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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/hess-2020-65
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-65
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 28 Feb 2020

Submitted as: research article | 28 Feb 2020

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This preprint is currently under review for the journal HESS.

Adaptive clustering: A method to analyze dynamical similarity and to reduce redundancies in distributed (hydrological) modeling

Uwe Ehret1, Rik van Pruijssen1, Marina Bortoli1, Ralf Loritz1, Elnaz Azmi2, and Erwin Zehe1 Uwe Ehret et al.
  • 1Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology – KIT, Karlsruhe, Germany
  • 2Steinbuch Centre for Computing, Karlsruhe Institute of Technology – KIT, Karlsruhe, Germany

Abstract. In this paper we propose adaptive clustering as a new way to analyse hydrological systems and to reduce computational efforts of distributed modelling, by dynamically identifying similar model elements, clustering them and inferring dynamics from just a few representatives per cluster. It is based on the observation that while hydrological systems generally exhibit large spatial variability of their properties, requiring distributed approaches for analysis and modelling, there is also redundancy, i.e. there exist typical and recurrent combinations of properties, such that sub systems exist with similar properties, which will exhibit similar internal dynamics and produce similar output when in similar initial states and when exposed to similar forcing. Being dependent on all these factors, similarity is hence a dynamical rather than a static phenomenon, and it is not necessarily a function of spatial proximity.

We explain and demonstrate adaptive clustering at the example of a conceptual, yet realistic and distributed hydrological model, fit to the Attert basin in Luxembourg by multi-variate calibration. Based on normalized and binned transformations of model states and fluxes, we first calculated time series of Shannon information entropy to measure dynamical similarity (or redundancy) among sub systems. This revealed that indeed high redundancy exists, that its magnitude differs among variables, that it varies with time, and that for the Attert basin the spatial patterns of similarity are mainly controlled by geology and precipitation. Based on these findings, we integrated adaptive clustering into the hydrological model. It constitutes a shell around the model hydrological process core and comprises: Clustering of model elements, choice of cluster representatives, mapping of results from representatives to recipients, comparison of clusterings over time to decide when re-clustering is advisable. Adaptive clustering, compared to a standard, full-resolution model run used as a virtual reality truth, reduced computation time to one fourth, when accepting a decrease of modelling quality, expressed as Nash–Sutcliffe efficiency of sub catchment runoff, from 1 to 0.84.

We suggest that adaptive clustering is a promising tool for both system analysis, and for reducing computation times of distributed models, thus facilitating applications to larger systems and/or longer periods of time. We demonstrate the potential of adaptive clustering at the example of a hydrological system and model, but it should apply to a wide range of systems and models across the earth system sciences. Being dynamical, it goes beyond existing static methods used to increase model performance, such as lumping, and it is compatible with existing dynamical methods such as adaptive time-stepping or adaptive gridding. Unlike the latter, adaptive clustering does not require adjacency of the sub systems to be joined.

Uwe Ehret et al.

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Uwe Ehret et al.

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In this paper we propose adaptive clustering as a new way to analyse hydrological systems and to reduce computational efforts of earth system models, by dynamically identifying similar model elements, clustering them and inferring dynamics from just a few representatives per cluster. Adaptive clustering goes beyond existing static methods used to increase model performance, and it is compatible with existing dynamical methods such as adaptive time-stepping or adaptive gridding.
In this paper we propose adaptive clustering as a new way to analyse hydrological systems and to...
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