CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 48

Chapter 4
CONTRIBUTION OF PRESENT
RESEARCH TO UNCERTAINTY
ASSESSMENT METHODS
Summary of Chapter 4
This chapter presents the original contributions of the present research
to the development of uncertainty assessment methods. Firstly, an
uncertainty assessment methodology using temporal disaggregation is
presented. It aims to estimate the uncertainty in model output from the
uncertainty in time series inputs. Three forms of uncertainty are
considered: (i) uncertainty due to the temporal structure of the time
series, (ii) uncertainty due to the spatial structure of the time series, and
(iii) uncertainty due to the observed or forecasted magnitude of the
input. Two algorithms are presented to implement the method in the
frameworks of the fuzzy Extension Principle and the Monte Carlo
simulation. The second contribution consists of an Improved
First-Order Second Moment (IFOSM) method, which is derived using
a second-order reconstruction of the model function. The improved
method aims to correct the undesirable behaviour of the conventional
FOSM method near extrema. The third contribution consists in
developing qualitative uncertainty scales for the mapping of qualitative
uncertainty estimated by the fuzzy set theory and expert
judgement-based method presented in Chapter 3. Fourthly, the results
of the investigation on hybrid approaches of modelling uncertainty and
probability-possibility (fuzzy) transformations are presented. The
differences and similarities in operation between random-random and
fuzzy-fuzzy variables are particularly explored. It is showed that the
addition and multiplication of two fuzzy variables by the Extension
Principle using the ! -cut method is similar to corresponding operations
between two functionally dependent random variables for some
specific conditions. It also provides an alternative method for the
evaluation of the Extension Principle for a monotonic function without
using the &-cut method. A transformation that is applicable in such
cases is derived and illustrated by an example.
4.1 Uncertainty assessment methodology using temporal disaggregation
In water systems modelling, some of the forcing may be observed with a period larger
than the typical reaction time of the catchment. A typical example is rainfall measured or
forecasted on an hourly basis when the catchment response time is half an hour. In this