APPLICATION: FLOOD FORECASTING MODEL FOR LOIRE RIVER (FRANCE) - Modelling Uncertainty in Flood Forecasting Systems - page 130

6.4.2 Analysis procedure and results

The computational detail of the expert judgement-based qualitative method is presented
in Subsection 3.2.2. In summary the calculation steps are as follows:

1. Derive the Quality for each parameter from the Qualities of the subpa-
rameters, Equation (3.22).
2. Compute the uncertainty contribution of each of the parameters to the
uncertainty in the output, Equation (3.24).
3. Estimate the total uncertainty in the forecast due to the uncertainty
parameters, Equation (3.25).
4. Repeat Steps 1 to 3 for each expert.
5. Compute the average total uncertainty for all the experts, Equation (3.26).
6. Repeat Steps 1 to 5 to evaluate the best-case scenario with the Qualities of
all the parameters as Very Good .
7. Repeat Steps 1 to 5 to evaluate the worst-case scenario with the Qualities of
all the parameters as Very Bad .
8. Develop Fuzzy Qualitative and Crisp Qualitative Scales using the proce
ures as described in Section 4.3.

The uncertainty estimates in the output (represented by membership functions) computed
from the evaluations made by each expert are presented in Figure 6.14. The average of
the four experts is also shown in the figure. Table 6.4 summaries the differences (in
terms of the defuzzified values) in the evaluations by the different experts. The
defuzzification, which is a process of representing a fuzzy set by a single crisp value, is
carried out using the centre-of-area method of defuzzification (Appendix I).

Figure 6.14. Output uncertainty computed form the individual assessments of
experts on the quality and importance of the parameters.

Table 6.4: Comparison of uncertainty evaluations by different experts.

Evaluations Defuzzified value % difference from the average

Expert-1 1.31 13.2

Expert-2 1.62 7.9

Expert-3 2.05 36.3