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A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model / R. Klees in Journal of geodesy, vol 92 n° 4 (April 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 4 (April 2018) . - pp 431 - 442 Titre : A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model Type de document : Article/Communication Auteurs : R. Klees, Auteur ; D.C. Slobbe, Auteur ; Hassan Hashemi Farahani, Auteur Année de publication : 2018 Article en page(s) : pp 431 - 442 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] fonction de base radiale [Termes descripteurs IGN] matrice de covariance [Termes descripteurs IGN] méthode des moindres carrés [Termes descripteurs IGN] modèle de géopotentiel [Termes descripteurs IGN] quasi-géoïde [Termes descripteurs IGN] résidu Résumé : (Auteur) The paper is about a methodology to combine a noisy satellite-only global gravity field model (GGM) with other noisy datasets to estimate a local quasi-geoid model using weighted least-squares techniques. In this way, we attempt to improve the quality of the estimated quasi-geoid model and to complement it with a full noise covariance matrix for quality control and further data processing. The methodology goes beyond the classical remove–compute–restore approach, which does not account for the noise in the satellite-only GGM. We suggest and analyse three different approaches of data combination. Two of them are based on a local single-scale spherical radial basis function (SRBF) model of the disturbing potential, and one is based on a two-scale SRBF model. Using numerical experiments, we show that a single-scale SRBF model does not fully exploit the information in the satellite-only GGM. We explain this by a lack of flexibility of a single-scale SRBF model to deal with datasets of significantly different bandwidths. The two-scale SRBF model performs well in this respect, provided that the model coefficients representing the two scales are estimated separately. The corresponding methodology is developed in this paper. Using the statistics of the least-squares residuals and the statistics of the errors in the estimated two-scale quasi-geoid model, we demonstrate that the developed methodology provides a two-scale quasi-geoid model, which exploits the information in all datasets. Numéro de notice : A2018-063 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1076-0 En ligne : https://doi.org/10.1007/s00190-017-1076-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89399 [article]

The impact of the dynamic sea surface topography on the quasi-geoid in shallow coastal waters / D.C. Slobbe in Journal of geodesy, vol 88 n° 3 (March 2014)  

Public [article]  inJournal of geodesy > vol 88 n° 3 (March 2014) . - pp 241 - 261 Titre : The impact of the dynamic sea surface topography on the quasi-geoid in shallow coastal waters Type de document : Article/Communication Auteurs : D.C. Slobbe, Auteur ; R. Klees, Auteur Année de publication : 2014 Article en page(s) : pp 241 - 261 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] levé gravimétrique [Termes descripteurs IGN] marée océanique [Termes descripteurs IGN] Nord, mer du [Termes descripteurs IGN] quasi-géoïde [Termes descripteurs IGN] surface de la mer [Termes descripteurs IGN] topographie Résumé : (Auteur) In this study, we examine the impact of instantaneous dynamic sea surface topography (DT) corrections to be applied to altimeter-derived sea surface slopes on the quasi-geoid in the shallow and coastal waters of the North Sea. In particular, we investigate the added value of DT corrections obtained from a shallow-water hydrodynamic model. These corrections comprise the contributions of ocean tides, wind- and pressure-driven (surge), and density-driven (baroclinic) water-level variations including the interactions between them. As a reference, we used tidal corrections derived from the global ocean tide model GOT4.7, surge corrections derived from the MOG2D model, and corrections for the time-averaged baroclinic contribution computed as differences between the DTU10 mean sea surface model and the EGG08 quasi-geoid. From a spectral analysis, we found that the baroclinic and surge parts of the DT mainly contribute to improvements in the signal-to-noise ratio (SNR) at longer wavelengths down to 100200 km and that the improvements increase towards the southern North Sea. We also found that the shallow-water hydrodynamic model provides better tidal corrections compared to the GOT4.7 global ocean tide model, which are most pronounced in the southern North Sea and affect almost the entire spectrum. Very small differences (mostly below +2 cm ) are observed between the quasi-geoid solutions obtained using the different sets of DT corrections. We showed that the variance component estimation provides too optimistic variance factors for the shipboard data set relative to the altimeter-derived quasi-geoid slopes. Hence, the limited impact of DT corrections is due to the fact that altimeter-derived quasi-geoid slopes hardly contribute to the estimated quasi-geoid if shipboard gravity data are included. When computing quasi-geoid solutions without shipboard gravity data, we found that less accurate or incomplete DT corrections may cause errors in the quasi-geoid with systematic spatial patterns. These systematic patterns disappear or are reduced significantly when using the DT corrections provided by the shallow-water hydrodynamic model. The main contributor to this improvement is the better tidal correction provided by the shallow-water hydrodynamic model compared to the GOT4.7 global ocean tide model. Seen the improvements of the global ocean tide models over the last two decades, we expect that in the near future global ocean tide models perform as well as dedicated regional models such as DCSM. Critical issue is, however, access to high-quality local bathymetric data. Numéro de notice : A2014-134 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0679-3 date de publication en ligne : 18/12/2013 En ligne : https://doi.org/10.1007/s00190-013-0679-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=33039 [article]

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The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value / Hassan Hashemi Farahani in Journal of geodesy, vol 87 n° 9 (September 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 9 (September 2013) . - pp 843 - 867 Titre : The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value Type de document : Article/Communication Auteurs : Hassan Hashemi Farahani, Auteur ; Pavel Ditmar, Auteur ; R. Klees, Auteur Année de publication : 2013 Article en page(s) : pp 843 - 867 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] champ de pesanteur terrestre [Termes descripteurs IGN] données GOCE [Termes descripteurs IGN] données GRACE [Termes descripteurs IGN] gradiométrie [Termes descripteurs IGN] modèle de géopotentiel Résumé : (Auteur) We present a global static model of the Earth’s gravity field entitled DGM-1S based on GRACE and GOCE data. The collection of used data sets includes nearly 7 years of GRACE KBR data and 10 months of GOCE gravity gradient data. The KBR data are transformed with a 3-point differentiation into quantities that are approximately inter-satellite accelerations. Gravity gradients are processed in the instrumental frame. Noise is handled with a frequency-dependent data weighting. DGM-1S is complete to spherical harmonic degree 250 with a Kaula regularization being applied above degree 179. Its performance is compared with a number of other satellite-only GRACE/GOCE models by confronting them with (i) an independent model of the oceanic mean dynamic topography, and (ii) independent KBR and gravity gradient data. The tests reveal a competitive quality for DGM-1S. Importantly, we study added value of GOCE data by comparing the performance of satellite-only GRACE/GOCE models with models produced without GOCE data: either ITG-Grace2010s or EGM2008 depending on which of the two performs better in a given region. The test executed based on independent gravity gradients quantifies this added value as 25–38 % in the continental areas poorly covered with terrestrial gravimetry data (Equatorial Africa, Himalayas, and South America), 7–17 % in those with a good coverage with these data (Australia, North America, and North Eurasia), and 14 % in the oceans. This added value is shown to be almost entirely related to coefficients below degree 200. It is shown that this gain must be entirely attributed to gravity gradients acquired by the mission. The test executed based on an independent model of the mean dynamic topography suggests that problems still seem to exist in satellite-only GRACE/GOCE models over the Pacific ocean, where noticeable deviations between these models and EGM2008 are detected, too. Numéro de notice : A2013-565 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0650-3 date de publication en ligne : 12/07/2013 En ligne : https://doi.org/10.1007/s00190-013-0650-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32701 [article]

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Lowest astronomical tide in the North Sea derived from a vertically referenced shallow water model, and an assessment of its suggested sense of safety / D. Slobbe in Marine geodesy, vol 36 n° 1 (January - March 2013)  

Public [article]  inMarine geodesy > vol 36 n° 1 (January - March 2013) . - pp 31 - 71 Titre : Lowest astronomical tide in the North Sea derived from a vertically referenced shallow water model, and an assessment of its suggested sense of safety Type de document : Article/Communication Auteurs : D. Slobbe, Auteur ; R. Klees, Auteur ; M. Verlaan, Auteur ; et al., Auteur Année de publication : 2013 Article en page(s) : pp 31 - 71 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Océanographie [Termes descripteurs IGN] géoïde local [Termes descripteurs IGN] geoïde marin [Termes descripteurs IGN] marée océanique [Termes descripteurs IGN] niveau de la mer [Termes descripteurs IGN] niveau moyen des mers [Termes descripteurs IGN] Nord, mer du [Termes descripteurs IGN] réduction Résumé : (Auteur) Water level reduction with global navigation satellite systems in bathymetric surveying requires knowledge of the ellipsoidal heights of lowest astronomical tide (LAT). The traditional approach uses tidal water levels of an ocean tide model, which are subtracted from mean sea level (MSL). This approach has two major drawbacks: the modeled water levels refer to an equipotential surface, which differs from MSL, and MSL may not be known close to the coast. Here, we propose to model LAT directly relative to an equipotential surface (geoid). This is conceptually consistent with the flow equations and allows the inclusion of temporal MSL variations into the LAT definition. Numerical experiments for the North Sea show that significant differences between the traditional and the pursued approach exist if average monthly variations in MSL are included. A validation of the modeled LAT using tide gauge records reveals systematic errors, which we attribute to both the model and the tidal analysis procedure. We also show that the probability that water levels drop below LAT is high, with maximum frequency of once per week in the eastern North Sea. Therefore, we propose to reconsider the deterministic concept of LAT by a probabilistic chart datum concept, and we quantified the differences between them. Numéro de notice : A2013-245 Thématique : POSITIONNEMENT Nature : Article DOI : 10.1080/01490419.2012.743493 date de publication en ligne : 13/03/2013 En ligne : https://doi.org/10.1080/01490419.2012.743493 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32383 [article]

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The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid / D. Slobbe in Journal of geodesy, vol 86 n° 8 (August 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 8 (August 2012) . - pp 609 - 628 Titre : The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid Type de document : Article/Communication Auteurs : D. Slobbe, Auteur ; F. Simons, Auteur ; R. Klees, Auteur Année de publication : 2012 Article en page(s) : pp 609 - 628 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes descripteurs IGN] algorithme de Gram-Schmidt [Termes descripteurs IGN] cohérence spectrale [Termes descripteurs IGN] filtre passe-bas [Termes descripteurs IGN] fonction de Slepian [Termes descripteurs IGN] fonction orthogonale [Termes descripteurs IGN] géoïde gravimétrique [Termes descripteurs IGN] niveau moyen des mers Résumé : (Auteur) The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the continents. In this paper, we consider the use of a bandlimited, spatially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian functions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experiments, we conclude that none of these methods provide a low-resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low-resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram–Schmidt orthogonalization for spherical harmonics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the instabilities but destroys the orthogonality and, therefore, provides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, perhaps by finding a different orthogonal basis that avoids it altogether. Numéro de notice : A2012-375 Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0543-x date de publication en ligne : 20/03/2012 En ligne : https://doi.org/10.1007/s00190-012-0543-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31821 [article]

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The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise / R. Klees in Journal of geodesy, vol 84 n° 12 (December 2010)  

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vol 83 n° 3-4 - March - April 2009 - The International GNSS Service (IGS) in a changing landscape of Global Navigation Satellite Systems (Bulletin de Journal of geodesy) / R. Klees  

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A data-driven approach to local gravity field modelling using spherical radial basis functions / R. Klees in Journal of geodesy, vol 82 n° 8 (August 2008)

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On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies / I. Prutkin in Journal of geodesy, vol 82 n° 3 (March 2008)

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Deos progress letter / R. Klees (1998)

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Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode / R. Klees (1992)

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Untersuchungen verschiedener Höhensysteme, dargestellt an einer Testschleife in Rheinland-Pfalz / M. Leismann (1992)

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