All Issue

2026 Vol.59, Issue 6 Preview Page
Conditional probability and return period of extreme summer heatwave events under preceding drought events

선행 가뭄 영향에 의한 여름철 극한 고온의 조건부 확률 및 재현기간 분석

Jeongwon Leea
,
Chaelim Leeb
,
Sangdan Kimc*
이 정원a
,
이 채림b
,
김 상단c*
aMaster Course Student, Division of Earth Environmental System Science (Major of Environmental Engineering), Pukyong National University, Busan, Korea
bPh.D. Student, Division of Earth Environmental System Science (Major of Environmental Engineering), Pukyong National University, Busan, Korea
cProfessor, Division of Earth Environmental System Science (Major of Environmental Engineering), Pukyong National University, Busan, Korea
a국립부경대학교 지구환경시스템과학부 환경공학전공 석사과정
b국립부경대학교 지구환경시스템과학부 환경공학전공 박사과정
c국립부경대학교 지구환경시스템과학부 환경공학전공 교수
*Corresponding Author
30 June 2026. pp. 533-544
PDF XML Citation
Abstract

The study quantitatively assessed the influence of preceding drought conditions on the occurrence risk of extreme summer heat at five representative ASOS observation sites in Korea using a copula-based joint distribution framework. Drought conditions were characterized using standardized precipitation indices (SPI) at multiple time scales, and the optimal SPI time scale for each site was identified based on Spearman’s rank correlation with daily maximum temperature (Tmax). Marginal distributions for SPI and Tmax were modeled independently, after which Clayton, Frank, and Gumbel copulas were evaluated to determine the most appropriate dependence structure at each site. The results consistently revealed a negative monotonic relationship between preceding SPI and Tmax across all sites. Under dry and extremely dry conditions (SPI < -0.5 and SPI < -1.3), the probability of exceeding extreme Tmax thresholds increased markedly relative to estimates derived from univariate distributions. In contrast, wet and extremely wet conditions (SPI > 0.5 and SPI > 1.3) were associated with a systematic reduction in extreme heat probabilities, indicating an asymmetric response to antecedent moisture conditions. Copula-based conditional return period analysis further demonstrated that extreme heat events of the same magnitude occurred at substantially shorter intervals under drought conditions than suggested by univariate frequency analysis, with risk amplification intensifying for more severe extremes. By moving beyond simple correlation or univariate approaches, this study provides a quantitative framework for assessing compound drought–heat risks using conditional probability and return period metrics, offering practical insights for early warning and climate risk management.

Keywords
Drought impact
Standard precipitation index
Daily maximum temperature
Copula joint distribution
Conditional exceedance probability
Conditional return period

본 연구는 한국의 대표적인 5개 ASOS 관측 지점을 대상으로 선행 가뭄 조건이 여름철 극한 고온 발생 위험에 미치는 영향을 Copula 기반 결합분포를 이용하여 정량적으로 평가하였다. 가뭄지수로는 다양한 time-scale의 SPI를 적용하고, 스피어만 상관계수 분석을 통해 지점별로 극한 고온(Tmax)과 가장 강한 연계를 보이는 최적 SPI time-scale을 선정하였다. 이후 SPI와 Tmax의 한계분포를 각각 모형화한 뒤, Clayton, Frank, Gumbel Copula를 비교하여 지점별 최적 결합구조를 도출하였다. 분석 결과, 모든 지점에서 1개월 선행 SPI와 Tmax 사이에는 음의 단조 관계가 확인되었으며, 건조 및 극심한 건조 조건(SPI < -0.5, SPI < -1.3) 하에서 Tmax의 극값 초과확률은 한계분포 기반 확률보다 유의하게 증가하였다. 반면, 습윤 및 극심한 습윤 조건(SPI > 0.5, SPI > 1.3)에서는 극한 고온 발생 확률이 일관되게 감소하는 비대칭적 반응이 나타났다. 특히 Copula 기반 조건부 재현기간 분석 결과, 선행 가뭄 조건에서는 동일한 수준의 극한 고온이 단변량 분석에서 추정된 재현기간보다 훨씬 짧은 주기로 발생함이 확인되었으며, 이러한 위험 증폭 효과는 극값 영역으로 갈수록 더욱 뚜렷해졌다. 본 연구는 단순 상관 분석이나 단변량 접근을 넘어, 조건부 확률과 재현기간 지표를 활용하여 복합 가뭄–고온 위험을 정량적으로 평가할 수 있는 분석 틀을 제시한다는 점에서 의의를 가진다.

키워드
가뭄 영향
표준 강수 지수
일 최고기온
Copula 결합분포
조건부 초과확률
조건부 재현기간
References
1

AghaKouchak, A., Cheng, L., Mazdiyasni, O., and Farahmand, A. (2014). “Global warming and changes in risk of concurrent climate extremes: Insights from the 2014 California drought”, Geophysical Research Letters, AGU, Vol. 41, No. 24, pp. 8847-8852.

10.1002/2014GL062308
2

Alizadeh, M.R., Adamowski, J., Nikoo, M.R., AghaKouchak, A., Dennison, P., and Sadegh, M. (2020). “A century of observations reveals increasing likelihood of continental-scale compound dry-hot extremes.” Science Advances, AAAS, Vol. 6, No. 39, eaaz4571.

10.1126/sciadv.aaz457132967839PMC7531886
3

Baillien, J., Gijbels, I., and Verhasselt, A. (2025). “Estimation in copula models with two-piece skewed margins using the inference for margins method.” Econometrics and Statistics, Elsevier, Vol. 34, pp. 91-108.

10.1016/j.ecosta.2022.05.002
4

Dong, C., Yan, Y., Guo, J., Lin, K., Chen, X., Okin, G.S., Gillespie, T.W., Dialesandro, J., and MacDonald, G.M. (2023). “Drought vulnerable vegetation increases exposure of disadvantaged populations to heatwaves under global warming: A case study from Los Angeles.” Sustainable Cities and Society, Elsevier, Vol. 93, 104488.

10.1016/j.scs.2023.104488
5

Genest, C., and Favre, A.-C. (2007). “Everything you always wanted to know about copula modeling but were afraid to ask.” Journal of Hydrologic Engineering, ASCE, Vol. 12, No. 4, pp. 347-368.

10.1061/(ASCE)1084-0699(2007)12:4(347)
6

Hamed, R., Van Loon, A.F., Aerts, J., and Coumou, D. (2021). “Impacts of compound hot–dry extremes on US soybean yields.” Earth System Dynamics, Copernicus Publications, Vol. 12, No. 4, pp. 1371-1391.

10.5194/esd-12-1371-2021
7

Hao, Z., Hao, F., Singh, V.P., Xia, Y., Shi, C., and Zhang, X. (2018). “A multivariate approach for statistical assessments of compound extremes.” Journal of Hydrology, Elsevier, Vol. 565, pp. 87-94.

10.1016/j.jhydrol.2018.08.025
8

Hao, Z., Hao, F., Singh, V.P., and Ouyang, W. (2017). “Quantitative risk assessment of the effects of drought on extreme temperature in eastern China.” Journal of Geophysical Research: Atmospheres, AGU, Vol. 122, No. 17, pp. 9050-9059.

10.1002/2017JD027030
9

Ji, S., Yang, S., Al-Sakkaf, A.S., Seka, A.M., and Zhang, J. (2025). “Intensified compound drought and heat events in typical aridsemiarid transition region over the last four decades based on a daily-scale index.” Science of the Total Environment, Elsevier, Vol. 1001, 180541.

10.1016/j.scitotenv.2025.180541
10

Joe, H. (2005). “Asymptotic efficiency of the two-stage estimation method for copula-based models.” Journal of Multivariate Analysis, Vol. 94, No. 2, pp. 401-419.

10.1016/j.jmva.2004.06.003
11

Kim, Y.-J., Yeh, S.-W., Choi, Y.-S., Son, S.-W., Oh, S.-G., Yang, Y.-M., and Kim, J. (2025). “The need for climate risk assessment in response to the increasing occurrence of compound drought–heatwave events in Republic of Korea.” Atmosphere-Korea, Korean Meteorological Society, Vol. 35, No. 1, pp. 13-27.

12

Ko, V., and Hjort, N.L. (2019). “Copula information criterion for model selection with two-stage maximum likelihood estimation.” Econometrics and Statistics, Elsevier, Vol. 12, pp. 167-180.

10.1016/j.ecosta.2019.01.001
13

Kwon, M., Sung, J.H., Kim, T.-W., and Ahn, J. (2018). “Drought assessment by bivariate frequency analysis using standardized precipitation index and precipitation deficit: Focused on Han river basin.” Journal of Korea Water Resources Association, KWRA, Vol. 51, No. 10, pp. 875-886.

14

Liu, D., Wang, G., Mei, R., Yu, Z., Yu, M. (2014). “Impact of initial soil moisture anomalies on climate mean and extremes over Asia.” Journal of Geophysical Research: Atmospheres, AGU, Vol. 119, No. 2, pp. 529-545.

10.1002/2013JD020890
15

Malik, I., and Mishra, V. (2025). “On the utility of soil moisture for monitoring and prediction of compound hot and dry extremes in India.” Water Resources Research, AGU, Vol. 61, No. 10, e2025WR040174.

10.1029/2025WR040174
16

Mukherjee, S., and Mishra, A.K. (2021). “Increase in compound drought and heatwaves in a warming world.” Geophysical Research Letters, AGU, Vol. 48, No. 1, Article e2020GL090617.

10.1029/2020GL090617
17

Röthlisberger, M., and Papritz, L. (2023). “Quantifying the physical processes leading to atmospheric hot extremes at a global scale.” Nature Geoscience, Springer Nature, Vol. 16, No. 3, pp. 210-216.

10.1038/s41561-023-01126-136920151PMC10005943
18

Sung, K., and Jung, H. (2025). “Spatio-temporal analysis of compound drought–heatwave events in Korea reveals summer intensification trends.” Journal of Korea Water Resources Association, KWRA, Vol. 58, No. 9, pp. 771-779.

19

Sutanto, S.J., Vitolo, C., Di Napoli, C., D’Andrea, M., and Van Lanen, H.A.J. (2020). “Heatwaves, droughts, and fires: Exploring compound and cascading dry hazards at the pan-European scale.” Environment International, Elsevier, Vol. 134, 105276.

10.1016/j.envint.2019.105276
20

Tian, Y., Giaquinto, D., Di Capua, G., Claassen, J.N., Ali, J., Li, H., and De Michele, C. (2024). “Historical changes in the causal effect networks of compound hot and dry extremes in central Europe.” Communications Earth & Environment, Springer Nature, Vol. 5, No. 1, 764.

10.1038/s43247-024-01934-2
21

Turco, M., von Hardenberg, J., AghaKouchak, A., Llasat, M.C., Provenzale, A., and Trigo, R.M. (2017). “On the key role of droughts in the dynamics of summer fires in Mediterranean Europe.” Scientific Reports, Springer Nature, Vol. 7, No. 1, 81.

10.1038/s41598-017-00116-928250442PMC5427854
22

Xu, P., Zhang, Z., Wang, D., Singh, V.P., Zhang, C., Fu, X., and Wang, L. (2023). “A time-varying Copula-based approach to quantify the effects of antecedent drought on hot extremes.” Journal of Hydrology, Elsevier, Vol. 627, No. Part B, 130418.

10.1016/j.jhydrol.2023.130418
23

Yu, J.S., Yoo, J.Y., Lee, J.-H., and Kim, T.-W. (2016). “Estimation of drought risk through the bivariate drought frequency analysis using copula functions.” Journal of Korea Water Resources Association, KWRA, Vol. 49, No. 3, pp. 217-225.

10.3741/JKWRA.2016.49.3.217
24

Yu, R., and Zhai, P. (2020). “More frequent and widespread persistent compound drought and heat event observed in China.” Scientific Reports, Springer Nature, Vol. 10, No. 1, 14576.

10.1038/s41598-020-71312-332884003PMC7471689
25

Zscheischler, J., and Fischer, E.M. (2020). “The record-breaking compound hot and dry 2018 growing season in Germany.” Weather and Climate Extremes, Elsevier, Vol. 29, 100270.

10.1016/j.wace.2020.100270
Information
  • Publisher :KOREA WATER RESOURECES ASSOCIATION
  • Publisher(Ko) :한국수자원학회
  • Journal Title :Journal of Korea Water Resources Association
  • Journal Title(Ko) :한국수자원학회 논문집
  • Volume : 59
  • No :6
  • Pages :533-544
  • Received Date : 2026-01-19
  • Revised Date : 2026-04-06
  • Accepted Date : 2026-04-07
  • DOI :https://doi.org/10.3741/JKWRA.2026.59.6.533
Journal Informaiton Journal of Korea Water Resources Association Journal of Korea Water Resources Association
Online Submission
Archives
  • scopus
  • KCI-수자원
  • NRF
  • KOFST
  • KISTI Current Status
  • KISTI Cited-by
  • crosscheck
  • orcid
  • open access
  • ccl
Journal Informaiton Journal Informaiton - close