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Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography / Matej Medl’a in Journal of geodesy, vol 92 n° 1 (January 2018)
[article]
Titre : Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography Type de document : Article/Communication Auteurs : Matej Medl’a, Auteur ; Karol Mikula, Auteur ; Robert Cunderlik, Auteur ; Marek Macák, Auteur Année de publication : 2018 Article en page(s) : pp 1 - 19 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur local
[Termes IGN] discrétisation
[Termes IGN] équation de Laplace
[Termes IGN] méthode des éléments finis
[Termes IGN] problème des valeurs limitesRésumé : (Auteur) The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model. Numéro de notice : A2018-011 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1040-z Date de publication en ligne : 30/05/2017 En ligne : https://doi.org/10.1007/s00190-017-1040-z Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89054
in Journal of geodesy > vol 92 n° 1 (January 2018) . - pp 1 - 19[article]A numerical test of the topographic bias / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)
[article]
Titre : A numerical test of the topographic bias Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur ; Mehdi S. Shafiei Joud, Auteur Année de publication : 2018 Article en page(s) : pp 14 - 17 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse numérique
[Termes IGN] anomalie de pesanteur
[Termes IGN] erreur systématiqueRésumé : (Auteur) In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre). Numéro de notice : A2018-612 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0002 Date de publication en ligne : 07/02/2018 En ligne : https://doi.org/10.1515/jogs-2018-0002 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92645
in Journal of geodetic science > vol 8 n° 1 (January 2018) . - pp 14 - 17[article]On the geoid and orthometric height vs. quasigeoid and normal height / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)
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Titre : On the geoid and orthometric height vs. quasigeoid and normal height Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur Année de publication : 2018 Article en page(s) : pp 115 - 120 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] altitude normale
[Termes IGN] altitude orthométrique
[Termes IGN] géoïde
[Termes IGN] quasi-géoïdeRésumé : (Auteur) The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling. Numéro de notice : A2018-115 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0011 Date de publication en ligne : 31/12/2018 En ligne : https://doi.org/10.1515/jogs-2018-0011 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92664
in Journal of geodetic science > vol 8 n° 1 (January 2018) . - pp 115 - 120[article]On the topographic bias and density distribution in modelling the geoid and orthometric heights / Lars E. Sjöberg in Journal of geodetic science, vol 8 n° 1 (January 2018)
[article]
Titre : On the topographic bias and density distribution in modelling the geoid and orthometric heights Type de document : Article/Communication Auteurs : Lars E. Sjöberg, Auteur Année de publication : 2018 Article en page(s) : pp 30 - 33 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] altitude orthométrique
[Termes IGN] analyse numérique
[Termes IGN] erreur systématique
[Termes IGN] géoïde
[Termes IGN] incertitude géométrique
[Termes IGN] montagneRésumé : (Auteur) It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators. Numéro de notice : A2018-614 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0004 Date de publication en ligne : 02/03/2018 En ligne : https://doi.org/10.1515/jogs-2018-0004 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92662
in Journal of geodetic science > vol 8 n° 1 (January 2018) . - pp 30 - 33[article]Hydrological excitation of polar motion by different variables from the GLDAS models / Malgorzata Winska in Journal of geodesy, vol 91 n° 12 (December 2017)
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Titre : Hydrological excitation of polar motion by different variables from the GLDAS models Type de document : Article/Communication Auteurs : Malgorzata Winska, Auteur ; Jolanta Nastula, Auteur ; David A. Salstein, Auteur Année de publication : 2017 Article en page(s) : pp 1461 - 1473 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] données GRACE
[Termes IGN] moment cinétique
[Termes IGN] mouvement du pôle
[Termes IGN] surcharge hydrologiqueMots-clés libres : Global Land Data Assimilation System model GLDAS model Résumé : (Auteur) Continental hydrological loading by land water, snow and ice is a process that is important for the full understanding of the excitation of polar motion. In this study, we compute different estimations of hydrological excitation functions of polar motion (as hydrological angular momentum, HAM) using various variables from the Global Land Data Assimilation System (GLDAS) models of the land-based hydrosphere. The main aim of this study is to show the influence of variables from different hydrological processes including evapotranspiration, runoff, snowmelt and soil moisture, on polar motion excitations at annual and short-term timescales. Hydrological excitation functions of polar motion are determined using selected variables of these GLDAS realizations. Furthermore, we use time-variable gravity field solutions from the Gravity Recovery and Climate Experiment (GRACE) to determine the hydrological mass effects on polar motion excitation. We first conduct an intercomparison of the maps of variations of regional hydrological excitation functions, timing and phase diagrams of different regional and global HAMs. Next, we estimate the hydrological signal in geodetically observed polar motion excitation as a residual by subtracting the contributions of atmospheric angular momentum and oceanic angular momentum. Finally, the hydrological excitations are compared with those hydrological signals determined from residuals of the observed polar motion excitation series. The results will help us understand the relative importance of polar motion excitation within the individual hydrological processes, based on hydrological modeling. This method will allow us to estimate how well the polar motion excitation budget in the seasonal and inter-annual spectral ranges can be closed. Numéro de notice : A2017-708 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1036-8 En ligne : https://doi.org/10.1007/s00190-017-1036-8 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=88089
in Journal of geodesy > vol 91 n° 12 (December 2017) . - pp 1461 - 1473[article]MICROSCOPE mission: First results of a space test of the equivalence principle / Pierre Touboul in Physical Review Letters, vol 119 n° 3 (December 2017)PermalinkNew adjustment of the Croatian first order gravity network / Marija Repanic in Geodetski vestnik, vol 61 n° 4 (December 2017 - February 2018)PermalinkOn the estimation of physical height changes using GRACE satellite mission data – A case study of Central Europe / Walyeldeen Godah in Geodesy and cartography, vol 66 n° 2 (December 2017)PermalinkBasic Earth's Parameters as estimated from VLBI observations / Ping Zhu in Geodesy and Geodynamics, vol 8 n° 6 (November 2017)PermalinkIGS polar motion measurement accuracy / Jim Ray in Geodesy and Geodynamics, vol 8 n° 6 (November 2017)PermalinkOn the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation / Vegard Ophaug in Journal of geodesy, vol 91 n° 11 (November 2017)PermalinkSeasonal low-degree changes in terrestrial water mass load from global GNSS measurements / Thierry Meyrath in Journal of geodesy, vol 91 n° 11 (November 2017)PermalinkExperiences with the QDaedalus system for astrogeodetic determination of deflections of the vertical / Markus Hauk in Survey review, vol 49 n° 355 (October 2017)PermalinkHydrologically-driven crustal stresses and seismicity in the New Madrid seismic zone / Timothy J. Craig in Nature communications, vol 8 (2017)PermalinkMobile precise trigonometric levelling system based on land vehicle: an alternative method for precise levelling / J. Zou in Survey review, vol 49 n° 355 (October 2017)Permalink