FORECASTING COASTAL CIRCULATION USING AN APPROXIMATE KALMAN FILTER BASED ON DYNAMICAL MODES

We present an approximate Kalman filter for nowcasting and forecasting of coastal ocean circulation. Reduction in the effective dimension of the ocean model, and consequently the Kalman filter, is achieved by r eformulating the original model in terms of its dynamical modes. A sub set of the modes preferentially excited by the model forcing is chosen as the basis for a reduced ocean model. Solving the Kalman filter equ ations in this reduced dimension modal space retains the important com ponents of the dynamics necessary for model forecasts and error propag ation, as well as allowing for a computationally efficient means to im plement this data assimilation scheme. The approximate Kalman filter w as applied to a prototype model of the Scotian Shelf off Canada's east coast. This limited-area model is based on the linearized, depth-aver aged shallow water equations. The dominant modes were identified for b oth wind and boundary forcing, leading to an approximately 90% reducti on in the dimension of the system. Synthetic data based on both fixed (coastal sea level and current meter) and moving (ship ADCP) observati on arrays were used to test the performance of the filter. Even with s ignificant observation noise, the results indicated that the approxima te filter is able to recover the temporal evolution of the actual (mod el generated) ocean state to within +/-1% at the observation locations for all test cases. Satisfactory performance was also achieved in rec overing the entire flow field (extrapolation) for the fixed observatio n array, but poorer results were found in the case of the moving array . (C) 1998 Elsevier Science Ltd. All rights reserved.