the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Dec 2024
Return period of high-dimensional compound events. Part I: Conceptual framework
Abstract. Natural hazards like floods and droughts result from the complex interplay of multiple physical processes across various spatial and temporal scales. Traditional univariate analyses fall short in capturing the devastating impacts of compound events—where multiple drivers interact, often leading to more severe outcomes. This study expands on existing methodologies to quantify compound events by introducing a robust framework that integrates hydrological, statistical, and machine learning techniques. We propose a novel approach for defining the critical layer associated with multivariate return periods in higher-dimensional spaces, addressing the challenges in modeling interactions beyond two or three variables. This research not only enhances the understanding of compound events but also provides practical tools for their analysis, offering significant implications for climate risk assessment and environmental management. A forthcoming second paper will demonstrate the practical application of this methodology, focusing on calculating the multivariate return period in five dimensions for rainfall dependencies across different locations.
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CC1: 'Comment on hess-2024-334', Hafidha Khebizi, 11 Dec 2024
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Dear colleagues of the scientific community,
I am pleased to comment on the article presented by Manuel Del Jesus et al., entitled: Return period of high-dimensional compound events. Part I: Conceptual framework.
First, I would like to congratulate the author for his scientific choice to be aware of the natural risks mainly linked to climate change. I congratulate him for having thought of a new approach to define the critical layer associated with multivariate return periods in higher-dimensional spaces, by taking up the challenges of modeling interactions beyond two or three variables. Finally, I encourage the author concerning the second part of the research, undoubtedly reflecting the relevance of the arguments of his new approach.
I would like to inform the author that I have started to learn the use of statistical and mathematical methods for a better understanding of flood scenarios and their return periods in the Algerian Sahara. Although the geographical areas differ, I find the author's new approach interesting and it helps to progress in mastering modeling methods in natural hazards studies.
If the author allows, my comment's objective is to understand how the valuable approach presented in this preprint can be used to analyze the floods produced in Spain on October 29 and 30, 2024 by very abundant rainfall due to a cold drop.
The effects of floods in the province of Valencia are reinforced by climate change and the significant urbanization of the affected areas that have unfortunately caused loss of life. For this, it seems very useful to me to learn with the author the following points in a general way if possible :
- How to integrate the floods of the Province of Valencia into a risk scenario?
- How to integrate the cold drop into the analysis of multivariate return periods according to your new approach based on Six steps?
- The spatial evolution of a cold drop occurs in a well-defined location and then gradually disappears with the weakening of its load. What variables can be used to define the compound extremes? How to choose the appropriate temporal and spatial scales to present a risk scenario?
Kind regards.
Hafidha KHEBIZI
Multidisciplinary geologist
https://orcid.org/0000-0002-3020-199
Citation: https://doi.org/10.5194/hess-2024-334-CC1 -
CC2: 'Reply on CC1', Diego Armando Urrea Méndez, 23 Dec 2024
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Dear Hafidha Khebizi,
Thank you for your thoughtful comment regarding our manuscript. We have prepared a detailed response to address your observation, which is included in the attached document.
Please do not hesitate to reach out if you have further questions or require additional clarification.
Kind regards
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CC3: 'Reply on CC2', Hafidha Khebizi, 25 Dec 2024
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Dear Diego Armando Urrea Méndez,
Thank you for your constructive and very objective answer. You have well explained the application of the different steps in the example of Valencia province's flood.
It will certainly facilitate my understanding of the second part. Thank you for this beneficial explanation. An objective comment will be made for part II.Best regards
Citation: https://doi.org/10.5194/hess-2024-334-CC3
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CC3: 'Reply on CC2', Hafidha Khebizi, 25 Dec 2024
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CC2: 'Reply on CC1', Diego Armando Urrea Méndez, 23 Dec 2024
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RC1: 'Comment on hess-2024-334', Anonymous Referee #1, 17 Jan 2025
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See attached PDF.
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RC2: 'Comment on hess-2024-334', Anonymous Referee #2, 19 Jan 2025
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The manuscript presents a general framework for understanding and applying the concept of return periods to compound events. It seeks to expand upon existing methodologies by introducing an integrated framework that combines hydrological, statistical, and machine learning techniques.
General Comments
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While the manuscript primarily reviews existing concepts of return periods for compound events, it is unclear how these concepts can be generalized to all typologies of compound events. Specifically, the application of return periods to preconditioned and temporally compounding events is not well addressed. To achieve the stated goal of extending the concept to any type of compound event, the manuscript would benefit from illustrative examples that demonstrate this applicability.
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Although the manuscript aims to include machine learning techniques, their description lacks detail and validation. The following areas require clarification and elaboration:
- Page 17, Points 5C-5D: The manuscript discusses the computation of copula values in higher dimensions via integration. However, the role of Gaussian processes in this context is insufficiently explained. The algorithm is not described in detail, its numerical performance is not evaluated, and there is no validation of the method.
- Page 18: The determination of the highest probability density point in the critical layer is attributed to "computational optimization techniques," but these techniques are neither named nor described.
- Section 3.6.2: The manuscript references the use of the Metropolis-Hastings algorithm. However, no algorithm details are provided, and no numerical validation or examples are included.
In summary, while the manuscript provides a comprehensive review of return period concepts, further clarification and illustrative examples are needed to demonstrate the applicability of these concepts to diverse types of compound events. Additionally, the integration of machine learning techniques should be substantiated with detailed methodologies and numerical validations.
Specific comments- Section 3.1.2: It is unclear to me the difference between parametric and non-parametric measures of dependence. I guess that the distinction is between rank-invariant measures and other measures like Pearson’s correlation. Also the intuitive distinction between Spearman’s rho and Kendall’s tau at line 150 should be better explained.
- Section 3.2: please, notice that AIC is not a test, but a selection criterion.
- Eq. (1): It is unclear what is x and what is R_i(x).
- Eq. (3) and (4): It is difficult to understand in which sense X and Y are conditional events rather than random variables. Analogously, F_X(X) should be a random variable and not a conditional event.
- Eq. (5): W is not the copula function but the random variable defined by C(U,V).
- Sections 4 and 5 are quite similar. They should be merged and their scope should be better defined.
Citation: https://doi.org/10.5194/hess-2024-334-RC2 -
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