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discharges and water tables in the catchment than simpler models. This was interpreted as a problem of
a priori
identification of effective values of the parameters needed. Indeed, it seemed that even in this
near ideal case, the uniqueness of place issue arises (Beven, 2000); there were sufficient heterogeneities
and complexities in the structure of the system to make it difficult to model. It was also stressed that
the interaction between modeller and model was important. The choice of modeller was as important
as the choice of model, in particular in the (subjective) interpretation of information about the dominant
processes at the site and expectations about the initial conditions in setting up the model runs (see also
Seibert and McDonnell, 2002; Fenicia
et al.
, 2008b).
The practical applications of this type of distributed model are often at much larger catchment scales
with larger calculation elements (e.g. Abbott and Refsgaard, 1996; Singh and Frevert, 2002b; Refsgaard
and Henriksen, 2004). If it has proven difficult to simulate the processes in very small catchments
using this type of distributed model, how should that guide good practice in practical applications of
such models at larger scales? Two important consequences are apparent. The first is that there should
be an expectation that the predictions of such models will be uncertain. Consequently, some effort
should be made to assess and constrain that uncertainty, perhaps by a targeted measurement programme
(although little information is available in the literature about the value of different types of data in this
respect). The second is that the modelling process should be treated as a learning process. Hollander
et al.
reported that most of the modellers changed their qualitative view of how the catchment processes were
working following a field visit. They suggested that there was a form of Bayesian learning process at
work here.
For example, suppose that the parameters of a distributed model have initially been calibrated only on
the basis of prior information about soil and vegetation type, with some adjustment of values being made
to improve the simulation of measured discharges (although the sheer number of parameters required by
distributed models makes any form of calibration difficult, see Chapter 7). Suppose that after this initial cal-
ibration a decision is made to collect more spatially distributed information about the catchment response.
Measurements might be made of water table heights, soil moisture storage and some internal stream gaug-
ing sites might be installed. We would expect the predictions of the calibrated distributed model to turn
out to be wrong in many places, since the calibration has taken little account of local heterogeneities in the
catchment characteristics (other than the broad classification of soil and vegetation types). There is now
the potential to use the new internal measurements not to evaluate the model, but to improve the local cal-
ibration, a process that will not necessarily improve the predictions of catchment discharge which was the
subject of the original calibration (see also the TOPMODEL case study in Section 6.4). It will generally
make a much greater improvement to predictions of the internal state variables for which measurements
have now been made available. But if the new data is being used to improve the local calibration, more
data will be need to make a model evaluation. In fact, in practice, there is generally little model evaluation
but rather the model is adapted to take account of the new data, without necessarily any impact on the
variables of greatest interest in prediction (discharge in rainfall-runoff modelling). The logical extension
of this process is the “models of everywhere” concepts of Beven (2007) that are discussed in Chapter 12.
5.9 Discussion of Distributed Models Based on Continuum
Differential Equations
In many respects, there has been a lot of progress in distributed hydrological models in the last decade.
There is now much more computer power available to support finer grid resolutions and more sensitivity,
calibration and uncertainty estimation runs. The SHE model, in particular, has been important in the
development of distributed modelling technology. It is now perfectly possible to run the SHE model
many times to support uncertainty estimation (Christiaens and Feyen, 2002; Vazquez
et al.
, 2009). The
application of this type of model is not, however, without limitations, some of which have been discussed
