A New Nonlinear Integral Transform Relating Ocean Wave Spectra to Phase Image Spectra of an Interferometric Radar Altimeter at Low Incidence Angle

Ocean waves can either be the target of interferometric radar altimeter (IRA) observations or may affect observations of mesoscale and submesoscale ocean dynamic phenomena. Due to the low incidence angle of the IRA, in addition to the azimuth shift caused by the motion of the ocean waves, the range shift caused by the height of the ocean wave is also significant. In this article, based on previous research, we propose a new nonlinear integral transform relating ocean wave spectra to phase image spectra of an IRA at a low incidence angle that includes the effect of range shift. This new nonlinear integral transformation can be replaced by a quasilinear transformation when the nonlinear variation is weak or the wavelength of the ocean wave is large. We analyze the effect of swell and wind waves on the phase spectra under different conditions based on the new nonlinear integral transform through simulation. The height of the ocean wave and the incidence angle of the radar affect the range shift, leading to a range nonlinear effect in the phase spectra. The orbital velocity of the ocean wave affects the azimuth shift, leading to an azimuth nonlinear effect in the phase spectra. The wavelength and propagation direction of the ocean wave also induces a distortion in the phase spectra. Overall, the nonlinear effect has a small effect on the swell and a large effect on the wind wave.