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

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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.

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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

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Acknowledgements

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

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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

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  1. Deepak Kumar
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  2. Thendiyath Roshni
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  3. Anshuman Singh
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  4. Madan Kumar Jha
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  5. Pijush Samui
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Correspondence to Thendiyath Roshni.

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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

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