Hierarchical Bayesian Extreme Value Modeling of Heatwave Intensities: Application to ERA5-Land in a Semi-Arid Region

Section: Articles

Abstract

     In arid and semi-arid areas, especially in Iraq, extreme heat has become one of the most significant impacts of climate change, as the long duration of summer heat is becoming a serious threat to human health, water supply and infrastructure. This paper explores the issue of summer extreme temperatures in Iraq based on ERA5-Land daily maximum temperature data of 1980-2024. Descriptive heatwave indicators were then computed after which annual summer maxima were modeled in a Bayesian non-stationary generalized extreme value (GEV) framework in three climatic regions: North, Central, and South Iraq. A linear time effect in the location parameter was used to introduce non-stationarity, whilst the scale and shape parameters were fixed to maintain inferential stability because of the small number of annual maxima to use in each region. The results reveal a clear north–south gradient in baseline extreme heat intensity and a statistically credible warming trend of approximately  per decade. Return-level analysis further indicates that 20-year and 50-year extreme temperature levels increased by about  between the early period (1980–1999) and the recent period (2000–2024), with the most severe extremes concentrated in southern Iraq. These findings provide probabilistic evidence that extreme heat risk in Iraq is intensifying under a non-stationary climate and demonstrate the value of Bayesian non-stationary extreme-value modeling for regional climate-risk assessment.

References

  1. Al-Sudani, Z. A.: Long-term trends of temperature extremes in Iraq during 1982–2020. Iraqi Journal of Science 61(11), 2835–2850 (2020).
  2. Calvin, K. et al.: IPCC, 2023: Climate Change 2023: Synthesis Report. Contribution of Working Groups I II and III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, H. Lee and J. Romero (eds.)]. IPCC, Geneva, Switzerland (2023).
  3. Coles, S.: An introduction to statistical modeling of extreme values. Springer, London (2001).
  4. Cooley, D., Nychka, D., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. Journal of the American Statistical Association 102(479), 824–840 (2007).
  5. Cornes, R. C., Van Der Schrier, G., Van Den Besselaar, E. J., Jones, P. D.: An ensemble version of the E‐OBS temperature and precipitation data sets. Journal of Geophysical Research: Atmospheres 123(17), 9391–9409 (2018).
  6. Croce, P., Formichi, P., Landi, F.: A Bayesian hierarchical model for climatic loads under climate change. In UNCECOMP 2019: 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering: proceedings (pp. 299–308). National Technical University of Athens (NTUA) (2019).
  7. Dyrrdal, A. V., Lenkoski, A., Thorarinsdottir, T. L., Stordal, F.: Bayesian hierarchical modeling of extreme hourly precipitation in Norway. Environmetrics 26(2), 89–106 (2015).
  8. Gelman, A., Shalizi, C. R.: Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology 66(1), 8–38 (2013).
  9. Haylock, M. R., Hofstra, N., Klein Tank, A. M. G., Klok, E. J., Jones, P. D., New, M.: A European daily high‐resolution gridded data set of surface temperature and precipitation for 1950–2006. Journal of Geophysical Research: Atmospheres 113(D20) (2008).
  10. Huser, R., Wadsworth, J. L.: Advances in statistical modeling of spatial extremes. Computational Statistics 14(1), e1537, Wiley Interdisciplinary Reviews (2022).
  11. International Energy Agency: National climate resilience assessment for Iraq. IEA, Paris (2025).
  12. Katz, R. W.: Statistics of extremes in climate change. Climatic change 100(1), 71–76 (2010).
  13. Lin, J.: An integrated procedure for Bayesian reliability inference using MCMC. Journal of Quality and Reliability Engineering 2014(1), 264920 (2014).
  14. Martins, E. S., Stedinger, J. R.: Generalized maximum‐likelihood generalized extreme‐value quantile estimators for hydrologic data. Water Resources Research 36(3), 737–744 (2000).
  15. McElreath, R.: Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and Hall/CRC (2018).
  16. Milly, P. C., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., Stouffer, R. J.: Stationarity is dead: Whither water management? Science 319(5863), 573–574 (2008).
  17. Muñoz-Sabater, J. et al.: ERA5-Land: A state-of-the-art global reanalysis dataset for land applications. Earth system science data 13(9), 4349–4383 (2021).
  18. Salman, S. A., Shahid, S., Ismail, T., Chung, E. S., Al-Abadi, A. M.: Long-term trends in daily temperature extremes in Iraq. Atmospheric research 198, 97–107 (2017).
  19. Sampaio, J., Costa, V.: Bayesian regional flood frequency analysis with GEV hierarchical models under spatial dependency structures. Hydrological Sciences Journal 66(3), 422–433 (2021).
  20. Stan Development Team: RStan: the R interface to Stan (R package version 2.32.6) (2024).
  21. Perkins, S. E., Alexander, L. V.: On the measurement of heat waves. Journal of climate 26(13), 4500–4517 (2013).
  22. Zittis, G. et al.: Business-as-usual will lead to super and ultra-extreme heatwaves in the Middle East and North Africa. Npj Climate and Atmospheric Science 4(1), 20 (2021).
  23. Vehtari, A., Gelman, A., Gabry, J.: Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and computing 27(5), 1413–1432 (2017).
Download this PDF file

Statistics

How to Cite

Hierarchical Bayesian Extreme Value Modeling of Heatwave Intensities: Application to ERA5-Land in a Semi-Arid Region. (2026). AL-Rafidain Journal of Computer Sciences and Mathematics, 20(1), 75-85. https://doi.org/10.33899/rjcsm.v20i1.60668
Copyright and Licensing

How to Cite

Hierarchical Bayesian Extreme Value Modeling of Heatwave Intensities: Application to ERA5-Land in a Semi-Arid Region. (2026). AL-Rafidain Journal of Computer Sciences and Mathematics, 20(1), 75-85. https://doi.org/10.33899/rjcsm.v20i1.60668