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https://doi.org/10.5194/hess-2020-5
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-5
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 22 Jan 2020

Submitted as: research article | 22 Jan 2020

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This preprint is currently under review for the journal HESS.

HER: an information theoretic alternative for geostatistics

Stephanie Thiesen1, Diego M. Vieira2,3, Mirko Mälicke1, J. Florian Wellmann4, and Uwe Ehret1 Stephanie Thiesen et al.
  • 1Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
  • 2Department for Microsystems Engineering, University of Freiburg, Freiburg, Germany
  • 3Bernstein Center Freiburg, University of Freiburg, Freiburg, Germany
  • 4Computational Geosciences and Reservoir Engineering, RWTH Aachen University, Aachen, Germany

Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, purely data-driven to geostatistical, and parametric to non-parametric methods. In this study, we propose a stochastic, geostatistical estimator which combines information theory with probability aggregation methods for minimizing predictive uncertainty, and predicting distributions directly based on empirical probability. Histogram via entropy reduction (HER) relaxes parametrizations, avoiding the risk of adding information not present in data (or losing available information). It provides a proper framework for uncertainty estimation that takes into account both spatial configuration and data values, while allowing to infer (or introduce) physical properties (continuous or discontinuous characteristics) of the field. We investigate the framework utility using synthetically generated datasets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties (different spatial correlation distances and addition of noise). HER shows comparable performance with popular benchmark models and the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.

Stephanie Thiesen et al.

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Data sets

HER: an information theoretic alternative for geostatistics S. Thiesen, D. Vieira, M. Mälicke, J. F. Wellmann, and U. Ehret https://doi.org/10.5281/zenodo.3614719

Model code and software

HER: an information theoretic alternative for geostatistics S. Thiesen, D. Vieira, M. Mälicke, J. F. Wellmann, and U. Ehret https://doi.org/10.5281/zenodo.3614719

Stephanie Thiesen et al.

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Latest update: 19 Feb 2020
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Short summary
A spatial interpolation model has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By construction, the method provides a proper framework for uncertainty analysis and decision-making.
A spatial interpolation model has been proposed for exploring the information content of the...
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