Geoscience Reference
In-Depth Information
Figure 7.12
Prediction bounds for spatially distributed piezometers in the Saeternbekken catchment for
three different discharges, showing prior bounds after conditioning on discharge and recording borehole
observations, bounds based on conditioning on the piezometer data alone and posterior bounds based on a
combination of both individual measures (after Lamb et al., 1998b, with kind permission of Elsevier).
Somerset, England. This is an interesting catchment in a number of ways, but was chosen because it
was used in the HYREX experiment (Moore
et al.
, 2000; Wood
et al.
, 2000) which involved a network
of 49 raingauges in the catchment over an extended period. Errors in the input data should therefore be
expected to be relatively small, except perhaps in some localised summer convective events. Another
point of interest was that when we investigated the rating curve for the gauging station, it proved to be
rather uncertain, so limits of acceptability were defined prior to running the model to span the range of
discharge observations (Figure 7.13; see also Pappenberger
et al.
(2006b), Blazkova and Beven (2009),
Liu
et al.
(2009) and Westerberg
et al.
(2010a) for other applications of discharge uncertainties within
the limits of acceptability GLUE framework). No internal state observations were available for model
evaluation in this case. It is worth noting at this point that other studies have looked at representing
discharge observational error within a statistical framework (e.g. Thyer
et al.
, 2009; Di Baldassarre and
Montanari, 2009; McMillan
et al.
, 2010).
Each model run was evaluated with respect to the limits of acceptability. Figure 7.14 shows the results
of two model runs with different parameter sets in the same dynamic TOPMODEL structure, expressed in
terms of the standardised scores (with zero at the value of the observation). Two things are quite striking.
The first is the nonstationarity in the residual characteristics when expressed in this way; the second is the
quite different characteristics of the two models. In fact, neither of the models is behavioural in making
