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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Preprints
https://doi.org/10.5194/hess-2020-148
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-148
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  17 Apr 2020

17 Apr 2020

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A revised version of this preprint is currently under review for the journal HESS.

Objective functions for information-theoretical monitoring network design: what is optimal?

Hossein Foroozand and Steven V. Weijs Hossein Foroozand and Steven V. Weijs
  • Department of Civil Engineering, University of British Columbia, Vancouver, British Columbia, Canada

Abstract. This paper concerns the problem of optimal monitoring network lay- out using information-theoretical methods. Numerous different objectives based on information measures have been proposed in recent literature, often focusing simultaneously on maximum information and minimum dependence between the chosen locations for data collection. We discuss these objective functions and conclude that a single objective optimization of joint entropy suffices to maximize the collection of information for a given number of sensors. Minimum dependence is a secondary objective that automatically follows from the first, but has no intrinsic justification. In fact, for two networks of equal joint entropy, one with a higher amount of redundant information should be preferred for reasons of robustness against failure. In attaining the maximum joint entropy objective, we investigate exhaustive optimization, a more computationally tractable greedy approach that adds one station at a time, and we introduce the greedy drop approach, where the full set of sensors is reduced one at a time. We show that only exhaustive optimization will give true optimum. The arguments are illustrated by a comparative case study.

Hossein Foroozand and Steven V. Weijs

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Hossein Foroozand and Steven V. Weijs

Hossein Foroozand and Steven V. Weijs

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Short summary
In monitoring network design, we have to decide what to measure, where to measure, and when to measure. In this paper, we focus on the question where to measure. Past literature has used the concept of information to choose a selection of locations that provides maximally informative data. In this paper, we look in detail at the proper mathematical formulation of the information concept. We argue that previous proposals for this formulation have been needlessly complicated.
In monitoring network design, we have to decide what to measure, where to measure, and when to...
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