EXISTING MATHEMATICAL METHODS FOR UNCERTAINTY ASSESSMENT - Modelling Uncertainty in Flood Forecasting Systems - page 46

the ! -cut method, all possible combinations of parameters values are considered and the
maximum and minimum model outputs obtained for the given intervals of the parameter
values are directly reflected in the output uncertainty. Therefore, the EP-based method is
by and large more conservative than the MC method. This suggests that the former is
desirable when the extreme values corresponding to the parameter values at the tails of
their distributions are important. This is generally the case in environmental and natural
hazard context where human lives are often at stake (Guyonnet et al., 1999).
Another important distinction between the MC and the EP methods is the dependencies
between the parameters. The MC method allows the effects of dependencies between the
parameters to be accounted for via correlation coefficients that indicate the degree of
correlation between parameters. In contrast, the current state of knowledge about the EP-
based method does not allow the incorporation of the effect of correlation between the
input parameters. In the EP by the ! -cut method, we take the same ! -cut level for all
variables to determine the output uncertainty (interval) at the same ! -cut level. This is not
the same as correlation/uncorrelation in the MC method, and should be distinguished. In
the simulation examples by Fishwick (1991), (fully) correlated and (fully) uncorrelated
simulations were distinguished. In his correlated example, only two values (upper bound
and lower bound) of each input are used to determine the interval in the output. This in
fact is equivalent to the EP by ! -cut for the case of a monotonic function (see Subsection
3.2.1). In the EP for non-monotonic function, all possible values of each parameter within
the interval specified by the given ! are considered. This case has been interpreted as
(fully) uncorrelated by Fishwick (1991).
3.6.2 FOSM and expert judgement-based qualitative method
Although the FOSM method and the expert judgement-based qualitative method are
based on two different theories (probability and possibility), they share some similarities.
Observing Equations (3.8) and (3.25) we can see that the basic forms of these equations
are same. Both are the summations of quantities resulting from the product of two
quantities. The two quantities are the “square of the sensitivity” and the “variance” in the
FOSM method and the “importance” and the “quality” (its mirror image) in the
qualitative method. Therefore, in these two equations, the sensitivity of a parameter is
equivalent to the importance of a parameter and the variance of a parameter is equivalent
to the mirror image of the quality of the parameter (Fig. 3.6). The difference is only in the
way the two multiplying quantities are represented and derived.
Figure 3.6. Comparison of equations for the FOSM method (probabilistic) and
the expert judgement-based qualitative method. The symbols used in
the figure are same as in Equations (3.8) and (3.25).