Geoscience Reference
In-Depth Information
In addition, it has been suggested that by combining hydrograph and environmental tracer informa-
tion in calibrating catchment response models, the hydrologist might be able to get closer to having a
catchment model that gets the right result for the right reasons. We return to this issue after discussing
how environmental and artificial tracers can be used to throw light on the sources and residence time
distributions of catchment discharges.
11.3
Simple Mixing Models
Tracers are also used to try to determine the sources of water in discharge hydrographs from hillslopes and
catchments. To carry out tracer experiments using artificial additions of tracer at these scales is difficult, so
it is generally necessary to resort to the use of naturally occurring substances or
environmental tracers
to
do this. The use of environmental tracer information to infer the sources of water in the hydrograph started
with the use of simple two-component mixing methods that distinguished between the contributions of
water that is added during an event (
new
water) and water that is stored in the catchment prior to an event
(
pre-event
or
old
water). The analysis depends on being able to assign characteristic concentrations to
each of the two sources, and a simple mass balance of mass of water and tracer in catchment hydrograph
(but not necessarily in the catchment as a whole).
Thus, at any time step, it is assumed that:
Q
=
Q
o
+
Q
n
QC
=
Q
o
C
o
+
Q
n
C
n
where
Q
is discharge,
C
is tracer concentration and the subscripts
o
and
n
refer to old and new
water, respectively.
Given these two equations, the proportion of new water in the hydrograph can be calculated as:
Q
n
Q
=
(
C
−
C
o
)
(11.1)
(
C
n
−
C
o
)
This calculation can then be repeated for all time steps for which concentration measurements
are available to provide a hydrograph separation based on water sources (e.g. the example shown in
Figure 1.6). Note that for a well-defined separation there must be a distinct difference between
C
o
and
C
n
. If this is not the case then the denominator in the mixing equation is very small or zero and the
separation cannot be made. Note also, in applying the equation at successive time steps it is necessary to
assume that
C
o
and
C
n
are constant in space and time (at least for that particular storm).
It is known that this latter assumption is generally only very approximately true. New water concentra-
tions often vary in space and time in a storm (McDonnell
et al.
, 1990; Harris
et al.
, 1995). In addition, for
some tracers, such as silica, rain water might actually change its concentration as it interacts with the soil
over rather short time scales. Old water concentrations are often taken to be the observed concentration in
the hydrograph measured prior to a storm, but such concentrations represent a mix of pathways in space
and there is no real reason why those concentrations should stay constant in either time or space during
the forcing due to a storm event (and in Section 11.4, we see that the mix of waters from subsurface
sources can change over a sequence of events).
Thus, this type of mixing model is a crude approximation. It has been an important approximation,
however, in causing hydrologists to recognise the dominant contribution of subsurface runoff to the
hydrograph in many catchments. However, it should not be assumed that this is always the case. Even in
