Geoscience Reference
In-Depth Information
samples that have been collected at Plynlimon since 2009 do not give a complete picture of
the variations in chemistry during storm periods. In addition, where studies of the variability in
tracer concentrations in the inputs have been made, distinct variability in the measured con-
centrations in space and time has been found (e.g. McGuire
et al.
, 2005). Thus, most analyses
are not based on a full characterisation of inputs and outputs.
The limitations of the assumption of a residence time distribution that is linear and stationary
are increasingly recognised. Theoretical frameworks that allow for the time variability of the
residence time distribution are being developed (e.g. Duffy, 2010; Botter
et al.
, 2010; Rinaldo
et al.
, 2011) and the prediction of tracer concentrations is being integrated with rainfall-runoff
models (Davies
et al.
, 2011). By making hypothetical simulations, it is relatively easy to show
that the changes in the residence time distribution, and hence in the inferred mean residence
time, can be very significant as the catchment wets and dries. These models involve additional
parameters, however, and have not to date been adequately tested against observational data
which may not (at least as yet) contain sufficient information to estimate all the parameters
required. It may indeed, be difficult to reproduce, or even to understand, the short time scale
variations in concentrations that have been observed in some experiments (Page
et al.
, 2007).
B11.2.3 Tracer Residence Times and Hydraulic Turnover Times
The mean residence time of a tracer derived from
f
() represents the effective turnover time for
water in the catchment system. We can also derive a hydraulic turnover time from the
h
() unit
hydrograph in Section 2.2. These will be different (even if they are parameterised within the
same family of distributions, such as the gamma). It might seem surprising that they should be
expected to be different if a tracer is conservative. A conservative tracer is, after all, expected to
follow the velocities of the water in the various storages in the catchment. However, there are
several reasons why the tracer mean residence time and effective storage might differ from the
hydraulic mean turnover time. One is the difference between wave celerities and velocities
discussed earlier in this chapter. The implication of the wave celerity being faster than the
mean pore velocity is that the effective storage for the hydrograph response is different from
that for a tracer response (see the case studies in Sections 11.7 and 11.9). In addition, if the
mean residence time is determined from a distribution fitted using the simplifying assumptions
discussed above, it will be subject to all the uncertainties inherent in the fitting process.
A second reason is that both the shorter and the longer residence times of water in catchments
might not be adequately represented by the available observations: the shorter because of the
sampling intervals of tracer concentrations missing the dynamics during storm periods, the
longer because of limited time series of data or choice of tracer. Thus, what appears in the
residence time distribution may not sample all the storages in the catchment, either because
it is relatively immobile (and may not interact with a mobile tracer except over very long time
periods) or because some of the fast flow pathways are simply missed by the sampling interval.
