Search

[EN] Space -temporal distribution of the contaminant plumes and aquifer properties is critical for groundwater management. However, most previous studies have focused on point source identification, barely exploring the identification of non -point sources. Xu et al. (2022) proposed to identify non -point sources but did not consider uncertainties in aquifer properties and release mass loading. In this work, we have implemented an application of the localized ensemble smoother with multiple data assimilation (LES-MDA) for the simultaneous identification of Gaussian hydraulic conductivities and non -point source parameters including Gaussian release mass -loading by assimilating both piezometric head and concentration observations in a synthetic confined aquifer. The results prove that the LES-MDA is not only capable of providing accurate identification of the spatial architecture of non -point contaminant sources and related release parameters (such as initial release time, and release duration) but also spatially heterogeneous release mass -loading and hydraulic conductivities.

[EN] Thermoelectric materials assembled in Peltier cells are an increasingly widespread option for generating electricity from residual sources and refrigeration, even at the nanoscale. These cells can cool below the nominal temperatures with an electric pulse, during short periods and for applications such as laser devices or microchips. The present article uses heuristic algorithms to improve the response of a Peltier cell by concurrently optimizing the pulse and geometry of its thermoelements. The study is based on the Finite Element method, handling full coupling and dynamics of the thermal, electric, and mechanical fields and temperature dependency of the material properties. The optimization algorithm is Simulated Annealing, capable of discarding local minima to reach robust results and permitting set limiting factors such as the maximum stress. The main novelty lies in multilayered geometries and pulse shapes that can reproduce any geometry and pulse virtually. First, a complete parametric analysis under constant pulse is presented to understand the complexities of the temperature, electric flux, and stress distributions in these layered geometries. Second, combined optimizations are discussed. The targets are overcooling temperature, time to reach it, overheating minimization, overcooling duration, and combinations. In the best cases, the first target is doubled, the second is reduced to a few milliseconds, the third is null, and the duration can be 95% of the pulse while reducing the stress up to 40%.

[EN] Thermoelectric materials assembled in Peltier cells are an increasingly widespread option for generating electricity from residual sources and refrigeration, even at the nanoscale. These cells can cool below the nominal temperatures with an electric pulse, during short periods and for applications such as laser devices or microchips. The present article uses heuristic algorithms to improve the response of a Peltier cell by concurrently optimizing the pulse and geometry of its thermoelements. The study is based on the Finite Element method, handling full coupling and dynamics of the thermal, electric, and mechanical fields and temperature dependency of the material properties. The optimization algorithm is Simulated Annealing, capable of discarding local minima to reach robust results and permitting set limiting factors such as the maximum stress. The main novelty lies in multilayered geometries and pulse shapes that can reproduce any geometry and pulse virtually. First, a complete parametric analysis under constant pulse is presented to understand the complexities of the temperature, electric flux, and stress distributions in these layered geometries. Second, combined optimizations are discussed. The targets are overcooling temperature, time to reach it, overheating minimization, overcooling duration, and combinations. In the best cases, the first target is doubled, the second is reduced to a few milliseconds, the third is null, and the duration can be 95% of the pulse while reducing the stress up to 40%.

[EN] Automatic interpolation of precipitation maps combining rain gauge and radar data has been done in the past but considering only the data collected at a given time interval. Since radar and rain gauge data are collected at short intervals, a natural extension of previous works is to account for temporal correlations and to include time into the interpolation process. In this work, rainfall is interpolated using data from the current time interval and the previous one. Interpolation is carried out using kriging with external drift, in which the radar rainfall estimate is the drift, and the mean precipitation is set to zero at the locations where the radar estimate is zero. The rainfall covariance is modeled as non-stationary in time, and the space system of reference moves with the storm. This movement serves to maximize the collocated correlation between consecutive time intervals. The proposed approach is analyzed for four episodes that took place in Catalonia (Spain). It is compared with three other approaches: (i) radar estimation, (ii) kriging with external drift using only the data from the same time interval, and (iii) kriging with external drift using data from two consecutive time intervals but not accounting for the displacement of the storm. The comparisons are performed using cross-validation. In all four episodes, the proposed approach outperforms the other three approaches. It is important to account for temporal correlation and use a Lagrangian system of coordinates that tracks the rainfall movement.

[EN] Automatic interpolation of precipitation maps combining rain gauge and radar data has been done in the past but considering only the data collected at a given time interval. Since radar and rain gauge data are collected at short intervals, a natural extension of previous works is to account for temporal correlations and to include time into the interpolation process. In this work, rainfall is interpolated using data from the current time interval and the previous one. Interpolation is carried out using kriging with external drift, in which the radar rainfall estimate is the drift, and the mean precipitation is set to zero at the locations where the radar estimate is zero. The rainfall covariance is modeled as non-stationary in time, and the space system of reference moves with the storm. This movement serves to maximize the collocated correlation between consecutive time intervals. The proposed approach is analyzed for four episodes that took place in Catalonia (Spain). It is compared with three other approaches: (i) radar estimation, (ii) kriging with external drift using only the data from the same time interval, and (iii) kriging with external drift using data from two consecutive time intervals but not accounting for the displacement of the storm. The comparisons are performed using cross-validation. In all four episodes, the proposed approach outperforms the other three approaches. It is important to account for temporal correlation and use a Lagrangian system of coordinates that tracks the rainfall movement.

[EN] Understanding a contaminant source may help in a better management and risk assessment of a polluted aquifer. However, contaminant source information may not be available when a pollutant is detected in a drinking well. The restart ensemble Kalman filter (restart EnKF, also named r-EnKF) has been demonstrated in synthetic and laboratory experiments as an efficient solution for the identification of a contaminant source. Recently, the ensemble smoother with multiple data assimilation (ES-MDA) has been proposed as an alternative to the r-EnKF as a more efficient solution given that the r-EnKF needs to restart the simulation of the state equation from time zero after each data assimilation step. An analysis, in a synthetic aquifer, of the accuracy of the ES-MDA for the simultaneous identification of a contaminant source and the spatial distribution of hydraulic conductivity by assimilating both piezometric head and concentration observations is carried out using the r-EnKF as a benchmark. The conclusion is that the ES-MDA can outperform the r-EnKF, but the expected speed advantage, associated with the possibility of assimilating all data at once, does not exist. For the ES-MDA to reach the same level of accuracy as the r-EnKF, the number of multiple data assimilations must be large, and final computing time is similar for both approaches. However, the ES-MDA can do much better than the r-EnKF if the number of iterations increases even further, with the consequent increase of computational cost.

This is the peer reviewed version of the following article: Butler, J. J., Gomez-Hernandez, J. J., Perrone, D., & Hyndman, D. (2021). Introduction to special section: The quest for sustainability of heavily stressed aquifers at regional to global scales. Water Resources Research, 57, e2021WR030446, which has been published in final form at https://doi.org/10.1029/2021WR030446. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

[EN] The source location and the time history of a pollutant released in an aquifer are very relevant information for the design of effective remediation strategies. Usually, their identification requires solving an inverse problem when the only available information about the groundwater contamination event is a sparse set of concentration data collected in the aquifer at a few points downstream from the source. Here, a novel approach is proposed to solve the inverse problem: the use of the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in the context of source contamination identification. This method is used for the simultaneous determination of the time history and the source location of a pollutant release based on observed concentration data and a calibrated numerical model of groundwater flow and mass transport in the aquifer. The ES-MDA is demonstrated in two case studies. The first one is based on an analytical solution of the flow and transport equations, aimed at the estimation of the source location and the release history of a nonreactive pollutant spreading in a two-dimensional homogeneous aquifer from a point source. For this case, different alternatives are considered for the spatial distribution of the observation points, the concentration sampling frequency, the ensemble size and the use of covariance localization and covariance inflation techniques in the formulation of the smoother. The purpose of this case is to test the new approach, analyze its performance and also to identify the conditions that render the problem ill-posed and, therefore, without solution; also, in this case, a new spatiotemporal iterative localization is presented. In the second case study, we use real data collected in a laboratory sandbox that reproduces a vertical cross-section of an unconfined aquifer with two-dimensional quasi-parallel flow between constant-head boundaries. The results show that the location, time and number of observations, the ensemble si

[EN] Stochastic upscaling of flow and reactive solute transport in a tropical soil is performed using real data collected in the laboratory. Upscaling of hydraulic conductivity, longitudinal hydrodynamic dispersion, and retardation factor were done using three different approaches of varying complexity. How uncertainty propagates after upscaling was also studied. The results show that upscaling must be taken into account if a good reproduction of the flow and transport behavior of a given soil is to be attained when modeled at larger than laboratory scales. The results also show that arrival time uncertainty was well reproduced after solute transport upscaling. This work represents a first demonstration of flow and reactive transport upscaling in a soil based on laboratory data. It also shows how simple upscaling methods can be incorporated into daily modeling practice using commercial flow and transport codes.

[EN] Spatial variation of the correlation among variables related to water flow and solute transport are important in the characterization of the spatial variability when performing uncertainty analysis and making uncertainty qualified solute transport predictions. However, the spatial variation of the correlation between solute transport parameters and soil properties are rarely studied. In this study, the spatial correlation among laboratory-measured transport parameters dispersivity and coefficient of distribution of a reactive and a nonreactive solute and soil properties were studied at the scale of a few meters using a dense sampling design. In an area of 84 m(2) and a depth of 2 m, 55 undisturbed soil samples were taken to determine the soil properties. Column experiments were performed, and the transport parameters were obtained by fitting the experimental data to the analytical solution of the advection-dispersion equation using the computer program CFITM. Stepwise multiple linear regression (MLR) was performed in order to identify the statistically significant variables. The spatial correlation of the variables and between variables were determined using the Stanford Geostatistical Modeling Software. Soil properties presented a moderate coefficient of variation, while hydraulic conductivity and transport parameters were widely dispersed. The difference between its minimum and maximum value was quite large for most of the studied variables evidencing their high variability. Both dispersivity and retardation factor were higher than the expected and this result can be related to the preferential pathways and to the non-connected micropores. None of the physical soil property was strongly correlated to the transport parameters. Coefficient of distribution was strongly correlated to the cation exchange capacity and significantly correlated to mesoporosity and microporosity. Hydraulic conductivity presented significant positive correlation to the effective porosi

[EN] Stochastic upscaling of flow and reactive solute transport in a tropical soil is performed using real data collected in the laboratory. Upscaling of hydraulic conductivity, longitudinal hydrodynamic dispersion, and retardation factor were done using three different approaches of varying complexity. How uncertainty propagates after upscaling was also studied. The results show that upscaling must be taken into account if a good reproduction of the flow and transport behavior of a given soil is to be attained when modeled at larger than laboratory scales. The results also show that arrival time uncertainty was well reproduced after solute transport upscaling. This work represents a first demonstration of flow and reactive transport upscaling in a soil based on laboratory data. It also shows how simple upscaling methods can be incorporated into daily modeling practice using commercial flow and transport codes.

[EN] Contaminant source identification is a key problem in handling groundwater pollution events. The ensemble Kalman filter (EnKF) is used for the spatiotemporal identification of a point contaminant source in a sandbox experiment, together with the identification of the position and length of a vertical plate inserted in the sandbox that modifies the geometry of the system. For the identification of the different parameters, observations in time of solute concentration are used, but not of piezometric head data since they were not available. A restart version of the EnKF is utilized because it is necessary to restart the forecast from time zero after each parameter update. The results show that the restart EnKF is capable of identifying both contaminant source information and aquifer-geometry-related parameters together with an uncertainty estimate of such identification.

[EN] Hydraulic conductivity (K), dispersivity (alpha) and partition coefficient (K-d) can change according to the measurement support (scale) and that is referred to as scale effect. However, there is no clear consensus about the behavior of these parameters with the change in the scale. Comparison between results obtained in different support of measurements in the field and in the laboratory can promote the discussion about scale effects on K, alpha, and K-d, and contribute to understanding how these parameters behave with the change in the scale of measurement, the main objectives of the present paper. Small and large-scale laboratory tests using undisturbed soil samples and field experiments at different scales were performed. Results show that for the same measurement condition, K, alpha, and K-d increase with scale in all studied magnitudes. Caution should be taken when using K, alpha, and K-d values in numerical models with no concern about the scale effect. The lack of consideration of the difference of scale between field and laboratory measurements and numerical model may compromise the reliability of the predictions and misrepresent the responses.

[EN] Contaminant source identification is a key problem in handling groundwater pollution events. The ensemble Kalman filter (EnKF) is used for the spatiotemporal identification of a point contaminant source in a sandbox experiment, together with the identification of the position and length of a vertical plate inserted in the sandbox that modifies the geometry of the system. For the identification of the different parameters, observations in time of solute concentration are used, but not of piezometric head data since they were not available. A restart version of the EnKF is utilized because it is necessary to restart the forecast from time zero after each parameter update. The results show that the restart EnKF is capable of identifying both contaminant source information and aquifer-geometry-related parameters together with an uncertainty estimate of such identification.

[EN] Hydraulic conductivity (K), dispersivity (alpha) and partition coefficient (K-d) can change according to the measurement support (scale) and that is referred to as scale effect. However, there is no clear consensus about the behavior of these parameters with the change in the scale. Comparison between results obtained in different support of measurements in the field and in the laboratory can promote the discussion about scale effects on K, alpha, and K-d, and contribute to understanding how these parameters behave with the change in the scale of measurement, the main objectives of the present paper. Small and large-scale laboratory tests using undisturbed soil samples and field experiments at different scales were performed. Results show that for the same measurement condition, K, alpha, and K-d increase with scale in all studied magnitudes. Caution should be taken when using K, alpha, and K-d values in numerical models with no concern about the scale effect. The lack of consideration of the difference of scale between field and laboratory measurements and numerical model may compromise the reliability of the predictions and misrepresent the responses.

[EN] Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known.

[EN] Hydraulic conductivity (K) heterogeneity is seldom considered in geotechnical practice for the impossibility of sampling the entire area of interest and for the difficulty of accounting for scale effects. Stochastic three-dimensional K upscaling can tackle these two problems, and a workflow is described with an application in a tropical soil. The application shows that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler while discussing the aspects to consider when performing the upscaling so that the upscaled models reproduce the average fluxes at the fine scale.

[EN] Hydraulic conductivity (K) heterogeneity is seldom considered in geotechnical practice for the impossibility of sampling the entire area of interest and for the difficulty of accounting for scale effects. Stochastic three-dimensional K upscaling can tackle these two problems, and a workflow is described with an application in a tropical soil. The application shows that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler while discussing the aspects to consider when performing the upscaling so that the upscaled models reproduce the average fluxes at the fine scale.

[EN] Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known.

[EN] The objective of this work is to determine the optimal shape, gains and duration of an electric pulse applied to a Peltier cell, together with the length of the thermoelectric to maximize cooling while min- imizing electric consumption. For this purpose, a fully coupled, multiphysics, dynamic finite-element model, which solves for the thermal, electric and mechanical fields is used. Because of the demanding computing requirements of the optimization process, a special mesh is designed and a convergence anal- ysis is carried out before using the multiphysics model. The highly non-linear optimization is done by simulated annealing, a heuristic algorithm in the Markov chain Monte-Carlo family. A preliminary para- metric investigation is presented, analyzing the impact of some of the parameters. The results of this pre- liminary analysis help to understand the effect of the different shapes in the evolution of the cold face temperature. Some of these results are expected and have already been discussed elsewhere, but others can only be explained after further analysis and a full system modeling. Pulse optimization is multiobjec- tive and multiparametric, i.e., it can consider several targets such as maximizing the cooling temperature, the cooling duration or others. The trade-offs between the different targets are studied. In all cases, stres- ses inside the thermoelement are examined at all points, and the pulses must meet the restriction that an equivalent stress is not above the allowable value.

Reliable characterization of hydraulic parameters is important for the understanding of groundwater flow and solute transport. The normal-score ensemble Kalman filter (NS-EnKF) has proven to be an effective inverse method for the characterization of non-Gaussian hydraulic conductivities by assimilating transient piezometric head data, or solute concentration data. Groundwater temperature, an easily captured state variable, has not drawn much attention as an additional state variable useful for the characterization of aquifer parameters. In this work, we jointly estimate non-Gaussian aquifer parameters (hydraulic conductivities and porosities) by assimilating three kinds of state variables (piezometric head, solute concentration, and groundwater temperature) using the NS-EnKF. A synthetic example including seven tests is designed, and used to evaluate the ability to characterize hydraulic conductivity and porosity in a non-Gaussian setting by assimilating different numbers and types of state variables. The results show that characterization of aquifer parameters can be improved by assimilating groundwater temperature data and that the main patters of the non-Gaussian reference fields can be retrieved with more accuracy and higher precision if multiple state variables are assimilated.

[EN] When a contaminant is detected in a drinking well, source location, initial contaminant release time, and initial contaminant concentration are, in many cases, unknown; the responsible party may have disappeared and the identification of when and where the contamination happened may become difficult. Although contaminant source identification has been studied extensively in the last decades, we proposeto our knowledge, for the first timethe use of the ensemble Kalman filter (EnKF), which has proven to be a powerful algorithm for inverse modeling. The EnKF is tested in a two-dimensional synthetic deterministic aquifer, identifying, satisfactorily, the source location, the release time, and the release concentration, together with an assessment of the uncertainty associated with this identification.

Reliable characterization of hydraulic parameters is important for the understanding of groundwater flow and solute transport. The normal-score ensemble Kalman filter (NS-EnKF) has proven to be an effective inverse method for the characterization of non-Gaussian hydraulic conductivities by assimilating transient piezometric head data, or solute concentration data. Groundwater temperature, an easily captured state variable, has not drawn much attention as an additional state variable useful for the characterization of aquifer parameters. In this work, we jointly estimate non-Gaussian aquifer parameters (hydraulic conductivities and porosities) by assimilating three kinds of state variables (piezometric head, solute concentration, and groundwater temperature) using the NS-EnKF. A synthetic example including seven tests is designed, and used to evaluate the ability to characterize hydraulic conductivity and porosity in a non-Gaussian setting by assimilating different numbers and types of state variables. The results show that characterization of aquifer parameters can be improved by assimilating groundwater temperature data and that the main patters of the non-Gaussian reference fields can be retrieved with more accuracy and higher precision if multiple state variables are assimilated.

[EN] When a contaminant is detected in a drinking well, source location, initial contaminant release time, and initial contaminant concentration are, in many cases, unknown; the responsible party may have disappeared and the identification of when and where the contamination happened may become difficult. Although contaminant source identification has been studied extensively in the last decades, we proposeto our knowledge, for the first timethe use of the ensemble Kalman filter (EnKF), which has proven to be a powerful algorithm for inverse modeling. The EnKF is tested in a two-dimensional synthetic deterministic aquifer, identifying, satisfactorily, the source location, the release time, and the release concentration, together with an assessment of the uncertainty associated with this identification.

Hu et al. (2013) proposed an approach to update complex geological fades models generated by multiple-point geostatistical simulation while keeping geological and statistical consistency. Their approach is based on mapping the fades realization onto the spatially uncorrelated uniform random numbers used by the sequential multiple-point simulation to generate the facies realization itself. The ensemble Kalman filter was then used to update the uniform random number realizations, which were then used to generate a new fades realization by multiple-point simulation. This approach has not a good performance that we attribute to the fact that, being the probabilities random and spatially uncorrelated, their correlation with the state variable (piezometric heads) is very weak, and the Kalman gain is always small. The approach is reminiscent of the probability field simulation, which also maps the conductivity realizations onto a field of uniform random numbers; although the mapping now is done using the local conditional distribution functions built based on a prior statistical model and the conditioning data. Contrary to Hu et al. (2013) approach, this field of uniform random numbers, termed a probability field, displays spatial patterns related to the conductivity spatial patterns, and, therefore, the correlation between probabilities and state variable is as strong as the correlation between conductivities and state variable could be. Similarly to Hu et al. (2013), we propose to use the ensemble Kalman filter to update the probability fields, and show that the existence of this correlation between probability values and state variables provides better results.

For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. © 2015 Elsevier Ltd. All rights reserved.

Inverse sequential simulation (iSS) is a new inverse modeling approach for the characterization of hydraulic conductivity fields based on sequential simulation. It is described and demonstrated in a synthetic aquifer with non-Gaussian spatial features, and compared against the normal-score ensemble Kalman filter (NS-EnKF). The new approach uses the sequential simulation paradigm to generate realizations borrowing from the ensemble Kalman filter the idea of using the experimental nonstationary cross-covariance between conductivities and piezometric heads computed on an ensemble of realizations. The resulting approach is fully capable of retrieving the non-Gaussian patterns of the reference field after conditioning on the piezometric heads with results comparable of those obtained by the NS-EnKF.

For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. © 2015 Elsevier Ltd. All rights reserved.

Inverse sequential simulation (iSS) is a new inverse modeling approach for the characterization of hydraulic conductivity fields based on sequential simulation. It is described and demonstrated in a synthetic aquifer with non-Gaussian spatial features, and compared against the normal-score ensemble Kalman filter (NS-EnKF). The new approach uses the sequential simulation paradigm to generate realizations borrowing from the ensemble Kalman filter the idea of using the experimental nonstationary cross-covariance between conductivities and piezometric heads computed on an ensemble of realizations. The resulting approach is fully capable of retrieving the non-Gaussian patterns of the reference field after conditioning on the piezometric heads with results comparable of those obtained by the NS-EnKF.

This is a book review

Hu et al. (2013) proposed an approach to update complex geological fades models generated by multiple-point geostatistical simulation while keeping geological and statistical consistency. Their approach is based on mapping the fades realization onto the spatially uncorrelated uniform random numbers used by the sequential multiple-point simulation to generate the facies realization itself. The ensemble Kalman filter was then used to update the uniform random number realizations, which were then used to generate a new fades realization by multiple-point simulation. This approach has not a good performance that we attribute to the fact that, being the probabilities random and spatially uncorrelated, their correlation with the state variable (piezometric heads) is very weak, and the Kalman gain is always small. The approach is reminiscent of the probability field simulation, which also maps the conductivity realizations onto a field of uniform random numbers; although the mapping now is done using the local conditional distribution functions built based on a prior statistical model and the conditioning data. Contrary to Hu et al. (2013) approach, this field of uniform random numbers, termed a probability field, displays spatial patterns related to the conductivity spatial patterns, and, therefore, the correlation between probabilities and state variable is as strong as the correlation between conductivities and state variable could be. Similarly to Hu et al. (2013), we propose to use the ensemble Kalman filter to update the probability fields, and show that the existence of this correlation between probability values and state variables provides better results.

This is a book review

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11004-013-9504-z"

[EN] Parameter identification is an essential step in constructing a groundwater model. The process of recognizing model parameter values by conditioning on observed data of the state variable is referred to as the inverse problem. A series of inverse methods has been proposed to solve the inverse problem, ranging from trial-and-error manual calibration to the current complex automatic data assimilation algorithms. This paper does not attempt to be another overview paper on inverse models, but rather to analyze and track the evolution of the inverse methods over the last decades, mostly within the realm of hydrogeology, revealing their transformation, motivation and recent trends. Issues confronted by the inverse problem, such as dealing with multiGaussianity and whether or not to preserve the prior statistics are discussed. (C) 2013 Elsevier Ltd. All rights reserved.

The final publication is available at Springer via http://dx.doi.org/10.1007/s12665-013-2704-5, Characterizing the spatial patterns of variability is a fundamental aspect when investigating what could be the causes behind the spatial spreading of a set of variables. In this paper, a large multivariate dataset from the southeast of Belgium has been analyzed using factorial kriging. The purpose of the study is to explore and retrieve possible scales of spatial variability of heavy metals. This is achieved by decomposing the variance-covariance matrix of the multivariate sample into coregionalization matrices, which are, in turn, decomposed into transformation matrices, which serve to decompose each regionalized variable as a sum of independent factors. Then, factorial cokriging is used to produce maps of the factors explaining most of the variance, which can be compared with maps of the underlying lithology. For the dataset analyzes, this comparison identifies a few point scale concentrations that may reflect anthropogenic contamination, and it also identifies local and regional scale anomalies clearly correlated to the underlying geology and to known mineralizations. The results from this analysis could serve to guide the authorities in identifying those areas which need remediation.

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11004-013-9498-6"

The final publication is available at Springer via http://dx.doi.org/10.1007/s12665-013-2704-5, Characterizing the spatial patterns of variability is a fundamental aspect when investigating what could be the causes behind the spatial spreading of a set of variables. In this paper, a large multivariate dataset from the southeast of Belgium has been analyzed using factorial kriging. The purpose of the study is to explore and retrieve possible scales of spatial variability of heavy metals. This is achieved by decomposing the variance-covariance matrix of the multivariate sample into coregionalization matrices, which are, in turn, decomposed into transformation matrices, which serve to decompose each regionalized variable as a sum of independent factors. Then, factorial cokriging is used to produce maps of the factors explaining most of the variance, which can be compared with maps of the underlying lithology. For the dataset analyzes, this comparison identifies a few point scale concentrations that may reflect anthropogenic contamination, and it also identifies local and regional scale anomalies clearly correlated to the underlying geology and to known mineralizations. The results from this analysis could serve to guide the authorities in identifying those areas which need remediation.

Bucket elevators are efficient machines to transport granular materials in industrial and civil engineering applications. These materials are composed of hundreds, thousands or even more particles, the global behavior of which is defined by contact interactions. The first attempts to analyze the transportation of granular materials were treated by very simple continuum methods that do not take into account these interactions, producing simulations that do not fit the experimental results accurately. Given the internal discontinuity nature of granular media, it is reasonable to use numerical methods to model their behavior, such as discontinuous deformation analysis (DDA)-a member of the discrete element method family that started to be used in the 90s to analyze similar problems. The version of DDA used in the current work treats grains as rigid circular particles with friction, damping and eventually cohesion with the objective of simulating and analyzing in detail the discharge of granular materials with bucket elevators. A deterministic computer code has been implemented and validated against simplified analytical formulae and experimental results taken from the literature. This computer code is then used to obtain optimum two-dimensional bucket geometries under specific working conditions. The optimization aims to maximize transport distance and to minimize remaining material, taking into account bucket velocity and the properties of the grains. The resulting geometries are discussed and compared against standard designs.

[EN] Parameter identification is an essential step in constructing a groundwater model. The process of recognizing model parameter values by conditioning on observed data of the state variable is referred to as the inverse problem. A series of inverse methods has been proposed to solve the inverse problem, ranging from trial-and-error manual calibration to the current complex automatic data assimilation algorithms. This paper does not attempt to be another overview paper on inverse models, but rather to analyze and track the evolution of the inverse methods over the last decades, mostly within the realm of hydrogeology, revealing their transformation, motivation and recent trends. Issues confronted by the inverse problem, such as dealing with multiGaussianity and whether or not to preserve the prior statistics are discussed. (C) 2013 Elsevier Ltd. All rights reserved.

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11004-013-9504-z"

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11004-013-9498-6"

Methods based on multiple-point statistics (MPS) have been routinely used to characterize complex geological formations in the last decade. These methods use the available static data (for example, measured conductivities) for conditioning. Integrating dynamic data (for example, measured transient piezometric head data) into the same framework is challenging because of the complex non-linear relationship between the dynamic response and geology. The Ensemble PATtern (EnPAT) search method was recently developed as a promising technique to handle this problem. In this approach, a pattern is postulated to be composed of both parameter and state variables, and then, parameter values are sequentially (point-wise) simulated by directly sampling the matched pattern from an ensemble of training images of both geologic parameters and state variables. As a consequence, the updated ensemble of realizations of the geological parameters preserve curvilinear structures (i.e., non-multiGaussanity) as well as the complex relationship between static and dynamic data. Moreover, the uncertainty of flow and transport predictions can be assessed using the updated ensemble of geological models. In this work, we further modify the EnPAT method by introducing the pilot-point concept into the algorithm. More specifically, the parameter values at a set of randomly selected pilot point locations are simulated by the pattern searching procedure, and then a faster MPS method is used to complete the simulation by conditioning to the previously simulated pilot point values. This pilot point guided MPS implementation results in lower computational cost and more accurate inference of the parameter field. In addition, in some situations where there is sparsity of measured geologic static data, the EnPAT algorithm is extended to work only with the dynamic data. We employed a synthetic example to demonstrate the effectiveness of pilot points in the implementation of EnPAT, and also the capability of d

Methods based on multiple-point statistics (MPS) have been routinely used to characterize complex geological formations in the last decade. These methods use the available static data (for example, measured conductivities) for conditioning. Integrating dynamic data (for example, measured transient piezometric head data) into the same framework is challenging because of the complex non-linear relationship between the dynamic response and geology. The Ensemble PATtern (EnPAT) search method was recently developed as a promising technique to handle this problem. In this approach, a pattern is postulated to be composed of both parameter and state variables, and then, parameter values are sequentially (point-wise) simulated by directly sampling the matched pattern from an ensemble of training images of both geologic parameters and state variables. As a consequence, the updated ensemble of realizations of the geological parameters preserve curvilinear structures (i.e., non-multiGaussanity) as well as the complex relationship between static and dynamic data. Moreover, the uncertainty of flow and transport predictions can be assessed using the updated ensemble of geological models. In this work, we further modify the EnPAT method by introducing the pilot-point concept into the algorithm. More specifically, the parameter values at a set of randomly selected pilot point locations are simulated by the pattern searching procedure, and then a faster MPS method is used to complete the simulation by conditioning to the previously simulated pilot point values. This pilot point guided MPS implementation results in lower computational cost and more accurate inference of the parameter field. In addition, in some situations where there is sparsity of measured geologic static data, the EnPAT algorithm is extended to work only with the dynamic data. We employed a synthetic example to demonstrate the effectiveness of pilot points in the implementation of EnPAT, and also the capability of d

The localized normal-score ensemble Kalman filter (NS-EnKF) coupled with covariance inflation is used to characterize the spatial variability of a channelized bimodal hydraulic conductivity field, for which the only existing prior information about conductivity is its univariate marginal distribution. We demonstrate that we can retrieve the main patterns of the reference field by assimilating a sufficient number of piezometric observations using the NS-EnKF. The possibility of characterizing the conductivity spatial variability using only piezometric head data shows the importance of accounting for these data in inverse modeling.

The localized normal-score ensemble Kalman filter (NS-EnKF) coupled with covariance inflation is used to characterize the spatial variability of a channelized bimodal hydraulic conductivity field, for which the only existing prior information about conductivity is its univariate marginal distribution. We demonstrate that we can retrieve the main patterns of the reference field by assimilating a sufficient number of piezometric observations using the NS-EnKF. The possibility of characterizing the conductivity spatial variability using only piezometric head data shows the importance of accounting for these data in inverse modeling.

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. By comparison with a more standard implementation of the EnKF, the NS-EnKF gives better results with regard to histogram preservation, uncertainty assessment, and transport predictions. © 2011 International Association for Mathematical Geosciences.