Extreme value theory applied to the millennial sunspot number series

TL;DR

This study applies Extreme Value Theory to millennial sunspot data reconstructed from radionuclide records, estimating upper bounds and return levels for solar activity over the past 9,000 years.

Contribution

It introduces a novel application of EVT to long-term sunspot series, revealing upper bounds and long-term return levels of solar activity.

Findings

Upper bounds of sunspot activity are implied by negative shape parameters.

Estimated 1000-year return levels are below observed maximums.

Main features of solar variability are captured within the telescopic observation period.

Abstract

In this work, we use two decadal sunspot number series reconstructed from cosmogenic radionuclide data (14C in tree trunks, SN-14C and 10Be in polar ice, SN-10Be) and the Extreme Value Theory to study variability of solar activity during the last 9 millennia. The peaks-over-threshold technique was used to compute, in particular, the shape parameter of the generalized Pareto distribution for different thresholds. Its negative value implies an upper bound of the extreme SN-10Be and SN-14C time series. The return level for 1000 and 10000 years were estimated leading to values lower than the maximum observed values, expected for the 1000-year, but not for the 10000-year return levels, for both series. A comparison of these results with those obtained using the observed sunspot numbers from telescopic observations during the last four centuries suggest that the main characteristics of solar activity have already been recorded in the telescopic period (from 1610 to nowadays) which covers the full range of solar variability from a Grand minimum to a Grand maximum.