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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 4
Nonlin. Processes Geophys., 15, 557–565, 2008
https://doi.org/10.5194/npg-15-557-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Extreme Events: Nonlinear Dynamics and Time Series Analysis

Nonlin. Processes Geophys., 15, 557–565, 2008
https://doi.org/10.5194/npg-15-557-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

  16 Jul 2008

16 Jul 2008

Extreme event return times in long-term memory processes near 1/f

R. Blender, K. Fraedrich, and F. Sienz R. Blender et al.
  • Universität Hamburg, Meteorologisches Institut, Bundesstrasse 55, 20146 Hamburg, Germany

Abstract. The distribution of extreme event return times and their correlations are analyzed in observed and simulated long-term memory (LTM) time series with 1/f power spectra. The analysis is based on tropical temperature and mixing ratio (specific humidity) time series from TOGA COARE with 1 min resolution and an approximate 1/f power spectrum. Extreme events are determined by Peak-Over-Threshold (POT) crossing. The Weibull distribution represents a reasonable fit to the return time distributions while the power-law predicted by the stretched exponential for 1/f deviates considerably.

For a comparison and an analysis of the return time predictability, a very long simulated time series with an approximate 1/f spectrum is produced by a fractionally differenced (FD) process. This simulated data confirms the Weibull distribution (a power law can be excluded). The return time sequences show distinctly weaker long-term correlations than the original time series (correlation exponent γ≈0.56).

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