Geoscience Reference
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6.4 Uncertainty analysis using qualitative method
Most physically-based models are complex by nature and involve many input variables
and model parameters that cannot be determined precisely. Uncertainty in some of such
parameters cannot be estimated quantitatively, such as using PDFs due to insufficient data. For
a complex model, particularly in real time use, the MC-type methods may not be feasible
due to time constraints. What is usually done in practice is to exclude some of the parameters/
variables (that are supposed to have less influence on the uncertainty) from the analysis.
Furthermore, there may exist some sources of uncertainty other than the model parameters and
variables, which obviously cannot be incorporated in such a quantitative method. Krzystofow-
icz (1999) also concluded that the uncertainty assessed by the methods like the MC method
alone is not sufficient unless the uncertain parameters that are ignored are insignificant.
In such situations the fuzzy set theory and expert judgement-based qualitative method
presented in Subsection 3.2.2 can be useful. Given the qualitative assessments of the
parameter uncertainty by experts, this type of qualitative method allows for the
estimation of the uncertainty due to all recognisable sources without a significant
increase in the computation time.
In this section the results of the application of a qualitative method based on fuzzy set and
expert judgement applied to the estimation of the uncertainty in the forecasting of floods using
the Loire model are reported. The forecasts at the station Orleans are considered, and the
forecasts are assumed to be on a daily basis (24 hours forecast horizon). Subsection 6.4.1
presents the evaluations by experts on different parameters of uncertainty with respect to
their contributions to the uncertainty in the output. The results are presented in Subsection 6.4.2.
6.4.1 Expert evaluation
Four parameters have been identified for the qualitative evaluation of uncertainty. They are (i)
the imprecision in the measurement of water levels, (ii) the uncertainty due to rating curve
conversions, (iii) the uncertainty due to propagation of flow, that is the propagation model, and
(iv) the uncertainty due to other reasons. Each parameter has two or more sub-paramters
(Table 6.3). The evaluation is carried out on Quality and Importance of the uncertainty
parameters regarding their contributions to uncertainty in the forecast. Five linguistic variables
are used for the qualitative evaluations of both quality and importance. The linguistic
variables used for the evaluation of Quality are Very Good, Good, Acceptable, Bad and
Very Bad and those used for Importance are Very Large, Large, Moderate, Small and
Very Small . The fuzzy membership functions representing these variables are given in
Figure 6.13. The Importance is evaluated for the parameters and the Quality is evaluated for
the subparameters. The Quality of the parameter is derived from the Qualities of the
subparameters using Equation (3.22). Four different individuals experienced in the forecasting
system, here referred to as experts, took part in the evaluation. The evaluation is presented in
Table 6.3. In the table, the evaluation of Importance which is for the paramter is given in italics.
 
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