Abstract
Using historical salinity data from nine drought periods in the Pearl River Delta of China, this study utilized two machine learning approaches to forecast the salinity time series for multistep lead times: random forest (RF) models and extreme learning machine (ELM) models. To improve conventional RF and ELM models, three signal decomposition techniques were applied to preprocess the input time series: empirical mode decomposition (EMD), wavelet decomposition (WD) and wavelet packet decomposition (WPD). The study results indicated that in contrast to conventional RF/ELM, a hybrid RF/ELM method accompanied by decomposition techniques displayed better forecasting performance and yielded reasonably accurate prediction results. More specifically, hybrid models coupled with WPD displayed the best performance for all three forecast lead times of one, three and five days, whereas EMD underperformed both WPD and WD because of the limited predictability of the components. Both the WPD and WD hybrid models using the \(coif5\) wavelet basis performed better than those using the other two bases (db8 and sym8). In addition, ELM method performed better for conventional and WD/WPD hybrid models, whereas the RF method worked better for EMD hybrid model. The findings of the study showed that the nonstationary salinity series could be transformed into several relatively stationary components in the decomposition process, which provided more accurate salinity forecasts. The developed hybrid models coupling RF/ELM method with decomposition techniques could be a feasible way for salinity prediction.
Similar content being viewed by others
References
Abdullah SS, Malek MA, Abdullah NS, Kisi O, Yap KS (2015) Extreme learning machines: a new approach for prediction of reference evapotranspiration. J Hydrol 527:184–195
Adamowski J, Chan HF, Prasher SO, Ozga-Zielinski B, Sliusarieva A (2012) Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour Res 48(1):273–279
Akusok A, Bjork K-M, Miche Y, Lendasse A (2015) High-performance extreme learning machines: a complete toolbox for big data applications. IEEE Access 3:1011–1025
Alizadeh MJ, Kavianpour MR (2015) Development of wavelet-ANN models to predict water quality parameters in Hilo Bay, Pacific Ocean. Mar Pollut Bull 98(1–2):171–178
Barzegar R, Moghaddam AA, Adamowski J, Ozga-Zielinski B (2017) Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model. Stoch Environ Res Risk Assess 32:1–15
Belayneh A, Adamowski J, Khalil B, Ozga-Zielinski B (2014) Long-term SPI drought forecasting in the Awash River Basin in Ethiopia using wavelet neural network and wavelet support vector regression models. J Hydrol 508:418–429
Biau G, Scornet E (2016) A random forest guided tour. Test 25(2):197–227
Bogner K, Pappenberger F (2011) Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system. Water Res Res 47(7):1772–1780
Bowden GJ, Dandy GC, Maier HR (2005a) Input determination for neural network models in water resources applications. Part 1—background and methodology. J Hydrol 301(1):75–92
Bowden GJ, Maier HR, Dandy GC (2005b) Input determination for neural network models in water resources applications. Part 2. Case study: forecasting salinity in a river. J Hydrol 301(1–4):93–107
Breiman L (2001) Random forests. Mach Learn 45(1):5–32
Cai H, Savenije HHG, Yang Q, Ou S, Lei Y (2012) Influence of river discharge and dredging on tidal wave propagation: modaomen estuary case. J Hydraul Eng 138(10):885–896
Campisi-Pinto S (2013) Erratum to: Forecasting urban water demand via wavelet-denoising and neural network models. Case study: City of Syracuse, Italy. Water Resourc Manag 27(1):319–321
Chen X, Chen Y (2002) Hydrological change and its causes in the river network of the pearl river delta. Acta Geogr Sin 57(4):429–436
Daubechies I, Heil C (1992) Ten lectures on wavelets. CBMS-NSF Series Appl Math, SIAM 6(3): 1671–1671
Fang YH, Chen XW, Cheng NS (2017) Estuary salinity prediction using a coupled GA-SVM model: a case study of the Min River Estuary, China. Water Sci Technol-Water Supply 17(1):52–60
Feng Q, Wen X, Li J (2015) Wavelet analysis-support vector machine coupled models for monthly rainfall forecasting in arid regions. Water Resour Manag 29(4):1049–1065
Galelli S, Castelletti A (2013) Tree-based iterative input variable selection for hydrological modeling. Water Resour Res 49(7):4295–4310
Gong W, Wang Y, Jia J (2012) The effect of interacting downstream branches on saltwater intrusion in the Modaomen Estuary, China. J Asian Earth Sci 45:223–238
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
Hamrick JM (1992) A three-dimensional environmental fluid dynamics computer code: theoretical and computational aspects. Special Report 317. Virginia Institute of Marine Science, Gloucester Point, VA, p 63
Huang WR, Foo S (2002) Neural network modeling of salinity variation in Apalachicola River. Water Res 36(1):356–362
Huang NE, Wu Z (2008) A review on Hilbert-Huang transform: method and its applications to geophysical studies. Rev Geophys 46:RG2006
Huang NE et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser A: Math Phys Eng Sci 454(1971):903–995
Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501
Huang G-B, Zhou H, Ding X, Zhang R (2012) Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern Part B-Cybern 42(2):513–529
Huang S, Chang J, Huang Q, Chen Y (2014) Monthly streamflow prediction using modified EMD-based support vector machine. J Hydrol 511(7):764–775
Kisi O, Latifoglu L, Latifoglu F (2014) Investigation of empirical mode decomposition in forecasting of hydrological time series. Water Resour Manag 28(12):4045–4057
Legates DR Jr, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241
Lima AR, Cannon AJ, Hsieh WW (2015) Nonlinear regression in environmental sciences using extreme learning machines: a comparative evaluation. Environ Model Softw 73:175–188
Liu N, Wang H (2010) Ensemble based extreme learning machine. IEEE Signal Process Lett 17(8):754–757
Liu B, Yan S, Chen X, Lian Y, Xin Y (2014a) Wavelet analysis of the dynamic characteristics of saltwater intrusion: a case study in the Pearl River Estuary of China. Ocean Coast Manag 95(4):81–92
Liu Z, Sun W, Zeng J (2014b) A new short-term load forecasting method of power system based on EEMD and SS-PSO. Neural Comput Appl 24(3–4):973–983
Liu S, Xu L, Li D (2016) Multi-scale prediction of water temperature using empirical mode decomposition with back-propagation neural networks. Comput Electr Eng 49:1–8
Liu B, Peng S, Liao Y, Long W (2017) The causes and impacts of water resources crises in the Pearl River Delta. J Clean Prod 177:413–425
Maheswaran R, Khosa R (2012) Comparative study of different wavelets for hydrologic forecasting. Comput Geosci 46(3):284–295
Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Model Softw 15(1):101–124
Maier HR, Jain A, Dandy GC, Sudheer KP (2010) Review: Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ Model Softw 25(8):891–909
Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693
Mayumi Oshiro T, Santoro Perez P, Baranauskas JA (2012) How many trees in a random forest? Machine Learning and Data Mining in Pattern Recognition. Proceedings 8th International Conference, MLDM 2012, 154–68 pp. https://doi.org/10.1007/978-3-642-31537-4_13
Miche Y, Bas P, Jutten C, Simula O, Lendasse A (2008) A methodology for building regression models using extreme learning machine: OP-ELM, Esann 2008, European symposium on artificial neural networks, Bruges, Belgium, April 23–25, 2008, Proceedings, pp 247–252
Miche Y et al (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Networks 21(1):158–162
Misiti M, Misiti Y, Oppenheim G, Poggi JM (1996) Wavelet toolbox users guide copyright. Math Works Inc
Montanari A, Koutsoyiannis D (2012) A blueprint for process-based modeling of uncertain hydrological systems. Water Res Res 48(9):9555
Moosavi V, Vafakhah M, Shirmohammadi B, Behnia N (2013) A wavelet-ANFIS hybrid model for groundwater level forecasting for different prediction periods. Water Resour Manag 27(5):1301–1321
Moosavi V, Talebi A, Hadian MR (2017) Development of a hybrid wavelet packet- group method of data handling (WPGMDH) model for runoff forecasting. Water Resour Manag 31(1):43–59
Moriasi DN et al (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans Asabe 50(3):885–900
Napolitano G, Serinaldi F, See L (2011) Impact of EMD decomposition and random initialisation of weights in ANN hindcasting of daily stream flow series: an empirical examination. J Hydrol 406(3):199–214
Nourani V, Komasi M, Mano A (2009) A multivariate ANN-wavelet approach for rainfall-runoff modeling. Water Resour Manag 23(14):2877
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):724–741
Nourani V, Baghanam AH, Adamowski J, Kisi O (2014) Applications of hybrid wavelet-artificial intelligence models in hydrology: a review. J Hydrol 514:358–377
Ouyang Q, Lu WX (2018) Monthly rainfall forecasting using echo state networks coupled with data preprocessing methods. Water Resour Manag 32(2):659–674
Partal T, Kişi Ö (2007) Wavelet and neuro-fuzzy conjunction model for precipitation forecasting. J Hydrol 342(1):199–212
Percival DB, Walden AT (2000) Wavelet methods for time series analysis (cambridge series in statistical and probabilistic mathematics)
Qiu C, Wan Y (2013) Time series modeling and prediction of salinity in the Caloosahatchee River Estuary. Water Resour Res 49(9):5804–5816
Qiu C, Sheng YP, Zhang Y (2008) [American Society of Civil Engineers 10th International Conference on Estuarine and Coastal Modeling - Newport, Rhode Island, United States (November 5–7, 2007)] Estuarine and Coastal Modeling (2007) - Development of a Hydrodynamic and Salinity Model in the caloosahatchee estuary and estero bay, florida. 106–123
Rao RM (1998) Wavelet transforms: introduction to theory and applications. Addison-Wesley, 478 pp
Rato RT, Ortigueira MD, Batista AG (2008) On the HHT its problems, and some solutions. Mech Syst Signal Process 22(6):1374–1394
Rengasamy P (2006) World salinization with emphasis on Australia. J Exp Bot 57(5):1017–1023
Rezaie-Balf M, Naganna SR, Ghaemi A, Deka PC (2017) Wavelet coupled MARS and M5 Model Tree approaches for groundwater level forecasting. J Hydrol 553:356–373
Rilling G, Flandrin P, Goncalves P (2011) On empirical mode decomposition and its algorithms. In: Proceedings of IEEE-EURASIP workshop on nonlinear signal and image processing NSIP-03, Grado (I)
Rohmer J, Brisset N (2017) Short-term forecasting of saltwater occurrence at La Comté River (French Guiana) using a kernel-based support vector machine. Environ Earth Sci 76(6):246
Seo Y, Kim S, Kisi O, Singh VP, Parasuraman K (2016) River stage forecasting using wavelet packet decomposition and machine learning models. Water Resour Manag 30(11):4011–4035
Sheng YP (1987) On modeling three-dimensional estuarine and marine hydrodynamics. Elsevier Oceanogr 45:35–54
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
Shortridge JE, Guikema SD, Zaitchik BF (2016) Machine learning methods for empirical streamflow simulation: a comparison of model accuracy, interpretability, and uncertainty in seasonal watersheds. Hydrol Earth Syst Sci 20(7):2611–2628
Shu Z, Guan W, Cai S, Xing W, Huang D (2014) A model study of the effects of river discharges and interannual variation of winds on the plume front in winter in Pearl River Estuary. Pearl River 73(2):31–40
Suen JP, Lai HN (2013) A salinity projection model for determining impacts of climate change on river ecosystems in Taiwan. J Hydrol 493:124–131
Sun Z-L, Choi T-M, Au K-F, Yu Y (2008) Sales forecasting using extreme learning machine with applications in fashion retailing. Decis Support Syst 46(1):411–419
Sun D, Wan Y, Qiu C (2016) Three dimensional model evaluation of physical alterations of the Caloosahatchee River and Estuary: impact on salt transport. Estuar Coast Shelf Sci 173:16–25
Taormina R, Galelli S, Karakaya G, Ahipasaoglu SD (2016) An information theoretic approach to select alternate subsets of predictors for data-driven hydrological models. J Hydrol 542:18–34
Walden AT (2001) Wavelet analysis of discrete time series. Birkhäuser Basel, 627–641
Wang W, Jing D (2003) Wavelet network model and its application to the prediction of hydrology. Nat Sci 1(1):67–71
Wang Z et al (2015) Flood hazard risk assessment model based on random forest. J Hydrol 527:1130–1141
Wei Z, Xiaohong R, Zheng JH, Zhu YL, Wu HX (2010) Long-term change in tidal dynamics and its cause in the Pearl River Delta, China. Geomorphology 120(3):209–223
Wong LA (2003) A model study of the circulation in the Pearl River Estuary (PRE) and its adjacent coastal waters: 1. Simulations and comparison with observations. J Geophys Res 108(C5):3156
Xinfeng Z, Jiaquan D (2010) Affecting factors of salinity intrusion in Pearl River Estuary and sustainable utilization of water resources in Pearl River Delta. Sustainability in food and water. Springer, Netherlands
Yang X, Zhang H, Zhou H (2014) A hybrid methodology for salinity time series forecasting based on wavelet transform and NARX neural networks. Arab J Sci Eng 39(10):6895–6905
Yang T et al (2017) Developing reservoir monthly inflow forecasts using artificial intelligence and climate phenomenon information. Water Resour Res 53(4):2786–2812
Yaseen ZM et al (2016) Stream-flow forecasting using extreme learning machines: a case study in a semi-arid region in Iraq. J Hydrol 542:603–614
Yin H et al (2017) An effective secondary decomposition approach for wind power forecasting using extreme learning machine trained by crisscross optimization. Energy Convers Manag 150:108–121
Yu PS, Yang TC, Chen SY, Kuo CM, Tseng HW (2017) Comparison of random forests and support vector machine for real-time radar-derived rainfall forecasting. J Hydrol 552:92–104
Zhang W, Ruan XH, Zheng JH, Zhu YL, Wu HX (2010) Long-term change in tidal dynamics and its cause in the Pearl River Delta, China. Geomorphology 120(3–4):209–223
Zhang X, Liang F, Yu B, Zong Z (2011) Explicitly integrating parameter, input, and structure uncertainties into Bayesian neural networks for probabilistic hydrologic forecasting. J Hydrol 409(3):696–709
Zhu J, Weisberg RH, Zheng L, Han S (2015) Influences of channel deepening and widening on the tidal and nontidal circulations of Tampa Bay. Estuaries Coasts 38(1):132–150
Acknowledgements
The research in this paper is fully supported by the National Key Research and Development Program of China (2016YFC0401300), the National Natural Science Foundation of China (Grant Nos. 51879289 and 91547108), the Open Research Foundation of Key Laboratory of the Pearl River Estuarine Dynamics and Associated Process Regulation, Ministry of Water Resources ([2017]KJ07), and the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Corresponding author
Additional information
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
Hu, J., Liu, B. & Peng, S. Forecasting salinity time series using RF and ELM approaches coupled with decomposition techniques. Stoch Environ Res Risk Assess 33, 1117–1135 (2019). https://doi.org/10.1007/s00477-019-01691-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-019-01691-1