the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Nov 2024
An extension of the logistic function to account for nonstationary drought losses
Abstract. While the intensity loss function is fundamental to drought impact assessment, the relationship between drought loss and intensity can be nonstationary, i.e., changing as time progresses, owing to socio-economic developments. This paper builds three novel intensity loss functions upon the classic logistic function to account for nonstationary drought losses. Specifically, the time is explicitly formulated as an explanatory variable and respectively incorporated into the magnitude, shape and location parameters of the logistic function to derive three nonstationary intensity loss functions. To examine the effectiveness, a case study is devised for the drought-affected population by province in mainland China during the period from 2006 to 2023. The results highlight the existence of nonstationarity in that the drought-affected population exhibits significant correlation not only with standard precipitation index but also with year. The three nonstationary intensity loss functions are shown to outperform the classic logistic function and also the linear regression. They present effective characterizations of observed drought loss in different ways: 1) the nonstationary function with the flexible magnitude parameter fits the data by adjusting the maximum drought loss by year; 2) the nonstationary function with the flexible shape parameter works by modifying the growth rate of drought loss with intensity; and 3) the nonstationary function with the flexible shape parameter acts by shifting the response curves along the axis by year. In general, the nonstationary function with the flexible magnitude parameter is shown to be the most promising in terms of high coefficient of determination, low Bayesian information criterion and explicit physical meaning. Taken together, the nonstationary intensity loss functions developed in this paper can serve as an effective tool for drought management.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-3476', Anonymous Referee #1, 02 Jan 2025
The relationship between socio-economic loss and drought intensity can be nonstationary, i.e., temporally changing, considering that economic growth can increase the exposure to droughts and that infrastructure developments can decrease the vulnerability to droughts. This study focused on an important issue that the response function of population to drought might be non-stationary. This work would provide rich information as references in guiding climate change mitigation. I have some minor suggestions for consideration.
The authors attempted to explore the relationship between drought-affected population and drought intensity. I think it is better to say it is the population exposure, rather than loss. For the definition of loss, the readers might think it is economic damages or death.
The current Introduction section provided a good summary of the socio-economic impacts of droughts. However, the story about socioeconomic exposure and loss is not clear. Most of previous studies focused on exposure only, very few studies quantified the economic loss (e.g., https://doi.org/10.1073/pnas.1802129115).
In the Method section, the authors showed many drought indices, such as SPEI, PDSI. But the authors only used the SPI. I would recommend only showing the drought indices in Introduction. Moreover, many recent studies have employed the TWS-DSI in exploring the drought events. For example, the following references show some applications of TWS-DSI.
https://www.nature.com/articles/s41893-022-01024-1
https://doi.org/10.1007/s11430-021-9927-x
In the Abstract and Results, the authors provide significant correlation of population and time/other factors. I would recommend providing the p-value to test its significance level.
In Figs. 4-5, I would recommend providing a statistical significance test.
I would recommend omitting the term ‘novel’ across the manuscript.
The writing quality can be improved. For example, “To examine the effectiveness, a case study is devised for the…” I would recommend using ‘designed’, rather than ‘devised’.
Climate change impacts on hydrological cycle and droughts have received growing attention. Could you briefly introduce some physical mechanism behind the drought evolution in mainland China? How about extending this framework to compound hazards?
https://doi.org/10.1029/2022GL100880
Citation: https://doi.org/10.5194/egusphere-2024-3476-RC1 - AC1: 'Reply on RC1', Tongtiegang Zhao, 24 Jan 2025
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RC2: 'Comment on egusphere-2024-3476', Anonymous Referee #2, 05 Jan 2025
The main research content of this paper focuses on the nonstationary relationship between drought losses and drought intensity, proposing nonstationary intensity-loss function based on the Logistic function. If the authors can address the following issues, this manuscript has the potential to be accepted:
- The abstract provides a concise summary of the study; however, it could benefit from a more explicit mention of the key findings and their significance. Consider highlighting the specific improvements your model offers over existing approaches and the practical implications of these improvements.
- In the introduction, this manuscript positions itself as addressing the nonstationarity of drought losses, it could benefit from a more explicit comparison with existing approaches. For instance, what specific limitations of traditional logistic functions or linear regression does this study overcome? The literature review could be expanded to include recent studies on the topic. This would provide a clearer picture of the current state of the field and where your work fits within it.
- The assumption of linear trends for the magnitude, shape, and location parameters may oversimplify the complex socio-economic influencing drought losses. It would strengthen the methodology to either justify this assumption or explore the feasibility of incorporating nonlinear trends.
- This manuscript mentions that changes in the disaster-affected population are related to socio-economic development. However, further details on how specific socio-economic changes (e.g., population growth, infrastructure development) affect drought losses could be elaborated. This would help to better illustrate the importance of the study. For example, the author should be attempted to include socio-economic variables together with SPI as model inputs to further enhance the model's explanatory power, instead of just considering time as a covariate.
- The analysis effectively highlights differences between regions such as Yunnan and Guangdong. However, the underlying drivers of these variations (e.g., climate conditions, socio-economic factors) are insufficiently explored. Adding a discussion on the interaction between climate and socio-economic variables would enrich the interpretation.
- The discussion should not merely restate the results but should also delve deeper into the interpretation of these results in the context of existing literature. The discussion could better position the proposed nonstationary models within the broader literature on drought loss modeling. For instance, how do the findings align with or differ from previous studies, such as those using alternative loss functions or indices?
- The conclusion summarizes the advantages of the proposed nonstationary models. However, emphasizing the methodological contributions and their potential for advancing drought impact assessment frameworks would make the conclusion more impactful.
- Figures 6 and 7 provide valuable insights, but the 3D surface plots may not be intuitive for all readers. Supplementary 2D plots or contour maps could improve accessibility while maintaining scientific rigor.
Citation: https://doi.org/10.5194/egusphere-2024-3476-RC2 - AC2: 'Reply on RC2', Tongtiegang Zhao, 24 Jan 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-3476', Anonymous Referee #1, 02 Jan 2025
The relationship between socio-economic loss and drought intensity can be nonstationary, i.e., temporally changing, considering that economic growth can increase the exposure to droughts and that infrastructure developments can decrease the vulnerability to droughts. This study focused on an important issue that the response function of population to drought might be non-stationary. This work would provide rich information as references in guiding climate change mitigation. I have some minor suggestions for consideration.
The authors attempted to explore the relationship between drought-affected population and drought intensity. I think it is better to say it is the population exposure, rather than loss. For the definition of loss, the readers might think it is economic damages or death.
The current Introduction section provided a good summary of the socio-economic impacts of droughts. However, the story about socioeconomic exposure and loss is not clear. Most of previous studies focused on exposure only, very few studies quantified the economic loss (e.g., https://doi.org/10.1073/pnas.1802129115).
In the Method section, the authors showed many drought indices, such as SPEI, PDSI. But the authors only used the SPI. I would recommend only showing the drought indices in Introduction. Moreover, many recent studies have employed the TWS-DSI in exploring the drought events. For example, the following references show some applications of TWS-DSI.
https://www.nature.com/articles/s41893-022-01024-1
https://doi.org/10.1007/s11430-021-9927-x
In the Abstract and Results, the authors provide significant correlation of population and time/other factors. I would recommend providing the p-value to test its significance level.
In Figs. 4-5, I would recommend providing a statistical significance test.
I would recommend omitting the term ‘novel’ across the manuscript.
The writing quality can be improved. For example, “To examine the effectiveness, a case study is devised for the…” I would recommend using ‘designed’, rather than ‘devised’.
Climate change impacts on hydrological cycle and droughts have received growing attention. Could you briefly introduce some physical mechanism behind the drought evolution in mainland China? How about extending this framework to compound hazards?
https://doi.org/10.1029/2022GL100880
Citation: https://doi.org/10.5194/egusphere-2024-3476-RC1 - AC1: 'Reply on RC1', Tongtiegang Zhao, 24 Jan 2025
-
RC2: 'Comment on egusphere-2024-3476', Anonymous Referee #2, 05 Jan 2025
The main research content of this paper focuses on the nonstationary relationship between drought losses and drought intensity, proposing nonstationary intensity-loss function based on the Logistic function. If the authors can address the following issues, this manuscript has the potential to be accepted:
- The abstract provides a concise summary of the study; however, it could benefit from a more explicit mention of the key findings and their significance. Consider highlighting the specific improvements your model offers over existing approaches and the practical implications of these improvements.
- In the introduction, this manuscript positions itself as addressing the nonstationarity of drought losses, it could benefit from a more explicit comparison with existing approaches. For instance, what specific limitations of traditional logistic functions or linear regression does this study overcome? The literature review could be expanded to include recent studies on the topic. This would provide a clearer picture of the current state of the field and where your work fits within it.
- The assumption of linear trends for the magnitude, shape, and location parameters may oversimplify the complex socio-economic influencing drought losses. It would strengthen the methodology to either justify this assumption or explore the feasibility of incorporating nonlinear trends.
- This manuscript mentions that changes in the disaster-affected population are related to socio-economic development. However, further details on how specific socio-economic changes (e.g., population growth, infrastructure development) affect drought losses could be elaborated. This would help to better illustrate the importance of the study. For example, the author should be attempted to include socio-economic variables together with SPI as model inputs to further enhance the model's explanatory power, instead of just considering time as a covariate.
- The analysis effectively highlights differences between regions such as Yunnan and Guangdong. However, the underlying drivers of these variations (e.g., climate conditions, socio-economic factors) are insufficiently explored. Adding a discussion on the interaction between climate and socio-economic variables would enrich the interpretation.
- The discussion should not merely restate the results but should also delve deeper into the interpretation of these results in the context of existing literature. The discussion could better position the proposed nonstationary models within the broader literature on drought loss modeling. For instance, how do the findings align with or differ from previous studies, such as those using alternative loss functions or indices?
- The conclusion summarizes the advantages of the proposed nonstationary models. However, emphasizing the methodological contributions and their potential for advancing drought impact assessment frameworks would make the conclusion more impactful.
- Figures 6 and 7 provide valuable insights, but the 3D surface plots may not be intuitive for all readers. Supplementary 2D plots or contour maps could improve accessibility while maintaining scientific rigor.
Citation: https://doi.org/10.5194/egusphere-2024-3476-RC2 - AC2: 'Reply on RC2', Tongtiegang Zhao, 24 Jan 2025
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Tongtiegang Zhao
Zecong Chen
Yongyong Zhang
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2200 KB) - Metadata XML