CONCLUSIONS AND RECOMMENDATIONS - Modelling Uncertainty in Flood Forecasting Systems - page 134

from flood forecasting and warning systems. Even with the lack of risk-based flood
warning procedures, quantifying uncertainty provides additional information about the
forecasts and helps decision makers to use their own judgement more appropriately.
7.1.2 Theories and methods for modelling uncertainty
In uncertainty representation and modelling, probability theory and relatively recently
fuzzy set theory (including fuzzy measures or possibility theory) have had the widest
application. In flood forecasting, however, the application of theories other than
probability are so far insignificant. The applications of fuzzy set theory in other fields of
engineering have demonstrated its potential in modelling uncertainty (Schulz and Huwe,
1997 & 1999; Guyonnet et al., 1999; Revelli and Ridolfi, 2002). This research has
extended the use of fuzzy set theory in flood forecasting. The successful implementation
of the uncertainty assessment methodology using temporal disaggregation of time series
inputs developed during this research showed the potential applicability of the fuzzy set
approach in flood forecasting.
The probability theory-based methods like MC and FOSM are the most widely used
and useful tools for uncertainty modelling. The use of the fuzzy Extension Principle
(fuzzy set theory-based method) is also growing. The FOSM method propagates only the
central values of the uncertain variables and requires less computational time. Unlike the
FOSM method, both the MC method and the fuzzy EP propagate the complete functions
representing the uncertainty in the variables. The computational requirements of the MC
method and the EP are also comparable. The differences between the MC method and the
EP are also significant. In the MC method, the scenarios that combine low probability
parameter values have less chance of being randomly selected; whereas, in the EP all
possible combinations of parameter 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 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. Another important distinction between the MC method and the EP is the
correlation between the parameters. The MC method allows the effects of correlation
between the parameters to be accounted for. In contrast, the current state of knowledge
about the EP does not allow the incorporation of the effect of the correlation between the
input parameters.
7.1.3 Disaggregation of time series inputs for uncertainty assessment
As a part of this research, a methodology is developed which uses temporal
disaggregation of time series inputs for uncertainty assessment. This methodology
explicitly considers the uncertainty in the time series inputs in the form of a probability
distribution or fuzzy membership function. The important characteristics of this approach
are that (i) it can be used with both MC method (for the probabilistic approach) and with
the EP (for the fuzzy approach), and (ii) it is independent of the structure of the
forecasting model. In other words, it can be used with any rainfall-runoff-routing type of
deterministic model. The methodology is applied to the flood forecasting model of