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statistical assumptions are made (though as noted earlier, very similar results should then be obtained
subject only to sampling of the parameter space). More usually, the uncertainties estimated by GLUE are
the empirical probabilities of the predictions of model output by the
ensemble
of behavioural models.
It has been suggested, however, that the GLUE approach might be better at revealing nonstationary
deficiencies in model structure (and input data) because such deficiencies are not obscured by a statistical
error variance. Thus the choice between approaches is not so easy.
There is, however, one feature that is common to both approaches. It is important to distinguish between
calibration or conditioning and the prediction of new events. For prediction, both methods need to assume
that the characterisation of the uncertainties in calibration or conditioning will hold when carried over
to prediction. In the statistical methods, this means carrying over the parameters of the structural model
of the different uncertainties. In GLUE this is more implicit. The errors associated with a behavioural
model in calibration are assumed to be similar in prediction. Thus, since the epistemic errors in prediction
might be different to those in calibration, particularly if the model is used to predict outside the range
of the calibration data, both approaches might not necessarily provide good estimates of the uncertainty
associated with new events.
This should not, however, suggest that it is not worth trying to make an assessment of uncertainty,
whichever method is used. It is, I would suggest, far more dangerous
not
to associate predictions with
some estimate of uncertainty and rely only on single deterministic simulations in assessing catchment
responses. Unfortunately, there are very many published contributions that still do so, particularly in
estimating the impacts of future catchment changes (see Chapter 8). However, taking account of the
uncertainty in such predictions might make a difference to the decisions that such predictions are intended
to inform.
7.15 Predictive Uncertainty, Risk and Decisions
Let us assume that it has been possible to make a realistic assessment of the uncertainty associated with
the predictions of a rainfall-runoff model, by whatever method (e.g. Figures 7.5, 7.7, 7.10 or 7.15). It is
important to remember that rainfall-runoff modelling, in practical applications, is done for a purpose:
to help some decision. How best then to interpret and make use of those uncertain predictions? One
interpretation is that the uncertainty represents the model error in representing the data but a better
interpretation is in terms of the risk of a certain outcome in certain circumstances, given the model
as a means of extrapolating knowledge and understanding to those circumstances. Both statistical and
nonstatistical approaches to uncertainty estimation can be interpreted in this way. In essence, evaluating
the risk of an outcome based on the model predictions is also an evaluation of the risk of the model
predictions being wrong (as they may well prove to be).
Risk, however, is something that is readily incorporated into modern decision-making processes, when
it may also be necessary to take account of the costs of mitigating that risk, for example, in enlarging a
reservoir spillway or raising flood embankments. The important point is that the risk associated with the
model predictions should be included in the decision analysis. In risk-based decision making, a common
technical definition of risk is as:
risk
(
outcome
)
=
probability
(
outcome
)
∗
consequences
(
outcome
) (7.7)
In the general case, both the probability and the consequences should be considered as uncertain
quantities themselves. The consequences are usually some expected loss (often expressed in monetary
terms). Such uncertainties might affect the decision that is made about reducing the risk, so it is important
that they be incorporated into the analysis. One rather simple way of doing so is to integrate over all
the uncertainties to produce a cumulative distribution of risk. This can then (as in the simple case of
estimating a flood frequency) be expressed in terms of the exceedance probability (
EP
)ofagivenlevel
