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.     

Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.     

Maximizing Net Extraction Using an Injection‐Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection‐extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation‐point locations and recirculation ratio, assuming steady‐state, sharp‐interface conditions. The injection‐extraction well‐pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m²/d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well‐pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.     

Modeling the Transient Response of Saline Intrusion to Rising Sea‐Levels

Sea levels are expected to rise as a result of global temperature increases, one implication of which is the potential exacerbation of sea water intrusion into coastal aquifers. Given that approximately 70% of the world's population resides in coastal regions, it is imperative to understand the interaction between fresh groundwater and sea water intrusion in order to best manage available resources. For this study, controlled investigation has been carried out concerning the temporal variation in sea water intrusion as a result of rising sea levels. A series of fixed inland head two‐dimensional sea water intrusion models were developed with SEAWAT in order to assess the impact of rising sea levels on the transient migration of saline intrusion in coastal aquifers under a range of hydrogeological property conditions. A wide range of responses were observed for typical hydrogeological parameter values. Systems with a high ratio of hydraulic conductivity to recharge and high effective porosity lagged behind the equilibrium sea water toe positions during sea‐level rise, often by many hundreds of meters, and frequently taking several centuries to equilibrate following a cease in sea‐level rise. Systems with a low ratio of hydraulic conductivity to recharge and low effective porosity did not develop such a large degree of disequilibrium and generally stabilized within decades following a cease in sea‐level rise. This study provides qualitative initial estimates for the expected rate of intrusion and predicted degree of disequilibrium generated by sea‐level rise for a range of hydrogeological parameter values.     

Impact of Sea-Level Rise on Sea Water Intrusion in Coastal Aquifers

Despite its purported importance, previous studies of the influence of sea-level rise on coastal aquifers have focused on specific sites, and a generalized systematic analysis of the general case of the sea water intrusion response to sea-level rise has not been reported. In this study, a simple conceptual framework is used to provide a first-order assessment of sea water intrusion changes in coastal unconfined aquifers in response to sea-level rise. Two conceptual models are tested: (1) flux-controlled systems, in which ground water discharge to the sea is persistent despite changes in sea level, and (2) head-controlled systems, whereby ground water abstractions or surface features maintain the head condition in the aquifer despite sea-level changes. The conceptualization assumes steady-state conditions, a sharp interface sea water-fresh water transition zone, homogeneous and isotropic aquifer properties, and constant recharge. In the case of constant flux conditions, the upper limit for sea water intrusion due to sea-level rise (up to 1.5 m is tested) is no greater than 50 m for typical values of recharge, hydraulic conductivity, and aquifer depth. This is in striking contrast to the constant head cases, in which the magnitude of salt water toe migration is on the order of hundreds of meters to several kilometers for the same sea-level rise. This study has highlighted the importance of inland boundary conditions on the sea-level rise impact. It identifies combinations of hydrogeologic parameters that control whether large or small salt water toe migration will occur for any given change in a hydrogeologic variable.     

Vulnerability indicators of sea water intrusion

In this paper, simple indicators of the propensity for sea water intrusion (SWI) to occur (referred to as "SWI vulnerability indicators") are devised. The analysis is based on an existing analytical solution for the steady-state position of a sharp fresh water-salt water interface. Interface characteristics, that is, the wedge toe location and sea water volume, are used in quantifying SWI in both confined and unconfined aquifers. Rates-of-change (partial derivatives of the analytical solution) in the wedge toe or sea water volume are used to quantify the aquifer vulnerability to various stress situations, including (1) sea-level rise; (2) change in recharge (e.g., due to climate change); and (3) change in seaward discharge. A selection of coastal aquifer cases is used to apply the SWI vulnerability indicators, and the proposed methodology produces interpretations of SWI vulnerability that are broadly consistent with more comprehensive investigations. Several inferences regarding SWI vulnerability arise from the analysis, including: (1) sea-level rise impacts are more extensive in aquifers with head-controlled rather than flux-controlled inland boundaries, whereas the opposite is true for recharge change impacts; (2) sea-level rise does not induce SWI in constant-discharge confined aquifers; (3) SWI vulnerability varies depending on the causal factor, and therefore vulnerability composites are needed that differentiate vulnerability to such threats as sea-level rise, climate change, and changes in seaward groundwater discharge. We contend that the approach is an improvement over existing methods for characterizing SWI vulnerability, because the method has theoretical underpinnings and yet calculations are simple, although the coastal aquifer conceptualization is highly idealized.     

Boundary condition effects on maximum groundwater withdrawal in coastal aquifers

Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.     

Stack unit mapping of coastal aquifer to predict and control sea water intrusion using remote sensing and a geographical information system

Aquifers are inherently susceptible to contamination and coastal aquifers in specific are highly vulnerable to sea water intrusion. For efficient planning and management of coastal aquifers in Kayalpattu and Tiruchopuram villages, which extend over 4·05 km², it is essential to delineate and predict the extent of intrusion into the shallow aquifer. Management of ground water in coastal aquifers is composed of major elements that should be properly evaluated, and special attention is given to the sea water intrusion problem. Different data, like hydro‐geomorphological and depth‐wise iso‐apparent resistivity, are integrated spatially using a geographical information system. The stack‐unit mapping approach is used to delineate the zones with iso‐apparent resistivity of less than 10 Ω m have been found to be increasing in areal extent with reference to depth. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of Sea‐Level Rise on Salt Water Intrusion near a Coastal Well Field in Southeastern Florida

A variable‐density groundwater flow and dispersive solute transport model was developed for the shallow coastal aquifer system near a municipal supply well field in southeastern Florida. The model was calibrated for a 105‐year period (1900 to 2005). An analysis with the model suggests that well‐field withdrawals were the dominant cause of salt water intrusion near the well field, and that historical sea‐level rise, which is similar to lower‐bound projections of future sea‐level rise, exacerbated the extent of salt water intrusion. Average 2005 hydrologic conditions were used for 100‐year sensitivity simulations aimed at quantifying the effect of projected rises in sea level on fresh coastal groundwater resources near the well field. Use of average 2005 hydrologic conditions and a constant sea level result in total dissolved solids (TDS) concentration of the well field exceeding drinking water standards after 70 years. When sea‐level rise is included in the simulations, drinking water standards are exceeded 10 to 21 years earlier, depending on the specified rate of sea‐level rise.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd.     

Brief Review on Methods of Estimation of the Location of a Fresh Water–Salt Water Interface with Hydraulic Heads or Pressures in Coastal Zones

Methods of estimation of the location of a sharp fresh water–salt water interface with hydraulic heads or pressures are relatively simple and are widely used. Progress has been made in the recent decade toward the mathematical relations describing the position of the sharp interface using hydraulic heads or pressures in coastal zones. This paper reviews several methods for estimation of the location of fresh water–salt water interface in coastal aquifers, including the classical Ghyben–Herzberg relation. The location of the fresh water–salt water interface in a coastal homogeneous, isotropic unconfined aquifer can be estimated based on piezometric heads at two points in the same vertical line tapping, respectively, the salt water zone (including the interface) and the fresh water zone (from the water table to the interface) when the groundwater flow system is in a steady state and satisfies the Dupuit assumption. If pressures are measured at two points in the fresh water and salt water zones in the same vertical line in the coastal aquifer under the same assumption, then the position of the interface can still be estimated with the pressure data. If the Dupuit assumption is not met in coastal aquifers and the vertical fresh water head gradients can be approximated with a straight line, the position of the interface can roughly be estimated by using the water level data in a partially penetrating well during drilling of the well.     

A simple method for locating the fresh water-salt water interface using pressure data

Salt water intrusion is a key issue in dealing with exploitation, restoration, and management of fresh ground water in coastal aquifers. Constant monitoring of the fresh water-salt water interface is necessary for proper management of ground water resources. This study presents a simple method to estimate the depth of the fresh water-salt water interface in coastal aquifers using two sets of pressure data obtained from the fresh and saline zones within a single borehole. This method uses the density difference between fresh water and saline water and can practically be used at coastal aquifers that have a relatively sharp fresh water-salt water interface with a thin transition zone. The proposed method was applied to data collected from a coastal aquifer on Jeju Island, Korea, to estimate the variations in the depth of the interface. The interface varied with daily tidal fluctuations and heavy rainfall in the rainy season. The estimated depth of the interface showed a good agreement with the measured electrical conductivity profile.     

Using Alternate Pumping and Cooperative Game Theory to Reduce Sea Water Intrusion

In this article, alternate pumping is studied as a means used to reduce the salinity concentration in coastal aquifers, pumped using a system of wells. This approach has been applied to a hypothetical confined coastal aquifer. Flow has been modeled, using SEAWAT. Two strategies are proposed based on cooperative game theory, to promote alternate pumping. In both strategies an external player will compensate the users that will pump during an unpopular pumping period. In the first strategy it is supposed that this external player aims at protecting a critical well, e.g. a municipal well, reducing its maximum salinity concentration by pumping alternately. In the second strategy proposed, the target is to reduce the overall salinity of the water pumped by the wells. In applying the cooperative game theory, the Shapley value is used to distribute the benefits of cooperation between the players (well users), according to their marginal contribution. Overall, well users can reduce sea water intrusion by cooperatively changing their pumping time schedules. The game theoretical model developed is a useful tool to promote cooperation toward this direction. The methods applied in the hypothetical aquifer, can be tested in actual aquifers to reduce sea water intrusion.     

Analytical Design Curves to Maximize Pumping or Minimize Injection in Coastal Aquifers

Explicit algebraic equations are derived to determine approximate maximum pumping rates or minimum injection rates to limit sea water intrusion to a prespecified distance from the coastline. The equations are based on Strack's (1976) single-potential solution. The maximum pumping rates and minimum injection rates applied at wells with uniform spacing to control the inland movement of the fresh water-salt water interface in a coastal aquifer could be calculated from Strack's (1976) solution without the need of a numerical optimization algorithm. When wells are distributed in a simple fashion, the maximum intrusion location can be identified precisely for pumping cases and approximately for injection cases. For pumping cases, critical points are the limit of allowable salt water intrusion, whereas no such limit exists for injection cases. Once an application site is identified, a series of design curves for pumping and injection rates can be developed for arbitrary intrusion limits. When a user is interested only in the largest pumping rates associated with critical points, one design curve can yield complete information.     

Anticipating the effects of groundwater withdrawal on seawater intrusion and soil settlement in urban coastal areas

Intensive pumping in urban coastal areas is a common threat to water resource quality due to seawater intrusion. In those areas where subsurface water resources are not usually used for human consumption or irrigation, intensive pumping is associated with other activities like the lowering of the water table necessary to support underground structures and building foundations. This activity also increases the likelihood of soil settlement that affects building stability and the corrosion of concrete structures due to groundwater salinity. Under these circumstances, the awareness of a certain municipality (Calonge, NE Spain) of the potential effects of groundwater withdrawal upon foundations has led to an integrated approach to anticipate seawater intrusion related to urban development. Geological mapping and correlation of borehole logs, electrical resistivity tomography, and hydrochemical data provide comprehensive knowledge of the geology and hydrogeology of the area and act as screening tools necessary to discern the influence of hydrological processes in coastal areas. Developing Strack's analytical solution, new comprehensive, dimensionless expressions are herein derived to determine the critical pumping rate necessary to prevent seawater intrusion, as well as to reproduce the evolution of the wedge toe and the water table stagnation point under different withdrawal rates. Furthermore, the Dupuit–Forchheimer well discharge formula allows the estimation of the effects of the water table lowering due to such critical pumping in the surrounding building foundations. Field data from the Calonge coastal plain illustrate this approach and provide assessment criteria for future urban development and planning. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of Seasonal Variations in Sea Level on the Salinity Regime of a Coastal Groundwater–Fed Wetland

Seasonal variations in sea level are often neglected in studies of coastal aquifers; however, they may have important controls on processes such as submarine groundwater discharge, sea water intrusion, and groundwater discharge to coastal springs and wetlands. We investigated seasonal variations in salinity in a groundwater‐fed coastal wetland (the RAMSAR listed Piccaninnie Ponds in South Australia) and found that salinity peaked during winter, coincident with seasonal sea level peaks. Closer examination of salinity variations revealed a relationship between changes in sea level and changes in salinity, indicating that sea level–driven movement of the fresh water‐sea water interface influences the salinity of discharging groundwater in the wetland. Moreover, the seasonal control of sea level on wetland salinity seems to override the influence of seasonal recharge. A two‐dimensional variable density model helped validate this conceptual model of coastal groundwater discharge by showing that fluctuations in groundwater salinity in a coastal aquifer can be driven by a seasonal coastal boundary condition in spite of seasonal recharge/discharge dynamics. Because seasonal variations in sea level and coastal wetlands are ubiquitous throughout the world, these findings have important implications for monitoring and management of coastal groundwater–dependent ecosystems.     

Using MODFLOW code to approach transient hydraulic head with a sharp‐interface solution

Saltwater intrusion problems have been usually tackled through analytical models 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, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (?). We propose to approach also the transient problem solving a single potential equation (using also the ? variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Analytical models of contaminant transport in coastal aquifers

The Henry formulation, which couples subsurface flow and salt transport via a variable-density flow formulation, can be used to evaluate the extent of sea water intrusion into coastal aquifers. The coupling gives rise to nontrivial flow patterns that are very different from those observed in inland aquifers. We investigate the influence of these flow patterns on the transport of conservative contaminants in a coastal aquifer. The flow is characterized by two dimensionless parameters: the Péclet number, which compares the relative effects of advective and dispersive transport mechanisms, and a coupling parameter, which describes the importance of the salt water boundary on the flow. We focus our attention on two regimes – low and intermediate Péclet number flows. Two transport scenarios are solved analytically by means of a perturbation analysis. The first, a natural attenuation scenario, describes the flushing of a contaminant from a coastal aquifer by clean fresh water, while the second, a contaminant spill scenario, considers an isolated point source.     

Optimal and sustainable extraction of groundwater in coastal aquifers

Four examples are investigated for the optimal and sustainable extraction of groundwater from a coastal aquifer under the threat of seawater intrusion. The objectives and constraints of these management scenarios include maximizing the total volume of water pumped, maximizing the profit of selling water, minimizing the operational and water treatment costs, minimizing the salt concentration of the pumped water, and controlling the drawdown limits. The physical model is based on the density-dependent advective-dispersive solute transport model. Genetic algorithm is used as the optimization tool. The models are tested on a hypothetical confined aquifer with four pumping wells located at various depths. These solutions establish the feasibility of simulating various management scenarios under complex three-dimensional flow and transport processes in coastal aquifers for the optimal and sustainable use of groundwater.     

Sea water intrusion by sea-level rise: scenarios for the 21st century

This study presents a method to assess the contributions of 21st-century sea-level rise and groundwater extraction to sea water intrusion in coastal aquifers. Sea water intrusion is represented by the landward advance of the 10,000 mg/L iso-salinity line, a concentration of dissolved salts that renders groundwater unsuitable for human use. A mathematical formulation of the resolution of sea water intrusion among its causes was quantified via numerical simulation under scenarios of change in groundwater extraction and sea-level rise in the 21st century. The developed method is illustrated with simulations of sea water intrusion in the Seaside Area sub-basin near the City of Monterey, California (USA), where predictions of mean sea-level rise through the early 21st century range from 0.10 to 0.90 m due to increasing global mean surface temperature. The modeling simulation was carried out with a state-of-the-art numerical model that accounts for the effects of salinity on groundwater density and can approximate hydrostratigraphic geometry closely. Simulations of sea water intrusion corresponding to various combinations of groundwater extraction and sea-level rise established that groundwater extraction is the predominant driver of sea water intrusion in the study aquifer. The method presented in this work is applicable to coastal aquifers under a variety of other scenarios of change not considered in this work. For example, one could resolve what changes in groundwater extraction and/or sea level would cause specified levels of groundwater salinization at strategic locations and times.