The effect of sea-surface roughness on shallow water waveguide propagation: A coherent approach

Standard propagation models in underwater acoustics (e.g., normal modes, PE) are deterministic in nature, i.e., they deal with a single realization of the environment. Additionally, for mathematical reasons, they typically treat the sea surface as a flat pressure-release surface. Effects of sea surface and bottom roughness are incorporated through a loss mechanism. This is accomplished by including an additional attenuation factor based on coherent loss of the surface-interacting component of the propagating field. This type of correction presents a mathematically inconsistent model, since usually results from stochastic scattering models are applied to results from single realizations of the stochastic medium. Moreover, scattering kernels are generally derived assuming a homogeneous medium underlying the sea surface, an assumption incompatible with a realistic environment. Using a numerical model [Norton et al., J. Acoust. Soc. Am. 97, 2173–2180 (1995)] that combines a high fidelity Parabolic Equation propagation model with the conformal mapping technique developed by Dozier [L. B. Dozier, J. Acoust. Soc. Am. 75, 1415–1432 (1984)] to handle surface roughness in a marching algorithm, forward propagation with a single realization of a rough sea surface overlying a complex ocean environment can be modeled in a mathematically consistent way. This technique is applied to the problem of shallow water propagation with a rough sea surface. For the adopted environment and range of rms roughnesses considered (0.28<kh<2.33, where k is the acoustic wave number and h is the rms surface height) the inclusion of the rough surface introduces a significant increase in the transmission loss and vertical-angle distribution of the propagating field. Results for this environment also show that, on average, the transmission loss is close to that calculated using the roughness-induced attenuation factor approximation. The transmission loss calculated with the roughness-induced attenuation factor exhibits a smoother range dependence, indicating strong attenuation of energy at steeper propagating angles. However, when strong upward refraction conditions exist, coherent effects and energy redistribution cannot be ignored and results from the procedure which incorporates the roughness through a loss mechanism are in error.