Ensemble of 4DVARs (En4DVar) data assimilation in a coastal ocean circulation model, Part I: Methodology and ensemble statistics

The ocean state off Oregon-Washington, U.S. West coast, is highly variable in time. Under these conditions the assumption made in traditional 4-dimensional variational data assimilation (4DVAR) that the prior model (background) error covariance is the same in every data assimilation (DA) window can be limiting. A DA system based on an ensemble of 4DVARs (En4DVar) has been developed in which the background error covariance is estimated from an ensemble of model runs and is thus time-varying. This part describes details of the En4DVar method and ensemble statistics verification tests. The control run and 39 ensemble members are forced by perturbed wind fields and corrected by DA in a series of 3-day windows. Wind perturbations are represented as a linear combination of empirical orthogonal functions (EOFs) for the larger scales and Daubechies wavelets for the smaller scales. The variance of the EOF expansion coefficients is based on estimates of the wind field error statistics derived using scatterometer observations and a Bayesian Hierarchical Model. It is found that the variance of the wind errors relative to the natural wind variability increases as the horizontal spatial scales decrease. DA corrections to the control run and ensemble members are calculated in parallel by the newly developed, cost-effective cluster search minimization method. For a realistic coastal ocean application, this method can generate a 30% wall time reduction compared to the restricted B-conjugate gradient (RBCG) method. Ensemble statistics are generally found to be consistent with background error statistics. In particular, ensemble spread is maintained without inflating. However, sea-surface height background errors cannot be fully reproduced by the ensemble perturbations.