Voici les éléments 1 - 10 sur 13
  • Publication
    Accès libre
    Conditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study
    Over the last decade, data assimilation methods based on the ensemble Kalman filter (EnKF) have been particularly explored in various geoscience fields to solve inverse problems. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multivariate Gaussian. To handle existing non-linearities between the observations and the variables to estimate, iterative methods have been proposed. In this paper, we investigate the feasibility of using the ensemble smoother and two iterative variants for the calibration of a synthetic 2D groundwater model inspired by a real nuclear storage problem in France. Using the same set of sparse and transient flow data, we compare the results of each method when employing them to condition an ensemble of multi-Gaussian groundwater flow parameter fields. In particular, we explore the benefit of transforming the state observations to improve the parameter identification performed by one of the two iterative algorithms tested. Despite the favorable case of a multi-Gaussian parameter distribution addressed, we show the importance of defining an ensemble size of at least 200 to obtain sufficiently accurate parameter and uncertainty estimates for the groundwater flow inverse problem considered.
  • Publication
    Accès libre
    Conditioning groundwater flow parameters with iterative ensemble smoothers: analysis and approaches in the continuous and the discrete cases
    L’assimilation de données consiste à combiner de façon optimale les observations (données) et les prévisions produites par un modèle numérique d’un système dynamique étudié. Au cours de la dernière décennie, les méthodes basées sur le filtre de Kalman d’ensemble (EnKF) pour l’assimilation de données ont été particulièrement explorées dans diverses disciplines des géosciences pour résoudre des problèmes inverses. Bien que ces méthodes d’ensemble aient été développées afin de pouvoir traiter efficacement des problèmes de grandes dimensions, elles supposent que les erreurs qui affectent les observations et le modèle suivent une loi de distribution Gaussienne multivariée. Pour traiter de potentielles nonlinéarités entre les données et les variables paramètres ou d’état que l’on souhaite conditionner, des variantes itératives de méthodes existantes ont été proposées. Dans cette thèse, nous nous intéressons dans un premier temps à la performance de deux principales méthodes de lisseur d’ensemble itératif pour le calage d’un modèle synthétique d’écoulement souterrain 2D. A partir du même jeu de données ponctuelles (locales) et transitoires (dynamiques), nous analysons la performance de chaque méthode pour le conditionnement d’un ensemble de champs multi-Gaussiens de valeurs de conductivité hydraulique. Nous explorons ensuite plus particulièrement l’application d’une des méthodes, ES-MDA, dans des situations plus ou moins complexes suivant la méthode de simulation géostatistique employée pour représenter l’information géologique a priori. Nous évaluons tout d’abord la pertinence d’une paramétrisation basée sur une transformation normal-score dans un cas non-multi-Gaussien. La robustesse de la méthode d’ensemble face aux nonlinéarités est ensuite plus particulièrement testée dans le cas de réalisations de variables discrètes de facies géologique obtenues par la technique des gaussiennes tronquées et mises à jour via leurs variables continues sous-jacentes. En nous basant sur les limitations et avantages observées expérimentalement pour les paramétrisations précédemment évoquées, nous proposons finalement une nouvelle méthodologie d’assimilation de données dynamiques. Bien qu’elle implique une méthode classique de Kalman d’ensemble, la méthodologie proposée permet spécifiquement le conditionnement de champs de facies géologiques, soit de variables discrètes, qui sont initialement simulés par statistiques à points multiples (MPS). Cette méthodologie s’appuie sur une paramétrisation multi-résolutions nouvelle de la simulation MPS catégorique où, l’ensemble de paramètres latents est défini initialement à partir des simulations à l’échelle la plus grossière d’un ensemble de simulations MPS multi-résolutions. Comme cet ensemble n’est pas multi-Gaussien, des étapes additionnelles précédant le calcul de la première correction sont proposées. Notamment, les paramètres sont corrigés à des points prédéfinis à l’échelle la plus grossière, puis intégrés en tant que données de conditionnement pour générer une nouvelle simulation MPS multi-résolutions. Les résultats obtenus sur le problème synthétique montrent que la méthode converge vers un ensemble de réalisations catégoriques finales cohérent avec l’ensemble catégorique initial. La convergence est fiable en ce sens qu’elle est contrôlée entièrement par l’intégration de la correction de ES-MDA dans les nouvelles simulations MPS multi-résolutions conditionnelles. De plus, grâce à la paramétrisation proposée, l’identification des structures géologiques durant l’assimilation des données est particulièrement efficace pour cet exemple. La comparaison entre l’incertitude estimée et une estimation de référence obtenue avec une méthode de Monte-Carlo révèle que l’incertitude n’est pas sévèrement réduite durant l’assimilation comme cela est souvent observé. La connectivité des structures est bien reproduite durant la procédure itérative malgré la distance plutôt élevée entre les points d’observation., Data assimilation (DA) consists in combining observations and predictions of a numerical model to produce an optimal estimate of the evolving state of a system. Over the last decade, DA methods based on the Ensemble Kalman Filter (EnKF) have been particularly explored in various geoscience fields for inverse modelling. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multi-Gaussian. To handle potential nonlinearities between the observations and the state or parameter variables to estimate, iterative variants have been proposed. In this thesis, we first focus on two main iterative ensemble smoother methods for the calibration of a synthetic 2D groundwater model. Using the same set of sparse and transient flow data, we analyse each method when employing them to condition an ensemble of multi-Gaussian hydraulic conductivity fields. We then further explore the application of one iterative ensemble smoother algorithm (ES-MDA) in situations of variable complexity, depending on the geostatistical simulation method used to simulate the prior geological information. The applicability of a parameterization based on the normal-score transform is first investigated. The robustness of the method against nonlinearities is then further explored in the case of discrete facies realizations obtained with a truncated Gaussian technique and updated via their underlying continuous variables. Based on the observed limitations and benefits of the forementioned parameterizations, we finally propose a new methodology for the conditioning of categorical multiple-point statistics (MPS) simulations to dynamic data with a state-of-the-art ensemble Kalman method by taking the example of the Ensemble Smoother with Multiple Data Assimilation (ES-MDA). Our methodology relies on a novel multi-resolution parameterization of the categorical MPS simulation. The ensemble of latent parameters is initially defined on the basis of the coarsest-resolution simulations of an ensemble of multi-resolution MPS simulations. Because this ensemble is non-multi-Gaussian, additional steps prior to the computation of the first update are proposed. In particular, the parameters are updated at predefined locations at the coarsest scale and integrated as hard data to generate a new multi-resolution MPS simulation. The results on the synthetic problem illustrate that the method converges towards a set of final categorical realizations that are consistent with the initial categorical ensemble. The convergence is reliable in the sense that it is fully controlled by the integration of the ES-MDA update into the new conditional multi-resolution MPS simulations. Moreover, thanks to the proposed parameterization, the identification of the geological structures during the data assimilation is particularly efficient for this example. The comparison between the estimated uncertainty and a reference estimate obtained with a Monte Carlo method shows that the uncertainty is not severely reduced during the assimilation as is often the case. The connectivity is successfully reproduced during the iterative procedure despite the rather large distance between the observation points.
  • Publication
    Accès libre
    Uncertainty propagation and global sensitivity analysis in multi-layered hydrogeological models of flow and lifetime expectancy
    (2015)
    Deman, Grégory
    ;
    ;
    The main focus of this thesis is the uncertainty propagation (UP) and global sensitivity analysis (GSA) in complex hydrogeological numerical models. Various methods are presented with applications on numerical models for the groundwater flow and mean lifetime expectancy (MLE) in the scope of Andra's (French National Radioactive Waste Management Agency) project for the geological disposal of high-level and intermediate-level long-lived radioactive wastes in a highly impermeable layer from Callovo-Oxfordian age (COX) in France.
    A state of the art is provided for the theory of uncertainty propagation and for the methodologies of sensitivity analyses in a broad sense. Methods for UP are provided from 2-levels Factorial Designs to quasi-random samplings. GSA techniques encompass screening methods such as the Morris Measures and the Derivative-based Global Sensitivity Measures (DGSM), and also the so-called Sobol' indices based upon the variance decomposition of the response of interest. Meta-modelling techniques such as polynomial regression and Polynomial Chaos Expansions (PCE) meta-models are employed as surrogate models for UP and GSA purpose at negligible computational-costs. A comparison of GSA techniques upon various complex analytical test-functions was undertaken with the purpose of determining a relevant method to be employed in the context of “screening” out unimportant variables in computer-intensive, high-dimensional models.
    A numerical model of groundwater flow and lifetime expectancy is employed for assessing the effect of uncertain advection-dispersion parameters and their spatial distributions upon the MLE from a target zone inside the domain. The model is a 2-dimensions synthetic cross-section of the eastern region of the Paris Basin (Meuse/Haute-Marne sector). This model was used as an exploratory tool for sensitivity analysis methods applied upon numerous sets of uncertain hydrodynamic and dispersion parameters in 15 layers. The uncertainty characterizing the permeability-porosity values in aquifer formations encompassing the COX have proved to add much of variability to the MLE calculated from the target zone. The model also served at exploring the effect of the spatial variability of permeability-porosity parameters in two main aquifer sequences on the groundwater flow rates and MLE in the model. The variabilities of the output responses are mainly due to the uncertainty upon the means and variances of the permeability-porosity distributions, as well as the longitudinal correlation lengths, in each sequence.
    Then, a 3-dimensions high-definition hydrogeological model representing the Meuse/Haute-Marne sector in the eastern region of the Paris Basin is a more comprehensive numerical model incorporating realistic geometries, fractures, heterogeneities and discontinuities encountered on field. A sensitivity analysis of the MLE from a given zone located in the middle of the COX layer was performed by perturbing the hydraulic conductivities and porosities values in fourteen hydrogeological formations. The uncertain permeability-porosity parameters in the aquifer formations from Bathonian in the Dogger sequence, and Rauracian-Sequanian in the Oxfordian sequence, have strong and rather non-linear effects on the variability of the output response of interest.
    The methodologies for UP and GSA employed in the present thesis have proved to be very efficient when applied to large hydrogeological models of groundwater flow and MLE. In particular, quasi-random sampling methods offer a flexible frame for providing the uncertainty distribution of the output response of interest at low computational costs. Screening techniques provide a fast estimation for the overall contribution of each input variable to the variability of the output. Meta-modelling techniques such as PCE proved highly accurate in individualising the low- and high-order effects of each input variable upon the output response of interest.
  • Publication
    Accès libre
    A numerical analysis of dimensionality and heterogeneity effects on advective dispersive seawater intrusion processes
    Two-dimensional (2D) and 3D numerical simulations of the dispersive Henry problem show that heterogeneity affects seawater intrusion differently in 2D and 3D. When the variance of a multi-Gaussian isotropic hydraulic conductivity field increases, the penetration of the saltwater wedge decreases in 2D while it increases in 3D. This is due to the combined influence of advective and dispersive processes which are affected differently by heterogeneity and problem dimensionality. First, the equivalent hydraulic conductivity controls the mean head gradient and therefore the position of the wedge. For an isotropic medium, increasing the variance increases the equivalent conductivity in 3D but not in 2D. Second, the macrodispersion controls the rotation of the saltwater wedge by affecting the magnitude of the density contrasts along the saltwater wedge. An increased dispersion due to heterogeneity leads to a decreasing density contrast and therefore a smaller penetration of the wedge. The relative magnitude of these two opposite effects depends on the degree of heterogeneity, anisotropy of the medium, and dimension. Investigating these effects in 3D is very heavy numerically; as an alternative, one can simulate 2D heterogeneous media that approximate the behaviour of the 3D ones, provided that their statistical distribution is rescaled.
  • Publication
    Accès libre
    Grid-enabled Monte Carlo analysis of the impacts of uncertain discharge rates on seawater intrusion in the Korba aquifer (Tunisia)
    (2010) ; ;
    Lecca, Giuditta
    ;
    Tarhouni, Jamila
    L'aquifère de Korba, situé au nord de la Tunisie, est gravement touché par une salinisation du à l'intrusion marine. En 2000, l'aquifère a été exploité par plus de 9000 puits. Le problème, c'est qu'il n'y a pas d'information précise concernant les débits de pompage, leur répartition dans l'espace ainsi que leur évolution dans le temps. Dans cette étude, un modèle géostatistique des débits d'exploitation a été construit en se basant sur une régression multilinéaire combinant des données directes incomplètes ainsi que des données secondaires exhaustives. Les impacts de l'incertitude associée à la distribution spatiale des débits de pompage sur l'intrusion marine ont été évalués en utilisant un modèle tridimensionnel d'écoulement et de transport à densité variable. Pour contourner les difficultés liées à de longs temps de calcul, nécessaires pour résoudre des problèmes en régime transitoire, les simulations ont été réalisées en parallèle sur une grille informatique de calcul mise à disposition par le projet “Enabling Grid for E-Science in Europe”. Les résultats des simulations de Monte Carlo ont montré que 8.3% de la surface de l'aquifère est affectée par l'incertitude liée aux données d'entrée., The Korba aquifer, located in the north of Tunisia, suffers heavily from salinization due to seawater intrusion. In 2000, the aquifer was exploited from more than 9000 wells. The problem is that no precise information was recorded concerning the current extraction rates, their spatial distribution, or their evolution in time. In this study, a geostatistical model of the exploitation rates was constructed based on a multi-linear regression model combining incomplete direct data and exhaustive secondary information. The impacts of the uncertainty on the spatial distribution of the pumping rates on seawater intrusion were evaluated using a 3-D density-dependent groundwater model. To circumvent the large amount of computing time required to run transient models, the simulations were run in a parallel fashion on the Grid infrastructure provided by the Enabling Grid for E-Science in Europe project. Monte Carlo simulations results showed that 8.3% of the aquifer area is affected by input uncertainty.
  • Publication
    Accès libre
    Status of the Korba groundwater resources (Tunisia): observations and three-dimensional modelling of seawater intrusion
    (2010) ; ;
    Tarhouni, Jamila
    The Korba aquifer is located in the east of the Cape Bon peninsula in Tunisia. A large groundwater depression has been created in the central part of the aquifer since the 1980s, due to intense groundwater pumping for irrigation. The data collected show that the situation continues to deteriorate. Consequently, seawater is continuing to invade a large part of the aquifer. To better understand the situation and try to forecast its evolution, a three-dimensional (3D) transient density-dependent groundwater model has been developed. The model building process was difficult because of data required on groundwater discharge from thousands of unmonitored private wells. To circumvent that difficulty, indirect exhaustive information including remote sensing data and the physical parameters of the aquifer have been used in a multi-linear regression framework. The resulting 3D model shows that the aquifer is over-exploited. It also shows that after 50 years of exploitation, the time needed to turn back to the natural situation would be about 150 years if the authorities would ban all exploitation now. Such an asymmetry in the time scales required to contaminate or remediate an aquifer is an important characteristic of coastal aquifers that must be taken into account in their management.
  • Publication
    Accès libre
  • Publication
    Accès libre
    Issues in characterizing heterogeneity and connectivity in non-multiGaussian media
    (2008) ; ;
    Hendricks Franssen, Harrie-Jan
    ;
    Lunatic, Ivan
    The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.
  • Publication
    Accès libre
    Deterministic and probabilistic numerical modelling towards sustainable groundwater management: application to seawater intrusion in the Korba aquifer (Tunisia)
    This PhD endeavours numerical groundwater modelling considering heterogeneous and uncertain hydraulic parameters. It is made of three parts. First, we investigated the effects of dimensionality and heterogeneity of the hydraulic conductivity on dispersive seawater intrusion (SWI) processes. Multiple 2D and 3D unconditional simulations of hydraulic conductivity fields sharing the same statistics were generated then used to solve density-dependent flow and solute transport equations with a finite element code. Monte Carlo simulations were analysed in terms of dimensionless criteria including the penetration length and width of the saltwater wedge. Results showed that the 2D heterogeneity is affecting more strongly the SWI processes than the 3D heterogeneity. The saltwater wedge length in the 2D models is smaller than in the 3D ones while there is more mixing in 2D models. Most important, results showed that there is a critical ratio between advection and dispersion processes which is controlling the behaviour of SWI in heterogeneous porous medium. The second part of the thesis dealt with deterministic and probabilistic modelling and long term forecasts of SWI in the Korba aquifer (Tunisia). The study started by the development of a 3D density-dependent flow and solute transport model of the regional Korba aquifer. Then, two geostatistical models of the exploitation rates and of the hydraulic conductivities within the aquifer were built by combining incomplete direct data and secondary information including aquifer physical parameters. The effects of the uncertainty on the spatial distribution of the pumping rates and the uncertainty on the hydraulic conductivity field on the 3D density-dependent model were analysed separately and then jointly. To circumvent the large computing time required to run hundreds of 44-years transient models, the simulations were made in a parallel fashion on the EGEE Grid infrastructure as well as on a local Linux cluster. The deterministic numerical model allowed to estimate the current over-exploitation of the Korba aquifer to 135%. It also allowed to estimate the time lapse needed to turn back the initial head and slat distributions (before exploitation start) to about 150 years. The results of the stochastic simulations showed that both uncertainties led to a zone representing 12% of the aquifer area, where the groundwater heads and salt concentrations are not known with accuracy. Most important, results showed that reducing the pumping rates progressively by 50% until 2048 will not result in a recession of the saltwater wedge ; instead an additional 9.5% of the surface of the aquifer will be contaminated in 2048. In the third part of the thesis, the performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multi-Gaussian synthetic 2D braided channel aquifer. In a first step, the performance of the three methods was compared in terms of reproducing the original reference transmissivity or head fields. In a second step, the methods were compared in terms of accuracy of flow and transport (capture zone) forecasts. Results showed that the errors remain large even for a dense data network. In addition, some unexpected behaviours are observed when large transmissivity datasets are used. We also observed an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This was interpreted as a consequence of the use of an inadequate multi-Gaussian stochastic model.