Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis

The time evolution of geophysical phenomena can be characterised by stochastic time series. The stochastic nature of the signal stems from the geophysical phenomena involved and any noise, which may be due to, e.g., un-modelled effects or measurement errors. Until the 1990's, it was usually assumed that white noise could fully characterise this noise. However, this was demonstrated to be not the case and it was proven that this assumption leads to underestimated uncertainties of the geophysical parameters inferred from the geodetic time series. Therefore, in order to fully quantify all the uncertainties as robustly as possible, it is imperative to estimate not only the deterministic but also the stochastic parameters of the time series. In this regard, the Markov Chain Monte Carlo (MCMC) method can provide a sample of the distribution function of all parameters, including those regarding the noise, e.g., spectral index and amplitudes. After presenting the MCMC method and its implementation in our MCMC software we apply it to synthetic and real time series and perform a cross-evaluation using Maximum Likelihood Estimation (MLE) as implemented in the CATS software. Several examples as to how the MCMC method performs as a parameter estimation method for geodetic time series are given in this chapter. These include the applications to GPS position time series, superconducting gravity time series and monthly mean sea level (MSL) records, which all show very different stochastic properties. The impact of the estimated parameter uncertainties on sub-sequentially derived products is briefly demonstrated for the case of plate motion models. Finally, the MCMC results for weekly downsampled versions of the benchmark synthetic GNSS time series as provided in Chapter 2 are presented separately in an appendix

Méthodologies en traitement de données GPS pour les Sciences de l’Environnement : Contributions à l’étude de la Mousson en Afrique de l’Ouest

Global Positioning System (GPS) is now very useful for meteorology and environmental sciences. This thesis focuses on the study of the water cycle (atmospheric and continental) in West Africa, as part of AMMA (African Monsoon Multidisciplinary Analyses) and GHYRAF (Gravity and Hydrology in Africa) projects.In the first part, we analyze the precision of GPS solutions in Africa. The integrated water vapor (IWV) is especially important in understanding the key atmospheric processes of the monsoon from subdiurne to multiyear periods. We pay much attention to sources of errors and the strategy of GPS data processing. A recall of the main theoretical elements allows us to identify the major sources of error that may affect the GPS estimates. We quantify the sensitivity of IWV for each of these sources of error and obtain a long-term precision of 1 kg m−2 on IWV. Meanwhile, station heights are really sensitive to errors and choices of parameterization. They are mainly subject to bias between 2 and 6 mm (choice of antenna models and the cut-off angle) and to seasonal signals whose amplitude is lesser than 2 mm (choice of tropospheric modeling). In the second part, we focus on estimates of station positions in order to quantify crustal deformation caused by continental hydrology. We compare the GPS solutions to estimates calculated from geophysical data and from GRACE space gravimetric data. Through this study, we also evaluate the quality of representation of the seasonal variation of soil moisture in West Africa with hydrological models and GRACE products. The three data sets are rather matching with the annual range of vertical deformations. An additional GPS signal is however detected, on the heights of AMMA GPS stations which appears to be an oscillation occurring between September and March with maximum amplitude in Ouagadougou evaluated between 12 and 16 mm. The hypothesis of an artifact GPS is rejected given previous sensitivity tests. The additional GPS signal is strongly correlated with the flooding of the Niger River to nearby stations (Timbuktu, Gao, and Niamey) or piezometric variations of the upper aquifer in Ouagadougou. It would be explained by hydrogeological and geotechnical mechanisms involving a sequence of shrinkage / swelling clays combined with local hydrological effects.Le Global Positioning System (GPS) présente aujourd’hui un grand intérêt dans le domaine de la météorologie et des Sciences de l’Environnement. Cette thèse s’intéresse plus particulièrement à l’étude du cycle de l’eau atmosphérique aussi bien que continentale, en Afrique de l’Ouest, dans le cadre des projets AMMA (Analyse Multidisciplinaire de la Mousson Africaine) et GHYRAF (Gravité et Hydrologie en Afrique).Dans une première partie, nous analysons la précision des calculs GPS en Afrique. Les contenus intégrés en vapeur d’eau (CIVE) sont particulièrement importants pour appréhender les processus atmosphériques clefs de la mousson couvrant des périodes subdiurnes à pluriannuelles. Nous prêtons alors une grande attention aux sources d’erreurs et à la stratégie de traitement des données GPS. Un rappel des principaux éléments théoriques nous permet d’identifier les sources d’erreur majeures susceptibles d’affecter les estimations. Nous quantifions la sensibilité des CIVE pour chacune de ces sources d’erreur et nous montrons que leur précision long terme est de l’ordre de 1 kg.m−2. Parallèlement, les hauteurs de station se montrent particulièrement sensibles aux erreurs et choix de paramétrisation. Elles sont principalement sujettes à des biais compris entre 2 et 6 mm (choix des modèles d’antenne et de l’angle de coupure) et à des signaux saisonniers d’amplitude inférieure à 2 mm (choix de la modélisation troposphérique). Dans une deuxième partie, nous nous intéressons aux estimations de position des stations dans le but de quantifier les déformations de la croûte terrestre induites par l’hydrologie continentale. Nous comparons les estimations GPS à des estimations de surcharge calculées à partir de produits de modèles géophysiques et de données de gravimétrie spatiale GRACE. À travers cette étude nous évaluons aussi la qualité de la représentation de la variation saisonnière de l’humidité des sols en Afrique de l’Ouest par les modèles hydrologiques et les produits GRACE. Les trois jeux de données considérés sont en bon accord concernant l’amplitude annuelle des déformations verticales. Un signal GPS additionnel est toutefois détecté sur les hauteurs des stations GPS AMMA qui apparaît comme une oscillation se produisant entre septembre et mars avec une amplitude maximale à Ouagadougou évaluée entre 12 et 16 mm. L’hypothèse d’un artefact GPS est écartée à la lumière des tests de sensibilité précédents. Le signal GPS additionnel est fortement corrélé avec la crue du fleuve Niger pour les stations situées à proximité (Tombouctou, Gao et Niamey) ou avec les variations piézométriques de l’aquifère supérieur à Ouagadougou. Il serait d’origine hydrogéologique et s’expliquerait par des mécanismes géotechniques impliquant une séquence de retrait/gonflement des argiles combinée à des effets hydrologiques locaux

Sensitivity of GPS tropospheric estimates to mesoscale convective systems in West Africa

International audienceThis study analyzes the characteristics of GPS tro-pospheric estimates (zenith wet delays-ZWDs, gradients, and post-fit phase residuals) during the passage of mesoscale convective systems (MCSs) and evaluates their sensitivity to the research-level GPS data processing strategy implemented. Here, we focus on MCS events observed during the monsoon season of West Africa. This region is particularly well suited for the study of these events due to the high frequency of MCS occurrences in the contrasting climatic environments between the Guinean coast and the Sa-hel. This contrast is well sampled with data generated by six African Monsoon Multidisciplinary Analysis (AMMA) GPS stations. Tropospheric estimates for a 3-year period (2006-2008), processed with both the GAMIT and GIPSY-OASIS software packages, were analyzed and intercompared. First, the case of a MCS that passed over Niamey, Niger, on 11 August 2006 demonstrates a strong impact of the MCS on GPS estimates and post-fit residuals when the GPS signals propagate through the convective cells as detected on reflectivity maps from the MIT C-band Doppler radar. The estimates are also capable of detecting changes in the structure and dynamics of the MCS. However, the sensitivity is different depending on the tropospheric modeling approach adopted in the software. With GIPSY-OASIS, the high temporal sampling (5 min) of ZWDs and gradients is well suited for detecting the small-scale, short-lived, convective cells, while the post-fit residuals remain quite small. With GAMIT, the lower temporal sampling of the estimated parameters (hourly for ZWDs and daily for gradients) is not sufficient to capture the rapid delay variations associated with the passage of the MCS, but the post-fit phase residuals clearly reflect the presence of a strong refractivity anomaly. The results are generalized with a composite analysis of 414 MCS events observed over the 3-year period at the six GPS stations with the GIPSY-OASIS estimates. A systematic peak is found in the ZWDs coincident with the cold pool crossing time associated with the MCSs. The tropospheric gradients reflect the path of the MCS propagation (generally from east to west). This study concludes that ZWDs, gradients, and post-fit phase residuals provide relevant and complementary information on MCSs passing over or in the vicinity of a GPS station

Méthodologies en traitement de données GPS pour les sciences de l'environnement (contributions à l'étude de la mousson en Afrique de l'Ouest)

Le Global Positioning System présente aujourd hui un grand intérêt dans le domaine de la météorologie et des Sciences de l Environnement. Cette thèse s intéresse plus particulièrement à l étude du cycle de l eau en Afrique de l Ouest, dans le cadre des projets AMMA (Analyse Multidisciplinaire de la Mousson Africaine) et GHYRAF (Gravité et Hydrologie en Afrique). Dans une première partie, nous analysons la précision des calculs GPS en Afrique. Les Contenus Intégrés en Vapeur d Eau sont particulièrement importants pour appréhender les processus atmosphériques clefs de la mousson couvrant des périodes subdiurnes à pluriannuelles. Nous prêtons alors une grande attention aux sources d erreurs et à la stratégie de traitement des données GPS. Un rappel des principaux éléments théoriques nous permet d identifier les sources d erreur majeures susceptibles d affecter ces estimations et d'en quantifier les effets. Dans une deuxième partie, nous nous intéressons aux estimations de position des stations dans le but de quantifier les déformations de la croûte terrestre induites par l hydrologie continentale. Nous comparons les estimations GPS à des estimations de surcharge calculées à partir de produits de modèles géophysiques et de données de gravimétrie spatiale GRACE. Les trois jeux de données considérés sont en bon accord concernant l amplitude annuelle des déformations verticales. Un signal GPS additionnel est toutefois détecté sur les hauteurs des stations GPS AMMA. Il est fortement corrélé avec l'hydrologie locale. Nous expliquons son origine par des mécanismes géotechniques impliquant une séquence de retrait/gonflement des argiles combinée à des effets hydrologiques locaux.Global Positioning System is now very useful for meteorology and environmental sciences. This thesis focuses on the study of the water cycle in West Africa, as part of AMMA (African Monsoon Multidisciplinary Analyses) and GHYRAF (Gravity and Hydrology in Africa) projects. In the first part, we analyze the precision of GPS solutions in Africa. The Integrated Water Vapour are especially important in understanding the key atmospheric processes of the monsoon from subdiurne to multiyear periods. We pay much attention to sources of errors and the strategy of GPS data processing. A recall of the main theoretical elements allows us to identify the major sources of error that may affect the GPS estimates and we quantify the sensitivity of IWV for each of these sources of error. In the second part, we focus on estimates of station positions in order to quantify crustal deformation caused by continental hydrology. We compare the GPS solutions to estimates calculated from geophysical data and from GRACE space gravimetric data. Through this study, we also evaluate the quality of representation of the seasonal variation of soil moisture in West Africa with hydrological models and GRACE products. The three data sets are rather matching with the annual range of vertical deformations. An additional GPS signal is however detected, on the heights of AMMA GPS stations. The additional GPS signal is strongly correlated with the flooding of the Niger River to nearby stations or piezometric variations of the upper aquifer in Ouagadougou. It would be explained by hydrogeological mechanisms involving a sequence of shrinkage /swelling clays combined with local hydrological effects.PARIS-BIUSJ-Sci.Terre recherche (751052114) / SudocSudocFranceF

Sensitivity of GPS tropospheric estimates to mesoscale convective systems in West Africa

International audienc

GRGS numerical simulations for a GRASP-like mission

International audienceIn 2009, the geoscience community has fixed an objective of 1 mm accuracy and 0.1 mm/yr stability for the terrestrial reference frame (TRF) realization (Global Geodetic Observing System, GGOS, Meeting the Requirements of a Global Society on a Changing Planet in 2020, Plag and Pearlman in Global geodetic observing system: meeting the requirements of a global society on a changing planet in 2020. Springer, Berlin, 2009. https://doi.org/10.1007/978-3-642-02687-4). This accuracy and stability are needed for diversified studies like climate change, tectonic sciences and more generally any geoscience requiring the use of an accurate and precise TRF. Unfortunately, they are still not reached by the last International Terrestrial Reference Frame. To reach this goal, the use of "multi-technique" satellites as "space-ties" has been studied since 2011 and a few proposals have been made in response to different space agency calls: the Geodetic Reference Antenna in Space (GRASP) mission—NASA Earth Venture 2 call, Eratosthenes-GRASP (E-GRASP)—ESA Earth Explorer 9 (EE9) call, MOBILE—ESA EE10 call, MARVEL—CNES Séminaire de Prospective Scientifique 2019). In this article, we present the numerical simulations carried out by the French Groupe de Recherche de Géodésie Spatiale (GRGS) for the E-GRASP proposal in response to the ESA EE-9 call and their improvements carried out afterwards. These simulations aim to answer three different questions: Is it possible to reach the GGOS requirements for the TRF with the measurements of a GRASP-like satellite like E-GRASP alone

GRGS simulations for a GRASP-like satellite

International audienceGRASP (Geodetic Reference Antenna in SPace) is a spacecraft system designed to provide the needed data for an enduring and stable TRF (Terrestrial Reference Frame) for accurately measuring and understanding changes in global and regional sea levels, ice sheets and other elements of the dynamic Earth system. To reach the goals for the TRF realization of 1 mm accuracy and 0.1 mm/yr stability (GGOS, Meeting the Requirements of a Global Society on a Changing Planet in 2020, Plag and Pearlman, eds., 2009), GRASP would carry very precise sensor systems for all the key geodetic techniques used to define and monitor the TRF (DORIS, GNSS, SLR, and VLBI). In this study, we present the results obtained regarding the simulations carried out by the French GRGS (Groupe de Recherche de Géodésie Spatiale) for a GRASP-like satellite. First, we searched for the optimal orbit for such a geodetic mission with Genetic Algorithms (stochastic optimization). Then, with the best found orbit, we simulated the measurements of the four geodetic techniques (DORIS and SLR measurements to GRASP, VLBI PPP or interferometric measurements to GRASP, and GNSS measurements received from ground stations and from GRASP) over three years, and we evaluated the expected accuracy and stability of the TRF obtained with the processing of these measurements. Finally, we also investigated the expected impact of the on-board instrument calibration on the quality of the TRF

GRGS simulations for a GRASP-like satellite

International audienceGRASP (Geodetic Reference Antenna in SPace) is a spacecraft system designed to provide the needed data for an enduring and stable TRF (Terrestrial Reference Frame) for accurately measuring and understanding changes in global and regional sea levels, ice sheets and other elements of the dynamic Earth system. To reach the goals for the TRF realization of 1 mm accuracy and 0.1 mm/yr stability (GGOS, Meeting the Requirements of a Global Society on a Changing Planet in 2020, Plag and Pearlman, eds., 2009), GRASP would carry very precise sensor systems for all the key geodetic techniques used to define and monitor the TRF (DORIS, GNSS, SLR, and VLBI). In this study, we present the results obtained regarding the simulations carried out by the French GRGS (Groupe de Recherche de Géodésie Spatiale) for a GRASP-like satellite. First, we searched for the optimal orbit for such a geodetic mission with Genetic Algorithms (stochastic optimization). Then, with the best found orbit, we simulated the measurements of the four geodetic techniques (DORIS and SLR measurements to GRASP, VLBI PPP or interferometric measurements to GRASP, and GNSS measurements received from ground stations and from GRASP) over three years, and we evaluated the expected accuracy and stability of the TRF obtained with the processing of these measurements. Finally, we also investigated the expected impact of the on-board instrument calibration on the quality of the TRF

GRGS simulations for a GRASP-like satellite

International audienceGRASP (Geodetic Reference Antenna in SPace) is a spacecraft system designed to provide the needed data for an enduring and stable TRF (Terrestrial Reference Frame) for accurately measuring and understanding changes in global and regional sea levels, ice sheets and other elements of the dynamic Earth system. To reach the goals for the TRF realization of 1 mm accuracy and 0.1 mm/yr stability (GGOS, Meeting the Requirements of a Global Society on a Changing Planet in 2020, Plag and Pearlman, eds., 2009), GRASP would carry very precise sensor systems for all the key geodetic techniques used to define and monitor the TRF (DORIS, GNSS, SLR, and VLBI). In this study, we present the results obtained regarding the simulations carried out by the French GRGS (Groupe de Recherche de Géodésie Spatiale) for a GRASP-like satellite. First, we searched for the optimal orbit for such a geodetic mission with Genetic Algorithms (stochastic optimization). Then, with the best found orbit, we simulated the measurements of the four geodetic techniques (DORIS and SLR measurements to GRASP, VLBI PPP or interferometric measurements to GRASP, and GNSS measurements received from ground stations and from GRASP) over three years, and we evaluated the expected accuracy and stability of the TRF obtained with the processing of these measurements. Finally, we also investigated the expected impact of the on-board instrument calibration on the quality of the TRF

GRGS simulations for a GRASP-like satellite

International audienceGRASP (Geodetic Reference Antenna in SPace) is a spacecraft system designed to provide the needed data for an enduring and stable TRF (Terrestrial Reference Frame) for accurately measuring and understanding changes in global and regional sea levels, ice sheets and other elements of the dynamic Earth system. To reach the goals for the TRF realization of 1 mm accuracy and 0.1 mm/yr stability (GGOS, Meeting the Requirements of a Global Society on a Changing Planet in 2020, Plag and Pearlman, eds., 2009), GRASP would carry very precise sensor systems for all the key geodetic techniques used to define and monitor the TRF (DORIS, GNSS, SLR, and VLBI). In this study, we present the results obtained regarding the simulations carried out by the French GRGS (Groupe de Recherche de Géodésie Spatiale) for a GRASP-like satellite. First, we searched for the optimal orbit for such a geodetic mission with Genetic Algorithms (stochastic optimization). Then, with the best found orbit, we simulated the measurements of the four geodetic techniques (DORIS and SLR measurements to GRASP, VLBI PPP or interferometric measurements to GRASP, and GNSS measurements received from ground stations and from GRASP) over three years, and we evaluated the expected accuracy and stability of the TRF obtained with the processing of these measurements. Finally, we also investigated the expected impact of the on-board instrument calibration on the quality of the TRF