Abstract
One of the main objectives of ESA’s Gravity Field and Steady-State Ocean Circulation mission GOCE (Gravity field and steady-state ocean circulation mission, 1999) is to allow global unification of height systems by directly providing potential differences between benchmarks in different height datum zones. In other words, GOCE provides a globally consistent and unbiased geoid. If this information is combined with ellipsoidal (derived from geodetic space techniques) and physical heights (derived from leveling/gravimetry) at the same benchmarks, datum offsets between the datum zones can be determined and all zones unified. The expected accuracy of GOCE is around 2–3 cm up to spherical harmonic degree n max ≈ 200. The omission error above this degree amounts to about 30 cm which cannot be neglected. Therefore, terrestrial residual gravity anomalies are necessary to evaluate the medium and short wavelengths of the geoid, i.e. one has to solve the Geodetic Boundary Value Problem (GBVP). The theory of height unification by the GBVP approach is well developed, see e.g. Colombo (A World Vertical Network. Report 296, Department of Geodetic Science and Surveying, 1980) or Rummel and Teunissen (Bull Geod 62:477–498, 1988). Thereby, it must be considered that terrestrial gravity anomalies referring to different datum zones are biased due to the respective datum offsets. Consequently, the height reference surface of a specific datum zone deviates from the unbiased geoid not only due to its own datum offset (direct bias term) but is also indirectly affected by the integration of biased gravity anomalies. The latter effect is called the indirect bias term and it considerably complicates the adjustment model for global height unification. If no satellite based gravity model is employed, this error amounts to about the same size as the datum offsets, i.e. 1–2 m globally. We show that this value decreases if a satellite-only gravity model is used. Specifically for GOCE with n max ≈ 200, the error can be expected not to exceed the level of 1 cm, allowing the effect to be neglected in practical height unification. The results are supported by recent findings by Gatti et al. (J Geod, 2012).
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References
Amos MJ, Featherstone WE (2009) Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations. Geod J 83: 57–68. doi:10.1007/s00190-008-0232-y
Colombo O (1980) A World Vertical Network. Report 296, Department of Geodetic Science and Surveying. Ohio State University, Ohio
Denker H (2001) On the effect of datum inconsistencies in gravity and position on European geoid computations. Paper presented at the IAG Scientific Assembley, September 2–8, 2001, Budapest, Hungary
Dufau C, Martin-Puig C, Moreno L (2011) User requirements in the coastal ocean for satellite altimetry. In: Vignudelli S, Kostianoy AG, Cipollini P, Benveniste J (eds) Coastal altimetry. Springer, Berlin
ESA (1999) Gravity field and steady-state ocean circulation mission. Report for mission selection of the four candidate earth explorer core missions. SP 1233(1) ESA
Gatti A, Reguzzoni M, Venuti G (2012) The height datum problem and the role of satellite gravity models. J Geod (accepted for publication)
Gerlach C (2001) Quasigeoid computation in Bavaria. Paper presented at the IAG Scientific Assembly, September 2–8, 2001. Budapest, Hungary
Gommenginger C, Thibaut P, Fenoglio-Marc L, Quartly G, Deng X, Gómez-Enri J, Challenor P, Gao Y (2011) Retracking altimeter waveforms near the coasts. In: Vignudelli S, Kostianoy AG, Cipollini P, Benveniste J (eds) Coastal altimetry. Springer, Berlin
Heck B (1990) An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull Geod 64: 88–108
Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco
Lemoine FG, Kenyon SC, Factor RG, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The development of the joint NASA GSFC and National Imagery and Mapping Agency (NIMA) geopotential model EGM96. NASA/TP-1998-206861,Goddard Space Flight Center, Greenbelt
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth gravitational model 2008 (EGM2008). Geophys J Res 117: B04406. doi:10.1029/2011JB008916
Rapp RH, Balasubramania N (1992) A conceptual formulation of a world height system. Report 421, Department of Geodetic Science and Surveying, Ohio State University
Reigber C, Schwintzer P, Neumayer KH, Barthelmes F, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Bruinsma S, Perosanz F, Fayard T (2003) The CHAMP–only Earth Gravity Field Model EIGEN–2. Adv Space Res 31(8): 1883–1888. doi:10.1016/S0273-1177(03)00162-5
Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Geod 62: 477–498
Rummel R (2001) Global unification of height systems and GOCE. In: Sideris MG (ed.) Gravity, geoid and geodynamics 2000. Springer, Berlin pp 13–20
Sacher M, Ihde J, Liebsch G, Mäkinen J (2009) EVRF2007 as the realization of the European Vertical Reference System. Boll Geod Scienze Affini, LXVIII 1: 35–50
Sacerdote F, Sansò F (2001) W0: A story of the height datum problem. In: Festschrift W. Torge. Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover, 4956
Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149: 768–775
Schwintzer P, Reigber C, Bode A, Kang Z, Zhu SY, Massmann FH, Raimondo JC, Biancale R, Balmino G, Lemoine JM, Moynot B, Marty JC, Barlier F, Boudon Y (1997) Long wavelength global gravity field models: GRIM4S4, GRIM4C4. J Geod 71(4): 189–208
Tapley BD, Watkins M, Ries J, Davis G, Eanes R, Poole S, Rim H, Schutz B, Shum CK, Nerem R, Lerch F, Marshall JA, Klosko SM, Pavlis N, Williamson R (1996) The joint gravity model 3. J Geophys Res 101(B12): 28029–28049
Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9): L09607. doi:10.1029/2004GL019920
Tapley BD, Ries J, Bettadpur S, Chambers D, Cheng M, Condi F, Gunter B, Kang Z, Nagel P, Pastor R, Poole S, Wang F (2005) GGM02—an improved Earth gravity field model from GRACE. J Geod 79(8): 467–478. doi:10.1007/s00190-005-0480-z
Xu P (1992) Quality investigation of global vertical datum connection. Geophys J Int 110(2): 361–370
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Gerlach, C., Rummel, R. Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geod 87, 57–67 (2013). https://doi.org/10.1007/s00190-012-0579-y
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DOI: https://doi.org/10.1007/s00190-012-0579-y