APPLICATION: FLOOD FORECASTING MODEL FOR LOIRE RIVER (FRANCE) - Modelling Uncertainty in Flood Forecasting Systems - page 116

The assumption of a constant celerity c (and consequently of a constant propagation
time T ) is obviously a major limitation of the model, because in reality the wave
propagation speed is related to the flow rate (see, for example, Cunge et al., 1980). As
acknowledged by the users of the model, the value of T can only be indicative, based on
experience and typical values assessed in the past. The value of T particularly influences
the arrival time of the flood, which consequently may give rise to an inaccurate flood
estimate for each forecast. In flood crisis management it is also very important to know
the time available (e.g. for evacuation or for any safety measures to be taken) before the
flood level reaches a given level and the time the flood level will remain above the given
threshold. Consequently, there was a strong need for an uncertainty analysis in T .
In this study the uncertainty in the forecasts from the model is analysed using the
probability theory based FOSM method and the fuzzy set theory and expert judgement
-based qualitative method. The IFOSM method detailed in Section 4.2 is also applied to
this model.
For the application of the FOSM method only the parameter uncertainty (in the rating
curve conversion and in the propagation) is considered. The input uncertainty in the
water level measurements is ignored assuming it is insignificant, and the “other sources”
of uncertainty are excluded as they are beyond the scope of the FOSM framework. In the
application of the qualitative approach based on expert judgement, all four sources of
uncertainty listed above are assessed. The applications of the FOSM and IFOSM
methods are presented in Sections 6.2 and 6.3, respectively, and the application of the
qualitative method is reported in Section 6.4.
6.2 Uncertainty analysis using the FOSM method
Methods of uncertainty estimation based on probability and fuzzy set theory are
presented in Chapter 3. The FOSM method is one of the widely used probability
theory-based method for uncertainty propagation through a model. The FOSM method
propagates only the moments of the distribution, and therefore does not require
information about the complete distribution of the parameters. This characteristic of the
FOSM method makes it suitable to apply to the Loire model. The uncertainty in the
forecasted water level from the Loire model due to the parameters of the flow
propagation and rating curve conversions is analysed. The river reach between Givry and
Orleans is considered, which is subdivided into 2 reaches: Givry to Gien and Gien to
Orleans. The results of the uncertainty assessment presented here are for the water levels
at the station Orleans.
6.2.1 Description of data
The flow propagation time T between any two consecutive stations is the parameter for
the propagation model. Very limited information is available about the estimates of
propagation time between any two stations and therefore the actual shape of the PDF of
T is unknown. From the experience of the users of the model, three different values of T
(minimum, most likely and maximum) are assessed corresponding, respectively, to
typical low, medium and high discharges experienced in the past. From this information,