CEPIS/OPS -Models and computers in ground

This chapter focuses on models that can be expressed in mathematical form and adapted for use in computer codes. The American Society for Testing and Materials (ASTM) defines model and computer code as follows (ASTM,1984):

A model is an assembly of concepts in the form of a mathematical equation that portrays understanding of a natural phenomenon.

A computer code is the assembly of numerical techniques, bookkeeping, and control languages that represents the model from acceptance of inputdata and instruction to delivery of output.

Modeling with computers is a specialized field that requires considerable training and experience. In the last few decades, literally hundreds of computer codes for simulating various aspects of ground-water systems have been developed. Refinements to existing codes and development of new codes proceed at a rapid pace. This chapter provides a basic understanding of modeling and data analysis with computers, including (1) their uses; (2) basic hydrogeologic parameters that define their type and capabilities; (3) classification according to mathematical approach and major types of hydrogeologic parameters simulated; (4) special management considerations in their use; and (5) their limitations.

Uses of Models and Computers

The great advantage of the computer is that large amounts of data can be manipulated quickly, and experimental modifications can be made with minimal effort, so that many possible situations for a given problem can be studied in great detail. The danger is that without proper selection, data collection and input, and quality control procedures, the computer's usefulness can be quickly undermined, bringing to bear the adage "garbage in, garbage out."

Computercodes involving groundwatercan be broadly categorized as (1) predictive, (2) resource optimizing, or (3) manipulative. Predictive codes simulate physical and chemical processes in the subsurface to provide estimates of how far, how fast, and in what directions a contaminant may travel. These are the most widely used codes and are the focus of most of this chapter.

Resource-optimizing codes combine constraining functions (e.g., total pumpage allowed) and optimization routines for objective functions (e.g., optimization of well field operations for minimum cost or minimum drawdown/pumping lift) with predictive codes. The U.S. Forest Service's multiple-objective planning process for management of national forests makes extensive use of resource-optimizing codes (Iverson and Alston, 1986). The availability of such codes for ground-water management is limited and is not a very active area of research and development (van der Heijde and others, 1985).

Manipulative codes primarily process and format data for easier interpretation or to assist in data input into predictive and resource-optimizing codes. A specific computer code may couple one or more of these types of codes. For example, codes that facilitate data entry (preprocessors) and data output (postprocessors) are becoming an increasingly common feature of predictive codes.

Computers can assist government decisions concerning ground-water evaluation/protection in the areas of (1) policy formulation, (2) rule-making, and (3) regulatory action.

A study by the Holcomb Research Institute (1976) of environmental modeling and decision-making in the United States provides a good overview of modeling for policy formulation, although most of the case studies involve surface water and resources other than ground water. The Office of Technology Assessment (1982) more specifically addresses the use of water resource models for policy formulation.

The U.S. EPA's Underground Injection Control Program regulations on restrictions and requirements for Class I wells exemplify the use of modeling to assist in rulemaking (Proposed Rules: 52 Federal Register 3244632476, August 27,1987; Final Rules:53 Federal Register 28118-28157, July 26, 1988). The 10,000-year nomigration standard in 40 CFR 128.20(a)(1) for injected wastes is based, in part, on numerical modeling of contaminant transport in four major hydrogeologic settings by Ward and others (1987). Furthermore, worst-case modeling of typical injection sites by EPA formed the basis for the decision not to require routine modeling of dispersion in no-migration petitions.

Ground-water flow and, possibly, solute transport modeling are required to obtain a permit to inject hazardous wastes into Class I wells. Permitting decisions involving activities that may pose a threat to groundwater quality, such as landfills and surface storage of industrial wastes, commonly require ground-water simulations to demonstrate that no hazard exists. U.S. EPA (1987) provides a good overview of the use of models in managing ground-water protection programs.

Use of modeling and computer codes can be valuable in three phases of site-specific ground-water investigations: (1) site characterizaton, (2) exposure assessment, and (3) remediation assessment.

Site Characterization. Relatively simple models (such as analytic solutions) may be useful at the early stage for roughly defining the possible magnitude of a contaminant problem. Solute transport models that account for dispersion but not retardation may be useful in providing aworst-case analysis of the situation. They may help in defining the size of the area to be studied and in siting of monitoring wells. If more sophisticated computer modeling is planned, the specific code to be used will, to a certain extent, guide site characterization efforts by the aquifer parameters required as inputs to the model. Site characterization, particularly where water-quality samples are tested for possible organic contaminants, can generate large amounts of data. Computers are invaluable in compiling and processing these data.

Exposure Assessment. There is growing use of exposure assessments across EPA's regulatory programs (U.S. EPA, 1987). Inthecaseofground-water contamination, the results of an exposure assessment will often determine whether remediation will be required.

Remediation. Predictive models can be particularly valuable in estimating the possible effectiveness of alternative approaches to remediating ground-water contamination (Boutwell and others, 1985). Table 6-1 summarizes the types of modeling required for various remediation design features.

All modeling involves simplifying assumptions concerning parameters of the physical system that is being simulated. Furthermore, these parameters will influence the type and complexity of the equations that are used to represent the model mathematically. There are six major parameters of ground-water systems that must be considered when developing or selecting a computercode for simulating ground-water flow and six additional parameters for contaminant transport.

Tyne of Aquifer. Confined aquifers of uniformthickness are easier to model than unconfined aquifers because the transmissivity remains constant. The thickness of unconfined aquifers varies with fluctuations in the water table, thus complicating calculations. Similarly, simulation of variable-thickness confined aquifers is complicated by the fact that velocities will generally increase in response to reductions and decrease in response to increases in aquifer thickness.

Matrix Characteristics. Flow in porous media is much easier to model than in rocks with fractures or solution porosity. This is because (1) equations governing laminar flow are simpler than those for turbulent flow, which may occur in fracture; and (2) effective porosity and hydraulic conductivity can be more easily estimated for porous media.

Homogeneity and Isotropy. Homogeneous and isotropic aquifers are easiest to model because their properties do not vary in any direction. If hydraulic properties and concentrations are uniform vertically, and in one of two horizontal dimensions, a one-dimensional simulation is possible. Horizontal variations in properties combined with uniform vertical characteristics can be modeled two-dimensionally. Most aquifers, however, show variation in all directions and, consequently, require three-dimensional simulation, which also necessitates more extensive site characterization data. The spatial uniformity or variability of aquifer parameters such as recharge, hydraulic conductivity, effective porosity, transmissivity, and storativitywill determine the number of dimensions to be modeled.

Phases. Flow of groundwater and contaminated ground water in which the dissolved constituents do not create a plume that differs greatly from the unpolluted aquifer in density orviscosityarefairlyeasytosimulate. Multiple phases, such as water and air in the vadose zone and NAPLs in ground water, are more difficult to simulate.

Flow Conditions. Steady-state flow, where the magnitude and direction of flow velocity are constant with time at any point in the flow field, is much easier to simulate than transient flow. Transient, or unsteady flow, occurs when the flow varies in the unsaturated zone in response to variations in precipitation, and in the saturated zone when the water table fluctuates.

Type of Source. For simulation purposes, sources can be characterized as point, line, area, or volume. A point source enters the ground water at a single point, such as a pipe oufflow or injection well, and can be simulated with either a one-, two-, or three-dimensional model. An example of a line source would be contaminants leaching from the bottom of a trench. An area source enters the ground water through a horizontal or vertical plane. The actual contaminant source may occupy three dimensions outside of the aquifer, but contaminant entry into the aquifer can be represented as a plane for modeling purposes. Leachate from a waste lagoon or an agricultural field are examples of area sources. A volume source occupies three dimensions within an aquifer. A DNAPL that has sunk to the bottom of an aquifer would be a volume source. Line and area sources may be simulated by either two- or three-dimensional models, whereas a volume source would require a three-dimensional model. Figure 6-1 illustrates the type of contaminant plume that results from a landfill in the following cases: (1) area source on top of the aquifer, (2) area source within the aquifer and perpendicular to the direction of flow, (3) vertical line source in the aquifer, and (4) point source on top of the aquifer.

Tyne of Source Release. Release of an instantaneous pulse, or slug, of contaminant is easier to model than a continuous release. A continuous release may be either constant or variable.

Dispersion. Accurate contaminant modeling requires incorporation of transport by dispersion. Unfortunately, the conventional convective-dispersion equation often does not accurately predict field-scale dispersion (U.S. EPA, 1988).

Adsorption. It is easiest to simulate adsorption with a single distribution or partition coefficient. Nonlinear adsorption and temporal and spatial variation in adsorption are more difficult to model.

Degradation. As with adsorption, simulation of degradation is easiest when using a simple first-order degradation coefficient. Second-order degradation coefficients, which result from variations in various parameters, such as pH, substrate concentration, and microbial population, are much more difficult to model. Simulation of radioactive decay is complicated but easierto simulate with precision because decay chains are well known.

DensityNiscosity Effects. If temperature or salinity of the contaminant plume is much different than that of the pristine aquifer, simulations must include the effects of density and viscosity variations.

Ground-water models and codes can be classified in many different ways, including the mathematical approaches used to develop computer codes, as computer prediction codes, and as manipulative codes.

Models and codes are usually described by the number of dimensions simulated and the mathematical approaches used. At the core of any model or computer code are governing equations that represent the system being modeled. Many different approaches to formulating and solving the governing equations are possible. The specific numerical technique embodied in a computercode is called an algorithm. The following discussion compares and contrasts some of the most important choices that must be made in mathematical modeling.

Figure 6-1. Definition of the Source Boundary Condition Under a Leaking Landfill
(numbers 1 to 4 refer to cases 1 to 4) (from van der Heijde and others, 1988)

Deterministic vs. Stochastic Models. A deterministic model presumes that a system or process operates so that a given set of events leads to a uniquely definable outcome. The governing equations define precise causeand-effect or input-response relationships. In contrast, a stochastic model presumes that a system or process operates so that a given set of events leads to an uncertain outcome. Such models calculate the probability, within a desired level of confidence, of a specific value occurring at any point.

Most available models are deterministic. However, the heterogeneity of hydrogeologic environments, particularly the variability of parameters, such as effective porosity and hydraulic conductivity, plays a key role in influencing the reliability of predictive ground-water modeling (Smith, 1987; Freeze and others, 1989). Stochastic approaches to characterizing variability with the use of geostatistical methods, such as kriging, are being used with increasing frequency to characterize soil and hydrogeologic data (Hoeksma and Kitandis, 1985; Warrick and others, 1986). The governing equations for both deterministic and stochastic models can be solved either analytically or numerically.

Analytical vs.Numerical Models. A model's governing equation can be solved either analytically or numerically.
Analytical models use exact closed-form solutions is continuous in space and time. In contrast, numerical models apply approximate solutions to the same equations.

Analytical models provide exact solutions, but employ many simplifying assumptions in order to produce tractable solutions; thus placing a burden on the user to test and justify the underlying assumptions and simplifications (Javendel and others, 1984).

Numerical models are much less burdened by these assumptions and, therefore, are inherently capable of addressing more complicated problems, but they require significantly more date, an their solutions are inexact (numerical approximations). For example, the assumptions of homogeneity and isotropicity are unnecessary because the model can assign point (nodal) values of transmissivity and storativity. Likewise, the capacity to incorporate complex boundary conditions provides greater flexibility. The user, however, faces difficult choices regarding time steps, spatial grid designs, and way to avoid truncation errors and numerical oscillations (Remson and others, 1971; Javendel and others, 1984). Improper choices may result in errors unlikely to occur with analytical approaches (e.g.mass imbalances, incorrect velocity distributions, and grid orientation effects).

Grid Desian. Afundamental requiremeMofthe numerical approach is the creation of a grid that represents the aquifer being simulated (see Figures 6-2 and 6-3). This grid of interconnected nodes, at which process input parameters must be specified, forms the basis for a matrix of equations to be solved. A new grid must be designed for each site-specific simulation based on data collected during site characterization. Good grid design is one of the most critical elements for ensuring accurate computational results.

Figure 6-2 Typical Ground-Water Contamination Scenario. Several Water-Supply
Production wells are located downgradient of a contaminant
source and the Geology is Complex

The grid design is influenced by the choice of numerical solution technique. Numerical solution techniques include (1) finite-difference methods (FD); (2) integral finite-difference methods (IFDM); (3) Galerkin and variational finite element methods (FE); (4) collocation methods; (5) boundary (integral) element methods (BIEM or BEM); (6) particle mass tracking methods, such as the RANDOM WALK (RW) model; and (7) the method of characteristics (MOC) (Huyakorn and Pinder, 1983; Kinzelbach, 1986). Figure 6-4 illustrates grid designs involving FD, FE, collocation, and boundary methods. Finite-difference and finite-element methods are the most frequently used and are discussed further below.

Finite Difference vs. Finite Element. The finite-element method approximates the solution of partial differential equations by usingfinite-difference equivalents, whereas the finite-difference method approximates differential equations by an integral approach. Figure 6-5 illustrates the mathematical and computational differences in the two approaches. Table 6-2 compares the relative advantages and disadvantages of the two methods. In general, finite-difference methods are best suited for relatively simple hydrogeologic settings, whereas finiteelement methods are required where hydrogeology is complex.

Figure 6-3. Possible Contaminant Transport Model Grid Design
for the Situations Shown in Figure 6-2

Terminology for classifying computer codes according to the kind of ground-water system they simulate is not uniformly established. There are so many different ways that such models can be classified (i.e., porous vs. fractured-rock flow, saturated vs. unsaturated flow, mass flow vs. chemical transport, single phase vs. multiphase, isothermal vs. variable temperature) that a systematic classification cannot be developed thatwould not require placement of single codes in multiple categories.

Figure 6-4. Influence of Numerical Solution Technique on Grid Design (from Pinder, 1984)

Figure 6-5. Generalized Model Development by Finite-Difference and Finite-Elment
Methods (from Mercer and Faust, 1981)

Table 6-3 identifies four major categories of codes and 11 major subdivisions, which are discussed below. This classification scheme differs from others (see, for example, Mangold and Tsang, 1987; van der Heijde and others, 1988), by distinguishing among solute transport models that simulate (1) only dispersion, (2) chemical reactions with a simple retardation or degradation factor, and (3) complex chemical reactions.

The literature on ground-water codes often is further confused by conflicting terminology. For example, the term "hydrochemical" has been applied to completely different types of codes. Van der Heidje and others (1988) used the term hydrochemical for codes listed in the geochemical category in Table 6-3, whereas Mangold and Tsang (1987) used the same term to describe coupled geochemical and flow models (chemicalreaction transport codes in Table 6-3).

Porous Media Flow Codes. Modeling of saturated flow in porous media is relatively straightforward; consequently, by far the largest number of codes are available in this category. Van der Heijde and others (1988) summarize 97 such models. These models are not suitable for modeling contaminant transport if dispersion is a significant factor, but they may be required for evaluating hydrodynamic containment of contaminants and pump-and-treat remediation efforts. Modeling variably saturated flow in porous media (most typically soils and unconsolidated geologic material) is more difficult because hydraulic conductivity varies with changes in water content in unsaturated materials. Such codes typically must model processes, such as capillarity, evapotranspiration, diffusion, and plant water uptake. Van der Heijde and others (1988) summarized 29 models in this category.

Solute Transport Codes. The most important types of codes in the study of ground-water contamination simulate the transport of contaminants in porous media. This is the second largest category (73 codes) identified by van der Heidje and others (1988) as being readily available. Solute transport codes fall into three major categories (see Table 6-3 for descriptions): (1) dispersion codes, (2) retardation/degradation codes, and (3) chemical-reaction transport codes.

Geochemical Codes Geochemical codes simulate chemical reactions in ground-water systems without considering transport processes. These fall into three major categories (see Table 6-3): (1) thermodynamic

codes, (2) distribution-of-species codes, and (3) reaction progresscodes. Thermodynamic codes perhaps would be classified more properly as manipulative codes, but are included here because of their special association with geochemical codes. Such codes are especially important for geochemical modeling of deep-well injection where temperatures and pressures are higher than near-surface conditions for which most geochemical codes were developed. Apps (1989) reviews the availability and use of thermodynamic codes

By themselves, geochemical codes can provide qualitative insights into the behavior of contaminants in the subsurface. They also may assist in identifying possible precipitation reactions that might adversely affect the performance of injection wells in pump-and treat remediation efforts. Chemical transport modeling of any sophistication requires coupling geochemical codes with flow codes. Over 50 geochemical codes have been described in the literature (Nordstrom and Ball, 1984), but only 15 are cited by van der Heijde and others (1988) as passing their screening criteria for reliability and usability.

Specialized Codes. This category contains special cases of flow codes and solute transport codes (see Table 63), including (1) fractured rock, (2) heat transport, and (3) multiphase flow. Fractured rock creates special problems in the modeling of contaminant transport for several reasons. First, mathematical representation is more complex due to the possibility of turbulent flow and the need to consider roughness effects. Furthermore, influence flow, such as orientation, length, and degree of connection between individual fractures, is extremely difficult. In spite of these difficulties, much work is being done in this area (Schmelling and Ross, 1989). Van der Heijde and others (1988) identified 27 fractured rock models.

Heat transport models have been developed primarily in connection with enhanced oil-recovery operations (Kayser and Collins, 1986) and programs assessing disposal of radioactive wastes. Van der Heijde and others (1988) summarized 36 codes of this type. Early work in multiphase flow centered in the petroleum industry focusing on oil-water-gas phases. In the last decade, multiphase behavior of nonaqueous phase liquids in near-surface ground-water systems has received increasing attention. However, the number of codes capable of simulating multiphase flow is still limited.

Manipulative codes that may be of value in groundwater investigationsinclude (1) parameter identification codes, (2) data processing codes, and (3) geographic information systems.

Parameter Identification Codes. Parameter identification codes most often are used to estimate the aquifer parameters that determine fluid flow and contaminant transport characteristics. Examples of such codes include annual recharge (Pettyjohn and Henning, 1979; Puri, 1984), coefficients of permeability and storage (Shelton, 1982; Khan, 1986a and 1986b), and dispersivity (Guven and others, 1984; Strecker and Chu, 1986).

Data Processing Codes. Data manipulation codes specifically designed to facilitate ground-water modeling efforts have received little attention until recently. They are becoming increasingly popular, because they simplify data entry (preprocessors) to other kinds of models and facilitate the production of graphic displays (postprocessors) of the data outputs of other models (van der Heijde and Srinivasan,1983; Srinivasan,1984; Moses and Herman, 1986). Other software packages are available for routine and advanced statistics, specialized graphics, and database management needs (Brown, 1986).

Geo-EAS (Geostatistical Environmental Assessment Software) is a collection of interactive software tools for performing two-dimensional geostatistical analyses of spatially distributed data. It includes programs for data file management, data transformations, univariate statistics, variogram analysis, cross validation, kriging, contour mapping, post plots, and line/scatter graphs in a user-friendly format. This package can be obtained from the Arizona Computer Oriented Geological Society (ACOGS), P.O. Box 44247, Tucson, AZ, 85733-4247.

Geographic Information Systems Geographic information systems (GIS) provide data entry, storage, manipulation, analysis, and display capabilities for geographic, environmental, cultural, statistical, and political data in a common spatial framework. EPA's Environmental Monitoring System Laboratory in Las Vegas (EMSL-LV) has been piloting use of GIS technology at hazardous waste sites that fall under RCRA and CERCLA guidance. The American Society for Photogrammetry and Remote Sensing is a primary source of information on GIS.

The effective use of ground-water models is often inhibited by a communication gap between managers who make policy and regulatory decisions and technical personnel who develop and apply the models (van der Heijde and others, 1988). This section focuses on the following management considerations for using models and codes: personnel and communication requirements, cost of hardware and software options, selection criteria, and quality assurance.

The successful use of mathematical models depends on the training and experience of the technical support staff applying the model to a problem, and on the degree of communication between these technical persons and management. Managers should be aware that a fair degree of specialized training and experience are necessary to develop and apply mathematical models, and relatively few technical support staff can be expected currently to have such skills (van der Heijde and others, 1985). Technical personnel need to be familiar with a numberof scientific disciplines, so that they can structure models to faithfully simulate real-world problems.

A broad, multidisciplinary team is mandatory for adequate modeling of complex problems, such as contaminant transport in ground water. No individual can master the numerous disciplines involved in such an effort; however, staff should have a working knowledge of many sciences so that they can address appropriate questions to specialists, and achieve some integration of the various disciplines involved in the project. In practice, ground-water modelers should become involved in continuing education efforts, which managers should be aware that a fair degree of specialized training and experience are necessary to develop and apply mathematical models, and relatively few technical support staff can be expected currently to have such skills (van de Heijde and others, 1985). Technical personnel need to be familiar with a number of scientific disciplines, so that they can structure models to faithfully simulate real-world problems.

A broad, multidisciplinary team is mandatory for adequate modeling of complex problems, such as contaminant transport in ground water. No individual can master the numerous disciplines involved in such an effort; however, staff should have a working knowledge of many sciences so that they can address appropriate questions to specialists, and achieve some integration of the various disciplines involved in the project. In practice, ground-water modelers should become involved in continuing education efforts, which managers should expect and encourage. The benefits of such efforts are likely to be large, and the costs of not engaging in them may be equally large.

Technical staff also must be able to communicate effectively with management. As with statistical analyses, an ill-posed problem yields answers to the wrong questions. Tables 6-3 through 6-5 list some useful questions managers and technical support staff should ask each other to ensure that the solution being developed is appropriate to the problems. Table 6-3 consists of "screening level" questions, Table 6-4 addresses correct conceptualizations, and Table 6-5 contains questions of sociopolitical concern.

The nominal costs of the support staff, computing facilities, and specialized graphics' production equipment associated with numerical modeling efforts can be high. In addition, quality control activities can result in substantial costs, depending on the degree to which a manager must be certain of the model's characteristics and accuracy of output.

As a general rule, costs are greatest for personnel, moderate for hardware, and minimal for software. An optimally outfitted business computer (e.g., VAX 11/ 785 or IBM 3031) costs about $100,000, but it can rapidly pay for itself in terms of dramatically increased speed and computational power. In contrast, a wellcomplemented personal computer (e.g., IBM-PC/AT or DEC Rainbow) may cost $10,000, but the significantly slower speed and limited computational power may incur hidden costs in terms of its inability to perform specific tasks. For example, highly desirable statistical packages like SAS and SPSS are unavailable or available only with reduced capabilities for personal computers. Many of the most sophisticated mathematical models are available in their fully capable form only on business computers.

Figure 6-6 compares typical software costs for different levels of computing power. Obviously, the software for less capable computers is less expensive, but the programs are not equivalent; managers need to seriously consider which level is appropriate. If the modeling decisions will be based on very little data, it may not make sense to insist on the most elegant software and hardware. If the intended use involves substantial amounts of data, however, and sophisticated analyses are desired, it would be unwise to opt for the least expensive combination.

There is an increasing trend away from both ends of the hardware and software spectrum and toward the middle; that is, the use of powerful personal computers is increasing rapidly, whereas the use of small programmable calculators and large business computers alike is declining. In part, this trend stems from significant improvements in the computing power and quality of printed outputs obtainable from personal computers. It also is due to the improved telecommunications capabilities of personal computers, which are now able to emulate the interactive terminals of large business computers so that vast computational power can be accessed and the results retrieved with no more than a phone call. Most importantly forground-water managers, many of the mathematical models and data packages have been "down-sized" from mainframe computers to personal computers; many more are now being written directly for this market. Figure 6-7 provides some idea of the costs of available software and hardware for personal computers.

Technical criteria for selecting ground-water modeling codes have been formulated by U.S. EPA (1988) in the form of a decision tree (Figure 6-8). These technical criteria correspond roughly to the hydrogeologic model parameters discussed earlier. Table 6-6 summarizes information with respect to these technical criteria for 49 analytical and numerical ground-water codes. More detailed information about these codes can be found in U.S. EPA (1988).

Figure 6-6. Average Price per Category for Ground-Water Models from the
International Ground Water Modeling Center

A code might meet all of the above technical criteria and still not be suitable for use due to deficiencies in the code itself. An ongoing program at the International Ground Water Modeling Center evaluates codes using performance standards and acceptance criteria (van der Heijde, 1987). The Center has rated 296 codes in seven major categories using a variety of usability and reliability criteria~(van der Heijde and others, 1988). Favorable ratings for the usability criteria include:

Documentation. Code has an adequate description of user's instructions and example data sets.

Hardware Dependency. Code is designed to function on a variety of hardware configurations.

Figure 6-7. Price Ranges for IBM-PC Ground-Water Models Available from
various sources (from Graves, 1986)

Figure 6-8. Ground-Water Computer Code Selection
Decision Tree (from U.S.EPA, 1988)

The increasing use of modeling and computer codes in regulatory settings where decisions may be contested in court requires careful attention to quality assurance and quality control in both model development and application. The American Society for Testing and Materials (ATSM) defines several important terms that relate to QA/QC procedures for computer code modeling (ASTM, 1984):

Verification involves examination of the numerical technique in the computer code to ascertain that it truly represents the conceptual model and that there are no inherent numerical problems associated with obtaining a solution.

Validation involves comparison of model results with numerical data independently derived from experiments or observations of the environment.

Calibration is a test of a model with known input and output information that is used to adjust or estimate factors for which data are not available.

Sensitivity is the degree to which the model result is affected by changes in a selected input parameter.

Huyakorn and others (1984) identified three major levels of quality control in the development of groundwater models:

1.Verification of the model's mathematics by comparison of its output with known analytical solutions to
specific problems.

2. Validation of the general framework of the model by successful simulation of observed field data.

3. Benchmarking of the model's efficiency in solving problems by comparison with other models.

These levels of quality control address the soundness and utility of the model alone, but do not treat questions of its application to a specific problem. Hence, at least two additional levels of quality control appear justified:

1. Critical review of the problem's conceptualization to ensure that the modeling effort considers all
physical and chemical aspects that may affect the problem.

2. Evaluation of the specifics of the application, e.g., appropriateness of the boundary conditions, grid
design, time steps, etc. Calibration and sensitivity analysis to determine if the model outputs vary
greatly with changes in input parameters are important aspects of this process.

Verification of the mathematical frameworkof a numerical model and of a code for internal consistency is relatively straightforward. Field validation of a numerical model consists of first calibrating the model using one set of historical records (e.g., pumping rates and water levels from a certain year), and then attempting to predict the next set of historical records. In the calibration phase, the aquifercoefficients and other model parameters are adjusted to achieve the best match between model outputs and known data; in the predictive phase, no adjustments are made (excepting actual changes in pumping rates, etc.). Presuming that the aquifer coefficients and other parameters were known with sufficient accuracy, a mismatch means that either the model is not correctly formulated or that it does not treat all of the important phenomena affecting the situation being simulated (e.g., does not allow for leakage between two aquifers when this is actually occurring).

Field validation exercises usually lead to additional data gathering efforts, because existing data forthe calibration procedure commonly are insufficient to provide unique estimates of key parameters. Such efforts may produce a "black box" solution that is so site-specific that the model cannot be readily applied to another site. For this reason, the blind prediction phase is an essential check on the uniqueness of the parameter values used. Field verification is easiest if the model can be calibrated to data sets from controlled research experiments.

Benchmarking routines to compare the efficiency of different models in solving the same problem have only recently become available (Ross and others, 1982; Huyakorn and others, 1984). Van der Heijde and others (1988) discuss, in some detail, procedures fordeveloping QA plans for code development/maintenance and code application.

Mathematical models are useful only within the context of the assumptions and simplifications on which they are based and according to their ability to approximate the field conditions being simulated. Faust and others (1981) rated the predictive capabilities of available models with respect to 10 issues involving quantity and quality of ground water (Table 6-7). A four-tiered classification scheme for models is shown in Table 6-7: (1) geographic scope (site, local, regional); (2) pollutant movement (flow only, transport without reactions, and transport with reactions); (3) type of flow (saturated or unsaturated); and (4)typeofmedia(porousorfractured). The rating scale by Faust and others (1981) in Table 67 also can be viewed as stages of model development:

2 = Models can serve as useful conceptual tools for synthesizing complicated hydrologic and quality
data.

3 = Models can make short-term predictions (a few years) with a moderate level of credibility, given
sufficient data.

4 = Models can make predictions with a high degree of reliability and credibility, given sufficient data.

The most advanced model is only able to simulate available supplies and conjunctive use atthe local level. Contaminant transport modeling is generally at stage 3 for transport without reactions in saturated porous flow at the site and local level. Models at the stage 2 level of development generally include transport without reactions (saturated fractured, unsaturated porous), and transport with reactions (saturated porous) at the site and local level. Models at the earliest stage of development involve transport with reactions in saturated, fractured media.

Advances have been made in all areas of modeling since the ratings in Table 6-7 were made, but the basic relationships are essentially unchanged. This is illustrated in Table 6-8, which shows the percentage of computer codes in seven categories that received favorable usability and reliability ratings by van der eijde and others (1988). The heat transport and geochemical model categories do not have direct counterparts in Table 6-7. The multiphase flow category is closest to the accidental petroleum products quality category in Table 6-8.

Table 6-7. Matrix Summarizing Reliability and Credibility of
Models Used in Ground-Water Resource Evaluation

Flows	issue and subissue areas
Columns	model types and scale of applications; for example, sixth column applies to a site-scale problem in which pollutant movement is described by a transport model without reactions and with saturated flow in fractured media
Application scale
Site	area modeled less than a few square miles
Local	area modeled greater than a few square miles but less tha a few thousand square miles
Regional	area modeled greater than a few thousand square miles
Abbreviations
w/	with
w/o	without
sat	saturated ground-water flow conditions
unsat	unsaturated flow conditions
P	porous media
F	fractured, fissured, or solution cavity media
Entries
4	a useable predictive tool having a high degree of rliabilit and credibility given sufficient data.
3	a reliable conceptual tool capable of short-term (a few years) prediction with a moderate level of credibility given sufficient data.
2	a useful conceptual tool for helping the hydrologist synthesize complicated hydrologic and quality data
1	a model that is still in the research stage
0	no model exists
blank	model type not applicable to issue area

Not surprisingly, the largest number of codes are in the saturated flow category (97), followed by the saturated solute-transport category (73). The more limited availability of models for unsaturated flow, fractured rock, muftiphaseflow, and geochemistry primarily reflects the difficulties in mathematical formulation due to complexity of processes, process interactions, and field heterogeneities.

Table 6-8 also provides an overview of the status of ground-water modeling from a quality assurance perspective. In general, a high percentage of codes have been peer reviewed in terms of the basic theory. The exceptions arefractured-rock (44%) and multiphase flow models (21%). In contrast, relatively few models have been reviewed in terms of actual coding. Only the geochemical model category has more than half its models (60%) meeting this criterion. As was noted earlier, model verification is a relatively straightforward procedure, which is demonstrated in Table 6-8 where high percentages of all categories have been verified. In contrast, very few codes have had any significant amount of field testing. Less than a third of the codes in the saturated flow category have been extensively field tested, and field testing of codes in the other categories ranges from none for fractured rock and geochemical to 21% for variable saturated flow. The percentages in Table 6-8 should be viewed with the following caveats: (1) many codes received an "unknown" rating, which means that the percentages may underestimate the number of codes with actual favorable ratings; and (2) many of the codes have been subjected to limited field testing.

A number of possible pitfalls will doom a ground-water modeling effort to failure (OTA, 1982; van der Heijde and others, 1985):

1. Inadequate conceptualization of the physical system, such as flow in fractured bedrock

Table 6-8. Percentage of computer codes with favorable usability and reliability ratings

References

American Society for Photogrammetry and Remote Sensing (ASPRS), 1989, Fundamental of GIS: a compendium, ASPRS, Falls Church, VA.

American Society for Testing and Materials (ASTM), 1984, Standard practices for evaluating environmental fate models of chemicals: Annual Book of ASTM Standards, E 978-84, ASTM, Philadelphia, PA.

Anderson, M.P., 1979, Using models to simulate the movement of contaminants through groundwater flow systems: CRC Critical Reviews on Environmental Control v. 9, no. 2, pp. 97-156.

Appel, C.A. and J.D. Bredehoeft, 1976, Status of groundwater modeling in the U.S. Geological Survey: U.S. Geological Survey Circular 737.

Apps, J.A.,1989, Current geochemical modelsto predict the fate of hazardous waste in the injection zones of deep disposal wells: in Assessing the Geochemical Fate of Deep-Well-Injected Hazardous Waste: Summaries of Recent Research, Chapter 6, EPA 625/ 6-89/025b.

Bachmat, Y., B. Andrews, D. Holtz, and S. Sebastian, 1978, Utilization of numerical groundwater models for water resource management: EPA 600/8-78/012.

Boutwell, S.H., S.M. Brown, B.R. Roberts, and D.F. Atwood, 1985, Modeling remedial actions at uncontrolled hazardous waste sites: EPA 540/2-85/001.

Brown, J., 1986, 1986 Environmental software review: Pollution Engineering, v. 18, no. 1, pp. 18-28.

Donigan, A.S., Jr. and P.S.C. Rao, 1986, Overview of terrestrial processes and modeling: in Hem and Melancon (eds.) pp. 3-35.

Faust, C.R., L.R. Silka, and J.W. Mercer, 1981, Computer modeling and ground-water protection: Ground Water, v. 19, no. 4, pp. 362-365.

Freeze, R.A., G. DeMarsily, L. Smith, and J. Massmann, 1989, Some uncertainties about uncertainty: ]n Proceedings of the Conference Geostatistical, Sensitivity, and Uncertainty Methods for Ground-Water Flow and Radionuclide Transport Modeling, San Francisco, CA, September 15-17,1987. CON F-870971. Battelle Press, Columbus, OH.

Graves, B., 1986, Ground water software-trimming the confusio: Ground Water Monitoring Review, v. 6, no. 1, pp. 44-53.

Guven, O., F.J. Molz, and J.G. Melville, 1984, An analysis of dispersion in a stratified aquifer: Water Resources Research v. 20, no. 10, pp. 1337-1354.

Hoeksma, R.J. and P.K. Kitandis, 1985, Analysis of the spatial structure of properties of selected aquifers: Water Resources Research, v. 21, no. 4, pp. 563-572.

Holcomb Research Institute, 1976, Environmental modeling and decision-making: Praeger Publishers, New York.

Huyakorn, P.S. and G.F. Pinder, 1983, Computational methods in subsurface flow: Academic Press, New York.

Huyakorn, P.S., A.G. Kretschek, R.W. Broome, J.W. Mercer, and B.H. Lester, 1984, Testing and validation of models for simulating solute transport in ground water: development, evaluation, and comparison of benchmark techniques: GWMI 84-13. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

Iverson, D.C. and R.M. Alston, 1986, The genesis of FORPLAN: A historical and analytical review of forest service planning models: GTR-INT-214. U.S. Forest Service Intermountain Research Station, Ogden, UT.

Javendel, I., C. Doughty, and C.F. Tsang, 1984, Groundwater transport: Handbook of mathematical models: AGU Water Resources Monograph No. 10. American Geophysical Union, Washington, DC.

Kayser, M.B. and A.G. Collins, 1986, Computer simulation models relevant to ground water contamination from FOR or other fluids-State-of-theArt. NIPER-102: National Institute for Petroleum and Energy Research, Bartlesville, OK.

Khan, I.A., 1986a, Inverse problem in ground water: model development: Ground Water v. 24, no. 1, pp. 3238.

Khan, I.A., 1986b, Inverse problem in ground water: model application: Ground Water v. 24, no. 1, pp. 3948.

Kincaid, C.T., J.R. Morrey, and J.E. Rogers, 1984, Geohydrochemical models for solute migration. Volume 1: process description and computer code selection: EPRI EA-3417-1. Electric Power Research Institute, Palo Alto, CA.

Kincaid, C.T. and J. R. Morrey,1984, Geohydrochemical models for solute migration. Volume 2: preliminary evaluation of selected computer codes: EPRI EA3417-2. Electric Power Research Institute, Palo Alto, CA.

Kinzelbach, W., 1986, Groundwater modeling: an introduction with simple programs in BASIC: Elsevier Scientific Publishers, Amsterdam, The Netherlands

Mangold, D.C. and C.-F. Tsang, 1987, Summary of hydrologic and hydrochemical models with potential applicationto deep underground injection performance: LBL-23497. Lawrence Berkeley Laboratory, Berkeley, CA.

Mercer, J.W. and C.R. Faust, 1981, Ground-water modeling: National Water Well Association, Dublin, OH.

Mills, W.B. and others,1985, Waterquality assessment: a screening procedure for Toxic and Conventional Pollutants (Revised 1985): EPA/600/6-85/002a&b.

Morrey, J.R., C.T. Kincaid, and C.J. Hostetler, 1986, Geohydrochemical modelsforsolute migration. Volume 3: evaluation of selected computer codes: EPRI EA3417-3. Electric Power Research Institute, Palo Alto, CA.

Moses, C.O. and J.S. Herman, 1986, Computer notes - WATIN - a computerprogram forgenerating input files for WATEQF: Ground Water, v. 24, no. 1, pp. 83-89.

National Water Well Association/International Ground Water Modeling Center, 1984, Proceedings of conference on practical applications of ground water models: NWWA, Dublin, OH. [44 papers]

National Water Well Association/International Ground Water Modeling Center, 1985, Proceedings of conference on practical applications of ground water models: NWWA, Dublin, OH. [27 papers]

National Water Well Association/International Ground Water Modeling Center, 1987, Proceedings of conference on solving ground Water Problems with Models. NWWA, Dublin, OH. [45+ papers]

National Water Well Association/Intemational Ground Water Modeling Center, 1989, Fourth international conference on solving ground water problems with models. NWWA, Dublin, OH. [44+ papers]

Nordstrom, D.K.and others, (19 total authors), 1979, A comparison of computerized chemical models for equilibrium calculations inaqueous systems: in Chemical Modeling in Aqueous Systems: Speciation, Sorption, Solubility and Kinetics, E.A. Jenne, (ed.), ACS Symp.
Series 93, American Chemical Society, Washington DC, pp. 857-892.

Nordstrom, D.K. and J.W. Ball, 1984, Chemical models, computer programs and metal complexation in natural waters: in Complexation of Trace Metals in Natural Waters, C.J.M. KramerandJ.C. Duinker(eds.), Martinus Nijhoff/Dr. W. Junk Publishers, The Hague, pp. 149 164.

Office of Technology Assessment (OTA), 1982, Use of models for water resources management, planning, and policy. OTA, Washington, DC.

Oster, C.A., 1982, Review of groundwater flow and transport models in the unsaturated zone. NUREG/CR- 2917, PNL-4427. Pacific Northwest Laboratory, Richland, WA.

Pettyjohn, Wayne A. and R.J. Henning, 1979, Preliminary estimate of ground-water recharge rates in Ohio: Water Resources Center, Ohio State Univ., 323p.

Pinder, G.F., 1984, Groundwater contaminant transport modeling. Environ. Sci. Technol. v.18, no.4, pp. 108 A-114A.

Puri, S., 1984, Aquifer studies using flow simulations. Ground Water v. 22, no. 5, pp. 538-543.

Remson, I., G.M. Hornberger, and F.J. Molz, 1971, Numerical methods in subsurface hydrology. John Whey & Sons, New York.

Ross, B., J.W. Mercer, S.D. Thomas, and B.H. Lester, 1982, Benchmark problems for repository siting models. NUREG/CR-3097. U.S. Nuclear Regulatory Commission, Washington, DC.

Schechter, R.S., L.W. Lake, and M.P. Walsh, 1985, Development of environmental attractive leachants. Vol. III. U.S. Bureau of Mines Mining Research Contract Report, Washington, DC.

Schmelling, S.G. and R.R. Ross, 1989, Contaminant transport in fractured media: models fordecision makers. Supertund Ground Water Issue Paper. EPA 540/4-89/ 004.

Shelton, M.L., 1982, Ground-water management in basalts. Ground Water, v. 20, no. 1, pp. 86-93.

Smith, L., 1987, The role of stochastic modeling in the analysis of groundwater problems. Ground Water Modeling Newsletter, v. 6, no. 1.

Sposito, G., 1985, Chemical models of inorganic pollutants in soils. CRC Critical Reviews in Environmental Control,v. 15, no. 1, pp. 1-24.

Srinivasan, P., 1984, PIG - A graphic interactive preprocessor for ground-water models. GWMI 84-15. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

Strecker, E.W. and W. Chu, 1986, Parameter Identification of a Ground-Water Contaminant Transport Model. Ground Water, v. 2, no. 1, pp. 56-62.

U.S. Environmental Protection Agency (EPA), 1987, The use of models in managing ground-water protection programs, EPA 600/8-87/003.

US. Environmental Protection Agency (EPA), 1988, Selection criteria for mathematical models used in exposure assessments: Ground-Water Models, EPA 600/8-88/075.

U.S. Environmental Protection Agency (EPA), 1989, Assessing the geochemical fate of deep-well-injected hazardous waste: A Reference Guide, EPA 625/6-89/ 025a.

van der Heijde, P.K.M., 1984a, Availability and applicability of numerical models for ground water resources management. GWMI 84-14. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

van der Heijde, P.K.M.,1984b, Utilization of models as analytic toolsforgroundwatermanagement. GWM18419. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

van der Heijde, P.K.M., 1985, The role of modeling in development of ground-water protection policies. Ground Water Modeling Newslette, v. 4, no. 2.

van der Heijde, P.K.M., 1987, Performance standards and acceptance criteria in groundwater modeling. Ground Water Modeling Newsletter, v. , no. 2.

vander Heijde, P.K.M. and P. Srinivasan,1983, Aspects of the use of graphic techniques in ground water modeling. GWMI 83-11. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

van der Heijde, P.K.M., Y. Bachmat, J. Bredehoeft, B. Andrews, D. Holtz, and S. Sebastian, 1985, Groundwater management: The use of numerical models. 2nd ed. AGU Water Resources Monograph No. 5, American Geophysical Union, Washington, DC.

van der Heijde, P.K.M., A.I. EI-Kadi, and S.A. Williams, 1988, Groundwater modeling: An overview and status report. International Ground Water Modeling Center, Butler University, Indianapolis, IN.

Walton, W.C., 1984, Practical aspects of groundwater modeling: Analytical and computer models for flow, mass and heat transport, and subsidence. National Water Well Association, Dublin, OH.

Wang, H.F. and M.P. Anderson, 1982, Introduction to groundwater modeling: Finite difference and finite element methods. W.H. Freeman and Company, San Francisco, CA.

Ward, D.S., D.R. Buss, and J.W. Mercer, 1987, A numerical evaluation of class I injection wells for waste confinement performance, Final Report. Prepared for U.S. EPA by GeoTrans, Herndon, VA.

Warrick, A.W., D.E. Myers, and D.R. Nielsen, 1986, Geostatistical methods applied to soil science: jja Methods of Soil Analysis, Part I-Physical and Mineralogical Methods, 2nd ed., A. Klute (ed.), ASA Monograph No. 9, American Society of Agronomy, Madison, WI, pp. 53-82.

Models and computers in ground-water investigations.

Uses of Models and Computers

References