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Improving Forecasting Accuracy of Annual Runoff Time Series Using ARIMA Based on EEMD Decomposition

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Abstract

Hydrological time series forecasting is one of the most important applications in modern hydrology, especially for effective reservoir management. In this research, the auto-regressive integrated moving average (ARIMA) model coupled with the ensemble empirical mode decomposition (EEMD) is presented for forecasting annual runoff time series. First, the original annual runoff time series is decomposed into a finite and often small number of intrinsic mode functions (IMFs) and one residual series using EEMD technique for a deep insight into the data characteristics. Then each IMF component and residue is forecasted, respectively, through an appropriate ARIMA model. Finally, the forecasted results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original annual runoff series. Three annual runoff series from Biuliuhe reservoir, Dahuofang reservoir and Mopanshan reservoir, in China, are investigated using developed model based on the four standard statistical performance evaluation measures (RMSE, MAPE, R and NSEC). The results obtained in this work indicate that EEMD can effectively enhance forecasting accuracy and that the proposed EEMD-ARIMA model can significantly improve ARIMA time series approaches for annual runoff time series forecasting.

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References

  • Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Stat Math 21(1):243–247

    Article  Google Scholar 

  • Awan J, Bae D-H (2014) Improving ANFIS based model for long-term dam inflow prediction by incorporating monthly rainfall forecasts. Water Resour Manag 28(5):1185–1199

    Article  Google Scholar 

  • Box GEP, Jenkins GM (1976) Times series analysis -forecasting and control. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis: forecasting and control, 3rd edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Burlando P, Rosso R, Cadavid LG, Salas JD (1993) Forecasting of short-term rainfall using ARMA models. J Hydrol 144(1–4):193–211

    Article  Google Scholar 

  • Chan WS (1999) A comparison of some of pattern identification methods for order determination of mixed ARMA models. Stat Probab Lett 42(1):69–79

    Article  Google Scholar 

  • Chen H, Rao A (2002) Testing hydrologic time series for stationarity. J Hydrol Eng 7(2):129–136

    Article  Google Scholar 

  • Cheng C-T, Xie J-X, Chau K-W, Layeghifard M (2008) A new indirect multi-step-ahead prediction model for a long-term hydrologic prediction. J Hydrol 361(1–2):118–130

    Article  Google Scholar 

  • Coughlin KT, Tung KK (2004) 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Adv Space Res 34(2):323–329

    Article  Google Scholar 

  • Dawson CW, Abrahart RJ, See LM (2007) HydroTest: a web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ Model Softw 22(7):1034–1052

    Article  Google Scholar 

  • Debert S, Pachebat M, Valeau V, Gervais Y (2011) Ensemble-empirical-mode-decomposition method for instantaneous spatial-multi-scale decomposition of wall-pressure fluctuations under a turbulent flow. Exp Fluids 50(2):339–350

    Article  Google Scholar 

  • Elliott G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64(4):813–836

    Article  Google Scholar 

  • Gideon S (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  Google Scholar 

  • Guo Z, Zhao W, Lu H, Wang J (2012) Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model. Renew Energy 37(1):241–249

    Article  Google Scholar 

  • Hu T, Wu F, Zhang X (2007) Rainfall-runoff modeling using principal component analysis and neural network. Nord Hydrol 38(3):235–248

    Article  Google Scholar 

  • Huang NE, Wu Z (2008) A review on Hilbert-Huang transform: method and its applications to geophysical studies. Rev Geophys 46(2), RG2006. doi:10.1029/2007RG000228

    Google Scholar 

  • Huang NE, Shen Z, Long SR, Wu MLC, Shih HH, Zheng QN, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc London Ser A Math Phys Eng Sci 454(1971):903–995

    Article  Google Scholar 

  • Huang NE, Wu ML, Long SR, Shen SSP, Qu W, Gloersen P, Fan KL (2003) A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc R Soc London Ser A Math Phys Eng Sci 459(2037):2317–2345

    Article  Google Scholar 

  • Huang Y, Schmitt FG, Lu Z, Liu Y (2009) Analysis of daily river flow fluctuations using empirical mode decomposition and arbitrary order Hilbert spectral analysis. J Hydrol 373(1–2):103–111

    Article  Google Scholar 

  • Jain A, Kumar AM (2007) Hybrid neural network models for hydrologic time series forecasting. Appl Soft Comput 7(2):585–592

    Article  Google Scholar 

  • Karthikeyan L, Nagesh Kumar D (2013) Predictability of nonstationary time series using wavelet and EMD based ARMA models. J Hydrol 502:103–119

    Article  Google Scholar 

  • Karunanithi N, Grenney WJ, Whitley D, Bovee K (1994) Neural networks for river flow prediction. J Comput Civ Eng ASCE 8(2):201–220

    Article  Google Scholar 

  • Koutroumanidis T, Sylaios G, Zafeiriou E, Tsihrintzis VA (2009) Genetic modeling for the optimal forecasting of hydrologic time-series: application in Nestos River. J Hydrol 368(1–4):156–164

    Article  Google Scholar 

  • Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241

    Article  Google Scholar 

  • Lei Y, He Z, Zi Y (2009) Application of the EEMD method to rotor fault diagnosis of rotating machinery. Mech Syst Signal Process 23(4):1327–1338

    Article  Google Scholar 

  • Li M, Chen SY (2008) Runoff forecasting approximate reasoning method with single factor based on variable fuzzy set theory. J Dalian Univ Technol 48(4):587–590

    Google Scholar 

  • McLeod AI, Hipel KW, Lennox WC (1977) Advances in Box-Jenkins modeling: 2. Applications. Water Resour Res 13(3):577–586

    Article  Google Scholar 

  • Mohammadi K, Eslami HR, Kahawita R (2006) Parameter estimation of an ARMA model for river flow forecasting using goal programming. J Hydrol 331(1–2):293–299

    Article  Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • Noori R et al (2011) Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction. J Hydrol 401(3–4):177–189

    Article  Google Scholar 

  • Pekárová P, Miklánek P, Pekár J (2003) Spatial and temporal runoff oscillation analysis of the main rivers of the world during the 19th–20th centuries. J Hydrol 274(1–4):62–79

    Article  Google Scholar 

  • Pektaş AO, Kerem Cigizoglu H (2013) ANN hybrid model versus ARIMA and ARIMAX models of runoff coefficient. J Hydrol 500:21–36

    Article  Google Scholar 

  • Salas JD, Delleur JW, Yevjevich VM, Lane WL (1980) Applied modeling of hydrologic time series. Water Resources Publications, Littleton

    Google Scholar 

  • Sang Y-F, Wang Z, Liu C (2012) Period identification in hydrologic time series using empirical mode decomposition and maximum entropy spectral analysis. J Hydrol 424–425:154–164

    Article  Google Scholar 

  • Shibata R (1976) Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika 63(1):117–126

    Article  Google Scholar 

  • Shiri J, Kisi O (2010) Short-term and long-term streamflow forecasting using a wavelet and neuro-fuzzy conjunction model. J Hydrol 394(3–4):486–493

    Article  Google Scholar 

  • Spolia SK, Chander S (1974) Modelling of surface runoff systems by an ARMA model. J Hydrol 22(3–4):317–332

    Article  Google Scholar 

  • Srikanthan R, McMahon TA (1999) Stochastic generation of annual, monthly and daily climate data: a review. Hydrol Earth Syst Sci 5(4):653–670

    Article  Google Scholar 

  • Stedinger JR, Lettenmaier DP, Vogel RM (1985) Multisite ARMA(1,1) and disaggregation models for annual streamflow generation. Water Resour Res 21(4):497–509

    Article  Google Scholar 

  • Turan M, Yurdusev M (2014) Predicting monthly river flows by genetic fuzzy systems. Water Resour Manag 28(13):4685–4697

    Article  Google Scholar 

  • Vahabie HA, Yousefi MMR, Araabi, BN, Lucas C, Barghinia S (2007) Combination of singular spectrum analysis and autoregressive model for short term load forecasting. Power Tech, IEEE Lausanne, pp. 1090–1093

  • Valipour M (2012) Parameters estimate of autoregressive moving average and autoregressive integrated moving average models and compare their ability for inflow forecasting. J Math Stat 8(3):330–338

    Article  Google Scholar 

  • Valipour M, Banihabib ME, Behbahani SMR (2013) Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J Hydrol 476:433–441

    Article  Google Scholar 

  • Wang W, Van Gelder PHAJM, Vrijling JK, Ma J (2005) Testing and modelling autoregressive conditional heteroskedasticity of streamflow processes. Nonlinear Process Geophys 12(1):55–66

    Article  Google Scholar 

  • Wang W-C, Chau K-W, Cheng C-T, Qiu L (2009) A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. J Hydrol 374(3–4):294–306

    Article  Google Scholar 

  • Wang WC, Xu DM, Chau KW, Yu CS (2013) Improved annual rainfall-runoff forecasting using PSO–SVM model based on EEMD. J Hydroinf 15(4):1377–1390

    Google Scholar 

  • Weeks WD, Boughton WC (1987) Tests of ARMA model forms for rainfall-runoff modelling. J Hydrol 91(1–2):29–47

    Article  Google Scholar 

  • Williams G (1961) Cyclical variations in world-wide hydrologic data. J Hydraul Div 87(6):71–88

    Google Scholar 

  • Wu CL, Chau KW (2010) Data-driven models for monthly streamflow time series prediction. Eng Appl Artif Intell 23(8):1350–1367

    Article  Google Scholar 

  • Wu CL, Chau KW (2011) Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. J Hydrol 399(3–4):394–409

    Article  Google Scholar 

  • Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1(1):1–41

    Article  Google Scholar 

  • Wu JD, Tsai YJ (2011) Speaker identification system using empirical mode decomposition and an artificial neural network. Expert Syst Appl 38(5):6112–6117

    Article  Google Scholar 

  • Wu CL, Chau KW, Fan C (2010) Prediction of rainfall time series using modular artificial neural networks coupled with data-preprocessing techniques. J Hydrol 389(1–2):146–167

    Article  Google Scholar 

  • Xu J, Chen Y, Li W, Nie Q, Song C, Wei C (2014) Integrating wavelet analysis and BPANN to simulate the annual runoff with regional climate change: a case study of Yarkand River, Northwest China. Water Resour Manag 28(9):2523–2537

    Article  Google Scholar 

  • Yarar A (2014) A hybrid wavelet and neuro-fuzzy model for forecasting the monthly streamflow data. Water Resour Manag 28(2):553–565

    Article  Google Scholar 

  • Yu L, Wang S, Lai KK (2008) Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm. Energy Econ 30(5):2623–2635

    Article  Google Scholar 

  • Zhang X, Lai KK, Wang SY (2008) A new approach for crude oil price analysis based on empirical mode decomposition. Energy Econ 30(3):905–918

    Article  Google Scholar 

  • Zhang J, Yan R, Gao RX, Feng Z (2010) Performance enhancement of ensemble empirical mode decomposition. Mech Syst Signal Process 24(7):2104–2123

    Article  Google Scholar 

  • Zhang Q, Wang B-D, He B, Peng Y, Ren M-L (2011) Singular spectrum analysis and ARIMA hybrid model for annual runoff forecasting. Water Resour Manag 25(11):2683–2703

    Article  Google Scholar 

  • Zhou H-C, Peng Y, Liang G-H (2008) The research of monthly discharge predictor-corrector model based on wavelet decomposition. Water Resour Manag 22(2):217–227

    Article  Google Scholar 

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Acknowledgments

This research was supported by Central Research Grant of Hong Kong Polytechnic University (4-ZZAD), Program for Science & Technology Innovation Talents in Universities of Henan Province (13HASTIT034), Science and technology innovation team in Colleges and universities in Henan Province (14IRTSTHN028) and the foundation for University Backbone Teacher of Henan Province (2012GGJS-099). We gratefully acknowledge the thorough and insightful comments by the editor and anonymous reviewers.

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Authors and Affiliations

  1. Department of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou, 450011, People’s Republic of China

    Wen-chuan Wang & Dong-mei Xu

  2. Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China

    Kwok-wing Chau & Xiao-Yun Chen

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  1. Wen-chuan Wang
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Correspondence to Kwok-wing Chau.

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Wang, Wc., Chau, Kw., Xu, Dm. et al. Improving Forecasting Accuracy of Annual Runoff Time Series Using ARIMA Based on EEMD Decomposition. Water Resour Manage 29, 2655–2675 (2015). https://doi.org/10.1007/s11269-015-0962-6

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