APPLICATION: FLOOD FORECASTING MODEL FOR LOIRE RIVER (FRANCE) - Modelling Uncertainty in Flood Forecasting Systems - page 127

6.3.3 Conclusions
The IFOSM method produced a satisfactory result when solving a particular problem
that is encountered in the application of the FOSM method to a flood forecasting model
for the Loire River. The problem concerns the misleading estimation of uncertainty when
the average value of the input variable corresponds to a maximum or minimum value or
to regions where the slope of the function is very mild and varies gradually compared to
the effects of a large curvature (non-linearity) of the function. There is no significant
computational burden in implementing the IFOSM method because it requires only three
function evaluations for each input (uncertain) variable, compared to two for the FOSM
method. In the presented examples, the unknown PDFs are approximated by a uniform
and a triangular PDFs. In principle the method can be applied to all possible PDFs.
However, the more complex the PDF the more complicated the derivation of the
solution. When the PDF is unknown, assuming a complex distribution cannot be justified
more than choosing a simpler one. Obviously the method is more suitable for the
problems that are less sensitive to the shape of the PDF, like the one presented in this
example. Selecting an appropriate perturbation size may compensate, to some extent, for
the error introduced by simplifying the PDFs.
Both the FOSM and IFOSM methods are sensitive to the size of the perturbation.
Therefore, it is important that before actually applying these methods to practical
problems an appropriate size of the perturbation must be selected. This problem has been
discussed in the literature but the recommendations differ according to the nature of the
cases. For example, Morgan and Henrion (1990) suggested a perturbation comparable to
the range of variation; Haldar and Mahadevan (2000a) adopted a perturbation equal to
the standard deviation of the variable, and Haldar and Mahadevan (2000b) suggested a
perturbation equal to one tenth of the standard deviation in a particular problem of solid
mechanics. Obviously, the best value of the perturbation varies from case to case. Several
experiments carried out with this flood forecasting model show that the best value of the
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. Generally the IFOSM method gives better results for large perturbation
ratios, because the approximate function becomes smoother when the three points used
for the second degree reconstruction are taken further apart. Conversely, the slopes and
curvature of the approximate parabolic function can be very large when the perturbation
ratio is very small. Therefore, the IFOSM method is best-suited for long-term forecasts.
It is however 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. This
has particular advantages in the problem of real time application, including flood
forecasting, where a decision has to be made in a very short time. The MC method
requires a large number of model runs depending on the complexity of the model and the
level of accuracy anticipated. The IFOSM method, if calibrated properly for the
perturbation size, can generate results as good as the MC method for a greatly reduced
computational effort.