Comparison of extended and ensemble Kalman filters for data assimilation in coastal area modelling

Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) based on a Monte Carlo simulation approach for propagation of errors. The filtering problem is formulated by utilising a general description of the model noise process related to errors in the model forcing, i.e. open boundary conditions and meteorological forcing. The performance of the two Kalman filters is evaluated using a twin experiment based on a hypothetical bay region. For both filters, the error covariance approximation sufficiently resolves the error propagation in the model at a computational load that is significantly smaller than required by the full Kalman filter algorithm. Furthermore, the Kalman filters are shown to be very robust with respect to defining the errors. Even in the case of a severely biased model error, the filters are able to efficiently correct the model. In general, the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter. The error covariance approximation in the RRSQRT KF is shown to be more efficient than the error representation in the EnKF. For strongly non-linear dynamics, however, the EnKF is preferable. Copyright © 1999 John Wiley & Sons, Ltd.