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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

Abstract

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.

Keywords

Wavelet Extreme learning machine Drought model Effective drought index Forecasting 

List of symbols

ACF

Autocorrelation function

ANN

Artificial neural network

BOM

Bureau of Meteorology

c

Y-intercept of linear function

CWT

Continuous wavelet transformation

DI

Drought index

DWC

Discrete wavelet coefficients

DWT

Discrete wavelet transformation

EDI

Effective drought index

EDIo

Observed (calculated) EDI

EDIp

Forecasted (predicted) EDI

ELM

Extreme learning machine

EMD

Empirical mode decomposition

ENS

Nash–Sutcliffe coefficient

FFBP

Feed-forward back-propagation

LSSVR

Least squares support vector regression

υ

Gradient of linear function

MAE

Mean absolute error

MPE

Mean P E

MSE

Mean square error

P

Precipitation

PACF

Partial autocorrelation function

Pdv

Peak percentage deviation

PE

Effective precipitation

|PE|

Absolute prediction error

R2

Coefficient of determination

RBF

Radial basis function

RCP

Representative concentration pathway

RDDI

Rainfall-decile drought index

RMSE

Root mean square error

SLFN

Single layer feed-forward network

SPE

Standard deviation of P E

SPI

Standardized precipitation index

SSA

Singular spectrum analysis

SVM

Support vector machines

SVR

Support vector regression

VC

Vapnik–Chervonenkis

W-ANN

Wavelet-based ANN

WI

Willmott’s index

W-ELM

Wavelet-based ELM

W-LSSVR

Wavelet-based LSSVR

Notes

Acknowledgments

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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