Semianalytical solutions for stream depletion in partially penetrating streams

In the analysis of streamflow depletion, the Hunt (1999) solution has an important advantage because it considers a partially penetrating stream. By extending the Hunt drawdown solution, this paper presents semianalytical solutions for gaining streams that evaluate the induced stream infiltration and base flow reduction separately. Simulation results show that for a given deltah (the initial hydraulic head difference between stream and aquifer beneath the channel), the base flow reduction is in direct proportion to the product of streambed leakage (lambda) and the distance between pumping well and stream (L), and the induced stream infiltration is in inverse proportion to lambdaL. Deltah has a significant effect on the ratio of stream infiltration to base flow reduction. The results from the semianalytical solutions agree well with those from MODFLOW simulations. The semianalytical solutions are useful in the verification of numerical simulations and in the analysis of stream-aquifer interactions where water quantity or quality is concerned.     

Stream depletion by a pumping well including the effects of nonlinear variation of captured evaporation from a phreatic aquifer / Vidange en cours d’eau par puits de pompage incluant les effets de la variation non-linéaire de l’évaporation capturée d’une nappe à surface libre

Abstract

Abstract A study was made to develop a model that can be used to predict the steady-state stream depletion rates caused by a continuous pumping well located in a water table aquifer. The effects of nonlinear variation of evaporation with the depth to water table on steady-state stream depletion rate were investigated using model results. Dimensional analysis was used to determine the relationship between the scaled steady-state stream depletion, the scaled pumping distance, the scaled hydraulic conductivity, and the scaled initial depth to the water table. A dimensionless graph was developed for a wide range of these parameters. Analysis of this graph showed that the steady-state stream depletion rate decreases as the pumping distance between the well and the stream increases. The dimensionless graph also showed that steady-state stream depletion rates strongly depended on the initial position of the water table. Analysis indicated that, as the saturated conductivity increased, the effect of the initial position of the water table on the magnitude of stream depletion rate was more influential. Analysis also showed that, as the value of saturated conductivity decreased, the relative error produced by the assumption that at steady state all the pumped water is captured from the evaporation, also decreased.     

Migration of induced-infiltrated stream water into nearby aquifers due to seasonal ground water withdrawal

Analysis of stream-aquifer interaction due to ground water extraction has traditionally focused on the determination of the amount of water depleted in the stream. Less attention has been paid to the movement of infiltrated stream water inside aquifer, particularly for agricultural areas. This paper presents a method of using particle-tracking techniques to evaluate the transport of the leaked stream water in the nearby aquifers. Simple stream-aquifer conditions are used to demonstrate the usefulness of the analysis. Travel times, pathlines, and influence zones of stream water were determined between a stream and nearby pumping wells for seasonal ground water extraction areas. When water quantity is a concern, the analyses provide additional information about stream depletion; when water quality is an issue, they offer information for wellhead protection. Analyses were conducted for transient conditions, and both pumping and nonpumping periods were considered. According to the results from the simulation examples, migration of infiltrated stream water into the nearby aquifers is generally slow and most infiltrated stream water does not arrive at the pumping well at the end of a 90-day irrigation season. Infiltrated stream water may remain in the aquifer for several years before arriving at the pumping well. For aquifers with a regional hydraulic gradient toward streams, part of the infiltrated stream water may discharge back to streams during a recovery period.     

Characterising groundwater–surface water interactions in idealised ephemeral stream systems

Transmission losses from the beds of ephemeral streams are thought to be a widespread mechanism of groundwater recharge in arid and semi-arid regions and support a range of dryland hydro-ecology. Dryland areas cover ~40% of the Earth's land surface and groundwater resources are often the main source of freshwater. It is commonly assumed that where an unsaturated zone exists beneath a stream, the interaction between surface water and groundwater is unidirectional and that groundwater does not exert a significant feedback on transmission losses. To test this assumption, we conducted a series of numerical model experiments using idealised two-dimensional channel-transects to assess the sensitivity and degree of interaction between surface and groundwater for typical dryland ephemeral stream geometries, hydraulic properties and flow regimes. We broaden the use of the term ‘stream–aquifer interactions’ to refer not just to fluxes and water exchange but also to include the ways in which the stream and aquifer have a hydraulic effect on one another. Our results indicate that deep water tables, less frequent streamflow events and/or highly permeable sediments tend to result in limited bi-directional hydraulic interaction between the stream and the underlying groundwater which, in turn, results in high amounts of infiltration. With shallower initial depth to the water table, higher streamflow frequency and/or lower bed permeability, greater ‘negative’ hydraulic feedback from the groundwater occurs which in turn results in lower amounts of infiltration. Streambed losses eventually reach a constant rate as initial water table depths increase, but only at depths of 10s of metres in some of the cases studied. Our results highlight that bi-directional stream–aquifer hydraulic interactions in ephemeral streams may be more widespread than is commonly assumed. We conclude that groundwater and surface water should be considered as connected systems for water resource management unless there is clear evidence to the contrary.     

Strategies for offsetting seasonal impacts of pumping on a nearby stream

Ground water pumping from aquifer systems that are hydraulically connected to streams depletes streamflow. The amplitude and timing of stream depletion depend on the stream depletion factor (SDF(i)) of the pumping wells, which is a function of aquifer hydraulic characteristics and the distance from the wells to the stream. Wells located at different locations, but having the same SDF and the same rate and schedule of pumping, will deplete streamflow equally. Wells with small SDF(i) deplete streamflow approximately synchronously with pumping. Wells with large SDF(i) deplete streamflow at approximately a constant rate throughout the year, regardless of the pumping schedule. For large values of SDF(i), artificial recharge that occurs on a different schedule from pumping can offset streamflow depletion effectively. The requirements are (1) that the pumping and recharge wells both have the same SDF(i) and (2) that the annual total quantities of recharge and pumping be equal. At larger SDF(i) values, it takes longer for pumping to impact streamflow in a wide aquifer than it does in a narrow aquifer. In basins that are closed to further withdrawals because streamflow is fully allocated, water-use changes replace new allocations as the source of water for new developments. Ground water recharge can be managed to offset the impacts of new ground water developments, allowing for changes in the timing and source of withdrawals from a basin without injuring existing users or instream flows.     

Empirical relationships for estimating stream depletion by a well pumping near a gaining stream

Siting wells near streams requires an accurate estimate of the quantity of water derived from the river due to pumping. A number of hydrogeological and hydraulic parameters influence this value. This study estimates stream depletion under steady-state conditions for a variety of hydrogeological systems. A finite differences model was used to analyze several hydrogeological situations, and for each of these the stream depletion was estimated using an advective transport method. An empirical equation for stream depletion was obtained for the case of a stream that partially penetrates the aquifer and a pumping well that is screened over a portion of the aquifer. The derived equation, which is valid for both isotropic and anisotropic conditions, expresses stream depletion as a function of the unit inflow to the river, the discharge of the pumping well, the well screen length, the distance between the river and pumping well, the wetted perimeter, and a new parameter called "overlap," which is defined to be the distance between the riverbed and the top of well screen. The overlap parameter makes it possible to consider indirectly the vertical component of flow, which is accentuated when the well is screened below the streambed. The formula proposed here should be useful in deciding where to locate a pumping well and to decide the appropriate length of its screen.     

Pumping-induced drawdown and stream depletion in a leaky aquifer system

The impact of ground water pumping on nearby streams is often estimated using analytic models of the interconnected stream-aquifer system. A common assumption of these models is that the pumped aquifer is underlain by an impermeable formation. A new semianalytic solution for drawdown and stream depletion has been developed that does not require this assumption. This solution shows that pumping-induced flow (leakage) through an underlying aquitard can be an important recharge mechanism in many stream-aquifer systems. The relative importance of this source of recharge increases with the distance between the pumping well and the stream. The distance at which leakage becomes the primary component of the pumping-induced recharge depends on the specific properties of the aquifer, aquitard, and streambed. Even when the aquitard is orders of magnitude less transmissive than the aquifer, leakage can be an important recharge mechanism because of the large surface area over which it occurs. Failure to consider aquitard leakage can lead to large overestimations of both the drawdown produced by pumping and the contribution of stream depletion to the pumping-induced recharge. The ramifications for water resources management and water rights adjudication can be significant. A hypothetical example helps illustrate these points and demonstrates that more attention should be given to estimating the properties of aquitards underlying stream-aquifer systems. The solution presented here should serve as a relatively simple but versatile tool for practical assessments of pumping-induced stream-aquifer interactions. However, this solution should not be used for such assessments without site-specific data that indicate pumping has induced leakage through the aquitard.     

Stream-aquifer interactions: evaluation of depletion volume and residual effects from ground water pumping

Numerical modeling techniques were used to simulate stream-aquifer interactions from seasonal ground water pumping. We used stream-aquifer models in which a shallow stream penetrates the top of an aquifer that discharges ground water to the stream as base flow. Because of the pumping, the volume of base flow discharged to the stream was reduced, and as the pumping continued, infiltration from the stream to the aquifer was induced. Both base-flow reduction and stream infiltration contributed to total stream depletion. We analyzed the depletion rates and volumes of the reduced base flow and induced stream infiltration during pumping and postpumping periods. Our results suggested that for a shallow penetrating stream with a low streambed conductance, base-flow reduction accounts for a significant percentage of the total stream depletion. Its residual effects in postpumping can last very long and may continue into the next pumping season for areas where recharge is nominal. In contrast, the contribution of the induced stream infiltration to the total stream depletion is much smaller, and its effects often become negligible shortly after pumping was stopped. For areas where surface recharge replenishes the aquifer, the residual effects of base-flow reduction and thus its depletion volume will be significantly reduced. A stream of large conductance has a high hydraulic connection to the aquifer, but the relationship between stream conductance and stream depletion is not linear.     

Evaluation of water‐use policies for baseflow recovery during droughts in an agricultural intensive karst watershed: Case study of the lower Apalachicola–Chattahoochee–Flint River Basin,southeastern United States

The lower Apalachicola–Chattahoochee–Flint River Basin in the Southeast United States represents a major agricultural area underlain by the highly productive karstic Upper Floridan aquifer (UFA). During El Niño Southern Oscillation‐induced droughts, intense groundwater withdrawal for irrigation lowers streamflow in the Flint River due to its hydraulic connectivity with the UFA and threatens the habitat of the federally listed and endangered aquatic biota. This study assessed the compounding hydrologic effects of increased irrigation pumping during drought years (2010–2012) on stream–aquifer water exchange (stream–aquifer flux) between the Flint River and UFA using the United States Geological Survey modular finite element groundwater flow model. Principal component and K‐means clustering analyses were used to identify critical stream reaches and tributaries that are adversely affected by irrigation pumping. Additionally, the effectiveness of possible water restriction scenarios on stream–aquifer flux was also analysed. Moreover, a cost–benefit analysis of acreage buyout procedure was conducted for various water restriction scenarios. Results indicate that increased groundwater withdrawal in Water Year 2011 decreased baseflow in the lower Apalachicola–Chattahoochee–Flint River Basin, particularly, in Spring Creek, where irrigation pumping during April, June, and July changed the creek condition from a gaining to losing stream. Results from sensitivity analysis and simulated water restrictions suggest that reducing pumping in selected sensitive areas is more effective in streamflow recovery (approximately 78%) than is reducing irrigation intensity by a prescribed percentage of current pumping rates, such as 15% or 30%, throughout the basin. Moreover, analysis of acreage buyout indicates that restrictions on irrigation withdrawal can have significant impacts on stream–aquifer flux in the Basin, especially in critical watersheds such as Spring and Ichawaynochaway Creeks. The proposed procedure for ranking of stream reaches (sensitivity analysis) in this study can be replicated in other study areas/models. This study provides useful information to policymakers for devising alternate irrigation water withdrawal policies during droughts for maintaining flow levels in the study area.     

Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.     

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

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

Analysis of Transient Flow to an Extended Fully Penetrating Well at Constant-Head Pumping

Vertical wells with radial extension at the well bottom can improve the rate of water production. No study has yet investigated the effects of the transient state and anisotropy in directional hydraulic conductivities on the wellbore flux rate for this type of well. This study derives a semianalytical transient drawdown solution for constant-head pumping at a fully penetrating well radially extended at the bottom of a confined, anisotropic aquifer by applying Laplace transform and separation of variables as well as conducting a Fourier analysis. The results of this new solution indicate that transient and steady-state wellbore flux rates can be increased by a factor of two for greater radial extension of the well. Compared with an isotropic aquifer (a ratio of vertical and horizontal hydraulic conductivities equal to one), an anisotropic aquifer with the ratio less than one may produce a higher transient wellbore flux rate and lower steady-state wellbore flux rate. Moreover, the time required to achieve the steady-state wellbore flux rate can be substantially affected by anisotropy of the aquifer.     

Effects of Improper Characterization of Aquifer Thickness on Estimates of Hydraulic Conductivity from Pumping Tests

Pumping test data for surficial aquifers are commonly analyzed under the assumption that the base of the aquifer corresponds to the bottom of the test wells (i.e., the aquifer is truncated). This practice can lead to inaccurate hydraulic conductivity estimates, resulting from the use of low saturated thickness values with transmissivity estimates, and not accounting for the effects of partially penetrating wells. Theoretical time-drawdown data were generated at an observation well in a hypothetical unconfined aquifer for various values of saturated thickness and were analyzed by standard curve-matching techniques. The base of the aquifer was assumed to be the bottom of the pumping and observation wells. The overestimation of horizontal hydraulic conductivity was found to be directly proportional to the error in assumed saturated thickness, and to the (actual) ratio of vertical to horizontal hydraulic conductivity (K_v/K_h). Inaccurately high estimates of hydraulic conductivity obtained by aquifer truncation can lead to overestimates of ground water velocity and contaminant plume spreading, narrow capture zone configuration estimates, and overestimates of available ground water resources.     

Flow‐Through Stream Modeling with MODFLOW and MT3D: Certainties and Limitations

This paper aims to assess MODFLOW and MT3D capabilities for simulating the spread of contaminants from a river exhibiting an unusual relationship with an alluvial aquifer, with the groundwater head higher than the river head on one side and lower on the other (flow‐through stream). A series of simulation tests is conducted using a simple hypothetical model so as to characterize and quantify these limitations. Simulation results show that the expected contaminant spread could be achieved with a specific configuration composed of two sets of parameters: (1) modeled object parameters (hydraulic groundwater gradient, hydraulic conductivity values of aquifer and streambed), and (2) modeling parameters (vertical discretization of aquifer, horizontal refinement of stream modeled with River [RIV] package). The influence of these various parameters on simulation results is investigated, and potential complications and errors are identified. Contaminant spread from stream to aquifer is not always reproduced by MT3D due to the RIV package's inability to simulate lateral exchange fluxes between stream and aquifer. This paper identifies the need for a MODFLOW streamflow package allowing lateral stream‐aquifer interactions and streamflow routine calculations. Such developments could be of particular interest for modeling contaminated flow‐through streams.     

A new method for the interpretation of pumping tests in leaky aquifers

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type-curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.     

Measuring the hydraulic conductivity of shallow submerged sediments

The hydraulic conductivity of submerged sediments influences the interaction between ground water and surface water, but few techniques for measuring K have been described with the conditions of the submerged setting in mind. Two simple, physical methods for measuring the hydraulic conductivity of submerged sediments have been developed, and one of them uses a well and piezometers similar to well tests performed in terrestrial aquifers. This test is based on a theoretical analysis that uses a constant-head boundary condition for the upper surface of the aquifer to represent the effects of the overlying water body. Existing analyses of tests used to measure the hydraulic conductivity of submerged sediments may contain errors from using the same upper boundary conditions applied to simulate terrestrial aquifers. Field implementation of the technique requires detecting minute drawdowns in the vicinity of the pumping well. Low-density oil was used in an inverted U-tube manometer to amplify the head differential so that it could be resolved in the field. Another technique was developed to measure the vertical hydraulic conductivity of sediments at the interface with overlying surface water. This technique uses the pan from a seepage meter with a piezometer fixed along its axis (a piezo-seep meter). Water is pumped from the pan and the head gradient is measured using the axial piezometer. Results from a sandy streambed indicate that both methods provide consistent and reasonable estimates of K. The pumping test allows skin effects to be considered, and the field data show that omitting the skin effect (e.g., by using a single well test) can produce results that underestimate the hydraulic conductivity of streambeds.     

Optimal design of pumping tests in leaky aquifers for stream depletion analysis

We analyze the optimal design of a pumping test for estimating hydrogeologic parameters that are subsequently used to predict stream depletion caused by groundwater pumping in a leaky aquifer. A global optimization method is used to identify the test’s optimal duration and the number and locations of observation wells. The objective is to minimize predictive uncertainty (variance) of the estimated stream depletion, which depends on the sensitivities of depletion and drawdown to relevant hydrogeologic parameters. The sensitivities are computed analytically from the solutions of Zlotnik and Tartakovsky [Zlotnik, V.A., Tartakovsky, D.M., 2008. Stream depletion by groundwater pumping in leaky aquifers. ASCE Journal of Hydrologic Engineering 13, 43–50] and the results are presented in a dimensionless form, facilitating their use for planning of pumping test at a variety of sites with similar hydrogeological settings. We show that stream depletion is generally very sensitive to aquitard’s leakage coefficient and stream-bed’s conductance. The optimal number of observation wells is two, their optimal locations are one close to the stream and the other close to the pumping well. We also provide guidelines on the test’s optimal duration and demonstrate that under certain conditions estimation of aquitard’s leakage coefficient and stream-bed’s conductance requires unrealistic test duration and/or signal-to-noise ratio.     

Hydrologic trade-offs in conjunctive use management

An aquifer, in a stream/aquifer system, acts as a storage reservoir for groundwater. Groundwater pumping creates stream depletion that recharges the aquifer. As wells in the aquifer are moved away from the stream, the aquifer acts to filter out annual fluctuations in pumping; with distance the stream depletion tends to become equal to the total pumping averaged as an annual rate, with only a small fluctuation. This is true for both a single well and an ensemble of wells. A typical growing season in much of the western United States is 3 to 4 months. An ensemble of irrigation wells spread more or less uniformly across an aquifer several miles wide, pumping during the growing season, will deplete the stream by approximately one-third of the total amount of water pumped during the growing season. The remaining two-thirds of stream depletion occurs outside the growing season. Furthermore, it takes more than a decade of pumping for an ensemble of wells to reach a steady-state condition in which the impact on the stream is the same in succeeding years. After a decade or more of pumping, the depletion is nearly constant through the year, with only a small seasonal fluctuation: ±10%. Conversely, stream depletion following shutting down the pumping from an ensemble of wells takes more than a decade to fully recover from the prior pumping. Effectively managing a conjunctive groundwater and surface water system requires integrating the entire system into a single management institution with a long-term outlook.     

Flow depletion in a small stream caused by ground water abstraction from wells

The interaction between a gaining stream and a water-table aquifer is studied at an outwash plain. The aquifer is hydraulically well connected to the stream. Pumping tests were carried out in 1997 and 1998 in two wells 60 m from the stream, screening different depths of the aquifer. Drawdown was measured on both sides of the stream. Hydraulic head, drawdown, and stream depletion data were analyzed using numerical flow models. Similar models were fitted to each of two different data sets: Model A was fitted to steady-state hydraulic head and streamflow gain data not influenced by pumping; and model B was fitted to drawdown data measured during the 1998 pumping test. Each calibrated model closely fits its calibration data; however, predictions were biased if model A was used to predict the calibration data of model B, and vice versa. To further test the models, they were used to predict streamflow depletion during the two pumping tests as well as the drawdown during the 1997 test. Neither of these data were used for calibration. Model A predicted the measured depletions fairly accurately during both tests, whereas the predicted drawdowns in 1997 were significantly larger than actually measured. Contrary to this, the 1997 drawdowns predicted by model B were nearly unbiased; the predicted depletions deviate significantly from the measured depletions in 1997, but they compare well with the observations in 1998. Thus, although field work and analyses were extensive and done carefully to develop a ground water flow model that could predict both drawdown and streamflow depletion, the model predictions are biased. Analyses indicate that the deviations between model and data may be because of error in the models' representations of either the release of water from storage or of the hydrology in the riparian zone.