Journal of Geodesy

, Volume 90, Issue 9, pp 815–835 | Cite as

A conventional value for the geoid reference potential \(W_{0}\)

  • L. SánchezEmail author
  • R. Čunderlík
  • N. Dayoub
  • K. Mikula
  • Z. Minarechová
  • Z. Šíma
  • V. Vatrt
  • M. Vojtíšková
Original Article


\(W_{0}\) is defined as the potential value of a particular level surface of the Earth’s gravity field called the geoid. Since the most accepted definition of the geoid is understood to be the equipotential surface that coincides with the worldwide mean ocean surface, a usual approximation of \(W_{0}\) is the averaged potential value \(W_{\mathrm{S}}\) at the mean sea surface. In this way, the value of \(W_{0}\) depends not only on the Earth’s gravity field modelling, but also on the conventions defining the mean sea surface. \(W_{0}\) computations performed since 2005 demonstrate that current published estimations differ by up to \(-2.6~\hbox {m}^{2}~\hbox {s}^{-2}\) (corresponding to a level difference of about 27 cm), which could be caused by the differences in the treatment of the input data. The main objective of this study is to perform a new \(W_{0}\) estimation relying on the newest gravity field and sea surface models and applying standardised data and procedures. This also includes a detailed description of the processing procedure to ensure the reproducibility of the results. The following aspects are analysed in this paper: (1) sensitivity of the \(W_{0}\) estimation to the Earth’s gravity field model (especially omission and commission errors and time-dependent Earth’s gravity field changes); (2) sensitivity of the \(W_{0}\) estimation to the mean sea surface model (e.g., geographical coverage, time-dependent sea surface variations, accuracy of the mean sea surface heights); (3) dependence of the \(W_{0}\) empirical estimation on the tide system; and (4) weighted computation of the \(W_{0}\) value based on the input data quality. Main conclusions indicate that the satellite-only component \((n = 200)\) of a static (quasi-stationary) global gravity model is sufficient for the computation of \(W_{0}\). This model should, however, be based on a combination of, at least, satellite laser ranging (SLR), GRACE and GOCE data. The mean sea surface modelling should be based on mean sea surface heights referring to a certain epoch and derived from a standardised multi-mission cross-calibration of several satellite altimeters. We suggest that the uncertainties caused by geographically correlated errors, including shallow waters in coastal areas and sea water ice content at polar regions should be considered in the computation of \(W_{0}\) by means of a weighed adjustment using the inverse of the input data variances as a weighting factor. This weighting factor should also include the improvement provided by SLR, GRACE and GOCE to the gravity field modelling. As a reference parameter, \(W_{0}\) should be time-independent (i.e., quasi-stationary) and it should remain fixed for a long-term period (e.g., 20 years). However, it should have a clear relationship with the mean sea surface level (as this is the convention for the realisation of the geoid). According to this, a suitable recommendation is to adopt a potential value obtained for a certain epoch as the reference value \(W_{0}\) and to monitor the changes of the mean potential value at the sea surface \(W_{\mathrm{S}}\). When large differences appear between \(W_{0}\) and \(W_{\mathrm{S}}\) (e.g., \({>}\pm 2\) m\(^{2}\) s\(^{-2})\), the adopted \(W_{0}\) may be replaced by an updated (best estimate) value. In this paper, the potential value obtained for the epoch 2010.0 (62,636,853.4 m\(^{2}\) s\(^{-2})\) is recommended as the present best estimate for the \(W_{0}\) value. It differs \(-2.6~\hbox {m}^{2}~\hbox {s}^{-2}\) from the so-called IERS \(W_{0}\) value (62,636,856.0 m\(^{2}\) s\(^{-2})\), which corresponds to the best estimate available in 1998.


Global \(W_{0}\) value \(W_{0}\) best estimate Potential value of the geoid Global reference potential value Conventional \(W_{0}\) value 



The support provided by Wolfgang Bosch and Roman Savcenko at DGFI-TUM in the computation of the yearly mean sea surface models is highly appreciated. In the same way, the insightful comments and recommendations provided by the reviewers and the editors are gratefully acknowledged. The contribution of the coauthors from the Slovak University of Technology in Bratislava has been supported by the Grants APVV-0072-11 and VEGA 1/0714/15.


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Authors and Affiliations

  • L. Sánchez
    • 1
    Email author
  • R. Čunderlík
    • 2
  • N. Dayoub
    • 3
  • K. Mikula
    • 2
  • Z. Minarechová
    • 2
  • Z. Šíma
    • 4
  • V. Vatrt
    • 5
  • M. Vojtíšková
    • 6
  1. 1.Deutsches Geodätisches ForschungsinstitutTechnische Universität MünchenMunichGermany
  2. 2.Department of Mathematics and Descriptive Geometry, Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislavaSlovakia
  3. 3.Department of Topography, Faculty of Civil EngineeringTishreen UniversityLatakiaSyria
  4. 4.Astronomical Institute, Academy of SciencesPragueCzech Republic
  5. 5.Faculty of Civil EngineeringBrno University of TechnologyBrnoCzech Republic
  6. 6.Military Geographic and Hydrometeorologic OfficeDobruškaCzech Republic

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