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

Bai, Zhixu; Wu, Yao; Ma, Di; Xu, Yue-Ping

doi:https://doi.org/10.5194/hess-25-3675-2021

Articles | Volume 25, issue 6

https://doi.org/10.5194/hess-25-3675-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-25-3675-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 25, issue 6

Research article

|

30 Jun 2021

Research article |

| 30 Jun 2021

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

Zhixu Bai, Yao Wu, Di Ma, and Yue-Ping Xu

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Final revised paper (published on 30 Jun 2021)
Preprint (discussion started on 13 Nov 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Anonymous Review Comment 1', Anonymous Referee #1, 09 Dec 2020
- AC1: 'Reply on RC1', Zhixu Bai, 01 Feb 2021
RC2: 'Anonymous referee comment #2', Anonymous Referee #2, 05 Jan 2021
- AC2: 'Reply on RC2', Zhixu Bai, 01 Feb 2021

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (08 Feb 2021) by Fabrizio Fenicia

AR by Zhixu Bai on behalf of the Authors (20 Feb 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (02 Mar 2021) by Fabrizio Fenicia

RR by Anonymous Referee #1 (17 Mar 2021)

Suggestions for revision or reasons for rejection

The overall idea that observed and modelled flow should have comparable Hausdorff dimensions (here, think about the RD) would remain solid to me if the method being introduced could be independently used for calibrating models. Unfortunately, the method being introduced requires other existing objective functions in reducing the mismatch between observed and modelled streamflows. In this line, it becomes difficult to quantify the significance of the contribution of the new method to the overall performance of the model. In other words, we can have Nash-Sutcliffe Efficiency (E) of, say, 0.95 (indicating a perfect or nearly perfect model) with or without the introduced method. Then, why the new method? However, the question is: Can it be possible to have E = 0.95 when the results of the model does not make sense with respect to RD? Intuitively, the answer is NO. Perhaps to avoid subjectivity of regarding the choice of E and RD to characterize the model's optimality, I suggest that the authors come up with a new metric (NM) in terms of the product of E and RD. In this way, an ideal model would have NM=1.

Alternatively, the authors could explore the possibility of incorporating RD within E. Of course, the well-known metric E comprises comparison of observed and modelled series in terms of (a) correlation, (b) measures of dispersion, and (c) difference in mean. This can be found in a number of articles, for instance, see the formula for computing the Kling-Gupta Efficiency (Gupta et al., 2009). The idea would be to try to replace correlation in E with RD and you assess model performance. In this way, you can come up with a formula which considers RD, ratio of standard deviation of observed flow to that of simulated flow, and ratio of mean of observed flow to that of simulated flow. The findings would be in terms of whether combination of RD with measures of dispersion, and means could lead to comparable model performance like for the case when E is used alone. This is just some suggestion which the authors could try to explore.

Lastly, the paper is to lengthy and its contribution not straightforward. I strongly suggest that the authors make the paper concise. In this line, one may find it apparent that further analyses (of trying to link RD to (i) the variation of sub-flows separated by WETSPRO, and (ii) parameters of the hydrological models) were somewhat unnecessary and could have instead engendered more uncertainties in results. There are some hydrological models that purely depend on flow splitting for their calibration and the authors need to know that HBV is not such a model. In other words, flow splitting is not that relevant for the introduced method for simplicity. Conclusively, these further analyses (of flow splitting and linking RD with model parameters) should be discarded from the revised manuscript or placed in a supplementary material.

My conclusion is that the authors require time to do more work which can make the paper compact and/or straight forward

Gupta H V, Kling H, Yilmaz KK, Martinez GF (2009) Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of Hydrology 377:80–91. doi: 10.1016/j.jhydrol.2009.08.003

Minor correction
Figure 3: Also include the latitudes and longitudes around the DEM of Dong.

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RR by Anonymous Referee #2 (12 Apr 2021)

Suggestions for revision or reasons for rejection

The authors carefully responded to the comments of the reviewers and incorporated corresponding changes in the revised manuscript. In general, the manuscript has improved and now is almost suitable for publication. I have some minor comments related to the response and corresponding changes in the manuscript, please see below. In addition, the paper needs an extensive English spelling and grammar check before it can be published.

Minor comments [related to original comment]:
[2]: The authors provided an explanation for several terms. However, they did not explicitly define the term 'periodicity' in their revised manuscript and hence they need to add this.
[6]: On line 666 of the tracked changes version of the revised manuscript the authors mention 2800 generations for 14 HBV parameters. It is not clear why this number of generalizations needs to be run. Also in their response the authors mention 106 generations for the Xiang case, where it also is not clear why this number is used.
[7]: Although for the Dong catchment only a data period of four years is available, temporal validations for the other two catchments can be carried out. The comparison with different time periods is not a fully independent temporal validation.
[9]: The added texts related to this comment are not completely clear. "The distance correlation is believed to have better performance ..."; compared to what? The explanation for the degree-day factor is not clear. For instance "The low temperature may be covered by averaging ..."? What do you mean with this? This explanation needs further clarification and reformulation. Finally, why is the percolation in Jinhua catchment larger than in Xiang catchment, where Jinhua catchment has a larger slope? I would expect the opposite behaviour, i.e. smaller percolation for larger slopes. Please clarify.

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ED: Publish subject to minor revisions (review by editor) (12 Apr 2021) by Fabrizio Fenicia

AR by Zhixu Bai on behalf of the Authors (08 May 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (18 May 2021) by Fabrizio Fenicia

AR by Zhixu Bai on behalf of the Authors (22 May 2021)

Short summary

To test our hypothesis that the fractal dimensions of streamflow series can be used to improve the calibration of hydrological models, we designed the E–RD efficiency ratio of fractal dimensions strategy and examined its usability in the calibration of lumped models. The results reveal that, in most aspects, introducing RD into model calibration makes the simulation of streamflow components more reasonable. Also, pursuing a better RD during calibration leads to only a minor decrease in E.