Statistics of Heat Waves




Statistical Methods



This web page serves as a resource on the Statistics of Heat Waves. The purpose of the page is to promote the use of appropriate statistical methods, including those based on the statistical theory of extreme values, for modeling hot spells and heat waves.

Statistical issues. Heat waves are a complex form of extreme climate event with substantial health impacts. Yet extreme value theory has rarely been applied. Challenges include how to model the temporal clustering of temperatures at high levels and whether multivariate extreme value theory can be used to model climate variables that can contribute to heat waves (e.g., maximum and minimum temperature, dew point or humidity, wind speed, cloud cover). Applications of such methods would include comparing the statistical characteristics of observed heat waves (e.g., frequency, duration, intensity) with those simulated by numerical models of the climate system, as well as detecting trends in observed heat wave statistics. Statistical modeling of the relationship between mortality and heat waves also poses challenges, especially concerning estimating the effects of changes in heat wave characteristics.

This web page was formed as one outcome of Exteme Events in Weather and Climate -- An Interdisciplinary Workshop, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 22-27 August 2010.


Extreme Heat, U.S. Department of Homeland Security, Federal Emergency Management Agency
Health Impacts of Climate Change -- What the Research Says, Health Impacts Working Group, ASA Advisory Committee on Climate Change Policy
Heat Safety Resources, U.S. National Weather Service
Heat Wave, PreventionWeb, UN Office for Disaster Risk Reduction
Heat Wave Plan for England, Public Health England
SCORCHER, Australian Heat Waves, ARC Centre of Excellence for Climate System Science

Statistical Methods

Under Development


Definitions | Mortality and Morbidity | Observed Climate Change

Predicted Climate Change | Reviews | Statistical Methods


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Mortality and Morbidity

Anderson, B.G., and M.L. Bell, 2009: "Weather-related mortality: How heat, cold, and heat waves affect mortality in the United States." Epidemiology, 20, 205-213.
Curriero, F.C., K.S. Heiner, J.M. Samet, S.L. Zeger, S.L. Strug, and J.A. Patz, 2002: "Temperature and mortality in 11 cities of the eastern United States." American Journal of Epidemiology, 155, 80-87.
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Harlan, S.L. et al., 2014: "Heat-related deaths in hot cities: Estimates of human tolerance to high temperature thresholds." International Journal of Environmental Research and Public Health, 11, 3304-3326.
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Li, B. et al., 2012: "The impact of extreme heat on morbidity in Milwaukee, Wisconsin." Climatic Change, 110, 959-976.
Sheridan, S.C., A.J. Kalkstein, and L.S. Kalkstein, 2009: "Trends in heat-related mortality in the United States, 1975-2004." Natural Hazards, 50, 145-160.

Observed Climate Change

Charpentier, A., 2011: "On the return period of the 2003 heat wave." Climatic Change, 109, 245-260.
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Katsoulis, B.D., and N. Hatzianastassiou, 2005: "Analysis of hot spell characteristics in the Greek region." Climate Research, 28, 229-241.
Khaliq, M.N., T.B.M.J. Ouarda, A. St-Hilaire, and P. Gachon, 2007: "Bayesian change-point analysis of heat spell occurrences in Montreal, Canada." International Journal of Climatology, 27, 805-818.
Khaliq, M.N., A. St-Hilaire, T.B.M.J. Ouarda, and B. Bobee, 2005: "Frequency analysis and temporal pattern of occurrences of southern Quebec heatwaves." International Journal of Climatology, 25, 485-504.
Kuglitsch, F.G. et al., 2010: "Heat wave changes in the eastern Mediterranean since 1960." Geophysical Research Letters, 37, L04802, doi:10.1029/2009GL041841.
Wang, W. et al., 2015: "Extreme rainfall and summer heat waves in Macau based on statistical theory of extreme values." Climate Research, 66, 91-101.

Predicted Climate Change

Clark, R.T., J.M. Murphy, and S.J. Brown, 2010: "Do global warming targets limit heatwave risk?" Geophysical Research Letters, 37, L17703.
Hunt, B.G., 2007: "A climatology of heat waves from a multimillennial simulation." Journal of Climate, 20, 3802-3821.
Koffi, B., and E. Koffi, 2008: "Heat waves across Europe by the end of the 21st century: multiregional climate simulations." Climate Research, 36, 153-168.
Meehl, G.A., and C. Tebaldi, 2004: "More intense, more frequent, and longer lasting heat waves in the 21st century." Science, 305, 994-997.
Russo, S. et al., 2014: "Magnitude of extreme heat waves in present climate and their projection in a warming world." Journal of Geophysical Research: Atmospheres, 119, 12,500-12,512.
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Tebaldi, C., K. Hayhoe, J.M. Arblaster, and G.A. Meehl, 2006: "Going to the extremes: an intercomparison of model-simulated historical and future changes in extreme events." Climatic Change, 79, 185-211.
Wang, W., W. Zhou, Y. Li, X. Wang, and D. Wang, 2015: "Statistical modeling and CMIP5 simulations of hot spell changes in China." Climate Dynamics, 44, 2859-2872.


Grotjahn, R. et al., 2016: "North American extreme temperature events and related large scale meteorological patterns: A review of statistical methods, dynamics, modeling, and trends." Climate Dynamics, 46, 1151-1184.
Peterson, T.C. et al., 2013: "Monitoring and understanding changes in heat waves, cold waves, floods and droughts in the United States: State of knowledge." Bulletin of the American Meteorological Society, 94, 821-834.

Statistical Methods

Abaurrea, J., J. Asin, A.C. Cebrian, and A. Centelles, 2007: "Modeling and forecasting extreme hot events in the central Ebro valley, a continental-Mediterranean area." Global and Planetary Change, 57, 43-58.
Coles, S.G., J.A. Tawn, and R.L. Smith, 1994: "A seasonal Markov model for extremely low temperatures." Environmetrics, 5, 221-239.
Dupuis, D.J., 2012: "Modeling waves of extreme temperature: The changing tails of four cities." Journal of the American Statistical Association, 107, 24-39.
Furrer, E.M., R.W. Katz, M.D. Walter, and R. Furrer, 2010: "Statistical modeling of hot spells and heat waves." Climate Research, 43, 191-205.
Keellings, D., and P. Waylen, 2015: "Investigating teleconnection drivers of bivariate heat waves in Florida using extreme value analysis." Climate Dynamics, 44, 3383-3391.
Kysely, J., 2002: "Probability estimates of extreme temperature events: Stochastic modelling approach vs. extreme value distributions." Studia Geophysica et Geodaetica, 46, 93-112.
Photiadou, C., M.R. Jones, D. Keellings, and C.F. Dewes, 2014: "Modeling European hot spells using extreme value analysis." Climate Research, 58, 193-207.
Reich, B.J., B.A. Shaby, and D. Cooley, 2013: "A hierarchical model for serially-dependent extremes: A study of heat waves in the western US." Journal of Agricultural, Biological, and Environmental Statistics, 19, 119-135.
Shaby, B.A., B.J. Reich, D. Cooley, and C.G. Kaufman, 2016: "A Markov-switching model for heat waves." Annals of Applied Statistics, 10, 74-93.

Maintained by Richard Katz (email: