APPLICATION OF THE DISTRIBUTED-PARAMETER FILTER TO PREDICT SIMULATED TIDAL INDUCED SHALLOW-WATER FLOW

Distributed parameter filtering theory is employed for estimating the state variables and associated error covariances of a dynamical distri buted system under highly tandem tidal and meteorological influences. The stochastic-deterministic mathematical model of the physical system under study consists of the shallow water equations described by the momentum and continuity equations in which the external forces such as Coriolis force, wind friction, and atmospheric pressure are considere d. White Gaussian noises in the system and measurement equations are u sed to account for the inherent stochasticity of the system. By using an optimal distributed parameter filter, the information provided by t he stochastic dynamical model and the noisy measurements taken from th e actual system are combined to obtain an optimal estimate of the stat e of the system, which in turn is used as the initial condition for th e prediction procedure. The approach followed here has numerical appro ximation carried out at the end, which means that the numerical discre tization is performed in the filtering equations, and not in the equat ions modeling the system. Therefore, the continuous distributive natur e of the original system is maintained as long as possible and the pro pagation of modelling errors in the problem is minimized. The appropri ateness of the distributed parameter filter is demonstrated in an appl ication involving the prediction of storm surges in the North Sea. The results confirm excellent filter performance with considerable improv ement with respect to the deterministic prediction.