FLOOD FORECASTING MODELS AND UNCERTAINY REPRESENTATION - Modelling Uncertainty in Flood Forecasting Systems - page 13

we move from empirical to conceptual to physically based models. But model uncertainty
is only a part of the total uncertainty. With the increasing complexity of the model, the
number of inputs and parameters increases. If there exists large uncertainty in the inputs
and if the parameters cannot be estimated with high precision, using complex models
does not guarantee less uncertain model results. In physically based models uncertainty
also arises due to the inadequate representation of the geometry and the schematisation of
the processes. In fact, Guinot and Gourbesville (2003) showed that the uncertainty
induced by the schematisation of the processes and of the geometry is much larger than
that induced by the lack of knowledge of the parameters. Moreover, integration of
uncertainty analysis with methods like Monte Carlo in models with a large number of
parameter values and finer discretisation is very expensive in computer time. Beven
(1989) presented more discussions on various issues of uncertainty assessment in
physically based models.
Some of the data-driven techniques, such as the fuzzy rule-based systems and fuzzy
regression, work with imprecise data and implicitly incorporate the uncertainty concept in
modelling. These models however do not have the flexibility of using uncertainty
methods based on other theories (e.g. the most popular probability theory), which is
possible in the first two types of models. In the case of the ANN-based model (most
popular so far of the data-driven techniques), model performance is, by and large,
expressed in a form based on the difference between the observed and model predicted
results using measures such as Root Mean Square Error (RMSE). Markus et al. (2003)
used the entropy measure (Shannon, 1948) to quantify uncertainty in the results of
ANN-based models. Methods for the application of more commonly used uncertainty
assessment techniques, such as those based on probability and fuzzy set theories, are yet
to be investigated for ANN-based models. Without the application of such uncertainty
assessment techniques, the data-driven model forecasts cannot be used in
uncertainty/risk-based decision makings that require all the uncertainties to be expressed
explicitly in probabilistic terms. The uncertainty aspect may be one of the reasons for the
fewer applications of the ANN-based models in operational systems.
2.2 Uncertainty types and sources
A unique definition of uncertainty is hard to find in the literature. It would not be a
surprise if a book on this very subject starts and ends without it being defined (see also
Zimmermann, 1997b). Because uncertainty exists virtually in all situations, its meaning is
conceived as something so obvious. Perhaps what everybody understands by uncertainty
is an antonym of certainty—anything that is not certain is uncertain. Zimmermann (1997a
& b) also defined uncertainty with respect to certainty:
“Certainty implies that a person has quantitatively and qualitatively the
appropriate information to describe, prescribe or predict deterministically and
numerically a system, its behaviour or other phenomena.”
Situations that are not described by the above definition, shall be called uncertainty .
In the context of the present thesis, uncertainty may be thought of as a measure of the
incompleteness of one's knowledge or information about an unknown quantity to be
measured or a situation to be forecast.