Abstract
A new method is proposed to connect the orthometric height datum of island far from mainland with measurements of both ship-borne gravimetry and GNSS along the ship route connecting these datums. The methodology of route height datum connection is based on the astronomical leveling principle. The effect of the deflection of the vertical (DOV) error and the ellipsoidal height difference error are major factors on the precision of the orthometric height connection. To improve the computational accuracy of DOVs along the ship route, the collinear adjustment is used to improve the accuracy of the gravity measurements and GNSS ellipsoidal heights. The remove-restore technique in conjunction with the measured DOVs on the mainland and island is used to improve the estimation accuracy of the DOVs along the ship route. The least squares collocation method is used to estimate the residual DOVs. The covariance of gravity anomalies and cross-covariance function between gravity anomalies and DOVs are derived from the disturbing potential spherical harmonic expansion. The optimal partition number is also studied for the high precision orthometric height connection across sea. Finally, we use the proposed method to connect the orthometric height datum point on Qingdao coast in Shandong Province of China with the datum point on Caoyu coast in Fujian Province of China.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen OB (2010) The DTU10 gravity field and mean sea surface. In: The 2nd international symposium of the gravity field of the earth (IGFS2), Fairbanks
Burša M, Kouba J, Kumar M, Müller A, Raděj K, True SA, Vatrt V, Vojtíšková M (1999) Geoidal geopotential and world height system. Stud Geophys Geod 43(4):327–337. doi:10.1023/A:1023273416512
Burša M, Kouba J, Müller A, Raděj K, True SA, Vatrt V, Vojtíšková M (2001) Determination of geopotential differences between local vertical datums and realization of a world height system. Stud Geophys Geod 45(2):127–132. doi:10.1023/A:1021860126850
Burša M, Kenyob S, Kouba J, Šíma Z, Vatrt V, Vojtíšková M (2004) A global vertical reference frame based on four regional vertical datums. Stud Geophys Geod 48:493–502. doi:10.1023/B:SGEG.0000037468.48585.e6
Fei ZL, Sideris MG (2001) GPS leveling and the second geodetic boundary value problem. In: Sideris MG (ed) Gravity, geoid, and goedynamics 2000. Springer-Verlag, Berlin, pp 341–346
Gerlach C, Rummel R (2013) Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geod 87:57–67. doi:10.1007/s00190-012-0579-y
Goldan HJ, Seeber G (1994) Precise tide gauge connection to the island of Helgoland. Mar Geod 17(2):147–152. doi:10.1080/15210609409379721
Guan ZL, Ning JS (1981) Earth shape and its exterior gravity field. Surveying and Mapping Press, Beijing (in Chinese)
Guo JY, Chen YN, Liu X, Zhong SX, Mai ZQ (2013) Route height connection across the sea by using the vertical deflections and ellipsoidal height data. China Ocean Eng 27(1):99–110. doi:10.1007/s13344-013-0009-9
Guo J, Liu X, Chen Y, Wang J, Li C (2014) Local normal height connection across sea with ship-borne gravity and GNSS techniques. Mar Geophy Res 35:141–148. doi:10.1007/s11001-014-9216-x
Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Seasurface topography and the geoid. Springer, Berlin, Germany, pp 116–128
Heiskanen W, Moritz H (1967) Physical geodesy. Freeman, San Francisco
Huang MT, Zhai GJ, Guan Z, Ouyang YZ, Liu YC (2005) Determination and applications of marine gravity field. Surveying and Mapping Press, Beijing (in Chinese)
Kumar M, Burke KJ (1998) Realizing a global vertical datum with the use of geoid. In: Vermeer M, Ádám J (eds) Proceedings of the second continental workshop on the geoid in Europe, Report 98:4, Finnish Geodetic Institute, Masala, pp 87–94
Li JC, Jiang WP (2001) Height datum transference within long distance across sea. Geomat Inf Sci Wuhan Univ 26(6):514–517 (in Chinese)
Li F, Chen W, Yue JL (2003) On solution and application of GPS/gravity boundary value problem. Chin J Geophys 46(5):595–599. doi:10.1002/cjg2.405
Liibusk A (2013) Precise hydrodynamic leveling using pressure gauges with application to improvement of the Estonian national leveling network. PhD thesis, Estonian University of Life Sciences
Mather RS, Rizos C, Morrison T (1978) On the unification of geodetic leveling datums using satellite altimetry. NASA Technical Memorandum, NASA-TM-79533
Nahavandchi H, Sjöberg LE (1998) Unification of vertical datums by GPS and gravimetric geoid models using modified Stokes formula. Mar Geod 21(4):261–273. doi:10.1080/01490419809388142
Pan M, Sjöberg LE (1998) Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia. J Geod 72(2):64–70. doi:10.1007/s001900050149
Pavlis NK, Holmes SA, Kenyon S, Factor JK (2012) The development and evaluation of the Earth gravitational model 2008. J Geophys Res 117:B04406. doi:10.1029/2011JB008916
Pouttanen M (1999) Use of GPS in unification of vertical datums and detection of levelling network errors. In: Lilje M (ed) Proceedings of geodesy and surveying in the future: the importance of heights, LMV Report 1999:3, National Land Survey, Gävle, pp 301–312
Rapp RH, Cruz J (1986) The representation of the earth’s gravitational potential in a spherical harmonic expansion to degree 250, Report 372, Department of Geodetic Science, Ohio State University, Columbus
Rapp RH, Rummel R (1975) Methods for the computation of detailed geoids and their accuracy, Report 233, Department of Geodetic Science, Ohio State University, Columbus
Rummel R (2012) Height unification using GOCE. J Geod Sci 2(4):355–362. doi:10.2478/v10156-011-0047-2
Rummel R, Teunissen PJG (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Géod 62(4):477–498. doi:10.1007/BF02520239
Sacerdote F, Sanso F (1989) On the analysis of the fixed boundary gravimetry BVP. In: The second Hotine-Marussi symposium on mathematical geodesy, Pisa
Xu HZ, Bao LF, Lu Y (2009) Precise transfer of height datum across ocean with gravimetric potential difference method. Institute of Geodesy and Geophysics, CAS, Wuhan (in Chinese)
Yu JH, Jekeli C, Zhu M (2003) The analytical solutions of the Dirichlet and Neumann boundary value problems with ellipsoidal boundary. J Geod 76(11):653–667. doi:10.1007/s00190-002-0271-8
Zhang L, Li F, Chen W, Zhang C (2009) Height datum unification between Shenzhen and Hong Kong using the solution of the linearized fixed-gravimetric boundary value problem. J Geod 83(5):411–417. doi:10.1007/s00190-008-0234-9
Acknowledgments
We thank anonymous reviewers for their helpful comments and suggestions. This study is supported by the National Natural Science Foundation of China (Grant No. 41374009), the Shandong Natural Science Foundation of China (Grant No. ZR2013DM009), the Basic Science and Technology Project of China (Grant No. 2015FY310200), and the SDUST Research Fund (Grant No. 2014TDJH101).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, J., Guo, J., Liu, X. et al. Orthometric height connection across sea with ship-borne gravimetry and GNSS measurement along the ship route. Acta Geod Geophys 52, 357–373 (2017). https://doi.org/10.1007/s40328-016-0174-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40328-016-0174-4