Radar imaging of Kelvin arms of ship wakes

The wave pattern generated by a moving ship is formed by two dominant features: the turbulent wake and a 'V'-shaped pattern trailing the ship, consisting of the two Kelvin arms. In this paper we investigate the radar imaging mechanism of Kelvin arms, which are formed by the cusp waves. A composite surface model for the radar backscattering at the ocean surface is used. The radar signatures of Kelvin arms can be attributed to tilt and hydrodynamic modulation of Bragg waves by the cusp waves. The proposed model allows the computation of the normalized radar backscattering cross-section (NRCS) as a function of radar frequency, polarization, incidence angle, wind speed and direction, and wavelength, direction, and slope of the cusp waves. By using this imaging model, radar signatures of cusp waves are calculated for several spaceborne Synthetic Aperture Radars (SARs): (1) the SEASAT L-band HH-polarized SAR, (2) the ERS-1/-2 VV-polarized SAR, (3) the RADARSAT C-band HH-polarized SAR, and (4) the X-, C- and L-band multipolarization SARs of the Space Radar Laboratory flown on the space shuttle during the SIR-C/X-SAR mission in 1994. The results of the simulations are compared with SEASAT and SIR-C/X-SAR imagery of ship wake patterns. It is shown that the dependence of the observed radar signatures of Kelvin arms on radar look direction is consistent with the proposed imaging theory and that the measured relative mean NRCS values induced by Kelvin arms can be fairly well reproduced by the proposed model. The simulations indicate that ship wake signatures should be more clearly visible on SEASAT L-band SAR than on ERS-1/-2 or RADARSAT C-band SAR images. The radar signatures of Kelvin arms are strongest at low wind speeds and are not very sensitive to wind direction.