A comparison of the hydrodynamic modulation in some existing models

Abstract

Abstract The action balance equation is solved numerically using the method of characteristics. The algorithm can handle any functional form of the current velocity and the source function. It therefore allows a comparison of the hydrodynamic parts of the models of Alpers and Hennings (1984), Shuchman el al. (1985) and Holliday et al. (1986,1987), all describing the imaging mechanism of mapping bottom topography with side-looking airborne radar (SLAR) and synthetic aperture radar (SAR). The effects of advection and second-order terms, neglected in the original work of Alpers and Hennings (1984), are included and studied. It is shown that advection is important, notably at L-band for features smaller than 1 km, such as sand waves, while the second-order terms shift the modulation of the wave spectrum upward. All models studied give similar results for L-band and X-band, showing that the dependence of the relaxation rate on wave number and wind speed variations due to variations in current velocity has only a small influence. The predicted modulations at L-band are of the order of 10 per cent, in agreement with the Seasat data. At X-band, however, the predicted modulations are an order of magnitude smaller than at L-band. This disagrees with the experimental data which seem to indicate that modulations at X-band are of the same order of magnitude as those at L-band. Advection is important for the positioning of modulations in the radar backscatter relative to the bottom topography. However, the positional accuracy of existing experimental data is not good enough to allow comparison with theoretical predictions.