Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.     

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright © 2015 John Wiley & Sons, Ltd.     

Pump-and-treat optimization using analytic element method flow models

Plume containment using pump-and-treat (PAT) technology continues to be a popular remediation technique for sites with extensive groundwater contamination. As such, optimization of PAT systems, where cost is minimized subject to various remediation constraints, is the focus of an important and growing body of research. While previous pump-and-treat optimization (PATO) studies have used discretized (finite element or finite difference) flow models, the present study examines the use of analytic element method (AEM) flow models. In a series of numerical experiments, two PATO problems adapted from the literature are optimized using a multi-algorithmic optimization software package coupled with an AEM flow model. The experiments apply several different optimization algorithms and explore the use of various pump-and-treat cost and constraint formulations. The results demonstrate that AEM models can be used to optimize the number, locations and pumping rates of wells in a pump-and-treat containment system. Furthermore, the results illustrate that a total outflux constraint placed along the plume boundary can be used to enforce plume containment. Such constraints are shown to be efficient and reliable alternatives to conventional particle tracking and gradient control techniques. Finally, the particle swarm optimization (PSO) technique is identified as an effective algorithm for solving pump-and-treat optimization problems. A parallel version of the PSO algorithm is shown to have linear speedup, suggesting that the algorithm is suitable for application to problems that are computationally demanding and involve large numbers of wells.     

Integrated modeling as a decision‐aiding tool for groundwater management in a Mediterranean agricultural watershed

A decision‐aiding methodology for agricultural groundwater management is presented; it is based on the combination of a watershed model, a groundwater flow model, and an optimization model. This methodology was applied to an agricultural watershed in northeastern Greece. The watershed model used was the Soil and Water Assessment Tool (SWAT), which provided recharge rates for the aquifers. These recharge rates were imported in the well‐known MODFLOW groundwater flow model. Both models were calibrated and verified using field data. Then, the nonlinear optimization problem was solved by a piecewise linearization process, in which the Simplex algorithm was applied sequentially. Apart from several pumping and climate change sensitivity scenarios, a land use change scenario and a climate change scenario, combining the three models, were tested, showing the ability of this methodology to be used in the decision‐making process. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi-Objective Optimization of Managed Aquifer Recharge

This study demonstrates the utilization of a multi-objective hybrid global/local optimization algorithm for solving managed aquifer recharge (MAR) design problems, in which the decision variables included spatial arrangement of water injection and abstraction wells and time-variant rates of pumping and injection. The objective of the optimization was to maximize the efficiency of the MAR scheme, which includes both quantitative and qualitative aspects. The case study used to demonstrate the capabilities of the proposed approach is based on a published report on designing a real MAR site with defined aquifer properties, chemical groundwater characteristics as well as quality and volumes of injected water. The demonstration problems include steady state and transient scenarios. The steady state scenario demonstrates optimization of spatial arrangement of multiple injection and recovery wells, whereas the transient scenario was developed with the purpose of finding optimal regimes of water injection and recovery at a single location. Both problems were defined as multi-objective problems. The scenarios were simulated by applying coupled numerical groundwater flow and solute transport models: MODFLOW-2005 and MT3D-USGS. The applied optimization method was a combination of global (the non-dominated sorting genetic algorithm [NSGA-2]) and local (the Nelder-Mead downhill simplex search algorithms). The analysis of the resulting Pareto optimal solutions led to the discovery of valuable patterns and dependencies between the decision variables, model properties, and problem objectives. Additionally, the performance of the traditional global and the hybrid optimization schemes were compared.     

Multi-objective optimization for sustainable groundwater resource management in a semiarid catchment

Abstract

Groundwater is an important water resource and its management is vital for integrated water resources development in semiarid catchments. The River Shiyang catchment in the semiarid area of northwestern China was studied to determine a sustainable multi-objective management plan of water resources. A multi-objective optimization model was developed which incorporated water supplies, groundwater quality, ecology, environment and economics on spatial and temporal scales under various detailed constraints. A calibrated groundwater flow model was supplemented by grey simulation of groundwater quality, thus providing two lines of evidence to use in the multi-objective water management. The response matrix method was used to link the groundwater simulation models and the optimization model. Multi-phase linear programming was used to minimize and compromise the objectives for the multi-period, conjunctive water use optimization model. Based on current water demands, this water use optimization management plan was able to meet ecological, environmental and economic objectives, but did not find a final solution to reduce the overall water deficit within the catchment.     

Numerical studies on the influences of the South‐to‐North Water Transfer Project on groundwater level changes in the Beijing Plain,China

Groundwater is an important component of the water supply, and overexploitation has triggered many problems in the Beijing Plain. The South‐to‐North Water Transfer Project has been proposed as a promising solution to alleviate these problems. Evaluation of different scenarios of groundwater management after the implementation of the South‐to‐North Water Transfer Project is necessarily required. In this study, a numerical model of groundwater flow was established using FEFLOW software and was well calibrated by parameter optimization and groundwater withdrawal inversion in the Beijing Plain. Sixteen scenarios that considered groundwater exploitation, artificial recharge, and precipitation were designed to simulate the groundwater dynamics after 11 years of the project. The results showed that the groundwater level in the study area would recover to various degrees due to the reductions of groundwater withdrawal and the increments of infiltration; additionally, it was concluded that groundwater was significantly affected by precipitation. Generally, in the designed scenarios, the groundwater‐level increment in the upper streams of the model area was higher than that in the lower streams. The groundwater level would obviously increase from artificial recharge in the immediate and adjacent areas. In addition, modes of reducing exploitation had no significant influence on the change in groundwater level during the 11‐year study period. The developed model offers a reliable and effective way to improve groundwater management.     

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.     

Identifying groundwater pumping source information using simulated annealing

This study develops an approach referred to as SA‐MF using simulated annealing (SA) and a three‐dimensional groundwater flow model (MODFLOW‐2000) to determine the pumping source information, namely the pumping source location, the pumping rate and the pumping period. Eight scenarios, each with various cases for aquifers with homogeneous or heterogeneous conductivities, are used to test the applicability and accuracy of SA‐MF in determining the pumping source information. The results show that at least five measured heads should be used to analyse the pumping source identification problem and at least three observation wells are required to effectively determine the pumping source information. The SA‐MF gives good estimated results in both synthetic and real problems even if the measured heads contain measurement errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite difference modeling of contaminant transport using analytic element flow solutions

The two-dimensional implementation of the analytic element method (AEM) is commonly used to simulate steady-state saturated groundwater flow phenomena at regional and local scales. However, unlike alternative groundwater flow simulation methods, AEM results are not ordinarily used as the basis for simulation of reactive solute transport. The use of AEM-simulated flow fields is impeded by the discrepancy between a continuous representation of flow and a typically discrete representation of transport, and requires translation of the flow solution to a discrete analog. This paper presents a variety of methods for analytically calculating conservative discrete water fluxes and integrated components of the dispersion tensor across cell interfaces. An Eulerian finite difference method based on these AEM-derived parameters is implemented for use in simulation of 2D (vertically averaged) solute transport. This implementation is first benchmarked against existing methods that use standard finite difference flow solutions, then used to investigate the effects of an inaccurate discrete water balance. It is shown that improper translation of AEM fluxes leads to significant water balance errors and inaccurate simulation of contaminant transport.     

Coupled surface water–groundwater model and its application in the arid Shiyang River basin,China

The planning and management of water resources in the Shiyang River basin, China require a tool for assessing the impact of groundwater and stream use on water supply reliabilities and improving many environment‐related problems such as soil desertification induced by recent water‐related human activities. A coupled model, integrating rule‐based lumped surface water model and distributed three‐dimensional groundwater flow model, has been established to investigate surface water and groundwater management scenarios that may be designed to restore the deteriorated ecological environment of the downstream portion of the Shiyang River basin. More than 66% of the water level among 24 observation wells have simulation error less than 1·0 m. The overall trend of the temporal changes of simulated and observed surface runoff at the Caiqi gauging station remains almost the same. The calibration was considered satisfactory. Initial frameworks for water allocation, including agricultural water‐saving projects, water diversion within the basin and inter‐basin water transfer, reducing agricultural irrigation area and surface water use instead of groundwater exploitation at the downstream were figured out that would provide a rational use of water resources throughout the whole basin. Sixteen scenarios were modelled to find out the most appropriate management strategies. The results showed that in the two selected management options, the groundwater budget at the Minqin basin was about 1·4 × 10⁸ m³/a and the ecological environment would be improved significantly, but the deficit existed at the Wuwei basin and the number was about 0·8 × 10⁸ m³/a. Water demand for domestic, industry and urban green area would be met in the next 30 years, but the water shortage for meeting the demand of agricultural water use in the Shiyang River basin was about 2·2 × 10⁸ m³/a. It is suggested that more inter‐basin water transfer should be required to obtain sustainable water resource use in the Shiyang River basin. Copyright © 2009 John Wiley & Sons, Ltd.     

On the importance of river hydrodynamics in simulating groundwater levels and baseflows

Research to date affirmed the key role of stream–aquifer interactions in integrated water resources management. The importance of river hydrodynamics on the spatial and temporal behaviour of groundwater was, however, not yet fully investigated. In contrast to the common approach where topography-based estimates of riverbed elevation may lead to inappropriate discretization and constant river stages, this study couples a fully hydrodynamic and one-dimensional river model to a two-dimensional catchment hydrological model. The surface and subsurface runoff, groundwater, and river components are integrated into a single modelling framework. The coupled model was applied to a medium sized catchment in Belgium with three model setups, in which the level of detail of representation of river hydrodynamics varies. Further model iterations were carried out for the most exhaustive setup to assess the importance of the bi-directional interactions between model components. Results show that higher details of river hydrodynamics help to improve the simulation of time-averaged groundwater levels. However, the impacts were not that clear for the time-varying groundwater levels. Moreover, visual and statistical model performance evaluation indicates a strong enhancement of the coupled models compared to the output from the hydrological model with respect to river discharge observations at catchment outlet and at internal stations. It also reveals the impact of river hydrodynamics on groundwater discharges when the most detailed setting delivered the highest performance among the three coupled models.     

Artificial neural networks as an alternative approach to groundwater numerical modelling and environmental design

Classical optimization methodologies based on mathematical theories have been developed for the solution of various constrained environmental design problems. Numerical models have been widely used to represent an environmental system accurately. The use of methodologies such as artificial neural networks (ANNs), which approximate the complicated behaviour and response of physical systems, allows the optimization of a large number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical model would be prohibitive. In this paper, a combination of an ANN with a differential evolution algorithm is proposed to replace the classical finite‐element numerical model in water resources management problems. The objective of the optimization problem is to determine the optimal operational strategy for the productive pumping wells located in the northern part of Rhodes Island in Greece, to cover the water demand and maintain the water table at certain levels. The conclusions of this study show that the use of ANN as an approximation model could (a) significantly reduce the computational burden associated with the accurate simulation of complex physical systems and (b) provide solutions very close to the optimal ones for various constrained environmental design problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Groundwater recharge amidst focused stormwater infiltration

Distributed, infiltration‐based approaches to stormwater management are being implemented to mitigate effects of urban development on water resources. One of the goals of this type of storm water management, sometimes called low impact development or green infrastructure, is to maintain groundwater recharge and stream base flow at predevelopment levels. However, the connection between infiltration‐based stormwater management and groundwater recharge is not straightforward. Water infiltrated through stormwater facilities may be stored in soil moisture, taken up by evapotranspiration or contribute to recharge and eventually base flow. This study focused on a 1.1 km² suburban, low impact development watershed in Clarksburg, Maryland, USA, that was urbanized and contained 73 infiltration‐based stormwater facilities. Continuous water table measurements were used to quantify the movement of infiltrated stormwater. Time series analyses were performed on hydrographs of 7 wells, and the episodic master recession method was used. Persistence in water levels, as measured by autocorrelation function, was found to be positively related to depth to water. Storm properties (precipitation rate and duration) and well location (proximity to the nearest stream) were significant in driving episodic recharge to precipitation ratios. The well that had the highest recharge to precipitation ratios and water table rises of up to 1.5 m in response to storm events was located furthest from the stream and down gradient of stormwater infiltration locations. This work may be considered in evaluating the effects of planned watershed‐scale infiltration‐based stormwater management on groundwater flow systems.     

Modeling the spatial distribution of landslide‐prone colluvium and shallow groundwater on hillslopes of Seattle,WA

Landslides in partially saturated colluvium on Seattle, WA, hillslopes have resulted in property damage and human casualties. We developed statistical models of colluvium and shallow‐groundwater distributions to aid landslide hazard assessments. The models were developed using a geographic information system, digital geologic maps, digital topography, subsurface exploration results, the groundwater flow modeling software VS2DI and regression analyses. Input to the colluvium model includes slope, distance to a hillslope–crest escarpment, and escarpment slope and height. We developed different statistical relations for thickness of colluvium on four landforms. Groundwater model input includes colluvium basal slope and distance from the Fraser aquifer. This distance was used to estimate hydraulic conductivity based on the assumption that addition of finer‐grained material from down‐section would result in lower conductivity. Colluvial groundwater is perched so we estimated its saturated thickness. We used VS2DI to establish relations between saturated thickness and the hydraulic conductivity and basal slope of the colluvium. We developed different statistical relations for three groundwater flow regimes. All model results were validated using observational data that were excluded from calibration. Eighty percent of colluvium thickness predictions were within 25% of observed values and 88% of saturated thickness predictions were within 20% of observed values. The models are based on conditions common to many areas, so our method can provide accurate results for similar regions; relations in our statistical models require calibration for new regions. Our results suggest that Seattle landslides occur in native deposits and colluvium, ultimately in response to surface‐water erosion of hillslope toes. Regional groundwater conditions do not appear to strongly affect the general distribution of Seattle landslides; historical landslides were equally dispersed within and outside of the area potentially affected by regional groundwater conditions. Published in 2007 by John Wiley & Sons, Ltd.     

Numerically modelling groundwater in an arid area with ANN‐generated dynamic boundary conditions

Groundwater is sensitive to the climate change and agricultural activities in arid and semi‐arid areas. Over the past several decades, human activities, such as groundwater extraction for irrigation, have resulted in aquifer overdraft and disrupted the natural equilibrium in these areas. Regional groundwater simulation is important to determine appropriate groundwater management policies, and numerical simulation has become the most popular method. However, most groundwater models were developed with static boundary conditions. In this research, the Minqin oasis, an arid region located in northwest China, was selected as the study area. An artificial neural network (ANN) was developed to simulate effects of weather conditions, agricultural activities and surface water on groundwater level in a dynamic boundary of the domain. Subsequently, a groundwater numerical model, named ANN‐FEFLOW model, was developed, with a dynamic boundary condition defined by the ANN model. The verifying results showed that the model has higher precision, with a root mean square error (RMSE) of 0·71 m, relative error (RE) of 17·96% and R² of 0·84 relative to the great groundwater change. Furthermore, the groundwater model has higher precision than the conventional groundwater model with static boundary condition, particularly in the area near the dynamic boundary. This study demonstrated that dynamic boundaries can improve the precision of the regional groundwater model in an arid area and that ANN can provide higher accuracy prediction capability for groundwater levels with dynamic boundary. Copyright © 2010 John Wiley & Sons, Ltd.     

Modification of the SWAT model to simulate regional groundwater flow using a multicell aquifer

The soil and water assessment tool (SWAT) has been widely used and thoroughly tested in many places in the world. The application of the SWAT model has pointed out that 2 of the major weaknesses of SWAT are related to the nonspatial reference of the hydrologic response unit concept and to the simplified groundwater concept, which contribute to its low performance in baseflow simulation and its inability to simulate regional groundwater flow. This study modified the groundwater module of SWAT to overcome the above limitations. The modified groundwater module has 2 aquifers. The local aquifer, which is the shallow aquifer in the original SWAT, represents a local groundwater flow system. The regional aquifer, which replaces the deep aquifer of the original SWAT, represents intermediate and regional groundwater flow systems. Groundwater recharge is partitioned into local and regional aquifer recharges. The regional aquifer is represented by a multicell aquifer (MCA) model. The regional aquifer is discretized into cells using the Thiessen polygon method, where centres of the cells are locations of groundwater observation wells. Groundwater flow between cells is modelled using Darcy's law. Return flow from cell to stream is conceptualized using a non‐linear storage–discharge relationship. The SWAT model with the modified aquifer module, the so‐called SWAT‐MCA, was tested in 2 basins (Wipperau and Neetze) with porous aquifers in a lowland area in Lower Saxony, Germany. Results from the Wipperau basin show that the SWAT‐MCA model is able (a) to simulate baseflow in a lowland area (where baseflow is a dominant source of streamflow) better than the original model and (b) to simulate regional groundwater flow, shown by the simulated groundwater levels in cells, quite well.     

Implementing a nonlinear groundwater module in the soil and water assessment tool (SWAT)

The Soil and Water Assessment Tool (SWAT) is widely used in modeling water quantity and quality. In the original SWAT, groundwater flow is calculated using a linear‐reservoir model, with outflow proportional to storage. However, observations show that this assumption is not always applicable; for example, macropores in Karst formations would seriously affect the groundwater behavior. A nonlinear groundwater algorithm was introduced in a new version of the SWAT model, called ISWAT. The Shenandoah Valley area in the Eastern U.S., which includes a number of geologic formations including Karst, was selected to test the modified ISWAT model. Parameter ESTimation (PEST) was coupled with ISWAT to auto‐calibrate the nonlinear parameter values. Ten years of record at 15 stream gauges were used to calibrate the model. The nonlinear ISWAT, statistically and visually, performed better in stream discharge estimation especially during baseflow recession and low‐flow periods. This indicated that the nonlinear algorithm can better represent groundwater behavior. The coupled ISWAT‐PEST approach can be used in future stream discharge simulation. Copyright © 2013 John Wiley & Sons, Ltd.     

A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional‐scale aquifers is typically neglected. In this work, a novel hillslope‐based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope‐storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two‐hillslope open‐book catchment are presented, and the results are compared against a benchmark three‐dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open‐book catchment, cumulative outflows are overestimated by 1–4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface–subsurface exchanges, local aquifer–regional aquifer interactions, and low flows play a key role in a watershed's dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytic element modelling for strip aquifers

The Analytic Element Method (AEM) provides a convenient tool for groundwater flow analysis in unbounded continuous domains. The AEM is based on the superposition of analytic functions, known as elements, useful at both regional and local scales. In this study, analytic elements for strip aquifers are presented. Such aquifers occur in riverine or coastal deposits and in outcrop zones of confined aquifers. Local flow field is modelled indirectly, using a reference plane related to the aquifer domain through the Schwarz‐Christoffel transform. The regional flow is obtained as a solution of the one‐dimensional flow equation. The proposed methodology was tested by modelling two hypothetical situations, which were compared to exact solutions. It is shown that regional boundaries can be reproduced exactly while local fields are adequately reproduced with analytic elements. The developed elements are applied to simulate a real flow field in northeastern Brazil showing good agreement with measured water levels. Copyright © 2011 John Wiley & Sons, Ltd.