APPLICATION: FLOOD FORECASTING MODEL FOR LOIRE RIVER (FRANCE) - Modelling Uncertainty in Flood Forecasting Systems - page 122

showed that the uncertainty in the forecast is generally increasing with an increasing
forecast horizon. These two conclusions are intuitive. Furthermore, it is also shown that
the observed data and the confidence intervals of the estimated uncertainty can be used
to make a reasonable estimate of the uncertainty in some of the inputs, when enough
information is not available.

6.3 Application of the improved FOSM method

The application of the FOSM method to the Loire model presented in Section 6.2 shows
that it can be a good tool for the assessment of uncertainty in flood forecasts in the
absence of detailed information about the uncertainty in the inputs and parameters of the
model. However, in some cases the estimated uncertainty may suffer from the limitations
of the method. The merits and limitations of the FOSM method are discussed in Section
4.2. In particular the limitation of the FOSM method arises from the linearisation of the
model function. One example of this was encountered when applying the method to the
Loire model to assess uncertainty at the station Givry for a specific flow condition. In an
effort to reduce such limitations the IFOSM method is developed and detailed in Chapter
4. The IFOSM method is applied as an alternative to the FOSM method. Since the MC
method can provide values close to the analytical solution, it was used as a standard
method against which results from the FOSM method and the IFOSM method can be
compared.

6.3.1 Description of data

The data of April 1998 flood are used. The uncertainty in the propagation time T for
seven reaches of the Loire River upstream of Givry are considered. Like the previous
example, the only information available about the estimates of the Ts are the minimum,
maximum and the most likely values corresponding respectively to typical low, medium
and high discharges experienced in the past. Therefore, the means and the standard
deviations are derived assuming a triangular PDF based on the minimum, maximum and
most likely values. The estimated properties of the propagation time for various reaches
of the river are presented in Table 6.2.

Table 6.2: Properties of the propagation time T for different river reaches (means and
standard deviations are computed assuming triangular PDFs).

Properties of the propagation time, T (h):
Mean

River reaches

Standard deviation

Villerest-Digoin 14.0 2.04

Digoin-Gilly 4.0 0.61

Gilly-Givry 24.0 3.27

Ebreuil-St. Pourcain 12.0 1.63