Water Resources Management

, Volume 33, Issue 3, pp 955–973 | Cite as

Input Selection of Wavelet-Coupled Neural Network Models for Rainfall-Runoff Modelling

  • Muhammad ShoaibEmail author
  • Asaad Y. Shamseldin
  • Sher Khan
  • Muhammad Sultan
  • Fiaz Ahmad
  • Tahir Sultan
  • Zakir Hussain Dahri
  • Irfan Ali


The use of wavelet-coupled data-driven models is increasing in the field of hydrological modelling. However, wavelet-coupled artificial neural network (ANN) models inherit the disadvantages of containing more complex structure and enhanced simulation time as a result of use of increased multiple input sub-series obtained by the wavelet transformation (WT). So, the identification of dominant wavelet sub-series containing significant information regarding the hydrological system and subsequent use of those dominant sub-series only as input is crucial for the development of wavelet-coupled ANN models. This study is therefore conducted to evaluate various approaches for selection of dominant wavelet sub-series and their effect on other critical issues of suitable wavelet function, decomposition level and input vector for the development of wavelet-coupled rainfall-runoff models. Four different approaches to identify dominant wavelet sub-series, ten different wavelet functions, nine decomposition levels, and five different input vectors are considered in the present study. Out of four tested approaches, the study advocates the use of relative weight analysis (RWA) for the selection of dominant input wavelet sub-series in the development of wavelet-coupled models. The db8 and the dmey (Discrete approximation of Meyer) wavelet functions at level nine were found to provide the best performance with the RWA approach.


Rainfall-runoff modelling Artificial neural network Discrete wavelet transformation Wavelet sub-series 


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Conflict of Interest



  1. Addison PS (2002) The illustrated wavelet transform handbook. Institute of Physics Publishing, LondonGoogle Scholar
  2. Azen R, Budescu DV (2003) The dominance analysis approach for comparing predictors in multiple regression. Psychol Methods 8(2):129Google Scholar
  3. Budescu DV (1993) Dominance analysis: a new approach to the problem of relative importance of predictors in multiple regression. Psychol Bull 114(3):542Google Scholar
  4. Cannas B, Fanni A, See L, Sias G (2006) Data preprocessing for river flow forecasting using neural networks: wavelet transforms and data partitioning. Physics and Chemistry of the Earth, Parts A/B/C 31(18):1164–1171. Google Scholar
  5. Daubechies I (1992) Ten lectures on wavelets (CBMS-NSF regional conference series in applied mathematics), vol 61. Society for Industrial and Applied mathematics, PhiladelphiaGoogle Scholar
  6. Johnson JW (2000) A heuristic method for estimating the relative weight of predictor variables in multiple regression. Multivar Behav Res 35(1):1–19Google Scholar
  7. Johnson JW (2004) Factors affecting relative weights: the influence of sampling and measurement error. Organ Res Methods 7(3):283–299Google Scholar
  8. Johnson JW, LeBreton JM (2004) History and use of relative importance indices in organizational research. Organ Res Methods 7(3):238–257Google Scholar
  9. Kisi O (2011) Wavelet regression model as an alternative to neural networks for river stage forecasting. Water Resour Manag 25(2):579–600. Google Scholar
  10. Kisi O, Shiri J (2011) Precipitation forecasting using wavelet-genetic programming and wavelet-neuro-fuzzy conjunction models. Water Resour Manag 25(13):3135–3152Google Scholar
  11. Kisi O, Shiri J, Tombul M (2013) Modeling rainfall-runoff process using soft computing techniques. Comput Geosci 51(0):108–117. Google Scholar
  12. Lebreton JM, Ployhart RE, Ladd RT (2004) A Monte Carlo comparison of relative importance methodologies. Organ Res Methods 7(3):258–282Google Scholar
  13. LeBreton JM, Tonidandel S (2008) Multivariate relative importance: extending relative weight analysis to multivariate criterion spaces. J Appl Psychol 93(2):329–345Google Scholar
  14. Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241Google Scholar
  15. Maheswaran R, Khosa R (2012) Comparative study of different wavelets for hydrologic forecasting. Comput Geosci 46(0):284–295. Google Scholar
  16. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptural models. Part 1: a discussion of principles. J Hydrol 10(3):282–290Google Scholar
  17. Nourani V, Komasi M, Alami MT (2012) Hybrid wavelet–genetic programming approach to optimize ANN modeling of rainfall–runoff process. J Hydrol Eng 17(6):724–741Google Scholar
  18. Nourani V, Hosseini Baghanam A, Adamowski J, Kisi O (2014) Applications of hybrid wavelet–artificial intelligence models in hydrology: a review. J Hydrol 514:358–377Google Scholar
  19. Partal T, Kişi Ö (2007) Wavelet and neuro-fuzzy conjunction model for precipitation forecasting. J Hydrol 342(1–2):199–212. Google Scholar
  20. Principe JC, Euliano NR, Lefebvre WC (2000) Neural and adaptive systems. Wiley, New YorkGoogle Scholar
  21. Rajaee T (2011) Wavelet and ANN combination model for prediction of daily suspended sediment load in rivers. Sci Total Environ 409(15):2917–2928. Google Scholar
  22. Shiri J, Kisi O (2010) Short-term and long-term streamflow forecasting using a wavelet and neuro-fuzzy conjunction model. J Hydrol 394(3):486–493Google Scholar
  23. Shoaib M, Shamseldin AY, Melville BW (2014) Comparative study of different wavelet based neural network models for rainfall–runoff modeling. J Hydrol 515:47–58Google Scholar
  24. Shoaib M, Shamseldin AY, Melville BW, Khan MM (2016) Hybrid wavelet neuro-fuzzy approach for rainfall-runoff modeling. J Comput Civ Eng 30(1):04014125. Google Scholar
  25. Shoaib M, Shamseldin AY, Khan S, Khan MM, Khan ZM, Sultan T, Melville BW (2018) A comparative study of various hybrid wavelet feedforward neural network models for runoff forecasting. Water Resour Manag 32(1):83–103. Google Scholar
  26. Singh R (2012) Wavelet-ANN model for flood events. In: Deep K, Nagar A, Pant M, Bansal JC (eds) Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20–22, 2011, vol 131. Springer Berlin, Heidelberg, pp 165–175Google Scholar
  27. Tonidandel S, LeBreton JM (2011) Relative importance analysis: a useful supplement to regression analysis. J Bus Psychol 26(1):1–9Google Scholar
  28. Tonidandel S, LeBreton JM, Johnson JW (2009) Determining the statistical significance of relative weights. Psychol Methods 14(4):387Google Scholar
  29. Van Iddekinge CH, Ployhart RE (2008) Developments in the criterion-related validation of selection procedures: a critical review and recommendations for practice. Pers Psychol 61(4):871–925Google Scholar
  30. Wang W, Ding J (2003) Wavelet network model and its application to the prediction of hydrology. Nat Sci 1(1):67–71Google Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Agricultural EngineeringBahauddin Zakariaya UniversityMultanPakistan
  2. 2.Department of Civil and Environmental EngineeringThe University of AucklandAucklandNew Zealand
  3. 3.Department of Civil EngineeringBahauddin Zakariaya UniversityMultanPakistan
  4. 4.Water Systems and Global ChangeWageningen University & ResearchWageningenNetherlands
  5. 5.Pakistan Agricultural Research CouncilIslamabadPakistan

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