Mapping submarine sand waves with multiband imaging radar: 1. Model development and sensitivity analysis

In 1989 and 1991, unexpected modulations caused by submarine sand waves were observed with the airborne imaging radar (AIR), a P, L, and C band synthetic aperture radar. The measurements were performed in a sand wave area off the Dutch coast. The sand waves have an asymmetric, sawtooth-shaped profile with the steep slope oriented toward the northeast. During the experiments, wind and current had opposite directions: the wind was directed toward the northeast and the current toward the southwest. Under these conditions, existing models for the imaging mechanism predict that the modulation depth decreases with increasing radar frequency and that the steep slopes show up as dark lines in radar images. The AIR images show a relation between modulation depth and radar frequency as predicted. However, only the P band image of 1989 shows the steep slopes of the sand waves as dark lines. The P band image of 1991 and the L band images of 1989 and 1991 show a sawtooth-shaped modulation which cannot be explained by existing theory. A new model is developed that is one dimensional in position space and fully two dimensional in wavenumber space. The radar cross section is calculated using both first-order Bragg and an integral equation scattering model in which the cross section originates from a spectral band rather than a single value. The new model contains two improvements over previous ones. First, wave blocking or, better, wave reflection is included, though in an approximate manner. It is shown to be of importance at P band only. Second, the contribution to the radar cross section from waves moving both to and from the radar is included, whereas some previous models consider only one of these contributions. This explains the observed modulations, at least qualitatively, under the assumptions that the angular distribution of short waves is almost constant and that waves moving against the wind have small relaxation rates.