Geoscience Reference
In-Depth Information
the early paper of Sklash and Farvolden (1979), it was shown that samples taken from surface runoff at
a particular location in a catchment were sometimes predominantly new water and sometimes old water
and many catchment hydrographs might be consistently dominated by new water. It is possible to carry
out an uncertainty analysis of the resulting hydrograph separations taking account of the uncertainties
in the input information. We return to this in respect of the more general end member mixing analysis
(Section 11.5).
11.4
Assessing Spatial Patterns of Incremental Discharge
This type of two-component mixing analysis can also be applied along discrete increments of a river to
determine the increments of discharge in space. In this case, rather than old and new water components,
in each reach of the channel the upstream and lateral contributions can be determined by applying
Equation (11.1) sequentially in each reach. It is again necessary that the characteristic concentrations for
the upstream and lateral contributions should be different. This can be achieved by adding an artifical
tracer at the upstream end of the reach (Huff
et al.
, 1982) or making use of an environmental tracer
(e.g. radon, as Genereux
et al.
, 1993, did). Some recent work has used water temperature, measured in
a continuous downstream fibre-optic cable, as a form of tracer in a similar type of analysis based on a
combination of mass and energy balances (Westhoff
et al.
, 2007), although this introduces additional
terms into the energy balance that require a number of parameters to be estimated. Since those parameters
are uncertain, the resulting estimates of lateral inflows are uncertain but, as yet, there has not been an
adequate uncertainty analysis of this approach published.
Despite the uncertainties, however, this type of analysis has revealed some very strong spatial variability
in the lateral inputs of discharge to stream channels under both high flow and low flow conditions. In
the case of the Walker Branch catchment, studied by Huff
et al.
(1982) and Genereux
et al.
(1993), this
variability appears to be related to dipping bedrock structures beneath the soil layers that are not manifest
in the surface topography of the catchment.
11.5
End Member Mixing Analysis (EMMA)
The type of simple mixing analysis of Section 11.4 can be extended to the identification of multiple
sources of water by the use of multiple tracers where the tracer concentrations can be used to distinguish
those sources or “end members”. This end member mixing analysis (EMMA) is most often used with two
tracers to differentiate three components: event water, water from soil storage and water from longer-term
groundwater storage. The three balance equations are then:
Q
=
Q
P
+
Q
SW
+
Q
GW
QC
=
Q
P
C
P
+
Q
SW
C
SW
+
Q
GW
C
GW
Q
GW
C
GW
where
Q
is discharge,
C
and
C
are the concentrations of two different tracers, and the subscripts
P
,
SW
and
GW
refer to precipitation, soil water and ground water respectively.
Q
,
C
and
C
are measured in
the stream and, if the concentrations of the three end members can also be assumed known and constant
in time, there are only three unknowns,
Q
P
,
Q
SW
and
Q
GW
. The system can therefore be solved at every
time step for which measurements of
Q
,
C
and
C
are available.
Similar assumptions to the two-component case are necessary: that there is a distinct difference between
the end member concentrations and that those concentrations can be assumed constant in time and space.
QC
=
Q
P
C
P
+
Q
SW
C
SW
+
