Geoscience Reference
In-Depth Information
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Figure 4.11
The structure of a neural network showing input nodes, output nodes and a single layer of hidden
nodes; each link is associated with at least one coefficient (which may be zero).
input signal (here we are interested in inputs comprising rainfall and past discharge measurements) to an
output signal (current or future discharge) by means of a series of weighting functions that may involve
a number of layers of interconnected nodes, including intermediate “hidden layers” (Figure 4.11). Some
applications have used additional filtering functions (essentially simple transfer functions) for each node
in a hidden layer, so that the outputs also depend on the form and parameterisation of these functions. A
variety of techniques are available for determining the appropriate model structure and weights given a
learning set
of input and output data.
The advantage of the ANN approach is that it provides a framework for reflecting complexities and
nonlinearities in the data (in so far as that is possible given the available input variables). The structure
of the resulting neural network should, therefore, reflect some characteristic processes for a particular
catchment (in the same way as the nonlinear input filter and transfer function of the DBM approach).
There is, then, an interesting question as to how far the calibrated neural network can be interpreted to
provide information about the dominant processes in a catchment. Jain
et al.
(2004) related weights on
the hidden nodes of an ANN runoff model to process interpretations, albeit for a network with only a
small number of links.
There are clear analogies between the neural network weights and the parameters of other modelling
approaches, and between the learning set and what we have before called a period of calibration data.
Work in neural networks often does not draw upon this analogy but it is a useful one in that, just as an
increase in the number of parameters gives a model more degrees of freedom in calibration but may result
in overparameterisation with respect to information in the data set, so in a neural network an increase in
the number of layers, nodes and interconnections also results in more degrees of freedom in fitting the
learning set, also with the possibility of overparameterisation.
Many studies of the rainfall-runoff problem using neural network techniques have now been published
(e.g. Lek
et al.
, 1996; Minns and Hall, 1996; Dawson and Wilby, 1998; Fernando and Jayawardena,
1998; Tokar and Johnson, 1999; Campolo
et al.
, 1999; Chibanga
et al.
, 2003). For the most part, these
models have been produced for the purposes of N-step ahead forecasting rather than simulation over
long periods. The availability of previous water level or discharge data as an input to the neural net
is generally important to the success of such modelling since it allows some of the nonlinearity of the
rainfall-runoff process to be reflected in the net for short-term forecasting. An interesting application
is that of Campolo
et al.
(2003), using a neural net based on multiple rainfall, discharge and power
production inputs to demonstrate good performance in up to six-hour-ahead forecasts for the 4000 km
2
Arno catchment in Italy (Figure 4.12). In forecasting, neural network models can also be used in the
same way as transfer functions to forecast downstream river levels or discharges given some upstream
data (e.g. Thirumalaiah and Deo, 1998). One study has used neural networks to predict the two-year
