Abstract
The performance comparison studies of the autoregressive integrated moving average model (ARIMA) and the artificial neural network (ANN) were mostly carried out between the selected model structures through trial-and-error, strongly influenced by model structure uncertainty. This research aims to make up for this inadequacy. First, a surface water quality prediction case study including eight monitoring sites in China was introduced. Second, the ARIMA and ANN’s performance was compared statistically between 6912 Seasonal ARIMA (SARIMA) and 110,592 feedforward ANN with different model structures, based on the mean square error (MSE) distributions depicted by boxplots. In a statistical view, the ANN models obtained a significantly lower median value and a more concentrated distribution of validation MSEs, which indicated lighter overfitting and better generalization ability. Furthermore, the optimal SARIMA models’ performance is inferior to even the median of the ANN models in the case study. In contrast with the previous comparisons among selected models, the statistical comparison in this study shows lower uncertainty.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The datasets and codes are available in our GitHub repository: https://github.com/MrBrenda/WaterResourcesFNNModels.git.
References
Ahmad S, Khan IH, Parida B (2001) Performance of stochastic approaches for forecasting river water quality. Water Res 35:4261–4266. https://doi.org/10.1016/S0043-1354(01)00167-1
Ansari M, Othman F, Abunama T, El-Shafie A (2018) Analysing the accuracy of machine learning techniques to develop an integrated influent time series model: case study of a sewage treatment plant, Malaysia. Environ Sci Pollut Res 25:12139–12149. https://doi.org/10.1007/s11356-018-1438-z
Bhagat SK, Tung TM, Yaseen ZM (2020) Development of artificial intelligence for modeling wastewater heavy metal removal: State of the art, application assessment and possible future research. J Clean Prod 250:119473. https://doi.org/10.1016/j.jclepro.2019.119473
Bhagat SK, Tiyasha T, Awadh SM, Tung TM, Jawad AH, Yaseen ZM (2021) Prediction of sediment heavy metal at the Australian Bays using newly developed hybrid artificial intelligence models. Environ Pollut 268:115663. https://doi.org/10.1016/j.envpol.2020.115663
Box GE, Jenkins GM (1976) Time series analysis: forecasting and control, vol 31, third edn. Holden Day, Oakland, p 303
Diez-Sierra J, del Jesus M (2020) Long-term rainfall prediction using atmospheric synoptic patterns in semi-arid climates with statistical and machine learning methods. J Hydrol 586:124789. https://doi.org/10.1016/j.jhydrol.2020.124789
Doshi-Velez F, Kim B (2017) Towards A Rigorous Science of Interpretable Machine Learning 1–13. https://arxiv.org/abs/1702.08608v2.
Edwin AI, Martins OY (2014) Stochastic Characteristics and Modelling of Monthly Rainfall Time Series of Ilorin, Nigeria. Open J Mod Hydrol 04:67–79. https://doi.org/10.4236/ojmh.2014.43006
Elkiran G, Nourani V, Abba SI (2019) Multi-step ahead modelling of river water quality parameters using ensemble artificial intelligence-based approach. J Hydrol 577:123962. https://doi.org/10.1016/j.jhydrol.2019.123962
García Nieto PJ, García-Gonzalo E, Alonso Fernández JR, Díaz Muñiz C (2019) Water eutrophication assessment relied on various machine learning techniques: A case study in the Englishmen Lake (Northern Spain). Ecol Model 404:91–102. https://doi.org/10.1016/j.ecolmodel.2019.03.009
García-Alba J, Bárcena JF, Ugarteburu C, García A (2018) Artificial neural networks as emulators of process-based models to analyse bathing water quality in estuaries. Water Res 150:283–295. https://doi.org/10.1016/j.watres.2018.11.063
Haghiabi AH, Nasrolahi AH, Parsaie A (2018) Water quality prediction using machine learning methods. Water Qual Res J Can 53:3–13. https://doi.org/10.2166/wqrj.2018.025
Hameed M, Sharqi SS, Yaseen ZM, Afan HA, Hussain A, Elshafie A (2017) Application of artificial intelligence (AI) techniques in water quality index prediction: a case study in tropical region, Malaysia. Neural Comput & Applic 28:893–905. https://doi.org/10.1007/s00521-016-2404-7
Hanson PC, Stillman AB, Jia X, Karpatne A, Dugan HA, Carey CC, Stachelek J, Ward NK, Zhang Y, Read JS, Kumar V (2020) Predicting lake surface water phosphorus dynamics using process-guided machine learning. Ecol Model 430:109136. https://doi.org/10.1016/j.ecolmodel.2020.109136
Hunter JM, Maier HR, Gibbs MS, Foale ER, Grosvenor NA, Harders NP, Kikuchi-Miller TC (2018) Framework for developing hybrid process-driven, artificial neural network and regression models for salinity prediction in river systems. Hydrol Earth Syst Sci 22:2987–3006. https://doi.org/10.5194/hess-22-2987-2018
Kang G, Gao JZ, Xie G (2017) Data-driven water quality analysis and prediction: A survey. Proc - 3rd IEEE Int Conf Big Data Comput Serv Appl BigDataService 2017 224–232. https://doi.org/10.1109/BigDataService.2017.40
Khairuddin N, Aris AZ, Elshafie A, Sheikhy Narany T, Ishak MY, Isa NM (2019) Efficient forecasting model technique for river stream flow in tropical environment. Urban Water J 16:1–10. https://doi.org/10.1080/1573062x.2019.1637906
Landeras G, Ortiz-Barredo A, López JJ (2009) Forecasting weekly evapotranspiration with ARIMA and artificial neural network models. J Irrig Drain Eng 135:323–334. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000008
Maier HR, Jain A, Dandy GC, Sudheer KP (2010) 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 25:891–909. https://doi.org/10.1016/j.envsoft.2010.02.003
Monteiro M, Costa M (2018) A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables. Hydrology 5:37. https://doi.org/10.3390/hydrology5030037
Mount NJ, Maier HR, Toth E, Elshorbagy A, Solomatine D, Chang FJ, Abrahart RJ (2016) Data-driven modelling approaches for socio-hydrology: Opportunities and challenges within the Panta Rhei Science Plan. Hydrol Sci J 61:1192–1208. https://doi.org/10.1080/02626667.2016.1159683
Ömer Faruk D (2010) A hybrid neural network and ARIMA model for water quality time series prediction. Eng Appl Artif Intell 23:586–594. https://doi.org/10.1016/J.ENGAPPAI.2009.09.015
Rafael A, Parmezan S, Souza VMA, Batista GEAPA (2019) Evaluation of statistical and machine learning models for time series prediction : Identifying the state-of-the-art and the best conditions for the use of each model. Inf Sci 484:302–337. https://doi.org/10.1016/j.ins.2019.01.076
Raman H, Sunilkumar N (1995) Multivariate modelling of water resources time series using artificial neural networks. Hydrol Sci J 40:145–163. https://doi.org/10.1080/02626669509491401
Salmani MH, Salmani Jajaei E (2016) Forecasting models for flow and total dissolved solids in Karoun river-Iran. J Hydrol 535:148–159. https://doi.org/10.1016/J.JHYDROL.2016.01.085
Schmidhuber J (2015) Deep learning in neural networks: An overview. Neural Netw 61:85–117. https://doi.org/10.1016/J.NEUNET.2014.09.003
Sheikhy Narany T, Aris AZ, Sefie A, Keesstra S (2017) Detecting and predicting the impact of land use changes on groundwater quality, a case study in Northern Kelantan, Malaysia. Sci Total Environ 599–600:844–853. https://doi.org/10.1016/J.SCITOTENV.2017.04.171
Shi B, Wang P, Jiang J, Liu R (2018) Applying high-frequency surrogate measurements and a wavelet-ANN model to provide early warnings of rapid surface water quality anomalies. Sci Total Environ 610–611:1390–1399. https://doi.org/10.1016/j.scitotenv.2017.08.232
Tiyasha, Tung TM, Yaseen ZM (2020) A survey on river water quality modelling using artificial intelligence models: 2000–2020. J Hydrol 585:124670. https://doi.org/10.1016/j.jhydrol.2020.124670
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. https://doi.org/10.1016/J.JHYDROL.2012.11.017
Wu W, May RJ, Maier HR, Dandy GC (2013) A benchmarking approach for comparing data splitting methods for modeling water resources parameters using artificial neural networks. Water Resour Res 49:7598–7614. https://doi.org/10.1002/2012WR012713
Wu W, Dandy GC, Maier HR (2014) Protocol for developing ANN models and its application to the assessment of the quality of the ANN model development process in drinking water quality modelling. Environ Model Softw 54:108–127. https://doi.org/10.1016/j.envsoft.2013.12.016
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 409:696–709. https://doi.org/10.1016/j.jhydrol.2011.09.002
Zhou J, Wang Y, Xiao F, Wang Y, Sun L (2018) Water Quality Prediction Method Based on IGRA and LSTM. Water 10:1148. https://doi.org/10.3390/w10091148
Acknowledgements
This study was financially supported by the Major Science and Technology Project of Water Pollution Control and Management in China (grant no. 2018ZX07208006) and the National Natural Science Foundation of China (grant no. 51778451). We also thank the 111 Project (B13017) of Tongji University.
Funding
Major Science and Technology Project of Water Pollution Control and Management in China (grant no. 2018ZX07208006). National Natural Science Foundation of China (grant no. 51778451). 111 Project (B13017) of Tongji University.
Author information
Authors and Affiliations
Contributions
Xuan Wang: conceptualization, methodology, software, data curation, writing—original draft preparation.
Wenchong Tian: methodology, investigation, writing—reviewing, and editing.
Zhenliang Liao: supervision, writing—reviewing, and editing.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Additional information
Responsible Editor: Xianliang Yi
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
ESM 1
(DOCX 1090 kb).
Rights and permissions
About this article
Cite this article
Wang, X., Tian, W. & Liao, Z. Statistical comparison between SARIMA and ANN’s performance for surface water quality time series prediction. Environ Sci Pollut Res 28, 33531–33544 (2021). https://doi.org/10.1007/s11356-021-13086-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11356-021-13086-3