Skip to main content
SpringerLink
Log in

Predicting groundwater depth fluctuations using deep learning, extreme learning machine and Gaussian process: a comparative study

  • Research Article
  • Published:
Earth Science Informatics Aims and scope Submit manuscript

Abstract

Groundwater depth has complex non-linear relationships with climate, groundwater extraction, and surface water flows. To understand the importance of each predictor and predictand (groundwater depth), different artificial intelligence (AI) techniques have been used. In this research, we have proposed a Deep Learning (DL) model to predict groundwater depths. The DL model is an extension of the conventional neural network with multiple layers having non-linear activation function. The feasibility of the DL model is assessed with well-established framework models [Extreme Learning Machine (ELM) and Gaussian Process Regression (GPR)]. The area selected for this study is Konan basin located in the Kochi Prefecture of Japan. The hydro-meteorological and groundwater data used are precipitation, river stage, temperature, recharge and groundwater depth. Identical set of inputs and outputs of all the selected stations were used to train and validate the models. The predictive accuracy of the DL, ELM and GPR models has been assessed considering suitable goodness-of-fit criteria. During training period, the DL model has a very good agreement with the observed data (RMSE = 0.04, r = 0.99 and NSE = 0.98) and during validation period, its performance is satisfactory (RMSE = 0.08, r = 0.95 and NSE = 0.87). To check practicality and generalization ability of the DL model, it was re-validated at three different stations (E2, E3 and E6) of the same unconfined aquifer. The significant prediction capability and generalization ability makes the proposed DL model more reliable and robust. Based on the finding of this research, the DL model is an intelligent tool for predicting groundwater depths. Such advanced AI technique can save resources and labor conventionally employed to estimate various features of complex groundwater systems.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

RMSE :

Root Mean Square Error

r :

Coefficient of correlation

NSE :

Nash–Sutcliffe efficiency coefficient

d :

index of agreement

MAE :

mean absolute error

ϕ(.):

activation function

w :

weight vector

b :

random bias

w j :

weight vector to the hidden neuron

β j :

denotes jth hidden node weight vector connection to input of the hidden node to the output node

ε :

observation errors

s 2 noise :

noise variance

ϕ :

latent variable function

ψ[·]:

denotes approximation

q 1 :

(hyper-parameter)

q 2 :

denotes the rating decay in correlation

H† :

inverse of matrix

D:

input training dataset to the model

μ:

mean

σ:

standard deviation

C:

Covariance

ψ[·]:

(Approximation)

Q:

random realization vector

R:

recharge,

P:

precipitation

S:

river stage

GWD:

groundwater depth

T:

current temperature data

t:

time period

Z:

data value

Z min :

minimum value of the whole dataset

Z max :

maximum value of whole data

Z normalized :

normalized dataset

References

  • Alizamir M, Kisi O, Zounemat-Kermani M (2018) Modelling long-term groundwater fluctuations by extreme learning machine using hydro-climatic data. Hydrol Sci J 63(1):63–73

    Article  Google Scholar 

  • Amodei D, Ananthanarayanan S, Anubhai R, Bai J, Battenberg E, Case C et al (2016) Deep speech 2: End-to-end speech recognition in english and mandarin. In: International conference on machine learning, 2016, pp 173–182

  • Bierkens MF (1998) Modeling water table fluctuations by means of a stochastic differential equation. Water Resour Res 34(10):2485–2499

    Article  Google Scholar 

  • Cannas B, Fanni A, See L, Sias G (2006) Data preprocessing for river flow forecasting using neural networks: wavelet transforms and data partitioning. Phys Chem Earth, Parts A/B/C 31(18):1164–1171

  • Chollet F (2017) Deep learning with Python. Manning Publications Co

  • Elkahky AM, Song Y, He X (2015) A multi-view deep learning approach for cross domain user modeling in recommendation systems. In: Proceedings of the 24th International Conference on World Wide Web, 2015, pp 278–288

  • Fan Z, Chen Y, Li H, Ma Y, Kurban A (2008) Determination of suitable ecological groundwater depth in arid areas in northwest part of China. J Arid Land Resour Environ 22(2):1–5

    Google Scholar 

  • Gosso, A., & Gosso, M. A. (2012). “Package ‘elmNN’,” ELM Package Version 1.0, July. 17, 2012. [Online]. Available: https://cran.rproject.org/web/packages/elmNN/index.html

  • Grinsted A, Moore JC, Jevrejeva S (2004) Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process Geophys 11(5/6):561–566

    Article  Google Scholar 

  • Hintze JL, Nelson RD (1998) Violin plots: a box plot-density trace synergism. Am Stat 52(2):181–184

    Google Scholar 

  • Hirschberg J, Manning CD (2015) Advances in natural language processing. Science 349(6245):261–266

    Article  Google Scholar 

  • Hoang N-D, Pham A-D, Nguyen Q-L, Pham Q-N (2016) Estimating compressive strength of high performance concrete with Gaussian process regression model. Adv Civ Eng 2016:8–8. https://doi.org/10.1155/2016/2861380

    Article  Google Scholar 

  • Huang G-B, Zhu Q-Y, Siew C-K (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on, 2004, IEEE, vol 2, pp 985–990

  • Huang G, Huang G-B, Song S, You K (2015) Trends in extreme learning machines: a review. Neural Netw 61:32–48

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Jha MK, Chikamori K, Kamii Y, Yamasaki Y (1999) Field investigations for sustainable groundwater utilization in the Konan basin. Water Resour Manag 13(6):443–470

    Article  Google Scholar 

  • Ji S, Xu W, Yang M, Yu K (2012) 3D convolutional neural networks for human action recognition. IEEE Trans Pattern Anal Mach Intell 35(1):221–231

    Article  Google Scholar 

  • Jiang GQ, Xu J, Wei J (2018) A deep learning algorithm of neural network for the parameterization of typhoon-ocean feedback in typhoon forecast models. Geophys Res Lett 45(8):3706–3716

    Article  Google Scholar 

  • Karatzoglou A, Smola A, Hornik K, Zeileis A (2004) Kernlab-an S4 package for kernel methods in R. J Stat Softw 11(9):1–20

    Article  Google Scholar 

  • Karbasi M (2018) Forecasting of multi-step ahead reference evapotranspiration using wavelet-Gaussian process regression model. Water Resour Manag 32(3):1035–1052

    Article  Google Scholar 

  • Kingma D, Ba JA (2015) Adam: A method for stochastic optimization. arXiv 2014. arXiv preprint arXiv:1412.6980v9 [cs.LG], 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA

  • Kottek M, Grieser J, Beck C, Rudolf B, Rubel F (2006) World map of the Köppen-Geiger climate classification updated. Meteorol Z 15(3):259–263

    Article  Google Scholar 

  • Krishna B, Satyaji Rao Y, Vijaya T (2008) Modelling groundwater levels in an urban coastal aquifer using artificial neural networks. Hydrol Process 22(8):1180–1188

    Article  Google Scholar 

  • Kumar D, Singh A, Samui P, Jha RK (2019) Forecasting monthly precipitation using sequential modelling. Hydrol Sci J 64(6):690–700

    Article  Google Scholar 

  • Lemon J, Bolker B, Oom S, Klein E, Rowlingson B, Wickham H et al (2009) Plotrix: various plotting functions. R package version 2.7–2. R Project for Statistical Computing Vienna, Austria

    Google Scholar 

  • Lin GF, Chen GR, Wu MC, Chou YC (2009) Effective forecasting of hourly typhoon rainfall using support vector machines. Water Resour Res 45(8)

  • Lv Y, Duan Y, Kang W, Li Z, Wang F-Y (2014) Traffic flow prediction with big data: a deep learning approach. IEEE Trans Intell Transp Syst 16(2):865–873

    Google Scholar 

  • Maheswaran R, Khosa R (2013) Long term forecasting of groundwater levels with evidence of non-stationary and nonlinear characteristics. Comput Geosci 52:422–436

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Njock PGA, Shen S-L, Zhou A, Lyu H-M (2020) Evaluation of soil liquefaction using AI technology incorporating a coupled ENN/t-SNE model. Soil Dyn Earthq Eng 130:105988

    Article  Google Scholar 

  • Nourani V, Mogaddam AA, Nadiri AO (2008) An ANN-based model for spatiotemporal groundwater level forecasting. Hydrol Process 22(26):5054–5066

    Article  Google Scholar 

  • Raghavendra NS, Deka PC (2016) Multistep ahead groundwater level time-series forecasting using gaussian process regression and ANFIS. In: Advanced Computing and Systems for Security, Springer, pp 289-302

  • Rasmussen CE (2004) Gaussian processes in machine learning. In: Advanced lectures on machine learning, Springer, pp 63-71

  • Roshni T, Jha MK, Deo RC, Vandana A (2019) Development and evaluation of hybrid artificial neural network architectures for modeling Spatio-temporal groundwater fluctuations in a complex aquifer system. Water Resour Manag 33:2381–2397. https://doi.org/10.1007/s11269-019-02253-4

  • Roshni T, Jha MK, Drisya J (2020) Neural network modeling for groundwater-level forecasting in coastal aquifers. Neural Comput & Applic 32:12737–12754

    Article  Google Scholar 

  • Sahoo BB, Jha R, Singh A, Kumar D (2019) Long short-term memory (LSTM) recurrent neural network for low-flow hydrological time series forecasting. Acta Geophys 67(5):1471–1481

    Article  Google Scholar 

  • Scher S (2018) Toward data-driven weather and climate forecasting: approximating a simple general circulation model with deep learning. Geophys Res Lett 45(22):12,616–612,622

    Article  Google Scholar 

  • Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117

    Article  Google Scholar 

  • Schölkopf B, Smola A, Müller K-R (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):1299–1319

    Article  Google Scholar 

  • Shiri J, Kisi O, Yoon H, Lee K-K, Nazemi AH (2013) Predicting groundwater level fluctuations with meteorological effect implications—a comparative study among soft computing techniques. Comput Geosci 56:32–44

    Article  Google Scholar 

  • Sun AY, Wang D, Xu X (2014) Monthly streamflow forecasting using Gaussian process regression. J Hydrol 511:72–81

    Article  Google Scholar 

  • Suryanarayana C, Sudheer C, Mahammood V, Panigrahi BK (2014) An integrated wavelet-support vector machine for groundwater level prediction in Visakhapatnam, India. Neurocomputing 145:324–335

    Article  Google Scholar 

  • Tapoglou E, Karatzas GP, Trichakis IC, Varouchakis EA (2014) A spatio-temporal hybrid neural network-Kriging model for groundwater level simulation. J Hydrol 519:3193–3203

    Article  Google Scholar 

  • Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106(D7):7183–7192

    Article  Google Scholar 

  • Wan ZY, Sapsis TP (2017) Reduced-space Gaussian process regression for data-driven probabilistic forecast of chaotic dynamical systems. Phys D: Nonlinear Phenom 345:40–55. https://doi.org/10.1016/j.physd.2016.12.005

  • Wang P, Yu J, Zhang Y, Fu G, Min L, Ao F (2011) Impacts of environmental flow controls on the water table and groundwater chemistry in the Ejina Delta, northwestern China. Environ Earth Sci 64(1):15–24

    Article  Google Scholar 

  • Ye L, Gao L, Marcos-Martinez R, Mallants D, Bryan BA (2019) Projecting Australia's forest cover dynamics and exploring influential factors using deep learning. Environ Model Softw 119:407–417

    Article  Google Scholar 

  • Yu H, Wen X, Feng Q, Deo RC, Si J, Wu M (2018) Comparative study of hybrid-wavelet artificial intelligence models for monthly groundwater depth forecasting in extreme arid regions, Northwest China. Water Resour Manag 32(1):301–323

    Article  Google Scholar 

  • Zhang N, Shen S-L, Zhou A, Xu Y-S (2019) Investigation on performance of neural networks using quadratic relative error cost function. IEEE Access 7:106642–106652

    Article  Google Scholar 

Download references

Acknowledgements

Authors would like to thank Editors and unknown reviewers for improving the quality of the research paper.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Patna, Ashok Rajpath, Bihar, 800005, India

    Deepak Kumar, Thendiyath Roshni, Anshuman Singh & Pijush Samui

  2. Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, West Bengal, 721302, India

    Madan Kumar Jha

Authors
  1. Deepak Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thendiyath Roshni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anshuman Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Madan Kumar Jha
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pijush Samui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thendiyath Roshni.

Ethics declarations

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Communicated by: H. Babaie

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, D., Roshni, T., Singh, A. et al. Predicting groundwater depth fluctuations using deep learning, extreme learning machine and Gaussian process: a comparative study. Earth Sci Inform 13, 1237–1250 (2020). https://doi.org/10.1007/s12145-020-00508-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12145-020-00508-y

Keywords

Search

Navigation