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(Beven, 1989, 2006a). The comparison cannot be done at all, of course, if the model state variables have
no measureable physical equivalents.
A second, related, problem is the use of spatially distributed parameters in a model. It is difficult to use
most observations of internal catchment states in model evaluation without making use of a distributed
model. But then, as noted above, in order to predict a local response correctly, distributed parameter fields
might be needed, which then introduce many additional degrees of freedom. If, on the other hand, global
values of parameters (such as hydraulic conductivity or transmissivity) are used, then we should expect
only approximate predictions of local variables nearly everywhere, where the global parameters cannot
reproduce the local responses (e.g. Lamb
et al.
, 1997; Blazkova
et al.
, 2002a; Vazquez
et al.
, 2009).
A third problem is that any prediction requires the knowledge of future boundary conditions. We
have already noted that the error characteristics of observations used in calibration might be different
from those in prediction, and there are very many reported hydrological modelling studies where poorer
performance in prediction, relative to calibration, has been accepted because there is an expectation that
this will be the case. Certainly, in the case of groundwater models, poor performance in post-audits could
often be assigned to poor specification of future boundary conditions (see the review by Konikow and
Bredehoeft, 1992).
12.4 Models of Everywhere
We have seen how detailed distributed models of large catchments and even of whole countries are
becoming more and more computationally feasible. We have also seen how many of the available dis-
tributed models depend on very approximate representations of hydrological processes. In implementing
such models of everywhere, however, it is a hydrological modelling aphorism that every catchment is
unique, making regionalisation or the prediction of the responses of ungauged catchments difficult (see
Chapter 10). That is for the water: it is even more so for water quality and ecological variables. So, given
this uniqueness, is it even useful to think in terms of models of everywhere and everything in catchment
management when such models will inevitably be wrong in some places or some of the time?
Looking ahead to the availability of models of everywhere, Beven (2007) argues that it will be useful,
and even necessary, to think in these terms. It will change the nature of the modelling process, from one in
which general model structures are used in particular catchment applications to one in which modelling
becomes a learning process about places. In particular, if a model is obviously wrong in its predictions
about a place, then this will be an important driver to do better. This has already been seen in Denmark,
where the National Water Resources Model is already in its fourth generation (in almost as many years)
because it was deemed to be wrong in its implementation in some parts of the groundwater system
(Henriksen
et al.
, 2008). Every successive generation should be an improvement. The uncertainties in the
modelling process will not, of course, disappear (particular with respect to future boundary conditions)
but they may be gradually constrained. If, in the words of George Box, all models are wrong but some
might be useful, then we would hope that models of everywhere would become increasingly useful to
the management process as the representation of processes in particular places is improved.
This learning process about place is a way of doing science in complex open adaptive systems. Model
hypotheses can be tested within the limitations of the uncertainties in available data and either survive
locally or be rejected. As new data become available, further tests can be carried out as part of the learning
process. If the models survive some agreed testing process then they can be retained for use in prediction.
Uncertainty might mean that multiple models survive. We can therefore only generally say that those
models that have survived a testing process up to now are the best we have available for prediction,
subject to future testing as new information becomes available.
Treating the modelling problem as a learning process implies a modelling system that needs to be
flexible, with the possibility of replacing a component or components to suit local conditions, or replacing
