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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 22, issue 7
Hydrol. Earth Syst. Sci., 22, 3663-3684, 2018
https://doi.org/10.5194/hess-22-3663-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Special issue: Thermodynamics and optimality in the Earth system and its...

Hydrol. Earth Syst. Sci., 22, 3663-3684, 2018
https://doi.org/10.5194/hess-22-3663-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 10 Jul 2018

Research article | 10 Jul 2018

On the dynamic nature of hydrological similarity

Ralf Loritz1, Hoshin Gupta2, Conrad Jackisch1, Martijn Westhoff3, Axel Kleidon4, Uwe Ehret1, and Erwin Zehe1 Ralf Loritz et al.
  • 1Karlsruhe Institute of Technology (KIT), Institute of Water and River Basin Management, Karlsruhe, Germany
  • 2University of Arizona, Department of Hydrology and Atmospheric Sciences, Tucson, AZ, USA
  • 3Vrije Universiteit, Department of Earth Science, Amsterdam, the Netherlands
  • 4Max Planck Institute for Biogeochemistry, Jena, Germany

Abstract. The increasing diversity and resolution of spatially distributed data on terrestrial systems greatly enhance the potential of hydrological modeling. Optimal and parsimonious use of these data sources requires, however, that we better understand (a) which system characteristics exert primary controls on hydrological dynamics and (b) to what level of detail do those characteristics need to be represented in a model.

In this study we develop and test an approach to explore these questions that draws upon information theoretic and thermodynamic reasoning, using spatially distributed topographic information as a straightforward example. Specifically, we subdivide a mesoscale catchment into 105 hillslopes and represent each by a two-dimensional numerical hillslope model. These hillslope models differ exclusively with respect to topography-related parameters derived from a digital elevation model (DEM); the remaining setup and meteorological forcing for each are identical. We analyze the degree of similarity of simulated discharge and storage among the hillslopes as a function of time by examining the Shannon information entropy. We furthermore derive a compressed catchment model by clustering the hillslope models into functional groups of similar runoff generation using normalized mutual information (NMI) as a distance measure.

Our results reveal that, within our given model environment, only a portion of the entire amount of topographic information stored within a digital elevation model is relevant for the simulation of distributed runoff and storage dynamics. This manifests through a possible compression of the model ensemble from the entire set of 105 hillslopes to only 6 hillslopes, each representing a different functional group, which leads to no substantial loss in model performance. Importantly, we find that the concept of hydrological similarity is not necessarily time invariant. On the contrary, the Shannon entropy as measure for diversity in the simulation ensemble shows a distinct annual pattern, with periods of highly redundant simulations, reflecting coherent and organized dynamics, and periods where hillslopes operate in distinctly different ways.

We conclude that the proposed approach provides a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time. Our approach is neither restricted to the model nor to model targets or the data source we selected in this study. Overall, we propose that the concepts of hydrological systems acting similarly (and thus giving rise to redundancy) or displaying unique functionality (and thus being irreplaceable) are not mutually exclusive. They are in fact of complementary nature, and systems operate by gradually changing to different levels of organization in time.

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In this study we explore the role of spatially distributed information on hydrological modeling. For that, we develop and test an approach which draws upon information theory and thermodynamic reasoning. We show that the proposed set of methods provide a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time and, hence, when which landscape characteristic is important in a model application.
In this study we explore the role of spatially distributed information on hydrological modeling....
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