Microwave Doppler Spectra of Sea Echoes at High Incidence Angles: Influences of Large-Scale Waves

Within the framework of the composite surface scattering model, analytical formulas for Doppler shift and bandwidth of radar echoes backscattered from time-varying sea surface are derived in the forms of three-dimensional integrals. In our derivations, the influences of the tilt modulation (TM), the hydrodynamic modulation (HM), the shadow and the curvature of large-scale undulating waves are all taken into account for achieving more reasonable results. Comparisons between our theoretical curves and the results obtained directly by exact numerical method demonstrate that our formulas can improve the simulated results. On the other hand, the simulations by our formulas can also help to estimate the effects of the TM, the HM, and the shadow of large-scale waves on Doppler behaviors individually. We find that the predicted Doppler shifts are always larger in HH-polarization than in VV-polarization due to the TM. Meanwhile, the simulations also show that the predicted Doppler shifts for both HH- and VV-polarizations would become larger when the HM is considered. In addition, at low-grazing angles (LGA), the shadow effect results in a rapid increase in the predicted Doppler shift, and on the contrary makes the bandwidth narrower.