Geoscience Reference
In-Depth Information
robust identification algorithm used in the CAPTAIN package of the TFM modelling package
(Appendix A) are also based on a filtering approach, in that case applied recursively (Young,
2011a).
The Fourier transform transforms the original observations into frequency amplitudes. The use
of standard Fourier-transform-based algorithms usually requires regularly spaced observations
with little or no missing data. This is not generally the case for catchment input and output
tracer concentrations. Kirchner (2005), however, presents an algorithm that can be used with
irregular spaced data and investigates the difficulties introduced by various factors including
the “aliasing” of the input and output signals.
B11.2.2 Introducing Time Variability
The steady state flow assumption and constant residence time distribution assumption greatly
simplify the identification problem and many of the published studies of catchment residence
time distributions are based on these assumptions. However, given the concern in much of
the rest of this topic with trying to reproduce the short time scale dynamics of catchment
response, these assumptions seem to be a rather extreme simplification. It greatly simplifies
the identification problem, but clearly we need to be wary about the interpretation of the
results. It is therefore worth considering whether at least some of the assumptions can be
relaxed.
The first simple modification that can be made is to allow for the variability in discharge
as the catchment wets and dries. This can be done very approximately by carrying out the
analysis in terms of a time scale transformed by discharge flux rather than time (Rodhe
et al.
,
1996; Simic and Destouni, 1999) so that
t
t
o
Q
(
t
)
dt
Q
t
Q
=
(B11.2.5)
where
Q
is the mean discharge over the period. This is a very useful approach where there is
a strong seasonal dependence of flow, such as in catchments dominated by snowmelt runoff.
Snowmelt also tends to affect the isotopic concentration of inputs to the system. Studies have
shown that the earliest melt can be relatively light in
18
O and deuterium, with progressive
enrichment over time. This has an effect on the inferred residence time distribution (Lyon
et
al.
, 2009).
It would be better still if both inputs and outputs could be transformed to normalised cumu-
lative mass flux scales so that
t
t
o
P
(
t
)
C
P
(
t
)
dt
T
t
o
M
P
=
(B11.2.6)
P
(
t
)
C
P
(
t
)
dt
t
t
o
Q
(
t
)
C
Q
(
t
)
dt
T
t
o
M
Q
=
(B11.2.7)
Q
(
t
)
C
Q
(
t
)
dt
where
T
is the length of the complete time period considered, but this immediately makes
two issues more readily apparent. The first is that normalising the inputs and outputs in this
way obscures any mass imbalance between inputs and outputs. The second is that the con-
centrations may not have been sampled frequently enough (particularly in the early days of
isotope analysis) to properly characterise the mass flux of tracer during storm periods. This is
still a problem with some of today's studies - the catchment studies of Soulsby
et al.
(2000)
were based on weekly to fortnightly samples of isotope concentrations; even the Kirchner
et al.
(2000, 2001) studies at Plynlimon were based on daily samples of chloride as a tracer, but in a
catchment where the hydrograph generally peaks in two to four hours. Even the seven-hourly
