CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 58

Figure 4.5. Relative frequency of b j generated by normalisation.
There is one thing common to the resulting distribution for each method: as b j (for all j )
tends to 1 the probability of it being generated tends to 0. In the first two methods the
probability is decreases linearly as the value of the coefficient increases. The question
then is “what are the implications of these methods for the resulting uncertainty?” The
choice of these methods does not influence the result in the fuzzy EP-based methodology
(Subsection 4.1.4) so long as enough values of the coefficients are taken as are required
for the determination of the maximum and the minimum. This is because, in the EP-based
method, it is not the probability that counts. Since we are concerned only to find the
maximum and minimum of the output, only one set of coefficients that results in
maximum and minimum is sufficient. On the other hand, in the MC based method
(Subsection 4.1.5), it is the number of occurrences of such sets that counts. If such sets
are very few, they will not have significance for the output uncertainty. Therefore, the
choice of the methods for generating the coefficients has a direct influence in the MC
based methodology. The normalisation method is perhaps the most rational one for use
with the MC-based methodology, as it gives a high probability of generating mean values.
4.2 Improved first-order second moment method
The FOSM method (see Subsection 3.1.2) is one of the most widely used methods for
uncertainty estimation in model results due to uncertainty of the parameters. Some
successful applications of FOSM in water related problems are presented by Lee and
Mays (1986), Melching (1992 & 1995) and Tung and Mays (1981). Several advantages
of the FOSM method are that (i) it does not require the knowledge of input parameter
distributions, (ii) it is computationally efficient and (iii) it provides a measure of the
sensitivity of the model outputs to the input random variables (Tyagi and Haan, 2001).
Like any other method, this method suffers from a number of limitations that arise from
the first-order approximation. To improve the accuracy of the uncertainty estimation by
this method, several improvements or modifications have been proposed in various
contexts (Kunstmann et al, 2002; Melching and Yoon, 1996; Tyagi and Haan, 2001).