Environmental Engineering Reference
In-Depth Information
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velocities of water movement: the tracer-profile
method, the peak-displacement method, and
the mass-balance method. Inherent to all of
these methods are assumptions that water and
tracers move vertically within the unsaturated
zone. Profile and mass-balance methods can
be applied by obtaining tracer concentration-
depth data at a single point in time, but these
methods require information on the rate and
timing at which tracers are introduced at land
surface. Peak-displacement methods do not
require information on tracer inputs, but con-
centration-depth data must be obtained at two
different times.
The tracer-profile method can be used to
analyze tracers that are introduced as a sin-
gle pulse at land surface. Thus, this method is
applicable for the study of most applied tracers
and some historical tracers (such as
3
H and
36
Cl).
Measurements of tracer concentration through-
out a vertical profile of the unsaturated zone at
some point in time after the pulse was intro-
duced are used to determine the penetration
depth of the tracer (zT).
T
). The equivalent depth of
water in the profile between land surface and
z
T
represents the total water flux since tracer
introduction. The idea is to determine the depth
of penetration of the tracer, measure soil-water
content between land surface and zT,
T
, and deter-
mine the drainage rate,
D
, as:
10
20
Diffuse flow
Piston flow
Data
30
40
0
0.2
0.4
0.6
0.8
1
Concentration (mg/L)
Figure 7.3
Hypothetical tracer concentration-depth
profiles in the unsaturated zone after pulse application of a
tracer at land surface followed by infiltration of tracer-free
water: typical field data (×), theoretical profile (solid line)
based on the Richards and advection-dispersion equations,
and piston-flow profile (dashed line).
usually is some scatter in the actual data points
as a result of microscopic variability in veloci-
ties (caused by heterogeneity in soil proper-
ties) and uncertainty in analytical methods for
determining tracer concentrations (
F ig u r e 7. 3
).
The piston-flow assumption provides a simpli-
fied explanation of water and tracer movement;
it states that water moves vertically downward
through the unsaturated zone, pushing exist-
ing water and solute to greater depths in the
soil column with no mixing or variation in
velocity (
F ig u r e 7. 3
). True piston flow probably
never occurs in real hydrologic systems, but the
assumption is inherent in some methods to be
discussed, and the term
piston-like flow
is com-
monly used to represent uniform flow with little
dispersion. In contrast, the term
preferential flow
refers to nonuniform downward movement of
water in which some water moves rapidly along
preferred pathways, such as decayed roots and
fractures, and bypasses much of the matrix.
Multiple peaks in tracer concentration-depth
profiles have been attributed to the presence of
preferential flow paths (Scanlon and Goldsmith,
1997
).
There are three general approaches for using
tracers in the unsaturated zone to estimate
z
T
=
∫
θ
∆
t
(7.1)
D
dz
/
0
where
θ
is volumetric water content, Δ
t
is the
time interval between tracer introduction at
land surface and subsurface sampling, and the
integral represents the mass of water in the
unsaturated zone column above zT.
T
. The pen-
etration depth is usually set equal to either the
depth of peak tracer concentration or the depth
of the center of tracer mass (Walker,
1998
):
∞
=
∫
M
(7. 2)
z
zC z
()()
θ
z dz
/
T
0
∞
=
∫
M
C z
()()
θ
z dz
0
where
C(z
) is tracer concentration in pore water
and
M
is total mass of tracer in the subsurface.
F ig u r e 7.4
describes a hypothetical application
