Empirical comparison between stochastic and deterministic modifiers over the French Auvergne geoid computation test-bed

Abstract

Since 2006, several different groups have computed geoid and/or quasigeoid (quasi/geoid) models for the Auvergne test area in central France using various approaches. In this contribution, we compute and compare quasigeoid models for the Auvergne test area using Curtin University of Technology's and the Swedish Royal Institute of Technology's approaches. These approaches differ in many ways, such as their treatment of the input data, choice of type of spherical harmonic model (combined or satellite-only), form and sequence of correction terms applied, and different modified Stokes's kernels (deterministic or stochastic). We have also compared our new results with most of the previously reported studies over Auvergne in order to seek any improvements with respect to time [exceptions are when different subsets of data have been used]. All studies considered here have compared the computed quasi/geoid models with the same 75 GPS-levelling heights over Auvergne. The standard deviation for almost all of the computations (without any fitting) is of the order of 30-40 mm, so there is not yet any clear indication whether any approach is necessarily better than any other nor improving over time. We also recommend more universal standardisation on the presentation of quasi/geoid comparisons with GPS-levelling data so that results from different studies over the same areas can be compared more objectively.

Assessment of recent global geopotential models based on the Auvergne test area data

“…Also, when the study by Goyal et al [36] is examined, an up-to-date summary of the studies in the literature for French Auvergne test area of computing quasigeoid/geoid values using different methods, softwares, parametric models, and GGMs, etc is presented. If it is desired to make a brief summary of the appendix of Goyal et al [36], the std values have been obtained from the EGM2008 (n max :360) model between approximately 3.0-3.8 cm for the quasigeoid, while for the geoid these have been obtained in the range of 3.8-4.0 cm. Similarly, the std values obtained from the EGM2008 (n max :2190) model were calculated as 2.6 cm for the quasigeoid and 2.9 cm for the geoid.…”

“…Therefore, this section briefly explains the theoretical knowledge of these quantities obtained from GGMs and how they are calculated. More comprehensive and detailed information on this subject can be found in [31][32][33][34][35][36]. If it is desired to calculate the geoid undulation value of a point using GGMs, it can be computed with a two-step methodology using the point's spherical coordinates.…”

“…Firstly, the conversion from height anomaly (ζ) to geoid undulation (N) is performed with equation (1). Later, equation (1) is modified to equation (2) for making calculations faster and improving computer efficiency [31][32][33][34][35][36].…”

An experimental Indian gravimetric geoid model using Curtin University’s approach

“…There are of course other approaches, such as radial basis functions (e.g., Li 2018;Liu et al 2020), but perhaps not yet applied as widely. The application areas of the above four approaches are listed in Goyal et al (2021b).…”

Integration of satellite geodetic observations for regional geoid modeling using remove-compute-restore technique

“…From these highlighted studies, as well as the pioneering studies of Vincent and Marsh (1974) and Rapp and Rummel (1975),we find a relatively stronger argument suggesting that geoidal height determination with accuracy of 1cm necessitates the adjustment of the present classical techniques for geoid/quasigeoidal height determination, and very precise gravimetric and digital terrain model of the region. Irrespective of the numerous methods which could be used in geoid/quasi geoid determination such as gravimetric, astro-gravimetric, astrogeodetic (e.g., van et al, 2021;Abd-Elmotaal and Kühtreiber, 2021;Joseph et al, 2021),4-parameter similarity datum shift, zanletnyik Hungarian model among others, the gravimetric method with the application of the stokes solution still remains the most common and reliable system for ground gravity analysis due to its cognizance of gravity anomaly data (e.g., Abd-Elmotaal and Kühtreiber, 2021;Işık et al, 2021;Ashry et al, 2021;Erol and Erol, 2021;Goyal et al, 2021).…”