On the dynamic nature of hydrological similarity

Ralf Loritz*, Hoshin Gupta, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Uwe Ehret, Erwin Zehe

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)3663-3684
Number of pages22
JournalHydrology and Earth System Sciences
Issue number7
Publication statusPublished - 10 Jul 2018


Acknowledgements. This research contributes to the Catchments As Organized Systems (CAOS) research group (FOR 1598) funded by the German Science Foundation (DFG). Laurent Pfister and Jean-Francois Iffly from the Luxembourg Institute of Science and Technology (LIST) are acknowledged for organizing the permissions for the experiments and providing discharge data for the Colpach catchment. We also thank the whole CAOS team of phase I and II. In particular, we thank Markus Weiler (University of Freiburg), Theresa Blume (GFZ Potsdam) and Britta Kattenstroth (University of Freiburg) for providing and collecting the soil moisture data. Furthermore, we thank Nina Kiese, Leonard Bartels and Malte Neuper for their general support and time for various discussions. Finally we thank the editor Hubert Savenije as well as the two referees Steven Weijs and Ciaran Harman for their critical but very constructive comments.

FundersFunder number
Deutsche Forschungsgemeinschaft


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