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We present the comprehensive discharge potential for steady three-dimensional flow in horizontally stratified coastal aquifers with a horizontal base and a vertical coastline. The gradient of this comprehensive potential gives the vertically integrated discharge throughout the aquifer, i.e., the specific discharge vector as a function of three-dimensional space integrated over the saturated portion of the aquifer. The boundary values of the comprehensive potential along the coast can be computed precisely, given the geometry of the aquifer: the hydraulic conductivities of the strata, the elevations of the horizontal planes that separate the strata, and the elevation of the impermeable base of the aquifer relative to sea level. Boundary conditions of the comprehensive potential may either be given in terms of its gradient, or computed from given heads along the boundaries. The governing equation of the comprehensive potential is the Poisson equation in areas of infiltration and the Laplace equation elsewhere. The computation of interface elevations, piezometric heads, and the vertical distribution of flow, requires that an assumption be made regarding the relation between the comprehensive potential and piezometric heads. We adopt the Dupuit-Forchheimer approximation for this purpose and make use of the Ghyben-Herzberg equation. We present several applications of the approach, and find that the stratification may have a significant effect on the boundary value of the comprehensive potential, and thus on the flow rates in the aquifer. This article is protected by copyright. All rights reserved.

[1] Water level rises associated with river flow events induce both pressure and solute movement into adjacent aquifers at vastly different rates. We present a simple analytical solution that relates the travel time and travel distance of solutes into an aquifer following river stage rise to aquifer properties. Combination with an existing solution for pressure propagation indicates that the ratio of solute to pressure travel times is proportional to the ratio of the volume of water stored in the aquifer before the river stage rise and the volume added by the stage rise and is independent of hydraulic conductivity. Two-dimensional numerical simulations of an aquifer slice perpendicular to a river demonstrate that the solutions are broadly applicable to variably saturated aquifers and partially penetrating rivers. The solutions remain applicable where river stage rise and fall occur, provided that regional hydraulic gradients are low and the duration of the river stage rise is less than pressure and solute travel times to the observation point in the aquifer. Consequently, the solutions provide new insight into the relationships between aquifer properties and distance and time of solute propagation and, in some cases, may be used to estimate system characteristics. Travel time metrics obtained for a flood event in the Cockburn River in eastern Australia using electrical conductivity measurements enabled estimates of aquifer properties and a lateral extent of river-aquifer mixing of 25 m. A detailed time series of any soluble tracer with distinctly different concentrations in river water and groundwater may be used.

[1] The value of using environmental tracer profiles in aquitards to quantify fluid flux and to reveal information about palaeohydrology is largely unknown for parts of the world that were not glaciated during the Cenozoic. We present deep, continuous vertical profiles of aquitard pore water chloride concentration and δ2H/δ18O composition from the western margin of the Great Artesian Basin, Australia, where upward leakage is the dominant groundwater discharge mechanism. At the deeper of the two sites studied, the Cl− and δ2H profiles exhibit a distinctive S-shape, which we interpret as a shift in the upper concentration boundary condition over time. Numerical simulations are used to support an hypothesis that the shallow phreatic aquifer was more saline and more enriched in δ2H compared to current conditions prior to ∼120 ka, followed by an extended freshening phase from ∼120 to 20 ka, then a saline phase similar to current conditions for the last ∼20 ka. These timeframes correspond favorably with results of previous studies into the palaeohydrology of nearby playa Lake Eyre. At the shallower site, the tracer profiles decrease exponentially with depth. We explore several models for the evolution of these profiles and adopt one of long-term salt input at ground surface. At both sites, tracer concentrations for groundwater sampled from the underlying artesian aquifer provide conclusive evidence that recharge occurred within the last 10–20 ka. Chloride was a more useful tracer than δ2H in this study, primarily due to lack of recent glaciation in central Australia to provide a dynamic δ2H tracer signal.

This paper presents the analytical solution of groundwater response to tidal fluctuation in a coastal multilayer aquifer system consisting of a leaky confined aquifer, a semipermeable layer, and an unconfined aquifer. The semipermeable layer, or the roof of the leaky confined aquifer, extends under the sea. Comparisons are made with solutions derived previously, which considered only a single aquifer, zero extension of the roof, or infinite roof length, and demonstrate that the previous solutions are special cases of the solution presented here. A hypothetical example is used to discuss the impact of the dimensionless roof length, dimensionless leakage, and tidal efficiency on the groundwater level fluctuations in the inland part of the confined aquifer. The fluctuation decreases significantly with the roof length when the roof length is small but is insensitive to the change of roof length when the roof length is greater than a threshold. The impacts of leakage from the offshore and inland portions of the confining unit are different. Leakage from the offshore portion tends to increase the fluctuation of the groundwater level, while leakage from the inland portion tends to decrease the fluctuation. The fluctuation increases as the tidal efficiency increases. This fact is significant only when the roof length is great and leakage is small.

Tidal fluctuations in a leaky confined coastal aquifer are damped significantly due to leakage into an overlying phreatic aquifer. Jiao and Tang [1999] presented an analytical solution to a simple model describing this phenomenon. Their solution assumes that the tidal fluctuations in the overlying phreatic aquifer are negligible (i.e., a static phreatic aquifer). Here we examine dynamic effects of the overlying aquifer based on a new approximate analytical solution. The numerical results indicate that the dynamic effects can be significant for a relatively large leakage and a high transmissivity of the phreatic aquifer.

Regional depressurization due to groundwater withdrawal from a large confined midcontinent aquifer may cause significant changes in the regional flow field and solute distributions through time. This study addresses the effects of depressurization in the Silurian-Devonian carbonate aquifer in the western flank of the Appalachian Basin in Ohio, where salinity-derived variable-density flow effects are significant. This complex hydrogeologic environment is examined using an interpretative, transient, numerical flow and transport model to examine the hydrodynamics involved in the salinization process, to simulate changes in the velocity field and solute distributions over the past 100-year period, and to forecast the effects of three different depressurizing scenarios over the next 100-year period. The results indicate that large-scale depressurization can lead to significant changes in the regional flow patterns, resulting in changes in solute distributions and salinization of a portion of the aquifer. Depressurization creates vertical flow gradients within the carbonate aquifer that transport brine from underlying and overlying shale units into the updip freshwater portion of the aquifer. Model results show the development of flow reversals in the downdip portions of the aquifer that facilitate transport of brine from the deeper portions of the carbonate aquifer. These processes result in significant water quality degradation in the updip portion of the aquifer, which is extensively used for municipal, industrial, and domestic water supplies. Our results indicate the need to monitor water levels, pumping rates, and water quality so that future management decisions regarding the sustainability of the resource are based on complete and accurate field data.

The extreme hydrologic response of gravelly, sandy soils in the Carnation Creek watershed is examined from observations at 12 standpipe piezometers. The nearly continuous piezometric data are reported as a time series of monthly maximum readings. Ten locations of measurement appear to exhibit an upper limit to the pore water pressure head that is independent of rainfall intensity and duration. Two locations exhibit artesian pressures that appear directly influenced by rainfall characteristics and may last for several hours. We found the impact of individual storms to be highly variable. The spatial variation in hydrologic response is attributed to the influence of preferential flow paths in the soil matrix.

A deep Paleozoic carbonate aquifer is of special concern for the proposed high-level nuclear repository at Yucca Mountain, Nevada. It provides a potential pathway for groundwater transport of contaminants from the repository back to the biosphere. The map of groundwater temperature at the water table has been interpreted by several investigators to indicate upwelling groundwater along major fault zones both east and west of Yucca Mountain. Of particular concern is the permeability of these fault zones. The deep carbonate aquifer has been penetrated by only one test hole in the vicinity of Yucca Mountain: UE-25pl. In this borehole the hydraulic head in the deep carbonate aquifer was 20 m higher than head in the overlying tuff aquifer. Observations in UE-25pl show good Earth tide water-level fluctuations in the deep carbonate aquifer. Both the large 2-cm amplitude of the tidal signal and the fact that it is in phase with the tidal potential indicate that the deep aquifer is well confined by a layer of low hydraulic conductivity. An estimate of the maximum hydraulic permeability of a fault zone that penetrates the confining is made by simulating the tidal response. Given a maximum permeability and the head difference, one can calculate the upward flow from the deep carbonate aquifer into the overlying tuffs. This analysis supports the interpretation of upward flow from the deep carbonate to the overlying tuffs. This is a favorable condition for the proposed repository. The upward potential for flow from the deep carbonate aquifer protects it from the downward movement of contaminants. Further deep drilling is necessary to confirm that the high head persists beneath the entire proposed repository. Nothing should be done either through construction of the repository or through groundwater development to reduce heads in the carbonate aquifer; the higher heads protect the carbonate aquifer.

The water level of the Dead Sea, a terminal hypersaline lake (total dissolved solids, approximately 340 g/L) has decreased at an average rate of 0.5 m/yr since 1960 and by 0.8 m/yr between 1981 and 1989. The dramatic long-term water level variation of the Dead Sea and the seasonal short-term fluctuations are accompanied by parallel variations of groundwater levels in an adjacent aquifer. A general methodology based on a simplified yet reliable one-dimensional flow model, together with continuous measurements of groundwater levels in observation wells, enables analysis of aquifer structural and hydraulic properties. Furthermore, this analysis enables prediction of future groundwater levels in unconfined and confined aquifers due to future changes in lake levels.

[1] Water table variation will result in considerable variation of the weight of the pore water, which has loading effects on the groundwater flow in the underlying confined aquifer. Here we present an analytical solution on such a loading effect in a coastal aquifer system consisting of an unconfined aquifer, a confined aquifer, and an impermeable layer between them, with the two lower layers extending under the sea. The solution generalizes several existing ones in the literature. The water table variation's loading effects tend to enhance the amplitude and to reduce the phase shift of the tide-induced head fluctuation. These effects become considerable when the tidal loading coefficient is large, the aquifer's offshore extending length is long, and the unconfined aquifer has large values of hydraulic conductivity and specific yield. Numerical examination indicated that the assumption of ignoring the density variation causes an error not greater than 2.5% of the tidal amplitude.

This paper discusses the hydrochemical evolution of groundwaters in the multilayer artesian aquifer of the Continental Intercalaire (the mainly Jurassic Agadez-Dabla sandstones) aquifer of northern Niger. Isotopic and chemical changes in relation to the geological setting suggest that the increasing HCO3− alkalinity of the groundwaters is caused by interaction of deep CO2 with the aquifer matrix. Alteration of feldspars by CO2 with a δ13C value of −3.0‰ accounts for the observed alkalinity and isotopic and trends. Carbon 14 ages have been estimated for recent and Holocene groundwaters which have a distinct stable isotopic (2H and 18O) signature compared with 14C dead groundwaters from further west on the Irhazer Plain. Recharge temperatures, estimated by analysis of noble gas contents, show that the 14C dead waters were recharged under conditions cooler than present averages in the region, possibly at the beginning of deglaciation (≈16 ka B.P.) or during the period 23–30 ka B.P. Trends in the hydrochemistry of U are related to the deep CO2 alteration process. Radiogenic He contents increase along the flow direction and extremely high values occur in the proximity of U ores. Denitrification in the paleowaters of the Irhazer was assessed by measurements of nitrogen/argon ratios.

Well water quality depends on the relative amounts of water drawn from the pumped aquifer and nearby surface water bodies, such as streams, lakes, and wetlands. Although a surface water body may normally gain water from the aquifer, pumping can reverse gradients, causing it to lose water near the well. Surface water then enters the well by induced infiltration. Two-dimensional vertically integrated models of induced infiltration are developed for various combinations of aquifer geometry and sources of recharge. The models, which have applications in wellhead protection, aquifer pollution characterization, and aquifer remediation, are presented graphically. They show that the propensity for and rate of induced infiltration are enhanced by higher pumping rates, proximity of the well to the stream, and the presence of nearby barrier boundaries. The propensity and rate are reduced by the presence of other surface water bodies. Ambient groundwater discharge rate to the surface water body also plays a role, but not its source, whether it is from local vertical recharge, lateral inflow, or both. The results are also largely indifferent to whether the aquifer transmissivity is assumed to be a constant, or a function of water table elevation. Finally, if the well is close enough to the surface water body, say, less than 5% of the aquifer width, then the aquifer acts as if it were semi-infinite.

Shallow groundwater under Kesterson Reservoir, Merced County, California, was contaminated over a period of 6 years while the reservoir was used for disposal of brackish subsurface agricultural drainage water from farmlands in the San Joaquin Valley. Drainage water contained an average of 10,000 mg/L total dissolved solids (TDS), high concentrations of selenium (300 μg/L), nitrate (37 mg/L as nitrogen), boron (15 mg/L), and lesser amounts of mercury, chromium, and molybdenum. Infiltration and lateral migration of this water created a 20-m-deep plume of high-TDS, boron-rich water covering an area of about 5 km2. Transport of selenium and nitrate was inhibited by biogeochemical reactions in the pond bottom sediments, so that migration of these two constituents into the aquifer was limited. This paper focuses on physical parameters affecting seepage and lateral migration of nonreactive solutes and on hydrogeological factors associated with selenium break-through into the shallow aquifer. An accompanying paper describes biogeochemical processes that limit nitrate and selenium migration (White et al., this issue). The regional hydrogeologic system at Kesterson Reservoir is dominated by the presence of four lithostratigraphic units. These are, in order of increasing depth, a fine-grained surfical layer extending to depths of as much as 8 m, a semiconfined sandy aquifer extending to 60 m, a widespread lacustrine clay confining layer, and a confined sandy aquifer. Within each of these units, order of magnitude variations in the hydrologic properties of the sediments occur ubiquitously over lateral distances of tens of meters and vertical distances of a fraction of a meter. Seepage rates from the ponds into the underlying aquifer are dominated by local hydrogeologic properties and thickness of the fine-grained surface layer. Selenium migrated into the aquifer in an area where the fine-grained surface layer was thin or absent. Once in the aquifer, local rates of migration are controlled by the small-scale structure and hydrogeologic properties of the sediments. The aquifer is composed of a heterogeneous mixture of sands, silts, and clays. Individual sand beds, which average about 0.3 m thick, do not appear to extend over lateral distances of more than 30 m. The large range of velocities combined with a limited lateral extent of individual layers are expected to create a broadly dispersed plume of solutes migrating downgradient from Kesterson. A noninvasive electromagnetic survey of electrical conductivity distributions in the shallow aquifer appears to confirm this conceptual model for transport in the shallow aquifer.

[1] The Biscayne aquifer is a highly transmissive karst limestone that serves as the sole source of drinking water to over two million residents in south Florida. The aquifer is characterized by eogenetic karst, where the most transmissive void space can be an interconnected, touching-vug, biogenically influenced porosity of biogenic origin. Public supply wells in the aquifer are in close proximity to lakes established by surface mining. The mining of the limestone has occurred to the same depths as the production wells, which has raised concerns about pathogen and chemical transport from these surface water bodies. Hydraulic and forced gradient tracer tests were conducted to augment geologic and geophysical studies and to develop a hydrogeologic conceptual model of groundwater flow and chemical transport in the Biscayne aquifer. Geologic and geophysical data indicate multiple, areally extensive subhorizontal preferential flow zones of vuggy limestone separated by rock with a matrix pore system. The hydraulic response from an aquifer test suggests that the Biscayne aquifer behaves as a dual-porosity medium; however, the results of the tracer test showed rapid transport similar to other types of karst. The tracer test and concurrent temperature logging revealed that only one of the touching-vug flow zones dominates transport near the production wells. On the basis of the rising limb of the breakthrough curve, the dispersivity is estimated to be less than 3% of the tracer travel distance, which suggests that the fastest flow paths in the formation are likely to yield limited dilution of chemical constituents.

[1] Although depletion of storage in low-permeability confining layers is the source of much of the groundwater produced from many confined aquifer systems, it is all too frequently overlooked or ignored. This makes effective management of groundwater resources difficult by masking how much water has been derived from storage and, in some cases, the total amount of water that has been extracted from an aquifer system. Analyzing confining layer storage is viewed as troublesome because of the additional computational burden and because the hydraulic properties of confining layers are poorly known. In this paper we propose a simplified method for computing estimates of confining layer depletion, as well as procedures for approximating confining layer hydraulic conductivity (K) and specific storage (Ss) using geologic information. The latter makes the technique useful in developing countries and other settings where minimal data are available or when scoping calculations are needed. As such, our approach may be helpful for estimating the global transfer of groundwater to surface water. A test of the method on a synthetic system suggests that the computational errors will generally be small. Larger errors will probably result from inaccuracy in confining layer property estimates, but these may be no greater than errors in more sophisticated analyses. The technique is demonstrated by application to two aquifer systems: the Dakota artesian aquifer system in South Dakota and the coastal plain aquifer system in Virginia. In both cases, depletion from confining layers was substantially larger than depletion from the aquifers.

[1] Bedrock groundwater in alpine watersheds is poorly understood, mainly because of a scarcity of wells in alpine settings. Groundwater noble gas, age, and temperature data were collected from springs and wells with depths of 3–342 m in Handcart Gulch, an alpine watershed in Colorado. Temperature profiles indicate active groundwater circulation to a maximum depth (aquifer thickness) of about 200 m, or about 150 m below the water table. Dissolved noble gas data show unusually high excess air concentrations (>0.02 cm3 STP/g, ΔNe > 170%) in the bedrock, consistent with unusually large seasonal water table fluctuations (up to 50 m) observed in the upper part of the watershed. Apparent 3H/3He ages are positively correlated with sample depth and excess air concentrations. Integrated samples were collected from artesian bedrock wells near the trunk stream and are assumed to approximate flow-weighted samples reflecting bedrock aquifer mean residence times. Exponential mean ages for these integrated samples are remarkably consistent along the stream, four of five being from 8 to 11 years. The tracer data in combination with other hydrologic and geologic data support a relatively simple conceptual model of groundwater flow in the watershed in which (1) permeability is primarily a function of depth; (2) water table fluctuations increase with distance from the stream; and (3) recharge, aquifer thickness, and porosity are relatively uniform throughout the watershed in spite of the geological complexity of the Proterozoic crystalline rocks that underlie it.

[1] A new analytical solution is presented for the delayed response process characterizing flow to a partially penetrating well in an unconfined aquifer. The new solution generalizes that of Neuman (1972, 1974) by accounting for unsaturated flow above the water table. Three-dimensional, axially symmetric flow in the unsaturated zone is described by a linearized version of Richards' equation in which hydraulic conductivity and water content vary exponentially with incremental capillary pressure head relative to its air entry value (defining the interface between the saturated and unsaturated zones). Unsaturated soil properties are characterized by an exponent κ having the dimension of inverse length or, equivalently, a dimensionless exponent κD = κb, where b is initial saturated thickness. Our treatment of the unsaturated zone is similar to that of Kroszynski and Dagan (1975), who, however, have ignored internal (artesian) aquifer storage. According to Kroszynski and Dagan, aquifers that are not excessively shallow have values of κD (their parameter a) much greater than 10. We find that in such typical cases, unsaturated flow has little impact on early and late dimensionless time drawdown a short distance below the water table. Unsaturated flow causes drawdown to increase slightly at intermediate dimensionless time values that represent transition from an early artesian-dominated to a late water-table-dominated flow regime. Delayed drainage from the unsaturated zone becomes less and less important as κD increases; as κD → ∞, this effect dies out, and drawdown is controlled entirely by delayed decline in the water table as in the model of Neuman. The unsaturated zone has a major impact on drawdown at intermediate time and a significant impact at early and late times, in the atypical case of κD ≤ 1, becoming the dominant factor as κD approaches zero (the soil water retention capacity becomes very large and/or saturated thickness becomes insignificant). Our new solution was used to analyze field data from a pumping test conducted by Moench et al. (2001) in a glacial outwash deposit at Cape Cod, Massachusetts. The solution was fitted individually and simultaneously to time-drawdown data from 20 piezometers and observation wells and simultaneously to data from three piezometers in each of two clusters at various depths and distances from the pumping well, with very good results. Our parameter estimates of hydraulic conductivities from the simultaneous fit are similar to those obtained previously by Moench (2004), but our estimates of specific yield and storage are smaller and larger, respectively, while our estimate of κ is not comparable with his estimates of three empirical parameters.

[1] In this paper the evolution of the groundwater chemical composition in aquifers from large sedimentary basins over geological timescale is investigated. The solutes upon which we focus are sulfate, chloride, and sodium because they often display concentration gradients at the regional scale and they are largely undersaturated with respect to any mineral. To explain these gradients, several phenomena are studied: leakage, dissolution of minerals or ion exchange within an aquifer, and dissolution of minerals or ion exchange from an overlying aquitard. Assuming local equilibrium, the study of dissolution within the aquifer shows that the minerals containing sulfate and chloride must have been leached out rapidly after aquifer flushing and should not exist after one million years of water flow. In addition, a simplified model of leakage shows that dissolution of minerals embedded in an aquitard could deliver a flux of ions able to explain significant gradients within the aquifer. Without water transfer from aquitard to aquifer, diffusion from the aquitard can also lead to significant concentration gradient along the aquifer. A detailed study of ion exchange shows that the clays existing in the aquifer are rapidly (thousands of years) saturated with calcium and will not release sodium later. On the other hand, exchange from the aquitard clays, followed by diffusion, is able to change sodium and calcium concentrations significantly over geological time intervals in the aquifer. The intensities of each process studied are compared. It is shown that given the assumptions made, the influence of each process can be differentiated where the aquifer-aquitard system is well enough characterized. Analysis of aquifers with clay beds, detailed in the discussion, suggests that these layers may play a secondary role over geological timescales. However, they can lead to disconnected parts of the aquifer that can show different water chemistry. Our work suggests that the composition of major aquitards may have a significant effect on the chemistry of the aquifer water.

[1] Overexploitation of aquifers may impair groundwater quality and cause salinization, as occurs in the sloping Coastal Aquifer in Israel. The current management policy risks the future of the aquifer as the country's most important water reservoir. The paper examines a variety of policies and studies their impact on the salinization of the aquifer. Two quantitative approaches were applied: (1) a balance approach which was used to calculate the mean salinity of the aquifer water and (2) a 2-D numerical solution of the flow and transport equations in a 10 × 15 km cell representing a portion of the aquifer. The policy alternatives include desalination of imported freshwater (180–250 ppm Cl−), desalination of treated wastewater, and injection of the desalinated water. An increased pumping from the aquifer compensates for the injection of these waters. The results show that desalination of imported freshwater or wastewater with no injection would reduce the salinization rate of the aquifer only slightly, and that the effect would be noticeable only after a period corresponding to the retention time of the vadose zone. The alternatives that involve injection of desalinated water would stop the salinization process; the aquifer mean salinity would stabilize around the level that prevailed at the time of implementation of the injection policy. The numerical solution confirmed the conclusions of the balance approach while including the complex effect of the high-salinity boundary condition on the east and the role of thickness variations in a sloping aquifer. This approach addressed the influence of the spatial densities of pumping and of injection and showed that as the density increases, the numerical and balance solutions converge. It is shown that the numerical simulation should be used for future planning of the injection and pumping layout. Finally, calculations based on our results show that the alternatives involving injection of desalinated freshwater provide the lowest cost of improving the aquifer water salinity.

[1] A coupled continuum-pipe flow model is employed to simulate the development of karst conduits in an artesian setting, where aggressive water flows upward from an insoluble aquifer into a gypsum unit. Speleogenetic processes and controlling parameters are identified first for single conduit development. It is demonstrated that transient flow from the conduit into the surrounding fissured system of the rock enhances solutional conduit enlargement. Moreover, single conduit development is found to be highly sensitive to variations in initial diameter and hydraulic gradient. Simulating the solutional enlargement of pipe networks reveals that these two factors determine the resulting conduit pattern. Structural preferences are found to be essential for horizontal conduit development, otherwise flow paths are solely enlarged in vertical direction following the hydraulic gradient. Hydraulic gradients that increase with time can limit the extension or completely inhibit the development of horizontal caves even if lateral conduit development was structurally preferred.

[1] A vertical cross section through a karst aquifer is modeled by means of the finite element method to study the evolution of fractures and flow in the aquifer. The karst aquifer receives a constant recharge along the top boundary by precipitation and drains toward a resurgence assumed to be the base level in a valley. Flow is allowed both in the permeable rock matrix and the fracture network, and the fractures are enlarged with time by chemical dissolution. Hence during the early evolution of the karst aquifer the conductivity increases over several orders of magnitude, and the initially high water table drops to a steady state base level niveau. As a consequence, fractures above the final water table change from phreatic to vadose flow conditions. A systematic parameter study is carried out to investigate the aquifer evolution over a wide range of parameters, such as recharge rate, initial fracture width and density, and initial calcium concentration. The numerical models cover a wide range of drainage patterns, from phreatic water table caves to deep bathyphreatic caves to vadose river caves. The models suggest that a single theoretical approach is capable of explaining most common cave passage patterns.

The water level in an open well tapping an artesian aquifer responds to pressure head disturbance caused by Earth tide dilatation of the aquifer. Because a finite amount of time is needed for water to flow into and out of the well, there exists a phase shift (or time lag) between the tidal dilatation of the aquifer and the water level response in the well. We derive an analytical solution that expresses the phase shift as a function of the aquifer transmissivity, storage coefficient, well radius, and the period of the harmonic disturbance. This solution is rather insensitive to the storage coefficient. Thus if the phase shift is known for a harmonic disturbance, the transmissivity can be calculated given a rough estimate of the storage coefficient. Theoretical analysis shows that a significant phase shift may be present even if the disturbance is slowly varying, as in the case of Earth tides. This opens the possibility of estimating aquifer transmissivity from water level records that show Earth tide fluctuations. A case study, using data from a site near Parkfield, California, is presented to illustrate application of the theory. Phase shifts of the O1 (25.82-hour period) and M2 (12.42-hour period) tidal constituents are chosen for analysis because they are free of systematic contamination by fluctuations in barometric pressure. A brief error analysis suggests that the computed O1 phase shift is subject to large uncertainty, while the computed M2 phase shift is substantially more accurate. Based on an assumed storage coefficient range of 10−4 to 10−6, the estimated transmissivity range is 8 × 10−6 to 2 × 10 −5 m2/s. While hydraulic tests have not been performed to validate these estimates, the range is consistent with the transmissivity value determined by other investigators from analysis of the water level response to an earthquake.

Recently, in Japan, a new interest has been shown to the specific discharge of groundwater from the lake bottom in order to elucidate its influence on the quality and quantity of lake water. Using conformal mapping techniques, the authors describe analytically the steady two-dimensional groundwater flow in an idealized confined aquifer, which extends infinitely with uniform thickness and constant inclination and is exposed to the lake bottom surface with a gentle slope. The techniques enable analytical calculation of the head and stream functions of groundwater in the aquifer and also the distribution of specific discharge at lake bottom surface. From the results of calculation, it is found that most of the aquifer water flows into the lake through the upper part of the surface of contact between lake and aquifer. This analysis may be useful in the evaluation of the role of groundwater seepage in the water balance of large lakes.

A methodology is developed for determining optimal pumping and recharge of large scale artesian and/or nonartesian aquifers. This methodology couples optimization techniques with existing groundwater simulation models. It can be applied to both groundwater policy evaluation (allocation) such as large-scale aquifers and to hydraulic management problems such as the dewatering of mining or excavation sites. The state variables which represent the heads and the control variables which represent the pumpages are implicitly related through the groundwater simulator. The simulator equations are used to express the states in terms of the controls, yielding a much smaller reduced problem. Techniques for computing gradients of reduced problem functions are described. The reduced problem is solved by combining augmented Lagrangian and reduced gradient procedures. The optimization-groundwater simulation system is referred to as GWMAN. Two small examples are solved in addition to both steady state and transient type dewatering problems. Also, an application to the Edwards Aquifer in Texas is presented.

Previously, a new mathematical model based on the ‘tension center’ or ‘strain nucleus’ concept was proposed by the author for the response characterizing flow in a confined aquifer undergoing three-dimensional consolidation. The new approach differs from Bio's [1941] in that it leads to the development of a unique integrodifferential equation for the pressure head decline occurring within the porous system. The consideration of the horizontal strain components results in a conceptually simple modification of the classical diffusion equation to which a further integrodifferential term accounting for the three-dimensional effect is added. In the present paper the new equation of flow is solved in a pumped artesian aquifer enclosed in a half space by an iterative finite element technique. It is shown that in shallow and relatively thick units (with W ≃ 0.5, where W is the ratio between the average depth and the thickness of the aquifer), downward vertical components of flow develop and that the average drawdown deviates moderately from the Theis solution and is no longer uniquely represented against the dimensionless time. The three-dimensional effect produces an additional soil compression which retards the piezometric decline. At large values of time the horizontal strain components vanish, the diffusion equation holds, and the solution becomes parallel to the Theis profile. As a major consequence the traditional aquifer tests can still be applied to assess the formation permeability, but they yield a 40% overestimate of the elastic storage coefficient. In deeper units (W > 0.5) the importance of the three-dimensional effect diminishes, is already small when W = 1, and becomes negligible for W ≥ 2. In this case the diffusion equation and its solutions are sufficiently accurate. From a practical standpoint the quantitative results given herein are limited by the condition that a mechanically homogeneous and isotropic half space is required.

The problem of abstraction from a well penetrating a two-layered confined aquifer, each layer being independently homogeneous, isotropic, and artesian, is considered. Three components of the total abstraction are identified: the contribution from well storage and contributions from flow in each of the aquifer layers. For the case of a constant total abstraction rate, analytical expressions are derived for each of these components. The transient variation of the three components is investigated by evaluating the expressions numerically with different sets of parameter values.

The accidental release of a tritium pulse of about 500 Ci into a river in northern Switzerland allowed the measurement of travel times at a site where the river recharges a granular aquifer almost perpendicularly to the groundwater flow. A series of sampling wells had been previously installed in the aquifer. Most wells give access to shallow freshly infiltrated water. The infiltrated water flows along in the top layer of the aquifer, thus allowing for a one-dimensional analysis of the spreading process from the river to the groundwater in the wells. The linear groundwater flow velocities calculated from the tritium responses at distances from the river of up to 500 m confirm the velocities determined from an earlier local-scale uranine experiment at the same site. The scarce data used to describe tracer transport in the aquifer allowed for an assessment of dispersivity with the method of moments. A linearly scale-dependent dispersivity is evaluated from the mode of increase of the temporal variance of the tracer concentration distribution. Some wells revealed bimodal responses; here the method of moments is applied in combination with a two-layer model.

The Milk River artesian aquifer underlies 15,000 km2 of southern Alberta, Canada. It consists of thin (30–75 m thick) sandstone and is confined above by the Pakowki shale (typically 120 m thick) and below by the Colorado shale. The aquifer subcrops in southern Alberta and northern Montana. Groundwater movement is to the north, west, and east from the outcrop area (dominant recharge area). Cl− and I− concentrations increase in the direction of flow from less than 0.05 and 0.001 mmol/L, respectively, near the recharge area to more than 140 and 0.15 mmol/L at the northern edge of the aquifer. Similarly, waters become more enriched in oxygen 18 and deuterium from less than −21.0 and −167‰ near the recharge area to values approaching −8.0 and −70.0‰ in the north. Isotope values in the recharge area plot on the global meteoric water line and indicate that the recharge waters are isotopically unaltered meteoric waters. Downgradient from the recharge area the data deviate from the meteoric water line (slope of 6.3 instead of 8.0). Three mechanisms have been advanced to explain the origin of the chemical and isotopic patterns: the introduction of connate formation water through the Colorado shale and subsequent mixing with infiltrating meteoric water; a finite source of meteoric recharge mixing with more saline water in the aquifer; and chemical and isotopic enrichment due to ion filtration. Hydraulic conductivity and hydraulic head data, Cl− concentrations of drill cuttings and isotopic values from groundwater from the Colorado shale provide arguments for reevaluating these ideas. An alternative mechanism, based on diffusion between saline, isotopically enriched water in the Colorado shale and fresher, isotopically depleted water in the aquifer, is tested using an analytical mass transport model. Although uncertainty exists in the model parameters, results showed that the patterns in Cl−, I−, δ18O, and δ2H in the aquifer can be explained by aquitard diffusion. Further, aquitard diffusion must be considered when using chlorine 36 dating methods in aquifer-aquitard systems such as the Milk River aquifer.

The Milk River artesian aquifer underlines an area of approximately 6300 km2 in southern Alberta. This aquifer fits almost exactly Chamberlain's (1885) concept of a classic artesian system. It crops out or is covered by a thin veneer of glacial drift in southern Alberta and northern Montana. It is believed that major recharge occurs in these areas (Meyboom, 1960). Structurally, the aquifer appears fan-like in form, dipping gently to the east, north and west from its areas of outcrop. It is overlain by the Pakowki Formation which is a grey shale that acts as a confining bed. Analysis of stable isotope and major ion data for water samples collected from the aquifer reveals a variety of striking patterns. Oxygen-18 and deuterium concentrations for groundwater from the recharging portion of the aquifer fall very close to the meteoric water line (Craig, 1961a) indicating that they are isotopically unaltered meteoric waters. Proceeding down-dip in the aquifer groundwaters become enriched isotopically to a maximum of 70 and 12‰ with respect to deuterium and oxygen-18 in the recharging waters. In addition, a systematic deviation (slope of 6.1 instead of 8) from the meteoric water line is also apparent. The most plausible explanation of these isotopic patterns is based on a process of dispersion or mixing on a regional scale. Waters probably enriched with respect to the isotopic composition of the aquifer recharge may be present and simply are being displaced by meteoric water, or leakage may have entered the aquifer from below progressively comprising an increased proportion of the aquifer water. This same type of mixing process appears to exert a major control on the major ion chemistry of the aquifer. In addition, chemical processes such as mineral dissolution and cation exchange play a role.

The problem of abstraction from a well penetrating a multiple-layered aquifer, each layer being independently homogeneous, isotropic, and artesian, is considered. For the two-layered case with a constant abstraction rate, an analytical solution is derived for the aquifer response. The solution is simplified to give an expression for the drawdown in the well, and it is shown that for certain special cases the two-layered solution reduces to an existing solution for the equivalent single-layered aquifer. The effects of aquifer stratification on the response in the well are investigated by comparing the solutions for different parameter values.

A solution for the drawdown in a large-diameter well discharging at a constant rate from a homogeneous isotropic artesian aquifer, which also takes into consideration the water derived from storage within the well, is presented. A set of type curves computed from this solution permits a determination of the transmissibility of the aquifer by analysis of drawdown observed in the pumped well.

The differential equation governing nonsteady flow to a well in a thick leaky system has been solved by using transform techniques. Routines to tabulate the most general solution in type curve form have been developed and are available. The limiting curve of the tabulated function is the Hantush partial penetration type curve. With knowledge of the geologic framework the technique can be applied to certain field problems.

A theoretical, approximate solution is presented for steady rainfall or steady irrigation water seeping into ditch and tile drains in soil when the rainfall water is reinforced by the simultaneous upward seepage of artesian water. In the approximation it is assumed that the head loss in the narrow portion of the flow region above the lowest point of the water table arch is negligible. Utilizing a derived potential function and stream function, flow nets are presented for different rainfall and artesian flow conditions and for the drains running full and half full. A table of numerical values is presented for computing maximum water table heights. The theory is for an artesian basin at finite depth; for infinite depth, others have solved the problem for heights of water tables but not for flow nets. (Key words: Drainage; groundwater; artesian flow; irrigation)

Unconfined flow of water to wells is related to anisotropy of the aquifer, changes in the coefficient of storage with time, degree of penetration of the pumping well, and position of the water table. Sluggish response of observation wells to changes of head in the aquifer may lead to erroneous analysis of pumping-test data. The manner and extent to which these factors affect water levels have been studied by field observation, by analytical equations, and by electric analogs. The typical S-shaped curves of log drawdown versus log time, observed around wells pumping from water table aquifers, can be explained by an infinity of combinations of possible flow patterns and observation conditions. Equations developed for artesian flow cannot be used for analysis of tests made under water table conditions unless steady-state conditions have been approached or reached. From a practical standpoint the time required to approach steady flow is much greater than the duration of most pumping tests. Thus if pumping tests are to be used for measuring the hydraulic properties of unconfined aquifers, the boundary conditions attending unconfined flow must be recognized in the analysis of test data.

A finite element method programed for a high-speed computer was developed to determine the unsteady drawdown around an artesian well. On the basis of assumptions that the well has a finite radius and that the discharge from a partially penetrating well is not uniform along the well bore, numerical solutions for various well penetrations are presented and compared with the experimental measurements from a sand model. It was found that the numerical solutions check reasonably with the experimental measurements; thus the validity of the numerical method was indicated.

A model recharge well was constructed to simulate recharge into wells in a fine sand aquifer. The sand in the model aquifer was uniform fine sand and had a uniformity coefficient of 1.25 and an effective diameter of 144 microns. Both clear tap water and sediment laden water were used for recharge. Sediment laden water was obtained by mixing 50% bentonite and 50% kaolinite with tap water. Sediment concentrations were 100, 200, and 500 ppm. The piezometric surfaces near the recharge well were measured during the tests. Migration of sediment into the aquifer was determined by sampling the aquifer sand after the tests at predetermined distances from the well. The sediment in the recharge water highly affected the rate of recharge. During the period of the tests a reduction in hydraulic conductivity of the model aquifer of 15–46% occurred as a result of recharge with sediment laden water. Most of the sediment deposited in the aquifer was retained near the well screen.

To understand the carbonate geochemistry of an aquifer system, it is helpful to determine the sources of carbon in the dissolved carbonate species. Samples of ground litter, soil organic matter, soil CO2, and groundwater were collected in the area of recharge to the principal artesian aquifer of central Florida and were analyzed for 3C content. Analytical results yield consistent 3C/2C values for soil organic matter, $aCrDB = 23 4- l0o. TheaC/2C ratio of the litter samples ranges from $SCrDB of --18.2 to --29.500 and indicates the presence of both Calvin and Hatch-Slack cycle plants. The xaC/x2C of the soil CO2 ranges from -14.7 to -21.3o, which is consistent with the trend observed in the litter. The relationship between x3C/x2C of the dissolved carbonate and the percent calcite saturation indicates that the $aCDB of the source CO_ is within the range of -25 4- 5o, as is expected for a humid, subtropical environment. To understand the carbonate chemistry of an aquifer system, it is necessary to determine the various sources of carbonate in that system. One approach is the use of stable carbon isotopes. The use of stable carbon isotope analyses in conjunction with standard chemical analyses aids in determining the sources of carbon in ground- water, because the carbon isotope compositions of various components of the global carbon reservoir generally fall within distinct ranges (Table 1). Carbon isotope data are reported in the standard notation relative to the PDB standard

Theoretical consideration of the thermal properties of unconsolidated deposits suggests that a shallow aquifer might form a heat sink that influences and modifies the temperature effects of heat originating at the land surface and within the crust. The unconsolidated water-yielding deposits apparently are not of the same temperature as the material surrounding them. If the shallow aquifer is nonuniformly distributed, it should produce a temperature anomaly in the surface soil. The size of the anomaly resulting from a shallow aquifer would depend on the thermal properties and thickness of the overburden and on temperature differences between the surface and the aquifer.

Measurement of the response of an artesian aquifer system to naturally occurring stress fields can be used to determine aquitard properties. One method proposed here uses the response of an artesian aquifer to a short-term rise of water levels by approximating a step function in the unconfined aquifer above it. An analysis of the corresponding change in artesian water levels gives a value for α/m2, the aquitard hydraulic diffusivity divided by the square of the aquitard thickness. The application of this method is demonstrated by using data from a well field in Pasco County, Florida. A second method uses the fact that the response of an artesian system to barometric or tidal stresses is frequency dependent. As an incidental consequence, it is necessary to restrict Jacob's definition of barometric and tidal efficiencies to aquifer responses to instantaneous stress changes. The methods described are easily applied and serve to check the values of a boundary condition that is assumed to be homogeneous in other analytical approaches.

Measurements of radial surface strains near a pumping well showed compression near the well that changed to tension farther away from the well. A theoretical model is presented. In general, this model reproduces the measured strains. Observations of anomalous increase in pore pressure in a clay adjacent to the pumped aquifer are related to the development of these strains. These increases in pressure are attributed to distortion of the pore space in the clay resulting from the transference of horizontal strain from the aquifer via shear. Applying a conceptual model that permits the transference of strain across confining layers to unpumped artesian aquifers accounts for reverse water level fluctuations.

Subsurface conditions may differ considerably from conditions indicated by surficial geologic maps, particularly in glaciated areas. Therefore, it is advantageous to use a series of lithofacies maps as a sequence of overlays plotted on transparent paper. Such maps permit direct visual determination of the lithology and areal extent of aquifers and indicate areas of possible stream losses or gains. They indicate areas and boundaries of confining layers and, in some places, they may be used to delineate areas of water-table and artesian conditions. They are especially useful in determining buried channels in glaciated areas. The porosity of rock units making up an aquifer may be plotted on a lithofacies map, and the product of the volume of each lithologic type and the porosity provides an estimate of the total water in storage. In addition, if the water-bearing properties are known, the quantity of water moving through an aquifer and the amount available to wells may be determined. Lithofacies maps also aid in the explanation of complex changes in water quality.

Many water-table and artesian wells exhibit annual cyclic fluctuations in their water levels between a maximum level in the spring and a minimum level in the summer or fall. These maximums and minimums, as well as their differences, exhibit a normal probability distribution, and the annual minimum level that will occur following the annual maximum level can be predicted within selected confidence limits. It has been found that the correlation between annual maximum and minimum levels in a particular observation well can be applied to other observation wells in the same aquifer or to observation wells in other aquifers of similar physical characteristics and with annual piezometric declines of comparable magnitude. Historical records for both water-table and artesian observation wells in California, Indiana, Washington, and Wisconsin have been investigated. An example of this method using selected Wisconsin wells and the results of this analysis are presented. (Key words: Forecasting; groundwater; hydrology; wells.)

A method for finding the flow pattern of several wells pumped into an unconfined aquifer under transient conditions is presented. The study of the well group is based on the results of the study of individual wells using the relationships between the hydraulic forces. The method is based in part on some of the available concepts, especially those of Theis, Jacob, and Hantush. A flow equation called the ‘unified well formula’ is developed and written in terms of the areas of the pressure head diagrams across vertical sections. The form of this equation is valid for both artesian and gravity wells. The free surface of an individual gravity well is derived in a general procedure similar to that for steady state cases but introducing time effects. The equation can be solved numerically in one iterative cycle at a given time. The results of the analysis of single wells are used to determine the flow pattern of a multiple well system under transient conditions of flow. The pumping of all wells may not necessarily begin at the same time. The restricted superposition principles used in a previous paper on steady state cases are also used for transient flow. Dupuit's assumptions are eliminated and the circumferential velocities are neglected. The derived equations are further investigated at small radii or at large values of time after the start of pumping. The equation of the free surface reduces to the same form of the corresponding steady state cases. However, the radius of influence, in the transient case, depends on the time and the diffusivity of the flow medium.