Abstract
Reliable long-term (decadal scale) streamflow prediction would provide significant planning information for water resources management, particularly in areas marked by significant variability at those time scales. In this study, a multi-model for prediction using four models that incorporate preprocessing methods along with data-driven forecast models coupled using the least absolute shrinkage and selection operator (LASSO) regression method is proposed. Models utilized complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet transform (WT) as the decomposition methods and autoregressive (AR) and hidden Markov models (HMM) as the predictive method. The model is evaluated in a comparative analysis with a variety of models previously proposed for hydrological time series prediction. We compare the predictive skill of alternative data-driven models for average annual streamflow (3 ~ 15 years) prediction. Results indicate that the multi-model performed better than the other models, presenting lower values of MAE and RSME. This multi-model can be a reliable tool for forecasting, which can be explored for hydrological data that have remarkably nonlinear and nonstationary features.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs41101-023-00184-1/MediaObjects/41101_2023_184_Fig11_HTML.png)
Similar content being viewed by others
Data Availability
Data was retrieved from the Brazilian National Water Agency (ANA) at http://www.snirh.gov.br/hidroweb/.
Code Availability
The calculations and figures were made using the R software.
References
Liang Z, Li Y, Hu Y, Li B, Wang J (2018) A data-driven SVR model for long-term runoff prediction and uncertainty analysis based on the Bayesian framework. Theor Appl Climatol 133:137–149. https://doi.org/10.1007/s00704-017-2186-6
Singh SK (2016) Long-term streamflow forecasting based on ensemble streamflow prediction technique: A case study in New Zealand. Water Resour Manag 30:2295–2309. https://doi.org/10.1007/s11269-016-1289-7
Wang L, Li X, Ma C, Bai Y (2019) Improving the prediction accuracy of monthly streamflow using a data-driven model based on a double-processing strategy. J Hydrol 573:733–745. https://doi.org/10.1016/j.jhydrol.2019.03.101
Szolgayova E, Parajka J, Blöschl G, Bucher C (2014) Long term variability of the Danube River flow and its relation to precipitation and air temperature. J Hydrol 519:871–880
Nazir HM, Hussain I, Faisal M, Shoukry AM, Gani S, Ahmad I (2019) Development of Multidecomposition Hybrid Model for Hydrological Time Series Analysis. Complexity. https://doi.org/10.1155/2019/2782715
Wen X, Feng Q, Deo RC, Wu M, Yin Z, Yang L, Singh VP (2019) Two-phase extreme learning machines integrated with the complete ensemble empirical mode decomposition with adaptive noise algorithm for multi-scale runoff prediction problems. J Hydrol 570:167–184. https://doi.org/10.1016/j.jhydrol.2018.12.060
Rolim LZR, de Souza Filho FDA (2020) Shift Detection in Hydrological Regimes and Pluriannual Low-Frequency Streamflow Forecasting Using the Hidden Markov Model. Water 12:2058. https://doi.org/10.3390/w12072058
Khan MMH, Muhammad NS, El-Shafie A (2020) Wavelet based hybrid ANN-ARIMA models for meteorological drought forecasting. J Hydrol 590:125380. https://doi.org/10.1016/j.jhydrol.2020.125380
Kisi O, Gorgij AD, Zounemat-Kermani M, Mahdavi-Meymand A, Kim S (2019) Drought forecasting using novel heuristic methods in a semi-arid environment. J Hydrol 578:124053. https://doi.org/10.1016/j.jhydrol.2019.124053
Dariane AB, Azimi S (2018) Streamflow forecasting by combining neural networks and fuzzy models using advanced methods of input variable selection. J Hydroinformatics 20(2):520–532. https://doi.org/10.2166/hydro.2017.076
Erkyihun ST, Zagona E, Rajagopalan B (2017) Wavelet and Hidden Markov-Based Stochastic Simulation Methods Comparison on Colorado River Streamflow. J Hydrol Eng 22(9):04017033. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001538
Meng E, Huang S, Huang Q, Fang W, Wu L, Wang L (2019) A robust method for non-stationary streamflow prediction based on improved EMD-SVM model. J Hydrol 568:462–478. https://doi.org/10.1016/j.jhydrol.2018.11.015
Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391:202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012
He Z, Wen X, Liu H, Du J (2014) A comparative study of artificial neural network, adaptive neuro fuzzy inference system and support vector machine for forecasting river flow in the semiarid mountain region. J Hydrol 509:379–386. https://doi.org/10.1016/j.jhydrol.2013.11.054
Zhang Z, Zhang Q, Singh VP, Shi P (2018) River flow modelling: comparison of performance and evaluation of uncertainty using data-driven models and conceptual hydrological model. Stoch Environ Res Risk Assess 32(9):2667–2682. https://doi.org/10.1007/s00477-018-1536-y
Yang S, Yang D, Chen J, Santisirisomboon J, Lu W, Zhao B (2020) A physical process and machine learning combined hydrological model for daily streamflow simulations of large watersheds with limited observation data. J Hydrol 590:125206. https://doi.org/10.1016/j.jhydrol.2020.125206
Clark MP, Bierkens MFP, Samaniego L, Woods RA, Uijlenhoet R, Bennett KE, Pauwels VRN, Cai X, Wood AW, Peters-Lidard CD (2017) The evolution of process-based hydrologic models: historical challenges and the collective quest for physical realism. Hydrol Earth Syst Sci 21:3427–3440. https://doi.org/10.5194/hess-21-3427-2017
Saraiva SV, de Oliveira Carvalho F, Santos CAG, Barreto LC, Freire PKDMM (2021) Daily streamflow forecasting in Sobradinho Reservoir using machine learning models coupled with wavelet transform and bootstrap**. Appl Soft Comput 102:107081. https://doi.org/10.1016/j.asoc.2021.107081
Remesan R, Mathew J (2016) Hydrological data driven modelling. Springer International Pu.
Thomas HA, Fiering MB (1962) Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In: Mass A et al (eds) Design of water resource systems. Harvard University Press, Cambridge, Massachusetts, pp 459–493
Salas JD, Obeysekera JTB (1982) ARMA model identification of hydrologic time series. Water Resour Res 18(4):1011–1021. https://doi.org/10.1029/WR018i004p01011
Koutsoyiannis D, Yao H, Georgakakos A (2008) Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods/Prévision du débit du Nil à moyen terme: une comparaison de méthodes stochastiques et déterministes. Hydrol Sci J 53(1):142–164. https://doi.org/10.1623/hysj.53.1.142
Papacharalampous GA, Tyralis H, Koutsoyiannis D (2017) Forecasting of geophysical processes using stochastic and machine learning algorithms. European Water 59:161–168
Papacharalampous G, Tyralis H, Koutsoyiannis D (2019) Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes. Stoch Environ Res Risk Assess 33(2):481–514. https://doi.org/10.1007/s00477-018-1638-6
Lall U (1995) Nonparametric function estimation: Recent hydrologic applications. Reviews of Geophysics, US National Report, 1093–1102.
Dettinger MD, Ghil M, Keppenne CL (1995) Interannual and interdecadal variability in United States surface-air temperatures, 1910–87. Clim Change 31(1):35–66. https://doi.org/10.1007/BF01092980
Souza Filho FA, Lall U (2003) Seasonal to interannual ensemble streamflow forecasts for Ceara, Brazil: Applications of a multivariate semiparametric algorithm. Water Resour Res 39(11):1307. https://doi.org/10.1029/2002WR001373
Kwon H-H, Lall U, Khalil AF (2007) Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature. Water Resour Res 43(5). https://doi.org/10.1029/2006WR005258
Chou CM, Wang RY (2004) Application of wavelet-based multi-model Kalman filters to real-time flood forecasting. Hydrol Process 18:987–1008. https://doi.org/10.1002/hyp.1451
Humphrey GB, Gibbs MS, Dandy GC, Maier HR (2016) A hybrid approach to monthly streamflow forecasting: Integrating hydrological model outputs into a Bayesian artificial neural network. J Hydrol 540:623–640. https://doi.org/10.1016/j.jhydrol.2016.06.026
Guo J, Zhou J, Qin H, Zou Q, Li Q (2011) Monthly streamflow forecasting based on improved support vector machine model. Expert Syst Appl 38:13073–13081. https://doi.org/10.1016/j.eswa.2011.04.114
Kasiviswanathan KS, He J, Sudheer KP, Tay JH (2016) Potential application of wavelet neural network ensemble to forecast streamflow for flood management. J Hydrol 536:161–173. https://doi.org/10.1016/j.jhydrol.2016.02.044
Nourani V, Kisi Ö, Komasi M (2011) Two hybrid Artificial Intelligence approaches for modeling rainfall–runoff process. J Hydrol 402:41–59. https://doi.org/10.1016/j.jhydrol.2011.03.002
Nourani V, Komasi M, Mano A (2009) A Multivariate ANN-Wavelet Approach for Rainfall-Runoff Modeling. Water Resour Manag 23:2877–2894. https://doi.org/10.1007/s11269-009-9414-5
Peng T, Zhou J, Zhang C, Fu W (2017) Streamflow forecasting using empirical wavelet transform and artificial neural networks. Water 9:1–20. https://doi.org/10.3390/w9060406
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, 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 454:903–995. https://doi.org/10.1098/rspa.1998.0193
Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 01:1–41. https://doi.org/10.1142/S1793536909000047
Torres ME, Colominas MA, Schlotthauer G, Flandrin P (2011) A complete ensemble empirical mode decomposition with adaptive noise, in: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, pp. 4144–4147. https://doi.org/10.1109/ICASSP.2011.5947265
Adarsh S, Reddy MJ (2018) Multiscale characterization and prediction of monsoon rainfall in India using Hilbert-Huang transform and time-dependent intrinsic correlation analysis. Meteorol Atmos Phys 130:667–688. https://doi.org/10.1007/s00703-017-0545-6
Gaiser T, Krol M, Frischkorn H, de Araújo JC (Eds.) (2003) Global Change and Regional Impact: Water availability and vulnerability of ecosystems and society in the semiarid Northeast of Brazil. Springer Science & Business Media. https://doi.org/10.1007/978-3-642-55659-3
Malveira VTC, de Araújo JC, Güntner A (2012) Hydrological Impact of a High-Density Reservoir Network in Semiarid Northeastern Brazil. J Hydrol Eng 17(1):109–117. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000404
Lima Neto IE, Wiegand MC, Carlos de Araújo J (2011) Redistribution des sédiments due à un réseau dense de réservoirs dans un grand bassin versant semi-aride du Brésil. Hydrol Sci J 56:319–333. https://doi.org/10.1080/02626667.2011.553616
Antico A, Schlotthauer G, Torres ME (2014) Analysis of hydroclimatic variability and trends using a novel empirical mode decomposition: Application to the Paraná River Basin. J Geophys Res Atmos 119:1218–1233. https://doi.org/10.1002/2013JD020420
Ren Y, Suganthan PN, Srikanth N (2014) A comparative study of empirical mode decomposition-based short-term wind speed forecasting methods. IEEE Trans Sustain Energy 6(1):236–244. https://doi.org/10.1109/TSTE.2014.2365580
Bowman D, Lees J (2013) The Hilbert-Huang Transform: A High-Resolution Spectral Method for Nonlinear and Nonstationary Time Series. Seismol Res Lett 84(6):1074–1080. https://doi.org/10.1785/0220130025
Torrence C, Compo GP (1998) A Practical Guide to Wavelet Analysis. Bull Am Meteorol Soc 79:61–78. https://doi.org/10.1175/1520-0477(1998)079%3c0061:APGTWA%3e2.0.CO;2
Labat D (2005) Recent advances in wavelet analyses: Part 1. A review of concepts J Hydrol 314:275–288. https://doi.org/10.1016/j.jhydrol.2005.04.003
Sang Y-F (2013) A review on the applications of wavelet transform in hydrology time series analysis. Atmos Res 122:8–15. https://doi.org/10.1016/j.atmosres.2012.11.003
Danandeh Mehr A, Kahya E, Olyaie E (2013) Streamflow prediction using linear genetic programming in comparison with a neuro-wavelet technique. J Hydrol 505:240–249. https://doi.org/10.1016/j.jhydrol.2013.10.003
Pathak P, Kalra A, Ahmad S, Bernardez M (2016) Wavelet-Aided Analysis to Estimate Seasonal Variability and Dominant Periodicities in Temperature, Precipitation, and Streamflow in the Midwestern United States. Water Resour Manag 30:4649–4665. https://doi.org/10.1007/s11269-016-1445-0
Sun Y, Niu J, Sivakumar B (2019) A comparative study of models for short-term streamflow forecasting with emphasis on wavelet-based approach. Stoch Environ Res Risk Assess 33:1875–1891. https://doi.org/10.1007/s00477-019-01734-7
Rösch A, Schmidbauer H (2016) WaveletComp 1.1: A guided tour through the R package. URL: http://www.hsstat.com/projects/WaveletComp/WaveletComp_guided_tour.pdf
Zucchini W, MacDonald IL, Langrock R (2016) Hidden Markov Models for Time Series, 2nd ed Chapman and Hall/CRC.
Tibshirani R (1996) Regression Shrinkage and Selection via the Lasso. J R Stat Soc Ser B 58:267–288
Friedman JH, Hastie T, Tibshirani R (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. J Stat Software 1.
Rocha RV, Souza Filho FDAD, Silva SMOD (2019) Análise da Relação entre a Precipitação Média do Reservatório Orós, Brasil-Ceará, e os índices PDO e AMO Através da Análise de Changepoints e Transformada de Ondeletas. Rev bras meteorol 34(1):139–149. https://doi.org/10.1590/0102-77863340034
Tang C, Chen D, Crosby BT, Piechota TC, Wheaton JM (2014) Is the PDO or AMO the climate driver of soil moisture in the Salmon River Basin, Idaho? Glob Planet Change 120:16–23. https://doi.org/10.1016/j.gloplacha.2014.05.008
Torrence C, Webster PJ (1999) Interdecadal changes in the ENSO–monsoon system. J Clim 12(8):2679–2690
Quilty J, Adamowski J (2018) Addressing the incorrect usage of wavelet-based hydrological and water resources forecasting models for real-world applications with best practices and a new forecasting framework. J Hydrol 563:336–353. https://doi.org/10.1016/j.jhydrol.2018.05.003
Marengo JA (2008) Água e mudanças climáticas. Estud Avançados 22:83–96. https://doi.org/10.1590/S0103-40142008000200006
Kayano MT, Andreoli RV (2007) Relations of South American summer rainfall interannual variations with the Pacific Decadal Oscillation. Int J Climatol 27:531–540. https://doi.org/10.1002/joc.1417
Knight JR, Folland CK, Scaife AA (2006) Climate impacts of the Atlantic Multidecadal Oscillation. Geophys Res Lett 33:L17706. https://doi.org/10.1029/2006GL026242
Pontes Filho JD, Souza Filho FA, Martins ESPR, Studart TMC (2020) Copula-Based Multivariate Frequency Analysis of the 2012–2018 Drought in Northeast Brazil. Water 12(3):834. https://doi.org/10.3390/w12030834
Acknowledgements
This study was financed in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico—Brasil (CNPq), the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES), and the Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP).
Author information
Authors and Affiliations
Contributions
Conceptualization, F.A.S.F.; Methodology, L.Z.R.R. and F.A.S.F.; Validation, L.Z.R.R., F.A.S.F. and C.B; Formal Analysis, L.Z.R.R., F.A.S.F. and C.B.; Investigation, L.Z.R.R; Resources, F.A.S.F.; Writing-Original Draft Preparation, L.Z.R.R.; Writing-Review & Editing, L.Z.R.R., F.A.S.F. and C.B; Supervision, F.A.S.F.; Funding Acquisition, F.A.S.F.
Corresponding author
Ethics declarations
Copyright Permission
The authors make sure that all data and figures originate from the authors’ study and there is no copyright issue.
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Rolim, L.Z.R., de Souza Filho, F.d. & Brown, C. A Multi-model Framework for Streamflow Forecasting Based on Stochastic Models: an Application to the State Of Ceará, Brazil. Water Conserv Sci Eng 8, 7 (2023). https://doi.org/10.1007/s41101-023-00184-1
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s41101-023-00184-1