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would be needed to make accurate local predictions. Essentially their conclusion was that knowledge
of local water tables greatly improved the prediction of local water tables (although even then there
were significant local anomalies) but did not help much in constraining the uncertainties in discharge
predictions as estimated using the GLUE methodology.
The difficulty of making measurements remains an issue here. It is much easier (and very much
cheaper) to make measurements at, or very close to, the surface. The types of measurements available
for the investigation of subsurface flows are much more limited and we still do not have any adequate
non-destructive way of assessing preferential flow pathways, whether they be due to natural piping or
through mechanically induced cracks to mole drains in an agricultural field. Our perceptual model might
allow for the possible importance of such processes but, if their effects must be inferred rather than
measured, it is difficult to define an appropriate model description or condition a model on the basis of
perceptions alone.
A view of model calibration as a process of hypothesis testing and model rejection would seem to be
a positive one in moving from a situation in which the limitations of a simple optimisation approach in
the face of parameter identifiability problems have become increasingly clear. It also brings together the
variety of methods described in Chapter 7 in which multiple criteria are used in the model evaluation,
from Pareto optimal sets to GLUE. Each has its own way of deciding on which models should be rejected
and what weighting coefficients should be used in projecting the predictions of the retained models. In the
Pareto optimal set method, all models that are not part of the set are rejected and each retained parameter
set is given equal weight. In formal Bayes methods, the likelihoods are based on a statistical model of
the residuals. In GLUE, different ways of combining informal likelihood measures can be chosen and
the weights are based on the current likelihood value associated with each set.
12.2 The Value of Prior Information
This type of conditioning framework does, however, allow for the use of prior information in the condi-
tioning process. There are many types of prior information that might be used, for example prior degrees
of belief in different types of model structure; prior estimates of ranges of parameter values that might
be appropriate for different vegetation, soil or rock types; and the perceptual model of how a particular
catchment might respond to rainfall. Such information can constrain, in a sensible way, the range of
modelling possibilities to be considered in an application as a result of previous experience.
The use of prior information requires making choices and, in particular, rejecting possibilities. As
stressed earlier, such choices need to be made with care. There is no shortage of examples in the literature
of prior choices of inappropriate models, particularly the use of models based on infiltration excess
concepts in applications where this may not be the dominant runoff mechanism. It might still be possible
to calibrate or condition the model parameters to reproduce the observed discharges but should a model
based on inappropriate concepts be used in extrapolation?
The fact that calibration can bring nearly all rainfall-runoff models into line with an observed discharge
record can therefore be a problem as well as an advantage, since in many cases we do not know if
an inappropriate model is being used. There is, for example, a very natural tendency in making prior
choices about model structures for every model developer to give a prior weight of one to his or her
model and a prior weight of zero to all other models. This is, however, not a necessary choice: multiple
models may be included, as additional dimensions of the model space, within the modelling framework
suggested here.
There is also a natural tendency to give a greater prior weight to models that are considered to be
physically based relative to those that are more conceptual or data based in formulation. physically based
models should, in principle, reflect our understanding of hydrological systems more closely and therefore
be more robust in extrapolation to other conditions. This is only true, however, if such models truly reflect
