We present the use of combined hydrodynamic and electromagnetic analytical models for the simulation of the polarized ocean Doppler spectrum at microwave frequencies. We consider linear and weakly nonlinear sea surfaces after the Choppy Wave Model and incorporate them in the Weighted Curvature Approximation surface scattering method. Statistical expressions are derived, for the Doppler spectrum as well as for its central frequency and width. Results compare favorably with rigorous numerical computations for one-dimensional surfaces published in the literature. The simplicity of the analytical models provide a valuable tool for the Doppler analysis of two-dimensional sea-surfaces.