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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-2020-543
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-543
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  13 Nov 2020

13 Nov 2020

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This preprint is currently under review for the journal HESS.

A new fractal-theory-based criterion for hydrological model calibration

Zhixu Bai, Yao Wu, Di Ma, and Yue-Ping Xu Zhixu Bai et al.
  • Institute of Hydrology and Water Resources, Civil Engineering, Zhejiang University, Hangzhou, 310058, China

Abstract. Fractality has been found in many areas and has been used to describe the internal features of time series. But is it possible to use fractal theory to improve the performance of hydrological models? This study aims to investigate the potential benefits of applying fractal theory in model calibration. A new criterion named ratio of fractal dimensions (RD) is defined as the ratio of fractal dimensions of simulated and observed streamflow series. To combine the advantages of fractal theory with classical criteria based on squared residuals, a multi-objective calibration strategy is designed. The selected classical criterion is Nash-Sutcliffe efficiency (E). The E-RD strategy is tested in three study cases with different climate and geography. The results of experiment reveal that, from most aspects, introducing RD into model calibration makes the simulation of streamflow components more reasonable. Besides, in calibration, only little decrease of E occurs when pursuing better RD. We therefore recommend choosing the best E among the parameter sets whose RD is around 1.

Zhixu Bai et al.

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Short summary
We think that fractal dimension of streamflow series can be used to improve the calibration of hydrological models. Thus, we designed the E-RD (efficiency-ratio of fractal dimension) strategy and examined its usability in the calibration of lumped model. The results reveal that, from most aspects, introducing RD into model calibration makes the simulation of streamflow components more reasonable. Besides, in calibration, only little decrease of E occurs when pursuing better RD.
We think that fractal dimension of streamflow series can be used to improve the calibration of...
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