Water Table Fluctuation in the Presence of a Time-Varying Exponential Recharge and Depth-Dependent ET in a Two-Dimensional Aquifer System with an Inclined Base

An analytical solution is presented for water table fluctuation between ditch drains in presence of exponential recharge and depth-dependent evapotranspiration (ET) from groundwater table in a two-dimensional gently sloping aquifer. The groundwater head above the drain is small compared to the saturated thickness of the aquifer. A sound mathematical transformation is devised to transform the two-dimensional groundwater flow equation into a simple form, which makes possible to obtain an analytical solution. The transient midpoint water table variations from the proposed solution compare well with the already existing solutions for horizontal aquifer. A numerical example is used to illustrate the combined effect of depth-dependent ET coupled with a time-varying exponential recharge on the water table fluctuation. The inclusion of a depth-dependent ET in the solution results in water table decline at a faster rate as compared to the case when ET is not considered. With an increase in slope of the aquifer base, water table profiles become asymmetric and the water table divide shifts towards the lower drain. The height of the water table profiles increases on moving away from the boundary of the aquifer and the highest level of the ground water table is obtained in the central portion of the aquifer basin due to the presence of drainage ditches on the aquifer boundary. When the effect of ET is incorporated in combination with recharge, the analytical solution results in accurate and reliable estimates of water table fluctuations under situations subjected to a number of controlling factors. This study will be useful for alleviation of drainage problems of the aquifers receiving surface recharge and surrounded by streams.     

Water Table Profiles and Discharges for an Inclined Ditch-Drained Aquifer under Temporally Variable Recharge

This paper presents the solution of the linearized Boussinesq equation for an inclined, ditch-drained aquifer, with a temporally varying recharge rate. Water-table profiles and flow rates into the ditches are calculated. As an initial condition the steady-state profile for a constant recharge rate is used, and the linearized Boussinesq equation is solved for a different recharge rate. Then, at a specified time, the transient water table profile is used as initial condition for the Boussinesq equation with a new recharge rate. The transient solution at a new specified time is then used as the initial condition for the Boussinesq equation with a different recharge rate, and so on. Using the Darcy equation, analytical expressions for the flow rates into the ditches can be obtained. The solution allows the calculation of the transient behavior of the groundwater table and its flow rates due to temporally variable recharge rates.     

Water Table Rise in Sloping Aquifer due to Canal Seepage and Constant Recharge

Analytical solutions of the linearized Boussinesq equation and a fully implicit finite-difference numerical solution of the nonlinear Boussinesq equation were obtained to study transient and steady-state water table rise in a homogeneous, isotropic, and incompressible unconfined sloping aquifer. The rise was due to seepage from two canals located at different elevations above the sloping impermeable barrier and constant recharge from the land surface. Proposed analytical solutions were verified with existing analytical solutions for a horizontal aquifer and were found in close agreement. The effect of recharge and slope of the impermeable barrier on water table rise predicted by both analytical and numerical solutions was studied by considering a numerical example. The effect of the linearization of the Boussinesq equation on water table rise was also studied by comparing the water table heights predicted by the numerical solution with those computed from the analytical solution. The analytical solution overestimates water table elevations compared to those obtained from the numerical solution, and the difference in water table in the middle region decreases with increase in time.     

Analytical Solution for Tidal Propagation in a Leaky Aquifer Extending Finite Distance under the Sea

This paper focuses on groundwater dynamics in response to the tidal fluctuation in a coastal aquifer system. An analytical solution is derived to describe groundwater level fluctuation in a leaky aquifer extending finite distance under the sea. Based on this solution, the joint effects of various parameters, such as the dynamic effect of water table fluctuation and the leakages of the inland and offshore, on the behavior of the groundwater level fluctuations in the inland part of the leaky confined aquifer can be thoroughly analyzed. When the roof length is increased, the dynamic effect of the water table fluctuation on the dimensionless groundwater amplitude, intrusion distance, and fixed phase shift in the unconfined aquifer become more important and the water table fluctuation approaches constant values when the roof length is greater than a threshold value. However, given the same values of dimensionless leakage and roof length, the dimensionless groundwater amplitude, intrusion distance, and fixed phase shift in the leaky aquifer with considering the dynamic effects are always larger than those of neglecting such effects.     

Ramp Kernels for Aquifer Responses to Arbitrary Stream Stage

Analytical expressions for ramp kernels (new kernels) for an improved convolution for obtaining aquifer responses, viz, groundwater head, rate, and cumulative volume of groundwater flow, to an arbitrary stage, are obtained. The use of the ramp kernels gives accurate aquifer responses and is superior to the conventional convolution in which numerical integration or pulse kernels are used. The extent of improvement in the results with the use of the ramp kernels is discussed and quantified for three examples, where the results are compared to analytical solutions. For the comparisons, the analytical solutions for linear and sinusoidal stream stages are derived. The use of the ramp kernels reproduces accurately the analytical solutions. The concept of ramp kernels can also be used for obtaining an accurate solution of convolution integrals observed in other fields.     

Tide-Induced Water Table Fluctuations in Coastal Aquifers Bounded by Rhythmic Shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer’s properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.     

Generalized Analytical Solutions for Groundwater Head in Inclined Aquifers in the Presence of Subsurface Drains

Analytical solutions for groundwater head in the presence of subsurface drains are important in assessing the effectiveness of an existing drainage system under a probable extreme variation in the rate of recharge and designing a new drainage system. Generalized analytical solutions for groundwater head in inclined aquifers in the presence of parallel subsurface drains are obtained considering the transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. An appropriate function, new to analytical drainage studies, is used for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the increase in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses. The analytical equations for discharge to drains for different cases considered are also obtained. The discharge equations used by prior investigators are found inappropriate.     

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.     

Generalized Analytical Solutions for Groundwater Head in a Horizontal Aquifer in the Presence of Subsurface Drains

Generalized analytical solutions for groundwater head in horizontal aquifers in the presence of parallel subsurface drains are obtained considering a transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. A function, new to analytical drainage studies, is proposed for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at a shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the changes in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses.     

Modification of Canal Flow due to Stream-Aquifer Interaction

Unsteady canal flow in an integrated canal-flow–groundwater-flow system is analyzed by solving the coupled equations governing canal flow, groundwater flow and the seepage between them. Analytical solutions are obtained for the coupled system for small water-level disturbances using Fourier analysis methods and complex variables. Dimensionless parameter groups characterizing the aquifer, the canal, and the sediment layer are identified using the governing equations and the solution. The influence in the aquifer and the semipermeable bottom sediment layer due to disturbances in canal flow is studied. The analytical solutions are compared to numerical solutions obtained using the MODFLOW model and the Hydrologic Simulation Engine of the South Florida Regional Simulation Model. Results of the analysis are useful in determining the range of aquifer, sediment, and canal characteristics for which stream-aquifer interaction is important. The results can be used to determine the conditions for which the canal is hydraulically disconnected from the aquifer because of the sediment layer. The analytical solution is useful to understand the propagation characteristics of small-amplitude water-level disturbances in the canal and the aquifer. The characteristics studied include the amplitude decay constant and the speed. The solution can be used to design benchmark problems that can be used to evaluate integrated canal-flow–groundwater-flow models. The results of the study can be used to estimate the space and time steps needed in the canal and the aquifer when simulating stream-aquifer interaction.     

Analytical Solutions for Constant-Flux and Constant-Head Tests at a Finite-Diameter Well in a Wedge-Shaped Aquifer

Neglecting the effect of well radius may lead to a significant error in the predicted drawdown distribution near the pumping well area. New analytical solutions describing aquifer responses to a constant pumping or a constant head maintained at a finite-diameter well in a wedge-shaped aquifer are derived based on the image-well method and applicable to an arbitrarily located well in the system. The solutions are useful for quantifying groundwater exploitation from a wedge-shaped aquifer and for determining the hydrogeological parameters of a wedge-shaped aquifer in inverse problems.     

Analytical Ground-Water Flow Solutions for Channel-Aquifer Interaction

A general solution scheme for determining ground-water levels for channel∕group-water systems with recharge is developed and verified. The analytical solution uses the Laplace transform method to solve a linearized form of the Boussinesq equation. Unlike other solutions, this scheme allows for both boundaries and sources∕sinks to vary as a function of time and space. To verify the analytical scheme, three one-dimensional case studies of flow between two line sources in an unconfined aquifer were explored through a base run and a set of sensitivity analyses. These runs involved comparisons to MODFLOW and changes in the boundary conditions and dimensions. As noted, the flow equations were linearized about a point called the representative flow depth. A value of havg, defined as the average water depth between the initial and steady flow conditions, was used as the representative flow depth. Results of the proposed method matched very well with MODFLOW solutions for all times and locations using an optimal linearization point. In addition, using havg improved the solutions compared to those obtained previously.     

Numerical Simulation of Groundwater Flow with Gradually Increasing Heterogeneity due to Clogging

Well injection replenishes depleting water levels in a well field. Observation well water levels some distance away from the injection well are the indicators of the success of a well injection program. Simulation of the observation well response, located a few tens of meters from the injection well, is likely to be affected by the effects of nonhomogeneous medium, inclined initial water table, and aquifer clogging. Existing algorithms, such as the U.S. Geological Survey groundwater flow software MODFLOW, are capable of handling the first two conditions, whereas time-dependent clogging effects are yet to be introduced in the groundwater flow models. Elsewhere, aquifer clogging is extensively researched in theory of filtration; scope for its application in a well field is a potential research problem. In the present paper, coupling of one such filtration theory to MODFLOW is introduced. Simulation of clogging effects during “Hansol” well recharge in the parts of western India is found to be encouraging.     

Vapor Flow to Trench in Leaky Aquifer

Soil-vapor extraction has become the most common innovative technology for treating subsurface soils contaminated with volatile and semivolatile organic compounds. This popularity is due partly to the low cost of vapor extraction and partly to the fact that mitigation is completed in situ. Previous applications of this technology have generally considered flow to either vertical or horizontal wells. However, vapor flow to a trench offers the advantages of a more uniform velocity field and lower construction costs at sites with shallow water tables. Therefore, an analytical solution is obtained for steady flow to a trench. The trench is assumed to partially penetrate an anisotropic aquifer and to have a finite horizontal length. The bottom aquifer boundary is assumed to be an impermeable water table, and the top boundary is a semipermeable aquitard. A comparison is made with field measurements to illustrate the application of the solution and to give confidence in its use.     

Analysis of Seepage from Polygon Channels

An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and a Schwarz-Christoffel transformation. The symmetry about the vertical axis has been utilized in obtaining the solution for half of the seepage domain only. The solution also includes relations for variation in seepage velocity along the channel perimeter and a set of parametric equations for the location of phreatic line. From this generalized case, particular solutions have also been deduced for rectangular and triangular channels with a drainage layer at finite depth and trapezoidal, rectangular, and triangular channels with a drainage layer and water table at infinite depth. Moreover, the analysis includes solutions for a slit, which is also a special case of polygon channels, for both cases of the drainage layer. These solutions are useful in quantifying seepage loss and/or artificial recharge of groundwater through polygon channels.     

Case Study of Water Table Evaporation at Ichkeul Marshes (Tunisia)

The method of Gardner was used to estimate the evaporation rate from bare soils under high water table conditions, at Ichkeul marshes, of northern Tunisia. For this purpose, water content, soil-water suction, and water table depth were measured at three sites. Other common approaches that provide estimates of water table evaporation such as the Averianov and Coudrain-Ribstein et al. empirical formulas and the approach used by the U.S. Geological Survey's groundwater flow model MODFLOW were also evaluated. Next, a 2D groundwater simulation model, using the Gardner equations for computing evaporation rate, was developed to quantify the aquifer budget and groundwater losses via evaporation at the total area of the marshes. The model was calibrated in a steady-state condition. The results indicated significant groundwater losses by water table evaporation. The sensitivity of the groundwater model to the Averianov and MODFLOW approaches was analyzed. The best results (piezometric head and the area distribution of the evaporation discharge) were obtained with the Averianov formula.     

Monthly Water Resources and Irrigation Planning: Case Study of Conjunctive Use of Surface and Groundwater Resources

The Tehran metropolitan area is one of the mega cities of the world and has an annual domestic water consumption close to one billion cubic meters. The sewer system mainly consists of traditional absorption wells. Therefore, the return flow from the domestic consumption has been one of the main sources of groundwater recharge. Some part of this sewage is drained into local rivers and drainage channels and partially contaminates the surface runoff and local flows. These polluted surface waters are used in conjunction with groundwater for irrigation purposes in the southern part of the Tehran. In this paper, a systematic approach to surface and groundwater resources modeling in the study area, with its complex system of water supply, groundwater recharge, and discharge, is discussed. A dynamic programming optimization model is developed for conjunctive use planning. The objective function of this model is developed to supply the agricultural water demands, to reduce pumping costs, and to control groundwater table fluctuations. To develop the response function of the aquifers located in the study area, a mathematical model for simulation of the Tehran aquifer water table fluctuations has been developed and calibrated with the available data. Different scenarios are defined to study the long-term impacts of the development projects on conjunctive use policies and water table fluctuations. Comparison of the results showed how significant is the effects of an integrated approach to the surface and groundwater resources allocation in Tehran metropolitan area. The proposed model is a useful tool for irrigation planning in this region.     

Multidimensional Infiltration with Arbitrary Surface Fluxes

A new solution to the multidimensional linearized Richards equation was derived using a Fourier integral transform. Exponential functional forms k = kseαψ and θ = θr + (θs ? θr)eαψ were used to represent the hydraulic conductivity and pressure relation and the soil water release curve. The analytical solutions consider the conditions of time dependence and nonuniform distribution of rainfall intensity and arbitrary initial water content distribution with a water table. The analytical solutions can be used to predict the ponding time and to obtain the volumetric water content distribution over time and space.     

Theory of Seepage into an Auger Hole in a Confined Aquifer Overlying a Gravel Substratum

An analytical solution is presented to the problem of steady groundwater flow seeping into a pumped cylindrical hole partially penetrating a homogeneous and anisotropic confined aquifer overlying a gravel substratum. Solutions are obtained for two general cases of the problem: (1) when the level of the pumped hole is below the confining layer; (2) when it is above it. The validity of the proposed theory is tested by comparing analytical predictions obtained for a few flow situations with corresponding results obtained by numerical means. The theory presented here can be utilized to convert the rate of rise of water in a pumped auger hole into directional conductivities of soil, in areas where water is found to be in a confined state overlying a gravel substratum. The study shows that the conductivity values calculated by neglecting the confining pressure of an artesian aquifer with a gravel base [i.e., by applying the existing (Boast and Kirkham in 1971), auger hole seepage theory for a phreatic aquifer with a gravel base to confined situations] may result in serious error; hence, the artesian head of an aquifer must be accounted for while computing the conductivity values. Further, it is observed that the area contributing flow to a pumped auger hole/well with a gravel base is mostly restricted to a short radial distance from the center of the hole, particularly for situations where the gravel substratum is located close to the bottom of the hole. This is in contrast to auger hole flow situations overlying an impervious substratum, where the domain contributing flow is mostly spread out to a considerable distance from the center of the hole.     

Analytical Solution for Conservative Solute Transport in One-Dimensional Homogeneous Porous Formations with Time-Dependent Velocity

The space-time variation in contaminant concentration in unsteady flow in a homogeneous finite aquifer subjected to point source contamination is analytically derived under two conditions: (1) the flow velocity in the aquifer is of sinusoidal form; and (2) the flow velocity is an exponentially decreasing function. The analytical solution is illustrated using an example. Analytical solutions are perhaps most useful for benchmarking numerical codes and solutions.