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Non‐exponential return time distributions for vorticity extremes explained by fractional Poisson processes
Author(s) -
Blender R.,
Raible C. C.,
Lunkeit F.
Publication year - 2014
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2354
Subject(s) - mathematics , middle latitudes , standard deviation , exponential function , weibull distribution , statistical physics , predictability , quantile , poisson distribution , statistics , shape parameter , meteorology , mathematical analysis , physics
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.