Hydrodynamic Modulation Transfer Functions for the Creamer and Choppy Wave Surface Models and Their Impact on Doppler Scattering Simulations

Doppler scattering simulations from sea-like surfaces are sensitive to non-linear hydrodynamic effects in wave propagation. Two commonly considered approaches to introduce such non-linearities – the Creamer transform and the Choppy wave model – are examined in this paper. It has been observed that the two models yield simulated Doppler spectra with conspicuously different centroids. Based on the modulation transfer function theory for the Doppler moments of sea backscatter, it seems plausible that such a behavior could result from model differences in the hydrodynamic modulation of smaller, scatter-producing ripples by larger waves. We perform numerical experiments to measure the corresponding hydrodynamic modulation transfer functions (HMTF). An established approach uses a single-harmonic large-scale surface. A correlation-based technique is also proposed that allows HMTFs to be estimated in Monte Carlo simulations of full-spectrum ocean-like surface profiles. Both methodologies show the Creamer HMTF values to be significantly larger than their Choppy-wave counterparts. Estimates made with ocean-like surfaces are also found higher than those based on the solitary-wave approach, particularly for the Creamer model. Application of the first-order Romeiser-Thompson theory with the estimated HMTF values produces Doppler shifts that are in general agreement with those observed in exact scattering simulations using either surface representation. The results of the study reveal considerable differences between the hydrodynamic modulation effects of the two surface models and demonstrate that those disparities are important contributors to the observed deviations in Doppler centroids. More work is required to conclusively determine a preference of one model over the other.