Mapping radar-derived sea surface currents with a variational method

High-frequency radars measure projections of surface velocity vectors on the directions of the radar beams. A variational method for reconstruction of the 2d velocity field from such observations is proposed. The interpolation problem is regularized by penalizing high-frequency variability of the surface vorticity and divergence fields. Twin-data experiments are used to assess the method's skill and compare it with two well-known approaches to HFR data processing: conventional local interpolation and more sophisticated non-local scheme known as open-boundary modal analysis (OMA). It is shown that the variational method and OMA have a significant advantage over local interpolation because of their ability to reconstruct the velocity field within the gaps in data coverage, near the coastlines and in the areas covered only by one radar. Compared to OMA, the proposed variational method appears to be more flexible in processing gappy observations and more accurate at noise levels below 30%.