Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework

Charity Mueni Mulwa; Herbert Imboga; Susan Mwelu

doi:doi:10.11648/j.ajmcm.20261101.11

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Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework

Charity Mueni Mulwa^*

, Herbert Imboga, Susan Mwelu

Published in American Journal of Mathematical and Computer Modelling (Volume 11, Issue 1)

Received: 26 October 2025 Accepted: 8 November 2025 Published: 15 January 2026

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Abstract

Compound drought-heatwave events pose serious threats to agriculture, ecosystems, and livelihoods in Kenya, where increasing climate variability amplifies their frequency and intensity. This study developed a hybrid Extreme Value Theory (EVT)-Copula-XGBoost framework to characterize and predict concurrent drought and heatwave extremes using ERA5 reanalysis data (2005-2024).The EVT component modeled the marginal tails of temperature and precipitation, revealing that temperature extremes follow a bounded Weibull-type tail, while rainfall deficits exhibit heavy tails, indicating a high potential for severe droughts. Copula modeling captured the dependence structure between drought and heatwave indices, showing weak but significant negative dependence (Kendall’s τ = −0.189 to 0.034), strongest during the short rains season (SON), implying that hot and dry conditions often co-occur. Joint risk analysis estimated return periods of 2.5-4.7 years, with five-year joint thresholds of 2.3-2.7 mm rainfall and 25.1-25.3◦C temperature, suggesting that compound drought-heatwave events recur roughly every three years. The XGBoost model achieved high predictive skill (AUC = 0.989), with EVT and Copula derived features contributing most to performance. This hybrid framework provides a robust, data driven foundation for early detection, risk mapping, and climate adaptation planning, supporting proactive management of compound climate extremes in Kenya.

Published in	American Journal of Mathematical and Computer Modelling (Volume 11, Issue 1)
DOI	10.11648/j.ajmcm.20261101.11
Page(s)	1-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Drought, Heatwave, Extreme Value Theory (EVT), Copula, XGBoost, Joint Risk Analysis, Kenya

References

[1]	Bevacqua, E., Lall, U., Maraun, D., Friederichs, P., & Lehner, F. (2019). Higher probability of compound flooding from precipitation and storm surge in Europe under anthropogenic climate change. Science Advances, 5(9), eaaw5531. https://doi.org/10.1126/sciadv.aaw5531
[2]	Bevacqua, E., Maraun, D., Hobæk Haff, I., Widmann, M., & Vrac, M. (2017). Multivariate statistical modelling of compound events via pair-copula constructions: Analysis of floods in Ravenna (Italy). Hydrology and Earth System Sciences, 21(5), 2701–2723. https://doi.org/10.5194/hess-21-2701-2017
[3]	Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794. https://doi.org/10.1145/2939672.2939785
[4]	Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. https://doi.org/10.1007/978-1-4471-3675-0
[5]	Embrechts, P., Kl¨uppelberg, C., & Mikosch, T. (1997). Modelling Extremal Events: For Insurance and Finance. Springer. https://doi.org/10.1007/978-3-642-33483-2
[6]	Food and Agriculture Organization of the United Nations.(2018). The Impact of Disasters and Crises on Agriculture and Food Security. FAO. https://www.fao.org/3/I8656EN/i8656en.pdf
[7]	Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44(2), 199–213. https://doi.org/10.1016/j.insmatheco.2007.07.002
[8]	Hao, Z., Singh, V. P., Xia, Y., & Sun, F. (2020). Impact of dependence changes on the likelihood of hot extremes under drought conditions in the United States. Journal of Hydrology, 581, 124410. https://doi.org/10.1016/j.jhydrol.2019.124410
[9]	Imboga, H. O., Orwa, G. O., & Otieno, R. O. (2017). Optimal nonparametric regression estimation of finite population total using Nadaraya-Watson incorporating jackknifing. International Journal of Theoretical and Applied Mathematics, 3(3), 102–110. https://doi.org/10.11648/j.ijtam.20170303.14
[10]	Intergovernmental Panel on Climate Change. (2021). Sixth Assessment Report. Intergovernmental Panel on Climate Change. https://www.ipcc.ch/assessment-report/ar6/
[11]	Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources, 25(8–12), 1287–1304. https://doi.org/10.1016/S0309-1708(02)00056-8
[12]	Kenya National Bureau of Statistics. (2020). Economic Survey 2020. Government Printer. https://www.knbs.or.ke/wp-content/uploads/2023/09/2020-Economic-Survey.pdf
[13]	Koh, J. (2023). Gradient boosting with extreme-value theory for wildfire prediction. Extremes, 26(2), 273–299. https://doi.org/10.1007/s10687-022-00454-6
[14]	Milly, P. C. D., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., & Stouffer, R. J. (2008). Stationarity is dead: Whither water management? Science, 319(5863), 573–574. https://doi.org/10.1126/science.1151915
[15]	National Drought Management Authority. (2019). Kenya Drought Early Warning Bulletin: April 2019. National Drought Management Authority. https://reliefweb.int/report/kenya/national-drought-early-warning-bulletin-april-2019
[16]	Nelsen, R. B. (2006). An Introduction to Copulas. Springer. https://doi.org/10.1007/0-387-28678-0
[17]	Song, M., Zhang, J., Liu, Y., Liu, C., Bao, Z., Jin, J., He, R., Bian, G., & Wang, G. (2024). Time-varying copula-based compound flood risk assessment of extreme rainfall and high water level under a non-stationary environment. Journal of Flood Risk Management, 17(2), e13032. https://doi.org/10.1111/jfr3.13032
[18]	United Nations Environment Programme. (2021). Kenya Country Profile: Climate Change Overview. United Nations Environment Programme. https://dicf.unepgrid.ch/kenya/climate-change
[19]	United Nations Office for the Coordination of Humanitarian Affairs. (2017). Horn of Africa: Humanitarian Impacts of Drought – Issue 2 (13 April 2017). ReliefWeb. https://reliefweb.int/report/somalia/horn-africa-humanitarian-impacts-drought-issue-2-13-april-2017
[20]	World Meteorological Organization. (2022). State of the Climate in Africa 2022. World Meteorological Organization. https://wmo.int/publication-series/state-of-climate-africa
[21]	Zscheischler, J., & Seneviratne, S. I. (2018). Dependence of drivers affects risks associated with compound events. Science Advances, 3(6), e1700263. https://doi.org/10.1126/sciadv.1700263
[22]	Jiang, T., Su, X., Zhang, G., Zhang, T., & Wu, H. (2023). Estimating propagation probability from meteorological to ecological droughts using a hybrid machine learning-copula method. Hydrology and Earth System Sciences, 27(2), 559–577. https://doi.org/10.5194/hess-27-559-2023
[23]	Liu, R., Yin, J., Slater, L., Kang, S., Yang, Y., Liu, P., Guo, J., Gu, X., Zhang, X., & Volchak, A. (2024). Machine-learning-constrained projection of bivariate hydrological drought magnitudes and socioeconomic risks over China. Hydrology and Earth System Sciences, 28, 3305–3326. https://doi.org/10.5194/hess-28-3305-2024
[24]	Alencar, P. H. L., & Paton, E. N. (2024). Which droughts are becoming more frequent? A copula-entropy analysis on the return period of droughts in Europe. Natural Hazards, 121, 543–565. https://doi.org/10.1007/s11069-024-06848-y
[25]	M., et al. (2024). Forecasting of meteorological drought using ensemble and machine learning models. Environmental Sciences Europe, 36, 160. https://doi.org/10.1186/s12302-024-00975-w

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APA Style

Mulwa, C. M., Imboga, H., Mwelu, S. (2026). Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. American Journal of Mathematical and Computer Modelling, 11(1), 1-12. https://doi.org/10.11648/j.ajmcm.20261101.11

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ACS Style

Mulwa, C. M.; Imboga, H.; Mwelu, S. Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. Am. J. Math. Comput. Model. 2026, 11(1), 1-12. doi: 10.11648/j.ajmcm.20261101.11

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AMA Style

Mulwa CM, Imboga H, Mwelu S. Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. Am J Math Comput Model. 2026;11(1):1-12. doi: 10.11648/j.ajmcm.20261101.11

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@article{10.11648/j.ajmcm.20261101.11,
  author = {Charity Mueni Mulwa and Herbert Imboga and Susan Mwelu},
  title = {Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework
},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {11},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.ajmcm.20261101.11},
  url = {https://doi.org/10.11648/j.ajmcm.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261101.11},
  abstract = {Compound drought-heatwave events pose serious threats to agriculture, ecosystems, and livelihoods in Kenya, where increasing climate variability amplifies their frequency and intensity. This study developed a hybrid Extreme Value Theory (EVT)-Copula-XGBoost framework to characterize and predict concurrent drought and heatwave extremes using ERA5 reanalysis data (2005-2024).The EVT component modeled the marginal tails of temperature and precipitation, revealing that temperature extremes follow a bounded Weibull-type tail, while rainfall deficits exhibit heavy tails, indicating a high potential for severe droughts. Copula modeling captured the dependence structure between drought and heatwave indices, showing weak but significant negative dependence (Kendall’s τ = −0.189 to 0.034), strongest during the short rains season (SON), implying that hot and dry conditions often co-occur. Joint risk analysis estimated return periods of 2.5-4.7 years, with five-year joint thresholds of 2.3-2.7 mm rainfall and 25.1-25.3◦C temperature, suggesting that compound drought-heatwave events recur roughly every three years. The XGBoost model achieved high predictive skill (AUC = 0.989), with EVT and Copula derived features contributing most to performance. This hybrid framework provides a robust, data driven foundation for early detection, risk mapping, and climate adaptation planning, supporting proactive management of compound climate extremes in Kenya.
},
 year = {2026}
}

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TY  - JOUR
T1  - Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework

AU  - Charity Mueni Mulwa
AU  - Herbert Imboga
AU  - Susan Mwelu
Y1  - 2026/01/15
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmcm.20261101.11
DO  - 10.11648/j.ajmcm.20261101.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20261101.11
AB  - Compound drought-heatwave events pose serious threats to agriculture, ecosystems, and livelihoods in Kenya, where increasing climate variability amplifies their frequency and intensity. This study developed a hybrid Extreme Value Theory (EVT)-Copula-XGBoost framework to characterize and predict concurrent drought and heatwave extremes using ERA5 reanalysis data (2005-2024).The EVT component modeled the marginal tails of temperature and precipitation, revealing that temperature extremes follow a bounded Weibull-type tail, while rainfall deficits exhibit heavy tails, indicating a high potential for severe droughts. Copula modeling captured the dependence structure between drought and heatwave indices, showing weak but significant negative dependence (Kendall’s τ = −0.189 to 0.034), strongest during the short rains season (SON), implying that hot and dry conditions often co-occur. Joint risk analysis estimated return periods of 2.5-4.7 years, with five-year joint thresholds of 2.3-2.7 mm rainfall and 25.1-25.3◦C temperature, suggesting that compound drought-heatwave events recur roughly every three years. The XGBoost model achieved high predictive skill (AUC = 0.989), with EVT and Copula derived features contributing most to performance. This hybrid framework provides a robust, data driven foundation for early detection, risk mapping, and climate adaptation planning, supporting proactive management of compound climate extremes in Kenya.

VL  - 11
IS  - 1
ER  -

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Author Information

Charity Mueni Mulwa

Department of Statistics and Acturial Sciences, Jomo Kenyatta University of Agriculture and Technoogy (JKUAT), Nairobi , Kenya

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http://orcid.org/0009-0008-9238-2996
Herbert Imboga

Department of Statistics and Acturial Sciences, Jomo Kenyatta University of Agriculture and Technoogy (JKUAT), Nairobi , Kenya

Contact Email
Susan Mwelu

Department of Statistics and Acturial Sciences, Jomo Kenyatta University of Agriculture and Technoogy (JKUAT), Nairobi , Kenya

Contact Email

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APA Style

Mulwa, C. M., Imboga, H., Mwelu, S. (2026). Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. American Journal of Mathematical and Computer Modelling, 11(1), 1-12. https://doi.org/10.11648/j.ajmcm.20261101.11

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ACS Style

Mulwa, C. M.; Imboga, H.; Mwelu, S. Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. Am. J. Math. Comput. Model. 2026, 11(1), 1-12. doi: 10.11648/j.ajmcm.20261101.11

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AMA Style

Mulwa CM, Imboga H, Mwelu S. Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework. Am J Math Comput Model. 2026;11(1):1-12. doi: 10.11648/j.ajmcm.20261101.11

Copy | Download

@article{10.11648/j.ajmcm.20261101.11,
  author = {Charity Mueni Mulwa and Herbert Imboga and Susan Mwelu},
  title = {Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework
},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {11},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.ajmcm.20261101.11},
  url = {https://doi.org/10.11648/j.ajmcm.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261101.11},
  abstract = {Compound drought-heatwave events pose serious threats to agriculture, ecosystems, and livelihoods in Kenya, where increasing climate variability amplifies their frequency and intensity. This study developed a hybrid Extreme Value Theory (EVT)-Copula-XGBoost framework to characterize and predict concurrent drought and heatwave extremes using ERA5 reanalysis data (2005-2024).The EVT component modeled the marginal tails of temperature and precipitation, revealing that temperature extremes follow a bounded Weibull-type tail, while rainfall deficits exhibit heavy tails, indicating a high potential for severe droughts. Copula modeling captured the dependence structure between drought and heatwave indices, showing weak but significant negative dependence (Kendall’s τ = −0.189 to 0.034), strongest during the short rains season (SON), implying that hot and dry conditions often co-occur. Joint risk analysis estimated return periods of 2.5-4.7 years, with five-year joint thresholds of 2.3-2.7 mm rainfall and 25.1-25.3◦C temperature, suggesting that compound drought-heatwave events recur roughly every three years. The XGBoost model achieved high predictive skill (AUC = 0.989), with EVT and Copula derived features contributing most to performance. This hybrid framework provides a robust, data driven foundation for early detection, risk mapping, and climate adaptation planning, supporting proactive management of compound climate extremes in Kenya.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Modelling the Dependence Between Drought and Heatwave Extremes in Kenya Using an Integrated EVT-Copula-XGBoost Framework

AU  - Charity Mueni Mulwa
AU  - Herbert Imboga
AU  - Susan Mwelu
Y1  - 2026/01/15
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmcm.20261101.11
DO  - 10.11648/j.ajmcm.20261101.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20261101.11
AB  - Compound drought-heatwave events pose serious threats to agriculture, ecosystems, and livelihoods in Kenya, where increasing climate variability amplifies their frequency and intensity. This study developed a hybrid Extreme Value Theory (EVT)-Copula-XGBoost framework to characterize and predict concurrent drought and heatwave extremes using ERA5 reanalysis data (2005-2024).The EVT component modeled the marginal tails of temperature and precipitation, revealing that temperature extremes follow a bounded Weibull-type tail, while rainfall deficits exhibit heavy tails, indicating a high potential for severe droughts. Copula modeling captured the dependence structure between drought and heatwave indices, showing weak but significant negative dependence (Kendall’s τ = −0.189 to 0.034), strongest during the short rains season (SON), implying that hot and dry conditions often co-occur. Joint risk analysis estimated return periods of 2.5-4.7 years, with five-year joint thresholds of 2.3-2.7 mm rainfall and 25.1-25.3◦C temperature, suggesting that compound drought-heatwave events recur roughly every three years. The XGBoost model achieved high predictive skill (AUC = 0.989), with EVT and Copula derived features contributing most to performance. This hybrid framework provides a robust, data driven foundation for early detection, risk mapping, and climate adaptation planning, supporting proactive management of compound climate extremes in Kenya.

VL  - 11
IS  - 1
ER  -

Copy | Download