A Kalman filter approach to realize the lowest astronomical tide surface

Abstract

In this paper, we present a novel Kalman filter approach to combine a hydrodynamic model-derived lowest astronomical tide (LAT) surface with tide gauge record-derived LAT values. In the approach, tidal water levels are assimilated into the model. As such, the combination is guided by the model physics. When validating the obtained “Kalman-filtered LAT realization” at all tide gauges, we obtained an overall root-mean-square (RMS) difference of 15.1 cm. At the tide gauges not used in the data assimilation, the RMS is 17.9 cm. We found that the assimilation reduces the overall RMS difference by ∼31% and ∼22%, respectively. In the Dutch North Sea and Wadden Sea, the RMS differences are 6.6 and 14.8 cm (all tide gauges), respectively. Furthermore, we address the problem of LAT realization in intertidal waters where LAT is not defined. We propose to replace LAT by pseudo-LAT, which we suggest to realize similarly as LAT except that all water level boundary conditions and assimilated tidal water levels have to be enlarged by a constant value that is removed afterwards. Using this approach, we obtained a smooth reference surface for the Dutch Wadden Sea that fits LAT at the North Sea boundary within a few centimeters.