ABSTRACT

1
Application of Conjunctive Nonlinear Model Based
on Wavelet Transforms and Artificial Neural
Networks to Drought Forecasting Abrishamchi,
A.1, Mehdikhani, H.1, Tajrishy, M1, Marino,
M.A.2, Abrishamchi, A2 1. Dept. of
Civil Engr., Sharif University of Technology,
Azadi Ave., Tehran, Iran. 2. Dept. of
Civil and Environmental Engr., University of
California, Davis, One Shields Avenue, Davis, CA
95616.
Case study Study area The study region is
Zayandeh-Rood reservoir river basin, with 5,000
km2 area in central part of Iran. Existence of
Zayandeh-Rood reservoir dam and of extended
agricultural area in this study region cause
drought forecasting play important role in
reduction of drought damages in that
region. Drought forecasting The length of
available records at these stations is from
October 1971 to September 2003. SPI and EDI
Drought indices for selected stations calculated
on the basis of these rainfall data. In this
study, first, original EDI (effective drought
indices) time series for all stations are
decomposed into the sub-time series at the
resolution level 1 and 2 by á trous Wavelet
transform algorithm with low-pass filter B3
spline. Then, ANN models are constructed. A
three-layer network- input layer, hidden layer
and output layer- is adopted here. The weight
parameters of network are estimated by
self-adapted BP algorithm. The number of training
of WNN is 20,000. Eventually, original EDI time
series are reconstructed using the forecasted
sub-time series. One of the most important
prerequisites for and steps in application of the
ANN is the selection of effective inputs (Yapo et
al., 1996) . In this study, over 22 different
input models with compositions of monthly EDI
sub-time series, precipitation and SPI time
series have been tested for 1,3,6 and 9 -month
forecasting. For selection of input models,
correlation coefficients between inputs are
calculated. For calibration and verification of
the models phases, first 26 years of data are
used for calibration/training, and the remaining
6 years are used for verification/testing
purposes. R2 , RMSE and NMSE criteria were used
as measures of forecast accuracy.
Results of forecasting models The forecast lead
times were 1, 3, 6 and 9 months, since it is the
medium and the long-range forecasts that are
critical for drought preparedness. We restrict
the discussion and illustrations to the results
of Chelgerd station (Fig. 1). Tables 1 to 4 show
comparisons between ANN, WNN-1 (Wavelet Network
Models at resolution 1) and WNN-2 models. As
Figure 1 shows that the WNN-2 models improve the
forecast accuracy.
ABSTRACT Drought is a creeping phenomenon and a
natural normal part of the climate that occurs
over different time periods and at various scales
and may cause significant economic,
environmental, and social damages. Drought
forecasting plays an important role in the
control and management of water resources systems
and mitigation of economic, environmental and
social impacts of drought. This poster presents a
new conjunctive nonlinear model using Wavelet
Transforms and Artificial Neural Network. It
plays an important role in improving the accuracy
of 1, 3, 6 and 9 months ahead forecasting of EDI
time series. The overall forecast accuracy of the
conjunction model is measured by R2, RMSE and
NMSE. The results indicate that the conjunctive
model significantly improves the ability of
artificial neural networks for 1, 3, 6 and 9
months drought forecasting in Zayandeh-Rood River
basin.
Introduction Drought forecasting plays an
important role in the control and management of
water resources systems and mitigation of
economic, environmental and social impacts of
drought (Mehdikhan and Abrishamchi,
2006). Traditionally, statistical time series
methods, such as simple/multiple regression,
autoregressive moving average (ARMA) and
autoregressive integrated moving average (ARIMA)
models are typical models for forecasting (Tao
and Delleur, 1976 Salas and Boes, 1980
Montanari et al., 1997) . In recent years,
Artificial Neural Network (ANN) has shown a great
ability in forecasting nonlinear and
nonstationary time series in hydrology due to the
highly flexible function estimator that has
self-learning and self-adaptive feature ,
therefore it has been widely applied in the
hydrology and water resource engineering (ASCE,
2000) . In time series forecasting,
decomposition approaches seek to decompose a time
series into its major subcomponents,
deterministic or seasonal components and random
components. Forecasting with using a
decomposition method is often more useful in
providing forecasts and information regarding the
component of a time series than trying to predict
a single pattern (Makridakis et al., 1983) .
Recently wavelet transforms have become a common
tool for analyzing local variation in time series
(Torrence and Compo, 1998) . Wavelet transforms
provide a useful decomposition of a signal, or
time series therefore, hybrid models have been
proposed for forecasting a time series based on a
wavelet transform preprocessing (Shensa, 1992
Aussem and Murtagh, 1997 Mallat, 1998 Wang and
Ding, 2003 Woong and Valdes, 2003 Mehdikhani
and Abrishamchi, 2006) . The purpose of this
study is developing a new conjunctive nonlinear
model for improving forecast accuracy for
regional droughts based on conjunction of Wavelet
transforms and Artificial Neural Network.
Table1. Comparison between best models for
1-month forecasting
Table2. Comparison between best models for
3-month forecasting
Conjunctive forecasting model based on ANN and
Wavelet Transform Artificial neural
networks Artificial neural networks (ANN)
modeling become extremely popular for the
prediction and forecasting of water resources
variables. In ANN, back-propagation algorithm
network models are common to engineer, so called
BP network models that are the feed-forward
artificial neural network structure and a
back-propagation algorithm (BP). It has proved
that BP network model with three-layer is
satisfied for the forecasting and simulating in
the science of water (French et al., 1993
Coulibaly, 2000) . Therefore in this study
three-layer models are used. Wavelet
transform The idea of wavelet preprocessing for
enhancing prediction comes from multi-resolution
analysis provided by wavelet transform (Labat et
al., 2000) . The wavelet transform can decompose
one time series into several time series with
different resolutions which have different levels
of smoothness. The smoother level is more
predictable, whereas the rougher (detailed) level
is less predictable, or more related to
noise. In real world, observed hydrologic time
series are discrete, such as rainstorm process,
flood process, monthly stream flow process, and
daily runoff sequence. So discrete wavelet
transform must be selected for decomposition and
reconstruction of time series. A discrete dyadic
wavelet transform can be computed with a fast
filter bank algorithm called the á trous
algorithm. Therefore, á trous algorithm has
been adopted in this paper. The á trous
algorithm allows the separation of low-frequency
information (approximation, Scale coefficients)
from high-frequency information (wavelet
coefficients) (Dutilleux, 1989 Shensa, 1992
Shensa, 1993 Aussem and Murtagh, 1997 Mallat,
1998 Zheng et al., 1999 Wang and Ding, 2003
Woong and Valdes, 2003 Mehdikhani and
Abrishamchi, 2006).
CONCLUSION This paper presents a new hybrid
wavelet network model. It plays an important role
in improving the accuracy of drought forecasting.
Calibration and verification of the wavelet
network model for drought forecasting in
Zayandeh-Rood reservoir river basin as the case
study have shown the applicability of the method.
For the case of the Zayandeh-Rood river basin,
the overall forecast accuracy of the conjunctive
model, as measured by R2, RMSE and NMSE was
better than conventional ANN prediction model.
Wavelet transform is a useful tool to forecast
time series with capturing the dynamics of
signals with a multi-resolution of decomposition
(As shown in Fig. 1). The conjunctive model can
make valuable forecasts for water management
through wavelet decompositions, when other
forecasting models have limitations due to the
embedded unpredictable components in the time
series. The results show that conjunctive
modeling promotes R2 criteria of 1 month
forecasting from 0.86 (ANN model) to 0.98, for 3
month forecasting from 0.60 (ANN model) to 0.92
(WNN model), for 6 month forecasting from 0.35
(ANN model) to 0.70 (WNN model), and for 9 month
forecasting to 0.50. Therefore, the conjunctive
model significantly improves the ability of
artificial neural networks for 1, 3, 6 and 9
months drought forecasting in Zayandeh-Rood
reservoir river basin.
Table3. Comparison between best models for
6-month forecasting
Table4. Comparison between best models for
9-month forecasting
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