4DVAR with Ensemble Model Error Estimation in a Coastal Ocean Model

Traditionally 4DVAR implementations for ocean forecasting proceed in a series of relatively short time windows and assume that the model background error covariance is static in time. This assumption is unlikely to hold in coastal waters, in particular over the Oregon-Washington shelf (US Pacific coast), where river outflow and coastal upwelling cause rapid changes in ocean properties. To include the natural variability of the coastal ocean into our estimate for the model background error covariance, we have constructed an ensemble-4DVAR implementation in which the estimate of the model background error covariance is based on a localized ensemble of perturbed analysis runs from the previous window. In our set-up the perturbations consist of linear combinations of wind field EOFs and geostrophically balanced alterations to the initial conditions. The localization is carried out by applying a parallel Monte-Carlo localization of the sample covariance with a rectangular window. The method has been tested by embedding it in the Oregon State University (OSU) ocean forecasting system. In this system the initial conditions at the beginning of each 3-day window are corrected with 4DVAR using assimilation of satellite altimetry, GOES SST, and high-frequency radar sea-surface current measurements. For the tangent linear and adjoint parts the system uses AVRORA codes, developed by our group at OSU, while forecasts and ensemble members are calculated using the 2-km nonlinear ROMS (Regional Ocean Modeling System). We find that model results, e.g. the location of the edge of the Columbia River plume, depend on the choice of the background error covariance. Comparison against unassimilated mooring and glider data shows that the system with an ensemble-based covariance provides better predictions of the subsurface temperature and a more accurate representation of the temperature-salinity relationship.