlinear integral transform relating the ocean wave spectrum to the along‐track interferometric synthetic aperture radar (AT‐INSAR) image spectrum. The AT‐INSAR, which is a synthetic aperture radar (SAR) employing two antennas displaced along the platform's flight direction, is considered to be a better instrument for imaging ocean waves than the SAR. This is because the AT‐INSAR yields the phase spectrum and not only the amplitude spectrum as with the conventional SAR. While the SAR and AT‐INSAR amplitude spectra depend strongly on the modulation of the normalized radar cross section (NRCS) by the long ocean waves, which is poorly known, the phase spectrum depends only weakly on this modulation. By measuring the phase difference between the signals received by both antennas, AT‐INSAR measures the radial component of the orbital velocity associated with the ocean waves, which is related to the ocean wave height field by a well‐known transfer function. The nonlinear integral transform derived in this paper differs from the one previously derived by Bao et al. [1999] by an additional term containing the derivative of the radial component of the orbital velocity associated with the long ocean waves. By carrying out numerical simulations, we show that, in general, this additional term cannot be neglected. Furthermore, we present two new quasi‐linear approximations to the nonlinear integral transform relating the ocean wave spectrum to the AT‐INSAR phase spectrum.