Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area

H Yildiz,R Forsberg,C Tscherning,J Ågren,L Sjöberg

doi:10.2478/v10156-011-0024-9

Abstract

Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test areaThe remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification of Stokes' Formula (LSMS) technique not requiring gravity reductions is implemented here with a Residual Terrain Modelling based interpolation of gravity data. The 2-D Spherical Fast Fourier Transform (FFT) and the LSC methods applying the RCR technique and the LSMS method are tested over the Auvergne test area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs best with 3.0 cm r.m.s difference with GPS-levelling while the LSMS method gives the best agreement with GPS-levelling with 2.4 cm r.m.s after a 4-parameter fit is used. However, the quasi-geoid models derived using two techniques differed from each other up to 33 cm in the high mountains near the Alps. Comparison of quasi-geoid models with EGM2008 showed that the LSMS method agreed best in term of r.m.s.

Highlights

Nowadays, a major goal for physical geodesy is the determination of the geoid with an accuracy on the cm level, matching the accuracy of GPS height determination
We found that K =85 yielded a standard devitation of 3.5 cm between Least Squares Modification of Stokes' Formula (LSMS) derived quasi-geoid model and GPS-levelling using a 1-parameter fit, indicating that K =85 is realistic taking into account the error characteristics of Gravity Recovery And Climate Experiment (GRACE) (Tapley et al, 2005)
Two methods using the RCR technique (2-D Spherical Fast Fourier Transform (FFT) and Least Squares Collocation (LSC)) and the LSMS technique are numerically tested over Auvergne test region

Summary

Introduction

A major goal for physical geodesy is the determination of the geoid with an accuracy on the cm level, matching the accuracy of GPS height determination. The manuscript solely reflects the personal views of the author and does not necessarily represent the views, positions, strategies or opinions of Turkish Armed Forces has been demonstrated in numerous cases in lowland areas with dense gravity data coverage, so far no convincing case of attaining a cm-geoid in mountainous regions has been reported. This is likely a consequence of insufficient gravity data coverage, theoretical shortcomings and insufficient quality of the levelling data, used to compute "ground truth" geoid (or quasi-geoid) values.

Objectives

Methods

Conclusion