Geoscience Reference
In-Depth Information
Figure 7.16
Observed and predicted daily discharges simulated by a version of TOPMODEL for the small
Ringelbach catchment (34 ha), Vosges, France: the model was run using an 18-minute time step; note the
logarithmic discharge scale; prediction limits are estimated using the GLUE methodology (after Freer
et al.
1996, with kind permission of the American Geophysical Union).
Three points should be made in respect of such model rejections. The first is that the rejection of a
model might be a result of using it with poor data. Thus, to avoid rejecting a good model, just because it
has been used with poor data, the data should be examined carefully (see Section 7.17). Secondly, in a
complex model space of high dimensions it might be difficult to find the areas yielding the best models,
so the modeller should ensure that the space has been searched adequately. Finally, if it is concluded that
even the best models are not fit for purpose, this is a good thing! It suggests that something has been
missed in defining either the perceptual or conceptual models, or in the numerical implementation of the
model equations. Improvements should therefore be possible. We suggest in Chapter 12 that this is one
important way in which rainfall-runoff modelling will progress in the future.
7.14 Comparison of GLUE and Bayesian Approaches to Uncertainty
Estimation
By this point, the reader may be feeling a little confused about so many approaches to uncertainty
estimation (and there are yet more, see Beven, 2009). Despite the considerable advances that have been
made in the last decade in understanding the issues involved, there is indeed still much uncertainty about
uncertainty estimation in hydrology. The methods we have concentrated on here, GLUE and Bayesian
statistical approaches, in fact, represent quite different philosophies in addressing the problem. GLUE is
an attempt at formulating a nonstatistical approach to uncertainty, based on the concept of equifinality of
different model structures and parameter sets in providing acceptable fits to calibration data. It allows that
sources of uncertainty are epistemic rather than statistical in nature. Bayesian statistical methods, on the
other hand, try to represent all sources of uncertainty within a coherent statistical framework assuming
epistemic uncertainties can be represented as if they were statistical in nature. The latter has an important
advantage that if (and only if) the assumptions required hold in prediction then the probability of predicting
an observation conditional on the model can be estimated. This is only the case in GLUE if the same
