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 reformulating the original model in terms of its dynamical modes. A subset of the modes preferentially excited by the model forcing is chosen as the basis for a reduced ocean model. Solving the Kalman filter equations in this reduced dimension modal space retains the important components of the dynamics necessary for model forecasts and error propagation, as well as allowing for a computationally efficient means to implement this data assimilation scheme. proximate Kalman filter was applied to a prototype model of the Scotian Shelf off Canadaʹs east coast. This limited-area model is based on the linearized, depth-averaged shallow water equations. The dominant modes were identified for both wind and boundary forcing, leading to an approximately 90% reduction in the dimension of the system. Synthetic data based on both fixed (coastal sea level and current meter) and moving (ship ADCP) observation arrays were used to test the performance of the filter. Even with significant observation noise, the results indicated that the approximate filter is able to recover the temporal evolution of the actual (model generated) ocean state to within ± 1 % at the observation locations for all test cases. Satisfactory performance was also achieved in recovering the entire flow field (extrapolation) for the fixed observation array, but poorer results were found in the case of the moving array.