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Colorado geoid computation experiment: overview and summary

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Abstract

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km \(\times \) 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′\(\times \)1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0, 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

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Data availability

The data that support the findings of this study are publically available here: https://geodesy.noaa.gov/GEOID/research/co-cm-experiment/; https://geodesy.noaa.gov/GEOID/GSVS17/index.shtml; The airborne gravity data are available at NGS: https://www.ngs.noaa.gov/GRAV-D/data_ms05.shtml; The standardized 1′ × 1′ geoid, quasigeoid grids, input and validation data sets are available at the International Service for the Geoid (Reguzzoni et al. 2021) https://www.isgeoid.polimi.it/Projects/colorado_experiment.html

Abbreviations

AUTh:

Aristotle University of Thessaloniki, Greece

CASM:

Chinese Academy of Surveying and Mapping, China

CGS:

Canadian Geodetic Survey, Canada

Curtin:

Curtin University, Australia

DGFI:

Deutsches Geodätisches Forschungsinstitut, Technical University of Munich, Germany

DTU:

Technical University of Denmark, Denmark

Minia:

Minia University, Egypt

NGS:

US National Geodetic Survey, NOAA, USA

GSI:

Geospatial Information Authority of Japan, Japan

IAPG:

Institute for Astronomical and Physical Geodesy, Technical University of Munich, Germany

ITU:

Istanbul Technical University, Turkey

KTH:

University of Gävle, Lantmäteriet, Royal Institute of Technology, Sweden

NTIS-GEOF:

New Technologies for the Information Society, University of West Bohemia, Czech Republic & University of Zagreb, Croatia

Polimi:

Politecnico di Milano, Italy

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Acknowledgements

This study was possible thanks to a strong international cooperation coordinated within IAG, in particular, the IAG Sub-commission 2.2: Methodology for geoid and physical height systems (Ågren and Ellmann 2019); the joint working group 2.2.2: The 1-cm geoid experiment in Colorado (Wang and Forsberg, 2019); the study group 0.15: Regional geoid/quasigeoid modeling—Theoretical framework for the sub-centimeter accuracy of the IAG Inter-Commission Committee on Theory – ICCT (Huang and Wang 2019); and the working group 0.1.2: Strategy for the realization of the IHRS of the Focus Area Unified Height System of the Global Geodetic Observing System—GGOS (Sánchez, 2019; Sánchez and Barzaghi 2020). The authors are especially indebted to the National Geodetic Survey for providing the gravity, topographic and GPS/leveling data sets for this experiment. The authors thank three anonymous reviewers, the Associate Editor and Editor for their time, constructive suggestions and comments, which helped improving the initial version of this manuscript.

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Authors and Affiliations

  1. National Geodetic Survey, 1315 East-West Highway, Silver Spring, MD, 20910-3282, USA

    Yan Ming Wang, Kevin Ahlgren, Jordan Krcmaric & Xiaopeng Li

  2. Deutsches Geodätisches Forschungsinstitut, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany

    Laura Sánchez, Qing Liu & Michael Schmidt

  3. Department of Computer and Geospatial Sciences, University of Gävle, 80176, Gävle, Sweden

    Jonas Ågren

  4. Lantmäteriet, Swedish Mapping, Cadastral and Land Registration Authority, 80182, Gävle, Sweden

    Jonas Ågren

  5. KTH Royal Institute of Technology, 10044, Stockholm, Sweden

    Jonas Ågren

  6. Canadian Geodetic Survey, Surveyor General Branch, Natural Resources Canada, 588 Booth Street, Ottawa, ON, K1A 0Y7, Canada

    Jianliang Huang & Marc Véronneau

  7. Technical University of Denmark, Elektrovej, Building 327, 2800, Kgs. Lyngby, Denmark

    René Forsberg

  8. Civil Engineering Department, Faculty of Engineering, Minia University, Minia, 61111, Egypt

    Hussein A. Abd-Elmotaal

  9. Department of Civil and Environmental Engineering, Politecnico Di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy

    Riccardo Barzaghi & Daniela Carrion

  10. Faculty of Geodesy, University of Zagreb, Kačićeva 26, 10000, Zagreb, Republic of Croatia

    Tomislav Bašić

  11. School of Earth and Planetary Sciences and The Institute for Geoscience Research, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Sten Claessens & Mick Filmer

  12. Geomatics Engineering Department, Civil Engineering Faculty, Istanbul Technical University, Ayazağa Campus, 34469, Maslak/İstanbul, Turkey

    Bihter Erol, Serdar Erol, Mustafa Serkan Isik & Öykü Koç

  13. Laboratory of Gravity Field Research and Applications, Department of Geodesy and Surveying, Aristotle University of Thessaloniki, University Box 440, 54124, Thessaloniki, Greece

    Vassilios N. Grigoriadis, Dimitris A. Natsiopoulos & Georgios S. Vergos

  14. Chinese Academy of Surveying and Mapping, 28 Lianhuachi West Road, Beijing, 100830, China

    Tao Jiang

  15. Geospatial Information Authority of Japan, 1, Kitasato, Tsukuba, 305-0811, Japan

    Koji Matsuo

  16. New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Technická 8, 30614, Pilsen, Czech Republic

    Pavel Novák & Martin Pitoňák

  17. Institute of Astronomical and Physical Geodesy, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany

    Roland Pail, Martin Willberg & Philipp Zingerle

  18. Institute of Geodesy and Photogrammetry, GSEG, ETH Zürich, Stefano-Franscini-Platz 5, 8093, Zurich, Switzerland

    Matej Varga

Authors
  1. Yan Ming Wang
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Contributions

YMW, LS, JÅ, JH and RF conceptualized and coordinated the Colorado experiment, outlined the standards for the data processing, participated in the computation of the solutions NGS, DGFI, KTH, CGS and DTU and prepared the original draft. YMW, XL, KA and JK computed the solution NGS and performed the comparison/evaluation of the delivered solutions. VNG, GSV and DAN computed the solution AUTh. TJ computed the solution CASM. MVé and JH computed the solution CGS. SC and MF computed the solution Curtin. QL, MS and LS computed the solution DGFI. RF computed the solution DTU. HAAE computed the solution Minia. KM computed the solution GSI. MW, PZ and RP computed the solution IAPG. BE, MSI and SE computed the solution ITU. JÅ computed the solution KTH. MV, TB, MP and PN computed the solution NTIS-GEOF. RB, DC and ÖK computed the solution Polimi. All authors contributed to review and editing.

Corresponding author

Correspondence to Yan Ming Wang.

Appendix. Fundamental parameters, zero-degree harmonic treatment and computation requirements

Appendix. Fundamental parameters, zero-degree harmonic treatment and computation requirements

Fundamental parameters, zero-degree harmonic treatment and computation requirements.

Since a main objective of the Colorado experiment is to compare gravity functionals (i.e., geoid, quasigeoid, potential values) determined using different methodologies, it was necessary to outline a set of basic (minimum) requirements to standardize as much as possible the data processing to avoid gross discrepancies as those caused for instance using different reference ellipsoids or permanent-tide systems. In this way, in addition to the use of the same input data (described in Sect. 3), we agreed to follow the conventions summarized in Table

Table 8 Constants and conventions agreed within the Colorado experiment (cf. Sánchez et al. 2018)
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8.

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Wang, Y.M., Sánchez, L., Ågren, J. et al. Colorado geoid computation experiment: overview and summary. J Geod 95, 127 (2021). https://doi.org/10.1007/s00190-021-01567-9

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