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On study of the Earth topography correction for the GRACE surface mass estimation / Fan Yang in Journal of geodesy, vol 96 n° 12 (December 2022)  

Public [article]  inJournal of geodesy > vol 96 n° 12 (December 2022) . - n° 95 Titre : On study of the Earth topography correction for the GRACE surface mass estimation Type de document : Article/Communication Auteurs : Fan Yang, Auteur ; Zhicai Luo, Auteur ; Hao Zhou, Auteur ; et al., Auteur Année de publication : 2022 Article en page(s) : n° 95 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] données GRACE [Termes IGN] formule de Stokes [Termes IGN] géoïde gravimétrique [Termes IGN] itération [Termes IGN] masse de la Terre [Termes IGN] topographie Résumé : (auteur) Traditional conversion from gravity Stokes coefficients into the surface mass, e.g., in the GRACE(-FO) applications, presumes the Earth as a perfect sphere that is apparently against the reality. Recent studies manage to correct the conversion by considering the Earth’s oblateness, in another word, the Earth is treated as an ellipsoid. However, the Earth’s geometry is far more complicated due to the topography, so that neither a sphere nor an ellipsoid is exact. Evidences from recent studies and this one demonstrate that any geometrical approximation of the Earth shape like a presumed sphere will inevitably lead to a bias in the surface mass estimation from GRACE gravity fields, resulting in a possible misinterpretation of geophysical signals that may occur in polar regions or mountain areas. In this context, we propose an iterative scaling factor method to numerically realize a more accurate surface mass estimate, considering a more realistic geometry of the Earth including its oblateness, topography and geoid undulation. Verified with a series of simulations, the proposed method is found to be efficient (less than four iterations), reliable (after a broad range of tests) and universally accurate (reducing at least 80% of the bias). Relative to our method, the mean linear trend in 2002–2015 estimated from GRACE under an ideal spherical Earth is found to be underestimated by about 3.1% and 5.5% over Greenland and West Antarctica, respectively. Among the trend underestimation, the topography-related contribution takes up − 0.5% (0.79 Gt/yr, the negative sign denotes an overestimation) and − 0.4% (0.34 Gt/yr), respectively. Although the value is small, it is a systematic bias worth considering, for example, it is greater than the influence (0.3 Gt/yr on the trend estimation over West Antarctica) by switching atmospherical de-aliasing products from RL05 to RL06. Besides, the topography-induced bias rapidly increases to 2.7% (0.26 mm/yr) at mountain Himalayas, which is even larger than the ellipsoid-induced bias (0.19 mm/yr). Based on the results obtained so far, the topography-induced bias is found to be roughly one order of magnitude smaller than GRACE’s present measurement error; nevertheless, it will be relevant once the GRACE is improved toward its baseline accuracy. In particular, the topography correction should be considered for NGGM that expects to map the Earth gravity field in an unprecedented accuracy and spatial resolution. Numéro de notice : A2022-878 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1007/s00190-022-01683-0 Date de publication en ligne : 02/12/2022 En ligne : https://doi.org/10.1007/s00190-022-01683-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=102189 [article]

Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula / Vegard Ophaug in Journal of geodesy, vol 94 n° 12 (December 2020)  

Public [article]  inJournal of geodesy > vol 94 n° 12 (December 2020) . - n° 120 Titre : Error propagation in regional geoid computation using spherical splines, least-squares collocation, and Stokes’s formula Type de document : Article/Communication Auteurs : Vegard Ophaug, Auteur ; Christian Gerlach, Auteur Année de publication : 2020 Article en page(s) : n° 120 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] altitude [Termes IGN] collocation par moindres carrés [Termes IGN] covariance [Termes IGN] erreur [Termes IGN] fonction spline [Termes IGN] formule de Stokes [Termes IGN] géoïde local [Termes IGN] propagation d'erreur Résumé : (auteur) 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. https://doi.org/10.1007/s00190-017-1030-1PANIST). 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 ms−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 ∼5 mm and the method agreement within 1 mm, while the errors in the correlated regime are on the level of ∼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. Numéro de notice : A2020-784 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-020-01443-y Date de publication en ligne : 27/11/2020 En ligne : https://doi.org/10.1007/s00190-020-01443-y Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=96528 [article]

Regional geoid computation by least squares modified Hotine’s formula with additive corrections / Silja Märdla in Journal of geodesy, vol 92 n° 3 (March 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 3 (March 2018) . - pp 253 - 270 Titre : Regional geoid computation by least squares modified Hotine’s formula with additive corrections Type de document : Article/Communication Auteurs : Silja Märdla, Auteur ; Artu Ellmann, Auteur ; Jonas Ågren, Auteur ; Lard Erik Sjöberg, Auteur Année de publication : 2018 Article en page(s) : pp 253 - 270 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] anomalie de pesanteur [Termes IGN] formule de Stokes [Termes IGN] géoïde local [Termes IGN] méthode des moindres carrés [Termes IGN] quasi-géoïde Résumé : (Auteur) Geoid and quasigeoid modelling from gravity anomalies by the method of least squares modification of Stokes’s formula with additive corrections is adapted for the usage with gravity disturbances and Hotine’s formula. The biased, unbiased and optimum versions of least squares modification are considered. Equations are presented for the four additive corrections that account for the combined (direct plus indirect) effect of downward continuation (DWC), topographic, atmospheric and ellipsoidal corrections in geoid or quasigeoid modelling. The geoid or quasigeoid modelling scheme by the least squares modified Hotine formula is numerically verified, analysed and compared to the Stokes counterpart in a heterogeneous study area. The resulting geoid models and the additive corrections computed both for use with Stokes’s or Hotine’s formula differ most in high topography areas. Over the study area (reaching almost 2 km in altitude), the approximate geoid models (before the additive corrections) differ by 7 mm on average with a 3 mm standard deviation (SD) and a maximum of 1.3 cm. The additive corrections, out of which only the DWC correction has a numerically significant difference, improve the agreement between respective geoid or quasigeoid models to an average difference of 5 mm with a 1 mm SD and a maximum of 8 mm. Numéro de notice : A2018-060 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1061-7 Date de publication en ligne : 11/09/2017 En ligne : https://doi.org/10.1007/s00190-017-1061-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89393 [article]

On 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)  

Public [article]  inJournal of geodesy > vol 91 n° 11 (November 2017) . - pp 1367 - 1382 Titre : On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation Type de document : Article/Communication Auteurs : Vegard Ophaug, Auteur ; Christian Gerlach, Auteur Année de publication : 2017 Article en page(s) : pp 1367 - 1382 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse comparative [Termes IGN] collocation par moindres carrés [Termes IGN] fonction de base radiale [Termes IGN] fonction spline [Termes IGN] formule de Stokes [Termes IGN] géoïde local [Termes IGN] précision millimétrique Résumé : (Auteur) This work is an investigation of three methods for regional geoid computation: Stokes’s formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223–232, 1995. doi:10.1007/BF00806734) that the equivalence of Stokes’s formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes’s formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level. Numéro de notice : A2017-707 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1030-1 En ligne : https://doi.org/10.1007/s00190-017-1030-1 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=88088 [article]

Calcul du quasi-géoïde QGF16 et de la grille de conversion altimétrique RAF16 : état d'avancement et perspectives / François L'écu in XYZ, n° 150 (mars - mai 2017) 

Public [article]  inXYZ > n° 150 (mars - mai 2017) . - pp 49 - 51 Titre : Calcul du quasi-géoïde QGF16 et de la grille de conversion altimétrique RAF16 : état d'avancement et perspectives Type de document : Article/Communication Auteurs : François L'écu, Auteur Année de publication : 2017 Article en page(s) : pp 49 - 51 Langues : Français (fre) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] conversion altimétrique [Termes IGN] formule de Stokes [Termes IGN] levé gravimétrique [Termes IGN] point GNSS nivelé [Termes IGN] précision centimétrique [Termes IGN] Quasi-Géoïde Français 2016 [Termes IGN] Référence d'Altitudes Françaises 2016 Résumé : (Auteur) Le nouveau quasi-géoïde gravimétrique QGF16 est en phase finale de calcul et de test au SGN (Service de la Géodésie et du Nivellement à l'Institut national de l'information géographique et forestière). Il a été obtenu par utilisation de la méthode de Stokes, avec rayon d'intégration de 2° et retrait-restauration du terrain résiduel. Son évaluation par rapport aux points GNSS nivelés issus du programme ERNIT (Entretien du réseau de nivellement par les triplets) conduit à une précision de 5 cm, alors que les différents modèles globaux de champ ne permettent pas d'atteindre mieux que 12 cm. On démontre donc une fois de plus l'intérêt des modèles locaux par rapport aux modèles mondiaux. La grille de conversion altimétrique associée RAF16 est également en cours de dernière mise au point. Elle devrait permettre l'accès à la référence verticale NGF-IGN69 avec une précision voisine du centimètre. Numéro de notice : A2017-095 Affiliation des auteurs : IGN (2012-2019) Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueNat DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=84433 [article]

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Documents numériques

en open access Calcul du quasi-géoïde - pdf éditeur Adobe Acrobat PDF

Auvergne dataset: Testing several geoid computation methods / Pierre Valty (2012)  

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Détermination du géoïde gravimétrique au nord de l'Algérie : méthodes de Stokes-Helmert / N. Zekkour in Bulletin des sciences géographiques, n° 24 (Septembre 2009)

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The topographic bias by analytical continuation in physical geodesy / Lard Erik Sjöberg in Journal of geodesy, vol 81 n° 5 (May 2007)  

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The ellipsoidal correction to the Stokes kernel for precise geoid determination / M. Najafi-Alamdari in Journal of geodesy, vol 80 n° 12 (December 2006)  

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The effects of Stokes's formula for an ellipsoidal layering of the Earth's atmosphere / Lard Erik Sjöberg in Journal of geodesy, vol 79 n° 12 (March 2006)  

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A strategy for determining the regional geoid by combining limited ground data with satellite-based global geopotential and topographical models: a case study of Iran / R. Kiamehr in Journal of geodesy, vol 79 n° 10-11 (February 2006)  

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Gravimétrie, géoïde et nivellement par GPS en Belgique / Henri Duquenne in XYZ, n° 105 (décembre 2005 - février 2006)

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MIRAS reference radiometer: a fully polarimetric noise injection radiometer / A. Colliander in IEEE Transactions on geoscience and remote sensing, vol 43 n° 5 (May 2005)  

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The effect on the geoid of lateral topographic density variations / Lard Erik Sjöberg in Journal of geodesy, vol 78 n° 1-2 (September 2004)  

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Two-step procedures for hybrid geoid modelling / Lard Erik Sjöberg in Journal of geodesy, vol 78 n° 1-2 (September 2004)  

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