Storm surge prediction using Kalman filtering

In this study the theory of Kalman filtering has been employed to develop a new method for predicting water-levels along the Dutch coast. The combination of the standard Kalman filter with a non-linear tidal model of the entire North Sea is, from a computational point of view, not (yet) feasible. Therefore, in this investigation two different approaches have been developed. The first is based on the approximation of the tidal movement in the Dutch coastal area by a one-dimensional model. The two-dimensional effects due to the wind and the Coriolis force are taken into account by introducing some additional, empirical equations. The finite difference scheme and the system noise processes, introduced to describe the uncertainty associated with the model, are chosen such that numerical difficulties are avoided. Water-levels and velocities as well as the uncertain parameters in the model are estimated on-line by the Kalman filter. Since the model is continuously being adapted to the changing conditions, even this simple conceptual model gives satisfactory predictions. However, the time interval over which accurate predictions can be produced is limited because the one-dimensional approximation is only realistic for a smal1 part of the southern North Sea. To increase the prediction interval the second Kalman filter approach that is developed in this investigation is based on a two-dimensional model of the entire North Sea. The extension of the one-dimensional filter to two space dimensions does not give rise to conceptual problems but, as noted before, impose an unacceptably greater computational burden. In order to reduce this burden, the Kalman filter is approximated by a time-invariant one. In this case the time-consuming filter equations do not have to be computed over again as new measurements become available, but need only be solved once. Furthermore, by defining the system noise processes on a coarse grid and by employing a Chandrasekhar-type filter algorithm; a computationally attractive implementation of the filter is obtained. It is shown that the algorithm can be vectorized efficiently and that using a CDC CYBER 205 vector processor it is possible to combine the steady-state filter approach with very large models. Numerical difficulties can be avoided by carefully choosing the finite difference scheme, the boundary treatment and most important, the system noise processes. The filter has been tested extensively using simulated data as well as field data. The results show excellent filter performance, especially if we take into account that the number of measurements available (as yet) has been very limited. With respect to the results of the deterministic model without using tbe water-levels measurements available, the improvement obtained by filtering these measurements is substantial.