Average annual total sunspot area in the last 410 yr: the most probable values and limits of their uncertainties

Abstract

ABSTRACT The aim of this work is to create a long (410-yr) series of average annual total sunspot areas AR – a physically based index of sunspot activity. We use telescopic observations of the AR index in 1832–1868 and 1875–2020, as well as the relationship between AR and long series of sunspot indices SN (international sunspot numbers, version 2.0) and sunspot groups GN (Svalgaard and Schatten’s version of group sunspot numbers). The Royal Greenwich Observatory series after 1976 is extended by the Kislovodsk Mountain Astronomical Station data. When reconstructing AR from SN, it is taken into account that the function AR  =  f(SN) has a non-linear systematic character and uncertainty associated with the heterogeneity of these indices. Therefore, in addition to modelling the most probable AR values, predictive limits of reconstruction uncertainty are determined. In the interval 1610–1699 we carried out the reconstruction on the basis of the GN series using the previously proposed decomposition in pseudo-phase space (DPS) method. The resulting series NO21y is freely available online. We show that for this series the empirical Gnevyshev–Ohl rule and Waldmeier effect are fulfilled. Wavelet analysis reveals periodicities of 8.4–13.8 yr for the main cycle (with a sharp decrease of the period before the global Maunder and Dalton minima) and a two-component Gleissberg cycle with typical periods of 50–60 and 90–110 yr.