Abstract
A methodology to select the maximum level of wavelet decomposition to forecast seven days of daily inflows by a hybrid model wavelet-based artificial neural network (WANN) is proposed. The wavelet decomposition was employed to decompose an input time series into approximation and detail components, and the approximations were used as inputs to artificial neural networks (ANN) for WANN hybrid models. In this study, it was used daily inflows from January 1931 to December 2010 to three Brazilian reservoirs with different discharge patterns, and evaluated the accuracy of the WANN models when using seven different mother-wavelets, including Haar, Daubechies, Biorthogonal, Biorthogonal Reverse, Symlet, Coiflet and Discrete Meyer. It was found that the model performance is dependent on the input sets and the selected mother-wavelets. Based on the obtained results, it was observed that the maximum level of decomposition was five, because upper than this level, independently on the inflow magnitude, there is no guarantee that the WANN hybrid models would perform better than the ANN model.
Graphical Abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adamowski J, Sun K (2010) Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. J Hydrol 390(1–2):85–91
Afan HA, Allawi MF, El-Shafie A et al (2020) Input attributes optimization using the feasibility of genetic nature inspired algorithm: application of river flow forecasting. Sci Rep 10:4684. https://doi.org/10.1038/s41598-020-61355-x
Akrami SA, El-Shafie A, Naseri M, Santos CAG (2014) Rainfall data analyzing using moving average (MA) model and wavelet multi-resolution intelligent model for noise evaluation to improve the forecasting accuracy. Neural Comput & Applic 25(7–8):1853–1861. https://doi.org/10.1007/s00521-014-1675-0
Alessio SM (2016) Discrete wavelet transform (DWT). In: Digital signal processing and spectral analysis for scientists. Signals and Communication Technology. Springer, Cham, pp 645–714. https://doi.org/10.1007/978-3-319-25468-5_14
Campolo M, Andreussi P, Soldati A (1999) River flood forecasting with a neural network model. Water Resour Res 35(4):1191–1197. https://doi.org/10.1029/1998WR900086
Cannas B, Fanni A, Sias G, Tronci S, Zedda MK (2005) River flow forecasting using neural networks and wavelet analysis. Geophys Res Abstr 7:08651
Cheng C, Chau K, Sun Y, Lin J (2005) Long-term prediction of discharges in Manwan reservoir using artificial neural network models. In: Wang J, Liao XF, Yi Z (eds) Advances in neural networks – ISNN 2005. Lecture Notes in Computer Science, vol 3498, Springer, Berlin, Heidelberg, pp 1040–1045. https://doi.org/10.1007/11427469_165
Cigizoglu HK (2003) Estimation, forecasting and extrapolation of flow data by artificial neural networks. Hydrological Sci J 48(3):349–361. https://doi.org/10.1623/hysj.48.3.349.45288
Cigizoglu HK, Kisi Ö (2005) Flow prediction by three back propagation techniques using k-fold partitioning of neural network training data. Nord Hydrol 36(1):1–16
Danandeh Mehr A, Kahya E, Sahin A, Nazemosadat MJ (2014) Successive-station monthly streamflow prediction using different artificial neural network algorithms. Int J Environ Sci Technol. https://doi.org/10.1007/s13762-0140613-0
Danh NT, Phien HN, Gupta A (1999) Neural network models for river flow forecasting. Water SA 25(1)
Daubechies I (1990) The wavelet transform, time-frequency localization and signal analysis. Inf Theory, IEEE Trans 36(5):961–1005
Demuth H, Beale M (2005) Neural network toolbox: for use with Matlab. The MathWorks, Inc., Natick, USA
Farias CAS, Santos CAG (2014) The use of Kohonen neural networks for runoff–erosion modeling. J Soils Sediments 14(7):1242–1250. https://doi.org/10.1007/s11368-013-0841-9
Farias CAS, Santos CAG, Lourenço AMG, Carneiro TC (2013) Kohonen neural networks for rainfall-runoff modeling: case of Piancó River basin. J Urban Environ Eng 7(1):176–182. https://doi.org/10.4090/juee.2013.v7n1.176182
Fernando DAK, Jayawardena AW (1998) Runoff forecasting using RBF networks with OLS algorithm. J Hydrol Eng 3:203–209. https://doi.org/10.1061/(ASCE)1084-0699(1998)3:3(203)
Freire PKMM, Santos CAG, Silva GBL (2019) Analysis of the use of discrete wavelet transforms coupled with ANN for short-term streamflow forecasting. Appl Soft Comput 80:494–505. https://doi.org/10.1016/j.asoc.2019.04.024
Goswami M, O’Connor KM, Bhattarai KP, Shamseldin AY (2005) Assessing the performance of eight real-time updating models and procedures for the Brosna River. Hydrol Earth Syst Sci 9:394–411. https://doi.org/10.5194/hess-9-394-2005
Hidalgo I, Fontane D, Arabi M, Lopes J, Andrade J, Ribeiro L (2012) Evaluation of optimization algorithms to adjust efficiency curves for hydroelectric generating units. J Energy Eng 138(4):172–178
Honorato AGSM, Silva GBL, Santos CAG (2018) Monthly streamflow forecasting using neuro-wavelet techniques and input analysis. Hydrol Sci J 63(15–16):2060–2075. https://doi.org/10.1080/02626667.2018.1552788
Jothiprakas V, Maga RB (2012) Multi-time-step ahead daily and hourly intermittent reservoir inflow prediction by artificial intelligent techniques using lumped and distributed data. J Hydrol 450–451:293–307. https://doi.org/10.1016/j.jhydrol.2012.04.045
Kagoda PA, Ndiritu J, Ntuli C, Mwaka B (2010) Application of radial basis function neural networks to short-term streamflow forecasting. Phys Chem Earth 35:571–581. https://doi.org/10.1016/j.pce.2010.07.021
Karunanithi N, Grenney WJ, Whitley D, Bovee K (1994) Neural networks for river flow prediction. J Comput Civ Eng 8(2):201–220. https://doi.org/10.1061/(ASCE)0887-3801(1994)8:2(201)
Kentel E (2009) Estimation of river flow by artificial neural networks and identification of input vectors susceptible to producing unreliable flow estimates. J Hydrol 375:481–488. https://doi.org/10.1016/j.jhydrol.2009.06.051
Kisi O (2009) Neural networks and wavelet conjunction model for intermittent stream-flow forecasting. J Hydrol Eng 14(8):773–782
Krishna B (2013) Comparison of wavelet based ANN and regression models for reservoir inflow forecasting. J Hydrol Eng. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000892
Krishna B, Satyaji Rao YR, Nayak PC (2011) Time series modeling of river flow using wavelet neural networks. J Water Resour and Prot 03(1):50–59. https://doi.org/10.4236/jwarp.2011.31006
Kumar DN, Raju KS, Sathish T (2004) River flow forecasting using recurrent neural network. Water Resour Manag 18(2)
Lauzon N, Rousselle J, Birikundavyi S, Trung HT (2000) Real-time daily flow forecasting using black-box models, diffusion processes, and neural networks. Can J Civ Eng 27(4):671–682. https://doi.org/10.1139/cjce-27-4-671
Liu Y, Weerts AH, Clark M, Hendricks Franssen H-J, Kumar S, Moradkhani H, Seo D-J, Schwanenberg D, Smith P, van Dijk AIJM, van Velzen N, He M, Lee H, Noh SJ, Rakovec O, Restrepo P (2012) Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities. Hydrol Earth Syst Sci 16:3863–3887. https://doi.org/10.5194/hess-16-3863-2012
Maheswaran R, Khosa R (2013) Wavelets-based non-linear model for real-time daily flow forecasting in Krishna River. J Hydroinf 15(3):1022–1041. https://doi.org/10.2166/hydro.2013.135
Mallat S (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions Pattern Analysis and Machine Intelligence 11(7):674–693
Misiti M, Misiti Y, Oppenheim G, Poggi JM (1996) Wavelet toolbox:for use with MATLAB. The MathWorks Inc., Natick (MA), p 262
Misiti M, Misiti Y, Oppenheim G, Poggi JM (2006) Wavelet toolbox User’s guide - for use with MATLAB. 3 ed. Massachusets (USA): The MathWorks, Inc.
Moradkhani H, Hsu K, Gupta HV, Sorooshian S (2004) Improved streamflow forecasting using self-organizing radial basis function artificial neural networks. J Hydrol 295:246–262. https://doi.org/10.1016/j.jhydrol.2004.03.027
Pramanik N, Panda RK, Singh A (2010) Daily river flow forecasting using wavelet ANN hybrid models. J Hydroinf 13(1):49–63. https://doi.org/10.2166/hydro.2010.040
Ravansalar M, Rajaee T, Ergil M (2015) Prediction of dissolved oxygen in river Calder by noise elimination time series using wavelet transform. J Exp Theor Artif In 28(4):689–706. https://doi.org/10.1080/0952813X.2015.104253
Renno C, Petito F, Gatto A (2015) Artificial neural network models for predicting the solar radiation as input of a concentrating photovoltaic system. Energy Convers Manag 106:999–1012. https://doi.org/10.1016/j.enconman.2015.10.033
Santos CAG, Silva GBL (2014) Daily streamflow forecasting using a wavelet transform and artificial neural network hybrid models. Hydrol Sci J 59(2):312–324. https://doi.org/10.1080/02626667.2013.800944
Santos CAG, Freire PKMM, Torrence C (2013) A Transformada wavelet e sua Aplicação na Análise de Séries Hidrológicas (the wavelet transform and its application for hydrological time series analysis). Brazilian J Water Resour 18(3):271–280. https://doi.org/10.21168/rbrh.v18n3.p271-280
Santos CAG, Freire PKMM, Silva GBL, Silva RM (2014) Discrete wavelet transform coupled with ANN for daily discharge forecasting into Três Marias reservoir. Proc IAHS 364:100–105. https://doi.org/10.5194/piahs-364-100-2014
Santos CAG, Freire PKMM, Silva RM, Akrami SA (2019) Hybrid wavelet neural network approach for daily inflow forecasting using tropical rainfall measuring mission data. J Hydrol Eng 24(2):04018062. https://doi.org/10.1061/(asce)he.1943-5584.0001725
Shamseldin AY, O’Connor KM (2001) A non-linear neural network technique for updating of river flow forecasts. Hydrol Earth Syst Sci 5:577–598. https://doi.org/10.5194/hess-5-577-2001
Sivakumar B, Jayawerdana AW, Fernando TMKG (2002) River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches. J Hydrol 265(1–4):225–245. https://doi.org/10.1016/S0022-1694(02)00112-9
Terzi Ö, Ergin G (2014) Forecasting of monthly river flow with autoregressive modeling and data-driven techniques. Neural Comput & Applic 25:179–188. https://doi.org/10.1007/s00521-013-1469-9
Tiwari MK, Chatterjee C (2011) A new wavelet–bootstrap–ANN hybrid model for daily discharge forecasting. J Hydroinf 13(3):500–519. https://doi.org/10.2166/hydro.2010.142
Toth E, Brath A, Montanari A (1999) Real-time flood forecasting via combined use of conceptual and stochastic models. Phys Chem Earth B 24:793–798
Wang W, Ding J (2003) Wavelet network model and its application to the prediction of the hydrology. J Nat Sci 1:67–71
Wei S, Yang H, Song JX, Abbaspour K, Xu ZX (2013) A wavelet-neural network hybrid modelling approach for estimating and predicting river monthly flows. Hydrol Sci J 58(2):374–389. https://doi.org/10.1080/02626667.2012.754102
Xiong LH, O’Connor KM (2002) Comparison of four updating models for real-time river flow forecasting. Hydrol Sci J 47:621–639. https://doi.org/10.1080/02626660209492964
Yaseen ZM, El-Shafie A, Afan HA, Hameed M, Mohtar WHMW, Hussain A (2015) RBFNN versus FFNN for daily river flow forecasting at Johor River, Malaysia. Neural Comput Appl 27:1533–1542. https://doi.org/10.1007/s00521-015-1952-6
Funding
This study was funded by National Council for Scientific and Technological Development, Brazil (304213/2017–9). This study was also financed in part by the Brazilian Agency for the Improvement of Higher Education (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES) – Fund Code 001 and the Federal University of Paraíba.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by: H. Babaie
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Freire, P.K.d.M., Santos, C.A.G. Optimal level of wavelet decomposition for daily inflow forecasting. Earth Sci Inform 13, 1163–1173 (2020). https://doi.org/10.1007/s12145-020-00496-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-020-00496-z