Data Assimilation in a Baroclinic Coastal Ocean Model: Ensemble Statistics and Comparison of Methods

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Abstract
The performance of data assimilation methods in an idealized three-dimensional time-dependent coastal baroclinic model is assessed by computing ensemble error statistics. The analytical representer solution allows for computation of posterior error statistics for the variational generalized inverse method (GIM) as well as sequential methods such as the Kalman filter (KF) and optimal interpolation (OI). Computations can be made in a straightforward way, given the statistics of errors in the model equations and data. The GIM yields solutions with significantly smaller variance than that given by KF or OI if the data contain valuable information about the past flow. This is the case, for instance, when a large fraction of the model error is due to uncertainty in the wind stress. In the scope of the model presented here, the plausibility of simplifications made in a practical OI scheme is analyzed. The unified study of the GIM, KF, and OI allows for the demonstratation of how the forecast error covariance used in a practical OI sequential scheme may be optimized with the use of lagged covariances for the model solution. The effect of the misspecified input error statistics on the solution quality is also assessed. In some practically relevant cases the use of future data by the GIM, in contrast to KF and OI, compensates for incorrectly specified input error covariances.