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This report describes the fundamental physics and basic numerical algorithms that form the basis of a range-dependent microwave propagation model. The model accounts for the effects of nonhomogeneous atmospheric refractivity fields, finite surface conductivity and variable surface terrain elevation. Both vertical and horizontal field polarization and general antenna radiation patterns are included in the analysis. The electromagnetic field propagation is modeled using the splitstep Fourier parabolic wave equation (SSFPE) algorithm, modified to account for an impedance-type boundary condition. The various approximations used in developing the SSFPE algorithm are discussed, along with local and global error estimates. Parabolic wave equation, Microwave propagation, Variable terrain microwave propagation, Pattern propagation factor.