Assimilation of surface velocity data into a primitive equation coastal ocean model

A data assimilation system (DAS) of the wind‐driven, mesoscale shelf circulation off the Oregon coast is developed. The DAS assimilates low‐pass filtered surface velocity measurements, obtained from land‐based high‐frequency coastal radar arrays, into a primitive equation coastal ocean model using a sequential optimal interpolation scheme. Inhomogeneous and anisotropic estimates of the forecast error covariances required for the assimilation are assumed to be proportional to typical cross‐correlations between modeled variables. These correlations are estimated from an ensemble of model simulations for 18 different summers. Similarly, the observation error covariances are assumed to be proportional to the actual covariances of the observations. A time‐distributed averaging procedure (TDAP) that effectively low‐pass filters the model forecast for comparison with the observations and introduces the corrections to the model state gradually over time is used in order to overcome problems of data compatibility and initialization. The correlations between direct subsurface current measurements and subsurface currents obtained from model‐only and assimilation experiments for the summer of 1998 are 0.42 and 0.78, respectively, demonstrating the effectiveness of the DAS. Our estimates of the error covariances are shown to be appropriate through a series of objective statistical tests. Analysis of the term balances of the model equations show that the dominant modeled dynamical balances are preserved by the DAS and that uncertainties in the spatial variability of the wind forcing are likely to be one source of model error. By varying the relative magnitudes of the estimated forecast and observation error covariances the DAS is shown to be most effective when approximately 80% of the analysis is made up of the model solution.