Towards a Kalman Filter based data assimilation module in a three-dimensional hydrodynamic modelling package

Data assimilation in a three-dimensional hydrodynamic model (MIKE 3) for bays, estuaries, coastal areas and shelf sea is considered. Two different methods based on the Kalman filter to assimilate water level measurements are presented. One is an extended Kalman filter, in which the error covariance matrix is approximated by a matrix of a lower rank using a square root (RRSQRT). The second method utilises an ensemble Kalman filter based on a Monte Carlo approach for propagation of model errors. The state considered in the two approaches consists of the two-dimensional fields of water level and the two horizontal depth averaged velocities in each grid point. The three dimensional horizontal velocity field is updated by using a constant predefined profile constrained by maintenance of dynamical balance. The updated vertical velocity is calculated from the hydrostatic balance equation. The formulation assumes that coloured noise enters the system in the meteorological and open boundary forcing terms. The performance of the filters is assessed using a twin experiment based on a hypothetical bay region. The methods are tested both in the case of known Gaussian error distribution in the meteorological and boundary forcing as well as in the more realistic case of phase and amplitude errors in the boundary and biased meteorological fields. The results are promising and the schemes show good robustness and sensitivity properties.