Synchronization of Sunspot Numbers and Sunspot Areas

Sunspot activity is usually described by either sunspot numbers or sunspot areas. The smoothed monthly mean sunspot numbers (SNs) and the smoothed monthly mean areas (SAs) in the time interval from November 1874 to September 2007 are used to analyze their phase synchronization. Both the linear method (fast Fourier transform) and some nonlinear approaches (continuous wavelet transform, cross-wavelet transform, wavelet coherence, cross-recurrence plot, and line of synchronization) are utilized to show the phase relation between the two series. There is a high level of phase synchronization between SNs and SAs, but the phase synchronization is detected only in their low-frequency components, corresponding to time scales of about 7 to 12 years. Their high-frequency components show a noisy behavior with strong phase mixing. Coherent phase variables should exist only for a frequency band with periodicities around the dominating 11-year cycle for SNs and SAs. There are some small phase differences between them. SNs lag SAs during most of the considered time interval, and they are in general more asynchronous around the minimum and maximum times of a cycle than at the ascending and descending phases.