Variational interpolation of high-frequency radar surface currents using DIVAnd

DIVAnd (Data-Interpolating Variational Analysis, in n-dimensions) is a tool to interpolate observations on a regular grid using the variational inverse method. We have extended DIVAnd to include additional dynamic constraints relevant to surface currents, including imposing a zero normal velocity at the coastline, imposing a low horizontal divergence of the surface currents, temporal coherence and simplified dynamics based on the Coriolis force and the possibility of including a surface pressure gradient. The impact of these constraints is evaluated by cross-validation using the HF (High-Frequency) radar surface current observations in the Ibiza Channel from the Balearic Islands Coastal Ocean Observing and Forecasting System (SOCIB). A small fraction of the radial current observations are set aside to validate the velocity reconstruction. The remaining radial currents from the two radar sites are combined to derive total surface currents using DIVAnd and then compared to the cross-validation data set and to drifter observations. The benefit of the dynamic constraints is shown relative to a variational interpolation without these dynamical constraints. The best results were obtained using the Coriolis force and the surface pressure gradient as a constraint which are able to improve the reconstruction from the Open-boundary Modal Analysis, a quite commonly used method to interpolate HF radar observations, once multiple time instances are considered together.