Mathematical Geosciences

, Volume 44, Issue 6, pp 739–763 | Cite as

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


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.


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



The authors are grateful to ONDRAF/NIRAS, the Belgian Agency for Radioactive Waste and Enriched Fissile Materials, for providing the data. Findings and conclusions in this paper are those of the authors and do not necessarily represent the official position of ONDRAF/NIRAS.


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Copyright information

© International Association for Mathematical Geosciences 2012

Authors and Affiliations

  • Bart Rogiers
    • 1
    • 2
  • Dirk Mallants
    • 5
  • Okke Batelaan
    • 2
    • 3
  • Matej Gedeon
    • 1
  • Marijke Huysmans
    • 2
  • Alain Dassargues
    • 2
    • 4
  1. 1.Institute for Environment, Health and SafetyBelgian Nuclear Research Centre (SCK•CEN)MolBelgium
  2. 2.Dept. of Earth and Environmental SciencesKU LeuvenHeverleeBelgium
  3. 3.Dept. of Hydrology and Hydraulic EngineeringVrije Universiteit BrusselBrusselsBelgium
  4. 4.Hydrogeology and Environmental Geology, Dept. of Architecture, Geology, Environment and Civil Engineering (ArGEnCo) and AquapoleUniversité de LiègeLiègeBelgium
  5. 5.Groundwater Hydrology ProgramCSIRO Land and WaterGlen OsmondAustralia

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