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[1] Data assimilation in operational forecasting systems is a discipline undergoing rapid development. Despite the ever increasing computational resources, it requires efficient as well as robust assimilation schemes to support online prediction products. The parameter considered for assimilation here is water levels from tide gauge stations. The assimilation approach is Kalman filter based and examines the combination of the Ensemble Kalman Filter with spatial and dynamic regularization techniques. Further, both a Steady Kalman gain approximation and a dynamically evolving Kalman gain are considered. The estimation skill of the various assimilation schemes is assessed in a 4-week hindcast experiment using a setup of an operational model in the North Sea and Baltic Sea system. The computationally efficient dynamic regularization works very well and is to be encouraged for water level nowcasts. Distance regularization gives much improved results in data sparse areas, while maintaining performance in areas with a denser distribution of tide gauges.

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The state estimation problem in hydrodynamic modelling is formulated. The three-dimensional hydrodynamic model MIKE 3 is extended to provide a stochastic state space description of the system and observations are related to the state through the measurement equation. Two state estimators, the maximum a posteriori (MAP) estimator and the best linear unbiased estimator (BLUE), are derived and their differences discussed. Combined with various schemes for state and error covariance propagation different sequential estimators, based on the Kalman filter, are formulated. In this paper, the ensemble Kalman filter with either an ensemble or central mean state propagation and the reduced rank square root Kalman filter are implemented for assimilation of tidal gauge data. The efficient data assimilation algorithms are based on a number of assumptions to enable practical use in regional and coastal oceanic models. Three measures of non-linearity and one bias measure have been implemented to assess the validity of these assumptions for a given model set-up. Two of these measures further express the non-Gaussianity and thus guide the proper statistical interpretation of the results. The applicability of the measures is demonstrated in two twin case experiments in an idealised set-up.

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