Application of spectral analysis to determine hydraulic diffusivity of a sandy aquifer (Pingtung County,Taiwan)

The study demonstrates spectral relationships in the time–frequency domain for one‐dimensional groundwater flow in aquifers bounded by fluctuating boundaries. By nature, the solutions of spectral equations are non‐linear complex functions. To determine hydraulic diffusivity in the governing equations, it is required that the data are collected from the spectra of water levels at the fluctuating boundaries and observation wells. Hydraulic diffusivity thus can be obtained by an iterative inverse approach. This paper presents an application in Pingtung County of Taiwan to determine the hydraulic diffusivity of a sandy aquifer under confined conditions. Spectral density function of water level obtained from tidal boundaries and observation wells are used to approximate hydraulic diffusivity, which yields an averaged value of 1·26 × 10⁶ m²/h. Copyright © 2004 John Wiley & Sons, Ltd.     

Determination of hydraulic diffusivity of aquifers by spectral analysis

This study uses the cyclical frequency to develop the mathematical relationship between hydraulic diffusivity and spectral density functions calculated from groundwater level variation. Such relationship can be applied to (1) unsteady state, one-dimensional confined aquifer with time-dependent water level on both end boundaries, and (2) linearized unconfined aquifer with or without vertical recharge. The spectral density functions of groundwater fluctuations are largely affected by the spectral density functions obtained from time-dependent end boundaries and their cross-spectral density functions. Hydraulic diffusivity of an aquifer can be solved by type-curve matching technique at a specified frequency band under the conditions of (1) confined aquifer having equal time-dependent boundaries on both ends, (2) unconfined aquifer having equal time-dependent boundaries on both ends with surface recharge, and (3) unconfined aquifer subjected to surface recharge but neglecting the water table fluctuations on both end boundaries.     

Storage in confined aquifer: Spectral analysis of groundwater in responses to Earth tides and barometric effect

Dilatation of aquifer and associated water level fluctuation in groundwater well is known to be driven periodically from lunar, solar, or other tidal forces. Time‐dependent variables in groundwater system, such as water level, can be converted to power spectra in the frequency domain using Fourier transform to evaluate significant fluctuation. The major innovation of this research is to develop spectral representation in frequency domain for the groundwater system that the storage in confined aquifer can be determined considering dilatation affected by Earth tides and barometric effect. In order to verify applicability of the evolved method, time series of Earth tides and barograph are collected; aquifer storage is then determined inversely by selecting significant semidiurnal and diurnal components in spectra computation. It suggests that to discover groundwater storage using groundwater level with barograph and tidal potential of Earth in frequency domain becomes accessible and feasible.     

An innovative method to estimate regional-scale hydraulic diffusivity using GRACE data

ABSTRACT

Estimation of hydraulic properties in the field is usually small-scale and not cost-effective. This paper proposes an innovative method for estimating hydraulic diffusivity at regional scale. Monthly groundwater storage change over the period from 2003 to 2013 is first estimated from GRACE-derived terrestrial water storage (TWS). Assuming that the aquifer system is unconfined and the hydraulic properties are uniform in a geographical cell, the water balance principle and Darcy’s law are used to establish a relation between groundwater storage and hydraulic diffusivity. The value of hydraulic diffusivity is then adjusted using the generalized least squares and linear correlation method. This GRACE-derived hydraulic diffusivity estimation method, or GHDE method for short, is first verified with a hypothetical case and then applied in the Beishan area with available field-measured hydraulic conductivity data. The hypothetical case study demonstrates that the method works perfectly if the TWS data are error free. The Beishan case study illustrates that the estimated hydraulic diffusivities using the GHDE method correlate reasonably well with field test results, suggesting that this method is applicable. The accuracy of this method is constrained by the resolution of the GRACE-derived TWS data and is most suitable for very large scale groundwater problems due to the current accuracy of the GRACE data.

EDITOR A. Castellarin ASSOCIATE EDITOR N. Verhoest     

Hydrogeological interactions between fault zones and alluvial aquifers in regional flow systems

The hydrological influence of fault zones in tectonic areas is usually difficult to depict from field data. Numerical simulation allows representation of such flow systems and an estimation of flow lines and rates. This paper reports on simulations of the groundwater flow in a range‐and‐basin area affected by a regional fault zone, which may drain or recharge an overlaying alluvial aquifer. Different hydraulic conductivity values for the range rocks, the fault‐zone, and the sedimentary infill of the basin are considered, as well as different fault‐zone widths and boundary conditions. Results show that upward and downward fluxes develop in the upper part of the fault zone, controlled by the action of the alluvial aquifer, influencing the recharge of the sedimentary basin. This paper shows the hydrological efficiency of fault zones as preferential flow; it also analyses the constraints that determine groundwater recharge to the surrounding basins. These results contribute to the understanding of hydrogeological dynamics in tectonic areas. Copyright © 2008 John Wiley & Sons, Ltd.     

Dissolution of nonaqueous phase liquid pools in anisotropic aquifers

A two-dimensional numerical transport model is developed to determine the effect of aquifer anisotropy and heterogeneity on mass transfer from a dense nonaqueous phase liquid (DNAPL) pool. The appropriate steady state groundwater flow equation is solved implicitly whereas the equation describing the transport of a sorbing contaminant in a confined aquifer is solved by the alternating direction implicit method. Statistical anisotropy in the aquifer is introduced by two-dimensional, random log-normal hydraulic conductivity field realizations with different directional correlation lengths. Model simulations indicate that DNAPL pool dissolution is enhanced by increasing the mean log-transformed hydraulic conductivity, groundwater flow velocity, and/or anisotropy ratio. The variance of the log-transformed hydraulic conductivity distribution is shown to be inversely proportional to the average mass transfer coefficient.     

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.     

Steady state flow with hydraulic conductivity change around large diameter wells

Darcian flow law in aquifers assumes that the aquifer hydraulic conductivity is constant and the groundwater movement is due only to the piezometric level changes through hydraulic gradient. In practice, after the well development the aquifer just around the well has comparatively larger hydraulic conductivity and gradient. Patchy aquifer solutions in the literature consider sudden hydraulic conductivity changes with distance for the steady state flow. The change of transmissivity is demonstrated by the application of slope‐matching procedure to actual field data. It is the main purpose of this paper to derive simple analytical expressions for aquifer parameter evaluations with steadily decreasing hydraulic conductivity around the well. Spatial nonlinear hydraulic conductivity changes around a large‐diameter well within the depression cone of a confined aquifer are considered as exponentially decreasing functions of the radial distance. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydraulic Performance of the Horizontal Reactive Media Treatment Well: Pilot and Numerical Study

This study is focused on a passive treatment system known as the horizontal reactive treatment well (HRX Well®) installed parallel to groundwater flow, which operates on the principle of flow focusing that results from the hydraulic conductivity (K) ratio of the well and aquifer media. Passive flow and capture in the HRX Well are described by simplified equations adapted from Darcy's Law. A field pilot-scale study (PSS) and numerical simulations using a finite element method (FEM) were conducted to verify the HRX Well concept and test the validity of the HRX Well-simplified equations. The hydraulic performance results from both studies were observed to be within a close agreement to the simplified equations and their hydraulic capture width approximately five times greater than the well diameter (0.20 m). Key parameters affecting capture included the aquifer thickness, well diameter, and permeability ratio of the HRX Well treatment media and aquifer material. During pilot testing, the HRX Well captured 39% of flow while representing 0.5% of the test pit cross-sectional volume, indicating that the well captures a substantial amount of surrounding groundwater. While uncertainty in the aquifer and well properties (porosity, K, well losses), including the effects of boundary conditions, may have caused minor differences in the results, data from this study indicate that the simplified equations are valid for the conceptual design of a field study. A full-scale HRX Well was installed at Site SS003 at Vanderberg Air Force Base, California, in July/August 2018 based on outcomes from this study.     

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.     

Applicability of spectral analysis to determine hydraulic diffusivity

This study is to evaluate the applicability of estimating the one-dimensional horizontal hydraulic diffusivity of an unconfined aquifer with time-dependent fluctuation of lateral head and vertical recharge boundaries using observed water level spectra. Different models of boundary condition are imposed to evaluate the statistical significance between the calculated hydraulic diffusivity (ξ^′) with the given hydraulic diffusivity (ξ). The auto-spectra of the water level in observation wells tapping the same aquifer are closely related to those at the disturbed boundaries. For an aquifer with a constant hydraulic diffusivity, the water level fluctuation in the monitoring wells is linearly related to the water level spectra observed at the boundaries. The spectral density function of aquifer hydraulic head varies inversely with specific yield (S _y) and directly with recharge. Given small variation in water level spectra at the disturbed boundaries, the water level fluctuation in the aquifer is affected by the recharge condition and the aquifer spectral density function is sensitive to S _y. Using an iterative technique to estimate ξ from 1400 sets of given parameters, 99% of the ξ^′/ξ values deviated within only one order of magnitude with the model length (L) being equal to 1 km and 10 km. For L equal to 100 m, approximately 82% of the ξ^′/ξ population falls within two orders of magnitude. Therefore, spectral analysis of aquifer hydraulic head response can be used to estimate the hydraulic diffusivity of an unconfined aquifer which is affected by periodic variations in recharge and head at boundaries.     

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.     

Using chlorofluorocarbons (CFCs) and tritium (3H) to estimate groundwater age and flow velocity in Hohhot Basin,China

The concentrations of chlorofluorocarbons (CFC‐11, CFC‐12 and CFC‐113) and tritium (³H) content in groundwater were used to date groundwater age, delineate groundwater flow systems and estimate flow velocity in the Hohhot basin. The estimated young groundwater age is fallen in the bracket of 21 ~ 50 a and indicates the presence of two different age profiles and flow systems in the shallow groundwater system. Older age waters occur under the topographically low areas, where the aquifer is double‐layer aquifer system consisting of shallow unconfined‐semi‐confined aquifer and deep confined aquifer. This reflects long flow paths associated with regional flow. Groundwater (range from 21 to 34 years) in the north piedmont and east hilly areas, where the aquifer is a single‐layer aquifer consisting of alluvial fans, are typically younger than those in the low areas. The combination of CFCs dating with hydrogeological information indicates that both local and regional flow systems are present at the basin. The regional groundwater flow mainly flows from the north and east to the southwest, the local groundwater flow system occurs nearby the Hohhot city. The mean regional groundwater flow velocity of the shallow groundwater is estimated about 0.73 km/a. These findings can aid in refining hydrogeological conceptual model of the study area. Copyright © 2012 John Wiley & Sons, Ltd.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.     

New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions

The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks’ method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer.     

Modeling Steady Sea Water Intrusion with Single‐Density Groundwater Codes

Steady interface flow in heterogeneous aquifer systems is simulated with single‐density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m³). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi‐aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben‐Herzberg formula. The transformed problem may be solved with a single‐density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi‐aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Effect of heterogeneity on spatiotemporal variations of groundwater level in a bounded unconfined aquifer

Spatiotemporal variations of groundwater level due to a white noise recharge time series and a random transmissivity field in a bounded unconfined aquifer was studied. The analytical solutions for the variance and covariance of groundwater level were derived with non-stationary spectral analyses and superposition principle. It was found that the fluctuations of groundwater level are spatially non-stationary due to a fixed head boundary condition and temporal non-stationary at early time but gradually became stationary as time progresses due to effect of the initial condition. The variation in groundwater level is mainly caused by the random source/sink in the case of temporally random recharge and spatially random transmissivity. The effect of heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The heterogeneity also enhances the correlation of groundwater level, especially at large time intervals and small spatial distances.     

Analytical studies on transient groundwater flow induced by land reclamation using different fill materials

Land reclamation may have a significant influence on groundwater regimes. Analytical solutions have been developed in the past to study the impact of land reclamation on a steady‐state groundwater flow and transient flow in fill materials, assuming that the reclamation site consists of a single zone of uniform hydraulic parameters. In this paper, we derive analytical solutions to describe the transient water table change in response to multi‐stage land reclamation where the fill material is uniform in each stage but the hydraulic conductivity of the fill material varies from stage to stage. By introducing the method of separation of variables, we develop a transient analytical solution to study the impact of land reclamation consisting of fill material with different hydraulic properties on groundwater dynamics. The results show that the water table first increases significantly into the reclaimed zone following the fill material deposition, and then the increase gradually propagates into the original aquifer. The change of water table in the original aquifer mainly depends on the value of hydraulic conductivity of the fill materials. Examples in this paper illustrate how the aquifer system experiences a long time unsteady‐state flow as a result of the reclamation, and it takes at least tens of years for the system to approach a new equilibrium. It is suggested that for a large‐scale reclamation project, the response of the groundwater regime to reclamation should be carefully studied. Copyright © 2013 John Wiley & Sons, Ltd.