Constant Recharge Research Articles

Interaction of Stream and Sloping Aquifer Receiving Constant Recharge

An analytical solution and finite-element numerical solution of a linearized and nonlinear Boussinesq equation, respectively, were obtained to describe water table variation in a semi-infinite sloping/horizontal aquifer caused by the sudden rise or fall of the water level in the adjoining stream. Transient water table profiles in recharging and discharging aquifers having 0, 5, and 10% slopes and receiving zero or constant replenishment from the land surface were computed for t = 1 and 5 days by employing analytical and finite-element numerical solutions. The effect of linearization of the nonlinear governing equation, recharge, and slope of the impermeable barrier on water table variation in a semi-infinite flow region was illustrated with the help of a numerical example. Results suggest that linearization of the nonlinear equation has only a marginal impact on the predicted water table heights (with or without considering constant replenishment). The relative errors between the analytical and finite-element numerical solution varied in the range of −0.39 to 1.59%. An increase in slope of the impermeable barrier causes an increase in the water table height at all the horizontal locations, except at the boundaries for the recharging case and a decrease for the discharging case.

Analytical solutions of water table variation in a horizontal unconfined aquifer: Constant recharge and bounded by parallel streams

AbstractAnalysis of groundwater flow in an unconfined aquifer has received increasing attention by hydrogeologists for the design of drainage systems or the prediction of drawdown patterns of the water table in an aquifer neighbouring a pumping well. In this study, we attempt to analyse mathematically the variation of the water table in a horizontal unconfined aquifer receiving uniform recharge and bounded by parallel streams during a continuous cycle of rising and falling head conditions. The Boussinesq equation was taken to be the governing equation describing the transient changes in the water table. This problem was simplified to a one‐dimensional heat equation based on the assumption that the aquifer thickness is large enough compared to the water table changes and that the Dupuit–Forchheimer approximations are valid. We solved the heat equation using a method of variable separation in which the solution consists of both the steady‐state and nonsteady‐state solutions. With this method, the solutions could be obtained for various initial conditions such as different heads at the left and right boundaries and variable head distribution. In addition, simultaneous analysis of water table changes for both rising and falling head cases could be obtained. Comparison with other analytical solutions obtained for the linearized Boussinesq equation with Laplace transformation gives a nearly identical result, supporting the validity of the assumption and mathematical method used in this study. Advantages of the method over Laplace transformation can be found from the fact that our method renders the initial condition more flexible and simultaneous analysis of water table changes during rising and falling head cases can be done. Copyright © 2001 John Wiley & Sons, Ltd.

Water table fluctuations due to canal seepage and time varying recharge

Transient water table variation in an unconfined horizontal aquifer, lying between two canals located at different elevations above the impermeable barrier and receiving time varying recharge, is predicted by obtaining an analytical solution to the linearized Boussinesq equation. The proposed solution is for the generalized form of time varying recharge and has been obtained by applying an indigenously devised transformation to the flow governing equation. The solution for constant rate of recharge, a special case of the proposed solution, is compared with the existing analytical solution and almost identical values of water table rise are obtained. The effect of constant recharge, exponentially decreasing recharge and a combination of constant and exponentially decreasing recharge on the water table rise is analyzed with the help of a numerical example.

A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth

A new model of the early evolution of limestone karst aquifers in the dimensions of length and depth is presented. In its initial state the aquifer consists of a rock massive with evenly spaced fractures of about 50 μm aperture widths with an hydraulic conductivity of 10 −7 ms −1. In addition to this a coarser network of prominent fractures with aperture widths of several 100 μm is also present. Boundary conditions of constant recharge 450 mm/year, or constant head from the input of allogenic streams are imposed. First the position of the water table in the aquifer is calculated, then dissolutional widening during a time step in all the fractures below the water table is found by use of the well-known nonlinear dissolution kinetics of limestone. This is iterated and the position of the water table as well as the fracture widths are found as a function of time. In the case of constant recharge to a karst plateau, the water table in any case drops to base level and conduits there propagate from the spring headwards. If constant head conditions are valid the position of the water table remains almost stable and conduits propagate along the water table from the input towards the spring. There is competition between conduit evolution along prominent fractures and along tight fissures close to the water table. In any case under constant head conditions one of these pathways wins, and early karst evolution is terminated by a breakthrough event with an explosive increase of the flow through the aquifer until constant head conditions break down. Depending on the boundary conditions of constant head or constant recharge or a combination of both it is possible to describe models of cave genesis, which have been derived from field evidence, such as the water table models of Swinnerton (Geol. Soc. Am. Bull., 34 (1932) 662) and Rhoades and Sinacori (J. Geol., 49 (1941) 785) as well as the four-state model by Ford and Ewers (Can. J. Earth Sci., 15 (1978) 1783).

Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer

Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.

Predicting the probabilities of groundwater contamination by pesticides under variable recharge

A major deficiency in many models used to assess the groundwater contamination potential of organic pesticides used in agricultural and horticultural systems has been the assumption of a constant average groundwater recharge rate. This paper describes an enhanced version of a simple model designed to screen out or identify those pesticides that have a high probability for causing groundwater contamination in a region (e.g. a catchment, farm, or cropping area), which enables the temporal variability of recharge to be taken into account and illustrates the influence of a seasonal pattern of leaching and variations in predicted mobilities and persistence from those associated with averaging the recharge rate. The model is available as a user-friendly software package (PESTSCRN 3). The model was formulated based on the following assumptions: (1) linear, equilibrium, and reversible sorption; (2) first-order breakdown or degradation; (3) pesticide leaching by steady convective flow; and (4) recharge rate varying with time. Random values of the input parameters required by the calculations are generated from probability distributions as specified by the means (m) and standard deviations (s), assuming normal distributions. Outputs provide a statistical analysis of travel time and fraction of pesticide remaining at different soil depths. Most distributions for travel time are near normal with slight positive skewness and can be approximated as normal distributions. The frequency distributions of residue fractions for all the pesticides examined to date show significant positive skewness (Beta distributions), with the peak frequency towards the lower bound of 0. Simulations using metalaxyl as an example demonstrate that, depending on recharge conditions, the use of daily data instead of mean recharge data can result in important differences in the predicted values of both travel times and residue percentages.

RECHARGE TO ALLUVIAL VALLEY AQUIFERS FROM OVERBANK FLOW AND EXCESS INFILTRATION1

ABSTRACT: Recharge is an important parameter for models that simulate water and contaminant transport in unconfined aquifers. Unfortunately, measurements of actual recharge are not usually available causing recharge to be estimated or possibly added to the calibration procedure. In this study, differences between observed water‐table elevations and water‐table elevations simulated with a model based on the one‐dimensional Boussinesq equation were used to identify both the timing and quantity of recharge to an alluvial valley aquifer. Observed water table elevations and river stage data were recorded during a five‐year period from 1991 to 1995 at the Ohio Management Systems Evaluation Area located in south‐central Ohio. Direct recharge attributed to overbank flow during and shortly after flood conditions accounted for 65 percent of the total recharge computed during the five‐year study period. Recharge of excess infiltration to the aquifer was intermittent and occurred soon after large rainfall events and high river stage. Specification of constant recharge with time values in ground‐water simulation models seems inappropriate for stream‐aquifer systems given the strong influence of the river on water table elevations in these systems.

A low‐dimensional model for concentration‐discharge dynamics in groundwater stream systems

In this paper we investigate the physical basis and validity of a dynamical model for environmental tracer response for a groundwater‐dominated stream reach or small catchments. The dynamical model is formed by volume averaging of the local equations of saturated flow and solute transport. The approach interprets the empirical concentration‐discharge C‐Q as a pair of integrated state variables from an underlying state space (or phase space) for the hillslope or catchment response. The inputs represent episodic, seasonal, and random recharge rate and concentration time series. A closed form solution is found for constant inputs. Results are compared with numerical solutions of the governing partial differential equations, and agreement is found for a full range of initial states and levels of forcing. For pulse‐type or piecewise constant recharge events, the phase plane trajectories for C‐Q are shown to exhibit looping behavior, without the need for an assumption of hysteresis in the model. The orientation and looping direction of these solutions are shown to be controlled by the dimensionless ratio of solute residence time to hydraulic relaxation time and the relative phase lag between recharge and recharge concentration. The closed form solution is extended to the case of piecewise constant, random, input sequences resulting in a “random map” for C‐Q. An application is presented for seasonal storage and flushing of SO−4 in runoff for a small catchment in central Pennsylvania.

On the prediction of ground-water mound formation in response to transient recharge from a circular basin

An analytical solution of the linearized Boussinesq equation is developed to predict the formation of a ground-water mound in an aquifer system in response to localized time-varying recharge. The recharge is applied from a centrally located circular basin. The solution is obtained using an eigenvalue-eigenfunction method. The solution for a constant recharge rate is shown as a special case of the solution for a time-varying recharge rate. Application of the solution to predict ground-water mound formation is demonstrated by a numerical example. Effects of variation in the rate of reachrge, size of recharge basin and the saturated hydraulic conductivity on the growth of the water-table are also investigated.

Estimating Ground‐Water Recharge from Streamflow Hydrographs for a Small Mountain Watershed in a Temperate Humid Climate, New Hampshire, USA

AbstractHydrographs of stream discharge were analyzed to determine ground‐water recharge for two small basins draining into Mirror Lake, New Hampshire. Two methods of hydrograph analysis developed for determining ground‐water recharge were evaluated, the instantaneous recharge method and the constant recharge method. For the instantaneous recharge method, recharge is assumed to be instantaneous and uniform over the basin. For the constant recharge method, recharge is assumed to be constant and uniform over the basin for a period of weeks to months. Both methods require that a ground‐water recession slope be determined. The recession slope is used directly in the calculation for the instantaneous recharge method, and it is used as a base of reference for fitting a type curve in the constant recharge method. Results of the study indicated that the estimates of ground‐water recharge for both methods agree to within about 10 percent. Two approaches to the instantaneous recharge method, manual and automated, were also evaluated, and the results were statistically similar.The baseflow component of streamflow commonly is assumed to be equivalent to ground‐water recharge; therefore, two methods developed for determining the baseflow component of streamflow, graphical partitioning and digital filtering, were evaluated also. Baseflow values determined by graphical partitioning of hydrographs were about 25 percent less than the ground‐water recharge values. Baseflow values determined by two different approaches to the mathematical digital filtering method were generally less than baseflow determined by graphical partitioning. However, one of the approaches to digital filtering agreed reasonably well with graphical partitioning if an appropriate filter constant was used. The other approach to digital filtering resulted in baseflow values that were much less than the other baseflow values and was therefore deemed inappropriate for use on these small mountain watersheds.

Effect of Recharge Duration on Water-Table Response

The problem of the effect of recharge duration on water-table response in areas with tile drains is studied using Green's function approach to the linearized Boussinesq's equation for one-dimensional, saturated flow with appropriate boundary conditions. Pulse and decaying sinusoidal type recharge excitations with given periods of drainage are fitted by Fourier series and used as forcing functions. The resulting response equation explicitly predicts water-table buildup over time and the oscillations at dynamic equilibrium, providing a method for analyzing the effect of recharge duration on water-table rise and flow toward the drains. The approach presented herein with this feature, is seen as an improvement on the drainage spacing approach of Maasland and McWhorter for annually repeated recharge events. However, it is seen that the duration of recharge, for constant recharge depth has negligible effect on the maximum water-table rise and flow toward drains at dynamic equilibrium in cases similar to those studied by McWhorter. Peak values of water-table height predicted by both the methods were close as parameters of the flow were changed but with different patterns. The method proposed in this paper results in drainage flow pattern different from the result of McWhorter and will be a useful tool for those cases where more realistic water-table heights and flow toward drains are important.

Transient Radius of Influence Model

In the traditional analysis, the radius is defined as a constant radial distance beyond which the aquifer is undisturbed by the pumping of water from a well. In the real world, the radius is a transient variable. Its value is zero when the pumping starts, and it expands radially in the aquifer as pumping proceeds. A transient radius of influence is a proper concept to describe well hydraulics. Traditional analyses in well hydraulics were focused on water table drawdown, and less attention was given to the cone of depression volume. From the conservation of mass principle, the cone of depression volume is related to the amount of water removed from the aquifer and is, therefore, related to the pumping time. Such an concept is employed to obtain transient solutions of well drawdown and radius of influence for a well in an unconfined aquifer under a constant recharge rate.

Groundwater buildup and depletion in islands during monsoon and summer

Closed-form analytical solutions for groundwater buildup and depletion under constant recharge and evaporation in unconfined aquifers on islands are presented. The solutions are obtained through the use of Grinisky's potential and Dupuit's assumptions and the results are provided in non-dimensional form. They can be used for long- and short-term predictions for estimating, assessing and managing groundwater potential in freshwater islands.

An Aquifer Simulation Program for Micro‐Based Processors

ABSTRACTA generalized aquifer simulation program is designed and developed to handle problems connected with different kinds of complex ground‐water systems on microprocessors. The characteristic aspect of this program, involving the “Strongly Implicit Procedure” is that it requires only 10K bytes of memory for the generated code.Using this program, the effect of pumping on an aquifer can be studied for multiple pumping periods and predictions or observations can be scrutinized at various time steps within each pumping period. The program can also handle conversion problems between confined and water‐table aquifers under leaky or nonleaky states along with the effects of evapotranspiration, constant recharge or discharge boundaries. The utility and precision of the program have been tested using a sample problem quoted by Trescott et al. (1976).

Estimating groundwater evapotranspiration from streamflow records

Methods for determining groundwater outflow from a drainage basin following sudden or constant recharge were presented by Rorabaugh in 1964. He then developed, but did not publish, a method for computing outflow from an aquifer underlain by a leaky boundary. This method can be extended to determine outflow from an aquifer subjected to constant evapotranspiration (ET). The unaffected aquifer outflow (streamflow) recession following recharge becomes a straight line on a semilogarithmic graph after sufficient time has elapsed. The slope of this recession is, in logarithm to base 10 form, − Tt/0.933a2S, where T and S are the transmissivity and storage coefficient of the aquifer, a is the distance from the stream to the groundwater divide, and t is the time since recharge occurred (sudden case) or began (constant case). A set of dimensionless type curves are developed for the case of constant ET (leakage) which diverge from and lie below the unaffected case. Streamflow records for the basin, Indian Creek near Troy, Alabama, were analyzed by using the method described. A constant ET rate of 0.037 m3/s was computed for the 23.00‐km2 basin during the period April through June 1963.

Determination of constant rate deep recharge or discharge from groundwater level data

Determination of constant rate deep recharge or discharge from groundwater level data

GRAPHICAL SOLUTION OF GROUND WATER FLOW PROBLEMS

Abstract Graphical solutions to linear and radial ground water flow problems are described. These methods are based on finite difference approximations which have been widely used in heat flow problems. The case of the leaky aquiclude and vertical recharge to unconfined aquifers is discussed as well as constant head at a control and constant discharge or recharge. These solutions are useful only when the physical factors are known and an estimate of water level changes under certain conditions is desired. The methods are not intended to replace more rigorous mathematical solutions.

Helium as a ground-water tracer

Laboratory and field experiments were conducted with helium as a ground-water tracer. Techniques were developed for the addition and extraction of helium from water. A mass spectrometer and a pressure-volume apparatus were used for helium measurements at concentrations in water ranging from 1.5 to 5.5×10−4 milligrams per liter. In the field investigation, flow was traced through a confined aquifer for a distance of 188 feet. Both laboratory and field experiments showed that helium traveled at a slightly lower velocity than chloride. The advantages of helium as a ground-water tracer are its safety, low cost, relative ease of analysis, low concentrations required, and chemical inertness. The disadvantages include the relatively large errors in analysis, difficulties of maintaining a constant recharge rate, time required to develop equilibrium conditions in unconfmed aquifers, and possible loss to the atmosphere in unconfined aquifers.

Water table fluctuations induced by intermittent recharge

The problem of water table fluctuations in response to repeated recharges is considered. The effect on the water table of intermittent constant recharge (recharge applied intermittently at a constant rate) and of intermittent instantaneous recharge (recharge applied instantaneoulsy at regular intervals) is analyzed in detail. The final results are shown to consist of a combination of periodic and transient components; the transients are monotonic decreasing functions. The theory may be applied to problems of ground-water flow through aquifers and to land drainage problems.