Relationship between group sunspot number and Wolf sunspot number

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.

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