Title: On the measurement of the dispersion relation by a radar and the implication on the current retrieval

Abstract: The work analyses the error in current retrievals from images of marine radars. The study is based on simulations of waves interacting with a shear current. The measured dispersion is related to the underlying wavenumber-dependent effective current. The highest tested radar antenna (H=45 m) with vertical polarization performed the best. For that case the root mean square error was at most 0.05 m/s above the one for the simulated wave field without imaging mechanism. The observation time of 20 minutes was compared to shorter windows. Depending on the needed accuracy, the time may be reduced to five minutes, associated with an loss of accuracy below 12%. The study shows the error of the current reconstruction depends on the shape of the profile and varies considerably from realization to realization