Agriculture Reference
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Grisak, 1981a). Later, Fried (1975) defined several scales in terms of the “mean
travel distance” of a tracer or contaminant. These scales are:
•
Local scale
, ranging between 2 and 4 m
•
Global scale 1
, ranging between 4 and 20 m
•
Global scale 2
, ranging between 20 and 100 m
•
Regional scale
, larger than 100 m (usually several kilometers)
Interestingly, some field as well as laboratory studies questioned whether
the “scale effect” exists. For example, Taylor and Howard (1987) concluded
based on their study in a sandy aquifer that a distance-dependent dispersiv-
ity was not observed. Based on column experiments, Khan and Jury (1990)
found that the dispersivity increased with increasing column length for
undisturbed soil columns but was not dependent on length for repacked col-
umns. Based on these studies one may conclude that scale effects may exist
for some systems but not for others.
4.1 Definition of Scale Effects
Based on the above discussion, it is conceivable that the so-called scale effect
has two meanin
g
s: one refers to the dispersivity (α) as a function of mean
travel distance (
x
) of a tracer; the other is a function of distance (
x
) from the
source of a tracer solute. When plotted against a test scale, with scale bein
g
either mean travel distance or distance from a source, α increases with
x
or
x
or both. Specifically, the relation between α and mean travel distance
x
is obtained by fitting solute concentration profiles at different times with
appropriate analytical or numerical solution of the CDE. Conversely, the rela-
tion between α and distance
x
is obtained from column studies by fitting
breakthrough curves sampled at different distances or depths
x
. Therefore, it
appears that the concept of scale effect is not well defined. If a clear definition
of the concept of scale effect is not realized, one expects to encounter misun-
derstanding and misinterpretation of result
s.
For example, one recognizes
that, in a geologic system, if α increases with
x
, then there exists a scale effect
for such a system. Likewise, if α increases with distance
x
from source, we
also recognize that there exists a scale effect. On the other hand, if we only
know that a scale effect exists for a geological formation, we cann
o
t distin-
guish beforehand whether α increases with mean travel distance
x
or with
distance from source
x
. This situation is awkward, and the ambiguous mean-
ing of the scale effects makes it difficult to implement. Suppose that we h
a
ve
sufficient data such that we can examine the relationship between α and
x
as
well as that betw
ee
n α and
x
for the same geologic system. If it happens that
α increases with
x
but not with distance
x
or α increases with distance
x
but
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