Spatial interpolation and filtering of surface current data based on open‐boundary modal analysis

The use of high‐frequency (HF) radar surface current measurements are limited by spatial coverage gaps and sparse sampling. The normal mode (NMA) and open‐boundary mode (OMA) current decomposition techniques developed by Lipphardt et al. (2000) and Lekien et al. (2004), respectively, produce smooth two‐dimensional current fields by fitting data to a set of spatial modes. These methods have the advantages of incorporating the coastal boundary condition and providing a controllable level of spatial smoothing. While computation of and fitting to modes has been previously examined, variations and limitations of the technique have not been fully explored. Here we expand on the original OMA algorithm to incorporate radial currents produced by individual HF radars. Assimilating radial measurements maximizes use of available data and avoids the additional step and error of creating vector currents from radial data. We also develop techniques for dealing with spatially nonuniform data distributions and data gaps. Estimates of measurement error are propagated to evaluate the uncertainty of interpolated current fields. We illustrate our findings and assess the robustness of the OMA technique for calculating currents, divergences, and vorticities using HF radar data from Bodega Bay and Monterey Bay, California. Though care must be taken when using the technique as occasional shortage of data (e.g., temporary failure of a radar station) can produce erroneous fitted currents, OMA provides a robust mechanism for interpolating and filtering two‐dimensional velocity measurements. Furthermore, OMA‐derived errors provide a transparent and useful estimate of spatial patterns of uncertainty.