Environmental Engineering Reference
In-Depth Information
This approach requires the collection of sam-
ples at two times, but no information on tracer
input is required. The approach is particularly
useful for analyzing a tracer that was acciden-
tally introduced to the environment, such as
through a contaminant spill, and for which
release dates and amounts are unknown.
Inherent to Equation (
7. 3b
) is the assump-
tion that velocity is constant over time. The
displacement method also can be useful in eval-
uating changes in drainage rates due to changes
in land use (Cook
et al
.,
1994
; Stonestrom
et al
.,
2004
; Scanlon
et al
.,
2007
). Following a change
in land use there will be a time period before
new equilibrium conditions are fully estab-
lished. Walker
et al
. (
1991
) proposed an alterna-
tive equation to determine drainage during that
period. This equation was originally developed
to describe displacement of a front of uniform
Cl concentration as a result of removal of native
vegetation in a semiarid region of Australia:
(7. 5)
D
=
PC
/
C
P
uz
where
P
is precipitation rate,
C
P
is average con-
centration in precipitation, and
C
uz
is average
concentration in unsaturated zone pore water.
Equation (
7. 5
) is quite simplistic. Precipitation
is assumed to be the sole source of the tracer.
All precipitation infiltrates the surface; there is
neither runoff nor runon, and the tracer is con-
servative. For a variable tracer source, the equa-
tion for estimating drainage takes on a more
complex form (Heilweil
et al
.,
2006
):
∞
∞
∑
∫
t
(7.6)
D
=
C
()()
z
θ
z dz
/
i
w C
∆
uz
i
Pi
i
=
1
0
where the integral represents the total mass of
tracer in the unsaturated zone, the summation
represents the total mass added to the unsat-
urated zone (again under the assumption that
precipitation is the only source of tracer),
w
i
is
a weighting factor to correct for variations in
annual drainage,
C
Pi
is tracer concentration in
precipitation
i
time increments before sam-
pling, and Δ
t
i
is time increment corresponding
to the periods of application (typically, 1 year for
historical tracers and days for applied tracers).
An obvious drawback to this approach is the
need to know the time history of application.
This method can be used with historical trac-
ers and with tracers applied specifically for tra-
cing water or with those applied as part of some
ongoing operation (e.g. agricultural chemicals,
such as nitrate). Allison (
1987
) recommends use
of Equation (
7.6
) because it is not overly influ-
enced by preferential flow and because it often
requires fewer sampling depths than profile
methods.
Z
Z
Z
C
T
1
r0
ZFP
∫
∫
n
∫
D
=
θ
()
z dz
+
∆
θ
()
z dz
+
∆
θ
()
z dz
/
∆
t
C
(7.4)
b
Z
Z
0
T
0
ZFP
where
z
T
0
is initial depth of the front,
z
T
1
is cur-
rent depth of the front,
z
ZFP
is depth of zero-flux
plane, Δ
θ
is the difference between current and
initial water content,
C
b
is the initial concen-
tration in the front,
C
n
is the concentration of
the new equilibrium front, and Δ
t
is the time
between land-use change and sampling. The
first term on the right side of Equation (
7.4
) is the
integral form of Equation (
7. 3b
). The second term
accounts for the change in water content in the
depth interval between the zero-flux plane and
the initial front, and the third term accounts
for the change in chloride mass within the
root zone. In practice, Equation (
7.4
) is not often
applied, but it is included here for completeness.
The mass-balance method relates the mass
of tracer in the unsaturated zone with the rate
at which the tracer arrives at land surface. As
with the profile method, tracer concentration
and soil-water content depth profiles and tracer
source term information are required. The
method can be used for constant or varying
tracer introduction. For the simplest constant-
source case, we can write:
7.2.1 Tracer sampling: unsaturated zone
Tracer concentrations can be determined
from soil samples collected throughout the
depth interval of interest or by installing
instruments more or less permanently at fixed
depths to allow sampling or analysis of pore
water. Each approach has benefits and limita-
tions. Obtaining soil cores allows data points
to be collected at many different depths and
thus provides detailed spatial information.
Installed instruments usually provide limited
