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Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
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5

Mathematical Models and Decision Support

Mathematical models are indispensable tools in ground and surface water hydrology. They provide a basic framework useful in codifying knowledge concerning the fundamental laws describing the flow of water and mass and energy transport. Beyond their use in fundamental studies of hydrologic processes and theory, models assist in decision making in relation to site- or region-specific problems. In such applications, models can reduce the uncertainty in decision making by providing a rational, self-consistent structure for data collection, site characterization, hypothesis testing, quantification of uncertainty, risk assessment, and the evaluation and design of remediation alternatives (National Research Council, 1992).

Through the years, the USGS has undertaken a spectrum of modeling activities, including those that pertain to contaminant transport and multiphase flow in ground and surface waters (Appel and Reilly, 1994). This chapter examines recent USGS activities in modeling related to hazardous materials research and examines opportunities for future work. Three general modeling types considered include: (1) predictive flow and transport models and their applications, (2) decision support models, and (3) optimization/decision support systems. The predictive models include those concerned with the solution of the classical differential equations for single and multiphase flow, as well as mass and energy transport. These models commonly find their most important applications in the elucidation of basic theory and the evaluation of actual problems. Optimization models represent mathematical approaches for the analysis of very complex systems with the specific view of finding the best course of action

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
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from a set of alternatives. They differ from the trial and error approach of conventional models in that they represent a more formal mathematical approach to decision making.

A decision support system can be broadly defined as a collection of data, models, process information, and other expertise that is integrated in a unified way for analysis and evaluation of problems and alternative solutions to these problems. Decision support systems differ from the conventional modeling approaches in that they typically address less well-defined problems, managerial or planning in nature, without established approaches for solution. In addition, they stress flexibility to allow for ongoing changes in the situation or approach of the decision maker (Sprague and Carlson, 1982; Newell et al., 1990).

Because the USGS has been historically active in the development of mathematical models for ground water flow and transport, and because similar activity for surface water quality models has been (at least in recent years) limited to the integration of existing models in decision support systems, the following discussion of predictive models for water quality is largely limited to ground water, whereas the analysis of decision support systems considers both ground water and surface water models.

PREDICTIVE FLOW AND TRANSPORT MODELS

Flow and transport models are now widely utilized and accepted as tools for basic scientific study and management of hazardous materials in surface and ground water environments (Friedman et al., 1984; National Research Council, 1990b). In assessing the state-of-the-art with respect to modeling and opportunities for research, this study refers to and builds on a recent National Research Council assessment of modeling carried out for the U.S. Army (National Research Council, 1992). The development of conventional modeling approaches is cast in the same framework developed earlier, with a pathway of evolution leading from process discovery to model application.

Within the context of this modeling approach, process discovery considers the mathematical formulation of the processes of interest. Process description refers to detailed studies to examine how the process works, the importance of one process relative to another, and the worth

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

of modeling parameters (National Research Council, 1992). The application of models usually involves the use of the model in a predictive mode to site-specific problems of assessment and remediation. The extent to which models can be productively used in practice is mixed. In many cases, such as multicomponent flow involving NAPLs and water or multispecies transport, there are usually insufficient data to routinely apply models in a predictive mode. Models can be used productively for sensitivity analysis to better understand real problems, however. In other areas, such as aquifer analysis, models are used routinely in practice. In terms of overall directions for research, ground water modeling issues with respect to problems of saturated and unsaturated flow in simple porous media therefore do not present the most important challenges. Similarly, hydrologic and hydrodynamic models for the quantity and velocity of surface water flow provide only a portion of the information needed to predict pollutant fate and transport in surface water systems, with effective representation of chemical and biological transformations also required. The difficulties in using more sophisticated models is well known, and it is in these areas where the greatest potential remains for research at the USGS.

Table 5.1 represents the committee's view of progress with respect to some of the most important flow and mass transport processes in ground water. The list of processes is divided into three parts, representing a set of flow processes, a set of mass transport and chemical mass transfer processes, and a set of other, generally more complicated processes. This latter category represent complexities in the manifestation of processes due to fractures and coupling among the flow and transport processes.

Saturated Flow in Porous Media

A previous National Research Council report determined that the state of knowledge with respect to the saturated flow of ground water in porous media is well developed, with the bulk of research activities at the applications end (National Research Council, 1992). This finding is not surprising given that problems of this type have formed the scientific basis of hydrogeology for more than 100 years. The pioneering efforts in the development of numerical approaches for the simulation of complex aqui-

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

Table 5.1. Range of Capabilities in Modeling

State of the Science

Process

Discovery

Description

Application

saturated flow in porous media

   

unsaturated flow in porous media

 
 

multiphase flow in porous media

   

advection/dispersion

 
 

radioactive decay

   

biological processes

   

multiphase interactions

   

coupled flow processes

   

fractured flow/transport

   
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

fer systems began in the USGS with the work of Pinder and Bredehoeft (1968), Pinder and Frind (1972), and Trescott et al. (1976).

Significant efforts have continued within the USGS in the area of aquifer simulation. The most well-known development in this area is MODFLOW (McDonald and Harbaugh, 1988), which is the industry standard code for aquifer analysis. In recent years, USGS efforts have been concerned with improving the efficiency and robustness of MODFLOW (e.g., Hill, 1990), and expanding the codes capabilities through useful extensions such as parameter estimation procedures in MODFLOWP (Hill, 1992), and the capability to treat narrow horizontal barriers.

A related code, directly relevant to the analysis of contamination problems, is MODPATH (Pollock, 1989). This code takes flow information from MODFLOW and computes three-dimensional pathlines. It is used extensively in industry to estimate directions and spreading rates for plumes and for the design of pump-and-treat systems.

The potential for scientific work in this area is on the applied side with prospects for algorithm refinement, improved design interfaces, and the further development of related “packages.” The MODFLOW family of codes in particular represent a significant achievement of the USGS. However, USGS efforts in recent years appear to have lagged behind many of the newest developments from other government agencies and industry. It is believed that the USGS must reassert its leadership role in the enhancement of this code, its distribution, and training in its use. Efforts should focus on ease of use, visualization technologies, and package integration. Additionally, there is a need for better links between data input for model codes and real-world spatial data. For example, the USGS is ideally suited to improve the somewhat crude links between model inputs and GIS systems. Such efforts would be very useful to those working in the area of hazardous waste.

Unsaturated Flow in Porous Media

Unsaturated flow processes refer to the flow of a single fluid (in this case, water) coexisting with a static gas phase. Traditionally, work on this problem has resided in the domain of soil physicists concerned with local scale fluxes of water in the vadose zone.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

Flow in an unsaturated medium is more complicated than saturated flow. Hydraulic conductivity, which is constant for saturated flow, varies as a function of moisture content and ultimately pressure head. In order to model unsaturated flow, information therefore must be provided on the form of soil hydraulic conductivity curves (hydraulic conductivity versus pressure head) or soil-water characteristic curves (soil moisture versus pressure head) (National Research Council, 1990b). Because the resulting equation of flow is generally nonlinear, the possibility of analytical modeling of flow is limited to exponential hydraulic conductivity curves that lead to linearized forms of the flow equation. Numerical solutions to forms of the unsaturated flow problem have existed for a long time (e.g., Freeze, 1969; Freeze, 1971).

There is relatively limited theoretical work underway for simple unsaturated flow problems. Research is now focused on problems involving dual porosity systems that develop due to the presence of fractures or macropores, and the more complex problem of mass transport through porous media. Although this area of modeling research has not received a high priority within the USGS, there has been work in the development of unsaturated flow and transport codes (e.g., Lappala et al., 1987).

Much of the most recent theoretical work in unsaturated flow is being carried out by the national laboratories (e.g., Lawrence Berkeley and Sandia National Laboratories) in relation to the proposed high-level nuclear waste repository project at Yucca Mountain, Nevada. In terms of code development for the assessment of industrial problems of contamination, much of the existing work is being conducted or sponsored by the U.S. Environmental Protection Agency and the U.S. Department of Agriculture.

Multiphase Flow in Porous Media

In this report, multiphase flow is used to refer to the simultaneous flow of water and other liquids or gases. Examples of these problems include the flow of a nonaqueous phase liquid (NAPL) such as gasoline in a medium that is saturated or partially saturated with water, or simply water and gases in the unsaturated zone. Given this report 's emphasis on

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

the USGS hazardous materials initiatives, the discussion will be restricted to NAPLs.

The basic theory of multiphase flow was developed in the petroleum industry. These fundamental concepts were adopted in the 1980s by hydrogeologists concerned with modeling the migration of NAPLs and developing technologies for their remediation. The NAPL problem, however, provided significant challenges because of the range in properties of organic contaminants, and the complex interphase mass transfers due to volatilization or dissolution of soluble compounds.

Several theoretical approaches were listed in National Research Council (1992) as available to model multiphase flow of contaminants. These include: sharp interface approaches, immiscible phase approaches incorporating capillarity, and compositional models that incorporate interphase transfer. Much of the ongoing research in the field is targeting the development of compositional models. However, the U.S EPA is sponsoring the development of simpler sharp interface models for the application to practical problems. The inherent complexity of multiphase models and relatively limited availability of appropriate flow parameters for various materials of interest has unfortunately limited the application of these models. In industry, there is nonetheless a history of modeling experience with immiscible approaches, using codes like SWANFLOW (Faust, 1985; Faust et al., 1989) and ARMOS (Parker et al., 1990). Table 5.1 reflects the need for considerably more work before the modeling technology evolves to a completed state, however.

Significant opportunities remain in the modeling and estimation of field parameters related to multicomponent systems. Continued work can be justified on the basis of fundamental interest in science, and the seriousness of the problem posed by LNAPLs and DNAPLs. Historically, little modeling work of this kind has been undertaken by the USGS. The main emphasis of research in the Toxic Waste Hydrology Program related to multiphase contamination problems has been in the geochemical and microbiological investigations of an oil spill at Bemidji, Minnesota, and a gasoline spill in New Jersey—both influenced by the unique compositional and chemical characteristics of organic contaminants. Given the recommendation of this report that the USGS move into the field aspects of remediation, and the large number of sites where multiphase contamination is present, there is a critical need for more research on

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

multiphase problems and for the development of expertise in modeling to support this work.

Advection and Dispersion

Advection and dispersion together account for the physical transport of mass from one point to another in a ground water system. Although research on aspects of dispersion began in the 1950s, the first quantitative description of advection and dispersion were published by Bear (1972) and USGS scientists (Bredehoeft and Pinder, 1973). Although the mathematical framework for describing dispersive processes has been known for more than two decades, it has been only in the last few years that these processes have been understood with the confidence represented in Table 5.1.

As National Research Council (1992) points out, the main difficulty in this area has been in explaining the complexity of dispersion at various scales. Although theoretical studies of macroscopic dispersion paved the way, it has been the large-scale field experiments at Canadian Forces Base Borden (e.g., Mackay et al., 1986, Sudicky, 1986) and the USGS Cape Cod research site that have provided the most important new insights on field-scale mass transport.

Mass transport models are now used routinely to model advection and dispersive processes. Analytical approaches work very well for simple problems and have formed the basis for practical inverse methods (Domenico and Robbins, 1985; Ala and Domenico, 1992). More complex problems must rely on powerful numerical approaches that are embodied in industry-standard codes like MOC (Konikow and Bredehoeft, 1978).

The number of theoretical studies of advection and dispersion has begun to decrease after decades of research elucidating the key features of these processes. Work continues on the development of sophisticated numerical approaches that overcome limitations with the current generation of codes. It appears, however, that much of this work is being conducted outside of the USGS, with noteworthy efforts at the University of Waterloo, Lawrence Berkeley National Laboratory, and the University of Alabama.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

Work remains to be done in this area, although much of the future emphasis will likely shift to model applications. The USGS could productively work in the area of new modeling technologies through the development of refinements designed to improve the robustness and usability of models.

Radioactive Decay, Biological Processes, and Multiphase Interactions

A variety of chemical, nuclear, and biological processes influence the transport of mass in geological systems. Due to the number and complexity of these processes, the list in Table 5.1 is illustrative rather than comprehensive. As indicated previously (National Research Council, 1992), a few simple processes such as radioactive decay are well known and can be modeled with relatively little uncertainty. Several other transport processes that are represented generally as biological processes and multiphase interactions are generally poorly known, however. Work to describe these latter groups of processes constitutes a major new focus of the hazardous substances programs at the USGS.

Generally speaking, most of the key processes have been “discovered.” Whether the processes involve biotransformation, surface reactions or mineral dissolution/precipitation reactions, there are valid mathematical representations of the processes in terms of several key parameters. Significant gaps in knowledge exist, however, in terms of the complex interactions that may occur among constituents, and with natural geological materials.

The USGS efforts in many of the field-oriented programs are targeted towards understanding diversity and complexity in biological systems, as well as chemical reactions involving organic and inorganic chemical systems. Limited knowledge of biological systems means that the fate of only a few common contaminants under relatively simple geochemical conditions can be predicted with any certainty. Data necessary to model the kinetic character of biological reactions are rudimentary. Although considerable research is needed to fully understand the operation of biological systems, some transport models have attempted to include biological effects. The simplest models represent the biotransformation

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

of organic compounds simply as a first-order kinetic process (Bouwer and McCarty, 1984). Other more mechanistic transport models (e.g., Borden and Bedient, 1986; Molz et al., 1986) incorporate kinetic models of the microbial populations. However, the kinetic (and other necessary) parameters for these formulations are poorly known and there has yet to be a field-scale validation of the approach.

Of all the chemical reactions that can affect contaminant fate, sorption is among the most important. Sorption effectively couples mass in solution to the solid surfaces, and in so doing can retard the rate of contaminant migration relative to that of ground water. Compared to biological processes, the problem of parameterizing such a system is a little less severe for two reasons. First, an extensive base of information on the equilibrium partitioning of hydrophobic organic compounds, appears to work reasonably well in ground water systems (Curtis et al., 1986). The situation is complicated, however, by the fact that desorption reactions often occur at rates different than sorption reactions. Second, it is believed that for engineering decisions, metal sorption can be modeled using site-specific estimates of distribution coefficients. It is generally conceded, however, that the Kd approach to modeling the surface behavior of metals is seriously flawed. Some of the first field oriented attempts to adapt more sophisticated process models (e.g., surface complexation, or cation exchange) are underway at Cape Cod (e.g., Stollenwerk, 1991).

Another type of multiphase process is that involving the redistribution of mass among the solids, other liquids, and gases that water encounters in moving through a ground water system. The simplest models of these processes are based on equilibrium mass law relationships for which relatively complete data bases of equilibrium constants are available. However, if the reactions of interest are best described using a kinetic viewpoint, then there are virtually no existing data to model these processes.

The state-of-practice in the application of transport models that can account for nuclear, chemical, and biological processes has advanced very little in recent years. Most codes used in applications typically work with a small subset of the possible reactions, and avoid coupling among the constituents through the use of first-order kinetic rate laws for biotransformation reactions, and simple equilibrium linear or Freundlich models for

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

sorption. More comprehensive codes have been developed (e.g., Lin and Narasimhan, 1989), but they are rarely used in solving practical problems. Beyond the considerable problem of collecting the necessary data to use the more complex models at a given site, is the more fundamental research need to validate the modeling approach at both laboratory and field scales.

Significant opportunities remain for field-oriented research in the elucidation of processes and the characterization of mass transfer parameters. The existing program in hazardous materials is exceptionally strong in this area and should continue. Progress in the modeling of complex geochemical systems has been much more modest and could be improved to take advantage of the impressive field-scale contributions.

Coupled Flow Processes

The term “coupled flow” is used to describe interdependent flow and transport processes where, for example, the flow of water depends strongly upon the concentration and/or temperature distributions, and the concentration and/or temperature distributions depend upon the flow of water. In even more complex situations, coupling may involve flow, transport, and mechanical contributions. The details of coupled flow processes will not be described in this report; interested readers can refer to a collection of papers on this topic by Tsang (1987).

Progress in the mathematical modeling of these kinds of problems has been mixed. For certain problems, such as the interaction between fresh water and sea water, there has been considerable effort in model development. In general, however, progress in modeling complex coupled processes is relatively limited (see Table 5.1). The most serious modeling effort in the area of coupled flow has been that associated with the proposed high-level nuclear waste repository at Yucca Mountain, Nevada. In particular, the coupled thermal hydrologic models V-TOUGH and NUFT likely will form the technical basis for the license application.

Historically, the USGS has played a role in the development of codes to simulate coupled phenomena. Examples include the work of Kipp (1987) with HST3D and Voss (1984) with SUTRA. In recent years, it appears that little further development work has been undertaken on these

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

codes. In relation to conventional problems of ground water contamination, recent modeling studies are examining the density driven transport of dense hydrocarbon vapors in partially saturated media (Mendoza and Frind, 1990a,b) or unstable mixed flows (Schincariol et al., 1993).

Coupled process modeling is emerging as a fertile area for both theoretical and applied research. Coupled systems represent the new frontier for research in computational hydrogeology. The field has been slow to develop in part because of the high level of sophistication needed to solve systems of partial differential equations, and because of the tremendous computational power required to solve even relatively small problems. Run times of days on state-of-the-art workstations, and many hours on supercomputers are the norm for even quite simple problems. The lack of clearly identified practical problems has also tended to limit development of the field. The emphasis on thermal approaches to contaminant remediation is one area likely to spur new research, however.

Flow and Transport in Fractured Media

Research efforts to model flow and transport in fractured media have been ongoing for several decades and are continuing. The main motivation for this work is the importance of fractured media in relation to contamination problems, and the scientific and computational challenges in the modeling of fractured rock systems. The earliest combined flow and transport models represented fractured systems either as an equivalent porous medium, or as a discrete network of fractures. With the first of these approaches, it is assumed that the behavior of the fractured system is describable in a straightforward manner with porous medium models once an appropriate choice of parameters is made. In the second approach, each fracture is represented discretely in terms of its geometry, mean aperture roughness, and interconnection with other fractures. Codes of this type (e.g., NAPSAC, UK Harwell; FracMan/MAFIC, Golder Associates, 1988) have been developed to handle flow and transport in relatively large and complex fracture networks, and have been applied to assess practical fractured rock problems related to the Stripa Project in Sweden.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

One limitation of the current generation of discrete fracture codes is the inability to handle fracture matrix coupling. Work underway at the University of Waterloo (Sudicky and McLaren, 1992), however, has led to a powerful new modeling approach that incorporates fracture matrix coupling. This work exemplifies the continuing interest in fractured media applied to many different types of process modeling. Fracture flow and transport codes are also being used in DOE sponsored studies on both the Waste Isolation Pilot Plant (WIPP) site in New Mexico and the Yucca Mountain site in Nevada.

The complexity of basic theory and computational burden associated with the discrete modeling approaches has limited progress in research. Considerable potential remains in the study of fractured rock problems, however.

Detailed information on the geometry and hydraulic characteristics of fracture networks is a necessary requirement for the application of sophisticated modeling codes. Not surprisingly, acquiring this kind of detailed information requires careful field measurements. The USGS has taken a valuable step forward in this regard with the initiative at the Mirror Lake Basin in New Hampshire. The new downhole, and cross-hole testing technologies being developed at this site will be of great assistance in the characterization of fractured rock systems.

Issues in Flow and Transport Modeling at the USGS

The leadership role that the USGS has played in the development of modeling methodologies is reflected in the extent to which models like MODFLOW, MODPATH, MOC, and others have been accepted by industry. This role has diminished in recent years, however, as the national laboratories, other government agencies (e.g., U.S. EPA, U.S. Army), universities and private industry have taken the lead role in many areas of the modeling field. In vitally important areas of multicomponent flow and transport, and reactive transport modeling, the USGS has minimal ongoing efforts.

The USGS should reinvigorate its internal modeling capabilities, and add to existing capabilities as practicable. Besides the addition of personnel, there is a critical need for new facilities to support high-speed

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

computation and visualization. Advanced modeling capabilities are a requirement for the detailed, field-oriented research programs now operated as part of the toxic materials program. The design of appropriate experiments, the interpretation of experimental results, and the development of initiatives in remediation all require the integration of modeling. It is not in the interest of the hazardous materials programs to be seen only as an investigator of field-oriented processes.

The emphasis in research in many areas is rapidly shifting away from process studies toward applications involving models. It is important for the USGS to recognize this change in emphasis and diversify activities to some extent toward the modeling areas. This diversification makes sense scientifically and tactically, for it is an imperative to develop new modeling capabilities within the districts as a follow on to the successful Regional Aquifer-System Analysis (RASA) Program.

Mathematical models for flow and transport are most useful for decision support when they can be interfaced with an effective data base management system. The ability to allow flexible data input, storage, retrieval, analysis, and visualization is an important part of advanced modeling systems. One important development in recent years is the ability to interface models with Geographic Information Systems (GIS). An obvious development of this capability would involve codes like MODFLOW and MODPATH. Basin-scale hydrologic models are particularly rich in these kinds of applications, including topographically-based modeling of watershed stream flow with digital terrain data (e.g., Hornberger and Boyer, 1994) and nonpoint source identification, modeling and control (e.g., Sivertum et al., 1988; Vieux, 1991; Tim et al., 1992; Srinivasan and Engel, 1994; Srinivasan and Arnold, 1994; Yoon and Padmanabhan, 1994).

DECISION SUPPORT SYSTEMS

In most current applications and usage, the concept of a decision support system is associated with computer-based tools and software packages used in support of decision making. However, decision support in a more general sense involves the unified application of information, expertise and experts from several related fields (such as hydrology,

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

geology, geochemistry, statistics, and database management) for problem solution. To a growing extent, these are the types of environmental problems faced by the USGS and its cooperators, where a range of hydrologic, chemical, biochemical, and economic factors must be integrated in a consistent, but often unique manner, in different problem applications.

A decision support system for an environmental problem can serve as a platform for integrating existing scientific knowledge and data sources on chemical transport, transformation, and exposure processes in the natural environment, and allow this information to be used to address critical decisions and policy concerns. It also can aid in the ability to characterize and assess current water quality problems, predict the effect of alternative management strategies, and guide in the selection and implementation of these management strategies. For example, in watershed-scale assessments, a decision support system would allow users to:

  1. input site or watershed data on hydrogeologic characteristics, meteorology, water flow, contaminant sources, and water quality directly or through remote data collection systems;

  2. access, manipulate, and utilize data files, including those from Geographic Information Systems (GIS), for visualization and input into predictive models;

  3. call and test alternative models for chemical transport and transformation for the site or watershed;

  4. allow assessments of the reliability and uncertainty of model predictions;

  5. use the models to examine alternative management options and aid in the selection of optimal strategies;

  6. identify data needs and the value of information to improve models and associated decisions;

  7. track ongoing implementation and monitoring of the management strategy; and

  8. encourage education and participation in the decision process by a wide range of user groups.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

Although this or a similar list of objectives can provide a target for much of the current research and development in decision support systems, available systems to date have only been able to provide some of these capabilities. Development efforts by the USGS should focus most appropriately on a subset of these capabilities. For example, automated data collection, input to GIS data base management systems and utilization for site characterization and assessment fit naturally with the historic mission of the USGS for resource description. The tracking of implementation of management strategies is heavily weighted towards the application end of resource management, and may thus involve more significant efforts by agencies such the EPA, DOD, or DOE. Even so, at the discovery end, when new decision support system technologies are developed, these eventual applications must be anticipated.

Existing and Potential USGS Initiatives

The USGS currently has underway a number of projects to support the development of decision support systems for evaluating surface water flow and quality. The center-piece of the USGS effort is the Modular Modeling System (MMS) of Leavesley et al. (1992, 1994, 1995), developed as part of the USGS initiative on Watershed Modeling Systems. The MMS is an integrated system of computer software developed to support the development, testing, and evaluation of hydrologic and ecosystem impact models for watersheds. It includes a GIS interface for input and management of the watershed data needed for hydrologic and water quality models, libraries for the selection of component models, capabilities for parameter estimation, visualization and statistical analysis of model results, and optimization for determination of management strategies. MMS allows researchers from a variety of disciplines to work cooperatively in the development, testing and application of linked modules in an integrated evaluation framework for multidisciplinary problems. Additional development work for decision support systems addressing surface water problems has occurred in selected projects supported by the state water resources institute programs (e.g., Cheng et al., 1993).

In ground water applications, the enormous quantity of site characterization data at many sites requires that predictive models be interfaced

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

with effective data base management systems. Decision support systems for ground water fate and transport evaluations have been developed, notably the OASIS system of Newell et al. (1990). The USGS has supported similar efforts through the state water resources institute programs (e.g., Peralta et al., 1992), and significant work has been done by private software firms to enhance the front- and back-end capabilities of the USGS MODFLOW program for more efficient input, output, and parameter estimation. In addition, advanced database management and visualization capabilities have been incorporated into a number of USGS ground water modeling studies. However, a complete and unified USGS effort for ground water assessment, comparable to that of the MMS program, is not in place.

In the future, the power of decision support systems to allow analysts and decision makers to synthesize complex data and model problems and visualize the impact of alternative management strategies will grow with the availability of new technologies utilizing 3-D color graphics and perhaps even virtual reality, where a decision maker could travel along with an “insiders view” of a proposed remediation option. For certain components of a predictive model, in which traditional approaches to simulation and data interpretation cannot fully capture important factors and relationships, approaches based on artificial intelligence and expert systems may be appropriate. Applications in ground water science include site characterization, interpretation of geophysical logs, and model selection and calibration (National Research Council, 1990b). Because these advanced computer technologies are evolving rapidly, the USGS should ensure that the scientific information produced by the Survey can be utilized along with these tools.

OPTIMIZATION AND DECISION ANALYSIS

Predictive models allow decision makers to examine the possible impact of alternative management strategies in a “what if?” manner. Often, however, the suite of alternatives is too large or complex to effectively explore in an ad hoc manner in search of a “best” (or simply “good”) strategy. In this case, more formal methods for strategy selection

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

are needed as part of the decision support package. These methods generally fall into the category of optimization or decision analysis tools.

Optimization methods have been widely applied to both surface water and ground water problems. Applications have evolved from simple linear, single criteria, deterministic formulations that consider only water quantity, to nonlinear, multicriteria formulations that consider uncertainty and address problems of both water quantity and quality (Hipel, 1992). Numerous formulations have recently been developed to address the design of ground water remediation, focusing on the optimal placement, timing, and flow rates of pump-and-treat capture wells (e.g., Gorelick et al., 1984; Wagner and Gorelick, 1987; Chang et al., 1992; Wang and Ahlfeld, 1994). Optimization is also an important tool for decision support, and research by the USGS has contributed significantly to its advancement. Optimization packages for both parameter estimation and management strategy selection are included as part of the MMS for watershed evaluation, and similar tools can now be interfaced with MODFLOW. These efforts are extremely valuable and should continue. Such an initiative also would be of tremendous industrial and regulatory interest.

A second approach to the selection of management strategies, the technique of decision analysis, is similar in many respects to optimization, but emphasizes different aspects of the decision problem. In decision analysis, the emphasis is on the role of uncertainty in affecting the optimal decision, and the role that information can play in reducing this uncertainty. The methods of decision analysis have recently been applied to structure models, data collection, and management decisions for ground water (e.g., Marin et al., 1989; Reichard and Evans, 1989; James and Freeze, 1993), and sediment remediation (Dakins et al., 1994). These methods allow iterative evaluation of ongoing data collection programs in concert with decisions on contaminant control and remediation. They are thus well suited for packages that integrate data-base management, modeling, characterization of uncertainty, and visualization of water flow and water quality problems.

An important limitation in the application of optimization and decision analysis methods to the management of hazardous materials in the environment is the inherent time lag in incorporation of state-of-the-art process knowledge and models. The critical geophysical, chemical, and

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
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biological processes discussed earlier in this chapter are only now being incorporated into contaminant transport models. A further lag occurs in the incorporation of these models into optimization or decision analysis evaluations. For example, virtually all of the optimization and decision analysis applications to ground water remediation cited earlier were for “pump-and-treat” applications assuming dissolved phase contaminant transport with simple adsorption/reaction processes. In this case, the principal source of uncertainty is assumed to evolve from the stochastic character of the subsurface hydraulic conductivity. Although this focus has allowed impressive scientific advancement and methods development, extension of these methods to consider other important processes—such as multiphase flow and microbially- and surface-mediated reactions, and the significant uncertainty present in these processes —is needed to address the many sites where the traditional model and pump-and-treat approaches are inadequate (National Research Council, 1994b). To help speed the transition from research to applied decision models, decision support systems should be designed in a flexible, modular manner, allowing easy substitution and testing of alternative model formulations (as is the design for the MMS). Advances in computing technology, which promote such a flexible, tool-box approach, can thus go hand-in-hand with advances in fundamental process knowledge in promoting more effective and useful decision support systems.

An important recent trend in the management of hazardous materials is the desire to include a broader range of participants in the decision making process. Greater stakeholder involvement in problem formulation and evaluation, and decision making is sought for the cleanup and management of contamination on both private and public lands. Methods for considering evaluation by multiple stakeholders have evolved in recent years, including techniques that help facilitate negotiation and conflict resolution (e.g., Ridgley and Rijsberman, 1992; Thiessen and Loucks, 1992). These features can help enhance a decision support system and allow it to be used as a focal point for evaluation in a group decision context.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

DECISION SUPPORT IN THE USGS HAZARDOUS MATERIALS SCIENCE PROGRAM

To help delineate the near-term potential for decision support systems to enhance the hazardous materials science research program of the USGS, a brief review of the types of decisions supported in this program is provided. In particular, the range of decision support exhibited in the USGS Federal-State Cooperative and DOD contamination programs, and whether and how research from the Core Hydrologic Research and Toxic Substances Hydrology programs could better interact with these through the aid of decision support systems, are considered.

The Core Hydrologic Research program and the Toxic Substances Hydrology program provide the long-term research for theoretical process understanding and the development of general methods and tools. Decision support systems fall within the general domain of such tools; system development efforts thus occur within these more basic research programs. However, the motivation for developing these tools is based, in part, on their potential applications in the Federal-State Cooperative and DOD contamination programs.

The Federal-State Cooperative program has encompassed approximately 2,000 projects since it was formally recognized in 1928. Both surface and ground water projects are included, with a somewhat greater portion of the current activity involving ground water problems. Both water flow and quality problems are addressed, though the latter have been more greatly emphasized in recent years. Models of one type or another are used in approximately half of these investigations. Models are used to a greater extent in ground water studies; studies of surface waters and non-point source pollution are more often descriptive in nature.

The DOD contamination hydrology program focuses on specific water and soil quality problems at DOD sites. In most cases, these problems involve subsurface soil and ground water contamination, often with the need to consider geochemical processes for metals and organic complexes. The studies are often conducted as part of ongoing remedial investigations, aimed at determining whether the proposed remedy is consistent with the hydrogeologic conditions at the site. Such sites thus provide the need for ongoing data collection for the purpose of tracking remediation

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×

progress, effectiveness, and compliance; while also providing the opportunity for post-audit confirmation studies of predictive models. This type of ongoing evaluation can be greatly served by decision support systems with integrated data base and modeling capabilities. To address the evolving needs for advanced process representation, these systems will require flexible configurations to allow new models and data configurations to be imported as the need arises.

Decision support systems with data base and modeling capabilities can play a direct and important role in expediting the implementation and interpretation of surface water and ground water studies in both the Federal-State Cooperative and DOD contamination programs. The capability to accomplish this for surface water evaluation is now in sight, through the work of the USGS initiative on Watershed Modeling Systems and the Modular Modeling System. Similar efforts are underway to enhance the capabilities of USGS ground water models, although a single, unified effort similar to that of the MMS is not apparent. The committee supports such integrated research, and encourages efforts to incorporate and apply this work in the evaluation studies of the hazardous materials science and technology research program. It is clear that the USGS research programs provide the information and expertise necessary for the solution of many critical water quality problems at the site and regional scale. Development of the next generation of decision support methodologies and platforms will allow these solutions to be identified in a more efficient, insightful, and generalizable manner.

OPPORTUNITIES FOR THE USGS IN MODELING

The field of modeling continues to be a fruitful area for potential research. Given current research directions, several areas in particular should provide significant opportunities within the USGS, including:

  • continued development of the MODFLOW family of codes with particular emphasis on the addition of state-of-the-art capabilities for mass transport, more modern solvers, and graphical interfaces;

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
  • development of robust, stand alone mass transport codes capable of modeling the complexities of reactive chemical transport and the kinetics of microbial processes;

  • modeling and parameterization of field parameters in relation to NAPL-water systems with emphasis on field and laboratory-based studies as well as modeling-related work;

  • validation of contaminant fate and transport models using field experiments;

  • fundamental work in the model investigation of coupled phenomena; and

  • development of new approaches for modeling flow and transport in fractured rock systems.

The area of decision support is a relatively new field that has not been studied extensively. Opportunities for research exist at the USGS in:

  • the linkage of powerful visualization technologies with the design of remedial systems;

  • the creation of decision support “tool-boxes” similar to MMS that would enable users to rapidly create and test decision support systems; and

  • the integration of model and data base capabilities in decision support schemes.

Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 48
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 49
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 50
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 51
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 52
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 53
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 54
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 55
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 56
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 57
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 58
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 59
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 60
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 61
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 62
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 63
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 64
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 65
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 66
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 67
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 68
Suggested Citation:"5 Mathematical Models and Decision Support." National Research Council. 1996. Hazardous Materials in the Hydrologic Environment: The Role of Research by the U.S. Geological Survey. Washington, DC: The National Academies Press. doi: 10.17226/9040.
×
Page 69
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