Relationship between group sunspot number and Wolf sunspot number

TL;DR

This study uses wavelet analysis to compare the phase and synchrony of monthly Wolf and group sunspot numbers from 1795 to 1995, revealing differences in their periodicity and cycle synchronization.

Contribution

It provides a detailed wavelet-based analysis of the relationship and asynchrony between Wolf and group sunspot numbers over two centuries.

Findings

Schwabe cycle is the only common period in Rg and Rz.

Asynchrony is more evident in cycles 5 and 6.

Rg fits Rz better during solar minimum periods.

Abstract

Continuous wavelet transform and cross-wavelet transform have been used to investigate the phase periodicity and synchrony of the monthly mean Wolf ($R_{z}$) and group ($R_{g}$) sunspot numbers during the period of June 1795 to December 1995. The Schwabe cycle is the only one common period in Rg and Rz, but it is not well-defined in case of cycles 5-7 of Rg and in case of cycles 5 and 6 of $R_{z}$. In fact, the Schwabe period is slightly different in $R_{g}$ and $R_{z}$ before cycle 12, but from cycle 12 onwards it is almost the same for the two time series. Asynchrony of the two time series is more obviously seen in cycles 5 and 6 than in the following cycles, and usually more obviously seen around the maximum time of a cycle than during the rest of the cycle. $R_{g}$ is found to fit $R_{z}$ better in both amplitudes and peak epoch during the minimum time time of a solar cycle than during the maximum time of the cycle, which should be caused by their different definition, and around the maximum time of a cycle, $R_{g}$ is usually less than $R_{z}$. Asynchrony of $R_{g}$ and $R_{z}$ should somewhat agree with different sunspot cycle characteristics exhibited by themselves.