Temporal Distribution of Extreme Precipitation in Barcelona (Spain) under Multi-Fractal n-Index with Breaking Point
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsReview of: B. Gacon et al. “Temporal distribution of extreme precipitations in Barcelona (Spain) under multi-fractal n-index with breaking point”
Submitted to Atmosphere 2024
Summary: This submission has all the earmarks of an important paper - cf. Fig. 6, which shows the “n -index” plotted over time for the historic record and future projections from a set of Earth System Models listed in Table 2*. The figure shows an increase of n-index that is said to imply a rise in the irregularity of precipitation, which is attributed to increase in energy of the climate system due to anthropogenic emissions and, in turn, to the rise in mid-tropospheric level water vapor content and reduction in low-level relativity humidity due to increase in surface temperatures.
This reviewer had considerable difficulty trying to develop a physical feel for the n-index concept, without success. The Monjo paper (cited ref 3) is a bit easier to understand in this regard – perhaps because the new ramifications of the multi-fractal intensity patterns of Sec. 3.2 are not considered there. That said, the underlying fractal structure to the temporal pattern of drizzle does seem intuitively correct. This is supported by effectively instantaneous snapshot measurements of polarimetric radar differential phase from DOE-ARM measurements of heavy drizzle (large deformable droplet) events [Giangrande et al., 2013**], which show a “devils staircase” type pattern on recordings of differential phase plotted vs range bin (see, for example, Fig. 1 of their paper).
Perhaps it is more difficult to discern quantities such as fractal dimension based on rain gauge measurements, and this is what complicates the multi-scale time averaging and n-index interpretation of these measurements – the reviewer has no experience here. Some pedagogical examples using a few artificial, e.g., statistically generated, temporal rainfall patterns might be useful to motivate at least the most important of equations 1-9 for the reader.
Other than that paper is well written and worth publishing.
*The color coding ssp126, etc. in Fig. 6 presumably relates somehow to the models listed in Table 2 and Observatories listed in Table 1. The authors should specify this connection better.
** S. Giangrande et al. (2013), An application of linear programming to polarimetric radar differential phase processing DOI: https://doi.org/10.1175/JTECH-D-12-00147.1
Author Response
Summary: This submission has all the earmarks of an important paper - cf. Fig. 6, which shows the “n -index” plotted over time for the historic record and future projections from a set of Earth System Models listed in Table 2*. The figure shows an increase of n-index that is said to imply a rise in the irregularity of precipitation, which is attributed to increase in energy of the climate system due to anthropogenic emissions and, in turn, to the rise in mid-tropospheric level water vapor content and reduction in low-level relativity humidity due to increase in surface temperatures.
This reviewer had considerable difficulty trying to develop a physical feel for the n-index concept, without success. The Monjo paper (cited ref 3) is a bit easier to understand in this regard – perhaps because the new ramifications of the multi-fractal intensity patterns of Sec. 3.2 are not considered there. That said, the underlying fractal structure to the temporal pattern of drizzle does seem intuitively correct. This is supported by effectively instantaneous snapshot measurements of polarimetric radar differential phase from DOE-ARM measurements of heavy drizzle (large deformable droplet) events [Giangrande et al., 2013**], which show a “devils staircase” type pattern on recordings of differential phase plotted vs range bin (see, for example, Fig. 1 of their paper).
Perhaps it is more difficult to discern quantities such as fractal dimension based on rain gauge measurements, and this is what complicates the multi-scale time averaging and n-index interpretation of these measurements – the reviewer has no experience here. Some pedagogical examples using a few artificial, e.g., statistically generated, temporal rainfall patterns might be useful to motivate at least the most important of equations 1-9 for the reader.
Done. We appreciate all the comments very much. Your suggestion has been implemented and we are glad because it has been useful to improve the understanding of our work.
Other than that paper is well written and worth publishing.
*The color coding ssp126, etc. in Fig. 6 presumably relates somehow to the models listed in Table 2 and Observatories listed in Table 1. The authors should specify this connection better..:
Thank you very much for the suggestion. More details have been specified now. Color coding is used to specify different climate change scenarios (socioeconomic pathways) used for the generation of climate projections. The curves are then the different climate projections calculated as the moving mean of the projections obtained through the application of the downscaling method to the 10 models listed in Table 2 on the observatories mentioned in Table1.
Each model is used for obtaining climate projections under 4 different climate change scenarios (ssp126…) on the observatories, giving us the 4 curves observed (after averaging and after applying the downscalling method) in the figure. Changes have been made to the figure label to specify better the connection.
** S. Giangrande et al. (2013), An application of linear programming to polarimetric radar differential phase processing DOI: https://doi.org/10.1175/JTECH-D-12-00147.1
Reviewer 2 Report
Comments and Suggestions for AuthorsThis manuscript is well-written and well-organized. Here are my comments:
1. Highlight the novelty of this study.
2. Include the data for each station used in this study in Table 1.
3. Verify the accuracy of equation (4); there may be an error.
4. On line 263, change "Another" to "another" in the phrase “This is the case of the Another finding…”
Author Response
This manuscript is well-written and well-organized. Here are my comments:
- Highlight the novelty of this study. Done (highlighted in the last paragraph of the Introduction section).
- Include the data for each station used in this study in Table 1. Done. Whe have added the time resolution and the time period available of each time series considered.
- Verify the accuracy of equation (4); there may be an error. Done. Thank you for the review.
- On line 263, change "Another" to "another" in the phrase “This is the case of the Another finding…”: Done
Thank you very much for all the suggestions, all of them have been implemented and we think that the paper has noticeably improved now.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe primary objective of the authors is to explore the application of a multi-fractal approach to establish a more precise method of time scaling. This method proves to be valuable in studying extreme precipitation events with a higher level of temporal accuracy. The study focuses on two variables, namely the n-index and the reference intensity I0, for return periods ranging from 2 to 50 years. Additionally, a new parameter called the "breaking point" is introduced to describe the reference intensity I0, which plays a significant role in shorter time intervals. The findings indicate that both parameters are influenced by the time steps and return period, and the results validate the effectiveness of the proposed approach.
In my opinion, the analysis presented is interesting and the results obtained merit publication.
However, there are a few weak points that can be necessarily treated, thus converting this version into a publishable one, namely:
1. Earlier findings published in 2012 in Theor Applied Clim on the intrinsic properties of the precipitation and rainfall, stated that: "the Sahel precipitation anomalies the period 1900–2010 exhibit persistent long-range correlations for all the time lags between 4 months and 28 years. This result states that the fluctuations of the Sahel precipitation anomalies in small time intervals are positively correlated to those in longer time intervals in a power law fashion. In opposite, the Sahel standardized rainfall fluctuations during the periods 1948–2001 show an almost random walk behavior." This should be briefly mentioned in the Introduction.
2. The subdivision between 0 and 1 as well as the entire tool proposed is reminiscent, but not the same, as the "natural time analysis (NTA)" performed for the El Nino prediction extreme events published in Atmos. Chem Phys in 2016 and in Forecasting journal this year. It should be of interest to briefly mention NTA and most probably the two methods could be combined in the future.
3. I invite the authors to read and probably cite the following:
Golitsyn G.S. The laws of random motions by A.N. Kolmogorov. Meteorology and Hydrology 2018. №3, 5-15.
Barenblatt G. I. Scaling. – CUP, 2003. – 171 p.
Turcotte, D.L. Fractals and Chaos in Geology and Geophysics; Cambridge University Press: Cambridge, UK, 1992.
In conclusion, I consider that the above-mentioned revisions are important before the consideration for publication. I would be happy to read the revised version.
Comments on the Quality of English LanguageThere are several edits that must be corrected/rewarded
Author Response
The primary objective of the authors is to explore the application of a multi-fractal approach to establish a more precise method of time scaling. This method proves to be valuable in studying extreme precipitation events with a higher level of temporal accuracy. The study focuses on two variables, namely the n-index and the reference intensity I0, for return periods ranging from 2 to 50 years. Additionally, a new parameter called the "breaking point" is introduced to describe the reference intensity I0, which plays a significant role in shorter time intervals. The findings indicate that both parameters are influenced by the time steps and return period, and the results validate the effectiveness of the proposed approach.
In my opinion, the analysis presented is interesting and the results obtained merit publication.
We appreciate all the suggestions and comments very much. All of them have been implemented and we are very glad because they have been useful to improve our paper.
However, there are a few weak points that can be necessarily treated, thus converting this version into a publishable one, namely:
- Earlier findings published in 2012 in Theor Applied Clim on the intrinsic properties of the precipitation and rainfall, stated that: "the Sahel precipitation anomalies the period 1900–2010 exhibit persistent long-range correlations for all the time lags between 4 months and 28 years. This result states that the fluctuations of the Sahel precipitation anomalies in small time intervals are positively correlated to those in longer time intervals in a power law fashion. In opposite, the Sahel standardized rainfall fluctuations during the periods 1948–2001 show an almost random walk behavior." This should be briefly mentioned in the Introduction.
Done. Thank you very much for the suggestion.
- The subdivision between 0 and 1 as well as the entire tool proposed is reminiscent, but not the same, as the "natural time analysis (NTA)" performed for the El Nino prediction extreme events published in Atmos. Chem Phys in 2016 and in Forecasting journal this year. It should be of interest to briefly mention NTA and most probably the two methods could be combined in the future.
Done. This work has been referenced too. Thank you.
- I invite the authors to read and probably cite the following:
Golitsyn G.S. The laws of random motions by A.N. Kolmogorov. Meteorology and Hydrology 2018. №3, 5-15.
Barenblatt G. I. Scaling. – CUP, 2003. – 171 p.
Turcotte, D.L. Fractals and Chaos in Geology and Geophysics; Cambridge University Press: Cambridge, UK, 1992.
Done. Thank you for the suggestions, we have add all of them, including the references of https://doi.org/10.3103/S1068373918030019
In conclusion, I consider that the above-mentioned revisions are important before the consideration for publication. I would be happy to read the revised version.
Comments on the Quality of English Language: There are several edits that must be corrected/rewarded
Done. Thank you very much for the excellent review and very useful comments and suggestions,
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors, your manuscript is interesting and topic relevant, however it needs some improvements to be ready for publishing.
Following some major concern:
1) Introduction section: Your argument is interesting and relevant, but your literature review is very short and does't provide proper introduction to your topic. You chose to use indices which can assume values between 0 and 1 (line 26-29), I can understand the advantages but It's not properly explained in the text. To be broader enough to properly introduce the scientific soundness of your research, you should take into account even other fields of water resources issues which uses 0-to-1 indices and compare advantages of this approach with other studies. At this regards, you can find reference and enrich your literature review on this issue taking inspiration from the following paper:
https://www.mdpi.com/2073-4441/14/11/1787
2) Figure 1: you should insert sub pannels (a and b) in this figure. Also a legend is recomended inside the figure, description of yellow dots in the caption is not sufficient for the figure to be clear enough.
3) Figure 2: labels should be plotted bigger to be easly readable, as the same size of figure 3.
4) Labels of figure 6 are too big. Organize all figures with the same estetical criteria.
5) Discussione section: contents of this section are interesting and relevant but not well organized. The section is too long, maybe while summarizing it the paper will benefit.
6) Conclusion section: in this section you are just making a recap of your results. In conclusion section you should emphatize why your research is scientifically relevant with respect to literature, which novelties you bring to science and which are future perspective. You should rewrite this section.
Author Response
Dear Authors, your manuscript is interesting and topic relevant, however it needs some improvements to be ready for publishing.
Following some major concern:
1) Introduction section: Your argument is interesting and relevant, but your literature review is very short and does't provide proper introduction to your topic. You chose to use indices which can assume values between 0 and 1 (line 26-29), I can understand the advantages but It's not properly explained in the text. To be broader enough to properly introduce the scientific soundness of your research, you should take into account even other fields of water resources issues which uses 0-to-1 indices and compare advantages of this approach with other studies. At this regards, you can find reference and enrich your literature review on this issue taking inspiration from the following paper:
https://www.mdpi.com/2073-4441/14/11/1787
Done. We appreciate all the comments very much. Your suggestion has been implemented and we are glad because it has been useful to improve the understanding of our work.
2) Figure 1: you should insert sub pannels (a and b) in this figure. Also a legend is recommended inside the figure, description of yellow dots in the caption is not sufficient for the figure to be clear enough.
Done, (a) and (b) labels have been added inside the figure, and the description in the figure caption was improved; hopefully it can be understood better.
3) Figure 2: labels should be plotted bigger to be easly readable, as the same size of figure 3.
Done
4) Labels of figure 6 are too big. Organize all figures with the same estetical criteria:
Done
5) Discussion section: contents of this section are interesting and relevant but not well organized. The section is too long, maybe while summarizing it the paper will benefit.
Thank you very much for the suggestions. We have reorganized the Discussion section to facilitate the reading. We hope it is clearer now.
6) Conclusion section: in this section you are just making a recap of your results. In conclusion section you should emphatize why your research is scientifically relevant with respect to literature, which novelties you bring to science and which are future perspective. You should rewrite this section. -
We agree with this comment. Finally, we have re-written it to make emphasis to the most relevant conclusions.
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThank you for the successful improvements performed. The revised version is ready for publication
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors, you improved your manuscript properly and now is ready for acceptance. Good Job
