Geoscience Reference
In-Depth Information
prediction by a single model or by an ensemble of model structures? How can we evaluate whether
particular model structures are given good results for the right reasons? These questions are much the
same as those posed by the availability of multiple models 40 years ago, but now we have much more
computing power that allows the performance of many different model structures to be evaluated. If each
of these models is considered as a potential hypothesis about how a catchment works, it will continue to
be frustratingly difficult to differentiate between them, given the information content of most catchment
data sets with an expectation of many different models providing equally good performance (Beven,
2006a, 2010). Chapter 7 goes into much more detail about model calibration, hypothesis testing, and
uncertainty estimation.
4.7 Key Points from Chapter 4
•
This chapter has dealt with models for the rainfall-runoff process derived directly from data, with-
out explicit consideration of the processes involved. These empirical or inductive models take a
variety of forms from transfer function methods to data mining techniques from the field of artifi-
cial intelligence (neural networks, support vector machines, classification and regression trees, and
fuzzy inference).
•
For some catchments where the hysteresis between storage and discharge is not greatly different
between wetting and drying, a very simple model of changes in discharge can be derived that depends
on deriving a function for the rate of change of storage with discharge, but which does not require
the estimation of absolute values of storage. This can also be used in “doing hydrology backwards”
to derive effective rainfalls and rates of actual evapotranspiration from changes in discharge (see also
Box 4.2).
•
Modern transfer function techniques, an extension of the unit hydrograph approach, can be used
to derive catchment scale parameters based directly on the analysis of the observations. Transfer
function techniques require a nonlinear transformation of the rainfall and the results depend on the
form of transformation adopted. In the data-based mechanistic approach of Young and Beven (1994),
a flexible approach to model structure is adopted in which time variable parameter estimation is used
to suggest a form for the nonlinear transformation.
•
The resulting transfer functions are often parallel in form, with one fast flow pathway and one slow
pathway. This does not directly imply any interpretation in terms of flow processes, and sensitivity
analysis shows that estimates of the proportion of effective rainfall following each pathway may be
subject to significant uncertainty.
•
Transfer functions may also be derived directly from the structure of the channel network in the
catchment. The use of the network width function and the geomorphological unit hydrograph were
discussed. Both only address the problem of routing an estimate of effective rainfall.
•
Neural network models can sometimes be interpreted in terms of a transfer function, but because
of the possibility of large numbers of weights (parameters) to be identified for all the linkages in
the network, such methods may be overparameterised and may not make accurate predictions when
predicting outside the range of conditions for which they have been calibrated.
•
Non-parametric methods (such as classsification and regression trees and some forms of fuzzy infer-
ence) do not generally require the estimation of parameters, but are very dependent on the range of
behaviour in the training data. They also may not predict well beyond the range of that data.
•
A recent method has been to test very many model structures against the available data as a form
of hypothesis testing exercise. Given the limitations of readily available hydrological data, it will
often be rather difficult to decide whether one structure is really better than another. It has, how-
ever, been shown that a combination of different models might give better predictions than any
single model.
