Article thumbnail

Extreme value theory and the solar cycle

By A. Asensio Ramos

Abstract

Aims.We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. Methods.The recent advances in the methodology of the theory of extreme values are applied to the maximal extremes of the time series of sunspots. We focus on the extreme events that exceed a carefully chosen threshold and a generalized Pareto distribution is fitted to the tail of the empirical cumulative distribution. A maximum likelihood method is used to estimate the parameters of the generalized Pareto distribution and confidence levels are also given to the parameters. Due to the lack of an automatic procedure for selecting the threshold, we analyze the sensitivity of the fitted generalized Pareto distribution to the exact value of the threshold. Results.According to the available data, which only span the previous ~250 years, the cumulative distribution of the time series is bounded, yielding an upper limit of 324 for the sunspot number. We also estimate that the return value for each solar cycle is ~188, while the return value for a century increases to ~228. Finally, the results also indicate that the most probable return time for a large event such as the maximum at solar cycle 19, happens once every ~700 years and that the probability of finding such a large event with a frequency smaller than ~50 years is very small. In spite of the essentially extrapolative character of these results, their statistical significance is very large

Topics: methods: data analysis, methods: statistical, Sun: activity, Sun: magnetic fields
Publisher: EDP Sciences
DOI identifier: 10.1051/0004-6361:20077574
OAI identifier: oai:edpsciences.org:dkey/10.1051/0004-6361:20077574
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://www.aanda.org/10.1051/... (external link)
  • https://doi.org/10.1051/0004-6... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.