Quasi-Saturated Layer: Implications for Estimating Recharge and Groundwater Modeling

This study presents an extension of the concept of “quasi-saturation” to a quasi-saturated layer, defined as the uppermost dynamic portion of the saturated zone subject to water table fluctuations. Entrapped air here may cause substantial reductions in the hydraulic conductivity (K) and fillable pore water. Air entrapment is caused by a rising water table, usually as a result of groundwater recharge. The most significant effects of entrapped air are recharge overestimation based on methods that use specific yield (S_y), such as the water table fluctuation method (WTF), and reductions in K values. These effects impact estimation of fluid flow velocities and contaminant migration rates in groundwater. In order to quantify actual groundwater recharge rates and the effects of entrapped air, numerical simulations with the FEFLOW (Version 7.0) groundwater flow model were carried out using a quasi-saturated layer for a pilot area in Rio Claro, Brazil. The calculated recharge rate represented 16% of the average precipitation over an 8-year period, approximately half of estimates using the WTF method. Air entrapment amounted to a fillable porosity of 0.07, significant lower that the value of 0.17 obtained experimentally for S_y. Numerical results showed that the entrapped air volume in the quasi-saturated layer can be very significant (0.58 of the air fraction) and hence can significantly affect estimates of groundwater recharge and groundwater flow rates near the water table.     

Estimating Groundwater Mounding in Sloping Aquifers for Managed Aquifer Recharge

Design of managed aquifer recharge (MAR) for augmentation of groundwater resources often lacks detailed data, and simple diagnostic tools for evaluation of the water table in a broad range of parameters are needed. In many large‐scale MAR projects, the effect of a regional aquifer base dip cannot be ignored due to the scale of recharge sources (e.g., wadis, streams, reservoirs). However, Hantush's (1967) solution for a horizontal aquifer base is commonly used. To address sloping aquifers, a new closed‐form analytical solution for water table mound accounts for the geometry and orientation of recharge sources at the land surface with respect to the aquifer base dip. The solution, based on the Dupiuit‐Forchheimer approximation, Green's function method, and coordinate transformations is convenient for computing. This solution reveals important MAR traits in variance with Hantush's solution: mounding is limited in time and space; elevation of the mound is strongly affected by the dip angle; and the peak of the mound moves over time. These findings have important practical implications for assessment of various MAR scenarios, including waterlogging potential and determining proper rates of recharge. Computations are illustrated for several characteristic MAR settings.     

Modelling of groundwater mound formation resulting from transient recharge

An analytical solution of a linearized Boussinesq equation is obtained to predict water table fluctuations as a result of time varying recharge from a strip basin for any number of recharge cycles. The analytical solution is obtained by using finite Fourier sine transform. Applications of the solution for the prediction of water table fluctuations and sensitivity analysis are demonstrated with the help of example problems. Copyright © 2001 John Wiley & Sons, Ltd.     

Groundwater recharge estimation from ephemeral streams. Case study: Wadi Tabalah,Saudi Arabia

Estimation of groundwater recharge to an unconfined aquifer is studied using analytical and numerical techniques and results are compared with field observations. There is an acute need for such estimation in water balance studies in arid climates, and the case study in this paper is for such a region. The wetting front movement in the unsaturated zone depends on antecedent soil moisture, the ponded water depth and its duration, and on the position of the water table and the hydraulic properties of the unsaturated zone. A hydraulic connection between the recharge basin and the aquifer is not immediately established because the wetting front is unsaturated. A numerical model is applied to estimate recharge in an arid-zone wadi, and its validity is tested by comparing it with an analytical solution of the equations. The calculated recharge values matched the piezometric levels observed at a well site at the edge of the wadi channel. The total recharge depths found by integration in the time domain provided a good estimate of the transmitted volume of water per unit length of wadi channel. The findings were confirmed by runoff volume measurements at gauging stations located in the basin. © 1997 John Wiley & Sons, Ltd.     

Estimating groundwater recharge in lowland watersheds

Little attention has been given to the role of groundwater in the hydrological cycle of lowland watersheds. Our objective in this study was to estimate total recharge to groundwater by analysing water table response to storm events and the rate at which water was transferred into the shallow aquifer. This was conducted at three sites in a rural watershed in the lower Atlantic coastal plain near Charleston, South Carolina, USA. A novel version of the water table fluctuation method was used to estimate total recharge to the shallow aquifer by comparing hourly data of water table position following storm events and measuring water table recession behavior, rather than subjective graphical analysis methods. Also, shallow aquifer recharge rates (vertical fluxes) were estimated using Darcy's Law by comparing static water levels in a water table well and in a shallow piezometer during dry periods. The total annual recharge estimated ranged from 107 ± 39 mm·yr^–1 (5–10% of annual precipitation) at a poorly drained topographic low area to 1140 ± 230 mm·yr^–1 (62–94% of annual precipitation) for a moderately well‐drained upland site. The average aquifer recharge rate was 114 ± 60 mm·yr^–1, which is similar to previous estimations of base flow for the ephemeral third‐order streams in this watershed. The difference in the two methods may have been caused by processes not accounted for in the Darcy flux method, soil moisture deficits, and average evapotranspiration demand, which is about 1100 mm·yr^–1 for this region. Although other factors also can affect partitioning of recharge, an integrated approach to inspecting easily gathered groundwater data can provide information on an often neglected aspect of water budget estimation. We also discuss the effects of land use change on recharge reduction, given a typical development scenario for the region. Copyright © 2011 John Wiley & Sons, Ltd.     

A Mathematical View of Water Table Fluctuations in a Shallow Aquifer in Brazil

Detailed monitoring of the groundwater table can provide important data about both short‐ and long‐term aquifer processes, including information useful for estimating recharge and facilitating groundwater modeling and remediation efforts. In this paper, we presents results of 4 years (2002 to 2005) of monitoring groundwater water levels in the Rio Claro Aquifer using observation wells drilled at the Rio Claro campus of São Paulo State University in Brazil. The data were used to follow natural periodic fluctuations in the water table, specifically those resulting from earth tides and seasonal recharge cycles. Statistical analyses included methods of time‐series analysis using Fourier analysis, cross‐correlation, and R/S analysis. Relationships could be established between rainfall and well recovery, as well as the persistence and degree of autocorrelation of the water table variations. We further used numerical solutions of the Richards equation to obtain estimates of the recharge rate and seasonable groundwater fluctuations. Seasonable soil moisture transit times through the vadose zone obtained with the numerical solution were very close to those obtained with the cross‐correlation analysis. We also employed a little‐used deep drainage boundary condition to obtain estimates of seasonable water table fluctuations, which were found to be consistent with observed transient groundwater levels during the period of study.     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

Reply

Abstract

This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated.

Editor D. Koutsoyiannis; Associate editor J. Simunek

Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172.     

Hillside seepage and the steady water table. I: Theory

Steady seepage through a hillslope aquifer results in the formation of a water table. In this paper, the boundary conditions governing the steady water table location are analysed, and an analytical series method applied to the problem, using eigenfunction expansions. Eigenfunction expansions, modified for non-orthogonal basis functions, provide a conceptually simple, efficient estimation process, that reduces the steady water table problem to a sequence of curve fitting exercises. A rigorous examination of the hodograph relationships reveals the possibility of more than one water table location, for given recharge rate. An elementary analysis reveals that one of these possibilities can always be eliminated. Also, the boundary conditions governing the steady water table are determined at a non-vertical upstream boundary. Hillslopes subjected to low recharge rates can be very difficult to analyse, and appropriate techniques for this case are detailed. In a companion paper (Adv. Water Resour., 19(2) (1996) 75–81), the techniques described in this paper are put to the test, and the upstream boundary conditions are investigated, using the series methods.     

Spatio‐temporal analysis of groundwater recharge and mound dynamics in an unconfined aquifer: a GIS‐based approach

Groundwater recharge and mounding of water‐table is a complex phenomenon involving time‐ and space‐dependent hydrologic processes. The effect of long‐term groundwater mounding in the aquifer depends on soil, aquifer geometry and the area contributing to recharge. In this paper, a GIS‐based spatio‐temporal algorithm has been developed for the groundwater mound dynamics to estimate the potential rise in the water‐table and groundwater volume balance residual in an unconfined aquifer. The recharge and mound dynamics as predicted using the methodology recommended here were compared with those using the Hantush equation, and the differences were quite significant. The significance of the study is to assess the effectiveness of the basin in terms of its hydrologic and hydraulic properties for sustainable management of groundwater recharge. Copyright © 2007 John Wiley & Sons, Ltd.     

A digital procedure for ground water recharge and discharge pattern recognition and rate estimation

A digital procedure to estimate recharge/discharge rates that requires relatively short preparation time and uses readily available data was applied to a setting in central Wisconsin. The method requires only measurements of the water table, fluxes such as stream baseflows, bottom of the system, and hydraulic conductivity to delineate approximate recharge/discharge zones and to estimate rates. The method uses interpolation of the water table surface, recharge/discharge mapping, pattern recognition, and a parameter estimation model. The surface interpolator used is based on the theory of radial basis functions with thin-plate splines. The recharge/discharge mapping is based on a mass-balance calculation performed using MODFLOW. The results of the recharge/discharge mapping are critically dependent on the accuracy of the water table interpolation and the accuracy and number of water table measurements. The recharge pattern recognition is performed with the help of a graphical user interface (GUI) program based on several algorithms used in image processing. Pattern recognition is needed to identify the recharge/discharge zonations and zone the results of the mapping method. The parameter estimation program UCODE calculates the parameter values that provide a best fit between simulated heads and flows and calibration head-and-flow targets. A model of the Buena Vista Ground Water Basin in the Central Sand Plains of Wisconsin is used to demonstrate the procedure.     

Hillside seepage and the steady water table. II: Applications

Solutions for steady hillside seepage depend on an accurate estimate of the water table location, before any of the flow parameters can be quantified. In this paper, solutions are obtained for hillslopes subjected to low recharge, using the series methods described in a companion paper (Adv. Water Resour., 19(2) (1996) 63–73). The recharge rate is bounded above, when the upstream boundary is not a vertical, impermeable dyke. The practical consequences of exceeding the maximum recharge rate are examined, for realistic hillslope geometry and recharge rates, and some modifications to the theory are suggested.     

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.     

Characteristics of Groundwater Recharge on the North China Plain

Groundwater recharge is an important component of the groundwater system. On the North China Plain (NCP), groundwater is the main water supply. Because of large‐scale overexploitation, the water table has declined, which has produced severe adverse effects on the environment and ecosystem. In this article, tracer experiment and watershed model were used to calculate and analyze NCP groundwater recharge. In the tracer experiment, average recharge was 108 mm/year and recharge coefficient 0.16. With its improved irrigation, vegetation coverage and evapotranspiration modules, the INFIL3.0 model was used for calculation of groundwater recharge. Regional modeling results showed an average recharge of 102 mm/year and recharge coefficient 0.14, for 2001–2009. These values are very similar to those from the field tracer experiment. Influences in the two methods were analyzed. The results can provide an important reference for NCP groundwater recharge.     

Evaluation of hydrologic data obtained from a local groundwater monitoring network in a metropolitan city,Korea

In the late 1980s, dramatic increases in water use caused over‐exploitation of groundwater resources and deterioration of water quality in Seoul metropolitan city. To monitor changes in quantity of groundwater resources and their quality, the metropolitan government established a local groundwater monitoring network in 1997 consisting of 119 monitoring wells. Groundwater resources in the urban area were affected by various human activities, including underground construction such as subways, pumping for public or private water use, leaky sewer systems and pavements. The variation patterns of the groundwater levels were mainly classified into four types, reflecting natural recharge due to rainfall events during the wet season, artificial recharge from leaky sewer or water supply systems, and heavy groundwater pumping for drainage or flood control purposes at underground construction sites. Significantly decreasing trends of groundwater levels in the suburbs of Seoul indicate groundwater use for various agricultural activities. Subway construction lowered the water level by an average of 25 m. Electrical conductivity values showed a wide range, from 100 to 1800 µS/cm (mean 470 µS/cm). Groundwater temperature generally showed a stable pattern, except for some sensitive increases at relatively shallow monitoring wells. Detailed analysis of the monitored groundwater data would provide some helpful implications for optimal and efficient management of groundwater resources in this metropolitan city. Copyright © 2005 John Wiley & Sons, Ltd.     

Importance of unsaturated zone flow for simulating recharge in a humid climate

Transient recharge to the water table is often not well understood or quantified. Two approaches for simulating transient recharge in a ground water flow model were investigated using the Trout Lake watershed in north-central Wisconsin: (1) a traditional approach of adding recharge directly to the water table and (2) routing the same volume of water through an unsaturated zone column to the water table. Areas with thin (less than 1 m) unsaturated zones showed little difference in timing of recharge between the two approaches; when water was routed through the unsaturated zone, however, less recharge was delivered to the water table and more discharge occurred to the surface because recharge direction and magnitude changed when the water table rose to the land surface. Areas with a thick (15 to 26 m) unsaturated zone were characterized by multimonth lags between infiltration and recharge, and, in some cases, wetting fronts from precipitation events during the fall overtook and mixed with infiltration from the previous spring snowmelt. Thus, in thicker unsaturated zones, the volume of water infiltrated was properly simulated using the traditional approach, but the timing was different from simulations that included unsaturated zone flow. Routing of rejected recharge and ground water discharge at land surface to surface water features also provided a better simulation of the observed flow regime in a stream at the basin outlet. These results demonstrate that consideration of flow through the unsaturated zone may be important when simulating transient ground water flow in humid climates with shallow water tables.     

Impact of Recharge Through Residual Oil Upon Sampling of Underlying Ground Water

At an aviation gasoline spill site in Traverse City, Michigan, historical records indicate a positive correlation between significant rainfall events and increased concentrations of slightly soluble organic compounds in the monitoring wells of the site. To investigate the recharge effect on ground water quality due to infiltrating, water percolating past residual oil and into the saturated zone, an in situ infiltration experiment was performed at the site. Sampling cones were set at various depths below a circular test area, 13 feet (4 meters) in diameter. Rainfall was simulated by sprinkling the test area at a rate sufficiently low to prevent runoff. The sampling cones for soil-gas and ground water quality were installed in the unsaturated and saturated zones to observe the effects of the recharge process. At the time of the test, the water table was below the residual oil layer. The responses of the soil-gas and ground water quality were monitored during the recharge and drainage periods, which resulted from the sprinkling.
Infiltrated water was determined to have transported organic constituents of the residual oil, specifically benzene, toluene, ethylbenzene, and ortho-xylene (BTEX), into the ground water beneath the water table, elevating the aqueous concentrations of these constituents in the saturated zone. Soil-gas concentrations of the organic compounds in the unsaturated zone increased with depth and time after the commencement of infiltration. Reaeration of the unconfined aquifer via the infiltrated water was observed. It is concluded that water quality measurements are directly coupled to recharge events for the sandy type of aquifer with an overlying oil phase, which was studied in this work. Ground water sampling strategies and data analysis need to reflect the effect of recharge from precipitation on shallow, unconfined aquifers where an oil phase may be present.     

An experimental study of water table recharge by seepage losses from a ditch with intermittent flow

Farmed catchments in the Mediterranean area often exhibit dense networks of ditches which are also preferential zones of water table recharge, and thereby of groundwater contamination. This study presents an experimental analysis of seepage losses and related groundwater recharge patterns during a typical Mediterranean runoff event at the scale of a ditch located above a shallow water table. The objectives were (i) to evaluate the patterns of water table recharge by seepage in a ditch, (ii) to study the main flow processes occurring during recharge, and (iii) to estimate solute propagation in case of contaminated flow in the ditch. The field observation indicated three major points. Firstly, they showed that seepage losses during a runoff event in a ditch can rapidly lead to a significant recharge of a shallow water table. Secondly, the recharge induces a groundwater mound much larger than the event plume. The infiltrated water and the accompanying solutes remained in the vicinity of the ditch. The patterns of groundwater recharge and contamination appeared very different. Lastly, both unsaturated and saturated‐piston flow processes were observed which suggests that a variably‐saturated flow modelling approach ought to be used to simulate the ditch‐water shallow table interaction. Finally, the study indicates that the patterns of water table recharge and contamination in Mediterranean catchments with dense ditches network vary largely in space and time, and will require dense monitoring networks to estimate the evolution of the average contamination levels. Copyright © 2008 John Wiley & Sons, Ltd.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling of water table variation in response to time-varying recharge from multiple basins using the linearised Boussinesq equation

A mathematical model is presented to describe the variations of the water table in an unconfined aquifer due to time-varying recharge applied from four rectangular basins. The model is developed by solving the linearised Boussinesq equation using the extended finite Fourier cosine transform. The time-varying recharge rate is approximated by a number of piecewise linear elements of different lengths and slopes depending on the nature of the variation in recharge rate. Application of this model for the prediction of water table fluctuations and in the sensitivity analysis of various controlling parameters on the aquifer response is demonstrated in an example.