Tide-induced groundwater head fluctuation in coastal multi-layered aquifer systems with a submarine outlet-capping

This paper considered the tide-induced head fluctuations in two coastal multi-layered aquifer systems. Model I comprises two semi-permeable layers and a confined aquifer between them. Model II is a four-layered aquifer system including an unconfined aquifer, an upper semi-permeable layer, a confined aquifer and a lower semi-permeable layer. In each model, the submarine outlet of the confined aquifer is covered with a skin layer (“outlet-capping”). Analytical solutions of the two models are derived. In both models, leakages of the semi-permeable layers decrease the tidal head fluctuations. The outlet-capping reduces the aquifer’s head fluctuation by a constant factor and shifts the phase by a positive constant. The solution to Model II explains the inconsistency between the relatively small lag time and the strong amplitude damping effect of the tidal head fluctuations reported by Trefry and Johnston [Ground Water 1998;36:427–33] near the Port Adelaide River, Australia.     

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.     

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.     

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.     

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.     

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Abstract

This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated.

Editor D. Koutsoyiannis; Associate editor J. Simunek

Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172.     

An analytical solution for the head distribution in a tidal leaky confined aquifer extending an infinite distance under the sea

A mathematical model is developed to investigate the effects of tidal fluctuations and leakage on the groundwater head of leaky confined aquifer extending an infinite distance under the sea. The leakages of the offshore and inland aquitards are two dominant factors controlling the groundwater fluctuation. The tidal influence distance from the coast decreases significantly with the dimensionless leakage of the inland aquitard (u_i). The fluctuation of groundwater level in the inland part of the leaky confined aquifer increases significantly with the dimensionless leakage of the offshore aquitard (u_o). The influence of the tidal propagation parameter of an unconfined aquifer on the head fluctuation of the leaky confined aquifer is comparatively conspicuous when u_i is large and u_o is small. In other words, ignoring water table fluctuation of the unconfined aquifer will give large errors in predicting the fluctuation, time lag, and tidal influence distance of the leaky confined aquifer for large u_i and small u_o. On the contrary, the influence of the tidal propagation parameter of a leaky confined aquifer on the head fluctuation of the leaky confined aquifer is large for large u_o and small u_i.     

Groundwater response to tidal fluctuations in a leaky confined coastal aquifer with a finite length

The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.     

Modelling tidal signals enhanced by a submarine spring in a coastal confined aquifer extending under the sea

Submarine springs discharge offshore groundwater from confined aquifers extending under the sea. The effects of these springs on the propagation of tidal oscillations in coastal confined aquifers are not known. This paper presents an approximate analytical solution of tidal head fluctuations in a confined aquifer with one submarine spring. The aquifer is assumed to extend in all directions infinitely. The spring is represented by a permeable round column on the seabed, which penetrates completely the impermeable layer overlying the confined aquifer. The error of the approximate solution is negligible if the distance from the spring to the coastline is much greater than the radius of the permeable column representing the spring. Through a hypothetical example, we demonstrate that it is possible to identify the spring’s location using tidal signals observed from inland wells. Tidal groundwater head fluctuations from three inland observation wells at least are needed to determine the 5 model parameters, including the location (2 parameters), the radius of the permeable column representing the spring, the diffusivity of the aquifer, and the tidal loading efficiency of the system.     

Hydrodynamic characterization of a Sahelian coastal aquifer using the ocean tide effect (Dridrate Aquifer,Morocco)

Abstract

In wells tapping coastal aquifers, piezometric fluctuations can be observed in response to the ocean tide. Simultaneous recordings of the ocean tide and of the piezometric variations may provide a basis for characterizing the hydrodynamics of the aquifer. This approach was attempted to characterize the Dridrate aquifer, located on the Atlantic coast of Morocco. This aquifer accounts for most of the regional drinking water resources. However, its hydrodynamic characteristics are very poorly known. The study compares observed and simulated piezometric fluctuations, under various assumptions (confined, semi-confined aquifer). The model, which best explains the hydrodynamic behaviour of this aquifer is a semi-confined and strongly heterogeneous aquifer model (calculated hydraulic diffusivity values vary over several orders of magnitude). This result is new and rather surprising, since to date this aquifer was considered confined in view of its geological setting. Consequently, new questions are raised regarding the protection and management of the groundwater resources of this aquifer.     

Analytic solutions for interface flow in combined confined and semi-confined,coastal aquifers

Analytic solutions are presented for steady interface flow in aquifers consisting of a confined and a semi-confined section. The total discharge is constant in the confined section and is directed towards the semi-confined section, which is bounded on top by a leaky layer that separates the aquifer from the sea. All solutions are based on the Dupuit approximation. The interface position is fully determined by two dimensionless parameters. The first parameter is the product of the uniform gradient towards the sea and the dimensionless leakage factor divided by the dimensionless density difference. The second dimensionless parameter is the length of the semi-confined section divided by the leakage factor. Four types of flow are distinguished. For cases I and II the interface does not reach the end of the semi-confined section, while it does for cases III and IV. For cases I and III the interface extends into the confined section, while for cases II and IV it remains entirely in the semi-confined section. Analytic solutions are presented for the position of the interface for all four cases. Diagrams are presented to determine the type of flow and the position of the interface toe based on the two dimensionless parameters. The pre-development position of the interface along the Georgia coast is computed as an illustration of the practical application of the presented formulas. Another practical application is the estimation of how far a numerical model of seawater intrusion should be extended into the sea for accurate simulations.     

The enhancing effect on tidal signals of a submarine spring connected to a semi-infinite confined aquifer

Abstract

Submarine springs play an important role in submarine groundwater discharge (SGD). To investigate the effects of these springs on the propagation of tidal signals in coastal confined aquifers, this paper considers a general coastal aquifer system with a submarine spring on the seabed where the length of the aquifer's offshore extent is finite and its submarine outlet is covered by an impermeable outlet-capping. An approximate analytical solution is obtained for describing the tidal head fluctuations in the aquifer. Solution analyses indicate that the error of the approximate analytical solution is negligible when both distances from the spring hole to the coastline and to the submarine outlet-capping are much greater than the radius of the spring hole. Sensitivity tests are conducted to investigate the effects of hydraulic properties, tidal and spring geometric configuration parameters on the tidal signal propagation in the inland aquifer. For aquifers with infinite offshore length, or without submarine springs, existing solutions in the literature are obtained. The comparison of groundwater head fluctuations for the cases with and without a submarine spring demonstrate the enhancing effect of the submarine spring on tidal signal propagation in the inland aquifer. Three situations that fit our model assumptions are given for future potential applications. A hypothetical example is used to show the possibility of identifying a spring's location using the present analytical solution together with tidal signals observed from inland wells.

Editor D. Koutsoyiannis; Associate editor Y. Guttmann

Citation Xia, Y.Q., Li, H.L., Yang, Y., and Huang, W., 2012. Enhancing effect on tidal signals of a submarine spring related to a semi-infinite confined aquifer. Hydrological Sciences Journal, 57 (6), 1231–1248.     

Analytical methods for transient flow to a well in a confined-unconfined aquifer

Concurrent existence of confined and unconfined zones of an aquifer can arise owing to ground water withdrawal by pumping. Using Girinskii's potential function, Chen (1974, 1983) developed an approximate analytical solution to analyze transient ground water flow to a pumping well in an aquifer that changes from an initially confined system to a system with both unconfined and confined regimes. This article presents the details of the Chen model and then compares it with the analytical model developed by Moench and Prickett (1972) for the same problem. Hypothetical pumping test examples in which the aquifer undergoes conversion from confined to water table conditions are solved by the two analytical models and also a numerical model based on MODFLOW. Comparison of the results suggests that the solutions of the Chen model give better results than the Moench and Prickett model except when the radial distance is very large or aquifer thickness is large compared with drawdown.     

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer’s permeability (semi-permeable and impermeable), of the boundary condition at the aquifer’s submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.     

Two-dimensional stochastic analysis of flow in leaky confined aquifers subject to spatial and periodic leakage

This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier–Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge.     

Methods to determine storativity of infinite confined aquifers from a recovery test

Starting from the equations of Theis and Cooper-Jacob, two new mathematical methods are proposed for interpreting the residual drawdown data for an infinite confined aquifer. Under Theis' assumptions and using the Cooper-Jacob approximation, the principal aquifer characteristics of transmissivity, pumping storativity, and recovery storativity are expressed without any correction or additional assumption. An actual case is used for illustration and confirms the validity of proposed equations and methods.     

Basin-scale transmissivity and storativity estimation using hydraulic tomography

While tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion.     

Rainfall infiltration‐derived submarine groundwater discharge from multi‐layered aquifer system terminating at the coastline

This article investigates the quantity of submarine groundwater discharge (SGD) from a coastal multi‐layered aquifer system in response to constant rainfall infiltration. The system comprises an unconfined aquifer, a leaky confined aquifer and an aquitard between them and terminates at the coastline. An approximate analytical solution is derived based on the following assumptions: (i) flow is horizontal in the aquifers and vertical in the aquitard, and (ii) flow in the unconfined aquifer is described by nonlinear Boussinesq equation. The analytical solution is compared with numerical solutions of the strictly two‐dimensional nonlinear model to validate the model assumptions used for the analytical solution. The SGD from the leaky confined aquifer increases with the inland rainfall infiltration recharge and the specific leakage of aquitard. The maximum SGD ranges from 1·87 to 10·37 m³ per day per meter of shoreline when rainfall infiltration ranges from 18·2 to 182 mm/year and the specific leakage of aquitard varies from 10^?9 to 10^?1 l/day. Copyright © 2011 John Wiley & Sons, Ltd.     

Non-Darcian flow to a well in an aquifer–aquitard system

In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity k_D results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter B_D results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.