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Documentation of a computer program to simulate aquifer-system compaction using the modular finite-difference ground-water flow model

Removal of ground water by pumping from aquifers may result in compaction of compressible fine-grained beds that are within or adjacent to the aquifers. Compaction of the sediments and resulting land subsidence may be permanent if the head declines result in vertical stresses beyond the previous maximum stress. The process of permanent compaction is not routinely included in simulations of ground-water flow. To simulate storage changes from both elastic and inelastic compaction, a computer program was written for use with the U.S. Geological Survey modular finite-difference ground- water flow model. The new program, the Interbed-Storage Package, is designed to be incorporated into this model. In the Interbed-Storage Package, elastic compaction or expansion is assumed to be proportional to change in head. The constant of proportionality is the product of the skeletal component of elastic specific storage and the thickness of the sediments. Similarly, inelastic compaction is assumed to be proportional to decline in head. The constant of proportionality is the product of the skeletal component of inelastic specific storage and the thickness of the sediments. Storage changes are incorporated into the ground-water flow model by adding an additional term to the right-hand side of the flow equation. Within a model time step, the package appropriately apportions storage changes between elastic and inelastic components on the basis of the relation of simulated head to the previous minimum (preconsolidation) head. Two tests were performed to verify that the package works correctly. The first test compared model-calculated storage and compaction changes to hand-calculated values for a three-dimensional simulation. Model and hand-calculated values were essentially equal. The second test was performed to compare the results of the Interbed-Storage Package with results of the one-dimensional Helm compaction model. This test problem simulated compaction in doubly draining confining beds stressed by head changes in adjacent aquifers. The Interbed-Storage Package and the Helm model computed essentially equal values of compaction. Documentation of the Interbed-Storage Package includes data input instructions, flow charts, narratives, and listings for each of the five modules included in the package. The documentation also includes an appendix describing input instructions and a listing of a computer program for time-variant specified-head boundaries. That package was developed to reduce the amount of data input and output associated with one of the Interbed-Storage Package test problems.

Techniques of Water-Resources Investigations↗

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

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A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

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A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 3: Design philosophy and programming details

A MODular Finite-Element, digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water-flow. The modular structure of MODFE places the computationally independent tasks that are performed routinely by digital-computer programs simulating ground-water flow into separate subroutines, which are executed from the main program by control statements. Each subroutine consists of complete sets of computations, or modules, which are identified by comment statements, and can be modified by the user without affecting unrelated computations elsewhere in the program. Simulation capabilities can be added or modified by either adding or modifying subroutines that perform specific computational tasks, and the modular-program structure allows the user to create versions of MODFE that contain only the simulation capabilities that pertain to the ground-water problem of interest. MODFE is written in a Fortran programming language that makes it virtually device independent and compatible with desk-top personal computers and large mainframes. MODFE uses computer storage and execution time efficiently by taking advantage of symmetry and sparseness within the coefficient matrices of the finite-element equations. Parts of the matrix coefficients are computed and stored as single-subscripted variables, which are assembled into a complete coefficient just prior to solution. Computer storage is reused during simulation to decrease storage requirements. Descriptions of subroutines that execute the computational steps of the modular-program structure are given in tables that cross reference the subroutines with particular versions of MODFE. Programming details of linear and nonlinear hydrologic terms are provided. Structure diagrams for the main programs show the order in which subroutines are executed for each version and illustrate some of the linear and nonlinear versions of MODFE that are possible. Computational aspects of changing stresses and boundary conditions with time and of mass-balance and error terms are given for each hydrologic feature. Program variables are listed and defined according to their occurrence in the main programs and in subroutines. Listings of the main programs and subroutines are given.

Techniques of Water-Resources Investigations↗

A coupled surface-water and ground-water flow model (MODBRANCH) for simulation of stream-aquifer interaction

Ground-water and surface-water flow models traditionally have been developed separately, with interaction between subsurface flow and streamflow either not simulated at all or accounted for by simple formulations. In areas with dynamic and hydraulically well-connected ground-water and surface-water systems, stream-aquifer interaction should be simulated using deterministic responses of both systems coupled at the stream-aquifer interface. Accordingly, a new coupled ground-water and surface-water model was developed by combining the U.S. Geological Survey models MODFLOW and BRANCH; the interfacing code is referred to as MODBRANCH. MODFLOW is the widely used modular three-dimensional, finite-difference ground-water model, and BRANCH is a one-dimensional numerical model commonly used to simulate unsteady flow in open- channel networks. MODFLOW was originally written with the River package, which calculates leakage between the aquifer and stream, assuming that the stream's stage remains constant during one model stress period. A simple streamflow routing model has been added to MODFLOW, but is limited to steady flow in rectangular, prismatic channels. To overcome these limitations, the BRANCH model, which simulates unsteady, nonuniform flow by solving the St. Venant equations, was restructured and incorporated into MODFLOW. Terms that describe leakage between stream and aquifer as a function of streambed conductance and differences in aquifer and stream stage were added to the continuity equation in BRANCH. Thus, leakage between the aquifer and stream can be calculated separately in each model, or leakages calculated in BRANCH can be used in MODFLOW. Total mass in the coupled models is accounted for and conserved. The BRANCH model calculates new stream stages for each time interval in a transient simulation based on upstream boundary conditions, stream properties, and initial estimates of aquifer heads. Next, aquifer heads are calculated in MODFLOW based on stream stages calculated by BRANCH, aquifer properties, and stresses. This process is repeated until convergence criteria are met for head and stage. Because time steps used in ground-water modeling can be much longer than time intervals used in surface- water simulations, provision has been made for handling multiple BRANCH time intervals within one MODFLOW time step. An option was also added to BRANCH to allow the simulation of channel drying and rewetting. Testing of the coupled model was verified by using data from previous studies; by comparing results with output from a simpler, four-point implicit, open-channel flow model linked with MODFLOW; and by comparison to field studies of L-31N canal in southern Florida.

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User's guide to SEAWAT; a computer program for simulation of three-dimensional variable-density ground-water flow

This report documents a computer program (SEAWAT) that simulates variable-density, transient, ground-water flow in three dimensions. The source code for SEAWAT was developed by combining MODFLOW and MT3DMS into a single program that solves the coupled flow and solute-transport equations. The SEAWAT code follows a modular structure, and thus, new capabilities can be added with only minor modifications to the main program. SEAWAT reads and writes standard MODFLOW and MT3DMS data sets, although some extra input may be required for some SEAWAT simulations. This means that many of the existing pre- and post-processors can be used to create input data sets and analyze simulation results. Users familiar with MODFLOW and MT3DMS should have little difficulty applying SEAWAT to problems of variable-density ground-water flow.

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Finite difference model for aquifer simulation in two dimensions with results of numerical experiments

The model will simulate ground-water flow in an artesian aquifer, a water-table aquifer, or a combined artesian and water-table aquifer. The aquifer may be heterogeneous and anisotropic and have irregular boundaries. The source term in the flow equation may include well discharge, constant recharge, leakage from confining beds in which the effects of storage are considered, and evapotranspiration as a linear function of depth to water. The theoretical development includes presentation of the appropriate flow equations and derivation of the finite-difference approximations (written for a variable grid). The documentation emphasizes the numerical techniques that can be used for solving the simultaneous equations and describes the results of numerical experiments using these techniques. Of the three numerical techniques available in the model, the strongly implicit procedure, in general, requires less computer time and has fewer numerical difficulties than do the iterative alternating direction implicit procedure and line successive overrelaxation (which includes a two-dimensional correction procedure to accelerate convergence). The documentation includes a flow chart, program listing, an example simulation, and sections on designing an aquifer model and requirements for data input. It illustrates how model results can be presented on the line printer and pen plotters with a program that utilizes the graphical display software available from the Geological Survey Computer Center Division. In addition the model includes options for reading input data from a disk and writing intermediate results on a disk.

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Computer model of two-dimensional solute transport and dispersion in ground water

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

Techniques of Water-Resources Investigations↗

Installation and service manual for the U.S. Geological Survey manometers

The purpose of this manual is to describe the installation, operation, and maintenance of the bubble-gage manometers currently (1982) used by the U.S. Geological Survey. Other applications of these devices, such as the long manometer and differential manometer, are discussed, and accessories available for them are described. The bubble gage (water-stage manometer with gas-purge system) described in the Installation and Service Manual, October 1962, has been extensively modified and developed into the STACOM (stabilized and temperature compensated) device. This chapter is the manual for the STACOM unit and an update of the manual for the screw-type bubble gage. A parts list is included for both units.

Techniques of Water-Resources Investigations↗

Calibration and maintenance of vertical-axis type current meters

The purpose of this chapter is to describe the procedures used in the manufacture and calibration of current meters and to present in detail information pertinent to their proper maintenance and repair. Recent intensive studies on the calibration of current meters and the effects of wear of the component parts on the performance of the meters have led to the adoption of new procedures for the manufacture, calibration, maintenance, and repair of meters. This chapter, therefore, updates the provisional manual 'Care and Rating of Current Meters' (1957) by including these new procedures.

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Preparations for water sampling

The National Field Manual for the Collection of Water-Quality Data (National Field Manual) provides guidelines and standard procedures for U.S. Geological Survey (USGS) personnel who collect data used to assess the quality of the Nation’s surface-water and ground-water resources. This chapter addresses field-trip preparations, including selection of sample-collection sites for studies of surface-water quality, site reconnaissance and well selection for studies of groundwater quality, and the establishment of electronic files and field files and folders for a sampling site. Each chapter of the National Field Manual is published separately and revised periodically. Newly published and revised chapters are posted on the World Wide Web on the USGS page "National Field Manual for the Collection of Water-Quality Data." The URL for this page is http://pubs.water.usgs.gov/twri9A/ (accessed Jan. 31, 2005).

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Chapter A2. Selection of equipment for water sampling

The National Field Manual for the Collection of Water-Quality Data (National Field Manual) describes protocols and provides guidelines for U.S. Geological Survey (USGS) personnel who collect data used to assess the quality of the Nation's surface-water and ground-water resources. This chapter of the manual addresses the selection of equipment commonly used by USGS personnel to collect and process water-quality samples. Each chapter of the National Field Manual is published separately and revised periodically. Newly published and revised chapters will be announced on the USGS Home Page on the World Wide Web under 'New Publications of the U.S. Geological Survey.'

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Chapter A3. Cleaning of equipment for water sampling

The National Field Manual for the Collection of Water-Quality Data (National Field Manual) describes protocols and provides guidelines for U.S. Geological Survey (USGS) personnel who collect data used to assess the quality of the Nation's surface-water and ground-water resources. Chapter A3 describes procedures for cleaning the equipment used to collect and process samples of surface water and ground water and procedures for assessing the efficacy of the equipment-cleaning process. This chapter is designed for use with the other chapters of this field manual. Each chapter of the National Field Manual is published separately and revised periodically. Newly published and revised chapters will be announced on the USGS Home Page on the World Wide Web under 'New Publications of the U.S. Geological Survey.'

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Chapter A4. Collection of water samples

The National Field Manual for the Collection of Water-Quality Data (National Field Manual) describes protocols and provides guidelines for U.S. Geological Survey (USGS) personnel who collect data that are used to assess the quality of the Nation's surface-water and ground-water resources. This chapter addresses preparations and appropriate methods for the collection of surface-water, groundwater, and associated quality-control samples. Among the topics covered are considerations and procedures to prevent sample contamination; establishing site files; instructions for collecting depth-integrated isokinetic and nonisokinetic samples at flowing- and still-water sites; and guidelines for collecting formation water from wells having various types of construction and hydraulic and aquifer characteristics. Each chapter of the National Field Manual is published separately and revised periodically. Newly published and revised chapters will be announced on the USGS Home Page on the World Wide Web under 'New Publications of the U.S. Geological Survey.'

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Chapter A5. Processing of water samples

The National Field Manual for the Collection of Water-Quality Data (National Field Manual) describes protocols and provides guidelines for U.S. Geological Survey (USGS) personnel who collect data used to assess the quality of the Nation's surface-water and ground-water resources. This chapter addresses methods to be used in processing water samples to be analyzed for inorganic and organic chemical substances, including the bottling of composite, pumped, and bailed samples and subsamples; sample filtration; solid-phase extraction for pesticide analyses; sample preservation; and sample handling and shipping. Each chapter of the National Field Manual is published separately and revised periodically. Newly published and revised chapters will be announced on the USGS Home Page on the World Wide Web under 'New Publications of the U.S. Geological Survey.'

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Chapter A5. Section 6.1.F. Wastewater, Pharmaceutical, and Antibiotic Compounds

The USGS differentiates between samples collected for analysis of wastewater compounds and those collected for analysis of pharmaceutical and antibiotic compounds, based on the analytical schedule for the laboratory method. Currently, only the wastewater laboratory method for field-filtered samples (SH1433) is an approved, routine (production) method. (The unfiltered wastewater method LC 8033 also is available but requires a proposal for custom analysis.) At this time, analysis of samples for pharmaceutical and antibiotic compounds is confined to research studies and is available only on a custom basis.

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