Spatial Ergodicity of Doppler Characteristics in Polarimetric Ocean Radar Scattering: A Numerical Study

This study numerically investigates the spatial ergodicity of Doppler characteristics in polarimetric ocean radar scattering. The full Apel wave spectrum is employed to generate two-dimensional time-varying sea surfaces that involve all dominant large-scale gravity waves and small-scale capillary waves. By solving the radar scattering from time-varying ocean surfaces with various illumination sizes using the second-order small-slope approximation (SSA-2) model, the Doppler spectra along with the Doppler shift and width are thus computed and analyzed. The numerical simulations are conducted at L-band for three typical fully-developed sea states. A Doppler shift error threshold is defined based on the accuracy requirements of sea surface current retrieval, and the spatial ergodicity of Doppler shift is evaluated quantitatively. Simulation results indicate that under co-polarization, the Doppler shift manifests spatial ergodicity when the sea surface size illuminated by radar is no less than one-quarter of the largest gravity wave wavelength at the corresponding sea state. For cross-polarization, the spatial ergodicity of Doppler shift is significantly reduced and is observed only when the illumination size exceeds about one-half of the largest gravity wave wavelength. The results also indicate that wind direction has a limited effect on the spatial ergodicity of Doppler shift.