Comparison of time-lapse GPR data collected under natural and forced infiltration conditions to estimate vadose zone hydraulic parameters

Time-lapse crosshole ground-penetrating radar (GPR) data, collected while infiltration occurs, can provide valuable information regarding the hydraulic properties of the unsaturated zone. In particular, the stochastic inversion of such data provides estimates of parameter uncertainties, which are necessary for hydrological prediction and decision making. Here, we investigate the effect of different infiltration conditions on the stochastic inversion of time-lapse, zero-offset-profile, GPR data. Inversions are performed using a Bayesian Markov-chain-Monte-Carlo methodology. Our results clearly indicate that considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions

Quantitative integration of geophysical and hydraulic data : from the local towards the regional scale range

Des progrès significatifs ont été réalisés dans le domaine de l'intégration quantitative des données géophysique et hydrologique l'échelle locale. Cependant, l'extension à de plus grandes échelles des approches correspondantes constitue encore un défi majeur. Il est néanmoins extrêmement important de relever ce défi pour développer des modèles fiables de flux des eaux souterraines et de transport de contaminant. Pour résoudre ce problème, j'ai développé une technique d'intégration des données hydrogéophysiques basée sur une procédure bayésienne de simulation séquentielle en deux étapes. Cette procédure vise des problèmes à plus grande échelle. L'objectif est de simuler la distribution d'un paramètre hydraulique cible à partir, d'une part, de mesures d'un paramètre géophysique pertinent qui couvrent l'espace de manière exhaustive, mais avec une faible résolution (spatiale) et, d'autre part, de mesures locales de très haute résolution des mêmes paramètres géophysique et hydraulique. Pour cela, mon algorithme lie dans un premier temps les données géophysiques de faible et de haute résolution à travers une procédure de réduction déchelle. Les données géophysiques régionales réduites sont ensuite reliées au champ du paramètre hydraulique à haute résolution. J'illustre d'abord l'application de cette nouvelle approche dintégration des données à une base de données synthétiques réaliste. Celle-ci est constituée de mesures de conductivité hydraulique et électrique de haute résolution réalisées dans les mêmes forages ainsi que destimations des conductivités électriques obtenues à partir de mesures de tomographic de résistivité électrique (ERT) sur l'ensemble de l'espace. Ces dernières mesures ont une faible résolution spatiale. La viabilité globale de cette méthode est testée en effectuant les simulations de flux et de transport au travers du modèle original du champ de conductivité hydraulique ainsi que du modèle simulé. Les simulations sont alors comparées. Les résultats obtenus indiquent que la procédure dintégration des données proposée permet d'obtenir des estimations de la conductivité en adéquation avec la structure à grande échelle ainsi que des predictions fiables des caractéristiques de transports sur des distances de moyenne à grande échelle. Les résultats correspondant au scénario de terrain indiquent que l'approche d'intégration des données nouvellement mise au point est capable d'appréhender correctement les hétérogénéitées à petite échelle aussi bien que les tendances à gande échelle du champ hydraulique prévalent. Les résultats montrent également une flexibilté remarquable et une robustesse de cette nouvelle approche dintégration des données. De ce fait, elle est susceptible d'être appliquée à un large éventail de données géophysiques et hydrologiques, à toutes les gammes déchelles. Dans la deuxième partie de ma thèse, j'évalue en détail la viabilité du réechantillonnage geostatique séquentiel comme mécanisme de proposition pour les méthodes Markov Chain Monte Carlo (MCMC) appliquées à des probmes inverses géophysiques et hydrologiques de grande dimension . L'objectif est de permettre une quantification plus précise et plus réaliste des incertitudes associées aux modèles obtenus. En considérant une série dexemples de tomographic radar puits à puits, j'étudie deux classes de stratégies de rééchantillonnage spatial en considérant leur habilité à générer efficacement et précisément des réalisations de la distribution postérieure bayésienne. Les résultats obtenus montrent que, malgré sa popularité, le réechantillonnage séquentiel est plutôt inefficace à générer des échantillons postérieurs indépendants pour des études de cas synthétiques réalistes, notamment pour le cas assez communs et importants où il existe de fortes corrélations spatiales entre le modèle et les paramètres. Pour résoudre ce problème, j'ai développé un nouvelle approche de perturbation basée sur une déformation progressive. Cette approche est flexible en ce qui concerne le nombre de paramètres du modèle et lintensité de la perturbation. Par rapport au rééchantillonage séquentiel, cette nouvelle approche s'avère être très efficace pour diminuer le nombre requis d'itérations pour générer des échantillons indépendants à partir de la distribution postérieure bayésienne. - Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending corresponding approaches beyond the local scale still represents a major challenge, yet is critically important for the development of reliable groundwater flow and contaminant transport models. To address this issue, I have developed a hydrogeophysical data integration technique based on a two-step Bayesian sequential simulation procedure that is specifically targeted towards larger-scale problems. The objective is to simulate the distribution of a target hydraulic parameter based on spatially exhaustive, but poorly resolved, measurements of a pertinent geophysical parameter and locally highly resolved, but spatially sparse, measurements of the considered geophysical and hydraulic parameters. To this end, my algorithm links the low- and high-resolution geophysical data via a downscaling procedure before relating the downscaled regional-scale geophysical data to the high-resolution hydraulic parameter field. I first illustrate the application of this novel data integration approach to a realistic synthetic database consisting of collocated high-resolution borehole measurements of the hydraulic and electrical conductivities and spatially exhaustive, low-resolution electrical conductivity estimates obtained from electrical resistivity tomography (ERT). The overall viability of this method is tested and verified by performing and comparing flow and transport simulations through the original and simulated hydraulic conductivity fields. The corresponding results indicate that the proposed data integration procedure does indeed allow for obtaining faithful estimates of the larger-scale hydraulic conductivity structure and reliable predictions of the transport characteristics over medium- to regional-scale distances. The approach is then applied to a corresponding field scenario consisting of collocated high- resolution measurements of the electrical conductivity, as measured using a cone penetrometer testing (CPT) system, and the hydraulic conductivity, as estimated from electromagnetic flowmeter and slug test measurements, in combination with spatially exhaustive low-resolution electrical conductivity estimates obtained from surface-based electrical resistivity tomography (ERT). The corresponding results indicate that the newly developed data integration approach is indeed capable of adequately capturing both the small-scale heterogeneity as well as the larger-scale trend of the prevailing hydraulic conductivity field. The results also indicate that this novel data integration approach is remarkably flexible and robust and hence can be expected to be applicable to a wide range of geophysical and hydrological data at all scale ranges. In the second part of my thesis, I evaluate in detail the viability of sequential geostatistical resampling as a proposal mechanism for Markov Chain Monte Carlo (MCMC) methods applied to high-dimensional geophysical and hydrological inverse problems in order to allow for a more accurate and realistic quantification of the uncertainty associated with the thus inferred models. Focusing on a series of pertinent crosshole georadar tomographic examples, I investigated two classes of geostatistical resampling strategies with regard to their ability to efficiently and accurately generate independent realizations from the Bayesian posterior distribution. The corresponding results indicate that, despite its popularity, sequential resampling is rather inefficient at drawing independent posterior samples for realistic synthetic case studies, notably for the practically common and important scenario of pronounced spatial correlation between model parameters. To address this issue, I have developed a new gradual-deformation-based perturbation approach, which is flexible with regard to the number of model parameters as well as the perturbation strength. Compared to sequential resampling, this newly proposed approach was proven to be highly effective in decreasing the number of iterations required for drawing independent samples from the Bayesian posterior distribution.

Examining the information content of time-lapse crosshole GPR data collected under different infiltration conditions to estimate unsaturated soil hydraulic properties

Time-lapse geophysical data acquired during transient hydrological experiments are being increasingly employed to estimate subsurface hydraulic properties at the field scale. In particular, crosshole ground-penetrating radar (GPR) data, collected while water infiltrates into the subsurface either by natural or artificial means, have been demonstrated in a number of studies to contain valuable information concerning the hydraulic properties of the unsaturated zone. Previous work in this domain has considered a variety of infiltration conditions and different amounts of time-lapse GPR data in the estimation procedure. However, the particular benefits and drawbacks of these different strategies as well as the impact of a variety of key and common assumptions remain unclear. Using a Bayesian Markov-chain-Monte-Carlo stochastic inversion methodology, we examine in this paper the information content of time-lapse zero-offset-profile (ZOP) GPR traveltime data, collected under three different infiltration conditions, for the estimation of van Genuchten-Mualem (VGM) parameters in a layered subsurface medium. Specifically, we systematically analyze synthetic and field GPR data acquired under natural loading and two rates of forced infiltration, and we consider the value of incorporating different amounts of time-lapse measurements into the estimation procedure. Our results confirm that, for all infiltration scenarios considered, the ZOP GPR traveltime data contain important information about subsurface hydraulic properties as a function of depth, with forced infiltration offering the greatest potential for VGM parameter refinement because of the higher stressing of the hydrological system. Considering greater amounts of time-lapse data in the inversion procedure is also found to help refine VGM parameter estimates. Quite importantly, however, inconsistencies observed in the field results point to the strong possibility that posterior uncertainties are being influenced by model structural errors, which in turn underlines the fundamental importance of a systematic analysis of such errors in future related studies.

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Estimating vadose zone hydraulic properties using ground penetrating radar: The impact of prior information

A number of geophysical methods, such as ground-penetrating radar (GPR), have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, the stochastic inversion of such data within a coupled geophysical-hydrological framework may allow for the effective estimation of vadose zone hydraulic parameters and their corresponding uncertainties. A critical issue in stochastic inversion is choosing prior parameter probability distributions from which potential model configurations are drawn and tested against observed data. A well chosen prior should reflect as honestly as possible the initial state of knowledge regarding the parameters and be neither overly specific nor too conservative. In a Bayesian context, combining the prior with available data yields a posterior state of knowledge about the parameters, which can then be used statistically for predictions and risk assessment. Here we investigate the influence of prior information regarding the van Genuchten-Mualem (VGM) parameters, which describe vadose zone hydraulic properties, on the stochastic inversion of crosshole GPR data collected under steady state, natural-loading conditions. We do this using a Bayesian Markov chain Monte Carlo (MCMC) inversion approach, considering first noninformative uniform prior distributions and then more informative priors derived from soil property databases. For the informative priors, we further explore the effect of including information regarding parameter correlation. Analysis of both synthetic and field data indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when we combine these data with a realistic, informative prior.

Bayesian-MCMC inversion of time-lapse geophysical data to characterize vadose zone hydraulic behaviour

Geophysical methods have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, time-lapse geophysical data, when coupled with a hydrological model and inverted stochastically, may allow for the effective estimation of subsurface hydraulic parameters and their corresponding uncertainties. In this study, we use a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach to investigate how much information regarding vadose zone hydraulic properties can be retrieved from time-lapse crosshole GPR data collected at the Arrenaes field site in Denmark during a forced infiltration experiment.

Impact of controlled changes in grain size and pore space characteristics on the hydraulic conductivity and spectral induced polarization response of "proxies" of saturated alluvial sediments

Understanding the influence of pore space characteristics on the hydraulic conductivity and spectral induced polarization (SIP) response is critical for establishing relationships between the electrical and hydrological properties of surficial unconsolidated sedimentary deposits, which host the bulk of the world's readily accessible groundwater resources. Here, we present the results of laboratory SIP measurements on industrial-grade, saturated quartz samples with granulometric characteristics ranging from fine sand to fine gravel, which can be regarded as proxies for widespread alluvial deposits. We altered the pore space characteristics by changing (i) the grain size spectra, (ii) the degree of compaction, and (iii) the level of sorting. We then examined how these changes affect the SIP response, the hydraulic conductivity, and the specific surface area of the considered samples. In general, the results indicate a clear connection between the SIP response and the granulometric as well as pore space characteristics. In particular, we observe a systematic correlation between the hydraulic conductivity and the relaxation time of the Cole-Cole model describing the observed SIP effect for the entire range of considered grain sizes. The results do, however, also indicate that the detailed nature of these relations depends strongly on variations in the pore space characteristics, such as, for example, the degree of compaction. The results of this study underline the complexity of the origin of the SIP signal as well as the difficulty to relate it to a single structural factor of a studied sample, and hence raise some fundamental questions with regard to the practical use of SIP measurements as site- and/or sample-independent predictors of the hydraulic conductivity.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.

Caregiver's interpret infants' early gestures based on shared knowledge about referents

Gestures are the first forms of conventional communication that young children develop in order to intentionally convey a specific message. However, at first, infants rarely communicate successfully with their gestures, prompting caregivers to interpret them. Although the role of caregivers in early communication development has been examined, little is known about how caregivers attribute a specific communicative function to infants' gestures. In this study, we argue that caregivers rely on the knowledge about the referent that is shared with infants in order to interpret what communicative function infants wish to convey with their gestures. We videotaped interactions from six caregiver-infant dyads playing with toys when infants were 8, 10, 12, 14, and 16 months old. We coded infants' gesture production and we determined whether caregivers interpreted those gestures as conveying a clear communicative function or not; we also coded whether infants used objects according to their conventions of use as a measure of shared knowledge about the referent. Results revealed an association between infants' increasing knowledge of object use and maternal interpretations of infants' gestures as conveying a clear communicative function. Our findings emphasize the importance of shared knowledge in shaping infants' emergent communicative skills.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

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Developing a predictive understanding of subsurface flow and transport is complicated by the disparity of scales across which controlling hydrological properties and processes span. Conventional techniques for characterizing hydrogeological properties (such as pumping, slug, and flowmeter tests) typically rely on borehole access to the subsurface. Because their spatial extent is commonly limited to the vicinity near the wellbores, these methods often cannot provide sufficient information to describe key controls on subsurface flow and transport. The field of hydrogeophysics has evolved in recent years to explore the potential that geophysical methods hold for improving the quantification of subsurface properties and processes relevant for hydrological investigations. This chapter is intended to familiarize hydrogeologists and water-resource professionals with the state of the art as well as existing challenges associated with hydrogeophysics. We provide a review of the key components of hydrogeophysical studies, which include: geophysical methods commonly used for shallow subsurface characterization; petrophysical relationships used to link the geophysical properties to hydrological properties and state variables; and estimation or inversion methods used to integrate hydrological and geophysical measurements in a consistent manner. We demonstrate the use of these different geophysical methods, petrophysical relationships, and estimation approaches through several field-scale case studies. Among other applications, the case studies illustrate the use of hydrogeophysical approaches to quantify subsurface architecture that influence flow (such as hydrostratigraphy and preferential pathways); delineate anomalous subsurface fluid bodies (such as contaminant plumes); monitor hydrological processes (such as infiltration, freshwater-seawater interface dynamics, and flow through fractures); and estimate hydrological properties (such as hydraulic conductivity) and state variables (such as water content). The case studies have been chosen to illustrate how hydrogeophysical approaches can yield insights about complex subsurface hydrological processes, provide input that improves flow and transport predictions, and provide quantitative information over field-relevant spatial scales. The chapter concludes by describing existing hydrogeophysical challenges and associated research needs. In particular, we identify the area of quantitative watershed hydrogeophysics as a frontier area, where significant effort is required to advance the estimation of hydrological properties and processes (and their uncertainties) over spatial scales relevant to the management of water resources and contaminants.

High-resolution numerical modelling of flow-vegetation interactions

In this paper, we present and apply a new three-dimensional model for the prediction of canopy-flow and turbulence dynamics in open-channel flow. The approach uses a dynamic immersed boundary technique that is coupled in a sequentially staggered manner to a large eddy simulation. Two different biomechanical models are developed depending on whether the vegetation is dominated by bending or tensile forces. For bending plants, a model structured on the Euler-Bernoulli beam equation has been developed, whilst for tensile plants, an N-pendula model has been developed. Validation against flume data shows good agreement and demonstrates that for a given stem density, the models are able to simulate the extraction of energy from the mean flow at the stem-scale which leads to the drag discontinuity and associated mixing layer.