Mapping surface currents from HF radar radial velocity measurements using optimal interpolation

Abstract

An optimal interpolation (OI) method to compute surface vector current fields from radial velocity measurements derived from high-frequency (HF) radars is presented. The method assumes a smooth spatial covariance relationship between neighboring vector currents, in contrast to the more commonly used un-weighted least-squares fitting (UWLS) method, which assumes a constant vector velocity within a defined search radius. This OI method can directly compute any quantities linearly related to the radial velocities, such as vector currents and dynamic quantities (divergence and vorticity) as well as the uncertainties of those respective fields. The OI method is found to be more stable than the UWLS method and reduces spurious vector solutions near the baselines between HF radar installations. The OI method produces a covariance of the uncertainty of the estimated vector current fields. Three nondimensional uncertainty indices are introduced to characterize the uncertainty of the vector current at a point, representing an ellipse with directional characteristics. The vector current estimation using the OI method eliminates the need for multiple mapping steps and optimally fills intermittent coverage gaps. The effects of angular interpolation of radial velocities, a commonly used step in the preprocessing of radial velocity data prior to vector current computation in the UWLS method, are presented.