FLOOD FORECASTING MODELS AND UNCERTAINY REPRESENTATION - Modelling Uncertainty in Flood Forecasting Systems - page 12

include the Sacramento model (Burnash et al., 1973), the NAM model (Nielsen and
Hansen, 1973), TOPMODEL (Beven and Kirkby, 1979; see also Beven et al, 1995), the
TANK model (Sugawara et al., 1983), and so on.
The empirical models, on the other hand, relate input to the output assuming a very
general relationship between the input and the output with little or no attempt to identify
the physical processes involved. The empirical models are also referred to as system-
theoretical models (Lettermann, 1991). Most of the unit hydrograph methods originally
introduced by Sherman (1932) are widely used examples of empirical models. Although
the derivation of this type of models is purely empirical the selection of the input-output
parameters are, by and large, dictated by some physical understanding of the processes.
The conceptual and empirical models are normally lumped models in the sense that
they use spatially averaged input data and parameters values. However, such models can
be applied as semi-distributed models by dividing the catchments in to an appropriate
number of sub-catchments.
2.1.3 Data-driven models
The basic idea of data-driven modelling techniques is to work with data only on the
'boundaries' of the domain where data are given, and to find a form of relationship(s) that
best connects specific data sets (Price, 2002). The relationships can take a form that has
little or nothing to do with the physical principles of the underlying processes.
Traditionally the simplest of these models is the linear regression model. Nowadays there
exists a host of nonlinear and sophisticated data-driven techniques, such as artificial
neural networks (ANN), fuzzy rule-based systems (Bardossy and Duckstein, 1995), fuzzy
regression (Bardossy et al., 1990), genetic programming (GP), support vector mechanics,
etc (see, for example, Solomatine, 2002). Over the last decade some of these techniques
have been used extensively, particularly in research, for water resources predictions,
including rainfall-runoff modelling. Advantages of data-driven models are reported
elsewhere (see, for example, Dawson and Wilby, 1998; Gautam and Holz, 2001; Dibike,
2002). The application of these relatively new techniques in operational forecasting
systems is, however, still in an early stage.
2.1.4 Flood forecasting models vis-à-vis uncertainty analysis
Every model is, by definition, an approximation to reality (Price, 2002). A common
feature of all these models (whether they be physically based or conceptual or
data-driven) therefore, is that predictions from these models are far from being exact and
they suffer from different degrees of uncertainty. Therefore, uncertainty quantification of
the model result is essential, which is the subject of the present research. Uncertainty
analysis is a well accepted procedure in the first two categories (physically based and
conceptual and empirical) of model, although many operational flood forecasting systems
may not have components for uncertainty analysis. Normally, increasing the complexity
of the model, which generally means using more detailed mathematical representation of
the physical processes, decreases uncertainty in the model output due to the lack of
knowledge or incompleteness in conceptualising the real system (see Subsection 2.2.2 for
sources of uncertainty). In this sense, model uncertainty should in principle decrease as