CONCLUSIONS AND RECOMMENDATIONS - Modelling Uncertainty in Flood Forecasting Systems - page 135

Klodzko catchment with the precipitation time series as uncertain inputs. The results also
show that the output uncertainty due to the uncertainty in the temporal distribution can
be significantly dominant over the uncertainty due to the uncertainty in the magnitude of
the precipitation. This suggests that using time-averaged precipitation over the catchment
may lead to erroneous forecasts. For the implementation of this methodology three
important issues were identified: (i) the generation of the disaggregation coefficients, (ii)
the selection of the number of subperiods, and (iii) the simplification of the
methodology. This study also attempted to provide some answers to these issues.
7.1.4 Use of genetic algorithms with fuzzy Extension Principle
The application of the EP to a non-monotonic function requires an algorithm for the
determination of the maximum and minimum of the function values. In the
implementation of the uncertainty assessment methodology using temporal disaggregation
in the framework of the EP, genetic algorithms are used for the determination of maxima
and minima. The global optimisation algorithms like GAs are particularly useful when
commercial off-the-shelf (black-box) software is used for building forecasting models
(Maskey et al., 2002b). The application results with two versions of GAs (conventional or
normal and micro) show a good potential of these algorithms to combine with the fuzzy EP for
the propagation of uncertainty. It is however advisable, where affordable, to evaluate the per-
formances of several algorithms and to find the most suitable algorithm for the given problem.
7.1.5 FOSM and Improved FOSM methods
The FOSM method is one of the widely used methods in uncertainty modelling. It is
simple in application, has less computational requirement than other methods and is
particularly useful when the information about detailed distributions of the uncertainty
parameters is not available. Like any other method, it suffers however from some
limitations (Melching and Yoon, 1996). As part of this research, an improvement to the
FOSM method is applied using the second-degree reconstruction of the function to be
modelled. The Improved FOSM method has a particular advantage when the average
value of the input variable corresponds to maximum/minimum values or to regions
where the slope of the function is very mild compared to the effects of curvature (non-
linearity). It is also important to note that the improved method retains the
simplicity and the smaller computational requirement of the FOSM method.
The sensitivity of both the FOSM and the IFOSM methods to the size of the
perturbation were analysed. The analysis carried out with the flood forecasting model
(Chapter 6) showed that the best value of the perturbation ratio (PR) is in the range from
0.75 to 1.5 for the FOSM method and from 1.25 to 1.75 for the IFOSM method. The re-
sults suggest that it is advisable to use some other standard method, for example the MC
method, to fix beforehand the best value of the perturbation for a range of possible scenarios.