The Water Budget Myth and Its Recharge Controversy: Linear vs. Nonlinear Models

The water budget myth, which is the idea that safe pumping must not exceed the initial recharge, gave rise to a controversy about the role of recharge in assessing the sustainability of groundwater development. To refute the concept of safe yield, a simplified water budget equation is used, which equals the total pumping rate to the sum of capture and storage change. Since initial recharge and discharge are canceled out from this equation, it is concluded that sustainable pumping has nothing to do with recharge. Investigating the assumptions underlying this equation, it is seen that it expresses the superposition principle, which implicitly assumes the groundwater reservoir can be depleted indefinitely and boundary conditions are an infinite source of water. To evaluate sustainability, however, the limits of the aquifer system must be examined accurately. Theoretically, this can only be accomplished applying nonlinear models, in which case setting up the simplified water budget equation is impossible without knowing the initial conditions. Hence, excluding recharge when assessing sustainable pumping may not be done inconsiderately, which is illustrated by two examples. An analytical solution, developed by Ernst in 1971 to simulate flow to a well in a polder area with a nonlinear function for drainage, even shows that it is not necessarily a misconception to assume the cone of depression stops expanding when the pumping rate is balanced by the infiltration rate.     

A critical review of groundwater budget myth, safe yield and sustainability

The principle of water balance is well known, but its application often causes controversy. One recent debate is the use of the water balance equation to determine the safe yield and sustainable yield. Two extreme opinions exist on natural groundwater recharge. One misconception is that the development of groundwater is considered to be safe if the pumping rate does not exceed the rate of natural recharge. Another is that the sustainable pumping rate has nothing to do with natural recharge, but depends on the increased recharge and decreased discharge (called capture) induced by pumping. The truth is that both the natural recharge and dynamic development of the capture determine the safe yield or sustainable yield of a groundwater basin. This paper clarifies the water budget controversy and uses the water balance equation to critically analyse the concepts of safe yield and sustainable yield. Numerical simulation of a hypothetical case was used to demonstrate the natural groundwater balance, effects of pumping and the dynamic development of the capture.     

Evaluating climate variability and pumping effects in statistical analyses

As development of ground water resources reaches the limits of sustainability, it is likely that even small changes in inflow, outflow, or storage will have economic or environmental consequences. Anthropogenic impacts of concern may be on the scale of natural variability, making it difficult to distinguish between the two. Under these circumstances, we believe that it is important to account for effects from both ground water development and climate variability. We use several statistical methods, including trend analysis, cluster analysis, and time series analysis with seasonal decomposition, to identify climate and anthropogenic effects in regional ground water levels and spring discharge in southern Nevada. We discuss the parameterization of climate and suggest that the relative importance of various measures of climate provides information about the aquifer system response to climate. In our system, which may be characteristic of much of the arid southwestern United States, ground water levels are much more responsive to wet years than to dry years, based on the importance of selected climate parameters in the regression. Using cluster analysis and time series seasonal decomposition, we relate differences in amplitude and phase in the seasonal signal to two major forcings—climate and pumping—and distinguish between a regional recharge response to an extremely wet year and a seasonal pumping/evapotranspiration response that decays with distance from the pumping center. The observed spring discharge data support our hypothesis that regional spring discharge, particularly at higher elevation springs, is sensitive to relatively small ground water level changes.     

Impact of coastal land reclamation on ground water level and the sea water interface

Land reclamation in coastal areas may have a significant effect on local ground water systems. Steady-state analytic solutions based on Dupuit and Ghyben-Herzberg assumptions are derived to evaluate this effect. Two situations are considered, both with ground water flow resulting from precipitation recharge: the coastal aquifer of an extensive landmass and an island. The results show that after reclamation, the water table rises and the salt water-fresh water interface moves seaward. The degree of these changes depends on the extent of reclamation and the hydraulic conductivity of the fill material. For the island situation, the reclamation displaces the ground water divide and changes the ground water conditions in the entire island. An unintended advantage of the reclamation is an increase of fresh ground water resource because the reclaimed land can be an additional aquifer and rain recharge takes place over a larger area.     

Recharge estimation for transient ground water modeling

Reliable ground water models require both an accurate physical representation of the system and appropriate boundary conditions. While physical attributes are generally considered static, boundary conditions, such as ground water recharge rates, can be highly variable in both space and time. A practical methodology incorporating the hydrologic model HELP3 in conjunction with a geographic information system was developed to generate a physically based and highly detailed recharge boundary condition for ground water modeling. The approach uses daily precipitation and temperature records in addition to land use/land cover and soils data. The importance of the method in transient ground water modeling is demonstrated by applying it to a MODFLOW modeling study in New Jersey. In addition to improved model calibration, the results from the study clearly indicate the importance of using a physically based and highly detailed recharge boundary condition in ground water quality modeling, where the detailed knowledge of the evolution of the ground water flowpaths is imperative. The simulated water table is within 0.5 m of the observed values using the method, while the water levels can differ by as much as 2 m using uniform recharge conditions. The results also show that the combination of temperature and precipitation plays an important role in the amount and timing of recharge in cooler climates. A sensitivity analysis further reveals that increasing the leaf area index, the evaporative zone depth, or the curve number in the model will result in decreased recharge rates over time, with the curve number having the greatest impact.     

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.     

Ground water flow analysis of a mid-Atlantic outer coastal plain watershed, Virginia, U.S.A

Models for ground water flow (MODFLOW) and particle tracking (MODPATH) were used to determine ground water flow patterns, principal ground water discharge and recharge zones, and estimates of ground water travel times in an unconfined ground water system of an outer coastal plain watershed on the Delmarva Peninsula, Virginia. By coupling recharge and discharge zones within the watershed, flowpath analysis can provide a method to locate and implement specific management strategies within a watershed to reduce ground water nitrogen loading to surface water. A monitoring well network was installed in Eyreville Creek watershed, a first-order creek, to determine hydraulic conductivities and spatial and temporal variations in hydraulic heads for use in model calibration. Ground water flow patterns indicated the convergence of flow along the four surface water features of the watershed; primary discharge areas were in the nontidal portions of the watershed. Ground water recharge zones corresponded to the surface water features with minimal development of a regional ground water system. Predicted ground water velocities varied between < 0.01 to 0.24 m/day, with elevated values associated with discharge areas and areas of convergence along surface water features. Some ground water residence times exceeded 100 years, although average residence times ranged between 16 and 21 years; approximately 95% of the ground water resource would reflect land use activities within the last 50 years.     

Darcian Flow Characteristics Upgradient of a Kettle Pond Determined by Direct Ground Water Flow Measurement

In glacial outwash deposits, the movement of ground water Is determined by small scale irregularities in the pattern of hydraulic conductivity. Permeability determinations on split spoon samples obtained from coring the site are not sufficient to predict the patchiness of flow since it cannot define continuity of the strata. The lattice work pattern can be determined by vertical profiling with direct ground water flow measurement. The rate and direction of flow is combined with head gradient changes to compute hydraulic conductivity changes across the site.
The results of the tests can be plotted on triangular graphs depicting the fundamental Darcy equation. The local conditions reflect a mathematical "patchiness" of hydraulic conductivity unique to outwash deposits.
The procedure was employed to determine flow characteristics and define the zone of contribution to porous bottom kettle lakes. The zone of contribution was defined by projecting backward from the vertical profiling and shallow measurements and taking into account the daily rain water recharge rate across the site.
For the unconfined aquifer north of the pond, shallow ground water flow measurements were necessary to define the recharge portion of the shoreline. Vertical profiling was required to define the recharge volume since the rate of flow was not even with depth. A simple differential equation for determining the recharge area is presented along with the calculations.     

Isotope methods for management of shared aquifers in northern Africa

Access to fresh water is one of the major issues of northern and sub-Saharan Africa. The majority of the fresh water used for drinking and irrigation is obtained from large ground water basins where there is minor contemporary recharge and the aquifers cross national borders. These aquifers include the Nubian Aquifer System shared by Chad, Egypt, Libya, and Sudan; the Iullemeden Aquifer System, extending over Niger, Nigeria, Mali, Benin, and Algeria; and the Northwest Sahara Aquifer System shared by Algeria, Libya, and Tunisia. These resources are subject to increased exploitation and may be severely stressed if not managed properly as witnessed already by declining water levels. In order to make appropriate decisions for the sustainable management of these shared water resources, planners and managers in different countries need an improved knowledge base of hydrological information. Three technical cooperation projects related to aquifer systems will be implemented by the International Atomic Energy Agency, in collaboration with the United Nations Educational, Scientific and Cultural Organization and United Nations Development Programme/Global Environmental Facility. These projects focus on isotope hydrology studies to better quantify ground water recharge and dynamics. The multiple isotope approach combining commonly used isotopes 18O and 2H together with more recently developed techniques (chlorofluorocarbons, 36Cl, noble gases) will be applied to improve the conceptual model to study stratification and ground water flows. Moreover, the isotopes will be an important indicator of changes in the aquifer due to water abstraction, and therefore they will assist in the effort to establish a sustainable ground water management.     

Ground water sustainability: methodology and application to the North China Plain

This article analyzes part of a ground water flow system in the North China Plain (NCP) subject to severe overexploitation and rapid depletion. A transient ground water flow model was constructed and calibrated to quantify the changes in the flow system since the predevelopment 1950s. The flow model was then used in conjunction with an optimization code to determine optimal pumping schemes that improve ground water management practices. Finally, two management scenarios, namely, urbanization and the South-to-North Water Transfer Project, were evaluated for their potential impacts on the ground water resources in the study area. Although this study focuses on the NCP, it illustrates a general modeling framework for analyzing the sustainability, or the lack thereof, of ground water flow systems driven by similar hydrogeologic and economic conditions. The numerical simulation is capable of quantifying the various components of the overall flow budget and evaluating the impacts of different management scenarios. The optimization modeling allows the determination of the maximum "sustainable pumping" that satisfies a series of prescribed constraints. It can also be used to minimize the economic costs associated with ground water development and management. Furthermore, since the NCP is one of the most water scarce and economically active regions in the world, the conclusions and insights from this study are of general interest and international significance.     

Vadose zone-attenuated artificial recharge for input to a ground water model

Accurate representation of artificial recharge is requisite to calibration of a ground water model of an unconfined aquifer for a semiarid or arid site with a vadose zone that imparts significant attenuation of liquid transmission and substantial anthropogenic liquid discharges. Under such circumstances, artificial recharge occurs in response to liquid disposal to the vadose zone in areas that are small relative to the ground water model domain. Natural recharge, in contrast, is spatially variable and occurs over the entire upper boundary of a typical unconfined ground water model. An improved technique for partitioning artificial recharge from simulated total recharge for inclusion in a ground water model is presented. The improved technique is applied using data from the semiarid Hanford Site. From 1944 until the late 1980s, when Hanford's mission was the production of nuclear materials, the quantities of liquid discharged from production facilities to the ground vastly exceeded natural recharge. Nearly all hydraulic head data available for use in calibrating a ground water model at this site were collected during this period or later, when the aquifer was under the diminishing influence of the massive water disposals. The vadose zone is typically 80 to 90 m thick at the Central Plateau where most production facilities were located at this semiarid site, and its attenuation of liquid transmission to the aquifer can be significant. The new technique is shown to improve the representation of artificial recharge and thereby contribute to improvement in the calibration of a site-wide ground water model.     

Ground water budget analysis and cross-formational leakage in an arid basin

Ground water budget analysis in arid basins is substantially aided by integrated use of numerical models and environmental isotopes. Spatial variability of recharge, storage of water of both modern and pluvial age, and complex three-dimensional flow processes in these basins provide challenges to the development of a good conceptual model. Ground water age dating and mixing analysis with isotopic tracers complement standard hydrogeologic data that are collected and processed as an initial step in the development and calibration of a numerical model. Environmental isotopes can confirm or refute a priori assumptions of ground water flow, such as the general assumption that natural recharge occurs primarily along mountains and mountain fronts. Isotopes also serve as powerful tools during postaudits of numerical models. Ground water models provide a means of developing ground water budgets for entire model domains or for smaller regions within the model domain. These ground water budgets can be used to evaluate the impacts of pumping and estimate the magnitude of capture in the form of induced recharge from streams, as well as quantify storage changes within the system. The coupled analyses of ground water budget analysis and isotope sampling and analysis provide a means to confirm, refute, or modify conceptual models of ground water flow.     

Using MODFLOW 2000 to model ET and recharge for shallow ground water problems

In environments with shallow ground water elevation, small changes in the water table can cause significant variations in recharge and evapotranspiration fluxes. Particularly, where ground water is close to the soil surface, both recharge and evapotranspiration are regulated by a thin unsaturated zone and, for accuracy, must be represented using nonconstant and often nonlinear relationships. The most commonly used ground water flow model today, MODFLOW, was originally designed with a modular structure with independent packages representing recharge and evaporation processes. Systems with shallow ground water, however, may be better represented using either a recharge function that varies with ground water depth or a continuous recharge and evapotranspiration function that is dependent on depth to water table. In situations where the boundaries between recharging and nonrecharging cells change with time, such as near a seepage zone, a continuous ground water flux relationship allows recharge rates to change with depth rather than having to calculate them at each stress period. This research article describes the modification of the MODFLOW 2000 recharge and segmented evapotranspiration packages into a continuous recharge-discharge function that allows ground water flux to be represented as a continuous process, dependent on head. The modifications were then used to model long-term recharge and evapotranspiration processes on a saline, semiarid floodplain in order to understand spatial patterns of salinization, and an overview of this process is given.     

Controls on Ground Water Chemistry in the Central Couloir Sud Rifain,Morocco

Irrigation, urbanization, and drought pose challenges for the sustainable use of ground water in the central Couloir sud rifain, a major agricultural region in north-central Morocco, which includes the cities of Fès and Meknès. The central Couloir is underlain by unconfined and confined carbonate aquifers that have suffered declines in hydraulic head and reductions in spring flow in recent decades. Previous studies have surveyed ground water flow and water quality in wells and springs but have not comprehensively addressed the chemistry of the regional aquifer system. Using graphical techniques and saturation index calculations, we infer that major ion chemistry is controlled (1) in the surficial aquifer by cation exchange, calcite dissolution, mixing with deep ground water, and possibly calcite precipitation and (2) in the confined aquifer and warm springs by calcite dissolution, dolomite dissolution, mixing with water that has dissolved gypsum and halite, and calcite precipitation. Analyses of ²H and ¹⁸O indicate that shallow ground water is affected by evaporation during recharge (either of infiltrating precipitation or return flow), whereas deep ground water is sustained by meteoric recharge with little evaporation. Mechanisms of recharge and hydrochemical evolution are broadly consistent with those delineated for similar regional aquifer systems elsewhere in Morocco and in southern Spain.     

The response of playa and sabkha hydraulics and mineralogy to climate forcing

Dry playa lakes and sabkhat often represent the terminus of large ground water flow systems and act as integrators of both upgradient (recharge) and downgradient discharge (evaporation). Ground water levels beneath playa/sabkha systems show a variety of surprising responses driven by large evaporation demands and chemical processes not typically encountered in more humid regions. When the water table is very close to the land surface, almost instantaneous rises can be observed with little observed change in either upgradient ground water recharge or potential evaporation. Conversely, when water tables are several meters below the playa surface, water table responses to interannual variability of recharge can be damped and lag significantly behind such changes. This review of the dynamics of shallow water tables in playa lakes and sabkhat discusses the pertinent hydraulic and solute processes and extracts a simple but comprehensive model based on soil physics for predicting the water table response to either upstream recharge changes or changes in potential evaporation at the playa/sabkha. Solutes and associated authigenic minerals are also shown to be important in discriminating both the causes and effects of water level fluctuations.     

Evaluation of volatilization as a natural attenuation pathway for MTBE

Volatilization and diffusion through the unsaturated zone can be an important pathway for natural attenuation remediation of methyl tert-butyl ether (MTBE) at gasoline spill sites. The significance of this pathway depends primarily on the distribution of immiscible product within the unsaturated zone and the relative magnitude of aqueous-phase advection (ground water recharge) to gaseous-phase diffusion. At a gasoline spill site in Laurel Bay, South Carolina, rates of MTBE volatilization from ground water downgradient from the source are estimated by analyzing the distribution of MTBE in the unsaturated zone above a solute plume. Volatilization rates of MTBE from ground water determined by transport modeling ranged from 0.0020 to 0.0042 g m(-2)/year, depending on the assumed rate of ground water recharge. Although diffusive conditions at the Laurel Bay site are favorable for volatilization, mass loss of MTBE is insignificant over the length (230 m) of the solute plume. Based on this analysis, significant volatilization of MTBE from ground water downgradient from source areas at other sites is not likely. In contrast, model results indicate that volatilization coupled with diffusion to the atmosphere could be a significant mass loss pathway for MTBE in source areas where residual product resides above the capillary zone. Although not documented, mass loss of MTBE at the Laurel Bay site due to volatilization and diffusion to the atmosphere are predicted to be two to three times greater than mass loading of MTBE to ground water due to dissolution and recharge. This result would imply that volatilization in the source zone may be the critical natural attenuation pathway for MTBE at gasoline spill sites, especially when considering capillary zone limitations on volatilization of MTBE from ground water and the relative recalcitrance of MTBE to biodegradation.     

On the interpretation of recharge estimates from steady-state model calibrations

Ground water recharge is often estimated through the calibration of ground water flow models. We examine the nature of calibration errors by considering some simple mathematical and numerical calculations. From these calculations, we conclude that calibrating a steady-state ground water flow model to water level extremes yields estimates of recharge that have the same value as the time-varying recharge at the time the water levels are measured. These recharge values, however, are a subdued version of the actual transient recharge signal. In addition, calibrating a steady-state ground water flow model to data collected during periods of rising water levels will produce recharge values that underestimate the actual transient recharge. Similarly, calibrating during periods of falling water levels will overestimate the actual transient recharge. We also demonstrate that average water levels can be used to estimate the actual average recharge rate provided that water level data have been collected for a sufficient amount of time.     

Delineation of regional arid karstic aquifers: an integrative data approach

This research integrates data procedures for the delineation of regional ground water flow systems in arid karstic basins with sparse hydrogeologic data using surface topography data, geologic mapping, permeability data, chloride concentrations of ground water and precipitation, and measured discharge data. This integrative data analysis framework can be applied to evaluate arid karstic aquifer systems globally. The accurate delineation of ground water recharge areas in developing aquifer systems with sparse hydrogeologic data is essential for their effective long-term development and management. We illustrate the use of this approach in the Cuatrociénegas Basin (CCB) of Mexico. Aquifers are characterized using geographic information systems for ground water catchment delineation, an analytical model for interbasin flow evaluation, a chloride balance approach for recharge estimation, and a water budget for mapping contributing catchments over a large region. The test study area includes the CCB of Coahuila, Mexico, a UNESCO World Biosphere Reserve containing more than 500 springs that support ground water-dependent ecosystems with more than 70 endemic organisms and irrigated agriculture. We define recharge areas that contribute local and regional ground water discharge to springs and the regional flow system. Results show that the regional aquifer system follows a topographic gradient that during past pluvial periods may have linked the Río Nazas and the Río Aguanaval of the Sierra Madre Occidental to the Río Grande via the CCB and other large, currently dry, upgradient lakes.     

Important observations and parameters for a salt water intrusion model

Sensitivity analysis with a density-dependent ground water flow simulator can provide insight and understanding of salt water intrusion calibration problems far beyond what is possible through intuitive analysis alone. Five simple experimental simulations presented here demonstrate this point. Results show that dispersivity is a very important parameter for reproducing a steady-state distribution of hydraulic head, salinity, and flow in the transition zone between fresh water and salt water in a coastal aquifer system. When estimating dispersivity, the following conclusions can be drawn about the data types and locations considered. (1) The "toe" of the transition zone is the most effective location for hydraulic head and salinity observations. (2) Areas near the coastline where submarine ground water discharge occurs are the most effective locations for flow observations. (3) Salinity observations are more effective than hydraulic head observations. (4) The importance of flow observations aligned perpendicular to the shoreline varies dramatically depending on distance seaward from the shoreline. Extreme parameter correlation can prohibit unique estimation of permeability parameters such as hydraulic conductivity and flow parameters such as recharge in a density-dependent ground water flow model when using hydraulic head and salinity observations. Adding flow observations perpendicular to the shoreline in areas where ground water is exchanged with the ocean body can reduce the correlation, potentially resulting in unique estimates of these parameter values. Results are expected to be directly applicable to many complex situations, and have implications for model development whether or not formal optimization methods are used in model calibration.     

Ground Water Remediation Using an Extraction, Treatment, and Recharge System

Ground water remediation of volatile organic compound (VOC) contamination at a site in Michigan was initiated as a result of a consent agreement between the Michigan Department of Natural Resources (MDNR) and the responsible party. Under the direction of the MDNR, the responsible party conducted a remedial investigation/feasibility study using federal guidelines to define the extent of contamination at the site and to select a response action for site remediation. The selected alternative included a combination of ground water extraction, treatment, and recharge, and soil flushing. The extraction system withdraws ground water from various depths in heavily contaminated areas. The ground water is treated using an air stripper. A spray distribution system spreads effluent from the stripper over a recharge basin constructed over the most contaminated areas. Additional contaminant removal is achieved by volatilization from the spray and percolation through the gravel bed. Recharge water moves downward through the contaminated soils, thus flushing residual soil contaminants. The initial operating data demonstrated that the system can effectively remove trichloroethylene (TCE) from ground water (approximately 95 percent overall removal efficiency). The annualized capital and operation and maintenance (O & M) costs of the remedial action were estimated for several operating periods (15, 20, and 30 years).