A parabolic approximation method for propagation prediction in an inhomogeneous atmosphere over irregular terrain

A standard parabolic equation is used to approximate the Helmholtz equation for electromagnetic propagation in an inhomogeneous atmosphere (troposphere). An implicit finite difference (IFD) scheme is applied between the irregularly shaped ground and an altitude z=z_h below which all lateral inhomogeneities of the medium are assumed localized. The boundary condition at z=z_h is obtained by matching the IFD solution to a Green function solution within the uniform region above z=z_h. This `IFDG´ method is the first to predict propagated fields in an inhomogeneous atmosphere over irregular terrain. For a standard atmosphere, IFDG results are shown to agree well with predictions using the WAGNER method. The efficiency of the method make it an ideal candidate for extension to three dimensional geometries