Roadmap to a mutually consistent set of offshore vertical reference frames

D.C. Slobbe,Roadmap to a mutually consistent set of offshore vertical reference frames, PhD thesis, TU Delft, 2013.

Abstract
This thesis presents 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 shallow water hydrodynamic model which provides water levels relative to a given (quasi-)geoid. The latter requires that the hydrodynamic model is vertically referenced to the same (quasi-)geoid. Vice versa, 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. The feasibility and performance of this approach is demonstrated for the Dutch North Sea and mainland. It is shown that the differences between modeled and observed instantaneous and mean dynamic sea surface topography is 8-10 cm and 5.8 cm, respectively, for the Dutch North Sea. On land, it is shown that the methodology provides a (quasi-)geoid which has a lower standard deviation than the European Gravimetric Geoid 2008 (EGG08) and the official Netherlands (quasi-)geoid NLGEO2004-grav when compared to GPS-levelling data. The standard deviation at 81 GPS-levelling points is below 1 cm; no correction surface is needed. Finally, it is shown that the chart datum (lowest astronomical tide, LAT) agrees with the observed chart datum at 92 onshore tide gauges to within 21.5 cm standard deviation.

This study also examines the impact of instantaneous dynamic sea surface topography (DT) corrections to be applied to altimeter-derived sea surface slopes on the quasi-geoid in the shallow and coastal waters of the North Sea. It is found that the steric and surge parts of the DT mainly contribute to improvements in the signal-to-noise ration at longer wavelengths down to 100-200 km and that the improvements increase towards the southern North Sea. It is also found that the shallow water hydrodynamic model provides better tidal corrections compared to a global ocean tide model, which are most pronounced in the southern North Sea and affect almost the entire spectrum. In terms of quasi-geoid heights, the differences are very small differences (mostly below ±2 cm). This is explained by the fact that altimeter-derived (quasi-)geoid slopes hardly contribute to the estimated quasi-geoid if shipboard gravity data are included.

The last question treated in this thesis is whether a spherical Slepian basis representation enables to obtain spectral consistency between a high- and low-resolution data set (following recent studies, this question is treated in the context of mean dynamic topography (MDT) estimation by computing the difference between a high-resolution mean sea level (MSL) model obtained from satellite altimetry and a low-resolution gravimetric geoid). The answer is no; a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. Furthermore, it is shown that a meaningful definition of a low-resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. One of these sets of orthogonal basis functions are computed using the Gram-Schmidt orthogonalization for spherical harmonics. For the oceans, an orthogonal basis could be constructed only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution failed due to inherent instabilities. More research is needed to solve the instability problem.

Contents
Preface ix
Summary xiii
Samenvatting xxi
1. Introduction  1
2. Overall approach to offshore vertical reference frame realization 23
3. Vertical referencing of a shallow water hydrodynamic model 29
4. Estimation of the quasi-geoid 67
5. LAT reference surface 129
6. The spherical Slepian basis as a means to obtain spectral consistency 157
7. Conclusions and recommendations 191
A. On the use of free-air gravity anomalies 203
B. Overview tide gauge data 205
C. Validation of LAT using tide gauge data 209
Bibliography 213
About the author 233