This paper proposes a Doppler velocity (DV) model based on dual co-polarized (co-pol) decomposition of a normalized radar cross-section of an ocean surface on polarized Bragg scattering and nonpolarized (NP) radar returns from breaking wave components. The dual co-pol decomposition provides a quantitative description of resonant and NP scattering, as well as their dependence on the incident angle, azimuth, and wind speed. Subsequently, the contributions of the facet (resonant Bragg waves and breakers) velocities, tilt, and hydrodynamic modulations due to long waves to the resulting DV can be quantified. The tilt modulation contributions to DV are estimated using the measured/empirical tilt modulation transfer function (MTF). The hydrodynamic modulations are mostly dominated by wave breaking and are estimated using a semiempirical model based on in situ measurements. In addition to the VV and HH radar data, which are required for dual co-pol decomposition and tilt MTF estimates, the surface wave spectrum is required in the DV determination for a given radar observation geometry. In this paper, qualitative and quantitative consistencies are presented between the model simulations and the empirical CDOP model. In a companion paper, DV analysis is presented to analyze the Sentinel-1 synthetic aperture radar measurements and collocated in situ measurements of surface wind and wave spectra.