The impact of the ocean wave-radar modulation transfer function on the inversion of ERS-1 SAR image spectra into ocean wave spectra

Hasselmann´s closed forward integral transform and its inversion includes, in addition to motion induced effects, the modulation of the normalized radar cross section (NRCS) due to long ocean waves. This modulation is described by a linear ocean wave-radar modulation transfer function (MTF). The authors compute the forward mapping integral by using a `theoretical´ and a parameterized form of the MTF with variable moduli and phases. For range propagating waves the transformation of SAR image spectra into ocean wave spectra depends strongly on this MTF. Significant wave heights (H_s) derived from inverted wave spectra decrease by 15-20% when increasing the modulus of the MTF by a factor of 2. Furthermore, H_s increases up to 50% if a phase of 0° is used in the forward mapping integral instead of the most likely phase of the MTF which is 90