Skip to main content
SpringerLink
Log in

The Use of NARX Neural Networks to Forecast Daily Groundwater Levels

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

The lack of information to manage groundwater for irrigation is one of the biggest concerns for farmers and stakeholders in agricultural areas of Mississippi. In this study, we present a novel implementation of a nonlinear autoregressive with exogenous inputs (NARX) network to simulate daily groundwater levels at a local scale in the Mississippi River Valley Alluvial (MRVA) aquifer, located in the southeastern United States. The NARX network was trained using the Levenberg-Marquardt (LM) and Bayesian Regularization (BR) algorithms, and the results were compared to identify an optimal architecture for the forecasting of daily groundwater levels over time. The training algorithms were implemented using different hidden node combinations and delays (5, 25, 50, 75, and 100) until the optimal network was found. Eight years of daily historical input time series including precipitation and groundwater levels were used to forecast groundwater levels up to three months ahead. The comparison between LM and BR showed that NARX-BR is superior in forecasting daily levels based on the Mean Squared Error (MSE), coefficient of determination (R2), and Nash-Sutcliffe coefficient of efficiency. The results showed that BR with two hidden nodes and 100 time delays provided the most accurate prediction of groundwater levels with an error of ± 0.00119 m. This innovative study is the first of its kind and will provide significant contributions for the implementation of data-based models (DBMs) in the prediction and management of groundwater for agricultural use.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abdulkadir SJ, Yong S-P (2015) Scaled UKF–NARX hybrid model for multi-step-ahead forecasting of chaotic time series data. Soft Comput 19:3479–3496. doi:10.1007/s00500-015-1833-z

    Article  Google Scholar 

  • Adeloye A, De Munari A (2006) Artificial neural network based generalized storage–yield–reliability models using the Levenberg–Marquardt algorithm. J Hydrol 326:215–230

    Article  Google Scholar 

  • Anderson MG (2005) Encyclopedia of hydrological sciences vol 1. Chichester; Hoboken: J. Wiley

  • Antonopoulos VZ, Georgiou PE, Antonopoulos ZV (2015) Dispersion coefficient prediction using empirical models and ANNs. Environ Process 2:379–394. doi:10.1007/s40710-015-0074-6

    Article  Google Scholar 

  • Arthur JK (2001) Hydrogeology, model description, and flow analysis of the Mississippi River alluvial aquifer in northwestern Mississippi, vol 1

  • Asefa T, Wanakule N, Adams A (2007) Field-scale application of three types of neural networks to predict ground-water levels. JAWRA J Am Water Resour Assoc 43:1245–1256

    Article  Google Scholar 

  • Barlow JRB, Clark BR (2011) Simulation of water-use conservation scenarios for the Mississippi Delta using an existing regional groundwater flow model. USGS

  • Cathcart TP, Wax CL, Pote JW, Triyono S (2007) A climatological basis for conserving groundwater and reducing overflow in aquaculture ponds in the Southeast United States. Aquac Eng 36:225–232

    Article  Google Scholar 

  • Chang F-J, Chen P-A, Liu C-W, Liao VH-C, Liao C-M (2013) Regional estimation of groundwater arsenic concentrations through systematical dynamic-neural modeling. J Hydrol 499:265–274. doi:10.1016/j.jhydrol.2013.07.008

    Article  Google Scholar 

  • Chang F-J, Tsai Y-H, Chen P-A, Coynel A, Vachaud G (2015) Modeling water quality in an urban river using hydrological factors–data driven approaches. J Environ Manag 151:87–96

    Article  Google Scholar 

  • Chang F-J, Chang L-C, Huang C-W, Kao IF (2016) Prediction of monthly regional groundwater levels through hybrid soft-computing techniques. J Hydrol. doi:10.1016/j.jhydrol.2016.08.006

    Google Scholar 

  • Coulibaly P, Anctil F, Aravena R, Bobée B (2001) Artificial neural network modeling of water table depth fluctuations. Water Resour Res 37:885–896. doi:10.1029/2000wr900368

    Article  Google Scholar 

  • Daliakopoulos IN, Coulibaly P, Tsanis IK (2005) Groundwater level forecasting using artificial neural networks. J Hydrol 309:229–240. doi:10.1016/j.jhydrol.2004.12.001

    Article  Google Scholar 

  • Diaconescu E (2008) The use of NARX neural networks to predict chaotic time series. WSEAS Trans Comp Res 3:182–191

    Google Scholar 

  • Dyer J, Mercer A, Rigby JR, Grimes A (2015) Identification of recharge zones in the lower Mississippi River alluvial aquifer using high-resolution precipitation estimates. J Hydrol 531, Part 2:360–369. doi:10.1016/j.jhydrol.2015.07.016

  • Emamgholizadeh S, Moslemi K, Karami G (2014) Prediction the groundwater level of bastam plain (Iran) by artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). Water Resour Manag 28:5433–5446

    Article  Google Scholar 

  • Foresee FD, Hagan MT (1997) Gauss-Newton approximation to Bayesian learning. In: International Conference on Neural Networks. IEEE, pp 1930–1935

  • Gong Y, Zhang Y, Lan S, Wang H (2016) A comparative study of artificial neural networks, support vector machines and adaptive neuro fuzzy inference system for forecasting groundwater levels near Lake Okeechobee, Florida. Water Resour Manag 30:375–391. doi:10.1007/s11269-015-1167-8

    Article  Google Scholar 

  • Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5:989–993

    Article  Google Scholar 

  • Jayawardena A (2014) Environmental and hydrological systems modelling. CRC Press

  • Kebede H, Fisher DK, Sui R, Reddy KN (2014) Irrigation methods and scheduling in the delta region of Mississippi: current status and strategies to improve irrigation efficiency. Am J Plant Sci 5:2917

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Kişi Ö (2007) Streamflow forecasting using different artificial neural network algorithms. J Hydrol Eng 12:532–539

    Article  Google Scholar 

  • Lee W-K, Tuan Resdi TA (2016) Simultaneous hydrological prediction at multiple gauging stations using the NARX network for Kemaman catchment, Terengganu, Malaysia. Hydrol Sci J :1–16 doi:10.1080/02626667.2016.1174333

  • Lee CC, Sheridan SC, Barnes BB, Hu C, Pirhalla DE, Ransibrahmanakul V, Shein K (2016) The development of a non-linear autoregressive model with exogenous input (NARX) to model climate-water clarity relationships: reconstructing a historical water clarity index for the coastal waters of the southeastern USA. Theor Appl Climatol :1–13. doi:10.1007/s00704-016-1906-7

  • Leontaritis IJ, Billings SA (1985) Input-output parametric models for non-linear systems part I: deterministic non-linear systems. Int J Control 41:303–328. doi:10.1080/0020718508961129

    Article  Google Scholar 

  • Lohani A, Krishan G (2015) Application of artificial neural network for groundwater level simulation in Amritsar and Gurdaspur districts of Punjab, India. J Earth Sci Clim Change 6:2

    Google Scholar 

  • MacKay DJ (1992) Bayesian interpolation. Neural Comput 4:415–447

    Article  Google Scholar 

  • 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 15:101–124. doi:10.1016/S1364-8152(99)00007-9

    Article  Google Scholar 

  • Maupin MA, Barber NL (2005) Estimated withdrawals from principal aquifers in the United States, 2000 [electronic resource] /by Molly A. Maupin and Nancy L. Barber. Circular: 1279. Reston; Denver: U.S. Dept. of the Interior, U.S. Geological Survey

  • Menne M, et al. (2012) Global historical climatology network-daily (GHCN-Daily), version 3. 2 NOAA national climatic data center

  • Mohanty S, Jha MK, Kumar A, Sudheer K (2010) Artificial neural network modeling for groundwater level forecasting in a river island of eastern India. Water Resour Manag 24:1845–1865

    Article  Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I — a discussion of principles. J Hydrol 10:282–290. doi:10.1016/0022-1694(70)90255-6

    Article  Google Scholar 

  • Nayak P, Rao YRS, Sudheer KP (2006) Groundwater level forecasting in a shallow aquifer using artificial neural network approach. Water Resour Manag 20:77–90. doi:10.1007/s11269-006-4007-z

    Article  Google Scholar 

  • Ruslan FA, Samad AM, Zain ZM, Adnan R (2013) Flood prediction using NARX neural network and EKF prediction technique: A comparative study. In: System Engineering and Technology (ICSET), 2013 I.E. 3rd International Conference on, 2013. IEEE, pp 203–208

  • Sahoo S, Jha MK (2013) Groundwater-level prediction using multiple linear regression and artificial neural network techniques: a comparative assessment. Hydrogeol J 21:1865–1887

    Article  Google Scholar 

  • Sarkar A, Pandey P (2015) River water quality modelling using artificial neural network technique. Aquatic Procedia 4:1070–1077

    Article  Google Scholar 

  • Seidl DR, Lorenz RD (1991) A structure by which a recurrent neural network can approximate a nonlinear dynamic system. In: Neural Networks, 1991., IJCNN-91-Seattle International Joint Conference on, 1991. IEEE, pp 709–714

  • Siegelmann HT, Horne BG, Giles CL (1997) Computational capabilities of recurrent NARX neural networks. IEEE Trans Syst Man Cybern B Cybern 27:208–215

    Article  Google Scholar 

  • Singh N, Chakrapani G (2015) ANN modelling of sediment concentration in the dynamic glacial environment of Gangotri in Himalaya. Environ Monit Assess 187:1–14

    Article  Google Scholar 

  • Snipes CE, Nichols S, Poston D, Walker T, Evans L, Robinson H (2005) Current agricultural practices of the Mississippi Delta. Bulletin 1143, Mississippi Agricultural and Forestry Experiment Station

  • Tóth J (1963) A theoretical analysis of groundwater flow in small drainage basins. J Geophys Res 68:4795–4812. doi:10.1029/JZ068i016p04795

    Article  Google Scholar 

  • Trichakis IC, Nikolos IK, Karatzas G (2011) Artificial neural network (ANN) based modeling for karstic groundwater level simulation. Water Resour Manag 25:1143–1152

    Article  Google Scholar 

  • Tsung-Nan L, Giles CL, Horne BG, Sun-Yuan K (1997) A delay damage model selection algorithm for NARX neural networks. Signal Process, IEEE Trans 45:2719–2730. doi:10.1109/78.650098

    Article  Google Scholar 

  • USGS (2014) National water information system data available on the world wide web (Water Data for the Nation). http://waterdata.usgs.gov/nwis/gw. Accessed 15 Jun 2014

  • Welch HL, Green CT, Coupe RH (2011) The fate and transport of nitrate in shallow groundwater in northwestern Mississippi, USA. Hydrogeol J 19:1239–1252

    Article  Google Scholar 

Download references

Acknowledgements

This material is based upon work that is supported by the National Institute of Food and Agriculture, U.S. Department of Agriculture, Hatch project under accession number 227246. The authors would like to acknowledge Ruiyi Wu for his contribution in the code development and Juan Perez-Gutiérrez for his suggestions during the preparation of this paper. Special thanks to the reviewers for their valuable comments that helped improve the paper.

Author information

Authors and Affiliations

  1. Department of Agricultural and Biological Engineering, Mississippi State University, Mississippi State, Starkville, MS, 39762, USA

    Sandra M. Guzman, Joel O. Paz & Mary Love M. Tagert

Authors
  1. Sandra M. Guzman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joel O. Paz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mary Love M. Tagert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joel O. Paz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guzman, S.M., Paz, J.O. & Tagert, M.L.M. The Use of NARX Neural Networks to Forecast Daily Groundwater Levels. Water Resour Manage 31, 1591–1603 (2017). https://doi.org/10.1007/s11269-017-1598-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-017-1598-5

Keywords

Search

Navigation