Abstract Using the parabolic wave equation (PWE) method, we model low elevation GPS L1 signal propagation in maritime atmospheric ducts. To consider sea surface impedance, roughness, and the effects of earth's curvature, we propose a new initial field model for the GPS PWE split-step solution. On the basis of the comparison between the proposed model and the conventional initial field model for a smooth, perfectly conducting sea surface on a planar earth, we conclude that both the amplitude and phase of the initial field are influenced by surface impedance and roughness, and that the interference behavior between direct and reflected GPS rays is affected by earth's curvature. The performance of the proposed model is illustrated with examples of low elevation GPS L1 signal propagation in three types of ducts: an evaporation duct, a surface-based duct, and an elevated duct. The GPS PWE is numerically implemented using the split-step discrete mixed Fourier transform algorithm to enforce impedance-type boundary conditions at the rough sea surface. Because the GPS signal is right hand circularly polarized, we calculate its power strength by combining the propagation predictions of the horizontally and the vertically polarized components. The effects of the maritime atmospheric ducts on low elevation GPS signal propagation are demonstrated according to the presented examples, and the potential applications of the GPS signals affected by ducts are discussed.