Realization of a consistent set of vertical reference surfaces in coastal areas

We present a combined approach for the realization of the (quasi-)geoid as a height reference surface and the vertical reference surface at sea (chart datum). This approach, specifically designed for shallow seas and coastal waters, provides the relation between the two vertical reference surfaces without gaps down to the coast. It uses a regional hydrodynamic model, which, after vertical referencing, provides water levels relative to a given (quasi-)geoid. Conversely, the hydrodynamic model is also used to realize a (quasi-)geoid by providing corrections to the dynamic sea surface topography, which are used to reduce radar altimeter-derived sea surface heights to the (quasi-)geoid. The coupled problem of vertically referencing the hydrodynamic model and computing the (quasi-)geoid is solved iteratively. After convergence of the iteration process, the vertically referenced hydrodynamic model is used to realize the chart datum. In this way, consistency between the chart datum and (quasi-)geoid is ensured. We demonstrate the feasibility and performance of this approach for the Dutch mainland and North Sea. We show that in the Dutch part of the North Sea, the differences between modeled and observed instantaneous and mean dynamic sea surface topography is 8-10 and 5.8 cm, respectively. On land, we show that the methodology provides a quasi-geoid which has a lower standard deviation (SD) than the European Gravimetric Geoid 2008 (EGG08) and the official Netherlands quasi-geoid NLGEO2004-grav when compared to GPS-levelling data. The root mean square at 81 GPS-levelling points is below 1.4 cm; no correction surface is needed. Finally, we show that the chart datum (lowest astronomical tide, LAT) agrees with the observed chart datum at 92 onshore tide gauges to within 21.5 cm (SD).