Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

Optimal interpolation (OI) has been used to produce analyses of quasi-geostrophic (QG) stream function over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys, each of about 6 days' duration, were assimilated into a QG open boundary ocean model. Since the true forecast error covariance function required for the OI is unknown, assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys, since there were too few independent data for other verification of the various analyses. For the hindcasts, the QG model was initialized with an analysis for one survey and then integrated according to boundary data supplied by the corresponding analysis for the next survey. Two sets of such hindcasts were conducted, since there were only three statistically independent realizations of the stream function field for the entire observing period. For the irregular sampling strategy of the first half of the observing period, the best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function (about 80 km): the root mean square difference between the hindcast stream function and the final analysis was only 23% of the observation standard deviation. The best hindcast (with a 31% error) for the second half of the observing period was obtained using an initial analysis based on an 80-km decorrelation scale and a final analysis based on a 40-km decorrelation scale. The change in decorrelation scale was apparently associated with a change in sampling strategy and the importance of the resolution of small-scale vorticity input across the open boundary. The last survey used a regular sampling scheme with good coverage (about 20-km resolution) of the entire domain so that smaller-scale features were resolved by the data. The earlier surveys used a coarser (about 75 km) sampling resolution, and smaller-scale features that were not well-resolved could not be inferred correctly even with short error covariance scales. During the hindcast integrations, the dynamical model effectively filtered the stream function fields to reduce differences between the various initial fields. Differences between the analyses near inflow boundary points ultimately dominated the differences between dynamical hindcasts. Analyses for the entire 59-day observing period of the five independent surveys were produced using continuous assimilation. A modified form of OI in which the forecast error variances were updated according to the analysis error variances and an assumed model error growth rate was also used, allowing the OI to retain information about prior assimilation. The analyses using the updated variances were spatially smoother and often in better agreement with the observations than the OI analyses using constant variances. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis (OA) and in good agreement with the only independent data available for comparison. Unfortunately, the limiting factor in the validation of the assimilation methodology remains the paucity of observations.