Estimation of Hydraulic Conductivity and Its Uncertainty from Grain-Size Data Using GLUE and Artificial Neural Networks

Bart Rogiers, Dirk Mallants, Okke Batelaan, Matej Gedeon, Marijke Huysmans, Alain Dassargues

    Research output: Contribution to journalArticlepeer-review

    36 Citations (Scopus)


    Various approaches exist to relate saturated hydraulic conductivity (K s) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods-multiple linear regression and artificial neural networks-that use the entire grain-size distribution data as input for K s prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling. Artificial neural networks (ANNs) are combined with a generalised likelihood uncertainty estimation (GLUE) approach to predict K s from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from the literature demonstrates the importance of site-specific calibration. The data set used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size K s-pairs. Finally, an application with the optimised models is presented for a borehole lacking K s data.

    Original languageEnglish
    Pages (from-to)739-763
    Number of pages25
    JournalMathematical Geosciences
    Issue number6
    Publication statusPublished - Aug 2012

    Bibliographical note

    Copyright 2012 Elsevier B.V., All rights reserved.


    • Artificial neural networks
    • Cross-validation
    • Data-driven modelling
    • Early stopping
    • Generalised likelihood uncertainty estimation
    • GLUE-ANN
    • Likelihood measures
    • Principal component analysis
    • Sedimentary aquifer


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