Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach

Janák, Juraj; Vaníček, Petr; Foroughi, Ismael; Kingdon, Robert; Sheng, Michael; Santos, Marcelo C.

doi:10.1515/congeo-2017-0011

Cited by 17 publications

(8 citation statements)

References 24 publications

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“…As one can see, a correction for lateral topographical density variations was not included in the computation because a density model was not available at the time of the computation. Also, the Hörmander effect has not been included, but is very small compared to our expected final centimetric accuracy (see Janák et al (2017)). Fig.…”

Section: Resultsmentioning

confidence: 92%

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A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Garbanzo-León

Fernández

Sánchez

et al. 2020

Contrib. Geophys. Geod.

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GNSS observations are a common solution for outdoor positioning around the world for coarse and precise applications. However, GNSS produces geodetic heights, which are not physically meaningful, limiting their functionality in many engineering applications. In Costa Rica, there is no regional model of the geoid, so geodetic heights (h) cannot be converted to physically meaningful orthometric heights (H). This paper describes the computation of a geoid model using the Stokes-Helmert approach developed by the University of New Brunswick. We combined available land, marine and satellite gravity data to accurately represent Earth's high frequency gravity field over Costa Rica. We chose the GOCO05s satellite-only global geopotential model as a reference field for our computation. With this combination of input data, we computed the 2020 Regional Stokes-Helmert Costa Rican Geoid (GCR-RSH-2020). To validate this model, we compared it with 4 global combined geopotential models (GCGM): EGM2008, Eigen6C-4, GECO and SGG-UM-1 finding an average difference of 5 cm. GECO and SGG-UM-1 are more similar to the GCR-RSH-2020 based on the statistics of the difference between models and the shape of the histogram of differences. The computed geoid also showed a shift of 7 cm when compared to the old Costa Rican height system but presented a slightly better fit with that system than the other models when looking at the residuals. In conclusion, GCR-RSH-2020 presents a consistent behaviour with the global models and the Costa Rican height systems. Also, the lowest variance suggests a more accurate determination when the bias is removed.

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Section: Resultsmentioning

confidence: 92%

“…In addition to the main steps described so far in this document, a geoid computation involves numerous small details, which can lead to an incorrect result if neglected (see Janák et al (2017)). Thus, to perform the computation, the researcher must thoroughly study the technique.…”

Section: The Process Of Geoid Computationmentioning

confidence: 99%

A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Garbanzo-León

Fernández

Sánchez

et al. 2020

Contrib. Geophys. Geod.

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“…These debates, while important, are not closely related to our thesis, so we will not refute them in detail. However, we do take issue with Popadyev reiterating the historical arguments for the Molodensky system while he, and any reviewers of his paper, have ignored the massive body of work showing that they are no longer valid (Vaníček and Martinec 1994;Martinec and Vaníček 1994;Vaníček et al 1999;Huang et al 2001;Janák and Vaníček 2001;Tenzer et al 2003;Tenzer and Vaníček 2003;Tenzer et al 2005;Kingdon et al 2005;Santos et al 2006;Cheraghi et al 2007;Kingdon et al 2012;Foroughi and Tenzer 2017;Foroughi et al 2017a, b;Janák et al 2017;Goli et al 2018;Foroughi 2018;Foroughi et al 2019;Sheng et al 2019;Vaníček and Santos 2019;Goli et al 2019a, b)-the references indicated come mostly from geodesists who follow the "University of New Brunswick's (UNB) line of thought" (as this is a rebuttal paper) but it is by no means complete, as many other colleagues dedicated to the classical theory validate our assumptions. Among other things, this substantial list of references shows that several quantities Popadyev claims are "unknown" or "unknowable" can be determined with sufficient accuracy.…”

Section: Auxiliary Argumentsmentioning

confidence: 97%

Assessing Molodensky’s Heights: A Rebuttal

Kingdon¹,

Vaníček²,

Santos³

et al. 2022

International Association of Geodesy Symposia

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This paper is written as a progression of the ongoing discussion in geodesy about the merits of the Molodensky height system versus the classical height system. It is a rebuttal of a publication in the Proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy by Victor Popadyev titled “On the Advantage of Normal Heights: Once More on the Shape of Quasigeoid.” Even though Popadyev’s paper was not presented at the symposium it was published in the proceedings regardless. It purports to address a presentation from the symposium titled “The shape of the quasigeoid”, that applied a set of criteria to judge the suitability of the quasigeoid as a vertical reference surface, ultimately finding it inferior due to its edges and folds. The proceedings paper acknowledges these irregularities in the quasigeoid, but instead argues that the Molodensky system, apart from any vertical reference surface, should be evaluated on two different and more favorable criteria, and finds it superior on that basis. Herein, we continue the ongoing discussion by clarifying some of the misunderstandings in the Popadyev paper and explaining that even on the favourable criteria proposed the Molodensky system holds no advantages over the classical system.

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“…Nowadays, the external accuracy of regional geoid models (e.g., by comparison with geometrical geoid heights, determined at sites observed by both Global Navigation Satellite Systems (GNSS) and spirit leveling) is typically on the level of a few centimeters (e.g., Denker 2013; Szelachowska and Kryński 2014;Bucha et al 2016;Ågren et al 2016;Gerlach and Ophaug 2017;Janák et al 2017), with a few sub-cm exceptions (e.g., Ellmann et al 2019;Foroughi et al 2019;Slobbe et al 2019). On this level, however, it is not a trivial task to differentiate between the errors from each contributing element (geoid, GNSS, leveling).…”

Section: Introductionmentioning

confidence: 99%

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula

Ophaug

Gerlach

2020

J Geod

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Current International Association of Geodesy efforts within regional geoid determination include the comparison of different computation methods in the quest for the “1-cm geoid.” Internal (formal) and external (empirical) approaches to evaluate geoid errors exist, and ideally they should agree. Spherical radial base functions using the spline kernel (SK), least-squares collocation (LSC), and Stokes’s formula are three commonly used methods for regional geoid computation. The three methods have been shown to be theoretically equivalent, as well as to numerically agree on the millimeter level in a closed-loop environment using synthetic noise-free data (Ophaug and Gerlach in J Geod 91:1367–1382, 2017. 10.1007/s00190-017-1030-1). This companion paper extends the closed-loop method comparison using synthetic data, in that we investigate and compare the formal error propagation using the three methods. We use synthetic uncorrelated and correlated noise regimes, both on the 1-mGal ($$=10^{-5}~{\mathrm {m s}}^{-2}$$ = 10 - 5 m s - 2 ) level, applied to the input data. The estimated formal errors are validated by comparison with empirical errors, as determined from differences of the noisy geoid solutions to the noise-free solutions. We find that the error propagations of the methods are realistic in both uncorrelated and correlated noise regimes, albeit only when subjected to careful tuning, such as spectral band limitation and signal covariance adaptation. For the SKs, different implementations of the L-curve and generalized cross-validation methods did not provide an optimal regularization parameter. Although the obtained values led to a stabilized numerical system, this was not necessarily equivalent to obtaining the best solution. Using a regularization parameter governed by the agreement between formal and empirical error fields provided a solution of similar quality to the other methods. The errors in the uncorrelated regime are on the level of $$\sim $$ ∼ 5 mm and the method agreement within 1 mm, while the errors in the correlated regime are on the level of $$\sim $$ ∼ 10 mm, and the method agreement within 5 mm. Stokes’s formula generally gives the smallest error, closely followed by LSC and the SKs. To this effect, we note that error estimates from integration and estimation techniques must be interpreted differently, because the latter also take the signal characteristics into account. The high level of agreement gives us confidence in the applicability and comparability of formal errors resulting from the three methods. Finally, we present the error characteristics of geoid height differences derived from the three methods and discuss them qualitatively in relation to GNSS leveling. If applied to real data, this would permit identification of spatial scales for which height information is preferably derived by spirit leveling or GNSS leveling.

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Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach

Cited by 17 publications

References 24 publications

A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation

Assessing Molodensky’s Heights: A Rebuttal

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula

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