Abstract
Groundwater resources (GWR) are vital to agricultural crop production, everyday life, and economic development. As a result, accurate groundwater level (GWL) prediction would aid in the long-term management of GWR. A comparative analysis was performed to test the predictive capabilities of models based on non-linear autoregressive with exogenous inputs (NARX) and extreme learning machine (ELM). Long-term predictions were performed using GWL and rainfall time series measured in two sites, Bogra and Dinajpur, in Bangladesh’s northwest region from 1981 to 2017. The delay between precipitation and GWL was assessed through the cross-correlation function, computing an input delay equal to 2 months for both sites. Furthermore, the auto-correlation of the GWL was also performed to evaluate the optimal feedback delay, showing the seasonality of GWL fluctuations with a peak at 12 months for both sites. However, the sensitivity to changes in the feedback delay was also assessed, comparing the predictions produced for a feedback delay equivalent to 12 months with those computed for delays ranging from 1 to 11 months. Outputs of the two proposed models were evaluated using different metrics: the root mean square error (RMSE), mean absolute error (MAE), relative absolute error (RAE), and correlation coefficient (CC). The results revealed that NARX models outperformed ELM models. NARX models were able to provide accurate long-term predictions, with R2 equal to 0.918 and 0.947 for Bogra and Dinajpur sites, respectively, with a forecasting horizon τ = 12 months. ELM models also provided good forecasts for Dinajpur, but less accurate for Bogra, with R2 respectively equal to 0.825 and 0.675 with τ = 12 months. This research would provide a practical and efficient approach to GWL prediction that could aid policymakers in implementing long-term GWR management.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abba SI, Elkiran G, Nourani V (2021) Improving novel extreme learning machine using PCA algorithms for multi-parametric modeling of the municipal wastewater treatment plant. Desalination and Water Treatment 215:414–426
Abba SI, Nguyen TTL, Jazuli A, Shaban IAA, Quoc BP, Rabiu AA, Romulus C, Nam VT, Anh DT (2020a) Hybrid machine learning ensemble techniques for modeling dissolved oxygen concentration. IEEE Access 8:157218–157237
Abba SI, Quoc BP, Usman AG, Nguyen TTL, Aliyu DS, Nguyen Q, Bach QV (2020b) Emerging evolutionary algorithm integrated with kernel principal component analysis for modeling the performance of a water treatment plant. J Water Process Eng 33:101081
Abbasi A, Khalili K, Behmanesh J, Shirzad A (2019) Drought monitoring and prediction using SPEI index and gene expression programming model in the west of Urmia Lake. Theoretic Appl Climatol 138(1):553–567. https://doi.org/10.1007/s00704-019-02825-9
Adamowski J, Chan FH (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407:28–40. https://doi.org/10.1016/j.jhydrol.2011.06.013
Adham MI, Jahan CS, Mazumder QH, Hossain MMA, Al-Mamunul Haque M (2010) Study on groundwater recharge potentiality of Barind Tract, Rajshahi District, Bangladesh using GIS and remote sensing technique. J Geol Soc India 75:432–438. https://doi.org/10.1007/s12594-010-0039-3
Alsumaiei AA (2020) A nonlinear autoregressive modeling approach for forecasting groundwater level fluctuation in urban aquifers. Water 12(3). https://doi.org/10.3390/w12030820
Barzegar R, Fijani E, Asghari Moghaddam A, Tziritis E (2017) Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network-based models. Sci Total Environ 599-600:20–31
Cadenas E, Rivera W, Campos-Amezcua R, Heard C (2016) Wind speed prediction using a univariate ARIMA model and a multivariate NARX model. Energies 9(2):109
Chang FJ, Chang LC, Huang CW, Kao I (2016) Prediction of monthly regional groundwater levels through hybrid soft-computing techniques. J Hydrol 541:965–976
Chen LH, Chen CT, Lin DW (2011) Application of integrated back-propagation network and self-organizing map for groundwater level forecasting. J Water Resour Plann Manag 137(4):352–365. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000121
Chen LH, Chen CT, Pan YG (2010) Groundwater level prediction using SOM-RBFN multisite model. J Hydrol Eng 15(8):624–631. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000218
Cho KH, Sthiannopkao S, Pachepsky YA, Kim KW, Kim JH (2011) Prediction of contamination potential of groundwater arsenic in Cambodia, Laos, and Thailand using artificial neural network. Water Res 45(17):5535–5544. https://doi.org/10.1016/j.watres.2011.08.010
Coulibaly P, Anctil F, Aravena R, Bobee B (2001) Artificial neural network modeling of water table depth fluctuations. Water Resour Res 37(4):885–896. https://doi.org/10.1029/2000WR900368
Cui Y, Liao Z, Wei Y, Xu X, Song Y, Liu H (2020) The response of groundwater level to climate change and human activities in Baotou City, China. Water 12. https://doi.org/10.3390/w12041078
Daliakopoulos IN, Coulibaly P, Tsanis IK (2005) Groundwater level forecasting using artificial neural networks. J Hydrol 309:229–240. https://doi.org/10.1016/j.jhydrol.2004.12.001
De Filippis G, Margiotta S, Caruso F, Negri SL (2020) Open questions about the hydrodynamic behaviour of the deep, coastal aquifer of the Salento peninsula (south-eastern Italy): coupling expert knowledge, data, and numerical modelling for testing hydrogeological conceptual models. Sci Total Environ 715. https://doi.org/10.1016/j.scitotenv.2020.136962
Dey NC, Saha R, Parvez M, Bala SK, Islam AKMS, Joyanta KP, Hossain M (2017) Sustainability of groundwater use for irrigation of dry-season crops in northwest Bangladesh. Groundw Sustain Dev 4:66–77. https://doi.org/10.1016/j.gsd.2017.02.001
Di Nunno F, Granata F (2020) Groundwater level prediction in Apulia region (Southern Italy) using NARX neural network. Environ Res 190. https://doi.org/10.1016/j.envres.2020.110062
Di Nunno F, Granata F, Gargano R, de Marinis G (2021a) Prediction of spring flows using nonlinear autoregressive exogenous (NARX) neural network models. Environ Monit Assess 193(6):350. https://doi.org/10.1007/s10661-021-09135-6
Di Nunno F, de Marinis G, Gargano R, Granata F (2021b) Tide prediction in the Venice Lagoon using nonlinear autoregressive exogenous (NARX) neural network. Water 13(9):1173. https://doi.org/10.3390/w13091173
Dixon B (2009) A case study using support vector machines, neural networks and logistic regression in a GIS to identify wells contaminated with nitrate-N. Hydrogeol J 17(6):1507–1520. https://doi.org/10.1007/s10040-009-0451-1
Evans S, Williams GP, Jones NL, Ames DP, Nelson EJ (2020) Exploiting earth observation data to impute groundwater level measurements with an extreme learning machine. Remote Sensing 12(12):2044. https://doi.org/10.3390/rs12122044
Frost, J. (2019). Introduction to statistics: an intuitive guide for analyzing data and unlocking discoveries., Statistics by Jim Publishing, p. 255.
Ghorbani MA, Deo RC, Yaseen ZM, Kashani MH, Mohammadi B (2018) Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: case study in North Iran. Theor Appl Climatol 133(2):1119–1131. https://doi.org/10.1007/s00704-017-2244-0
Granata F, Di Nunno F (2021a) Forecasting evapotranspiration in different climates using ensembles of recurrent neural networks. Agri Water Manag 255. https://doi.org/10.1016/j.agwat.2021.107040
Granata F, Di Nunno F (2021b) Artificial Intelligence models for prediction of the tide level in Venice. Stochastic Environ Res Risk Assess. https://doi.org/10.1007/s00477-021-02018-9
Guzman SM, Paz JO, Tagert MLM (2017) The use of NARX neural networks to forecast daily groundwater levels. Water Resour Manag 31:1591–1603. https://doi.org/10.1007/s11269-017-1598-5
Guzman SM, Paz JO, Tagert MLM, Mercer AE (2019) Evaluation of seasonally classified inputs for the prediction of daily groundwater levels: NARX networks vs support vector machines. Environ Model Assess 24:223–234. https://doi.org/10.1007/s10666-018-9639-x
Hadi SJ, Abba SI, Sammen SS, Salih SQ, Al-Ansari N, Yaseen ZM (2019) Non-linear input variable selection approach integrated with non-tuned data intelligence model for streamflow pattern simulation. IEEE Access 7:141533–141548. https://doi.org/10.1109/ACCESS.2019.2943515
Huang G, Huang GB, Song S, You K (2015) Trends in extreme learning machines: a review. Neural Netw 61:32–48. https://doi.org/10.1016/j.neunet.2014.10.001
Huang GB, Qin-Yu Z, Chee-Kheong S (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501
Iannello JP (1982) Time delay estimation via cross-correlation in the presence of large estimation errors. IEEE Trans Signal Process 30(6):998–1003. https://doi.org/10.1109/tassp.1982.1163992
Islam ARMT, Shen S, Hu Z, Rahman MA (2017) Drought hazard evaluation in Boro paddy cultivated areas of western Bangladesh at current and future climate change conditions. Adv Meteorol 3514381:12. https://doi.org/10.1155/2017/3514381
Islam ARMT, Shen S, Yang S (2018) Predicting design water requirement of winter paddy under climate change condition using frequency analysis in Bangladesh. Agri Water Manag 195(C):58–70. https://doi.org/10.1016/j.agwat.2017.10.003
Islam ARMT, Shen S, Yang SB, Hu Z, Chu R (2019) Assessing recent impacts of climate change on design water requirement of Boro rice season in Bangladesh. Theor Appl Climatol 138(1-2):97–113. https://doi.org/10.1007/s00704-019-02818-8
Islam ARMT, Karim MR, Mondol MAH (2021) Appraising trends and forecasting of hydroclimatic variables in the north and northeast regions of Bangladesh. Theor Appl Climatol 143:33–50. https://doi.org/10.1007/s00704-020-03411-0
Izady A, Davary K, Alizadeh A, Ziaei AN, Hasheminia SM (2013) Application of NN-ARX model to predict groundwater levels in the Neishaboor Plain, Iran. Water Resour Manag 27(14):4773–4794. https://doi.org/10.1007/s11269-013-0432-y
Jahan CS, Mazumder QH, Islam ATMM, Adham MI (2010) Impact of irrigation in Barind area, NW Bangladesh—an evaluation based on the meteorological parameters and fluctuation trend in groundwater table. J Geol Soc India 76:134–142
Jami AA, Himel MU, Hasan K, Basak SR, Mita AF (2020) NARX neural network approach for the monthly prediction of groundwater levels in Sylhet Sadar, Bangladesh. J Groundw Sci Eng 8(2):118–126
Jha MK, Sahoo S (2015) Efficacy of neural network and genetic algorithm techniques in simulating spatio-temporal fluctuations of groundwater. Hydrol Process 29(5):671–691
Juan C, Genxu W, Tianxu M (2015) Simulation and prediction of suprapermafrost groundwater level variation in response to climate change using a neural network model. J Hydrol 529:1211–1220. https://doi.org/10.1016/j.jhydrol.2015.09.038
Khaki M, Yusoff I, Islami N (2015) Application of the artificial neural network and neuro-fuzzy system for assessment of groundwater quality. Clean-Soil, Air, Water 43:551–560. https://doi.org/10.1002/clen.201400267
Khurshid Alam MD, Shahidul Hasan AKM, Khan MR, Whitney JW, Abdullah SKM, Queen JE (1990) Geological map of Bangladesh. Geological Survey of Bangladesh, Dhaka
Kim S, Seo Y, Rezaie-Balf M, Kisi O, Ghorbani MA, Singh VP (2018) Evaluation of daily solar radiation flux using soft computing approaches based on different meteorological information: Peninsula vs Continent. Theor Appl Climatol 137(1–2):693–712. https://doi.org/10.1007/s00704-018-2627-x
Kisi O, Alizamir M, Zounemat-Kermani M (2017) Modeling groundwater fluctuations by three different evolutionary neural network techniques using hydroclimatic data. Natural Hazards 87(1):367–381
MacKay DJC (1992) Bayesian Interpolation. Neural Computing 4:415–447. https://doi.org/10.1162/neco.1992.4.3.415
Malekzadeh, M., Kardar, S., Saeb, K., Shabanlou, S. and Taghavi, L. (2019). A novel approach for prediction of monthly ground water level using a hybrid wavelet and non-tuned self-adaptive machine learning model. Water Resources Management, 33, pp. 1609-1628, doi: 10.1007/s11269-019-2193-8.
MathWorks (2020). MATLAB Deep Learning Toolbox Release 2020a. Natick, Massachusetts, United States.
Mohammadi B, Mehdizadeh S, Ahmadi F, Lien NTT, Linh NTT, Pham QB (2020) Developing hybrid time series and artificial intelligence models for estimating air temperatures. Stochastic Environ Res Risk Assess. https://doi.org/10.1007/s00477-020-01898-7
Morgan JP, McIntire WG (1959) Quaternary geology of Bengal Basin, East Pakistan and India. Geol Soc Am Bull 70:319–342
Natarajan N, Sudheer C (2020) Groundwater level forecasting using soft computing techniques. Neural Comput Appl 32:7691–7708. https://doi.org/10.1007/s00521-019-04234-5
Nayak PC, Rao YRS, Sudheer KP (2006) Groundwater level forecasting in a shallow aquifer using artificial neural network approach. Water Resour Manag 20(1):77–90
Persits, F.M., Wandrey, C.J., Milici, R.C. and Manwar, A. (2001). US Geological Survey.
Praveen B, Talukdar S, Shahfahad M, S., Mondal, J., Sharma, P., Islam, A.R.M.T., Rahman, A. (2020) Analyzing trend and forecasting of rainfall changes in India using non-parametrical and machine learning approaches. J Hydrol 10(1):10342. https://doi.org/10.1038/s41598-020-67228-7
Rahman MS, Islam ARMT (2019) Are precipitation concentration and intensity changing in Bangladesh overtimes? Analysis of the possible causes of changes in precipitation systems. Sci Total Environ 690:370–387. https://doi.org/10.1016/j.scitotenv.2019.06.529
Rajaee T, Ebrahimi H, Nourani V (2019) A review of the artificial intelligence methods in groundwater level modeling. J Hydrol 572:336–351. https://doi.org/10.1016/j.jhydrol.2018.12.037
Sahoo GB, Ray C, Wade HF (2005) Pesticide prediction in ground water in North Carolina domestic wells using artificial neural networks. Ecol Modell 183(1):29–46. https://doi.org/10.1016/j.ecolmodel.2004.07.021
Sahoo S, Russo TA, Elliott J, Foster I (2017) Machine learning algorithms for modeling groundwater level changes in agricultural regions of the U.S. Water Resour Res 53(5):3878–3895
Salam R, Islam ARMT, Islam S (2020) Spatiotemporal distribution and prediction of groundwater level linked to ENSO teleconnection indices in the northwestern region of Bangladesh. Environ Dev Sustain 22(5):4509–4535. https://doi.org/10.1007/s10668-019-00395-4
Salam R, Islam ARMT (2020) Potential of RT, Bagging and RS ensemble learning algorithms for reference evapotranspiration prediction using climatic data-limited humid region in Bangladesh. J Hydrol 590:125241. https://doi.org/10.1016/j.jhydrol.2020.125241
Shahid S, Hazarika MK (2010) Groundwater drought in the northwestern districts of Bangladesh. Water Resour Manag 24(10):1989–2006. https://doi.org/10.1007/s11269-009-9534-y
Shamsudduha M, Taylor R, Ahmed KM, Zahid A (2011) The impact of intensive groundwater abstraction on recharge to a shallow regional aquifer system: evidence from Bangladesh. Hydrogeol J 19(4):901–916. https://doi.org/10.1007/s10040-011-0723-4
Shiri J, Kisi O, Yoon H, Lee KK, Nazemi AH (2013) Predicting groundwater level fluctuations with meteorological effect implications—a comparative study among soft computing techniques. Comput Geosci UK 56:32–44. https://doi.org/10.1016/j.cageo.2013.01.007
Sreekanth PD, Geethanjali N, Sreedevi PD, Ahmed S, Kumar NR, Kamala Jayanthi PD (2009) Forecasting groundwater level using artificial neural networks. Curr Sci 96(7):933–939
Talukdar S, Eibek KU, Akhter S, Ziaul SK, Islam ARMT, Mallick J (2021) Modeling fragmentation probability of land-use and land-cover using the bagging, random forest and random subspace in the Teesta River Basin, Bangladesh. Ecol Indicators 126:107612. https://doi.org/10.1016/j.ecolind.2021.107612
Wang X, Liu T, Zheng X, Peng H, Xin J, Zhang B (2018) Short-term prediction of groundwater level using improved random forest regression with a combination of random features. Applied Water. Science 8(125). https://doi.org/10.1007/s13201-018-0742-6
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 Modell Softw 54:108–127. https://doi.org/10.1016/j.envsoft.2013.12.016
Wunsch A, Liesch T, Broda S (2018) Forecasting groundwater levels using nonlinear autoregressive networks with exogenous input (NARX). J Hydrol 567:743–758. https://doi.org/10.1016/j.jhydrol.2018.01.045
Yadav B, Chintalapati S, Mathur S, Adamowski J (2017) Assessing the suitability of extreme learning machines (ELM) for groundwater level prediction. J Water Land Dev 32(1):103–112. https://doi.org/10.1515/jwld-2017-0012
Yaseen ZM, Allawi MF, Yousif AA, Jaafar O, Hamzah MF, El-Shafie A (2018) Non-tuned machine learning approach for hydrological time series forecasting. Neural Computing and Application 30:1479–1491. https://doi.org/10.1007/s00521-016-2763-0
Yaseen ZM, Sadeq OS, Ravinesh CD, Chau KW (2019) An enhanced extreme learning machine model for river flow forecasting: state-of-the-art, practical applications in water resource engineering area and future research direction. J Hydrol 569:387–408
Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK (2011) A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J Hydrol 396(1-2):128–138
Yosefvand F, Shabanlou S (2020) Forecasting of groundwater level using ensemble hybrid wavelet–self-adaptive extreme learning machine-based models. Natural Resour Res 29:3215–3232. https://doi.org/10.1007/s11053-020-09642-2
Zahid A, Ahmed SRU (2006) Groundwater resources development in Bangladesh: contribution to irrigation for food security and constraints to sustainability. Groundw Gov Asia S1:25–46
Availability of data and materials
The data that support the findings of this study are available from the corresponding author, [Quoc Bao Pham, quoc_bao.pham@us.edu.pl], upon reasonable request.
Author information
Authors and Affiliations
Contributions
DNF and QBP: Project administration, conceptualization, writing-original draft, software, formal analysis, and visualization. SIA and ARMTI: Formal analysis; writing-original draft, and visualization. ST and GF: Data curation, formal analysis, investigation, writing-review and editing.
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent to publish
Not applicable.
Competing interests
The authors declare no competing interests.
Additional information
Responsible Editor: Broder J. Merkel
Highlights
1. A comparative analysis was performed based on capabilities of NARX and ELM
2. Long-term predictions were performed using GWL measured in two sites in Bangladesh
3. ELM model was firstly applied for GWL forecasting and provided good performance
4. The results revealed that NARX model outperformed ELM model
5. This research could aid policymakers in implementing long-term GWR management
Rights and permissions
About this article
Cite this article
Fabio, D.N., Abba, S.I., Pham, B.Q. et al. Groundwater level forecasting in Northern Bangladesh using nonlinear autoregressive exogenous (NARX) and extreme learning machine (ELM) neural networks. Arab J Geosci 15, 647 (2022). https://doi.org/10.1007/s12517-022-09906-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-022-09906-6