A three-dimensional parabolic equation applied to VHF/UHF propagation overirregular terrain

The two-dimensional (2-D) parabolic equation (PE) is widely used for making radiowave propagation predictions in the troposphere, The effects of trans verse terrain gradients, propagation around the sides of obstacles, and sca ttering from large obstacles to the side of the great circle path are not m odeled, leading to prediction errors in many situations. In this paper, the se errors are addressed by extending the 2-D PE to three dimensions. This c hanges the matrix form of the PE making it difficult to solve. A novel iter ative solver technique, which is highly efficient and guaranteed to converg e, is being presented, In order to confine the domain of computation, a thr ee-dimensional (3-D) rectangular box is placed around the region of interes t. A new second-order nonreflecting boundary condition is imposed on the su rface of this box and its angular validity is established. The boundary con dition is shown to keep unwanted fictitious reflections to an acceptable le vel in the domain of interest, The terrain boundary conditions for this 3-D PE method are developed and an original technique for incorporating them i nto the matrix form of the iterative solver is described, This is done usin g the concept of virtual field points below the ground. The prediction accu racy of the 3-D PE in comparison to the 2-D PE is tested both against indoo r scaled frequency measurements and very high frequency (VHF) field trials.