Semi-Empirical Model for the Ka-band Sea Surface Doppler Centroid

The sea surface Doppler spectrum centroid is a principal parameter for the sea surface current retrieval from Doppler radar measurements. Satellite Doppler scatterometers are proposed to operate in the Ka-band (SKIM, DopplerScatt/WaCM, SEASTAR) in order to achieve sufficient measurement accuracy. Todays documentation of the Ka-band sea surface backscattering parameters is poor, thus this work is aimed at presenting a model for the sea surface Doppler spectrum centroid (DC) deducted from field data collected from the Black Sea research platform. The model relies on the well-known two-scale surface separation approach. Within this framework, the small-scale waves are the scatterers moving at their inherent speed (Bragg wave phase velocity or specular point velocity), which, in turn, are advected by the large-scale wave orbital velocities. These modulations lead to correlated variations of local scatterer cross-section and speed. The inherent scatterer velocity is computed theoretically, while the modulation term is described by the empirical modulation transfer function (MTF) which naturally involves both tilt and hydrodynamics components as a function of look geometry and sea state. The proposed semi-empirical DC model is in good agreement with measurements if in situ wave gauge directional spectrum is used as a wave input. Based on this finding, we extrapolate the semi-empirical DC model on the arbitrary surface described by the physical model of the wind wave spectrum. The resulting DC model is compared to the published empirical models and measurements (SAXON-FPN, DopplerScatt, AirSWOT, Wavemill field campaigns, and CDOP Envisat ASAR model). The model DC dependencies on incidence angle and wind speed are consistent with Ku-band
SAXON-FPN, Ka-band AirSWOT, and DopplerScatt datasets, but differs from C-band CDOP model and X-band Wavemill dataset, which generally have higher DC magnitude (besides longer operating radar wavelength, the difference can be attributed to swell dominated sea observed in the CDOP and Wavemill cases). The model predicts that the DC rises with wind speed at small incidence angles, 20–30^o, but the DC level is almost independent of wind at larger incidence angles, 50–55^o. Such behavior is explained by the balance between opposing wind dependencies of the MTF magnitude and the magnitude of modulating wave orbital velocities.

The work is supported by the Russian Science Foundation under grant No. 17-77-30019.