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The numerical simulation of long-distance, over-terrain propagation of electromagnetic waves has received considerable attention due to its strong impact on radar and communication technology. One highly desirable feature of the methods currently used in these simulations is numerical efficiency, which is typically achieved by approximating the actual three-dimensional (3-D) propagation medium by a two-dimensional (2-D) medium. In this medium, the atmospheric variations are confined to the range/altitude (x/z) propagation plane while terrain variations are confined to the range direction (one-dimensional terrain). With an additional, paraxial assumption, these models arrive at an extremely efficient, scalar parabolic wave equation (PWE) that can be solved with marching techniques. A significant drawback, however, is that the 2-D approximation discards propagation effects associated with the lateral variations of the 2-D terrain-namely lateral diffraction, lateral scattering and depolarization. These effects may have substantial impact on clutter modeling in radar detection and imaging. In this paper, the propagation effects associated with lateral terrain variations are examined via 3DVPWE, a full 3-D numerical model based on the vector PWE. A notional urban terrain configuration, as well as a realistic digital-map terrain example is considered. The 3DVPWE results are then compared to results from 2-D PWE model to assess the performance of this commonly used approximation. The main emphasis of the paper will be placed on lateral diffraction and scattering. The examination of depolarization effects will be deferred to a future publication.