Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Accounting for Aquifer Heterogeneity from Geological Data to Management Tools

A nested workflow of multiple‐point geostatistics (MPG) and sequential Gaussian simulation (SGS) was tested on a study area of 6 km² located about 20 km northwest of Quebec City, Canada. In order to assess its geological and hydrogeological parameter heterogeneity and to provide tools to evaluate uncertainties in aquifer management, direct and indirect field measurements are used as inputs in the geostatistical simulations to reproduce large and small‐scale heterogeneities. To do so, the lithological information is first associated to equivalent hydrogeological facies (hydrofacies) according to hydraulic properties measured at several wells. Then, heterogeneous hydrofacies (HF) realizations are generated using a prior geological model as training image (TI) with the MPG algorithm. The hydraulic conductivity (K) heterogeneity modeling within each HF is finally computed using SGS algorithm. Different K models are integrated in a finite‐element hydrogeological model to calculate multiple transport simulations. Different scenarios exhibit variations in mass transport path and dispersion associated with the large‐ and small‐scale heterogeneity respectively. Three‐dimensional maps showing the probability of overpassing different thresholds are presented as examples of management tools.     

Identification and mapping of riverbed sediment facies in the Columbia River through integration of field observations and numerical simulations

In the Hanford Reach of the Columbia River, a thin layer of recent alluvium overlies the sedimentary formations that comprise the unconfined groundwater aquifer. Experimental and modelling studies have demonstrated that this alluvial layer exerts significant control on the exchange of groundwater and surface water (hydrologic exchange flux), and is associated with elevated levels of biogeochemical activity. This layer is also observed to be strongly heterogeneous, and quantifying the spatial distribution of properties over the range of scales of interest is challenging. Facies are elements of a sediment classification scheme that groups complex geologic materials into a set of discrete classes according to distinguishing features. Facies classifications have been used as a framework for assigning heterogeneous material properties to grid cells of numerical models of flow and reactive transport in subsurface media. The usefulness of such an approach hinges on being able to relate facies to quantitative properties needed for flow and reactive transport modelling, and on being able to map facies over the domain of interest using readily available information. Although aquifer facies have been used in various modelling contexts, application of this concept to riverbed sediments is relatively new. Here, we describe an approach for categorizing and mapping recent alluvial (riverbed) sediments based on the integration of diverse observations with numerical simulations of river hydrodynamics. The facies have distinct distributions of sediment texture that correspond to variations in hydraulic properties, and therefore provide a useful framework for assigning heterogeneous properties in numerical simulations of hydrologic exchange flows and biogeochemical processes.     

Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model

The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of K_sat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones).     

Constraining complex aquifer geometry with geophysics (2-D ERT and MRS measurements) for stochastic modelling of groundwater flow

Stochastic modelling is a useful way of simulating complex hard-rock aquifers as hydrological properties (permeability, porosity etc.) can be described using random variables with known statistics. However, very few studies have assessed the influence of topological uncertainty (i.e. the variability of thickness of conductive zones in the aquifer), probably because it is not easy to retrieve accurate statistics of the aquifer geometry, especially in hard rock context. In this paper, we assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework.The study site was a small experimental watershed in South India, where the aquifer consisted of a clayey to loamy–sandy zone (regolith) underlain by a conductive fissured rock layer (protolith) and the unweathered gneiss (bedrock) at the bottom. The spatial variability of the thickness of the regolith and fissured layers was estimated by electrical resistivity tomography (ERT) profiles, which were performed along a few cross sections in the watershed. For stochastic analysis using Monte Carlo simulation, the generated random layer thickness was made conditional to the available data from the geophysics. In order to simulate steady state flow in the irregular domain with variable geometry, we used an isoparametric finite element method to discretize the flow equation over an unstructured grid with irregular hexahedral elements.The results indicated that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux and that using the conditional simulations reduced the uncertainty of the simulated seepage flux.As a conclusion, combining information on the aquifer geometry obtained from geophysical surveys with stochastic modelling is a promising methodology to improve the simulation of groundwater flow in complex hard-rock aquifers.     

Permeability profiles in granular aquifers using flowmeters in direct-push wells

Numerical hydrogeological models should ideally be based on the spatial distribution of hydraulic conductivity (K), a property rarely defined on the basis of sufficient data due to the lack of efficient characterization methods. Electromagnetic borehole flowmeter measurements during pumping in uncased wells can effectively provide a continuous vertical distribution of K in consolidated rocks. However, relatively few studies have used the flowmeter in screened wells penetrating unconsolidated aquifers, and tests conducted in gravel-packed wells have shown that flowmeter data may yield misleading results. This paper describes the practical application of flowmeter profiles in direct-push wells to measure K and delineate hydrofacies in heterogeneous unconsolidated aquifers having low-to-moderate K (10(-6) to 10(-4) m/s). The effect of direct-push well installation on K measurements in unconsolidated deposits is first assessed based on the previous work indicating that such installations minimize disturbance to the aquifer fabric. The installation and development of long-screen wells are then used in a case study validating K profiles from flowmeter tests at high-resolution intervals (15 cm) with K profiles derived from multilevel slug tests between packers at identical intervals. For 119 intervals tested in five different wells, the difference in log K values obtained from the two methods is consistently below 10%. Finally, a graphical approach to the interpretation of flowmeter profiles is proposed to delineate intervals corresponding to distinct hydrofacies, thus providing a method whereby both the scale and magnitude of K contrasts in heterogeneous unconsolidated aquifers may be represented.     

Analysis of subsurface contaminant migration and remediation using high performance computing

Highly resolved simulations of groundwater flow, chemical migration and contaminant recovery processes are used to test the applicability of stochastic models of flow and transport in a typical field setting. A simulation domain encompassing a portion of the upper saturated aquifer materials beneath the Lawrence Livermore National Laboratory was developed to hierarchically represent known hydrostratigraphic units and more detailed stochastic representations of geologic heterogeneity within them. Within each unit, Gaussian random field models were used to represent hydraulic conductivity variation, as parameterized from well test data and geologic interpretation of spatial variability. Groundwater flow, transport and remedial extraction of two hypothetical contaminants were made in six different statistical realizations of the system. The effective flow and transport behavior observed in the simulations compared reasonably with the predictions of stochastic theories based upon the Gaussian models, even though more exacting comparisons were prevented by inherent nonidealities of the geologic model and flow system. More importantly, however, biases and limitations in the hydraulic data appear to have reduced the applicability of the Gaussian representations and clouded the utility of the simulations and effective behavior based upon them. This suggests a need for better and unbiased methods for delineating the spatial distribution and structure of geologic materials and hydraulic properties in field systems. High performance computing can be of critical importance in these endeavors, especially with respect to resolving transport processes within highly variable media.©1998 Elsevier Science Limited. All rights reserved     

Characteristics of distribution and transport of petroleum contaminants in fracture-karst water in Zibo Area, Shandong Province, China

Fracture-karst water is an important water resource for the water supply in North China. Petroleum contamination is one of the most problematic types of the groundwater pollution. The characteristics of distribution and transport of the petroleum contaminants in fracture-karst water are different from those in porous water. The flow velocity of fracture-karst water is much faster than the velocity of porous water on an average. Therefore, contaminant transport in fracture-karst water is an absolute advection-dominated problem. The plume of the petroleum contamination may extend to several kilometers from pollution sources. It was not caused by the oil pool floating on the water table but by the oil components dissolved and scattered in groundwater. The distribution of the petroleum contaminants over space are concentrated in the strong conductive zone on the plane. On the vertical section the highest concentration of the oil contaminants appeared in the strata where the contamination sources were located. The concentrations of the oil contaminants in wells changed greatly over time. Therefore, the curves of concentration versus time fluctuated greatly. The reasons are as follows. (a) Fracture-karst water has a very great velocity. (b) Local flow fields which were caused by pumping and stoppage in some wells changed frequently. (c) In fracture-karst aquifer the transport channels are complicated. (d) Residual oil in vadose zone was leached after rainfall. It is of great practical value for the control and remediation of petroleum contamination in fracture-karst aquifer to understand those characteristics.     

Comparison of approaches for predicting solute transport: sandbox experiments

The main purpose of this paper was to compare three approaches for predicting solute transport. The approaches include: (1) an effective parameter/macrodispersion approach (Gelhar and Axness 1983); (2) a heterogeneous approach using ordinary kriging based on core samples; and (3) a heterogeneous approach based on hydraulic tomography. We conducted our comparison in a heterogeneous sandbox aquifer. The aquifer was first characterized by taking 48 core samples to obtain local-scale hydraulic conductivity (K). The spatial statistics of these K values were then used to calculate the effective parameters. These K values and their statistics were also used for kriging to obtain a heterogeneous K field. In parallel, we performed a hydraulic tomography survey using hydraulic tests conducted in a dipole fashion with the drawdown data analyzed using the sequential successive linear estimator code (Yeh and Liu 2000) to obtain a K distribution (or K tomogram). The effective parameters and the heterogeneous K fields from kriging and hydraulic tomography were used in forward simulations of a dipole conservative tracer test. The simulated and observed breakthrough curves and their temporal moments were compared. Results show an improvement in predictions of drawdown behavior and tracer transport when the K tomogram from hydraulic tomography was used. This suggests that the high-resolution prediction of solute transport is possible without collecting a large number of small-scale samples to estimate flow and transport properties that are costly to obtain at the field scale.     

An Application of HFE-D for Evaluating Sea Water Intrusion in Coastal Aquifers of Southern Vietnam

The coastal aquifers and inland waters of the Long Xuyen Quadrangle and Ca Mau Peninsula of southern Vietnam have been significantly impacted by sea water intrusion (SI) as a result of recent anthropogenic activities. This study identified the evolution and spatial distribution of hydrochemical conditions in coastal aquifers at this region using Hydrochemical Facies Evolution Diagram (HFE-D) and Geographical Information System mapping. Hydraulic heads and water chemistry were measured at 31 observation wells in four layered aquifers during dry and rainy seasons in early (2005), and more recent (2016), stages of agricultural development. Hydrochemical facies associated with intrusion or freshening stages were mapped in each aquifer after assigning mixing index values to each facies. The position of groundwater freshening and SI phases differed in Holocene, Upper Pleistocene, Middle Pleistocene, and Lower Pleistocene aquifers. The geographic position of freshening and intrusion fronts differ in dry and rainy seasons, and shifted after 11 years of groundwater abstraction in all four aquifers. The spatial and temporal differences in hydrochemical facies distributions according to HFE-D reflect the relative impact of SI in the four aquifers. The study results provide a better understanding of the evolution of groundwater quality associated with SI in a peninsular coastal aquifer system, and highlight the need for improving groundwater quality and management in similar coastal regions.     

Matching solute breakthrough with deterministic and stochastic aquifer models

Two different deterministic and two alternative stochastic (i.e., geostatistical) approaches to modeling the distribution of hydraulic conductivity (K) in a nonuniform (sigma2ln(K)) = 0.29) glacial sand aquifer were used to explore the influence of conceptual model selection on simulations of three-dimensional tracer movement. The deterministic K models employed included a homogeneous effective K and a perfectly stratified 14 layer model. Stochastic K models were constructed using sequential Gaussian simulation and sequential i ndicator simulation conditioned to available K values estimated from measured grain size distributions. Standard simulation software packages MODFLOW, MT3DMS, and MODPATH were used to model three-dimensional ground water flow and transport in a field tracer test, where a pulse of bromide was injected through an array of three fully screened wells and extracted through a single fully screened well approximately 8 m away. Agreement between observed and simulated transport behavior was assessed through direct comparison of breakthrough curves (BTCs) and selected breakthrough metrics at the extraction well and at 26 individual multilevel sample ports distributed irregularly between the injection and extraction wells. Results indicate that conceptual models incorporating formation variability are better able to capture observed breakthrough behavior. Root mean square (RMS) error of the deterministic models bracketed the ensemble mean RMS error of stochastic models for simulated concentration vs. time series, but not for individual BTC characteristic metrics. The spatial variability models evaluated here may be better suited to simulating breakthrough behavior measured in wells screened over large intervals than at arbitrarily distributed observation points within a nonuniform aquifer domain.     

The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.     

Ergodicity and the ‘scale effect’

Solute plume spreading in an aquifer exhibits a ‘scale effect’ if the second spatial concentration moment of a plume has a non-constant time-derivative. Stochastic approaches to modeling this scale effect often rely on the critical assumption that ensemble averages can be equated to spatial averages measured in a single field experiment. This ergodicity assumption should properly be evaluated in a strictly dynamical context, and this is done in the present paper. For the important case of trace plume convection by steady groundwater flow in an isotropic, heterogeneous aquifer, ergodicity does not obtain because of the existence of an invariant function on stream surfaces that is not uniform throughout the aquifer. The implications of this result for stochastic models of solute transport are discussed. © 1997 Elsevier Science Ltd. All rights reserved     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.     

Surface water-groundwater exchange dynamics in buried-valley aquifer systems

Groundwater is a primary source of drinking water worldwide, but excess nutrients and emerging contaminants could compromise groundwater quality and limit its usage as a drinking water source. As such contaminants become increasingly prevalent in the biosphere, a fundamental understanding of their fate and transport in groundwater systems is necessary to implement successful remediation strategies. The dynamics of surface water-groundwater (hyporheic) exchange within a glacial, buried-valley aquifer system are examined in the context of their implications for the transport of nutrients and contaminants in riparian sediments. High conductivity facies act as preferential flow pathways which enhance nutrient and contaminant delivery, especially during storm events, but transport throughout the aquifer also depends on subsurface sedimentary architecture (e.g. interbedded high and low conductivity facies). Temperature and specific conductance measurements indicate extensive hyporheic mixing close to the river channel, but surface water influence was also observed far from the stream-aquifer interface. Measurements of river stage and hydraulic head indicate that significant flows during storms (i.e., hot moments) alter groundwater flow patterns, even between consecutive storm events, as riverbed conductivity and, more importantly, the hydraulic connectivity between the river and aquifer change. Given the similar mass transport characteristics among buried-valley aquifers, these findings are likely representative of glacial aquifer systems worldwide. Our results suggest that water resources management decisions based on average (base) flow conditions may inaccurately represent the system being evaluated, and could reduce the effectiveness of remediation strategies for nutrients and emerging contaminants.     

Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach

This paper describes an innovative procedure that is able to simultaneously identify the release history and the source location of a pollutant injection in a groundwater aquifer (simultaneous release function and source location identification, SRSI). The methodology follows a geostatistical approach: it develops starting from a data set and a reliable numerical flow and transport model of the aquifer. Observations can be concentration data detected at a given time in multiple locations or a time series of concentration measurements collected at multiple locations. The methodology requires a preliminary delineation of a probably source area and results in the identification of both the sub-area where the pollutant injection has most likely originated, and in the contaminant release history. Some weak hypotheses have to be defined about the statistical structure of the unknown release function such as the probability density function and correlation structure. Three case studies are discussed concerning two-dimensional, confined aquifers with strongly non-uniform flow fields. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix and the recent step input function procedure has been successfully applied.     

Multifractal properties of the peak flow distribution on stochastic drainage networks

In this paper, we examined the peak flow distribution on a realization of networks obtained with stochastic network models. Three network models including the uniform model, the Scheidegger model, and the Gibbsian model were utilized to generate networks. The network efficiency in terms of drainage time is highest on the Scheidegger model, whereas it is lowest on the uniform model. The Gibbsian model covers both depending on the parameter value of β. The magnitude of the peak flow at the outlet itself is higher on the Scheidegger model compared to the uniform model. However, the results indicate that the maximum peak flows can be observed not just at the outlet but also other parts of the mainstream. The results show that the peak flow distribution on each stochastic model has a common multifractal spectrum. The minimum value of α, which is obtained in the limit of a sufficiently large q, is equal to the fractal dimension of a single river. The multifractal properties clearly show the difference among three stochastic network models and how they are related. Moreover, the results imply that the multifractal properties can be utilized to estimate the value of β for a given drainage network.     

Stochastic estimation of facies using ground penetrating radar data

Explicitly defining large-scale heterogeneity is a necessary step of groundwater model calibration if accurate estimates of flow and transport are to be made. In this work, neural networks are used to estimate radar facies probabilities from ground penetrating radar (GPR) images, yielding stochastic facies-based models that honour the large-scale architecture of the subsurface. For synthetic GPR images, a neural network was able to correctly identify radar facies with an accuracy of approximately 90%. Manual interpretation of a set of 450 MHz GPR field data from the Borden aquifer resulted in the identification of four radar facies. Of these, a neural network was able to identify two facies with an accuracy of near 80% and one with an accuracy of 44%. The neural network was not able to identify the fourth facies, likely due to the choice of defining facies characteristics. Sequential indicator simulation was used to generate facies realizations conditioned to the radar facies probabilities. Numerical simulations indicate that significant improvements in the prediction of solute transport are possible when GPR is used to constrain the facies model compared to using well data alone, especially when data are sparse.This work was supported by funding to R. Knight under Grant No. DE-FG07–00ER15118-A000, Environmental Management Science Program, Office of Science and Technology, Office of Environment Management, United States Department of Energy (DOE). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE. Further support was provided by a Stanford Graduate Fellowship to S. Moysey. The authors would also like to thank James Irving for his assistance with processing of the radar data.     

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs