The Iranian height datum offset from the GBVP solution and spirit-leveling/gravimetry data

  • Amir EbadiEmail author
  • Alireza A. Ardalan
  • Roohollah Karimi
Original Article


The gravity potential of the zero point of the Iranian height datum (IRHD) is determined as well as the IRHD offset from a global geoid. For this purpose, the geodetic boundary value problem (GBVP) solution based on the remove–compute–restore (RCR) technique is used. In the RCR technique, a global geopotential model (GGM) is required as a reference to remove and restore the long wavelengths of the gravity field. Since the GGMs do not have adequate accuracy over Iran, the IRHD offset is not precisely estimated by the GBVP solution. In this study, aiming to improve the latter, a combination solution based on the GBVP approach and spirit-leveling/gravimetry (LG) data, called the GBVP_LG solution, is proposed. To obtain the GBVP_LG solution, gravity potential obtained from the GBVP solution and the gravity potential differences derived from the LG data are used as two types of observations in a least-squares adjustment. The proper relative weight matrices are determined using the variance component estimation method. To evaluate the proposed method, the gravity potential differences between the start and end points of several check-lines in the leveling network derived from the GBVP and GBVP_LG solutions are compared with those of the LG data. The results show that the dependency of the GBVP_LG solution on the reference model used is much less than that of the GBVP solution. In addition, the results indicate that the GBVP_LG solution has a 42% improvement with respect to the GBVP solution in terms of root-mean-square error. As a result of the GBVP_LG solution, the gravity potential of the IRHD zero point is estimated equal to \( W_{0}^{\text{IRHD}} = 62,636,855.89 \pm 0.16\,{\text{m}}^{2} / {\text{s}}^{2} \). Therefore, the IRHD offset with respect to the geoid defined by \( W_{0} = 62,636,853.4\,{\text{m}}^{2} / {\text{s}}^{2} \) is obtained equal to \( - \,25.4 \pm 1.6\,{\text{cm}} \), which means that the IRHD is 25.4 cm below the geoid.


Geodetic boundary value problem Spirit-leveling/gravimetry data Height system unification Iranian height datum offset Remove–compute–restore technique Variance component estimation 



We would like to thank the National Cartographic Center (NCC) of Iran for providing the data and supporting this study under contract No. 4142. We would also like to thank the editor-in-chief, Prof. J. Kusche, and the responsible editor, Prof. I.N. Tziavos, for taking the time and handling our manuscript. We are very grateful to three anonymous reviewers for very constructive and valuable comments, which helped us to improve the manuscript.


  1. Amiri-Simkooei AR (2007) Least squares variance component estimation: theory and GPS applications. Ph.D. thesis, Delft University of Technology, Delft, The NetherlandsGoogle Scholar
  2. Amjadiparvar B, Rangelova E, Sideris MG (2015) The GBVP approach for vertical datum unification: recent results in North America. J Geodesy 90:45–63. Google Scholar
  3. Amos MJ, Featherstone WE (2009) Unification of New Zealand’s local vertical datums: iterative gravimetric quasi-geoid computations. J Geodesy 83:57–68Google Scholar
  4. Andersen OB (2010) The DTU10 gravity field and mean sea surface, second international symposium of the gravity field of the Earth (IGFS2), Fairbanks, AlaskaGoogle Scholar
  5. Ardalan AA (2000) High resolution regional geoid computation in the World Geodetic Datum 2000, based upon collocation of linearized observational functional of the type GPS, gravity potential and gravity intensity. Ph.D. thesis, Stuttgart UniversityGoogle Scholar
  6. Ardalan AA, Karimi R (2013) On correct application of one-step inversion of gravity data. Stud Geophys Geod 57:401–425Google Scholar
  7. Ardalan AA, Safari A (2005) Global height datum unification: a new approach in gravity potential space. J Geodesy 79:512–523Google Scholar
  8. Ardalan A, Grafarend E, Kakkuri J (2002) National height datum, the Gauss–Listing geoid level value W0 and its time variation W0 (Baltic Sea Level project: epochs 1990.8, 1993.8, 1997.4). J Geodesy 76(1):1–28Google Scholar
  9. Ardalan AA, Karimi R, Poutanen M (2010) A bias-free geodetic boundary value problem approach to height datum unification. J Geodesy 84:123–134Google Scholar
  10. Balmino G (1994) Gravitational potential harmonics from the shape of a homogeneous body. Celest Mech Dyn Astron 60:331–364Google Scholar
  11. Balmino G, Vales N, Bonvalot S, Briais A (2012) Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. J Geodesy 86:499–520Google Scholar
  12. Barzaghi R, Carrion D, Vergos GS, Tziavos IN, Grigoriadis VN, Natsiopoulos DA, Bruinsma S, Reinquin F, Seoane L, Bonvalot S, Lequentrec-Lalancette MF, Salaun C, Andersen O, Kundsen P, Abulaitijiang A, Rio MH (2018) GEOMED2: high-resolution geoid of the mediterranean. In: International association of geodesy symposia. Springer, Berlin, Heidelberg.
  13. Bossler JD (1984) Standards and specifications for geodetic control networks. Federal Geodetic Control Committee (FGCC), Rear Adm. John D. Bossler-Chairman, Rockville, Maryland, September 1984Google Scholar
  14. Bruinsma SL, Förste C, Abrikosov O, Marty J-C, Rio M-H, Mulet S, Bonvalot S (2013) The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett 40:3607–3612Google Scholar
  15. Burša M, Radˇej K, Šíma Z, True S, Vatrt V (1997) Determination of the geopotential scale factor from TOPEX/Poseidon satellite altimetry. Stud Geophys Geod 41:203–215. Google Scholar
  16. Burša M, Kenyon S, Kouba J, Šíma Z, Vatrt V, Vitek V, Vojtíšková M (2007) The geopotential value Wo for specifying the relativistic atomic time scale and a global vertical reference system. J Geodesy 81:103–110. Google Scholar
  17. Dayoub N et al (2012) The Gauss–Listing geopotential value W0 and its Rate from altimetric mean sea level and GRACE. J Geodesy 86(9):681. Google Scholar
  18. Drewes H, Kuglitsch F, Adám J, Rózsa S (2016) The geodesist’s handbook 2016. J Geodesy 90:907–1205Google Scholar
  19. Ekman M (1999) Using mean sea surface topography for determination of height system differences across the Baltic Sea. Mar Geodesy 22:31–35Google Scholar
  20. Featherstone WE (2003) Improvement to long-wavelength Australian gravity anomalies expected from the CHAMP, GRACE and GOCE dedicated satellite gravimetry missions. Explor Geophys 34(1–2):69–76. Google Scholar
  21. Featherstone WE, Kuhn M (2006) Height systems and vertical datums: a review in the Australian context. J Spat Sci 51(1):21–41. Google Scholar
  22. Filmer MS, Featherstone WE (2012) A re-evaluation of the offset in the australian height datum between mainland Australia and Tasmania. Mar Geodesy 35:107–119Google Scholar
  23. Foroughi I, Safari A, Novák P, Santos MC (2018) Application of radial basis functions for height datum unification. Geosciences 8:369. Google Scholar
  24. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. The Ohio State University, OSU report no. 355, ColumbusGoogle Scholar
  25. Forsberg R (1985) Gravity field terrain effect computations by FFT. Bull Geod 59:342–360Google Scholar
  26. Forsberg R, Sideris M (1993) Geoid computations by the multi-band spherical FFT approach. Manuscr Geod 18:82–90Google Scholar
  27. Forsberg R, Tscherning CC (1981) The use of height data in gravity field approximation by collocation. J Geophys Res 86:7843–7854Google Scholar
  28. Förste C, Bruinsma SL, Abrikosov O, Lemoine JM, Marty JC, Flechtner F, Balmino G, Barthelmes F, Biancale R (2014) EIGEN-6C4; The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Serv. Google Scholar
  29. Förste C, Bruinsma S, Abrikosov O, Rudenko S, Lemoine JM, Marty JC, Neumayer KH, Biancale R (2016) EIGEN-6S4 A time-variable satellite-only gravity field model to d/o 300 based on LAGEOS, GRACE and GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse. V. 2.0. GFZ Data Services.
  30. Fotopoulos G (2003) An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data. Ph.D. thesis, University of Calgary, Geomatics Eng., report no. 20185Google Scholar
  31. Gatti A, Reguzzoni M, Venuti G (2013) The height datum problem and the role of satellite gravity models. J Geodesy 87:15–22Google Scholar
  32. Gauss CF (1828) Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona. Vandenhoek und Ruprech, GöttingenGoogle Scholar
  33. Gerlach C, Rummel R (2013) Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geodesy 87:57–67Google Scholar
  34. Grigoriadis VN, Kotsakis C, Tziavos IN, Vergos GS (2014) Estimation of the reference geopotential value for the local vertical datum of continental Greece using EGM08 and GPS/leveling data. In: International association of geodesy symposia, vol 141. Springer, Cham, pp 249–255.
  35. Groten E (1999) Report of the international association of geodesy special commission SC3: fundamental constants. XXII IAG General Assembly, BirminghamGoogle Scholar
  36. Gruber T, Gerlach C, Haagmans R (2012) Intercontinental height datum connection with GOCE and GPS-levelling data. J Geod Sci 2(4):270–280Google Scholar
  37. Haagmans R, Min E, Gelderen M, Eynatten M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT and a comparison with existing methods for Stokes’ integral. Manuscr Geod 18:227–241Google Scholar
  38. Hayden T, Amjadiparvar B, Rangelova E, Sideris MG (2012) Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models. J Geod Sci 2(4):257–269Google Scholar
  39. He L, Chu Y, Yu N (2017) Evaluation of the geopotential value W 0LVD of China. Geodesy Geodyn 8(2017):408–412Google Scholar
  40. Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Sea surface topography and the geoid, IAGsymposia series, vol 104. Springer, Berlin, pp 116–128Google Scholar
  41. Heiskanen WA, Moritz H (1967) Physical geodesy. WH Freeman & Co, San Francisco, p 364Google Scholar
  42. Hipkin RG (2000) Modelling the geoid and sea-surface topography in coastal areas. Phys Chem Earth Ser A 25(1):9–16Google Scholar
  43. Hirt C et al (2010) Residual terrain model data to improve quasi-geoid computations in mountainous areas devoid of gravity data. J Geodesy 84:557–567. Google Scholar
  44. Ihde J, Adam J, Gurtner W, Harsson BG, Sacher M, Schlüter W, Wöppelmann G (2000) The height solution of the European vertical reference network (EUVN). In: Veröffentlichungen der BayerischenKommission fur die Internationale Erdmessung, Bayerische AkademieGoogle Scholar
  45. Ihde J, Sánchez L, Barzaghi R, Drewes H, Foerste C, Gruber T, Liebsch G, Marti U, Pail R, Sideris MG (2017) Definition and proposed realization of the international height reference system (IHRS). Surv Geophys. Google Scholar
  46. Jekeli C (2000) Heights, the geopotential, and vertical datums. The Ohio State University, OSU report no. 459, ColumbusGoogle Scholar
  47. Jekeli C, Yang HJ, Kwon JH (2012) The offset of the south korean vertical datum from a global geoid. KSCE J Civ Eng 16(5):816–821. Google Scholar
  48. Kiamehr R (2006) The impact of lateral density variation model in the determination of precise gravimetric geoid in mountainous areas: a case study of Iran. Geophys J Int 167:521–527Google Scholar
  49. Kim, MC, Tapley BD, Shum CK and Ries JC (1995) Center for space research mean sea surface model, presented at the TOPEX/POSEIDON working team meeting, Pasadena CaliforniaGoogle Scholar
  50. Koch KR, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geodesy 76:259–268Google Scholar
  51. Kotsakis C, Sideris MG (1999) On the adjustment of combined GPS/leveling/geoid networks. J Geodesy 73(8):412–421Google Scholar
  52. Kotsakis C, Katsambalos K, Ampatzidis D (2012) Estimation of the zero-height geopotential level W 0LVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands. J Geodesy 86(6):423. Google Scholar
  53. Kuhn M, Featherstone WE (2003) On the optimal spatial resolution of crustal mass distributions for forward gravity field modelling. In: Gravity and geoid 2002, proceedings. pp 195–200Google Scholar
  54. Listing JB (1873) Über unsere jetzige Kenntnis der Gestalt und Größe der Erde. Dietrichsche Verlagsbuchhandlung, GöttingenGoogle Scholar
  55. Martinec Z, Grafarend EW (1997) Construction of Green’s function to an external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution. J Geodesy 71:562–570Google Scholar
  56. Merry C, Vaníček P (1983) Investigation of local variations of sea surface topography. Mar Geodesy 7:101–126Google Scholar
  57. Mukul M, Srivastava V, Mukul M (2015) Analysis of the accuracy of shuttle radar topography mission (SRTM) height models using international global navigation satellite system service (IGS) Network. J Earth Syst Sci 124(6):1343–1357Google Scholar
  58. Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geodesy 74(7):552–560. Google Scholar
  59. Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh W, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geodesy 85:819–843Google Scholar
  60. Pavlis NK, Factor JK, Holmes SA (2007) Terrain-related gravimetric quantities computed for the next EGM. In: Kiliçoglu A, Forsberg R (eds) Gravity field of the earth. Proceedings of the 1st international symposium of the international gravity field service (IGFS), special issue 18. Gen. Command of Mapp, Ankara, pp 318–323Google Scholar
  61. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development of the earth gravitational model 2008 (EIGEN). J Geophys Res 117:B04406Google Scholar
  62. Ramillien G (2002) Gravity/magnetic potential of uneven shell topography. J Geodesy 76:139–149Google Scholar
  63. Rapp RH (1998) The development of a degree 360 expansion of the dynamic ocean topography of the POCM 4B global circulation model, NASA/CR-1998–206877. NASA, GreenbeltGoogle Scholar
  64. Rapp RH, Balasubramania N (1992) A conceptual formulation of a world height system. The Ohio State University, OSU report no. 421, ColumbusGoogle Scholar
  65. Reigber C, Balmino G, Schwintzer P, Biancale R, Bode A, Lemoine JM, Konig R, Loyer S, Neumayer H, Marty JC, Barthelmes F, Perosanz F, Zhu SY (2003) Global gravity field recovery using solely GPS tracking and accelerometer data from CHAMP. Space Sci Rev 108:55–66Google Scholar
  66. Rodriguez E, Morris CS, Belz JE (2006) A global assessment of the SRTM performance. Photogramm Eng Remote Sens 72:249–260Google Scholar
  67. Rülke A, Liebsch G, Sacher M, Schäfer U, Schirmer U, Ihde J (2012) Unification of European height system realizations. J Geod Sci 2(4):343–354. Google Scholar
  68. Rummel R (2000) Global unification of height systems and GOCE. In: Sideris MG (ed) Gravity, geoid and geodynamics. International association of geodesy symposia, vol 123. Springer, Berlin, pp 15–20Google Scholar
  69. Rummel R (2012) Height unification using GOCE. J Geod Sci 2(4):355–362. Google Scholar
  70. Rummel R, Ilk KH (1995) Height datum connection: the ocean part. Allg Vermessungsnachrichten 8–9:321–330Google Scholar
  71. Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Geod 62:477–498Google Scholar
  72. Rummel R, Rapp RH, Sünkel H, Tscherning CC (1988) Comparisons of global topographic-isostatic models to the Earth’s observed gravity Field. Report no. 388. Department of Geodetic SC and Surveying, Ohio State University, ColumbusGoogle Scholar
  73. Saadat A, Safari A, Needell D (2017) IRG2016: RBF-based regional geoid model of Iran. Stud Geophys Geod. Google Scholar
  74. Safari A, Sharifi M, Foroughi I, Amin H (2014) An approach to height datum unification based on local gravity field modeling using radial base function case study: Height datum unification of leveling network of class 1 in Iran. J Earth Space Phys 40:69–81Google Scholar
  75. Sánchez L (2007) Definition and realization of the SIRGAS vertical reference system within a globally unified height system. In: Tregoning P, Rizos C (eds) Dynamic planet, IAG symposia series, vol 130. Springer, Berlin, pp 638–645Google Scholar
  76. Sánchez L (2009) Strategy to establish a global vertical reference system. In: Drewes H (ed) Geodetic reference systems, IAG symposia series, vol 134. Springer, Berlin, pp 273–278Google Scholar
  77. Sánchez L, Cunderlík R, Dayoub N, Mikula K, Minarechová Z, Šíma Z, Vatrt V, Vojtíšková M (2016) A conventional value for the geoid reference potential W0. J Geodesy. Google Scholar
  78. Sánchez L, Čunderlík R, Dayoub N, Mikula K, Minarechová K, Šíma Z, Vatrt V, Vojtíšková M (2017) A conventional value for the geoid reference potential W0. J Geodesy 90(9):815–835. Google Scholar
  79. Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149(3):768–775Google Scholar
  80. Schwarz KP, Sideris MG, Forsberg R (1990) Use of FFT methods in physical geodesy. Geophys J Int 100:485–514Google Scholar
  81. Sideris MG, Rangelova E (2012) Global height system unification by means of the GOCE Geoid. In: International jubilee conference UACEG2012, SofiaGoogle Scholar
  82. Sjöberg LE (2005) A discussion on the approximations made in the practical implementation of the remove–compute–restore technique in regional geoid modelling. J Geodesy 78:645–653Google Scholar
  83. Strang van Hees G (1990) Stokes formula using fast Fourier technique. Manuscr Geod 15:235–239Google Scholar
  84. Tapley BD, Bettadpu S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett. Google Scholar
  85. Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geodesy 82:65–82Google Scholar
  86. Thompson KR, Huang J, Véronneau M, Wright DG, Lu Y (2009) Mean surface topography of the northwest Atlantic: comparison of estimates based on satellite, terrestrial gravity, and oceanographic observations. J Geophys Res 114:C07015Google Scholar
  87. Torge W (2001) Geodesy 3, completely rev. and extended ed. de Gruyter, Berlin, New York, 2001 ISBN 3-11-017072-8Google Scholar
  88. Tsoulis D (2001) Terrain correction computations for a densely sampled DTM in the Bavarian Alps. J Geodesy 75:291–307Google Scholar
  89. Tziavos IN (1996) Comparisons of spectral techniques for geoid computations over large regions. J Geodesy 70:357–373Google Scholar
  90. Tziavos IN, Vergos GS, Mertikas SP, Daskalakis A, Grigoriadis VN, Tripolitsiotis A (2013) The contribution of local gravimetric geoid models to the calibration of satellite altimetry data and an outlook of the latest GOCE GGM performance in GAVDO. Adv Space Res 51(8):1502–1522. Google Scholar
  91. Vaníček P, Krakiwsky EJ (1986) Geodesy the concepts. Elsevier, Amsterdam. ISBN 0444877754Google Scholar
  92. Vergos GS, Grigoriadis VN, Tziavos IN, Kotsakis C (2014) Evaluation of GOCE/GRACE global geopotential models over greece with collocated GPS/levelling observations and local gravity data. In: Marti U (ed) Gravity, geoid and height systems, international association of geodesy symposia 141. Springer International Publishing, Switzerland, pp 85–92.
  93. Vergos GS, Erol B, Natsiopoulos DA, Grigoriadis VN, Işık MS, Tziavos IN (2018) Preliminary results of GOCE-based height system unification between Greece and Turkey over marine and land areas. Acta Geod Geophys 53:61–79. Google Scholar
  94. Weigelt M, Baur O, Reubelt T, Sneeuw N, Roth M (2011) Long wavelength gravity field determination from GOCE using the acceleration approach. In: Proceedings of the ‘4th international GOCE user workshop, Munich, Germany 31 March–1 April 2011 (ESA SP-696, July 2011)Google Scholar
  95. Wieczorek MA, Phillips RJ (1998) Potential anomalies on a sphere: applications to the thickness of the lunar crust. J Geophys Res 103:1715–1724Google Scholar
  96. Willberg M, Gruber T, Vergos GS (2017) Analysis of GOCE omission error and its contribution to vertical datum offsets in Greece and its Islands. In: International Association of geodesy symposia. Springer, Berlin.
  97. Woodworth PL, Hughes CW, Bingham RJ, Gruber T (2012) Towards worldwide height system unification using ocean information. J Geod Sci 2(4):302–318Google Scholar
  98. Xiaogang L, Xiaoping W (2015) Construction of Earth’s gravitational field model from CHAMP, GRACE and GOCE data. Geodesy Geodyn 6(4):292–298Google Scholar
  99. Xu P, Rummel R (1991) A quality investigation of global vertical datum connection. New Series, Number 34. Netherlands Geodetic Commission, Publications on Geodesy, DelftGoogle Scholar
  100. 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 Geodesy 83:411–417Google Scholar

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Authors and Affiliations

  • Amir Ebadi
    • 1
    Email author
  • Alireza A. Ardalan
    • 1
  • Roohollah Karimi
    • 2
  1. 1.School of Surveying and Geospatial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Geodesy and Surveying EngineeringTafresh UniversityTafreshIran

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