the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Sep 2024
The Return Period Analysis of Heavy Rainfall Disasters Based on Copula Joint Statistical Modeling
Abstract. In the last few years, with the frequent occurrence of extreme weather across the globe, it has become clear that a comprehensive understanding of the patterns and main characteristics of disaster occurrence is essential, and the willingness to study these variables has become more urgent than ever. This paper analyses the multivariate and spatial distribution characteristics of heavy precipitation disasters and proposes a method for estimating the degree of disaster-causing risk using a joint statistical model. This paper tests the model's validity with hourly precipitation data from 122 national meteorological stations in Shandong from 1990 to 2023. Based on heavy precipitation events in the past thirty years, different marginal distribution functions fit the duration of heavy precipitation and precipitation amount. The joint probability distribution model of two related variables is established based on the Copula joint distribution to analyze the change rule of heavy precipitation recurrence period in different periods and to analyze the characteristics of heavy precipitation causing disasters in Shandong Province on this basis. Compared with the disaster return period calculated by relying on univariate variables, the Copula function can more reasonably simulate the natural occurrence of the degree of disaster. The joint return period (JRP) estimated by the Copula function shows that the JPR of heavy rainfall with a duration of 1 hour is 89 % higher than that of 6 hours, indicating a significant increase in the risk of disasters caused by short-term heavy rainfall in Shandong region. This method can more scientifically describe the risk of disasters caused by heavy precipitation in different scenarios, especially the characteristics of disasters caused by short-term heavy precipitation, which can provide an adequate scientific basis for disaster prevention and mitigation planning and disaster risk management.
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Status: closed (peer review stopped)
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RC1: 'Comment on egusphere-2024-2139', Anonymous Referee #1, 09 Oct 2024
Title: The Return Period Analysis of Heavy Rainfall Disasters Based on Copula Joint Statistical Modeling
This manuscript intends to use a new statistical approach to evaluate past heavy rainfall events and return periods, aiming to provide a new tool for decision-makers and urban planning. My general comments can be found as follows:
If the authors' main idea is not a global approach, they must specify the study region location in the title of the manuscript.
Abstract:
Lines 15-16: The forecast of extreme weather, especially regarding extreme rainfall events, is a global challenge due to intrinsic physical and local environment dependence, which can originate from it. So, the authors must be cautious in proposing a statistical approach to forecast (estimate) them.
Line 18: Specify the country where Shandong is located.
Lines 32-34: How can a statistical approach for past events be used to forecast possible future extreme rainfall events?
Line 59: Heavy precipitation and extreme rainfall precipitation are distinct terms. Please clarify and use an adequate definition throughout the manuscript.
Lines 53-57: The authors mention the number related to the damage caused by an extreme rainfall event but do not specify the precipitation volume recorded. Please insert this information.
Line 60: Return period, also known as return time, recurrence interval, or recurrence time, is the estimated interval between occurrences of equal magnitude of a natural phenomenon. Please correct the definition.
Line 63: Please specify the "previous studies".
Line 79: Specify the "flexible assumptions" made.
Lines 92-93: The authors explain that the Copula function could be an alternative to the classical statistical approach for considering the variables' independence. However, the work of De Michele et al. (2023) used variables that are interligated. How do they explain that?
Lines 103-104: Rewrite the sentence. It isn't apparent.
Line 105: What problems do the authors intend to resolve?
Lines 105-130: The paragraph is confusing and complicated to understand. Please rewrite.
Line 154-155: The definition of an extreme event is an event that is not frequent (in general, above the 99th percentile) and seasonally dependent. The definition used in this sentence is not correct.
Lines 158-164: The authors must follow the WMO guidelines and rewrite the sentence.
Lines 186-188: Does the rainfall threshold refer to the daily accumulation (24h)? Why 15 mm and 5 mm thresholds?
Lines 194-195: Are the mentioned occurrences related to continuous rainfall? How were the values considered? Above 0,1 mm?
Lines 191-204: The authors compare extreme rainfall events with different long-time durations. To compare them, it is essential to consider the same time interval.
Lines 235-237: What references are the authors using to affirm that?
Lines 261-262: The sentence "When the risk of heavy precipitation is influenced by the combination of two 262 variables, for example, the degree of damage caused by heavy precipitation" is wrong. Rainfall is the cause of possible damage. Not otherwise.
Line 286: Using 50 mm for at least six hours is not an objective criterion for characterizing heavy rainfall events. If a precipitation event presents an accumulated volume of 50 mm during 72h, it is not heavy rainfall.
Lines 317-334: The physical nature of the rainfall is different considering the time duration.
Lines 366-367: This manuscript does not discuss the atmospheric conditions that lead to extreme rainfall events. So, the authors cannot extrapolate their results for topics not shown in the manuscript.
Lines 416-417: How do the authors think the proposed methodology can be used to forecast extreme rainfall?
Lines 443—447: It is well known that the higher the rainfall volume and also its duration, the more damages are expected. I don't believe the decision-makers need the results presented in this manuscript in an operational procedure (short-term forecasting).
Citation: https://doi.org/10.5194/egusphere-2024-2139-RC1 -
AC1: 'Reply on RC1', Siyu Liu, 23 Oct 2024
Thank you for your comments and suggestions from the experts, we will respond and add to the questions you have raised.
Line 15-16: The statistical model used in the article for estimation, which does not involve the mechanism of physical processes, and the precipitation that has already occurred is used for the estimation of the return period.
Line 18: Thanks to the expert for reminding us that the country where Shandong is located is Shandong, which will be added in the article.
Lines 32-34: This paper does not deal with the problem of prediction, it is a statistical model of heavy precipitation to estimate the return period.
Lines 59: Thanks to the expert's reminder, there are some problems with the description of belonging in the paper, which will be revised.
Lines 53-57: The addition of precipitation due to extreme precipitation will be considered here.
Line 60: A revised and authoritative description of the definitions in the article will be considered here.
Line 63: Consider adding a detailed description of “previous studies” in the article.
Line 79: Flexibility in this context is a relative concept, referring to an increase in the selection of function types relative to previous studies.
Lines 92-93: The work in De Michele et al. (2023) uses staggered variables, which is not the same idea as in this paper.
Lines 103-104: Consider a recharacterization of this sentence.
Lines 105: The problem in the article will be further clarified at this location.
Lines 105-130: There may be some issues with the syntax of this sentence that will be further clarified.
Lines 154-155: Consider further clarification of the description of the definition in the question.
Lines 158-164: There may be some problems with the grammar and description of this sentence, which will be revised here.
Lines 186-188: The thresholds here are referenced from the China Meteorological Administration (CMA) specification, which is not publicly available.
Lines 194-195: The correlation relationship is a prerequisite for modeling in this study.
Lines 191-204: This paper is essentially a return period threshold for precipitation intensity estimation for heavy precipitation.
Lines 235-237: Additional references will be considered here.
Lines 261-262: There are some descriptive or grammatical problems here, and a revision will be considered.
Lines 286: This criterion is based on a document from the China Meteorological Administration (CMA).
Lines 317-334: This paper does not deal with relevant physical properties, but adopts statistical methods using historical precipitation data.
Lines 366-367: The physical background of the atmosphere is not involved.
Lines 416-417: Estimates of historical precipitation, not forecasts.
Lines 443-447: Adjustments to the content are considered here.
Citation: https://doi.org/10.5194/egusphere-2024-2139-AC1
-
AC1: 'Reply on RC1', Siyu Liu, 23 Oct 2024
-
RC2: 'Comment on egusphere-2024-2139', Anonymous Referee #2, 28 Oct 2024
This paper focuses on the application of Copulas to estimate the joint probability density distribution of precipitation duration and precipitation amount to calculate the return period of heavy precipitation in Shandong, China. The authors propose to analyze the changes and connections of the multi-scenarios of heavy precipitation in the Shandong region from the viewpoint of the return period, analysing the risk of extreme events. Copulas allow an understanding of the complex dynamics of combinative occurrences of different variables.
The subject discussed in the present article is of great importance, the methodologies used are sound. The paper is well-structured and easy to follow. Nevertheless, some points need further work, particularly: 1) the lack of references in some key points of the introduction, methods and discussion/conclusions, citing the most important works on the topic and focusing on the study region; 2) regarding the abusive use of the term risk analysis; 3) the lack of novelty as the authors fail to highlight where is the novelty of this manuscript; and finally, the absence of a clear discussion.
Below I discuss the main comments and suggestions, which hopefully can help the authors to enhance the manuscript.
Major comments and questions:
1) Title: The title does not reflect the application to a certain area. The method is not new and I think adding the region's name in the title would highlight that
2) Keywords: The authors could add some more keywords, namely the name of the region as it is not referred in the title, or the family of copulas used. These are suggestions and are not mandatory.
3) Abstract: The methods part of the abstract is a bit repetitive and long. Consider revising the following "Based on heavy precipitation events in the past thirty years, different marginal distribution functions fit the duration of heavy precipitation and precipitation amount. The joint probability distribution model of two related variables is established based on the Copula joint distribution to analyze the change rule of heavy precipitation recurrence period in different periods and to analyze the characteristics of heavy precipitation causing disasters in Shandong Province on this basis."
4) Lack of references in the text:
Lines 49-59: Please add some references, both in China and globally. The numbers in the paragraph should possible to verify by means of a reference.
Lines 63-64 and 74-76: Please add examples/references.
Lines 158-161: Please add reference.
Lines 161-164: Please add references.
5) Inconsistent referencing: The authors don't use the same referencing nomenclature throughout the manuscript and this should be revised.
6) Introduction:
Lines 105-120: The goals of the study are disorganized and repetitive. Please state the general goal and then enumerate the more specific goals on a concise manner.
Lines 123-126. The tense of the verb. Change "The study has a positive effect on improving disaster prevention and mitigation during (...)" to "The study is expected to have a positive effect on improving disaster prevention and mitigation during (...)".
Lines 126-130: Remove as they are repeated.
Lines 143-147: Results. Remove.
Please highlight the novelty of the article and what are the main gaps addressed.
7) Materials:
Lines 158-176: It is unclear if you use the WMO or the CMA definition. This is only clarified in lines 186-190. I would move these lines here.
Lines 221-227: Why do you opt to use just three Archimedean copulas? Please justify and add advantages and disadvantages.
The authors use the term "risk" a bit at ease. I would advise the authors to look at the IPCC report on risk Risk-guidance-FINAL_15Feb2021.pdf and use the term carefully. Plus, you don't calculate risk, but a probability based on the use of copulas. Please clarify throughout the manuscript.
8) Results
Lines 310-315: Move to materials.
Lines 317-321: The copulas are better fitted for certain events, and not the other way around. Please change accordingly.
Lines 451, 454, 458: What does 10 a means? Please clarify.
Characterization of precipitation regimes is lacking.
9) Conclusions and discussion:
Please highlight the novelty of the article and what are the main gaps addressed.
The authors start this section by saying they "introduce" the method, but the method is not new. They should carefully address what is novel and what they intend to address.
Lines 485-497 should be moved for the results. Figure 9 is not clear. Please explain what is represented clearly.
The discussion lacks references to other works and does not any clear comparison between the results achieved and other approaches, namely in the same area, or different areas, or the same approach but in other areas, or even with other goals.
The main conclusions are not clearly identified and nor the identified gaps.
10) Figures
Figure 1: Please complement with a zoom out figure to include China. Not everyone knows where Shandong is.
Figure 2 and Figure 3 and Figure 9: Review caption.
Figure 2 and Figure 6 need to be redone to improve quality (lines difficult to read, labels too small, legends in front of lines)
Minor comments:
1) I suggest changing "precipitation time" . It is not clear to time if it is time of the day, the duration or some other thing.
Citation: https://doi.org/10.5194/egusphere-2024-2139-RC2
Status: closed (peer review stopped)
-
RC1: 'Comment on egusphere-2024-2139', Anonymous Referee #1, 09 Oct 2024
Title: The Return Period Analysis of Heavy Rainfall Disasters Based on Copula Joint Statistical Modeling
This manuscript intends to use a new statistical approach to evaluate past heavy rainfall events and return periods, aiming to provide a new tool for decision-makers and urban planning. My general comments can be found as follows:
If the authors' main idea is not a global approach, they must specify the study region location in the title of the manuscript.
Abstract:
Lines 15-16: The forecast of extreme weather, especially regarding extreme rainfall events, is a global challenge due to intrinsic physical and local environment dependence, which can originate from it. So, the authors must be cautious in proposing a statistical approach to forecast (estimate) them.
Line 18: Specify the country where Shandong is located.
Lines 32-34: How can a statistical approach for past events be used to forecast possible future extreme rainfall events?
Line 59: Heavy precipitation and extreme rainfall precipitation are distinct terms. Please clarify and use an adequate definition throughout the manuscript.
Lines 53-57: The authors mention the number related to the damage caused by an extreme rainfall event but do not specify the precipitation volume recorded. Please insert this information.
Line 60: Return period, also known as return time, recurrence interval, or recurrence time, is the estimated interval between occurrences of equal magnitude of a natural phenomenon. Please correct the definition.
Line 63: Please specify the "previous studies".
Line 79: Specify the "flexible assumptions" made.
Lines 92-93: The authors explain that the Copula function could be an alternative to the classical statistical approach for considering the variables' independence. However, the work of De Michele et al. (2023) used variables that are interligated. How do they explain that?
Lines 103-104: Rewrite the sentence. It isn't apparent.
Line 105: What problems do the authors intend to resolve?
Lines 105-130: The paragraph is confusing and complicated to understand. Please rewrite.
Line 154-155: The definition of an extreme event is an event that is not frequent (in general, above the 99th percentile) and seasonally dependent. The definition used in this sentence is not correct.
Lines 158-164: The authors must follow the WMO guidelines and rewrite the sentence.
Lines 186-188: Does the rainfall threshold refer to the daily accumulation (24h)? Why 15 mm and 5 mm thresholds?
Lines 194-195: Are the mentioned occurrences related to continuous rainfall? How were the values considered? Above 0,1 mm?
Lines 191-204: The authors compare extreme rainfall events with different long-time durations. To compare them, it is essential to consider the same time interval.
Lines 235-237: What references are the authors using to affirm that?
Lines 261-262: The sentence "When the risk of heavy precipitation is influenced by the combination of two 262 variables, for example, the degree of damage caused by heavy precipitation" is wrong. Rainfall is the cause of possible damage. Not otherwise.
Line 286: Using 50 mm for at least six hours is not an objective criterion for characterizing heavy rainfall events. If a precipitation event presents an accumulated volume of 50 mm during 72h, it is not heavy rainfall.
Lines 317-334: The physical nature of the rainfall is different considering the time duration.
Lines 366-367: This manuscript does not discuss the atmospheric conditions that lead to extreme rainfall events. So, the authors cannot extrapolate their results for topics not shown in the manuscript.
Lines 416-417: How do the authors think the proposed methodology can be used to forecast extreme rainfall?
Lines 443—447: It is well known that the higher the rainfall volume and also its duration, the more damages are expected. I don't believe the decision-makers need the results presented in this manuscript in an operational procedure (short-term forecasting).
Citation: https://doi.org/10.5194/egusphere-2024-2139-RC1 -
AC1: 'Reply on RC1', Siyu Liu, 23 Oct 2024
Thank you for your comments and suggestions from the experts, we will respond and add to the questions you have raised.
Line 15-16: The statistical model used in the article for estimation, which does not involve the mechanism of physical processes, and the precipitation that has already occurred is used for the estimation of the return period.
Line 18: Thanks to the expert for reminding us that the country where Shandong is located is Shandong, which will be added in the article.
Lines 32-34: This paper does not deal with the problem of prediction, it is a statistical model of heavy precipitation to estimate the return period.
Lines 59: Thanks to the expert's reminder, there are some problems with the description of belonging in the paper, which will be revised.
Lines 53-57: The addition of precipitation due to extreme precipitation will be considered here.
Line 60: A revised and authoritative description of the definitions in the article will be considered here.
Line 63: Consider adding a detailed description of “previous studies” in the article.
Line 79: Flexibility in this context is a relative concept, referring to an increase in the selection of function types relative to previous studies.
Lines 92-93: The work in De Michele et al. (2023) uses staggered variables, which is not the same idea as in this paper.
Lines 103-104: Consider a recharacterization of this sentence.
Lines 105: The problem in the article will be further clarified at this location.
Lines 105-130: There may be some issues with the syntax of this sentence that will be further clarified.
Lines 154-155: Consider further clarification of the description of the definition in the question.
Lines 158-164: There may be some problems with the grammar and description of this sentence, which will be revised here.
Lines 186-188: The thresholds here are referenced from the China Meteorological Administration (CMA) specification, which is not publicly available.
Lines 194-195: The correlation relationship is a prerequisite for modeling in this study.
Lines 191-204: This paper is essentially a return period threshold for precipitation intensity estimation for heavy precipitation.
Lines 235-237: Additional references will be considered here.
Lines 261-262: There are some descriptive or grammatical problems here, and a revision will be considered.
Lines 286: This criterion is based on a document from the China Meteorological Administration (CMA).
Lines 317-334: This paper does not deal with relevant physical properties, but adopts statistical methods using historical precipitation data.
Lines 366-367: The physical background of the atmosphere is not involved.
Lines 416-417: Estimates of historical precipitation, not forecasts.
Lines 443-447: Adjustments to the content are considered here.
Citation: https://doi.org/10.5194/egusphere-2024-2139-AC1
-
AC1: 'Reply on RC1', Siyu Liu, 23 Oct 2024
-
RC2: 'Comment on egusphere-2024-2139', Anonymous Referee #2, 28 Oct 2024
This paper focuses on the application of Copulas to estimate the joint probability density distribution of precipitation duration and precipitation amount to calculate the return period of heavy precipitation in Shandong, China. The authors propose to analyze the changes and connections of the multi-scenarios of heavy precipitation in the Shandong region from the viewpoint of the return period, analysing the risk of extreme events. Copulas allow an understanding of the complex dynamics of combinative occurrences of different variables.
The subject discussed in the present article is of great importance, the methodologies used are sound. The paper is well-structured and easy to follow. Nevertheless, some points need further work, particularly: 1) the lack of references in some key points of the introduction, methods and discussion/conclusions, citing the most important works on the topic and focusing on the study region; 2) regarding the abusive use of the term risk analysis; 3) the lack of novelty as the authors fail to highlight where is the novelty of this manuscript; and finally, the absence of a clear discussion.
Below I discuss the main comments and suggestions, which hopefully can help the authors to enhance the manuscript.
Major comments and questions:
1) Title: The title does not reflect the application to a certain area. The method is not new and I think adding the region's name in the title would highlight that
2) Keywords: The authors could add some more keywords, namely the name of the region as it is not referred in the title, or the family of copulas used. These are suggestions and are not mandatory.
3) Abstract: The methods part of the abstract is a bit repetitive and long. Consider revising the following "Based on heavy precipitation events in the past thirty years, different marginal distribution functions fit the duration of heavy precipitation and precipitation amount. The joint probability distribution model of two related variables is established based on the Copula joint distribution to analyze the change rule of heavy precipitation recurrence period in different periods and to analyze the characteristics of heavy precipitation causing disasters in Shandong Province on this basis."
4) Lack of references in the text:
Lines 49-59: Please add some references, both in China and globally. The numbers in the paragraph should possible to verify by means of a reference.
Lines 63-64 and 74-76: Please add examples/references.
Lines 158-161: Please add reference.
Lines 161-164: Please add references.
5) Inconsistent referencing: The authors don't use the same referencing nomenclature throughout the manuscript and this should be revised.
6) Introduction:
Lines 105-120: The goals of the study are disorganized and repetitive. Please state the general goal and then enumerate the more specific goals on a concise manner.
Lines 123-126. The tense of the verb. Change "The study has a positive effect on improving disaster prevention and mitigation during (...)" to "The study is expected to have a positive effect on improving disaster prevention and mitigation during (...)".
Lines 126-130: Remove as they are repeated.
Lines 143-147: Results. Remove.
Please highlight the novelty of the article and what are the main gaps addressed.
7) Materials:
Lines 158-176: It is unclear if you use the WMO or the CMA definition. This is only clarified in lines 186-190. I would move these lines here.
Lines 221-227: Why do you opt to use just three Archimedean copulas? Please justify and add advantages and disadvantages.
The authors use the term "risk" a bit at ease. I would advise the authors to look at the IPCC report on risk Risk-guidance-FINAL_15Feb2021.pdf and use the term carefully. Plus, you don't calculate risk, but a probability based on the use of copulas. Please clarify throughout the manuscript.
8) Results
Lines 310-315: Move to materials.
Lines 317-321: The copulas are better fitted for certain events, and not the other way around. Please change accordingly.
Lines 451, 454, 458: What does 10 a means? Please clarify.
Characterization of precipitation regimes is lacking.
9) Conclusions and discussion:
Please highlight the novelty of the article and what are the main gaps addressed.
The authors start this section by saying they "introduce" the method, but the method is not new. They should carefully address what is novel and what they intend to address.
Lines 485-497 should be moved for the results. Figure 9 is not clear. Please explain what is represented clearly.
The discussion lacks references to other works and does not any clear comparison between the results achieved and other approaches, namely in the same area, or different areas, or the same approach but in other areas, or even with other goals.
The main conclusions are not clearly identified and nor the identified gaps.
10) Figures
Figure 1: Please complement with a zoom out figure to include China. Not everyone knows where Shandong is.
Figure 2 and Figure 3 and Figure 9: Review caption.
Figure 2 and Figure 6 need to be redone to improve quality (lines difficult to read, labels too small, legends in front of lines)
Minor comments:
1) I suggest changing "precipitation time" . It is not clear to time if it is time of the day, the duration or some other thing.
Citation: https://doi.org/10.5194/egusphere-2024-2139-RC2
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