Paul M. Barlow

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

Abstract In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifers response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.

Aquifer response to stream-stage and recharge variations. I. Analytical step-response functions

Abstract Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.

Mass-balance analysis of reactive transport and cation exchange in a plume of wastewater-contaminated groundwater

Mass-balance calculations were used to quantify reactive transport processes and cation exchange in a plume of groundwater contaminated with septage-effluent wastewater on Cape Cod, Massachusetts. Of the chloride mass recharged to the aquifer in effluent, as much as 72% was accounted for using spatial moment analysis and finite-element integration of groundwater concentrations, which were sampled at ≤69 wells and supplemented by borehole electromagnetic-induction logging. Comparison of chloride transport and mass balances with transport and mass balances of other species indicated that reactive processes substantially altered concentrations of all major chemical constituents. Calcium in effluent was exchanged for magnesium on aquifer sediments. Potassium also was attenuated, possibly through exchange with magnesium, sodium, and/or hydrogen ions. Sufficient hydrogen ions were generated by microbial nitrification in the unsaturated zone to consume effluent alkalinity and lower the effluent pH from 7.2 to 5.0 in the recharged groundwater; the resultant acid conditions may have facilitated anion adsorption and silicate-mineral dissolution. Retardation factors (R) calculated from breakthrough curves indicated that calcium (R = 1.4−2.2) and boron (R = 1.3−2.1) were similarly retarded, whereas potassium experienced greater retardation (R = 1.8−5.2). Retardation of calcium, boron, and potassium was greater in the unsaturated zone than in the saturated zone; this may have resulted from spatial heterogeneity in exchange properties and preferential saturated-zone flow through coarse-grained sediments not present in the unsaturated zone. Although concentrations may stabilize and chemical reactions reach equilibrium at fixed points along paths in the plume, the mass-balance analysis illustrated that steady-state conditions will not be established throughout the aquifer and the cumulative mass of reacted constituents in the plume will increase until the plume reaches its discharge area. The analysis also indicates that retrospective study of dissolved concentrations in an established plume after many years of transport may not identify reactive transport and attenuation of plume constituents, if precise data on source concentrations (or masses) and the spatial distribution of solutes during plume development are not available. Finally, transport of the effluent-contaminated groundwater also altered the geochemistry of the aquifer, for example, through cation exchange, such that the introduction of clean, uncontaminated water into the aquifer will not immediately restore pre-plume conditions.

A nitrogen-rich septage-effluent plume in a glacial aquifer, Cape Cod, Massachusetts, February 1990 through December 1992

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GWM-2005 - A Groundwater-Management Process for MODFLOW-2005 with Local Grid Refinement (LGR) Capability

This report describes the Groundwater-Management (GWM) Process for MODFLOW-2005, the 2005 version of the U.S. Geological Survey modular three-dimensional groundwater model. GWM can solve a broad range of groundwater-management problems by combined use of simulationand optimization-modeling techniques. These problems include limiting groundwater-level declines or streamflow depletions, managing groundwater withdrawals, and conjunctively using groundwater and surface-water resources. GWM was initially released for the 2000 version of MODFLOW. Several modifications and enhancements have been made to GWM since its initial release to increase the scope of the program’s capabilities and to improve its operation and reporting of results. The new code, which is called GWM-2005, also was designed to support the local grid refinement capability of MODFLOW-2005. Local grid refinement allows for the simulation of one or more higher resolution local grids (referred to as child models) within a coarser grid parent model. Local grid refinement is often needed to improve simulation accuracy in regions where hydraulic gradients change substantially over short distances or in areas requiring detailed representation of aquifer heterogeneity. GWM-2005 can be used to formulate and solve groundwatermanagement problems that include components in both parent and child models. Although local grid refinement increases simulation accuracy, it can also substantially increase simulation run times.

Depletion Mapping and Constrained Optimization to Support Managing Groundwater Extraction

Groundwater models often serve as management tools to evaluate competing water uses including ecosystems, irrigated agriculture, industry, municipal supply, and others. Depletion potential mapping-showing the model-calculated potential impacts that wells have on stream baseflow-can form the basis for multiple potential management approaches in an oversubscribed basin. Specific management approaches can include scenarios proposed by stakeholders, systematic changes in well pumping based on depletion potential, and formal constrained optimization, which can be used to quantify the tradeoff between water use and stream baseflow. Variables such as the maximum amount of reduction allowed in each well and various groupings of wells using, for example, K-means clustering considering spatial proximity and depletion potential are considered. These approaches provide a potential starting point and guidance for resource managers and stakeholders to make decisions about groundwater management in a basin, spreading responsibility in different ways. We illustrate these approaches in the Little Plover River basin in central Wisconsin, United States-home to a rich agricultural tradition, with farmland and urban areas both in close proximity to a groundwater-dependent trout stream. Groundwater withdrawals have reduced baseflow supplying the Little Plover River below a legally established minimum. The techniques in this work were developed in response to engaged stakeholders with various interests and goals for the basin. They sought to develop a collaborative management plan at a watershed scale that restores the flow rate in the river in a manner that incorporates principles of shared governance and results in effective and minimally disruptive changes in groundwater extraction practices.

Capture Versus Capture Zones: Clarifying Terminology Related to Sources of Water to Wells: P.M. Barlow et al. Groundwater XX, no. X: XX-XX

The term capture, related to the source of water derived from wells, has been used in two distinct yet related contexts by the hydrologic community. The first is a water-budget context, in which capture refers to decreases in the rates of groundwater outflow and (or) increases in the rates of recharge along head-dependent boundaries of an aquifer in response to pumping. The second is a transport context, in which capture zone refers to the specific flowpaths that define the three-dimensional, volumetric portion of a groundwater flow field that discharges to a well. A closely related issue that has become associated with the source of water to wells is streamflow depletion, which refers to the reduction in streamflow caused by pumping, and is a type of capture. Rates of capture and streamflow depletion are calculated by use of water-budget analyses, most often with groundwater-flow models. Transport models, particularly particle-tracking methods, are used to determine capture zones to wells. In general, however, transport methods are not useful for quantifying actual or potential streamflow depletion or other types of capture along aquifer boundaries. To clarify the sometimes subtle differences among these terms, we describe the processes and relations among capture, capture zones, and streamflow depletion, and provide proposed terminology to distinguish among them.

A tool for efficient, model-independent management optimization under uncertainty

Abstract To fill a need for risk-based environmental management optimization, we have developed PESTPP-OPT, a model-independent tool for resource management optimization under uncertainty. PESTPP-OPT solves a sequential linear programming (SLP) problem and also implements (optional) efficient, “on-the-fly” (without user intervention) first-order, second-moment (FOSM) uncertainty techniques to estimate model-derived constraint uncertainty. Combined with a user-specified risk value, the constraint uncertainty estimates are used to form chance-constraints for the SLP solution process, so that any optimal solution includes contributions from model input and observation uncertainty. In this way, a “single answer” that includes uncertainty is yielded from the modeling analysis. PESTPP-OPT uses the familiar PEST/PEST++ model interface protocols, which makes it widely applicable to many modeling analyses. The use of PESTPP-OPT is demonstrated with a synthetic, integrated surface-water/groundwater model. The function and implications of chance constraints for this synthetic model are discussed.

Use of multi-node wells in the Groundwater-Management Process of MODFLOW-2005 (GWM-2005)

Many groundwater wells are open to multiple aquifers or to multiple intervals within a single aquifer. These types of wells can be represented in numerical simulations of groundwater flow by use of the Multi-Node Well (MNW) Packages developed for the U.S. Geological Survey’s MODFLOW model. However, previous versions of the Groundwater-Management (GWM) Process for MODFLOW did not allow the use of multi-node wells in groundwater-management formulations. This report describes modifications to the MODFLOW–2005 version of the GWM Process (GWM–2005) to provide for such use with the MNW2 Package. Multi-node wells can be incorporated into a management formulation as flow-rate decision variables for which optimal withdrawal or injection rates will be determined as part of the GWM–2005 solution process. In addition, the heads within multi-node wells can be used as head-type state variables, and, in that capacity, be included in the objective function or constraint set of a management formulation. Simple head bounds also can be defined to constrain water levels at multi-node wells. The report provides instructions for including multi-node wells in the GWM–2005 data-input files and a sample problem that demonstrates use of multi-node wells in a typical groundwater-management problem.

WTAQ - A computer program for aquifer-test analysis of confined and unconfined aquifers

Computer program WTAQ was developed to implement a Laplace-transform analytical solution for axial-symmetric flow to a partially penetrating, finite-diameter well in a homogeneous and anisotropic unconfined (water-table) aquifer. The solution accounts for well-bore storage and skin effects at the pumped well, delayed response at an observation well, and delayed or instantaneous drainage from the unsaturated zone. For the particular case of zero drainage from the unsaturated zone, the solution simplifies to that of axial-symmetric flow in a confined aquifer. WTAQ calculates theoretical time-drawdown curves for the pumped well and observation wells and piezometers. The theoretical curves are used with measured time-drawdown data to estimate hydraulic parameters of confined or unconfined aquifers by graphical type-curve methods or by automatic parameter-estimation methods. Parameters that can be estimated are horizontal and vertical hydraulic conductivity, specific storage, and specific yield. A sample application illustrates use of WTAQ for estimating hydraulic parameters of a hypothetical, unconfined aquifer by type-curve methods.