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.     

Tracking Groundwater Discharge to a Large River using Tracers and Geophysics

Few studies have investigated large reaches of rivers in which multiple sources of groundwater are responsible for maintaining baseflow. This paper builds upon previous work undertaken along the Fitzroy River, one of the largest perennial river systems in north‐western Australia. Synoptic regional‐scale sampling of both river water and groundwater for a suite of environmental tracers (⁴He, ⁸⁷Sr/⁸⁶Sr, ²²²Rn and major ions), and subsequent modeling of tracer behavior in the river, has enabled definition and quantification of groundwater input from at least three different sources. We show unambiguous evidence of both shallow “local” groundwater, possibly recharged to alluvial aquifers beneath the adjacent floodplain during recent high‐flow events, and old “regional” groundwater introduced via artesian flow from deep confined aquifers. We also invoke hyporheic exchange and either bank return flow or parafluvial flow to account for background ²²²Rn activities and anomalous chloride trends along river reaches where there is no evidence of the local or regional groundwater inputs. Vertical conductivity sections acquired through an airborne electromagnetic (AEM) survey provide insights to the architecture of the aquifers associated with these sources and general groundwater quality characteristics. These data indicate fresh groundwater from about 300 m below ground preferentially discharging to the river, at locations consistent with those inferred from tracer data. The results demonstrate how sampling rivers for multiple environmental tracers of different types—including stable and radioactive isotopes, dissolved gases and major ions—can significantly improve conceptualization of groundwater—surface water interaction processes, particularly when coupled with geophysical techniques in complex hydrogeological settings.     

Advantages of the analytic element method for the solution of groundwater management problems

In the simulation‐optimization approach, a coupled optimization and groundwater flow/transport model is used to solve groundwater management problems. The efficiency of the numerical method, which is used to simulate the groundwater flow, is one the major reason to obtain the best solution for a management problem. This study was carried out to examine the advantages of the analytic element method (AEM) in the simulation‐optimization approach, for the solution of groundwater management problems. For this study, the AEM and finite difference method (FDM) based flow models were developed and coupled with the particle swarm optimization (PSO)‐based optimization model. Furthermore, the AEM‐PSO and FDM‐PSO models developed were applied in hypothetical as well as real field conditions to address groundwater management problems and the results were compared. For the real field situation, the models developed were applied to the Dore River basin in France to minimize the installation and operational cost of new pumping wells taking the location and discharge of the pumping wells as decision variables. The constraints of the problem were identified with the help of stakeholders and water authority officials. The AEM flow model was developed to facilitate the management model particularly when at each iteration, the optimization model calls for a simulation model to calculate the values of groundwater heads. The results show that, at some points, the AEM‐PSO model is efficient in identifying the optimal location of wells and consequently results in optimal costs, sometimes difficult when using the FDM. Copyright © 2011 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.     

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.     

The development of new analytic elements for transient flow and multiaquifer flow

We deal in this paper with an ongoing development of the analytic element method. We present in outline new analytic line elements that are suitable to model general flow fields, i.e., flow fields that possess a continuously varying areal inflow or outflow. These elements are constructed specifically to model the leakage through leaky layers that separate aquifers in leaky systems and to model transient effects. The leakage or release from storage underneath linear features is modeled precisely by the new elements; the singularity in leakage is matched exactly by the approximate solution. Applications are given for a problem involving leakage and for a case of transient flow. We note that the analytic elements can be used also to reproduce the effect of continuously varying aquifer properties, e.g., the hydraulic conductivity or the elevation of the base of the aquifer. In the latter case, the elements would reproduce the rotation of the flow field caused by the variation in properties, rather than the divergence as for the case of leakage.     

The AEM and regional carbonate aquifer modeling

The analytic element method (AEM) has been applied to a 15,000-km2 area of the Paleozoic carbonate rock terrain of Nevada. The focus is the Muddy River springs area, which receives 1.44 m3/s (51 ft3/s) of regionally derived ground water, and forms the Muddy River. The study was undertaken early in 2000 to support the development of a cooling water supply for a gas-fired generation facility 20 km south of the Muddy River springs. The primary objectives of the AEM modeling were to establish a better understanding of regional fluxes and boundary conditions and to provide a framework for examination of more local transient effects using MODFLOW. Geochemical evidence available in 2000 suggested two separate flow fields, one in the north discharging at the springs, and a southern area of small hydraulic gradients. To be conservative, however, hydraulic continuity between the two areas was maintained in the 2000 AEM model. Using new monitoring well data collected in the south, and analyses confirming that seasonal pumping effects in the north are not propagated to the south, a later AEM model that included a barrier calibrated with relative ease. The analytic element model was well suited for simulating an area larger than the immediate area of interest, was easy to modify as more information became available, and facilitated the stepwise development of multiple conceptual models of the site.     

Aquifer Vulnerability Assessment Based on Sequence Stratigraphic and 39Ar Transport Modeling

A large‐scale groundwater flow and transport model is developed for a deep‐seated (100 to 300 m below ground surface) sedimentary aquifer system. The model is based on a three‐dimensional (3D) hydrostratigraphic model, building on a sequence stratigraphic approach. The flow model is calibrated against observations of hydraulic head and stream discharge while the credibility of the transport model is evaluated against measurements of ³⁹Ar from deep wells using alternative parameterizations of dispersivity and effective porosity. The directly simulated 3D mean age distributions and vertical fluxes are used to visualize the two‐dimensional (2D)/3D age and flux distribution along transects and at the top plane of individual aquifers. The simulation results are used to assess the vulnerability of the aquifer system that generally has been assumed to be protected by thick overlaying clayey units and therefore proposed as future reservoirs for drinking water supply. The results indicate that on a regional scale these deep‐seated aquifers are not as protected from modern surface water contamination as expected because significant leakage to the deeper aquifers occurs. The complex distribution of local and intermediate groundwater flow systems controlled by the distribution of the river network as well as the topographical variation (Tóth 1963) provides the possibility for modern water to be found in even the deepest aquifers.     

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.     

An analytic element approach for modeling polygonal inhomogeneities in multi-aquifer systems

An analytic element approach is presented for the modeling of steady groundwater flow through multi-aquifer systems with piecewise constant aquifer and leaky layer properties. Different properties may be specified for domains bounded by closed polygons, referred to as polygonal inhomogeneities. The boundary of these inhomogeneities is modeled with two types of high-order line elements. First, a string of single-aquifer line-doublets is used; these elements cut through all aquifers and are valid both inside and outside the inhomogeneity. Second, two strings of multi-aquifer line-sinks are used, one string that is valid inside the inhomogeneity and one string that is valid outside; the comprehensive extraction of these line-sinks is zero at any point along the string. The proposed approach results in a comprehensive flow field of which the component normal to the boundary of the inhomogeneity is continuous across the boundary at any point. Within each individual aquifer, continuity of head and the component of flow normal to the boundary are met approximately across the boundary; the accuracy increases when the order of the line elements is increased and/or when shorter line elements are used. The proposed analytic element approach produces results that are virtually identical to the exact solution for a cylindrical inhomogeneity, and a high-resolution MODFLOW2000 model of two rectangular inhomogeneities with a shared boundary. The practical application of the approach is demonstrated through the solution of a problem with an irregularly shaped inhomogeneity with rivers crossing the inhomogeneity boundary.     

Understanding and modelling spatial drain–aquifer interactions in a low‐lying coastal aquifer—the Thurne catchment,Norfolk, UK

Seawater intrusion into fresh groundwater formations generally results inadvertently from human activities, such as over‐abstraction from coastal aquifers. This article describes the data analysis to quantify drain–aquifer interactions in a low‐lying pump‐drained coastal aquifer, which is subject to saline intrusion due to widespread land drainage, and the resulting development and application of a numerical groundwater model to understand the spatial groundwater system behaviour (including groundwater salinity fluxes). Without measured flow data in this pump‐drained catchment, a novel groundwater head‐dependent approach to hydrograph separation is described. Time‐variant and time‐invariant MODFLOW analyses are utilised to examine the flow processes. A new approach to calculate drain coefficients, which represent the extensive network of drainage ditches in the regional model, using field information, is described; the sum of the drainage coefficients are close to the values independently estimated from the head‐dependent hydrograph separation. Results show that (1) the groundwater flows into the drainage systems are well reproduced using the new drain coefficients, (2) particle tracking of fresh and saline water can explain observed spatial salinity distribution within drainage networks and (3) the modelled flow of seawater across the coast is approximately 25% greater than that discharged by the pumps, demonstrating the need for drainage management to be aware of the slow response of groundwater systems to past drainage system changes. The article demonstrates that numerical groundwater modelling can produce the improved understanding needed to inform management decisions in such complex environments. Copyright © 2010 John Wiley & Sons, Ltd.     

Tidal effects on groundwater dynamics in unconfined aquifers

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi‐steady‐state rise in the mean water‐table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed and this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water‐table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright © 2001 John Wiley & Sons, Ltd.     

Analytic element ground water modeling as a research program (1980 to 2006)

Scientists and engineers who use the analytic element method (AEM) for solving problems of regional ground water flow may be considered a community, and this community can be studied from the perspective of history and philosophy of science. Applying the methods of the Hungarian philosopher of science Imre Lakatos (1922 to 1974), the AEM "research program" is distinguished by its hard core (theoretical basis), protective belt (auxiliary assumptions), and heuristic (problem solving machinery). AEM has emerged relatively recently in the scientific literature and has a relatively modest number of developers and practitioners compared to the more established finite-element and finite-difference methods. Nonetheless, there is evidence to support the assertion that the AEM research program remains in a progressive phase. The evidence includes an expanding publication record, a growing research strand following Professor Otto Strack's book Groundwater Mechanics (1989), the continued placement of AEM researchers in academia, and the further development of innovative analytical solutions and computational solvers/models.     

Multilayer analytic element modeling of radial collector wells

A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms.     

Local vs. Regional Groundwater Flow Delineation from Stable Isotopes at Western North America Springs

The recharge location for many springs is unknown because they can be sourced from proximal, shallow, atmospheric sources or long‐traveled, deep, regional aquifers. The stable isotope (¹⁸O and ²H) geochemistry of springs water can provide cost‐effective indications of relative flow path distance without the expense of drilling boreholes, conducting geophysical studies, or building groundwater flow models. Locally sourced springs generally have an isotopic signature similar to local precipitation for that region and elevation. Springs with a very different isotopic composition than local meteoric inputs likely have non‐local recharge, representing a regional source. We tested this local vs. regional flow derived hypothesis with data from a new, large springs isotopic database from studies across Western North America in Arizona, Nevada, and Alberta. The combination of location‐specific precipitation data with stable isotopic groundwater data provides an effective method for flow path determination at springs. We found springs in Arizona issue from a mix of regional and local recharge sources. These springs have a weak elevation trend across 1588 m of elevation where higher elevation springs are only slightly more depleted than low elevation springs with a δ¹⁸O variation of 5.9‰. Springs sampled in Nevada showed a strong elevation‐isotope relationship with high‐elevation sites discharging depleted waters and lower elevation springs issuing enriched waters; only a 2.6‰ difference exists in ¹⁸O values over an elevation range of more than 1500 m. Alberta's springs are mostly sourced from local flow systems and show a moderate elevation trend of 1200 m, but the largest range in δ¹⁸O, 7.1‰.     

Laplace-transform analytic element solution of transient flow in porous media

A Laplace-transform analytic element method (LT-AEM) is described for the solution of transient flow problems in porous media. Following Laplace transformation of the original flow problem, the analytic element method (AEM) is used to solve the resultant time-independent modified Helmholtz equation, and the solution is inverted numerically back into the time domain. The solution is entirely general, retaining the mathematical elegance and computational efficiency of the AEM while being amenable to parallel computation. It is especially well suited for problems in which a solution is required at a limited number of points in space–time, and for problems involving materials with sharply contrasting hydraulic properties. We illustrate the LT-AEM on transient flow through a uniform confined aquifer with a circular inclusion of contrasting hydraulic conductivity and specific storage. Our results compare well with published analytical solutions in the special case of radial flow.     

Conceptualizing leakage and storage contributions from long open interval wells in regional deep basin flow models

Deep basin aquifers are increasingly used in water‐stressed areas, though their potential for sustainable development is inhibited by overlying aquitards and limited recharge rates. Long open interval wells (LOIWs)—wells uncased through multiple hydrostratigraphic units—are present in many confined aquifer systems and can be an important mechanism for deep basin aquifers to receive flow across aquitards. LOIWs are a major control on flow in the deep Cambrian–Ordovician sandstone aquifers of the upper Midwest, USA, providing a source of artificial leakage from shallow bedrock aquifers and equilibrating head within the sandstone aquifers despite differential pumpage. Conceptualizing and quantifying this anthropogenic flow has long been a challenge for groundwater flow modellers, particularly on a regional scale. Synoptic measurements of active production wells and well completion data for northeast Illinois form the basis for a transient, head‐specified MODFLOW model that determines mass balance contributions to the region and estimates LOIW leakage to the aquifers. Using this insight, transient LOIW leakage was simulated using transiently changing K_V zones in a traditional, Q‐specified MODFLOW‐USG model, a novel approach that allows the K_V in a cell containing a LOIW to change transiently by use of the time‐variant materials (TVM) package. With this modification, we achieved a consistent calibration through time, averaging 19.9 m root mean squared error. This model indicates that artificial leakage via LOIWs contributed a minimum of 10–13% of total flow to the sandstone aquifers through the entire history of pumping, up to 50% of flow around 1930. Removal from storage exceeds 40% of flow during peak withdrawals, much of this flow sourced from units other than the primary sandstone aquifers via LOIWs. As such, understanding the timing and magnitude of LOIW leakage is essential for predicting future water availability in deep basin aquifers.     

The Analytic Element Method for rectangular gridded domains,benchmark comparisons and application to the High Plains Aquifer

Groundwater studies face computational limitations when providing local detail (such as well drawdown) within regional models. We adapt the Analytic Element Method (AEM) to extend separation of variable solutions for a rectangle to domains composed of multiple interconnected rectangular elements. Each rectangle contains a series solution that satisfies the governing equations and coefficients are adjusted to match boundary conditions at the edge of the domain and continuity conditions across adjacent rectangles. A complete mathematical implementation is presented including matrices to solve boundary and continuity conditions. This approach gathers the mathematical functions associated with head and velocity within a small set of functions for each rectangle, enabling fast computation of these variables. Benchmark studies verify that conservation of mass and energy conditions are accurately satisfied using a method of images solution, and also develop a solution for heterogeneous hydraulic conductivity with log normal distribution. A case study illustrates that the methods are capable of modeling local detail within a large-scale regional model of the High Plains Aquifer in the central USA and reports the numerical costs associated with increasing resolution, where use is made of GIS datasets for thousands of rectangular elements each with unique geologic and hydrologic properties, Methods are applicable to interconnected rectangular domains in other fields of study such as heat conduction, electrical conduction, and unsaturated groundwater flow.     

Analytic modeling of groundwater dynamics with an approximate impulse response function for areal recharge

An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.