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Reducing errors in the GRACE gravity solutions using regularization / H. Save in Journal of geodesy, vol 86 n° 9 (September 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 9 (September 2012) . - pp 695 - 711 Titre : Reducing errors in the GRACE gravity solutions using regularization Type de document : Article/Communication Auteurs : H. Save, Auteur ; S. Bettadpur, Auteur ; B. Tapley, Auteur Année de publication : 2012 Article en page(s) : pp 695 - 711 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] données GRACE [Termes IGN] gravimétrie [Termes IGN] harmonique sphérique [Termes IGN] levé gravimétrique [Termes IGN] régularisation de Tychonoff Résumé : (Auteur) The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE. Numéro de notice : A2012-467 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0548-5 Date de publication en ligne : 10/03/2012 En ligne : https://doi.org/10.1007/s00190-012-0548-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31913 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-2012091	RAB	Revue	Centre de documentation	En réserve L003	Disponible

On computing ellipsoidal harmonics using Jekeli’s renormalization / J. Sebera in Journal of geodesy, vol 86 n° 9 (September 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 9 (September 2012) . - pp 713 - 726 Titre : On computing ellipsoidal harmonics using Jekeli’s renormalization Type de document : Article/Communication Auteurs : J. Sebera, Auteur ; Johannes Bouman, Auteur ; W. Bosch, Auteur Année de publication : 2012 Article en page(s) : pp 713 - 726 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] Earth Gravity Model 2008 [Termes IGN] fonction hypergéométrique [Termes IGN] harmonique ellipsoïdale [Termes IGN] potentiel de pesanteur terrestre [Termes IGN] transformation de Legendre Résumé : (Auteur) Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli’s renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions—as well as that of their ratio—up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli’s renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an input, the high resolution global gravity field model EGM2008 was used. The relative agreement we found between the results of ellipsoidal and spherical syntheses is 10-14, 10-12 and 10-8 for the potential and its first and second derivatives, respectively. Using the original renormalization, this agreement is 10-12, 10-8 and 10-5, respectively. In addition, our optimized recurrences require less computation time as the number of required terms for the hypergeometric functions is less. Numéro de notice : A2012-468 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0549-4 Date de publication en ligne : 07/03/2012 En ligne : https://doi.org/10.1007/s00190-012-0549-4 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31914 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-2012091	RAB	Revue	Centre de documentation	En réserve L003	Disponible