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In-Depth Information
scales. Those that were involved in the generation of fast runoff would be sensitive to wet periods over short
time scales; those that were controlling baseflows would be sensitive during dry periods and over a longer
time scale. This was used to allow parameter distributions to evolve over time within the GLUE framework.
Within a more statistical uncertainty framework, particle-filtering techniques have also been used to
allow posterior parameter distributions to evolve over time (e.g. Smith
et al.
, 2008b; Bulygina and Gupta,
2009, 2010; Salamon and Feyen, 2009). In Chapter 4, it was also shown how the recursive estimation of
parameters could be used to define the structure of a model within the DBM methodology (see Box 4.3).
7.17 Quality Control and Disinformation in Rainfall-Runoff Modelling
The GLUE approach to uncertainty estimation has been criticised in a number of articles. The main
criticism has been that it is not objective because it does not make use of the full power of statistical
theory (Mantovan and Todini, 2006; Stedinger
et al.
, 2008). Mantovan and Todini (2006) go further and
suggest that the GLUE methodology is not “coherent” in the technical sense that additional observations
should lead to further refinement of the posterior parameter distributions. The demonstrations of the
advantages of a formal statistical approach to uncertainty estimation, however, have generally relied on
hypothetical test cases, in which the assumptions of a formal statistical analysis are valid, because the
experiment is designed to ensure that they are valid. Thus the model structure is known to be correct and
the model residuals are known to have a simple statistical structure.
In response, Beven
et al.
(2008) argue that this is a special case in GLUE. If it is
known
that the
residuals have a simple statistical structure then that knowledge can be used in the analysis and a formal
statistical likelihood function can be used within GLUE. The outputs from the uncertainty analysis should
then be identical, subject only to sampling differences. This is not, however, the type of situation that
GLUE was intended to deal with and they also show that even small changes to the assumptions of a
hypothetical example can lead to bias in the posterior parameter distributions, even for cases when the
model structure is still known to be correct. This is never the case in real applications, of course, and
Beven (2006a) differentiates between ideal cases (where the strong assumptions required by a formal
statistical analysis can be accepted) and non-ideal cases (where such strong assumptions are not justified,
which will be case for most real applications).
But this also raises the issue as to just how far each model residual should be considered as informative
in real applications. If, as suggested for example by Figure 7.5, some event inputs are poorly estimated,
then it might be difficult for a good model to predict the observed discharges. The residuals might not then
be so informative in identifying a good model or parameter set. In extreme cases, for example where the
volume of discharges is greater than the observed volume of inputs for a simple rainstorm, the residuals
could actually be disinformative in the calibration process. However, model calibration and uncertainty
estimation methods have not generally tried to identify disinformative periods of data.
There is, of course, a difficulty in doing so. In the most extreme cases, perhaps, it might be obvious that
there is a problem, but the effect is often more subtle. In Figure 7.17, for example, at the end of the period
the model predicts a hydrograph when no change in discharge is observed. This can happen if the model
underestimates the available storage prior to that hydrograph, but in this case it follows a relatively wet
period. It would therefore appear as if either the observed inputs have overestimated the real inputs to the
catchment or there is a problem with the discharge observations. Earlier in the simulation, in the largest
observed hydrograph peak, the model residuals are also significant. This might also be a problem of the
observed inputs and discharges but here it could also be informative about whether the model structure
itself is adequate.
Disinformation in data and how it affects hydrological inference is a topic that has not been discussed
much in the hydrological literature. There are a number of measures for information content that are
conditional on an assumed model structure in being, directly or indirectly, derived from series of model
