Groundwater Management Problems Research Articles

A new discrete differential evolution algorithm coupled with simulation–optimization model for groundwater management problems

A new discrete differential evolution algorithm coupled with simulation–optimization model for groundwater management problems

Exploring Simulation–Optimization for Sustainable Groundwater Management: A Critical Review

ABSTRACTSimulation–optimization (S–O) is a well‐regarded method for solving groundwater (GW) management problems. Although S–O has significantly improved the decision support system for GW management, it still lacks practical applicability. As a result, many researchers have been improving its components, leading to slightly or significantly better performance. To understand these challenges efficiently, this article delves into principal components of S–O that offer in‐depth critical insights into GW's sustainability. The discussed segments are divided into simulation models, optimization methods, categories and conceptualization of management problems, and the formulation of real‐world objective functions. This review also examines surrogate‐assisted simulation models to reduce computational challenges. Methods to address model uncertainty and decision‐making in applying S–O for sustained yield problems are addressed. The review outlays critical steps in S–O methodology and recommends potential research directions to aid researchers in further enhancing the practicality of S–O.

Transforming groundwater sustainability, management and development through deep learning

Groundwater (GW) availability is at risk due to over-extraction, pollution, and climate change, despite their vital role in satisfying the world's freshwater needs. Decisions made using outdated, under-data-driven models for groundwater management are not always the best option. Traditional approaches often fail to tackle groundwater systems' intricacies and ever-changing nature, even if groundwater management has come a long way. Groundwater over-extraction, pollution, and depletion are consequences of ineffective monitoring, prediction, and management, which endangers environmental sustainability and water security.The rising problems of Sustainable Groundwater Management (SGM) and development in the context of global freshwater demand and climate change were addressed in this study. A revolutionary technique for predicting models and the Water Quality Assessment (WQA) by employing the potential of Deep Learning (DL), a type of Artificial Intelligence (AI). Then, the limitations faced by the existing Groundwater Management methods (GM) in predicting the Variations in the GW levels were identified, and it also predicted the quick detection of the WQ (Water Quality) deterioration. The application of DL algorithms offers precise prediction and early detection, and this study also aims to fill the gaps by executing DL on past and present data. By addressing the drawbacks of these traditional methods, Pattern Recognition (PR) and analysis in the DL can revolutionize these procedures. For predicting the modelling of GW levels, the Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and particularly Long Short Term Memory (LSTM) networks are employed in this study.For WQA, Deep CNN (DCNN) are employed. The hidden patterns are revealed within the large datasets by applying Deep Transformer Analysis (DTA), which supports specific management approaches. The outcomes demonstrated the revolutionary impact of DL techniques. The LSTM networks facilitated the precise predictions for GW variations and Proactive Resource management. CNN accurately determined the GQA, detecting indicators like PH and level of pollutants early. The DTA contributed to classifying the GW quality levels effectively and optimizing the management techniques. The precise predictive models for GW level variations and accurate WQA parameters were presented in this study by applying these advanced techniques to historical and real-time data. The proactive resource management, early detection capabilities, and sustainability of GW resources facilitate the transformative potential of DL and the outcomes obtained. The enhanced accuracy rate of 97.2%, F1 score rate of 96.2%, MAE (Mean Absolute Error) rate of 0.8%, RMSE (Root Mean Square Error) of 1.1%, loss rate of 0.04% were attained by the suggested CNN-DTA model when compared to other current techniques.

Urban Water Management in Milan Metropolitan Area, a review

The increasing rate of urbanisation and extreme climatic events represent a constant threat for urban water resources management. In recent decades, Milan Metropolitan Area (Lombardy Region, Northern Italy) has been affected by a) frequent extreme rainfall events, responsible for the flooding of major surface water courses, and b) groundwater management problems, both from a quantitative (i.e. interaction with underground infrastructures) and qualitative point of view. Moreover, the increasing use of groundwater geothermal systems also requires further considerations. This work analyses the literature available in the area regarding surface floods, groundwater quantity, quality, and temperature. Finally, a discussion is provided to understand a) which approaches could promote an effective management of both surface water and groundwater resources b) which points of contact emerge between these two aspects of the urban water cycle, and c) which possible urban interventions could contribute to an integrated and functional management of water resources, also reducing some current issues.

The Pliocene succession of Lyon Metropolis (SE France): an overfill of a Messinian incised-valley

The Pliocene ria, a narrow seaway running up the Rhône Valley, has been mapped for a while by field geologists. Only much later, after the DSDP Leg 13 in 1970, a consensus was reached that this unique geological feature of the Rhône Valley was created by the major Mediterranean sea-level drop associated with the Messinian Salinity Crisis, followed by a sudden sea-level rise caused by the breach of the Strait of Gibraltar and the invasion of the Mediterranean Basin by the Atlantic waters. At the regional level of the Lyon Metropolis in the upper Rhône Valley, main issues were however remaining about the course and depth of the Messinian valley, and about the valley fill, namely where and how do the Pliocene marine strata of the Rhône Valley pass to the continental deposits of the Bresse Basin to the north? These are key-questions in that the Plio-Pleistocene makes up a large fraction of the basement that holds up a large city, not free from potential geological hazards and subject to problems of groundwater management, high-cost tunneling projects, etc. Our survey reviews first the historical researches − descriptions of the outcrops and fossil assemblages. It is followed by an unprecedented analysis and correlation of a thousand boreholes, which makes it possible to physically link and reconcile ancient local observations. Sections across the Messinian valley reveal a proper canyon morphology for the segments that cut the crystalline basement. The magnitude of the incision has been calculated as 335 m to a minimum, three hundred kilometers away from the river mouth. Three major depositional systems are distinguished for the Pliocene − Lower Pleistocene succession. The valley that initially ran much farther north of Lyon was occupied in the Zanclean by a series of pounded lakes, dammed by transverse local alluvial fans, filled by minor Gilbert-type deltas, and repeatedly flooded by marine ingressions. The valley wings were then encroached during the Piacenzian by a major, Alps-rooted alluvial sheet. At the level of Lyon, the fluvial deposits were deflected to the north (Sables de Trévoux) and to the south (Alluvions jaunes) as a dichotomy. The succession was then capped by a gravel-dominated fluvio-glacial fan (Alluvions jaunes sommitales) at the Plio-Pleistocene transition. It spread out from the north-east to the south, and intersected the previous valley overfill due to the shift to the north, i.e., South Jura, of the feeder stream. The depositional and current elevations of the marine-influenced episodes, i.e. marker bands that punctuate the regional Neogene succession, are used to bring out successive uplift and subsidence phases of the region. Finally, we tentatively link the major shifts in the depositional patterns of the Late Neogene succession in the Lyon area to major changes in the thrust belt activity, exhumation story, and outset of glaciers in the western Alps.

Stream-Aquifer Systems in Semi-Arid Regions: Hydrologic, Legal, and Management Issues

Integrated solutions to groundwater management problems require effective analysis of stream-aquifer connections, especially in irrigated semi-arid regions where groundwater pumping affects return flows and causes streamflow depletion. Scientific research can explain technical issues, but legal and management solutions are difficult due to the complexities of hydrogeology, the expense of data collection and model studies, and the inclination of water users not to trust experts, regulatory authorities, and in some cases, their management organizations. The technical, legal, and management issues are reviewed, and experiences with integrated management of stream-aquifer systems are used to illustrate how governance authorities can approach engineering, legal, regulatory, and management challenges incrementally. The situations in three basins of the State of Colorado with over-appropriated water resources are explained to identify modeling and control issues confronting regulators and managers of water rights. Water rights administration in the state follows the strict appropriation method and a workable technical-legal approach to establishing regulatory and management strategies has been developed. The explanations show how models and data management are improving, but the complexities of hydrogeology and institutional systems must be confronted on a case-by-case basis. Stream-aquifer systems will require more attention in the future, better data will be needed, model developers must prove superiority over simpler methods, and organizational arrangements will be needed to facilitate successful collective action amidst inevitable legal challenges. Continued joint research between technical, legal, and management communities will also be needed.

Investigating the Impact of Seawater Intrusion on the Operation Cost of Groundwater Supply in Island Aquifers

AbstractManaging fragile island freshwater resources requires identifying pumping strategies that trade off the financial cost of groundwater supply against controlling the seawater intrusion (SWI) associated with aquifer pumping. In this work, these tradeoffs are investigated through a sensitivity analysis conducted in the context of an optimization formulation of the groundwater management problem, which aims at minimizing the groundwater supply operation cost associated with groundwater pumping and desalination treatment, subject to constraints on SWI control, as quantified by the water table drawdown over the well (∆s), the reduction in freshwater volume (∆FV) in the aquifer, or the salt mass increase (∆SM) in the aquifer. This study focuses on a simplified two‐dimensional model of the San Salvador Island aquifer (Bahamas). Pumping strategies are characterized by the distance of the pumping system from the shoreline (WL), the abstraction screen depth (D) and overall pumping rate (Q), constituting the decision variables of the optimization problem. We investigate the impacts of pumping strategies on the operation cost, ∆s, ∆FV and ∆SM. Findings indicate increasing D or decreasing WL reduces ∆s, ∆FV and ∆SM, thus preserving the aquifer hydrogeologic stability, but also leads to extracting saltier groundwater, thus increasing the water treatment requirements, which have a strong impact on the overall groundwater supply cost. From a financial perspective, groundwater abstraction near the island center and at shallow depths seems the most convenient strategy. However, the analysis of the optimization constraints reveals that strategies where the pumping system approaches the island center tend to cause more severe SWI, highlighting the need to trade off groundwater supply cost against SWI control.

Multi-dimensional management framework on fresh groundwater lens of Kish Island in the Persian Gulf, Iran

Groundwater in arid and semi-arid coastal aquifers is vulnerable to seawater intrusion and quality deterioration despite being one of the most reliable sources of water supply due to the increasing number of development plans and competition between water consumers. A multi-dimensional groundwater management framework is developed to trade-off between groundwater abstraction, allocation equity, groundwater quality, and energy considerations in the reverse osmosis (RO) filtration process in the fresh groundwater lens of Kish Island, Iran. An arid island confined in the Persian Gulf is modeled using 3D simulation and three well-occupied multi-objective evolutionary optimization algorithms. Four objectives include: maximizing the groundwater abstraction, minimizing the Gini coefficient (allocation inequity), minimizing the total energy required to pass saline water through the RO membrane to reach the standard total dissolved solids (TDS), and minimizing the average TDS concentration of water abstraction positions from 11 management zones have been considered over a 50-year management horizon. Solutions obtained in the simulation-based constrained multi-objective optimization framework allow managers to choose from 587 Pareto optimal solutions. They provide an abstraction scheme with a range of 1.44 to 4.53 MCM/yr, a Gini coefficient of 0 to 0.98, filtration energy of 988,562 to 1,935,760 kWh/yr, and an average TDS of 19,663 to 21,351 mg/L. The Pareto optimal solutions can help decision-makers decide on the multi-dimensional problems of sustainable coastal groundwater management and show patterns among different objectives.

Enhancements to explicit stochastic reservoir operation optimization method

The Fletcher-Ponnambalam (FP) method is an explicit stochastic optimization method for design and operations management of real-world storage systems including surface water reservoir and groundwater management problems. The FP method faces no curse of dimensionality and no need for scenario generation. The paper introduces a novel implementation for the FP method, named FP-2022 here for clarity, by removing the need for nonlinear constraints and by decreasing the number of decision variables to just one third of its original value, significantly reducing solving time (∼27 times faster than the original formulation). Additionally, new expressions derived for the first and second moments of both reservoir release deficit and surplus variables and the already-derived expression for the second moments of reservoir storages are incorporated into the FP-2022 formulation enabling the method to reach an improved optimality for a nonlinear objective function. The enhanced procedure is applied to solving a reservoir operation optimization problem for a major dam in Brazil. The result comparisons made with other methods along with a thorough analysis of release operation policies prove the optimality of this highly numerically efficient and convenient-to-use FP-2022 method. Finally, a multi-reservoir application of the model is also tested with corrective simulations for improved estimates of some additional variables of interest. A specific constraint-handling approach regarding reservoir release lower and upper bounds is also presented. Satisfactory results are obtained for solving the Parambikulam-Aliyar reservoir system, a real world five-reservoir operation optimization problem from India.

Hydrodynamics, Hydrochemistry, and Stable Isotope Geochemistry to Assess Temporal Behavior of Seawater Intrusion in the La Yarada Aquifer in the Vicinity of Atacama Desert, Tacna, Peru

The La Yarada aquifer is the primary water resource for municipal, irrigation, and industrial uses in the semi-arid Tacna, Peru. Presently, over-pumping has caused severe groundwater management problems, including the abandonment of saline water wells. This study presents multivariate analysis and chemical–isotopic trends in water to investigate seawater intrusion and hydrogeological processes affecting water quality. The chemical and isotopic analysis of water samples, collected in two campaigns in the dry (August 2020) and wet (November 2020) seasons, together with the 1988 data, were evaluated with a mixing model, cluster, and factor analysis. The hydrochemical and isotopic mixing model suggested the formation of a wedge with 20% seawater intrusion. The heterogeneity of piezometric map isolines corroborates the wedge formation associated with the groundwater movement. The spatial distributions of factors, FA1 and FA2, suggest two processes of seawater front movement: dispersion (diffusion) of chemical elements and different types of water mixing, respectively. At the edge of the La Yarada aquifer, the water head was relatively low, permitting seawater and freshwater mixing. On the other hand, along the sea-land boundary, the water head of the La Yarada aquifer was relatively high, avoiding seawater and freshwater mixing; however, the chemical species were migrating from the seawater to the groundwater due to the diffusion processes. The cluster 4 samples are in the region corresponding to the isotopic mixing process represented by the FA2, while cluster 4 describes the chemical diffusion process represented by the FA2. Thus, the integrated approach is helpful to assess the seawater intrusion mechanisms in coastal aquifers in a semi-arid region.

Ecosystem Shifts: Implications for Groundwater Management

Freshwater ecosystems provide a large number of benefits to society. However, extensive human activities threat the viability of these ecosystems, their habitats, and their dynamics and interactions. One of the main risks facing these systems is the overexploitation of groundwater resources that hinders the survival of several freshwater habitats. In this paper, we study optimal groundwater paths when considering freshwater ecosystems. We contribute to existing groundwater literature by including the possibility of regime shifts in freshwater ecosystems into a groundwater management problem. The health of the freshwater habitat, which depends on the groundwater level, presents a switch in its status that occurs when a critical water level (‘tipping point’) is reached. Our results highlight important differences in optimal extraction paths and optimal groundwater levels compared with traditional models. The outcomes suggest that optimal groundwater withdrawals are non-linear and depend on the critical threshold and the ecosystem’s health function. Our results show that the inclusion of regime shifts in water management calls for a reformulation of water policies to incorporate the structure of ecosystems and their interactions with the habitat.

Estimation of Groundwater Recharge in Semarang City, Indonesia

In regional groundwater management, it is necessary to find out the water balance between the supply and demand of groundwater. One of the most important in analyzing the water balance of groundwater is groundwater recharge. Semarang city that has a groundwater management problem needs to know the groundwater recharge to analyze the groundwater balance. On the other hand, it is difficult to measure groundwater recharge accurately, consequently, the groundwater recharge should be estimated. There are several methods to estimate groundwater recharge. To verify the groundwater recharge estimation, more than one method of groundwater recharge estimation should be used. In this paper, the determination of groundwater recharge is using the Chaturvedi formula and Krishna Rao formula based on the amount of rainfall, and well level data method that based on the difference in water level. Based on the final results, the well level data method seems the best fit in estimating the groundwater recharge.

Adaptative DNN emulator-enabled multi-objective optimization to manage aquifer−sea flux interactions in a regional coastal aquifer

This study focuses on the analyses of influx and efflux of groundwater at the aquifer−sea interface in response to the total groundwater extraction from a regional coastal aquifer. The groundwater planning and management goal is formulated as a multi-objective optimization problem to optimize the total pumping, groundwater influx and efflux through the coastal boundary. A four-stage optimization strategy is implemented for solving this optimization problem, whereby the first three stages are the iterative optimizations using the proposed Multi-Objective Particle Swarm Optimization algorithm and the analysis of Pareto-optimal solutions, and the last stage is the selection of one bargaining solution using the Kalai-Smorodinsky approach considering compromises among multiple objectives. In order to improve the efficiency of the simulation-optimization model, Deep Neural Networks emulators are fitted to approximate individual optimization objective, and a novel dynamic sampling strategy is applied to adaptively improve the accuracy of the emulators. This study demonstrates that accurate and efficient emulators can be achieved for the regional coastal aquifer with zone-based pumping rate multipliers from eight bands (Band 1 to Band 8) of increasing distance from the coastal boundary as the decision variables. The results from the Pareto-front suggest that the abstractions of Band 2 (close to the sea) can be reduced to the lower boundary of the rate multiplier (0.5) whereas the abstraction of farther bands can be significantly enhanced. The water influx through the coastal boundary was decreased by 15.69% under the slight compromise of the total pumping and water efflux by the selected compromising pumping pattern in the regional model. The final Pareto-optimal solution set and the compromised solution provide valuable information for the groundwater manager to plan sustainable groundwater use. The proposed simulation-optimization approach used in this study can be applied for a wide range of groundwater management problems.

Improved Flower Pollination Algorithm for Optimal Groundwater Management

Groundwater management problems are typically of a large-scale nature, involving complex nonlinear objective functions and constraints, which are commonly evaluated through the use of numerical simulation models. Given these complexities, metaheuristic optimization algorithms have recently become popular choice for solving such complex problems which are difficult to solve by traditional methods. However, the practical applications of metaheuristics are severely challenged by the requirement of large number of function evaluations to achieve convergence. To overcome this shortcoming, many new metaheuristics and different variants of existing ones have been proposed in recent years. In this study, a recently developed algorithm called flower pollination algorithm (FPA) is investigated for optimal groundwater management. The FPA is improved, combined with the widely used groundwater flow simulation model MODFLOW, and applied to solve two groundwater management problems. The proposed algorithm, denoted as IFPA, is first tested on a hypothetical aquifer system, to minimize the total pumping to contain contaminated groundwater within a capture zone. IFPA is then applied to maximize the total annual pumping from existing wells in Rhis-Nekor unconfined coastal aquifer on the northern of Morocco. The obtained results indicate that IFPA is a promising method for solving groundwater management problems as it outperforms the standard FPA and other algorithms applied to the case studies considered, both in terms of convergence rate and solution quality.

Transboundary extraction of groundwater in the presence of hydraulic fracturing

AbstractWe studied transboundary groundwater management problems in the presence of hydraulic fracturing. We found that the presence of risk suggests there should be caution when considering hydraulic fracturing. Our results from the cooperative solution show a decrease in hydraulic fracturing and increase in the steady state survival rate of groundwater. We also provide a Pigouvian type tax that could be imposed on natural gas developers.

A Simulation-Optimization Model for Seawater Intrusion Management at Pingtung Coastal Area, Taiwan

The coastal regions of Pingtung Plain in southern Taiwan rely on groundwater as their main source of fresh water for aquaculture, agriculture, domestic, and industrial sectors. The availability of fresh groundwater is threatened by unsustainable groundwater extraction and the over-pumpage leads to the serious problem of seawater intrusion. It is desired to find appropriate management strategies to control groundwater salinity and mitigate seawater intrusion. In this study, a simulation–optimization model has been presented to solve the problem of seawater intrusion along the coastal aquifers in Pingtung Plain and the objective is using injection well barriers and minimizing the total injection rate based on the pre-determined locations of injection barriers. The SEAWAT code is used to simulate the process of seawater intrusion and the surrogate model of artificial neural networks (ANNs) is used to approximate the seawater intrusion (SWI) numerical model to increase the computational efficiency during the optimization process. The heuristic optimization scheme of differential evolution (DE) algorithm is selected to identify the global optimal management solution. Two different management scenarios, one is the injection barriers located along the coast and the other is the injection barrier located at the inland, are considered and the optimized results show that the deployment of injection barriers at the inland is more effective to reduce total dissolved solids (TDS) concentrations and mitigate seawater intrusion than that along the coast. The computational time can be reduced by more than 98% when using ANNs to replace the numerical model and the DE algorithm has been confirmed as a robust optimization scheme to solve groundwater management problems. The proposed framework can identify the most reliable management strategies and provide a reference tool for decision making with regard to seawater intrusion remediation.

Application of genetic algorithm for the groundwater management of a coastal aquifer

Drinking water wells close to coastal areas getting contaminated groundwater can be minimized by developing an optimal pumping strategy of pumping, both in space and time. Groundwater management problems are solved in a more efficient way by combining simulation and optimization in a single framework. Simulation–optimization-based development of the groundwater system is required, to reduce the risk of pumping contaminated water. This paper presents a study where a simulation–optimization model based on a 3D groundwater model and genetic algorithm was developed and applied to a case study. A 3D groundwater model has been developed, for the case study system of South Chennai Aquifer System where significant amount of groundwater is being pumped for domestic consumption. The calibrated groundwater model was used as the simulation component in the linked simulation–optimization model. The combined model was then used to identify the optimum pumping strategy.

Groundwater overexploitation: why is the red flag waved? Case study on the Kairouan plain aquifer (central Tunisia)

In many parts of the world, groundwater users regularly face serious resource-depletion threat. At the same time, “groundwater overexploitation” is massively cited when discussing groundwater management problems. A kind of standard definition tends to relegate groundwater overexploitation only as a matter of inputs and outputs. However, a thorough state-of-the-art analysis shows that groundwater overexploitation is not only a matter of hydrogeology but also a qualification of exploitation based on political, social, technical, economic or environmental criteria. Thus, an aquifer with no threat to groundwater storage can rightly be considered as overexploited because of many other prejudicial aspects. So, why is groundwater overexploitation so frequently only associated with resource-depletion threat and so rarely related to other prejudicial aspects? In that case, what really lies behind the use of the overexploitation concept? The case of the Kairouan plain aquifer in central Tunisia was used to analyze the way that the overexploitation message emerges in a given context, how groundwater-use stakeholders (farmers, management agencies and scientists) each qualify the problem in their own way, and how they see themselves with regard to the concept of overexploitation. The analysis shows that focusing messages on overexploitation conceals the problems encountered by the various stakeholders: difficulties accessing water, problems for the authorities in controlling the territory and individual practices, and complications for scientists when qualifying hydrological situations. The solutions put forward to manage overexploitation are at odds with the problems that arise locally, triggering tensions and leading to misunderstandings between the parties involved.

A New Groundwater Management Model by Coupling Analytic Element Method and Reverse Particle Tracking with Cat Swarm Optimization

The performance of groundwater management models mostly depends upon the methodology employed to simulate flow and transport processes and the efficiency of optimization algorithms. The present study examines the effectiveness of cat swarm optimization (CSO) for groundwater management problems, by coupling it with the analytic element method (AEM) and reverse particle tracking (RPT). In this study, we propose two coupled simulation-optimization models, viz. AEM-CSO and AEM-RPT-CSO by combining AEM with RPT and CSO. Both the models utilize the added advantages of AEM, such as precise estimation of hydraulic head at pumping location and generation of continuous velocity throughout the domain. The AEM-CSO model is applied to a hypothetical unconfined aquifer considering two different objectives, i.e., maximization of the total pumping of groundwater from the aquifer and minimization of the total pumping costs. The model performance reflects the superiority of CSO in comparison with other optimization algorithms. Further, the AEM-RPT-CSO model is successfully applied to a hypothetical confined aquifer to minimize the total number of contaminant sources, within the time related capture zone of the wells, while maintaining the required water demand. In this model, RPT gets continuous velocity information directly from the AEM model. The performance evaluation of the proposed methodology, illustrates its ability to solve groundwater management problems.

Pareto-based efficient stochastic simulation–optimization for robust and reliable groundwater management

Summary Simulation–optimization methods are used to develop optimal solutions for a variety of groundwater management problems. The true optimality of these solutions is often dependent on the reliability of the simulation model. Therefore, where model predictions are uncertain due to parameter uncertainty, this should be accounted for within the optimization formulation to ensure that solutions are robust and reliable. In this study, we present a stochastic multi-objective formulation of the otherwise single objective groundwater optimization problem by considering minimization of prediction uncertainty as an additional objective. The proposed method is illustrated by applying to an injection bore field design problem. The primary objective of optimization is maximization of the total volume of water injected into a confined aquifer, subject to the constraints that the resulting increases in hydraulic head in a set of control bores are below specified target levels. Both bore locations and injection rates were considered as optimization variables. Prediction uncertainty is estimated using stacks of uncertain parameters and is explicitly minimized to produce robust and reliable solutions. Reliability analysis using post-optimization Monte Carlo analysis proved that while a stochastic single objective optimization failed to provide reliable solutions with a stack size of 50, the proposed method resulted in many robust solutions with high reliability close to 1.0. Results of the comparison indicate potential gains in efficiency of the stochastic multi-objective formulation to identify robust and reliable groundwater management strategies.