1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Environmental Science and Engineering, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
This thesis consists of seven research papers published or submitted for publication in the period 2002-2004 together with a summary report. The thesis mainly deals with data assimilation of tide gauge data in two- and three-dimensional hydrodynamic models of the continental shelf seas. Assimilation of sea surface temperature and parameter estimation in hydrodynamic models are also considered. The main focus has been on the development of robust and efficient techniques applicable in real operational settings. The applied assimilation techniques all use a Kalman filter approach. They consist of a stochastic state propagation step using a numerical hydrodynamic model and an update step based on a best linear unbiased estimator when new measurements are available. The main challenge is to construct a stochastic model of the high dimensional ocean state that provides su cient skill for a proper update to be calculated. Such a stochastic model requires model and measurement errors to be described, which is a di cult task independent of the computational resources at hand. Further, the need for e cient solutions necessitates further assumptions to be imposed that maintain a skillful and robust state estimate. The assimilation schemes used in this work are primarily based on two ensemble based schemes, the Ensemble Kalman Filter and the Reduced Rank Square Root Kalman Filter. In order to investigate the applicability of these and derived schemes, the sensitivity to filter parameters, nonlinearity and bias is examined in artificial tests. Approximate schemes, which are theoretically presented as using regularised Kalman gains, are introduced and successfully applied in artificial as well real case scenarios. Particularly, distant dependent and slowly time varying or constant Kalman gains are shown to possess good hindcast and forecast skill in the Inner Danish Waters. The framework for combining data assimilation and off-line error correction techniques is discussed and presented. Early results show a potential for such an approach, but a more elaborate investigation is needed to further develop the idea. Finally, work has been initiated on parameter estimation in two-dimensional hydrodynamic models with an approach that avoids the development of an adjoint code by using an algorithmic structure that favours application of office-grids as they are envisaged to look in the near future. The main contribution is the development of a number of regularisation techniques for tide gauge assimilation. Further, the techniques used to assess the validity of underlying assumptions (weak non-linearity, unbiasedness or error model skill) provide a valuable tool-box for investigating a dynamical system prior to potentially selecting an assimilation approach. The combined data assimilation error correction framework may be an important contribution to future improvements of forecast skill for a number of systems. The work done on parameter estimation is expected to mature into a future standard procedure for model calibration for models with rapidly evolving complex codes.