Propagation of vertically polarized waves over rough ocean surfaces

Abstract

The problem of propagation of vertically polarized radiowaves in an inhomogeneous atmosphere and over rough ocean surfaces is solved using the parabolic equation method. The solution of the parabolic equation is accomplished through the use of the Fourier split-step algorithm. Formulation of the equations is based upon (1) recognizing that the Fourier kernels of the transform equations in the split step algorithm represent planes waves and (2) compensating for the effects of rough ocean surfaces by using a rough surface reduction factor directly in the spectral domain. To accomplish this a redefinition of the Fourier transform pair is done to ensure mathematical consistency. The formulation also incorporates the first and second derivatives of the refractivity index to accommodate steep gradients in the refractivity profile. Hanning windows are used in both the spatial and wavenumber domains to contain computational requirements. The effects on propagation by varying parameters such as wave heights, computational domain ceilings, frequency and step size are investigated