Two-sample Kalman filter and system error modelling for storm surge forecasting

Two directions for improving the accuracy of sea level forecast are investigated in this study. The first direction seeks to improve the forecast accuracy of astronomical tide component. Here, a method is applied to analyze and forecast the remaining periodic components of harmonic analysis residual. This method is found to work reasonably well during calm weather, but poorly during stormy period. This finding has led to continue the study with the second direction, which is about data assimilation implemented into the operational two-dimensional storm surge forecast model. The operational storm surge forecast system in the Netherlands uses a steady-state Kalman filter to provide more accurate initial conditions for forecast runs. An important factor, which determines the success of a Kalman filter, is the specification of system error covariance. In the operational system, the system error covariance is modelled explicitly by assuming isotropy and homogeneity. In this study, we investigate the use of the difference between wind products of two similarly skillful atmospheric models as proxy to the unknown error of the storm surge forecast model. To accommodate this investigation, a new method for computing a steady-state Kalman gain, called the two-sample Kalman filter, is developed in this study. It is an iterative procedure for computing the steadystate Kalman gain of a stochastic process by using two samples of the process. A number of experiments have been performed to demonstrate that this algorithm produces correct solutions and is potentially applicable to different models. The two-sample Kalman filter algorithm is implemented by using the wind products from two meteorological centers: the Royal Dutch Meteorological Institute (KNMI) and UK Met Office (UKMO). Here, the investigation is focused on random component of the system error. Therefore, bias or systematic error is eliminated prior to the implementation of the wind products to the two-sample Kalman filter. The system error spatial correlation estimated from these two wind products is found to be anisotropic, in contrast to the one assumed in the operational system. The steady-state Kalman filter based on this error covariance estimate is found to work well in steering the model closer to the observation data. For the stations along the Dutch coast, the data assimilation is found to improve the forecast accuracy up to about 12 hours. Moreover, it is also demonstrated that this data assimilation system outperforms a steady-state Kalman filter based on isotropy assumption. To further improve the data assimilation system, the two-sample Kalman filter is extended to work with more samples. By using more samples, the computation of the error covariance can be done by averaging over shorter time. This relaxes the stationarity assumption and is expected to simulate better the state-dependence model error. In this study, this algorithm is implemented by using wind ensemble of the LAMEPS, which is operational at the Norwegian Meteorological Institute. This setup is found to perform similarly well as the steady-state Kalman filter during large positive surge. However, the steady-state Kalman filter is found to perform better than the ensemble system in forecasting negative surge. The resulting ensemble spread during negative surge is found to be narrower than the standard deviation assumed by the steady-state Kalman filter. A further investigation on the wind ensemble is required