Brazil’s Daily Precipitation Concentration Index (CI) Using Alternative Fitting Equation and Ensemble Data
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsI have carefully read the paper you submitted and expressed interest in your research. I think your research topic has certain academic value, but there are still some areas that need improvement in the current version of the paper. Below, I will elaborate on my views and suggestions in detail.
The article aims to verify the performance of Ananthakrishnan and Soman's Lorentz curve fitting curve replacement equation by considering more precipitation sequence information and different climatic conditions. This article uses a grid dataset containing 735 time series in CABra to calculate the 30-year precipitation concentration index of Brazil, and evaluates the goodness of fit by combining empirical data. The research results provide strong support for the view that alternative equations have more advantages in identifying high concentration index precipitation. There are several points that need to be noted:
1. Is the formula format on lines 98, 102, 109, 111, and 115 appropriate?
2. Should a statement be added to line 156 'Back et al.' to enhance clarity and readability?
3. On line 178, 'Which shows that both concentration values are linearly related', is adding a significance test to the argument more convincing?
4. Does line 216 'empirical data' refer to the CABra grid dataset? Suggest providing appropriate explanations in the preceding text.
5. Should 'SRE' be 'RSS' on line 220?
6. Should the image captions on lines 230, 231, 254, and 255 be more distinguishable, and should the meanings represented by the corresponding subgraphs be explained in detail?
7. Should the relationship between the coefficient of variation, skewness coefficient, and regression constant in statistics be explained in the preceding text, starting from line 233.
Author Response
Dear reviewer
I sincerely acknowledge your review. All your observations are very important to improving the manuscript. I attended to them, and it shows in the following lines and the corrected version of the manuscript.
- Is the formula format on lines 98, 102, 109, 111, and 115 appropriate?
According to the instructions for the authors, it is possible to write it as it appears in the manuscript.
2. Should a statement be added to line 156 'Back et al.' to enhance clarity and readability?
The paragraph was rewritten to improve the redaction. Now it appears like:
According to both equations, critical values for the concentration index are located mainly on the east side of the country in states near the Atlantic Ocean, such as Ceará, Bahia, Minas Gerais, Espíritu Santo, and Rio Grande do Sul. Monjo and Martin-Vide have reported this spatial behavior in the past [32], and recently, Back et al. [29] also found higher concentration values over the same region.
3. On line 178, 'Which shows that both concentration values are linearly related', is adding a significance test to the argument more convincing?
The paragraph was rewritten in order to improve the manuscript; now it is written as:
The determination coefficient (R2) indicates that the concentration values of equation 2 can be reasonably approximated based on the concentration values obtained with equation 1 (R2 = 0.966), which shows that both concentration values are linearly related. The result of the significance test of the model shown in Figure 3b (p-value = 2.2 e-16 according to ANOVA test) shows that concentration values obtained according to the Martin-Vide equation (equation 1) are significant.
4. Does line 216 'empirical data' refer to the CABra grid dataset? Suggest providing appropriate explanations in the preceding text.
To clarify the information, it was decided to refer to the CABra dataset instead of using the phrase "empirical data," as can be observed now on line 257.
Regarding the goodness of fit of the two equations for the fit of the Lorenz curve with the CABra dataset, results using three metrics for the functions used to approximate the Lorenz curve show similar behavior (Figure 4).
5. Should 'SRE' be 'RSS' on line 220?
That is correct; a written mistake made SRE appear, but the correct spelling is RSS, which was corrected in the manuscript.
6. Should the image captions on lines 230, 231, 254, and 255 be more distinguishable, and should the meanings represented by the corresponding subgraphs be explained in detail?
The image captions were improved, including a description of each subgraph so that it could be understood easily.
7. Should the relationship between the coefficient of variation, skewness coefficient, and regression constant in statistics be explained in the preceding text, starting from line 233.
A new paragraph was added to describe the possible relationship between the regression constants, the coefficient of variation, and the skewness coefficient. It was written like this:
In their research, Ananthakrishnan & Soman [22] found that regression constants were related to the variation coefficient when they studied the normalized rainfall curves, which can be considered the Lorenz curve in the precipitation concentration index. They found that high values of the variation coefficient were related to high rainfalls. However, according to the distribution of precipitation, which is widely recognized, it is fitted to negative exponential distributions; it was decided to analyze the relationship between the regression constants of equations 1 and 2 versus the skewness coefficient since these regression constants control the exponential growth rate of the fitted equation.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Author,
In order to significantly improve this very interesting work, I suggest that you review some key points throughout the manuscript:
1. In the Abstract, it is interesting to present some of the main quantitative statistical results of the study.
2. In the keywords, I see that the word precipitation is very recurrent, which is already highlighted in the title. Why not something related to the statistical technique?
3. In the Introduction section, an important problem on the subject was presented. In this sense, it is necessary to talk more broadly about the potential of the statistical distribution technique to work with precipitation. Therefore, making the novelty and perspective of this study clearer.
4. At the same time, review the objectives and list, in addition to the general objective already presented, more specific objectives that were answered in the conclusions.
5. In the material and methods, the level of specific information of the study should be improved. Detail the processes even more. This will be important for other researchers to replicate this methodology.
6. Please clearly specify the study period in the material and methods.
7. In Table 1, correct the names of the following states:
- Sao Paulo as São Paulo;
- Tacantis as Tocantins;
- Maranhao as Maranhão;
- Pernanmbuco as Pernambuco;
- Rondonia as Rondônia.
Author Response
Dear reviewer
I sincerely acknowledge your review. All your observations are very important to improving the manuscript. I attended to them, and it shows in the following lines and the corrected version of the manuscript.
- In the Abstract, it is interesting to present some of the main quantitative statistical results of the study.
The abstract was rewritten to include quantitative results from the statistical analysis as shown in the following lines and the corrected manuscript:
Abstract: In the last time, precipitation concentration indices have become popular, and the daily precipitation concentration index has been widely used worldwide. This index is based on the Lorenz curve fitting. Recently, in some research, some biases in the fitting process have been observed. Therefore, this research’s objective consisted of testing the performance of one alternative equation for fitting the Lorenz curve through the analysis of the daily precipitation concentration in Brazil. Daily precipitation data from 735-time series were used to fit the Lorenz curve and calculate the concentration index. Therefore, the goodness of fit was evaluated to determine which equation better describes the empirical data. Results show that the mean value for the concentration index based on equation 1 was 0.650 ± 0.079, while the mean value based on equation 2 was 0.624 ± 0.070. The results of the fitting performance show a better fitting with equation 2 compared to equation 1 as indicated by R2, RSS, and RMSE values, R2 = 0.9959 for equation 1 versus 0.9996 for equation 2, RSS = 252.78 versus 22.66, and RMSE = 1.5092 versus 0.0501. Thus, equation 2 can be considered an alternative to improve the calculation of the concentration index.
2. In the keywords, I see that the word precipitation is very recurrent, which is already highlighted in the title. Why not something related to the statistical technique?
Some keywords were changed to avoid the recurrence:
Keywords: daily precipitation concentration; concentration indices; Lorenz curve; fitting equations; CABra dataset.
3. In the Introduction section, an important problem on the subject was presented. In this sense, it is necessary to talk more broadly about the potential of the statistical distribution technique to work with precipitation. Therefore, making the novelty and perspective of this study clearer.
It was added a new subparagraph to express the relevance of taking into account an alternative functional form to approximate the Lorenz curve and its effect:
On the other hand, the second equation shown by Martin-Vide [10] and proposed by Ananthakrishnan and Soman [22] to approximate the Lorenz curve has been used only in a few research works. The curve fitting is crucial because, in the literature, it was recognized that different data could produce equal concentration values [20], which indicates that one of the fitted curves did not fit the data correctly. This result can under or over-estimate the actual daily precipitation concentration, affecting the evaluation of possible precipitation-related risks. Recently, Núñez-González et al. [21] evaluated the performance of this equation to approximate the Lorenz curve for calculating the concentration index and compare the results with that obtained using the equation of Riehl and Olascoaga [9, 10].
4. At the same time, review the objectives and list, in addition to the general objective already presented, more specific objectives that were answered in the conclusions.
Based on the recommendation, the objective was modified to be widened and include the statemens in the conclusions:
Therefore, the objective of this research is threefold; the first part consisted of the analysis of the daily precipitation concentration of Brazil using the ensemble dataset provided by Almagro et al. [24], then the test of the performance of the alternative equation proposed by Ananthakrishnan and Soman [22] in a broad context than that of Núñez-González et al. [21] and comparing the result with that obtained with the equation proposed by Riehl [8] and Olascoaga [9], and finally into the analysis of the relationship of the concentration values obtained through the fitting with both equations.
5. In the material and methods, the level of specific information of the study should be improved. Detail the processes even more. This will be important for other researchers to replicate this methodology.
The processes followed in the calculation were detailed to be more explicit, as seen in the corrected version of the manuscript, which is included as an attachment.
6. Please clearly specify the study period in the material and methods.
The study period was shown explicitly:
The concentration index was calculated following the methodology proposed by Martin-Vide [10] using a 30-year time series from the CABra dataset from 1980 to 2010.
7. In Table 1, correct the names of the following states:
- Sao Paulo as São Paulo;
- Tacantis as Tocantins;
- Maranhao as Maranhão;
- Pernanmbuco as Pernambuco;
- Rondonia as Rondônia.
The names of the states were corrected, as seen in Table 2 in the corrected manuscript.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Author,
Thank you for resubmitting the revised version.
Still aiming to improve and increase the impact of this article, I suggest some minor revisions.
I think you must pay attention and observe some notes, such as:
1. In the abstract, correct "R2" with the number 2 in superscript. Check this format throughout the text.
2. On line 165, replace "y" with "and" in the citation Siqueira y Nery [28]. Check the entire text in case you need to replace this or other citations in this model elsewhere.
3. In Table 2, in the State column, correct the following: replace "Rondõnia" with "Rondônia".
4. On line 247, replace "&" with "and" in the citation. Check the entire text in case you need to replace this or other citations in this model in other places.
5. In the conclusions section, I suggest relocating the text from lines 338-347 to the end of the Results and Discussion section. This is an excerpt that is not a conclusion.
Author Response
I sincerely thank you for your help in patiently reviewing the manuscript to improve its quality. I appreciate such a remarkable effort.
I reviewed the observations, and all the points from 1 to 4 were made as corrected, as seen in the new version of the manuscript.
1. In the abstract, correct "R2" with the number 2 in superscript. Check this format throughout the text.
2. On line 165, replace "y" with "and" in the citation Siqueira y Nery [28]. Check the entire text in case you need to replace this or other citations in this model elsewhere.
3. In Table 2, in the State column, correct the following: replace "Rondõnia" with "Rondônia".
4. On line 247, replace "&" with "and" in the citation. Check the entire text in case you need to replace this or other citations in this model in other places.
For point five, which says ...
5. In the conclusions section, I suggest relocating the text from lines 338-347 to the end of the Results and Discussion section. This is an excerpt that is not a conclusion.
Trying to improve the manuscript, I decided to move the lines referred to in point 5 to start in line 196 and use it as an introduction to comparing results between the two equations. Now, the paragraph is written like this:
The daily precipitation concentration has been used worldwide during the last years to explore the statistical distribution of precipitation. One of the methodologies most used for that purpose is the one established by Martin-Vide [10]. This methodology is based on fitting the Lorenz curve, which describes the distribution of precipitation data versus the rainfall events. Most research based on Martin-Vide’s methodology focuses on the index's spatial and temporal behavior, and only a few studies have investigated the performance of the equations used. In previous research, Núñez-González et al. [21] found that in cases where a high concentration of precipitation is recognized, equation 2 shows a better performance to fit the Lorenz curve than equation 1; however, their results were based only on data from forty-four stations.
In this sense, results obtained from 735 Brazil stations, shown in Table 2, Figures 2 and 3a, show that all the values of the concentration index based on equation 2 are lower than those based on equation 1. However, they seem related, as was highlighted by Nuñez-González et al. [21].
Author Response File: Author Response.docx
