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See detailUncertainty in training image-based inversion of hydraulic head data constrained to ERT data: workflow and case study
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Caers, Jef

in Water Resources Research (2015), 51

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the ... [more ▼]

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper-Bayes philosophy, that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site specific data (proportions of facies). Prior spatial uncertainty is modeled using multiple-point geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a non-zero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimate prior uncertainty (without data) through a process of probabilistic falsification. [less ▲]

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See detailModeling climate change impacts on groundwater resources using transient stochastic climatic scenarios
Goderniaux, Pascal ULg; Brouyère, Serge ULg; Blenkinsop, Stephen et al

in Water Resources Research (2011), 47

Several studies have highlighted the potential negative impact of climate change on groundwater reserves but additional work is required to help water managers to plan for future changes. In particular ... [more ▼]

Several studies have highlighted the potential negative impact of climate change on groundwater reserves but additional work is required to help water managers to plan for future changes. In particular, existing studies provide projections for a stationary climate representative of the end of the century, although information is demanded for the near-future. Such time-slice experiments fail to account for the transient nature of climatic changes over the century. Moreover, uncertainty linked to natural climate variability is not explicitly considered in previous studies. In this study, we substantially improve upon the state-of-the-art by using a sophisticated transient weather generator (WG) in combination with an integrated surface-subsurface hydrological model (Geer basin, Belgium) developed with the finite element modelling software 'HydroGeoSphere'. This version of the WG enables the stochastic generation of large numbers of equiprobable climatic time series, representing transient climate change, and used to assess impacts in a probabilistic way. For the Geer basin, 30 equiprobable climate change scenarios from 2010 to 2085 have been generated for each of 6 different RCMs. Results show that although the 95% confidence intervals calculated around projected groundwater levels remain large, the climate change signal becomes stronger than that of natural climate variability by 2085. Additionally, the WG ability to simulate transient climate change enabled the assessment of the likely timescale and associated uncertainty of a specific impact, providing managers with additional information when planning further investment. This methodology constitutes a real improvement in the field of groundwater projections under climate change conditions. [less ▲]

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See detailQuantifying hyporheic exchange at high spatial resolution using natural temperature variations along a first order stream
Westhoff, Martijn ULg; Gooseff, M. N.; Bogaard, T. A. et al

in Water Resources Research (2011), 47

Hyporheic exchange is an important process that underpins stream ecosystem function, and there have been numerous ways to characterize and quantify exchange flow rates and hyporheic zone size. The most ... [more ▼]

Hyporheic exchange is an important process that underpins stream ecosystem function, and there have been numerous ways to characterize and quantify exchange flow rates and hyporheic zone size. The most common approach, using conservative stream tracer experiments and 1-D solute transport modeling, results in oversimplified representations of the system. Here we present a new approach to quantify hyporheic exchange and the size of the hyporheic zone (HZ) using high-resolution temperature measurements and a coupled 1-D transient storage and energy balance model to simulate in-stream water temperatures. Distributed temperature sensing was used to observe in-stream water temperatures with a spatial and temporal resolution of 2 and 3 min, respectively. The hyporheic exchange coefficient (which describes the rate of exchange) and the volume of the HZ were determined to range between 0 and 2.7 × 10−3 s−1 and 0 and 0.032 m3 m−1, respectively, at a spatial resolution of 1–10 m, by simulating a time series of in-stream water temperatures along a 565 m long stretch of a small first-order stream in central Luxembourg. As opposed to conventional stream tracer tests, two advantages of this approach are that exchange parameters can be determined for any stream segment over which data have been collected and that the depth of the HZ can be estimated as well. Although the presented method was tested on a small stream, it has potential for any stream where rapid (in regard to time) temperature change of a few degrees can be obtained. [less ▲]

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See detailBayesian Data Fusion for water table interpolation: incorporating a hydrogeological conceptual model in kriging
Peeters, Luk; Fasbender, Dominique; Batelaan, Okke et al

in Water Resources Research (2010), 46(8), 08532

The creation of a contour map of the water table in an unconfined aquifer based on head measurements is often the first step in any hydrogeological study. Geostatistical interpolation methods (e.g ... [more ▼]

The creation of a contour map of the water table in an unconfined aquifer based on head measurements is often the first step in any hydrogeological study. Geostatistical interpolation methods (e.g. kriging) may provide exact interpolated groundwater levels at the measurement locations, but often fail to represent the hydrogeological flow system. A physically based, numerical groundwater model with spatially variable parameters and inputs is more adequate in representing a flow system. Due to the difficulty in parameterization and solving the inverse problem however, an often considerable difference between calculated and observed heads will remain. In this study the water table interpolation methodology presented by Fasbender et al. (2008), in which the results of a kriging interpolation are combined with information from a drainage network and a Digital Elevation Model (DEM), using the Bayesian Data Fusion framework (Bogaert and Fasbender, 2007), is extended to incorporate information from a tuned analytic element groundwater model. The resulting interpolation is exact at the measurement locations while the shape of the head contours is in accordance with the conceptual information incorporated in the groundwater flow model. The Bayesian Data Fusion methodology is applied to a regional, unconfined aquifer in Central Belgium. A cross-validation procedure shows that the predictive capability of the interpolation at unmeasured locations benefits from the Bayesian Data Fusion of the three data sources (kriging, DEM and groundwater model), compared to the individual data sources or any combination of two data sources. [less ▲]

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See detailOn the value of conditioning data to reduce conceptual model uncertainty in groundwater modeling
Rojas, Rodrigo; Feyen, Luc; Batelaan, Okke et al

in Water Resources Research (2010), 46(8), 08520

Recent applications of multi-model methods have demonstrated their potential in quantifying conceptual model uncertainty in groundwater modeling applications. To date, however, little is known about the ... [more ▼]

Recent applications of multi-model methods have demonstrated their potential in quantifying conceptual model uncertainty in groundwater modeling applications. To date, however, little is known about the value of conditioning to constrain the ensemble of conceptualizations, to differentiate among retained alternative conceptualizations, and to reduce conceptual model uncertainty. We address these questions by conditioning multi-model simulations on measurements of hydraulic conductivity and observations of system-state variables and evaluating the e ffects on (i) the posterior multi-model statistics and (ii) the contribution of conceptual model uncertainty to the predictive uncertainty. Multi-model aggregation and conditioning is performed by combining the generalized likelihood uncertainty estimation (GLUE) method and Bayesian model averaging (BMA). As an illustrative example we employ a 3-dimensional hypothetical system under steady-state conditions, for which uncertainty about the conceptualization is expressed by an ensemble (M) of 7 models with varying complexity. Results show that conditioning on heads allowed for the exclusion of the two simplest models, but that their information content is limited to further diff erentiate among the retained conceptualizations. Conditioning on increasing numbers of conductivity measurements allowed for a further reffinement of the ensemble M and resulted in an increased precision and accuracy of the multi-model predictions. For some groundwater flow components not included as conditioning data, however, the gain in accuracy and precision was partially o ffset by strongly deviating predictions of a single conceptualization. Identifying the conceptualization producing the most deviating predictions may guide data collection campaigns aimed at acquiring data to further eliminate such conceptualizations. Including groundwater flow and river discharge observations further allowed for a better diff erentiation among alternative conceptualizations and drastic reductions of the predictive variances. Results strongly advocate the use of observations less commonly available than groundwater heads to reduce conceptual model uncertainty in groundwater modeling. [less ▲]

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See detailInfluence of evaporation and seepage on the convergence of a ventilated cavity
Gerard, Pierre ULg; Charlier, Robert ULg; Chambon, René et al

in Water Resources Research (2008), 44

In the design of nuclear waste disposals, an important topic concerns the development of an excavated damage zone, where permeability increases. A correct numerical prediction of the coupled processes ... [more ▼]

In the design of nuclear waste disposals, an important topic concerns the development of an excavated damage zone, where permeability increases. A correct numerical prediction of the coupled processes occurring during excavation is therefore needed. In this paper, a nonclassical hydraulic boundary condition is described. It mixes two modes of water exchanges in partial saturation: seepage and evaporation flows. Seepage flow avoids unphysical water inflow into the rock mass, which might be obtained with usual boundary condition in dilatant geomaterial. Evaporation flows enable the thermodynamical equilibrium between air relative humidity in the cavity and in the rock mass. The numerical modeling of a cavity excavation in dilatant geomaterial is carried out. The results show the influence of the hydraulic boundary condition on the convergence of the cavity. Depending on the value of the transfer coefficient, the proposed numerical model can recover the results obtained with an imposed atmospheric pressure or suction at the cavity wall. The determination of the mass transfer coefficient is thus needed and can be achieved through drying experiments or can be estimated thanks to in situ measurements. [less ▲]

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See detailConceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging
Rojas, Rodrigo; Feyen, Luc; Dassargues, Alain ULg

in Water Resources Research (2008), 44

Uncertainty assessments in groundwater modeling applications typically attribute all sources of uncertainty to errors in parameters and inputs, neglecting what may be the primary source of uncertainty ... [more ▼]

Uncertainty assessments in groundwater modeling applications typically attribute all sources of uncertainty to errors in parameters and inputs, neglecting what may be the primary source of uncertainty, namely, errors in the conceptualization of the system.Confining the set of plausible system representations to a single model leads to underdispersive and prone-to-bias predictions. In this work, we present a general and flexible approach that combines generalized likelihood uncertainty estimation (GLUE) and Bayesian model averaging (BMA) to assess uncertainty in model predictions that arise from errors in model structure, inputs, and parameters. In a prior analysis, a set of plausible models is selected, and the joint prior input and parameter space is sampled to form potential simulators of the system. For each model, the likelihood measures of acceptable simulators, assigned to thembased on their ability to reproduce observed systembehavior, are integrated over the joint input and parameter space to obtain the integrated model likelihood. The latter is used to weight the predictions of the respective model in the BMA ensemble predictions. For illustrative purposes, we applied the methodology to a three-dimensional hypothetical setup. Results showed that predictions of groundwater budget terms varied considerably among competing models; despite this, a set of 16 head observations used for conditioning did not allow differentiating between the models. BMA provided average predictions that were more conservative than individual predictions obtained for individual models. Conceptual model uncertainty contributed up to 30% of the total uncertainty. The results clearly indicate the need to consider alternative conceptualizations to account for model uncertainty. [less ▲]

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See detailBayesian data fusion applied to water table spatial mapping
Fasbender, D.; Peeters, Luk; Bogaert, P. et al

in Water Resources Research (2008), 44

Water table elevations are usually sampled in space using piezometric measurements that are unfortunately expensive to obtain and are thus scarce over space. Most of the time, piezometric data are ... [more ▼]

Water table elevations are usually sampled in space using piezometric measurements that are unfortunately expensive to obtain and are thus scarce over space. Most of the time, piezometric data are sparsely distributed over large areas, thus providing limited direct information about the level of the corresponding water table. As a consequence, there is a real need for approaches that are able at the same time to (1) provide spatial predictions at unsampled locations and (2) enable the user to account for all potentially available secondary information sources that are in some way related to water table elevations. In this paper, a recently developed Bayesian data fusion (BDF) framework is applied to the problem of water table spatial mapping. After a brief presentation of the underlying theory, specific assumptions are made and discussed to account for a digital elevation model and for the geometry of a corresponding river network. On the basis of a data set for the Dijle basin in the north part of Belgium, the suggested model is then implemented and results are compared to those of standard techniques such as ordinary kriging and cokriging. Respective accuracies and precisions of these estimators are finally evaluated using a ‘‘leave-one-out’’ cross-validation procedure. Although the BDF methodology was illustrated here for the integration of only two secondary information sources (namely, a digital elevation model and the geometry of a river network), the method can be applied for incorporating an arbitrary number of secondary information sources, thus opening new avenues for the important topic of data integration in a spatial mapping context. [less ▲]

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See detailDistributed fiber-optic temperature sensing for hydrologic systems
Selker, John S.; Thévenaz, Luc; Huwald, Hendrik et al

in Water Resources Research (2006), 42(12), 12202

Instruments for distributed fiber-optic measurement of temperature are now available with temperature resolution of 0.01°C and spatial resolution of 1 m with temporal resolution of fractions of a minute ... [more ▼]

Instruments for distributed fiber-optic measurement of temperature are now available with temperature resolution of 0.01°C and spatial resolution of 1 m with temporal resolution of fractions of a minute along standard fiber-optic cables used for communication with lengths of up to 30,000 m. We discuss the spectrum of fiber-optic tools that may be employed to make these measurements, illuminating the potential and limitations of these methods in hydrologic science. There are trade-offs between precision in temperature, temporal resolution and spatial resolution, following the square root of the number of measurements made; thus brief, short measurements are less precise than measurements taken over longer spans in time and space. Five illustrative applications demonstrate configurations where the distributed temperature sensing (DTS) approach could be used: (1) lake bottom temperatures using existing communication cables, (2) temperature profile with depth in a 1400 m deep decommissioned mine shaft, (3) air-snow interface temperature profile above a snow-covered glacier (4) air-water interfacial temperature in a lake, and (5) temperature distribution along a first-order stream. In examples 3 and 4 it is shown that by winding the fiber around a cylinder, vertical spatial resolution of millimeters can be achieved. These tools may be of exceptional utility in observing a broad range of hydrologic processes including evaporation, infiltration, limnology, and the local and overall energy budget spanning scales from 0.003 to 30,000 m. This range of scales corresponds well with many of the areas of greatest opportunity for discovery in hydrologic science. [less ▲]

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See detailModeling tracer injection and well-aquifer interactions: A new mathematical and numerical approach
Brouyère, Serge ULg

in Water Resources Research (2003), 39(3),

[1] A new mathematical and numerical approach is presented to model solute exchange between a well and the surrounding aquifer for the interpretation of field tracer tests. On the basis of water and ... [more ▼]

[1] A new mathematical and numerical approach is presented to model solute exchange between a well and the surrounding aquifer for the interpretation of field tracer tests. On the basis of water and tracer mass balance equations integrated over the volume of water in the well, the approach allows for finite volumes of tracer fluid and water flush. It deals with tracer mixing and capturing in the well bore, local distortion of the flow field around the well, and possible tracer back-migration into the well. A numerical solution, implemented in the three-dimensional finite element groundwater flow and transport simulator SUFT3D, is proposed that allows for modeling nonuniform distributions of tracer mass fluxes along the well screens related to variations in aquifer hydraulic conductivity. Showing its ability to reproduce concentration evolutions monitored in a well during field tracer experiments, considering various injection conditions, validates the approach. [less ▲]

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See detailEnergy Partitioning Between Latent And Sensible Heat Flux During The Warm Season At Fluxnet Sites
Wilson, Kell B.; Baldocchi, Dennis D.; Aubinet, Marc ULg et al

in Water Resources Research (2002), 38(12),

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See detailModeling groundwater with ocean and river interaction
Carabin, Guy; Dassargues, Alain ULg

in Water Resources Research (1999), 35(8), 2347-2358

We develop and implement the groundwater model, Saturated/Unsaturated Flow and Transport in 3D (SUFT3D), to integrate water quantity/quality data and simulations with models of other hydrologic cycle ... [more ▼]

We develop and implement the groundwater model, Saturated/Unsaturated Flow and Transport in 3D (SUFT3D), to integrate water quantity/quality data and simulations with models of other hydrologic cycle components, namely, rivers and the ocean. This work was done as part of the Sea Air Land Modeling Operational Network (SALMON) project supported by the IBM International Foundation through its Environmental Research Program. The first research steps, presented here, address the simulation of typical hydrologic conditions to demonstrate SUFT3D's effectiveness and accuracy. The theory behind the modeling of seawater intrusion and groundwater-river interaction is summarized along with the numerical methods and characteristics of SUFT3D. The code was applied to different, increasingly complex scenarios: confined to unconfined conditions, local to regional scale, homogeneous to increasing heterogeneity, two- to three-dimensional. Of particular interest were the impacts of different boundary conditions and influence of river interactions on seawater intrusion. Results are illustrated, discussed, and compared, when possible, to those in the literature. Simulating groundwater exchange between both the river and the ocean has provided interesting results that better depict the dynamics of flow and transport in coastal zone groundwater systems. [less ▲]

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