Geology Reference
In-Depth Information
Systems (ANFIS), Auto-Regressive Moving Average with Exogenous Inputs
(ARMAX), Support vector machines (SVM) are other system theoretic approaches
widely applied to map relation between rainfall and runoff [
16
,
23
,
25
]. Nourani
et al. [
17
] surveyed different wavelet based hybrid arti
cial models in hydrology.
However some unsolved questions in data driven models including ANNs are (i)
what architecture (hidden layer nodes) (ii) what input vector and (iii) what training
length of input vector should be used in the modelling process to obtain accurate
modelling results. Some empirical or analytical approaches could be used externally
in data based models to determine the above mentioned issues related to the
structure of the model. Sudheer et al. [
21
] applied a standard algorithm for training
to determine the inputs for multivariate ANN models employing data from a river
basin in India. Similarly Maier and Dandy [
12
] applied Haugh and Box and a new
neural network-based approach can be used to identify the inputs. The aim of this
chapter is to outline several input selection procedures based on pre-processing of
the input space. Kourentzes [
10
] highlighted that there is not a rigorous empirical
evaluation of input selection methodologies in data bases (especially ANNs) in the
field of forecasting. May et al. [
14
] suggests that ANNs are often developed without
due consideration on the effect of input choices in modelling and reviewed algo-
rithms based input selection tasks. May et al. [
15
] introduced an input variable
selection algorithm, based on estimation of partial mutual information for ANN
modelling.
There is a general misconception that data based models, especially ANNs, have
high
flexibility and ability to handle redundancy in any modelling situation;
whereas these scenarios may affect the modelling capabilities (e.g. over
tting,
modelling time, calibration process and accuracy) considerably. In this chapter, we
use statistical data learning approaches like Gamma Test, Entropy theory, AIC and
BIC externally to avoid modelling issues such as model complexity, learning dif-
ficulties. This chapter employs models like ANNs, ANFISs, SVMs, wavelet based
W-ANN, W-ANFIS and W-SVMs to map rainfall runoff dynamics in a catchment.
The study is illustrated in Beas basin meteorological data sets and subsequently
different data driven models are applied to the data sets.
6.2 Study Area: Brue Catchment
In this chapter we have used a 7-year time series of 15-min rainfall from the average
of rain gauge network in the Brue catchment. The 15 min precipitation data is
aggregated to other data frequencies including daily data for data based modelling.
The 7 year monthly average precipitation and runoff measured at Brue catchment is
shown in the Fig.
6.1
. The time series showing variations in daily rainfall and runoff
for 1994
-
2000 periods is shown in the Fig.
6.2
.
