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c Scaling Issues Applicable to Environmental Systems The essential problem with using models to predict the behavior of environmental systems is that the scale of interest for predictions is rarely, if ever, the scale for which information is available to construct and validate the model. As a consequence, projections in time and space must be made often without needed validation at the target scale. The goal of scaling is to capture essential system characteristics at a scale of direct observation and to extrapolate to a different scale. Although all environmental systems present scaling problems, the natural heterogeneity of the subsurface environment requires model predictions of contaminant transport over spatial scales that may range from the "grain" scale of several millimeters to field scales of kilometers; in addition, temporal scales may require accommodating the simulation of events that require hundreds or thousands of years to complete (e.g., the dissolution of minerals). Predictions of contaminant behavior at scales of interest to environmental managers is currently problematic because of a general lack of understanding of both theoretical and applied approaches to scaling environmental phenomena. Figure C.1A-C illustrates some of the scaling issues at the Hanford Site. One scale length of importance at Hanford is the site itself. An example of a problem at this scale is the need to quantify the potential effect that 200 Area contaminants will have on Columbia River water quality. This scale length is shown schematically as bar a in Figure C.1A and C.1 B. The site scale is at the upper limit of length scales in this analysis. Other environmental scales of interest to groundwater modeling include the vertical and horizontal extent of a lithologic unit, c and e, respectively; the vadose zone thickness, d (which is itself a complex hydrologic environment; see Chapter 6~; and the scale of individual minerals and colloids, b. Given these differences, a further complication in scaling is the development of an accurate understanding of the scale length of a portion of the target system that can be considered to be homogeneous with respect to geochemical and hydrologic properties `fl. It is possible to determine the scale length of such representative units, but the scale is dependent on location in the environmental system and the time of system evolution. Scales of observation for experiments, which are used to develop models, rarely conform to the environmental scale of interest to the environmental manager. At one end of the spectrum are observations of system behavior and characteristics at the molecular to grain scale (g, h), 171
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174 Science and Technology for Environmental Cleanup which are essential for understanding fundamental processes and providing confidence that models capture essential processes. Bench- scale experimentation (I) may capture the geochemical or hydrologic properties of meter-scale systems, but such information does not readily scale up to larger systems 00 of 10 meters in size, for example. Part of the problem in scaling geochemical processes is a lack of understanding of the nature of geochemical heterogeneity and the ways in which the distribution of heterogeneity effects processes at different scales. The vadose zone field experiment at Hanford (Ward and Gee, 2000) is a proposal to evaluate in situ properties. Despite its proposed scale (Figure C.1 C: / and k), it is unclear whether the test bed will capture the complexity of the vadose zone sufficiently well that extrapolation to other scales of interest (c-e) will be possible. UPSCALING TRANSPORT BEHAVIOR Because of spatial variability in the subsurface and the time required for of physical and chemical processes to occur in groundwater, it is not possible to use measured transport properties from a few laboratory experiments to model field-scale behaviors accurately. A key parameter in any model of groundwater movement is permeability. Permeability is important because it determines the potential speed of contaminant migration associated with subsurface water movement. Permeability is observed to vary by several orders of magnitude over distances as small as meters in a given geologic unit. Variations of permeability and other transport properties occur over scales of fractions of a meter, making it impractical to completely map out these characteristics at the field scale of interest. Without this detailed mapping, exact predictive modeling is problematic. Stochastic characterization of the spatial variability of transport properties has been found to be an effective way to treat subsurface heterogeneity and to represent transport properties at the field scale. For example, for a nonreactive solute in a saturated aquifer, variations in permeability cause variations in velocity that produce spreading of contaminants relative to the bulk flow. Stochastic analyses describing the variations in velocity are used to derive the mean transport equation that represents the large-scale transport process and the transport parameters, such as macrodispersivity, appearing in the large-scale transport equation.
Scaling Issues The stochastic upscaling approach has been developed extensively over the past 20 years (see Dagan, 1989; Gelhar, 1993; 1997) and has been tested in field experiments demonstrating that field- scale transport properties, such as macrodispersivity, could be predicted independently by carefully designed measurements of the logarithm of permeability covariance. This stochastic upscaling approach has the advantage that it provides a systematic framework through which feasible small-scale laboratory or field measurements of medium properties can be used to predict large-scale transport properties, thereby showing explicitly how additional data will improve the estimated large-scale transport properties. This approach also has the advantage that it can be used to quantify the uncertainty in large-scale predictions by evaluating the concentration variance as a measure of the variation around the mean solution. A disadvantage of the stochastic upscaling approach is the extensive, statistically focused data requirements; standard site characterization efforts typically do not provide the type of data required to implement this approach. Vadose zone transport processes are influenced strongly by natural heterogeneity in the subsurface environment because of the nonlinear nature of unsaturated flow (see Chapter 6~. Permeability in an unsaturated system depends on both the medium and the fluid. Stochastic upscaling treatments have been applied to unsaturated systems and show that layered heterogeneity can strongly enhance horizontal moisture movement under low-moisture conditions (Yeh et al., 1985~. The data requirements for stochastic upscaling in the unsaturated zone are more severe because of the difficulties of measuring unsaturated properties accurately and efficiently in the laboratory. Transport properties such as macrodispersivity are, in principle, predictable via stochastic upscaling (Gelhar, 1993, p. 261; Russo, 1997), but this approach has not been tested under field conditions. Heterogeneity of chemical properties and the relationship to flow properties can have an important influence on large-scale transport properties for reactive contaminants in the vadose zone. Stochastic analyses and numerical simulations show that variations in retardation factors and their relationship to permeability can significantly increase the macrodispersivity of the sorbed contaminant relative to that of the nonsorbing species (Gelhar, 1993, p. 256; Talbott and Gelhar, 1994~. To determine the relationship between chemical and flow properties, sampling programs for describing reactive transport characteristics must be designed carefully to ensure that both chemical and flow properties are determined for individual samples. 175
176 Science and Technology for Environmental Cleanup GEOCHEMICAL HETEROGENEITY AND SYSTEM SCALING A long-standing problem in subsurface transport modeling has been the accurate description of chemical processes regulating contaminant retardation. The development of sorption models explicitly considering physicochemical processes that produce accumulation of ions at interfaces has relied on the analysis of well-characterized monomineralic systems with the often implicit assumption that overall system behavior can be described through a "summation" of component behavior (e.g., Honeyman, 1984~. However, interactive effects confound this approach. Alternatively, it is possible to incorporate surface chemical models using the Generalized Composite Method (Davis et al., 1998) in which the representative geomedia is treated as an undifferentiated whole. Both the explicit consideration of interracial processes in regulating contaminant retardation and the role of permeability distribution in affecting macrodispersivity rely on the development of a means of representing the distribution of heterogeneity. Considerable work has been done on the distribution of permeability in geomedia of different scale lengths and its contribution to solute transport. Lagging far behind, however, is the development of an understanding of the distribution of geochemical parameters (i.e., the heterogeneity field) that regulates the retardation of surface-active contaminants. In either case, the ability to scale up from well-defined systems to scales of environmental interest requires sampling and system characterization campaigns designed specifically to capture the uncertainty in such a manner as to adequately bridge the scales. SCALE ISSUES AND WATERSHEDS As an environmental system, river channels also present important scaling issues, and like the subsurface environment, river channels have boundaries defined in both space and time. In analyzing these dimensional issues with reference to water quality, the primary issue is the importance of length scales, which range from microscopic to watershed scales of hundreds of kilometers. In addition to water quality, channel characteristics, which constrain habitat for aquatic organisms, also present scale issues in both time and space domains. Geomorphologists have developed an effective method of working with temporal scales in channel networks. Schumm and Lichty (1965) proposed a conceptual framework for geomorphological time that classifies temporal dynamics and changing relationships among system variables when temporal scales are traversed. Though the three temporal modes-
Scaling Issues 177 cyclic, graded and steady not have an absolute value, they differ in duration. Cyclic time is long, related to an erosion cycle of uplift and erosion to some level, a time frame associated with landscape change. Graded time is a short period of cyclic time that is associated with graded river profiles that represent periods of channel stability over hundreds to thousands of years. Steady time is short and applies to processes that occur along a river reach in seconds to years. With these definitions of temporal scales, Schumm and Lichty provided a system that relates channel and flow variables in each time mode by considering how independence-dependence relationships among variables change with the perspective of time scale. Independence-dependence is important in any analysis because the independent variable (the cause) will be the controlling factor in an analysis by producing a response in the dependent variable. Following the Schumm and Lichty approach, it is possible to consider spatial and temporal scales in analyzing water quality issues in watersheds that include both chemical water quality and physical conditions that define habitat. At large spatial and temporal scales, the emphasis of analysis will be on source development and contaminant loading. At smaller spatial scales, the emphasis will be on concentration and duration of exposure. Further, spatial and temporal scales define external factors that relate dependent to independent variables and, most importantly, cause and effect. As scales of analysis are reduced, greater numbers of environmental and water quality variables can be considered independent, leading to a better definition of cause and effect, and directing management efforts to specific actions. Frissell et al. (1986) proposed a habitat-centered view of stream systems, a modified version of which is shown in Table C.1. Their view is based on a hierarchical organization of habitat types. In this hierarchical organization, subsystems (stream segments, reaches, pools or riffles, and microhabitats) develop and persist within a specified spatiotemporal scale. In this "systems" view, high-frequency, low-magnitude geomorphic events of the steady time scale predominate in subsystems, while the system as a whole is subject to low-frequency, high-magnitude events of graded or cyclic time scales. A critical issue in the hierarchy, particularly when considering water quality issues, is that the setting within which components, process, and dynamics are defined is provided by the next- higher level in the hierarchy. These "nested" relationships in the hierarchy provide an example of the integration of Schumm and Lichty's time-scale perspective, illustrating the change in dependence relationships at different levels of the hierarchy. Recognition of this change in controlling variables with time-scale perspective is particularly important in the management of riverine ecosystems.
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Scaling Issues REFERENCES Dagan, G. 1989. Flow and Transport in Porous Formations. Berlin: Springer-Verlag. Davis, J.A., J.A Coston, D.B. Kent, and C.C. Fuller. 1998. Application of the surface complexation concept to complex mineral assemblages. Environ. Sci. Technol. 32: 2820-2828. Frissell, C.A., W.J. Liss, C.E. Warren, and M.D. Hurley. 1986. A hierarchical framework for stream habitat classification: viewing streams in a watershed context. Environmental Management, 10: 1 99-214. Gelhar, L.W. 1993. Stochastic Subsurface Hydrology. Englewood Cliffs, N.J.: Prentice Hall. Gelhar, L.W. 1997. Perspectives on field scale application of stochastic subsurface hydrology: in Subsurface Flow and Transport: The Stochastic Approach, G. Dagan and S.P. Neuman, ads., Cambridge University Press/UNESCO. Honeyman, B.D. 1984. Cation and Anion Sorption in Binary Mixtures of Adsorbents: An Investigation of the Concept of Adsorptive Additivity. Ph.D. thesis, Stanford University. Russo, D. 1997. Stochastic analysis of solute transport in partially saturated heterogeneous soils: in Subsurface Flow and Transport: The Stochastic Approach, pp.196-206, G. Dagan and S. P. Neuman, eds., Cambridge University Press/UNESCO. Shcumm, S.A., and R.W. Lichty. 1965. Time, space and causality in geomorphology. American Journal of Science, 263: 1 10-1 19. Talbott, M.E., and L.W Gelhar. 1994. Performance Assessment of a Hypothetical Low-Level Waste Facility: Groundwater Flow and Transport Simulation. Washington, D.C.: U.S. Nuclear Regulatory Commission Report NUREG/CR-6114, Vol. 3. Ward, A.L.. and G.W. Gee. 2000. Vadose Zone Transport Field Study: 179 Detailed Test Plan for Simulated Leak Tests. Richland, Wash.: Pacific Northwest National Laboratory. PNNL-13263. Yeh, T.-C., L.W. Gelhar, and A.L. Gutjahr. 1985. Stochastic analysis of unsaturated flow in heterogeneous soils. 3. Observations and applications. Water Resources Research 21~4~: 465-471.
