the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Mar 2026
Nonlinear Quantitative Relationship Between the Duration and Occurrence Frequency of Droughts
Abstract. This study aims to quantify the relationship between the duration and occurrence frequency of droughts in China, particularly focusing on different drought intensities. By analyzing daily meteorological drought composite index (MCI) data from 1897 meteorological stations across China spanning from 1961 to 2020, the study reveals a significant double-logarithmic relationship between drought duration and occurrence frequency. The results show that shorter drought durations are associated with higher occurrence frequencies, while longer durations correspond to lower frequencies. This relationship is characterized by one parameter (k or b), which can independently describe the nonlinear association between drought duration and frequency. Spatially, the values of the parameter exhibit a gradient from northwest to southeast, with higher values in arid and semi-arid regions and lower values in humid and semi-humid regions. Notably, the parameter k aligns well with precipitation isolines, effectively distinguishing arid, semi-arid, and humid regions. Additionally, droughts in arid and semi-arid regions tend to last longer (often exceeding 60 days), while those in humid and semi-humid regions are shorter but more frequent. These findings provide critical insights for optimizing water resource management, agricultural planning, and disaster mitigation strategies, enhancing societal resilience to drought impacts.
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Notice on discussion status
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
(2202 KB)
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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.
- Preprint
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- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-6401', Anonymous Referee #1, 03 Apr 2026
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AC1: 'Reply on RC1', Pengcheng Yan, 06 Apr 2026
Thanks for the comments. Please see the attachment.
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RC2: 'Reply on AC1', Anonymous Referee #1, 07 Apr 2026
All issues I raised have been satisfactorily addressed. I recommend the paper for acceptance.Citation: https://doi.org/
10.5194/egusphere-2025-6401-RC2 -
AC2: 'Reply on RC2', Pengcheng Yan, 08 Apr 2026
Thank you so much for your valuable suggestions, which have greatly enhanced both the scientific rigor and readability of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-6401-AC2
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AC2: 'Reply on RC2', Pengcheng Yan, 08 Apr 2026
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RC2: 'Reply on AC1', Anonymous Referee #1, 07 Apr 2026
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AC1: 'Reply on RC1', Pengcheng Yan, 06 Apr 2026
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RC3: 'Comment on egusphere-2025-6401', Anonymous Referee #2, 13 Apr 2026
Based on the China daily-scale meteorological drought index, this manuscript revealed a double-logarithmic relationship between drought duration and occurrence frequency, and proposed that a single parameter can characterize this nonlinear feature. The findings provide quantitative evidence for water resource management, agricultural planning, and drought disaster prevention and mitigation. The following issues need to be corrected.
General comments
- Page3: The manuscript mentions “Qinghai-Tibet Plateau (gray area in Fig. 1) region isnot included in our study due to sparse station data”, and “the selected stations distribute in most regions of China except Hainan and Taiwan”. However, the impact of such exclusion on the representativeness of conclusions at the national scale was not discussed.
- Page4: Formula (2) uses log2 instead of natural logarithm or common logarithm. There is no justification for selecting base 2. It is recommended to briefly explain the rationale for this choice in the text or to uniformly use natural logarithm.
- Page12: The article states that parameter k/bcan independently characterize the relationship between drought duration and occurrence frequency (page 8), but Figure 5a shows a highly linear correlation between k and b (R²=0.95). This does not imply that k itself contains all information, but rather indicates a strong linear relationship between the two. It is recommended to phrase more cautiously as “in practical applications, k can be used alone for regional comparisons.”
- Page12: In practical drought management, mild and frequent short-duration droughts have significantly different socioeconomic impacts compared to rare long-duration droughts. It is recommended to supplement the conclusions or discussion with the implications of these findings in this regard.
Text and Formatting Issues
- Page 2, line 35: “Generally, drought events occur on various time scales, including inter-decadal(Xu et al., 2017), inter-annua(e. g. Wang et al, 2018; Zhang et al, 2020)”
- → “inter-annua”should be “inter-annual”.
- Page 2, line 45: “As it can be seen, droughts occurring on different time scales...”
- → is recommended changeto be “Thus, droughts occurring on different time scales...”.
- Page 9, Figure 7: The title is written as “Distribution of parameter k (a) and the relationship... (a)” → The second "(a)" should be corrected to "(b)", and Figure 7b is described as Figure 7b in the main text but lacks a title. It is recommended to maintain consistency.
- Page13-14: Some references include DOI, while others do not. It is recommended to standardize the format or complete the DOI information for all references.
Citation: https://doi.org/10.5194/egusphere-2025-6401-RC3 -
AC3: 'Reply on RC3', Pengcheng Yan, 18 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-6401/egusphere-2025-6401-AC3-supplement.pdf
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RC4: 'Comment on egusphere-2025-6401', Anonymous Referee #3, 18 Apr 2026
The manuscript targets to find the observed relationship between the duration and occurrence frequency of droughts in China. Generally, the study is very focused on that region, it would be very helpful to put this in context with droughts in other regions of the world. As it is not a new finding that longer droughts occur more frequent and that it has regional differences depending on the climate of the region. These results are not new and I struggle a bit with finding what is new as it does not reveal any new features and is unclear how it can be used.
The authors base their study on a daily index that they briefly discuss the derivation and discusses the concept of flash droughts which seems like an impossibility to me. The main result of the study is the fitting of a double-logarithmic function for the combination of frequency and duration of the drought periods. As one of the motivations are these flash droughts, how can this research help with that?
Is the derived function well-constrained and in what range is it valid? In Figure 7b, the frequency curve seems to not approach zero rather flatten at a constant value, what does that do to the overall distribution?
The discussion section of the manuscript is extremely short and does not enlighten the reader on how more specifically this can be used, in what way, uncertainties, limitations, differences to other index used in other areas of the world etc.
Citation: https://doi.org/10.5194/egusphere-2025-6401-RC4 -
AC4: 'Reply on RC4', Pengcheng Yan, 19 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-6401/egusphere-2025-6401-AC4-supplement.pdf
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AC4: 'Reply on RC4', Pengcheng Yan, 19 Apr 2026
Peer review completion
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-6401', Anonymous Referee #1, 03 Apr 2026
Detailed comments could be found in the supplement.
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AC1: 'Reply on RC1', Pengcheng Yan, 06 Apr 2026
Thanks for the comments. Please see the attachment.
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RC2: 'Reply on AC1', Anonymous Referee #1, 07 Apr 2026
All issues I raised have been satisfactorily addressed. I recommend the paper for acceptance.Citation: https://doi.org/
10.5194/egusphere-2025-6401-RC2 -
AC2: 'Reply on RC2', Pengcheng Yan, 08 Apr 2026
Thank you so much for your valuable suggestions, which have greatly enhanced both the scientific rigor and readability of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-6401-AC2
-
AC2: 'Reply on RC2', Pengcheng Yan, 08 Apr 2026
-
RC2: 'Reply on AC1', Anonymous Referee #1, 07 Apr 2026
-
AC1: 'Reply on RC1', Pengcheng Yan, 06 Apr 2026
-
RC3: 'Comment on egusphere-2025-6401', Anonymous Referee #2, 13 Apr 2026
Based on the China daily-scale meteorological drought index, this manuscript revealed a double-logarithmic relationship between drought duration and occurrence frequency, and proposed that a single parameter can characterize this nonlinear feature. The findings provide quantitative evidence for water resource management, agricultural planning, and drought disaster prevention and mitigation. The following issues need to be corrected.
General comments
- Page3: The manuscript mentions “Qinghai-Tibet Plateau (gray area in Fig. 1) region isnot included in our study due to sparse station data”, and “the selected stations distribute in most regions of China except Hainan and Taiwan”. However, the impact of such exclusion on the representativeness of conclusions at the national scale was not discussed.
- Page4: Formula (2) uses log2 instead of natural logarithm or common logarithm. There is no justification for selecting base 2. It is recommended to briefly explain the rationale for this choice in the text or to uniformly use natural logarithm.
- Page12: The article states that parameter k/bcan independently characterize the relationship between drought duration and occurrence frequency (page 8), but Figure 5a shows a highly linear correlation between k and b (R²=0.95). This does not imply that k itself contains all information, but rather indicates a strong linear relationship between the two. It is recommended to phrase more cautiously as “in practical applications, k can be used alone for regional comparisons.”
- Page12: In practical drought management, mild and frequent short-duration droughts have significantly different socioeconomic impacts compared to rare long-duration droughts. It is recommended to supplement the conclusions or discussion with the implications of these findings in this regard.
Text and Formatting Issues
- Page 2, line 35: “Generally, drought events occur on various time scales, including inter-decadal(Xu et al., 2017), inter-annua(e. g. Wang et al, 2018; Zhang et al, 2020)”
- → “inter-annua”should be “inter-annual”.
- Page 2, line 45: “As it can be seen, droughts occurring on different time scales...”
- → is recommended changeto be “Thus, droughts occurring on different time scales...”.
- Page 9, Figure 7: The title is written as “Distribution of parameter k (a) and the relationship... (a)” → The second "(a)" should be corrected to "(b)", and Figure 7b is described as Figure 7b in the main text but lacks a title. It is recommended to maintain consistency.
- Page13-14: Some references include DOI, while others do not. It is recommended to standardize the format or complete the DOI information for all references.
Citation: https://doi.org/10.5194/egusphere-2025-6401-RC3 -
AC3: 'Reply on RC3', Pengcheng Yan, 18 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-6401/egusphere-2025-6401-AC3-supplement.pdf
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RC4: 'Comment on egusphere-2025-6401', Anonymous Referee #3, 18 Apr 2026
The manuscript targets to find the observed relationship between the duration and occurrence frequency of droughts in China. Generally, the study is very focused on that region, it would be very helpful to put this in context with droughts in other regions of the world. As it is not a new finding that longer droughts occur more frequent and that it has regional differences depending on the climate of the region. These results are not new and I struggle a bit with finding what is new as it does not reveal any new features and is unclear how it can be used.
The authors base their study on a daily index that they briefly discuss the derivation and discusses the concept of flash droughts which seems like an impossibility to me. The main result of the study is the fitting of a double-logarithmic function for the combination of frequency and duration of the drought periods. As one of the motivations are these flash droughts, how can this research help with that?
Is the derived function well-constrained and in what range is it valid? In Figure 7b, the frequency curve seems to not approach zero rather flatten at a constant value, what does that do to the overall distribution?
The discussion section of the manuscript is extremely short and does not enlighten the reader on how more specifically this can be used, in what way, uncertainties, limitations, differences to other index used in other areas of the world etc.
Citation: https://doi.org/10.5194/egusphere-2025-6401-RC4 -
AC4: 'Reply on RC4', Pengcheng Yan, 19 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-6401/egusphere-2025-6401-AC4-supplement.pdf
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AC4: 'Reply on RC4', Pengcheng Yan, 19 Apr 2026
Peer review completion
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Pengcheng Yan
Guolin Feng
Cailing Zhao
Ping Yang
Hao Wu
Dongdong Zuo
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2202 KB) - Metadata XML
Detailed comments could be found in the supplement.