Beyond the Primer: Water Sources and Residence Times in Catchments - Rainfall-Runoff Modelling: The Primer - page 343

only slowly and are treated as uncertain parameters within the ranges indicated by Figure 11.2. This is
equivalent to saying that the inputs in this period are causing a displacement of soil water and groundwater
from storages that are large relative to the inputs. Even this very simple model of three components has
17 parameters. The model was calibrated within the GLUE framework, using constraints on matching the
stream discharges, silica and calcium concentrations based on the residual errors (Iorgulescu et al. , 2005).
To search such a high-dimensional model space, two billion realisations of the parameters were run and
evaluated. Some 216 were accepted as behavioural (see Figure 11.3). The model can be interpreted to
illustrate how the contribution of the different components changes as a function of relative storage in the
system (Figure 11.4). The nonlinear nature of the response is clear, with a steep rise in the contribution
of the soil water component as the system wets up. Interestingly the transfer functions of precipitation
and soil water are inferred as being very similar. This implies either that the precipitation component
has a relatively slow pathway or that it is taking up some silica and appearing as part of the soil water
contribution. Probably both are actually occurring.
The constant source concentration assumption in this analysis means that nothing can be inferred
about residence times and effective storages in the system. The transfer functions in the model are related
to the hydrograph response, not to the actual travel times of water through the system. The isotope
observations, however, can be used to take the analysis a step further. Thus, Iorgulescu et al. (2007) used
Figure 11.3 Observed and predicted discharges, silica and calcium concentrations for the Bois-Vuacoz sub-
catchment; lines represent the range and quantiles of the predictions from the 216 behavioural models (after
Iorgulescu et al., 2005, with kind permission of John Wiley and Sons).