Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model

  • Ravinesh C. Deo
  • Mukesh K. Tiwari
  • Jan F. Adamowski
  • John M. Quilty
Original Paper


A drought forecasting model is a practical tool for drought-risk management. Drought models are used to forecast drought indices (DIs) that quantify drought by its onset, termination, and subsequent properties such as the severity, duration, and peak intensity in order to monitor and evaluate the impacts of future drought. In this study, a wavelet-based drought model using the extreme learning machine (W-ELM) algorithm where the input data are first screened through the wavelet pre-processing technique for better accuracy is developed to forecast the monthly effective DI (EDI). The EDI is an intensive index that considers water accumulation with a weighting function applied to rainfall data with the passage of time in order to analyze the drought-risk. Determined by the autocorrelation function (ACF) and partial ACFs, the lagged EDI signals for the current and past months are used as significant inputs for 1 month lead-time EDI forecasting. For drought model development, 97 years of data for three hydrological stations (Bathurst Agricultural, Wilsons Promontory and Merredin in Australia) are partitioned in approximately 90:5:5 ratios for training, cross-validation and test purposes, respectively. The discrete wavelet transformation (DWT) is applied to the predictor datasets to decompose inputs into their time–frequency components that capture important information on periodicities. DWT sub-series are used to develop new EDI sub-series as inputs for the W-ELM model. The forecasting capability of W-ELM is benchmarked with ELM, artificial neural network (ANN), least squares support vector regression (LSSVR) and their wavelet-equivalent (W-ANN, W-LSSVR) models. Statistical metrics based on agreement between the forecasted and observed EDI, including the coefficient of determination, Willmott’s index, Nash–Sutcliffe coefficient, percentage peak deviation, root-mean-square error, mean absolute error, and model execution time are used to assess the effectiveness of the models. The results demonstrate enhanced forecast skill of the drought models that use wavelet pre-processing of the predictor dataset. Based on statistical measures, W-ELM outperformed traditional ELM, LSSVR, ANN and their wavelet-equivalent counterparts (W-ANN, W-LSSVR). It is found that the W-ELM model is computationally efficient as shown by a faster running time with the majority of forecasting errors in lower frequency bands. The results demonstrate the usefulness of W-ELM over W-ANN and W-LSSVR models and the benefits of wavelet transformation of input data to improve the performance of drought forecasting models.


Wavelet Extreme learning machine Drought model Effective drought index Forecasting 

List of symbols


Autocorrelation function


Artificial neural network


Bureau of Meteorology


Y-intercept of linear function


Continuous wavelet transformation


Drought index


Discrete wavelet coefficients


Discrete wavelet transformation


Effective drought index


Observed (calculated) EDI


Forecasted (predicted) EDI


Extreme learning machine


Empirical mode decomposition


Nash–Sutcliffe coefficient


Feed-forward back-propagation


Least squares support vector regression


Gradient of linear function


Mean absolute error


Mean P E


Mean square error




Partial autocorrelation function


Peak percentage deviation


Effective precipitation


Absolute prediction error


Coefficient of determination


Radial basis function


Representative concentration pathway


Rainfall-decile drought index


Root mean square error


Single layer feed-forward network


Standard deviation of P E


Standardized precipitation index


Singular spectrum analysis


Support vector machines


Support vector regression




Wavelet-based ANN


Willmott’s index


Wavelet-based ELM


Wavelet-based LSSVR



The research paper utilised precipitation data from Australian Bureau of Meteorology. USQ Academic Division funded Dr. RC Deo through a “Research Activation Incentive Scheme (RAIS, July–September 2015)” for collaboration with McGill and Anand Agricultural University. Dr. RC Deo, as Senior Visiting Scholar, also held an Endeavour Executive Fellowship (4293-2015) funded by Australian Government Department of Education. Finally we thank both reviewers, journal Editors and McGill MSc student Sasha Rodrigues whose comments have enhanced the integrity of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ravinesh C. Deo
    • 1
  • Mukesh K. Tiwari
    • 2
  • Jan F. Adamowski
    • 3
  • John M. Quilty
    • 3
  1. 1.School of Agricultural Computational and Environmental Sciences, International Centre of Applied Climate Sciences (ICACS)University of Southern QueenslandSpringfieldAustralia
  2. 2.Department of Soil and Water Engineering, College of Agricultural and TechnologyAnand Agricultural UniversityAnandIndia
  3. 3.Department of Bioresource Engineering, Faculty of Agricultural and Environmental ScienceMcGill UniversityMontrealCanada

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