Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Blender, R.; Raible, Christoph; Lunkeit, F. (2015). Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes. Quarterly Journal of the Royal Meteorological Society, 141(686), pp. 249-257. Royal Meteorological Society 10.1002/qj.2354

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Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Item Type:

Journal Article (Original Article)


10 Strategic Research Centers > Oeschger Centre for Climate Change Research (OCCR)
08 Faculty of Science > Physics Institute > Climate and Environmental Physics
08 Faculty of Science > Physics Institute

UniBE Contributor:

Raible, Christoph


500 Science > 530 Physics
500 Science > 550 Earth sciences & geology




Royal Meteorological Society




Doris Rätz

Date Deposited:

29 Sep 2014 16:34

Last Modified:

14 Nov 2016 08:28

Publisher DOI:





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