High-resolution geoid modeling using least squares modification of Stokes and Hotine formulas in Colorado

Mustafa Serkan Işık*, Bihter Erol, Serdar Erol, Fatıma Feyza Sakil

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22 Atıf (Scopus)


The Colorado geoid experiment was initiated and organized as a joint study by the Joint Working Group (JWG) 2.2.2 (1-cm geoid experiment) of the International Association of Geodesy (IAG) in 2017, and different institutions and research groups contributed to this study. The aim of this experiment was to clarify the repeatability of gravity potential values as International Height Reference System (IHRS) coordinates from different geoid determination approaches carried out with the same input dataset. The dataset included the terrestrial and airborne gravity observations, a digital terrain model, the XGM2016 global geopotential model and GPS/leveling data for model validations belonging to a mountainous area of approximately 550 km × 730 km in Colorado, US. The dataset was provided by National Geodetic Survey (NGS) department. In this frame, this article aims providing a discussion on Colorado geoid modeling through individual experimental results obtained by Istanbul Technical University-Gravity Research Group (ITU-GRG). This contribution mainly focused on modeling the Colorado geoid using the least squares modifications of Stokes and Hotine integral formulas with additive corrections. The computations using each formula were carried out using ITU-GRG software, including the solution variants based on terrestrial-only, airborne-only and combined gravity datasets. Then, the calculated experimental geoid models were validated using historical and recently measured profile-based GPS/leveling datasets, and they were also compared with the official solutions submitted by different institutions for the “1-cm geoid experiment” of IAG JWG 2.2.2. For all validation results, the Hotine and Stokes integral formulas yielded similar performances in terms of geoid accuracy; however, the models computed using the combined data had better accuracy than those using the terrestrial-only and airborne-only solutions. The geoid model solutions using the combined data had an accuracy of 2.69 cm for the Hotine method and 2.87 cm for the Stokes method in the test results using GPS/leveling data of the GSVS17 (Geoid Slope Validation Survey 2017) profile. Airborne data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project contributed significantly towards improving the geoid model, especially in the mountainous parts of the area.

Orijinal dilİngilizce
Makale numarası49
DergiJournal of Geodesy
Basın numarası5
Yayın durumuYayınlandı - May 2021

Bibliyografik not

Publisher Copyright:
© 2021, Springer-Verlag GmbH Germany, part of Springer Nature.


The research presented in this article constitutes a part of the first author’s PhD thesis study at the Graduate School of Istanbul Technical University. The authors would like to thank Dr. Yan Ming Wang from the National Geodetic Survey and Dr. Laura Sánchez from the Technical University of Munich for their valuable efforts in coordinating the Colorado geoid experiment of the IAG Joint Working Group 2.2.2. and preparing and documenting the summary statistics of the official solutions from the contributing research groups. The terrestrial and airborne gravity data, historical and GSVS17 GPS/leveling data, used in the study, were provided by the US National Geodetic Survey. Dr. Artu Ellmann of the Tallinn University of Technology is acknowledged for the general discussions on the Stokes and Hotine geoid modeling methods. Most of the figures presented in this paper were generated using Generic Mapping Tools (GMT) software. The valuable efforts and contributions of the editors and four anonymous reviewers during the review process for this article are highly appreciated.

FinansörlerFinansör numarası
National Geodetic Survey
Technische Universität München
Tallinna Tehnikaülikool
Istanbul Teknik Üniversitesi

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