Tide‐induced groundwater head fluctuation in a coastal aquifer system with a submarine outcrop covered by a thin silt layer

We present an analytical solution of groundwater head response to tidal fluctuation in a coastal multilayered aquifer system consisting of an unconfined aquifer, a leaky confined aquifer and a semi‐permeable layer between them. The submarine outcrop of the confined aquifer is covered by a thin silt layer. A mathematical model and the analytical solution of this model are given. The silt layer reduces the amplitude of the hydraulic head fluctuation by a constant factor, and shifts the phase by a positive constant (time lag), both of which depend on the leakances of the silt layer and the semi‐permeable layer. The time lag is less than 1·5 h and 3·0 h for semi‐diurnal and diurnal sea tides respectively. When the leakance of the semi‐permeable layer or the silt layer assumes certain special values, the solution becomes the existing solutions derived by previous researchers. The amplitude of the hydraulic head fluctuation in the confined aquifer increases with the leakance of the silt layer and decreases with the leakance of the semi‐permeable layer, whereas the phase shift of the fluctuation decreases with both of them. A hypothetical example shows that neglecting the silt layer may result in significant parameter estimation discrepancy between the amplitude attenuation and the time‐lag fittings. Copyright © 2007 John Wiley & Sons, Ltd.     

A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer

A two‐dimensional semi‐analytical solution to analyse stream–aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two‐dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non‐dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one‐dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water‐level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water‐level variations due to stream and tidal boundaries are sensitive to specific yield. Copyright © 2006 John Wiley & Sons, Ltd.     

Drawdown and stream depletion produced by pumping in the vicinity of a partially penetrating stream

Commonly used analytical approaches for estimation of pumping-induced drawdown and stream depletion are based on a series of idealistic assumptions about the stream-aquifer system. A new solution has been developed for estimation of drawdown and stream depletion under conditions that are more representative of those in natural systems (finite width stream of shallow penetration adjoining an aquifer of limited lateral extent). This solution shows that the conventional assumption of a fully penetrating stream will lead to a significant overestimation of stream depletion (> 100%) in many practical applications. The degree of overestimation will depend on the value of the stream leakance parameter and the distance from the pumping well to the stream. Although leakance will increase with stream width, a very wide stream will not necessarily be well represented by a model of a fully penetrating stream. The impact of lateral boundaries depends upon the distance from the pumping well to the stream and the stream leakance parameter. In most cases, aquifer width must be on the order of hundreds of stream widths before the assumption of a laterally infinite aquifer is appropriate for stream-depletion calculations. An important assumption underlying this solution is that stream-channel penetration is negligible relative to aquifer thickness. However, an approximate extension to the case of nonnegligible penetration provides reasonable results for the range of relative penetrations found in most natural systems (up to 85%). Since this solution allows consideration of a much wider range of conditions than existing analytical approaches, it could prove to be a valuable new tool for water management design and water rights adjudication purposes.     

A general solution for tide‐induced groundwater fluctuation in an estuarine‐coastal confined and unconfined aquifer system

This paper presents an analytical solution to tide‐induced head fluctuations in a two‐dimensional estuarine‐coastal aquifer system that consists of an unconfined aquifer and a heterogeneous confined aquifer extending under a tidal river with a semipermeable layer between them. This study considers the joint effects of tidal‐river leakage, inland leakage, dimensionless transmissivity between the tidal‐river and inland confined aquifer, and transmissivity anisotropic ratios. The analytical solution for this model is obtained via the separation of variables method. Three existing solutions related to head fluctuation in one‐ or two‐dimensional leaky confined aquifers are considered as special cases in the present solution. This study shows that there is a threshold of tidal‐river confined aquifer length. When the tidal‐river length is greater than the threshold length, the inland head fluctuations remain sensitive to the leakage effect but become insensitive to the tidal‐river width and dimensionless transmissivity. Considering leakage and transmissivity anisotropy, this study also demonstrates that at a location farther from the river–inland boundary, head fluctuations increase with increasing leakage and transmissivity anisotropy; the maximum head fluctuation occurs when leakage and transmissivity anisotropy are both at their maximum values. The combined action of the 3 effects of loading, tidal‐river aquifer leakage, and inland aquifer leakage differs significantly according to various aquifer parameters. The analytical solution in this paper can be applied to demonstrate the behaviours of the head fluctuations of an estuarine‐coastal aquifer system, and the head fluctuations can be clearly described when the tidal and hydrogeological parameters are derived from field measurement data or hypothetical cases.     

Factors Influencing the Stream‐Aquifer Flow Exchange Coefficient

Knowledge of river gain from or loss to a hydraulically connected water table aquifer is crucial in issues of water rights and also when attempting to optimize conjunctive use of surface and ground waters. Typically in groundwater models this exchange flow is related to a difference in head between the river and some point in the aquifer, through a “coefficient.” This coefficient has been defined differently as well as the location for the head in the aquifer. This paper proposes a new coefficient, analytically derived, and a specific location for the point where the aquifer head is used in the difference. The dimensionless part of the coefficient is referred to as the SAFE (stream‐aquifer flow exchange) dimensionless conductance. The paper investigates the factors that influence the value of this new conductance. Among these factors are (1) the wetted perimeter of the cross‐section, (2) the degree of penetration of the cross‐section, and (3) the shape of the cross‐section. The study shows that these factors just listed are indeed ordered in their respective level of importance. In addition the study verifies that the analytical correct value of the coefficient is matched by finite difference simulation only if the grid system is sufficiently fine. Thus the use of the analytical value of the coefficient is an accurate and efficient alternative to ad hoc estimates for the coefficient typically used in finite difference and finite element methods.     

Terrestrial‐originated submarine groundwater discharge through deep multilayered aquifer systems beneath the seafloor

A large quantity of submarine groundwater discharge (SGD) of about 1000 m³ day^?1 m^?1 of the 600‐km‐long shoreline of South Atlantic Bight has been estimated by Moore (Global Biogeochemical Cycles, 2010b, 24, GB4005, doi: 10.1029/2009GB003747 ). However, there is great uncertainty in estimating the percentage of net, land‐originated groundwater recharge of SGD. Moreover, most previous studies considered the homogeneous case for the coastal superficial aquifers. Here, we investigated the terrestrial‐originated SGD through a multilayered submarine aquifer system, which comprises two confined aquifers and two semi‐permeable layers. The inland recharge includes a constant part representing the annual average and a periodical part representing its seasonal variation. An analytical solution was derived and used to analyse the distributions of the terrestrial‐originated SGD from the multilayered aquifers along the Winyah Bay transect, South Atlantic Bight. It is found that the width of the zone of SGD from the upper aquifer ranges from ~0.8 to ~8.0 km depending on the leakance of the seabed semi‐permeable layer. A head of the upper aquifer at a coastline 1.0 m higher than the mean sea level will cause a SGD of 1.82– 18.3 m³ day^?1 m^?1 from that aquifer as the seabed semi‐permeable layer's leakance varies from 0.001 to 0.1 day^?1, providing considerable possibility for considerable land‐originated SGD. Seasonal terrestrial‐originated SGD variations predicted by the analytical model provide consistent explanation of the seasonal variation of ²²⁶Ra observed by Moore (Journal of Geophysics, 2007, 112, C10013, doi: 10.1029/2007JC004199 ). The contribution of the lower aquifer to SGD is only 1.2–12% of that of the upper aquifer. Copyright © 2014 John Wiley & Sons, Ltd.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

Three-dimensional flow in the storative semiconfining layers of a leaky aquifer

An analytical solution for three-dimensional (3D) flow in the storative semiconfining layers of a leaky aquifer fully penetrated by a production well is developed in this article to provide a method from which accurate hydraulic parameters in the semiconfining layers can be derived from aquifer test data. The analysis of synthetic aquifer test data with the 3D analytical solution in the semiconfining layers provided more accurate optimal hydraulic parameters than those derived using the available quasi-two-dimensional (2D) solution. Differences between the 3D and 2D flow solutions in the semiconfining layers become larger when a no flow boundary condition is imposed at either at the top of the upper semiconfining layer or at the bottom of the lower semiconfining layer or when the hydraulic conductivity ratio of the semiconfining layer to the aquifer is larger than 0.001. In addition, differences between the 3D and 2D flow solutions in the semiconfining layers are illustrated when the thickness ratio of the semiconfining layer to the aquifer is changed. Analysis of water level data from two hypothetical and one real aquifer test showed that the 3D solution in the semiconfining layers provides lower correlation coefficients among hydraulic parameters than the 2D solution.     

Application of an integrated surface water‐groundwater model to multi‐aquifers modeling in Choushui River alluvial fan,Taiwan

This research proposes a combination of SWAT and MODFLOW, MD‐SWAT‐MODFLOW, to address the multi‐aquifers condition in Choushui River alluvial fan, Taiwan. The natural recharge and unidentified pumping/recharge are separately estimated. The model identifies the monthly pumping/recharge rates in multi‐aquifers so that the daily streamflow can be simulated correctly. A multi‐aquifers condition means a subsurface formation composed of at least the unconfined aquifer, the confined aquifer, and an in‐between aquitard. In such a case, the variation of groundwater level is related to pumping/recharge activities in vertically adjacent aquifer and the river‐aquifer interaction. Both factors in turn affect the streamflow performance. Results show that MD‐SWAT‐MODFLOW performs better than SWAT alone in terms of simulated streamflow, especially during low flow period, when pumping/recharge rates are properly estimated. A sensitivity analysis of individual parameter suggests that the vertical leakance may be the most sensitive among all investigated MODFLOW parameters in terms of the estimated pumping/recharge among aquifers, and the Latin‐Hypercube‐One‐factor‐At‐a‐Time sensitivity analysis indicates that the hydraulic conductivity of channel is the most sensitive to the model performance. It also points out the necessity to simultaneously estimate pumping/recharge rates in multi‐aquifers. The estimated net pumping rate can be treated as a lower bound of the actual local pumping rate. As a whole, the model provides the spatio‐temporal groundwater use, which gives the authorities insights to manage groundwater resources. Copyright © 2012 John Wiley & Sons, Ltd.     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantifying River‐Groundwater Interactions of New Zealand's Gravel‐Bed Rivers: The Wairau Plain

New Zealand's gravel‐bed rivers have deposited coarse, highly conductive gravel aquifers that are predominantly fed by river water. Managing their groundwater resources is challenging because the recharge mechanisms in these rivers are poorly understood and recharge rates are difficult to predict, particularly under a more variable future climate. To understand the river‐groundwater exchange processes in gravel‐bed rivers, we investigate the Wairau Plain Aquifer using a three‐dimensional groundwater flow model which was calibrated using targeted field observations, “soft” information from experts of the local water authority, parameter regularization techniques, and the model‐independent parameter estimation software PEST. The uncertainty of simulated river‐aquifer exchange flows, groundwater heads, spring flows, and mean transit times were evaluated using Null‐space Monte‐Carlo methods. Our analysis suggests that the river is hydraulically perched (losing) above the regional water table in its upper reaches and is gaining downstream where marine sediments overlay unconfined gravels. River recharge rates are on average 7.3 m³/s, but are highly dynamic in time and variable in space. Although the river discharge regularly hits 1000 m³/s, the net exchange flow rarely exceeds 12 m³/s and seems to be limited by the physical constraints of unit‐gradient flux under disconnected rivers. An important finding for the management of the aquifer is that changes in aquifer storage are mainly affected by the frequency and duration of low‐flow periods in the river. We hypothesize that the new insights into the river‐groundwater exchange mechanisms of the presented case study are transferable to other rivers with similar characteristics.     

Analytical solution for drainage and recession from an unconfined aquifer

One-dimensional transient groundwater flow from a divide to a river in an unconfined aquifer described by the Boussinesq equation was studied. We derived the analytical solution for the water table recession and drainage change process described with a linearized Boussinesq equation with a physically based initial condition. A method for determining the average water table in the solutions was proposed. It is shown that the solution derived in the form of infinite series can be well approximated with the simplified solution which contains only the leading term of the original solution. The solution and their simplification can be easily evaluated and used by others to study the groundwater flow problems, such as drainage and base flow estimation, in an unconfined aquifer.     

Two‐dimensional flow response to tidal fluctuation in a heterogeneous aquifer‐aquitard system

In alluvial coastal aquifers, finer sediments are preferentially deposited along the downstream direction, so the hydraulic conductivity is generally heterogeneous and changes with distance from the coastline. To investigate the influence of aquifer heterogeneity on seawater‐groundwater interaction, a new two‐dimensional model characterising groundwater flow in an aquifer‐aquitard system was developed assuming that the hydraulic conductivity of the aquifer linearly increases with the distance from the coastline along the inland direction. A closed‐form analytical solution was derived using the separation‐of‐variables method. Comparing the new solution with the numerical solution by comsol Multiphysics (Sweden) based on the finite‐element method, one can see that the new solution agreed with the numerical solution very well except at the early time. We found that both aquitard leakance and the heterogeneity factor (b) could result in the propagation bias. The propagation bias represents the inconsistency between the theoretical calculation and the observed strong attenuation and small time lag between the head and tide fluctuations. The attenuation decreased with perpendicular distance from the coastline (x‐axis), whereas the time lag increased with distance along the x‐axis. The relationship between the time lag and the distance along the x‐axis seemed to be linear when b was 0.001 m^?1, whereas it obeyed a power function when b was greater than 0.01 m^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.     

Estimating River Conductance from Prior Information to Improve Surface‐Subsurface Model Calibration

Most groundwater models simulate stream‐aquifer interactions with a head‐dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill‐posed and individual model parameters are likely to be poorly constrained. Ill‐posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface‐subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water‐groundwater use.     

A two‐dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water

Groundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

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.     

Applying the HPT‐GWS for Hydrostratigraphy,Water Quality and Aquifer Recharge Investigations

The primary objective of this study was to evaluate use of the hydraulic profiling tool‐groundwater sampler (HPT‐GWS) log data as an indicator of water quality (level of dissolved ionic species) in an alluvial aquifer. The HPT‐GWS probe is designed for direct push advancement into unconsolidated formations. The system provides both injection pressure logs and electrical conductivity (EC) logs, and groundwater may be sampled at multiple depths as the probe is advanced (profiling). The combination of these three capabilities in one probe has not previously been available. During field work it was observed that when HPT corrected pressure (P_c) indicates a consistent aquifer unit then bulk formation EC can be used as an indicator of water quality. A high correlation coefficient (R ² = 0.93) was observed between groundwater specific conductance and bulk formation EC in the sands and gravels of the alluvial aquifer studied. These results indicate that groundwater specific conductance is exerting a controlling influence on the bulk formation EC of the coarse‐grained unit at this site, and probably many similar sites, consistent with Archie's Law. This simple relationship enables the use of the EC and P_c logs, with targeted water samples and a minimum of core samples, to rapidly assess groundwater quality over extended areas at high vertical resolution. This method was used to identify both a brine impacted zone at the base of the aquifer investigated and a groundwater recharge lens developing below storm water holding ponds in the upper portion of the same aquifer. Sample results for trace level, naturally occurring elements (As, Ba, U) further demonstrate the use of this system to sample for low level groundwater contamination.