Modeling Earth Systems and Environment

, Volume 3, Issue 4, pp 1371–1382 | Cite as

Application of automatic relevance determination model for groundwater quality index prediction by combining hydro-geochemical and geo-electrical data

  • Saumen Maiti
  • Anasuya Das
  • Rhythm Shah
  • Gautam Gupta
Original Article


In this study, an automatic relevance determination-based Bayesian neural network (ARD-BNN) approach is employed combing hydro-geochemical and geo-electrical information to predict groundwater quality index (GWQI) of coastal Maharashtra, India. In the first step, to incorporate geo-electrical information for GWQI forward computation, the weight corresponding to true resistivity of the earth layer is estimated via ARD-BNN modelling using training sample generated for groundwater classification. In the second step, incorporating earth resistivity weight information, a total of 1500 training samples are created honouring World Health Organisation (WHO) guidelines for GWQI prediction. Prior to actual data analysis, we explored the algorithm on GWQI variable series assorted with different level of complex (red) noise to examine the bounds of network hyper-parameter. What distinguishes our approach from previous approach for ARD-BNN optimization is that we seek to develop a mechanism which allows specific weight estimation and provides insight into which hyper parameters and their bounds are appropriate to predict GWQI from noise intervened GWQI data. The model shows excellent performance between predicted and computed GWQI both in training (trn) and test (tst) data with Pearson’s correlation coefficient (rtrn ~ 0.91 and rtst ~ 0.90), root-mean-squared-error (RMSE) error (RMSEtrn ~ 1.2 and RMSEtst ~ 1.4), reduction of error (RE) (REtrn ~ 0.98 and REtst ~ 0.97), and index of agreement (IA) (IAtrn ~ 0.95 and IAtst ~ 0.93). Red noise analysis shows that the ARD-BNN model is robust up to the noise level of 20% in the input variable for GWQI prediction. The network adopted relevance analysis to indicate the relative importance of input parameter in the prediction of GWQI via ARD-BNN modelling which showed that chloride [Cl], [pH], [HCO3 ] and sodium [Na+] are dominant while considering various simulations for characterizing the GWQI of coastal Maharashtra. The approach used here, could be useful in understanding the relative contribution and/or modelling pollution source in many other environmental applications.


Bayesian neural networks Automatic relevance determination Groundwater quality parameter Groundwater quality index Konkan 



Authors are thankful to the Director, IIT (ISM), Dhanbad and Director, IIG, Navi Mumbai for their kind permission to publish the work. AD is thankful to ISM JRF fellowship in which the some analysis work is done Partial financial benefit from the Ministry of Earth Sciences, Govt. of India, New Delhi, India, is also thankfully acknowledged (Grant no: MoES/P.O. (Geosci)/44/2015).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Saumen Maiti
    • 1
  • Anasuya Das
    • 1
  • Rhythm Shah
    • 1
  • Gautam Gupta
    • 2
  1. 1.Department of Applied GeophysicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Indian Institute of Geomagnetism (DST)Navi MumbaiIndia

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