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On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

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Abstract

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.

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Acknowledgements

The authors acknowledge the financial support provided by the German Research Foundation (DFG) under Grant Number HE1433/20-2. Furthermore, we would like to thank the German Federal Agency for Cartography and Geodesy (BKG), the Austrian Federal Office for Metrology and Surveying (BEV), and the Brazilian Institute of Geography and Statistics (IBGE) for kindly providing the GNSS/leveling data sets. Finally, two anonymous reviewers as well as the Editor-in-Chief are acknowledged for their valuable comments.

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  1. Geodetic Institute, Karlsruhe Institute of Technology (KIT), Englerstr. 7, 76128, Karlsruhe, Germany

    Thomas Grombein, Kurt Seitz & Bernhard Heck

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  1. Thomas Grombein
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Correspondence to Thomas Grombein.

Appendix

Appendix

In addition to the results presented for the TIM R5 model in Fig. 6 (Sect. 5.1), this appendix provides corresponding plots for the DIR R5 and GOCO05s model as displayed in Figs. 8 and 9, respectively. Furthermore, as a supplement to Fig. 7 (Sect. 5.2), the spatial distributions of the least squares residuals are displayed in Fig. 10.

Fig. 8
figure 8

Results for different combinations of DIR R5 and EGM2008 with respect to the used SH degree of combination \(N\) and the transition bandwidth \(dN\). The achieved STD values of the residuals \(v_j\) are shown in the left column, while the estimated height datum offsets \(\delta H\) are presented in the right column. The different results for the three study areas Germany, Austria, and Brazil are displayed in the first, second, and third row, respectively. Note the different scaling of the color bars

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Fig. 9
figure 9

Results for different combinations of GOCO05s and EGM2008 with respect to the used SH degree of combination \(N\) and the transition bandwidth \(dN\). The achieved STD values of the residuals \(v_j\) are shown in the left column, while the estimated height datum offsets \(\delta H\) are presented in the right column. The different results for the three study areas Germany, Austria, and Brazil are displayed in the first, second, and third row, respectively. Note the different scaling of the color bars

Full size image
Fig. 10
figure 10

Least squares adjusted residuals \(v_j\) at the respective GNSS/leveling benchmarks \(P_j\), shown for the topo and non-topo scenario (right and left column, respectively), and the three study areas Germany, Austria, and Brazil (first, second, and third row, respectively). Note the different scaling of the color bars

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Grombein, T., Seitz, K. & Heck, B. On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models. Surv Geophys 38, 443–477 (2017). https://doi.org/10.1007/s10712-016-9400-4

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