Environmental Engineering Reference
In-Depth Information
0
(a)
(b)
1
2
3
4
5
6
0
10
20
30
40
50
60
70
80
0
0.1
0.2
0.3
0.4
Water content (m
3
/m
3
)
Concentration (mg/L)
Figure 7.4
Hypothetical tracer concentration-depth
profile (a) and water-content profile (b) in the unsaturated
zone are used to describe application of the tracer-profile
method for estimating drainage rates. Depth of peak
concentration is 4 m (dashed line); depth of center of mass,
as calculated with Equation (
7. 2
), is 3.46 m (dotted line).
The mass of water in the soil column (the integral term in
Equation (
7.1
)) is equivalent to 0.64 m above the 3.46 m
depth (represented by shaded area) and 0.79 m above the
4 m depth. Assuming 20 years between tracer-application
and sampling dates, drainage rates calculated with Equation
(
7.1
) are 32 mm/yr for
z
T
= 3.46 m and 40 mm/yr for
z
T
=
4 m. Evaluation of integrals in these equations is by the
trapezoid rule as described in
Figure 5.3
.
the ZFP; most of that water is returned to the
atmosphere via evapotranspiration. Ideally,
tracers would be introduced at or below the
ZFP, and the integral in Equation (
7.1
) would
extend from the depth of the ZFP to
z
T
. Only
applied tracers provide the option of injecting
tracers below land surface. If the root zone is
thin relative to the depth of tracer movement,
variable water contents in the root zone will
h ave l it t le i mp ac t on es t i m ate d d r a i n a g e r ates.
However, when tracer peaks are located above
the ZFP, such as has been found for
3
H and
36
Cl
in arid regions (Norris
et al
.,
1987
; Phillips
et
al
.,
1988
; Scanlon,
1992
), it is not possible to
accurately quantify long-term average drain-
age rates (Tyler and Walker,
1994
). For situ-
ations in between these extremes, Equation
(
7.1
) should be modified to use average annual
soil-water contents for depths above the ZFP
and water contents measured at the time of
sampling for greater depths.
The peak-displacement method is similar to
the profile method. Profiles of tracer concen-
trations and soil-water contents are obtained
at two times. Vertical tracer velocity,
v
, is cal-
culated by dividing the change in penetration
depth (Δ
z
T
) by the length of time (Δ
t
) between
the two profile samplings:
of the profile method. If transport is by piston
flow, similar drainage rates can be calculated by
using either the depth of the peak or the center
of mass. Where preferential flow occurs, drain-
age rate should be based on the depth of the
center of tracer mass (Walker,
1998
; Cook
et al
.,
1994
). The integrals in Equations (
7.1
) and (
7. 2
)
can be evaluated with the trapezoid rule on the
basis of water-content and tracer-concentration
measurements at discrete depths, as described
in
Figure 5.3
.
The integral in Equation (
7.1
) extends from
z
= 0 ( l a n d s u r f a c e) t o
z
T
and so includes the root
zone. Soil-water content in the root zone can
vary widely over the course of a year, a fact that
complicates drainage calculations. Typically,
only a small portion of infiltrating water in
natural or agricultural settings drains past
v z
=∆∆
/
t
(7. 3 a)
T
Drainage rate is equal to velocity multiplied by
average volumetric water content:
Dv
(7. 3b)
=
θ
