Lightning Current Distribution of the First and Subsequent Strokes Based on the Lightning Location System: Survey in Yunnan Power Grid
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript presents an analysis of lightning current distribution in the Yunnan Power Grid based on data from a lightning location system. Analysis of the combined relationship between the first return stroke and the subsequent strokes is very interesting. The study addresses an important topic, however, there are several major issues that need to be resolved to improve the clarity of the paper.
Major Comments:
1) The mountainous terrain can significantly affect the lightning current amplitudes due to the electromagnetic field propagation. This effect should be mentioned and needs to be fully reviewed and discussed through the paper. See reference:
Azadifar, M., F. Rachidi, M. Rubinstein, M. Paolone, G. Diendorfer, H. Pichler, W. Schulz, D. Pavanello, and C. Romero (2016), Evaluation of the performance characteristics of the European Lightning Detection Network EUCLID in the Alps region for upward negative flashes using direct measurements at the instrumented Säntis Tower, J. Geophys. Res. Atmos., 121, 595–606.
Li, D., Azadifar, M., Rachidi, F., Rubinstein, M., Paolone, M., Pavanello, D., Metz, S., Zhang, Q. and Wang, Z., 2015. On lightning electromagnetic field propagation along an irregular terrain. IEEE Transactions on Electromagnetic Compatibility, 58(1), pp.161-171.
2) The manuscript lacks details about the type of antennas used in the lightning location system (magnetic loop antennas or electric field sensors?). It is also necessary to specify the system’s location accuracy and the coverage.
3) The identification criteria for multiple return strokes are not clearly defined. Clarify whether strokes are distinguished based on temporal interval, spatial distance, or both. What is the minimum temporal interval or spatial distance required to classify strokes as part of the same lightning event.
4) The title does not accurately reflect the scope of the study, as it suggests the analysis is limited to subsequent strokes, but the paper also analyzes first return strokes.
Specific Comments:
1) The title does not adequately reflect the work, since the analysis evaluates both the first return strokes and subsequent strokes, not just the subsequent strokes.
2) The sentence, “Researchers have explored the influences of factors such as terrain, altitude, and temperature on the amplitude of lightning currents through cluster analysis, statistical analysis, and field measurements, proposing corresponding conclusions and methodologies,” in the abstract is inappropriate. It should be moved to the introduction and needs to be revised for clarity.
3) The first sentence in the abstract, “Lightning is an electrical discharge phenomenon in the atmosphere caused by the separation of strong charges,” and the similar phrase in the introduction, “caused by the separation of strong charges in the atmosphere,” are incorrect. They should be revised to “caused by charge separation in clouds.”
4) What is meant by “preprocesses” the data? Please clarify.
5) Line 45, Is “satellite time” refers to GPS time or another standard?
6) Regarding the abbreviation FMRS, where does the “F” come from?
7) By “lightning ground flashes,” do you mean CG flashes?
8) The header in Table 1 should be changed to “Number of Strokes” instead of “Number” to improve clarity.
9) In Line 115, what is meant by “reference 5.”
10) Figure 1 seems to repeat the same parameters and information as Table 1. Consider deleting it. Additionally, clarify the meaning of “total” in the caption.
11) In Line 127, confirm if “PFMSS” is meant to be “PFMRS.” There are too many unnecessary abbreviations in the manuscript, making it hard to read. For example, in Lines 108–111, you could keep MRS but remove NF and TF, replacing them with descriptive terms (negative flash and total flash) instead. This would make the manuscript clearer.
12) In Table 2, the percentage symbol is missing in the title row. Additionally, the header “number” should be revised to “Number of Strokes” to avoid confusion.
13) References should be provided for the fitting equation (1). Explain why this equation was used instead of a simpler exponential model. Considering that there are only 8 data points and 5 fitting parameters, the uncertainty may be significant. Include R^2 and RMSE values to evaluate the goodness of fit.
14) What does “amplitude interval” mean in Figures 3 and 4? Please clarify.
15) The physical meaning of parameters “a” and “b” in the fit expression requires further explanation.
16) In Figures 3–5, explain what the value “0” represents in the “number of strokes” column.
17) The phrase “from a cluster” in Line 245 needs further explanation.
18) In Figure 7, what parameters are represented on the y-axis? Additionally, clarify why the direction appears inverted.
19) In Line 259, the sentence “As a result, the probability density of multiple lightning strokes can be obtained in smaller errors” is unclear and needs further clarification.
Comments on the Quality of English Language
English language needs to be improved to enhance the readability of the paper.
Author Response
Dear reviewer:
We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. The revised part for reviewer 1, 2 and 3 are highlighted as yellow, green and blue, separately
Reviewer 1:
The manuscript presents an analysis of lightning current distribution in the Yunnan Power Grid based on data from a lightning location system. Analysis of the combined relationship between the first return stroke and the subsequent strokes is very interesting. The study addresses an important topic, however, there are several major issues that need to be resolved to improve the clarity of the paper.
Major Comments:
1) The mountainous terrain can significantly affect the lightning current amplitudes due to the electromagnetic field propagation. This effect should be mentioned and needs to be fully reviewed and discussed through the paper. See reference:
Azadifar, M., F. Rachidi, M. Rubinstein, M. Paolone, G. Diendorfer, H. Pichler, W. Schulz, D. Pavanello, and C. Romero (2016), Evaluation of the performance characteristics of the European Lightning Detection Network EUCLID in the Alps region for upward negative flashes using direct measurements at the instrumented Säntis Tower, J. Geophys. Res. Atmos., 121, 595–606.
Li, D., Azadifar, M., Rachidi, F., Rubinstein, M., Paolone, M., Pavanello, D., Metz, S., Zhang, Q. and Wang, Z., 2015. On lightning electromagnetic field propagation along an irregular terrain. IEEE Transactions on Electromagnetic Compatibility, 58(1), pp.161-171.
Answer: we sincerely thank the reviewer for careful reading. As suggested by the reviewer, we have added more references to support this idea. The added references can be found in lines 52-54 on page 2.
2) The manuscript lacks details about the type of antennas used in the lightning location system (magnetic loop antennas or electric field sensors?). It is also necessary to specify the system’s location accuracy and the coverage.
Answer: we sincerely thank the reviewer for careful reading. The Lightning Location System in our test consists of 56 detection stations, each equipped with electric field sensors as antennas. The system features high positioning accuracy, with a location error of less than 2k and a time error of less than 1. The above revisions have been added to the article in lines109-112 of page 3.
3) The identification criteria for multiple return strokes are not clearly defined. Clarify whether strokes are distinguished based on temporal interval, spatial distance, or both. What is the minimum temporal interval or spatial distance required to classify strokes as part of the same lightning event.
Answer: we sincerely thank the reviewer for careful reading. According to the national standard GB/T 37047-2022, a single-return-stroke lightning flash is defined as a lightning flash with only one return stroke, whereas a FMSS is defined as one with two or more return strokes. The condition for classifying a subsequent stroke and the first return stroke as a single lightning flash is that the time interval between the subsequent stroke and the first return stroke must be less than or equal to 1, the spatial distance between them must be less than or equal to 10, and the time interval between adjacent strokes must be less than or equal to 500. The above revisions have been added to the article in lines 64-71 on page 2.
4) The title does not accurately reflect the scope of the study, as it suggests the analysis is limited to subsequent strokes, but the paper also analyzes first return strokes.
Answer: we feel sorry for our carelessness. In our resubmitted manuscript, the title is revised as “Lightning Current Distribution of the First and Subsequent Strokes Based on the Lightning Location System: Survey in Yunnan Power Grid”. Thanks for your correction.
Specific Comments:
1) The title does not adequately reflect the work, since the analysis evaluates both the first return strokes and subsequent strokes, not just the subsequent strokes.
Answer: we feel sorry for our carelessness. In our resubmitted manuscript, the title is revised as “Lightning Current Distribution of the First and Subsequent Strokes Based on the Lightning Location System: Survey in Yunnan Power Grid”. Thanks for your correction.
2) The sentence, “Researchers have explored the influences of factors such as terrain, altitude, and temperature on the amplitude of lightning currents through cluster analysis, statistical analysis, and field measurements, proposing corresponding conclusions and methodologies,” in the abstract is inappropriate. It should be moved to the introduction and needs to be revised for clarity.
Answer: we think this is an excellent suggestion. We've removed this part of the abstract.
3) The first sentence in the abstract, “Lightning is an electrical discharge phenomenon in the atmosphere caused by the separation of strong charges,” and the similar phrase in the introduction, “caused by the separation of strong charges in the atmosphere,” are incorrect. They should be revised to “caused by charge separation in clouds.”
Answer: we sincerely thank the reviewer for careful reading. As suggested by the reviewer, we have corrected the “Lightning is an electrical discharge phenomenon in the atmosphere caused by the separation of strong charges” and “caused by the separation of strong charges in the atmosphere” into “caused by charge separation in clouds”.
4) What is meant by “preprocesses” the data? Please clarify.
Answer: we sincerely thank the reviewer for careful reading, "preprocesses" has no actual meaning, it is an inaccurate word we used and has been modified to "obtains".
5) Line 45, Is “satellite time” refers to GPS time or another standard?
Answer: we sincerely thank the reviewer for careful reading. The “satellite time” refers to GPS time, we've added it in line 44 on page 1.
6) Regarding the abbreviation FMRS, where does the “F” come from?
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations. “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
7) By “lightning ground flashes,” do you mean CG flashes?
Answer: yes, we have modified it in the revised paper.
8) The header in Table 1 should be changed to “Number of Strokes” instead of “Number” to improve clarity.
Answer: we feel sorry for our carelessness. We have modified.
9) In Line 129, what is meant by “reference 5.”
Answer: "Reference 5" refers to the fifth reference in the references, so sorry for not using the article citation format correctly. We have revised it.
10) Figure 1 seems to repeat the same parameters and information as Table 1. Consider deleting it. Additionally, clarify the meaning of “total” in the caption.
Answer: we sincerely thank the reviewer for careful reading. Figure 1 and Table 1 are indeed derived from the same data, and we have merged the two contents. In the Table 1, "total" refers to the total quantity.
11) In Line 127, confirm if “PFMSS” is meant to be “PFMRS.” There are too many unnecessary abbreviations in the manuscript, making it hard to read. For example, in Lines 108–111, you could keep MRS but remove NF and TF, replacing them with descriptive terms (negative flash and total flash) instead. This would make the manuscript clearer.
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations, “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
12) In Table 2, the percentage symbol is missing in the title row. Additionally, the header “number” should be revised to “Number of Strokes” to avoid confusion.
Answer: we feel sorry for our carelessness. We have modified.
13) References should be provided for the fitting equation (1). Explain why this equation was used instead of a simpler exponential model. Considering that there are only 8 data points and 5 fitting parameters, the uncertainty may be significant. Include R^2 and RMSE values to evaluate the goodness of fit.
Answer: we sincerely thank the reviewer for careful reading. We have noticed that the fitting formula is complex and meaningless, and we have modified it to an exponential function in line 162 on page 5.
14) What does “amplitude interval” mean in Figures 3 and 4? Please clarify.
Answer: we sincerely thank the reviewer for careful reading. The amplitude interval refers to the statistical intervals divided within the range of lightning current amplitudes. It has been added to the article in line 188 on page 6.
15) The physical meaning of parameters “a” and “b” in the fit expression requires further explanation.
Answer: we sincerely thank the reviewer for careful reading, “a” denotes the median probability density of lightning current (); and “b” indicates the steepness of the probability density of lightning current amplitudes. “a” reflects the central tendency of the lightning current amplitude distribution, a larger value of “a” indicates a higher median lightning current, representing a greater lightning current amplitude; “b” determines the steepness of the cumulative probability curve for lightning current amplitudes, a larger value of “b” results in a faster change in the cumulative probability curve, indicating a more concentrated distribution, while a smaller value leads to a slower change and a more dispersed distribution. we've added it in lines 178-184 on page 5.
16) In Figures 3–5, explain what the value “0” represents in the “number of strokes” column.
Answer: we sincerely thank the reviewer for careful reading. Among them,"0" refers to the lightning without subsequent stroke to the lightning, that is the first return stroke. We've added it in lines 198 on page 6.
17) The phrase “from a cluster” in Line 245 needs further explanation.
Answer: we feel sorry for our carelessness, "from a cluster" doesn't make any real sense, here is the expression error, and we've fixed it.
18) In Figure 7, what parameters are represented on the y-axis? Additionally, clarify why the direction appears inverted. (Number of strokes)
Answer: the y-axis means number of strokes. The 3-D figure somehow confuses the direction and we do not label the y-axis correctly. The revised figure has been illustrated in line 268 on page 9.
19) In Line 259, the sentence “As a result, the probability density of multiple lightning strokes can be obtained in smaller errors” is unclear and needs further clarification
Answer: we feel sorry for our carelessness. Here is the expression error, we want to illustrate that the probability density of multiple lightning strokes can be obtained by just one equation as Eq (3). We've fixed it.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsAt the beginning of the article, the abbreviations PFMRS, NFMRS, TFMRS are used, and later from LINE 127... PFMSS, NFMSS, TFMSS. The names of the abbreviations need to be harmonized.
Author Response
Dear reviewer:
We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. The revised part for reviewer 1, 2 and 3 are highlighted as yellow, green and blue, separately.
Reviewer 2:
- At the beginning of the article, the abbreviations PFMRS, NFMRS, TFMRS are used, and later from LINE 127... PFMSS, NFMSS, TFMSS. The names of the abbreviations need to be harmonized.
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations, “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsIn the manuscript entitled "Lightning Current Distribution of Subsequent Strokes Based on the Lightning Location System: A Survey in Yunnan Power Grid" by Yutang Ma, Hongchun Shu, Changxin Xiao, Gaohui Yang, Chengwei Xie, Mengmeng Zhu, and Pulin Cao, statistical properties of currents in multiple stroke lightning in the Yunnan administrative region are investigated based on the observations in years from 2008 to 2019. The paper presented is rather solid and interesting to read but not free from shortcomings.
While the paper pronounce lightning statistics in different terrains it would be helpful to describe terrain characteristics of the Yunnan administrative region and its difference or similarity with terrain characteristics of Hubei, Beijing, Lanzhou, and, perhaps, Florida that are used to compare some lightning parameters (see lines 101-103 and 116).
The main comment is that from the Eq.(2) (page 5) a value of 'a' should be in current units, but in the line 184 and after in the text including Figs. 3,5,7 and Table 3 it is given as undimensional that does not correspond to its meaning.
Less valuable comments are as follows.
Eq.(1) (page 5) fits 8-point curve using 5 (too much) parameters. If there is a physical sense in parameters m, n, t1, and t2 it should be clearly pronounced, otherwise this is just one of possible fittings.
Lines 245,246: Seems, the reference should be to Eq.(2), not to Eq.(1).
Eq.(3) (page 9): What does it mean * in the equation? If just a multiplication it would be better to use a dot (or nothing).
Table 3 (page 10): Value of 'e' as well as value of 'a' should be in current units.
Author Response
Dear reviewer:
We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. The revised part for reviewer 1, 2 and 3 are highlighted as yellow, green and blue, separately
Reviewer 3:
In the manuscript entitled "Lightning Current Distribution of Subsequent Strokes Based on the Lightning Location System: A Survey in Yunnan Power Grid" by Yutang Ma, Hongchun Shu, Changxin Xiao, Gaohui Yang, Chengwei Xie, Mengmeng Zhu, and Pulin Cao, statistical properties of currents in multiple stroke lightning in the Yunnan administrative region are investigated based on the observations in years from 2008 to 2019. The paper presented is rather solid and interesting to read but not free from shortcomings.
While the paper pronounce lightning statistics in different terrains it would be helpful to describe terrain characteristics of the Yunnan administrative region and its difference or similarity with terrain characteristics of Hubei, Beijing, Lanzhou, and, perhaps, Florida that are used to compare some lightning parameters (see lines 101-103 and 116).
1)The main comment is that from the Eq.(2) (page 5) a value of 'a' should be in current units, but in the line 184 and after in the text including Figs. 3,5,7 and Table 3 it is given as undimensional that does not correspond to its meaning.
Answer: we sincerely thank the reviewer for careful reading. Parameters a and e have units of kiloamperes (kA). We've fixed it.
Less valuable comments are as follows.
2)Eq.(1) (page 5) fits 8-point curve using 5 (too much) parameters. If there is a physical sense in parameters m, n, t1, and t2 it should be clearly pronounced, otherwise this is just one of possible fittings.
Answer: we sincerely thank the reviewer for careful reading. We have noticed that the fitting formula is complex and meaningless, and we have modified it to an exponential function.
3)Lines 245,246: Seems, the reference should be to Eq.(2), not to Eq.(1).
Answer: we feel sorry for our carelessness. We have modified.
4)Eq.(3) (page 9): What does it mean * in the equation? If just a multiplication it would be better to use a dot (or nothing).
Answer: we feel sorry for our carelessness. We have modified.
5)Table 3 (page 10): Value of 'e' as well as value of 'a' should be in current units.
Answer: we sincerely thank the reviewer for careful reading. Parameters a and e have units of kiloamperes (kA). We've fixed it.
Author Response File: Author Response.docx
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors applied all my comments such that I can recommend publication in present form.
Author Response
Dear reviewer:
We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. The revised part for reviewer 1, 2 and 3 are highlighted as yellow, green and blue, separately
Reviewer 1:
The manuscript presents an analysis of lightning current distribution in the Yunnan Power Grid based on data from a lightning location system. Analysis of the combined relationship between the first return stroke and the subsequent strokes is very interesting. The study addresses an important topic, however, there are several major issues that need to be resolved to improve the clarity of the paper.
Major Comments:
1) The mountainous terrain can significantly affect the lightning current amplitudes due to the electromagnetic field propagation. This effect should be mentioned and needs to be fully reviewed and discussed through the paper. See reference:
Azadifar, M., F. Rachidi, M. Rubinstein, M. Paolone, G. Diendorfer, H. Pichler, W. Schulz, D. Pavanello, and C. Romero (2016), Evaluation of the performance characteristics of the European Lightning Detection Network EUCLID in the Alps region for upward negative flashes using direct measurements at the instrumented Säntis Tower, J. Geophys. Res. Atmos., 121, 595–606.
Li, D., Azadifar, M., Rachidi, F., Rubinstein, M., Paolone, M., Pavanello, D., Metz, S., Zhang, Q. and Wang, Z., 2015. On lightning electromagnetic field propagation along an irregular terrain. IEEE Transactions on Electromagnetic Compatibility, 58(1), pp.161-171.
Answer: we sincerely thank the reviewer for careful reading. As suggested by the reviewer, we have added more references to support this idea. The added references can be found in lines 52-54 on page 2.
2) The manuscript lacks details about the type of antennas used in the lightning location system (magnetic loop antennas or electric field sensors?). It is also necessary to specify the system’s location accuracy and the coverage.
Answer: we sincerely thank the reviewer for careful reading. The Lightning Location System in our test consists of 56 detection stations, each equipped with electric field sensors as antennas. The system features high positioning accuracy, with a location error of less than 2k and a time error of less than 1. The above revisions have been added to the article in lines109-112 of page 3.
3) The identification criteria for multiple return strokes are not clearly defined. Clarify whether strokes are distinguished based on temporal interval, spatial distance, or both. What is the minimum temporal interval or spatial distance required to classify strokes as part of the same lightning event.
Answer: we sincerely thank the reviewer for careful reading. According to the national standard GB/T 37047-2022, a single-return-stroke lightning flash is defined as a lightning flash with only one return stroke, whereas a FMSS is defined as one with two or more return strokes. The condition for classifying a subsequent stroke and the first return stroke as a single lightning flash is that the time interval between the subsequent stroke and the first return stroke must be less than or equal to 1, the spatial distance between them must be less than or equal to 10, and the time interval between adjacent strokes must be less than or equal to 500. The above revisions have been added to the article in lines 64-71 on page 2.
4) The title does not accurately reflect the scope of the study, as it suggests the analysis is limited to subsequent strokes, but the paper also analyzes first return strokes.
Answer: we feel sorry for our carelessness. In our resubmitted manuscript, the title is revised as “Lightning Current Distribution of the First and Subsequent Strokes Based on the Lightning Location System: Survey in Yunnan Power Grid”. Thanks for your correction.
Specific Comments:
1) The title does not adequately reflect the work, since the analysis evaluates both the first return strokes and subsequent strokes, not just the subsequent strokes.
Answer: we feel sorry for our carelessness. In our resubmitted manuscript, the title is revised as “Lightning Current Distribution of the First and Subsequent Strokes Based on the Lightning Location System: Survey in Yunnan Power Grid”. Thanks for your correction.
2) The sentence, “Researchers have explored the influences of factors such as terrain, altitude, and temperature on the amplitude of lightning currents through cluster analysis, statistical analysis, and field measurements, proposing corresponding conclusions and methodologies,” in the abstract is inappropriate. It should be moved to the introduction and needs to be revised for clarity.
Answer: we think this is an excellent suggestion. We've removed this part of the abstract.
3) The first sentence in the abstract, “Lightning is an electrical discharge phenomenon in the atmosphere caused by the separation of strong charges,” and the similar phrase in the introduction, “caused by the separation of strong charges in the atmosphere,” are incorrect. They should be revised to “caused by charge separation in clouds.”
Answer: we sincerely thank the reviewer for careful reading. As suggested by the reviewer, we have corrected the “Lightning is an electrical discharge phenomenon in the atmosphere caused by the separation of strong charges” and “caused by the separation of strong charges in the atmosphere” into “caused by charge separation in clouds”.
4) What is meant by “preprocesses” the data? Please clarify.
Answer: we sincerely thank the reviewer for careful reading, "preprocesses" has no actual meaning, it is an inaccurate word we used and has been modified to "obtains".
5) Line 45, Is “satellite time” refers to GPS time or another standard?
Answer: we sincerely thank the reviewer for careful reading. The “satellite time” refers to GPS time, we've added it in line 44 on page 1.
6) Regarding the abbreviation FMRS, where does the “F” come from?
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations. “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
7) By “lightning ground flashes,” do you mean CG flashes?
Answer: yes, we have modified it in the revised paper.
8) The header in Table 1 should be changed to “Number of Strokes” instead of “Number” to improve clarity.
Answer: we feel sorry for our carelessness. We have modified.
9) In Line 129, what is meant by “reference 5.”
Answer: "Reference 5" refers to the fifth reference in the references, so sorry for not using the article citation format correctly. We have revised it.
10) Figure 1 seems to repeat the same parameters and information as Table 1. Consider deleting it. Additionally, clarify the meaning of “total” in the caption.
Answer: we sincerely thank the reviewer for careful reading. Figure 1 and Table 1 are indeed derived from the same data, and we have merged the two contents. In the Table 1, "total" refers to the total quantity.
11) In Line 127, confirm if “PFMSS” is meant to be “PFMRS.” There are too many unnecessary abbreviations in the manuscript, making it hard to read. For example, in Lines 108–111, you could keep MRS but remove NF and TF, replacing them with descriptive terms (negative flash and total flash) instead. This would make the manuscript clearer.
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations, “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
12) In Table 2, the percentage symbol is missing in the title row. Additionally, the header “number” should be revised to “Number of Strokes” to avoid confusion.
Answer: we feel sorry for our carelessness. We have modified.
13) References should be provided for the fitting equation (1). Explain why this equation was used instead of a simpler exponential model. Considering that there are only 8 data points and 5 fitting parameters, the uncertainty may be significant. Include R^2 and RMSE values to evaluate the goodness of fit.
Answer: we sincerely thank the reviewer for careful reading. We have noticed that the fitting formula is complex and meaningless, and we have modified it to an exponential function in line 162 on page 5.
14) What does “amplitude interval” mean in Figures 3 and 4? Please clarify.
Answer: we sincerely thank the reviewer for careful reading. The amplitude interval refers to the statistical intervals divided within the range of lightning current amplitudes. It has been added to the article in line 188 on page 6.
15) The physical meaning of parameters “a” and “b” in the fit expression requires further explanation.
Answer: we sincerely thank the reviewer for careful reading, “a” denotes the median probability density of lightning current (); and “b” indicates the steepness of the probability density of lightning current amplitudes. “a” reflects the central tendency of the lightning current amplitude distribution, a larger value of “a” indicates a higher median lightning current, representing a greater lightning current amplitude; “b” determines the steepness of the cumulative probability curve for lightning current amplitudes, a larger value of “b” results in a faster change in the cumulative probability curve, indicating a more concentrated distribution, while a smaller value leads to a slower change and a more dispersed distribution. we've added it in lines 178-184 on page 5.
16) In Figures 3–5, explain what the value “0” represents in the “number of strokes” column.
Answer: we sincerely thank the reviewer for careful reading. Among them,"0" refers to the lightning without subsequent stroke to the lightning, that is the first return stroke. We've added it in lines 198 on page 6.
17) The phrase “from a cluster” in Line 245 needs further explanation.
Answer: we feel sorry for our carelessness, "from a cluster" doesn't make any real sense, here is the expression error, and we've fixed it.
18) In Figure 7, what parameters are represented on the y-axis? Additionally, clarify why the direction appears inverted. (Number of strokes)
Answer: the y-axis means number of strokes. The 3-D figure somehow confuses the direction and we do not label the y-axis correctly. The revised figure has been illustrated in line 268 on page 9.
19) In Line 259, the sentence “As a result, the probability density of multiple lightning strokes can be obtained in smaller errors” is unclear and needs further clarification
Answer: we feel sorry for our carelessness. Here is the expression error, we want to illustrate that the probability density of multiple lightning strokes can be obtained by just one equation as Eq (3). We've fixed it.
Reviewer 2:
- At the beginning of the article, the abbreviations PFMRS, NFMRS, TFMRS are used, and later from LINE 127... PFMSS, NFMSS, TFMSS. The names of the abbreviations need to be harmonized.
Answer: we sincerely thank the reviewer for careful reading. We also noticed that there are too many abbreviations for lightning, and we only use “CG” and “FMSS” for lightning abbreviations, “CG” stands for “cloud-to-ground”, and “FMSS” stands for “flashes with multiple subsequent strokes”.
Reviewer 3:
In the manuscript entitled "Lightning Current Distribution of Subsequent Strokes Based on the Lightning Location System: A Survey in Yunnan Power Grid" by Yutang Ma, Hongchun Shu, Changxin Xiao, Gaohui Yang, Chengwei Xie, Mengmeng Zhu, and Pulin Cao, statistical properties of currents in multiple stroke lightning in the Yunnan administrative region are investigated based on the observations in years from 2008 to 2019. The paper presented is rather solid and interesting to read but not free from shortcomings.
While the paper pronounce lightning statistics in different terrains it would be helpful to describe terrain characteristics of the Yunnan administrative region and its difference or similarity with terrain characteristics of Hubei, Beijing, Lanzhou, and, perhaps, Florida that are used to compare some lightning parameters (see lines 101-103 and 116).
1)The main comment is that from the Eq.(2) (page 5) a value of 'a' should be in current units, but in the line 184 and after in the text including Figs. 3,5,7 and Table 3 it is given as undimensional that does not correspond to its meaning.
Answer: we sincerely thank the reviewer for careful reading. Parameters a and e have units of kiloamperes (kA). We've fixed it.
Less valuable comments are as follows.
2)Eq.(1) (page 5) fits 8-point curve using 5 (too much) parameters. If there is a physical sense in parameters m, n, t1, and t2 it should be clearly pronounced, otherwise this is just one of possible fittings.
Answer: we sincerely thank the reviewer for careful reading. We have noticed that the fitting formula is complex and meaningless, and we have modified it to an exponential function.
3)Lines 245,246: Seems, the reference should be to Eq.(2), not to Eq.(1).
Answer: we feel sorry for our carelessness. We have modified.
4)Eq.(3) (page 9): What does it mean * in the equation? If just a multiplication it would be better to use a dot (or nothing).
Answer: we feel sorry for our carelessness. We have modified.
5)Table 3 (page 10): Value of 'e' as well as value of 'a' should be in current units.
Answer: we sincerely thank the reviewer for careful reading. Parameters a and e have units of kiloamperes (kA). We've fixed it.
Author Response File: Author Response.docx
