Two-dimensional shallow water flow identification

Abstract

A discrete time-invariant Kalman filter for the identification and prediction of two-dimensional shallow water flow using observations of the water level registered at some locations, has been developed. The filter is based on a set of difference equations derived from the linear two-dimensional shallow water equations using the finite difference scheme proposed by Sielecki. By introducing a system noise process, we can embed the difference equations inot a stochastic environment. This enables us to take into account the uncertainties of these equations. A Chandrasekhar-type algorithm is employed to obtain the steady-state filter. In this way the fact that the noise is less spatially variable than the underlying process can be exploited to reduce the computational burden. The capabilities of the filter are illustrated by applying it to the six-hours-ahead prediction of storm surges in the North Sea. The results show excellent filter performance, and, with respect to the results of the underlying deterministic model which were achieved without using the water-level measurements available, the improvement obtained by filtering the measurements is substantial.