A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery

When imaging ocean surface waves by X-band marine radar, the radar backscatter from the sea surface is modulated by the long surface gravity waves. The modulation transfer function (MTF) comprises tilt, hydrodynamic, and shadowing modulations. A conventional linear MTF was derived using HH-polarized radar observations under conditions of deep water. In this study, we propose a new quadratic polynomial MTF based on VV-polarized radar measurements taken from heterogeneous nearshore wave fields. This new MTF is obtained using a radar-observed image spectrum and in situ buoy-measured wave frequency spectrum. We validate the MTF by comparing peak and mean wave periods retrieved from X-band marine radar image sequences with those measured by the buoy. It is shown that the retrieval accuracies of peak and mean wave periods of the new MTF are better than the conventional MTF. The results also show that the bias and root mean square errors of the peak and mean wave periods of the new MTF are 0.05 and 0.88 s, and 0.32 and 0.53 s, respectively, while those of the conventional MTF are 0.61 and 0.98 s, and 1.39 and 1.48 s, respectively. Moreover, it is also shown that the retrieval results are insensitive to the coefficients in the proposed MTF.