In this paper, numerical simulations of the scattering from time‐dependent realizations of one‐dimensional ocean surface waves are described. A new technique is used that allows efficient generation of ocean surface realizations that preserve the dominant nonlinear hydrodynamic characteristics. Thus unique scattering effects of real ocean surface waves can be explored. Until very recently, numerical simulations of rough‐surface scattering were used mainly to test and/or improve theoretical models that predict the average bistatic scatter cross section. We carry the simulations further by generating Doppler spectra from dynamically evolving surface realizations. Doppler spectra of signals scattered from the ocean surface are affected by both hydrodynamic nonlinearities and higher‐order scatter terms. The simulated Doppler spectra from nonlinear surface realizations reproduce the measured characteristics of ocean and wave‐tank data for low and high wind conditions. We also show that the results are essentially reproduced by the second‐order Kirchhoff approximation.