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OCR for page 171
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
OCR for page 172
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OCR for page 174
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.
OCR for page 175
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
OCR for page 176
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-
OCR for page 177
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.
OCR for page 178
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OCR for page 179
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.
Representative terms from entire chapter:
water quality
