Three kinds of wavelet transform methods\u2014continuous wavelet transform, cross-wavelet transform, and wavelet coherence\u2014have been proposed to investigate the phase synchrony of the smoothed monthly mean sunspot areas in the time interval of 1874 May to 2008 March in the solar northern and southern hemispheres. For both time series, the Schwabe cycle is the only period of statistical significance, whose mean value is 10.61 yr. The length of the Schwabe cycle for the smoothed monthly mean sunspot areas in the northern hemisphere actually differs from that in the southern hemisphere, which should lead to phase asynchrony between the two series. Both the cross-wavelet transform and wavelet coherence analyses show an asynchronous behavior with phase mixing in the high-frequency components of hemispheric sunspot activity and a strong synchronous behavior with coherent phase angles in the low-frequency components corresponding to period scales around the Schwabe cycle. Although a phase coherence is found at timescales of about 8.5-13.5 yr (which is similar to those of Donner & Thiel, but within a shorter period), phases are not always coherent at the timescales in the considered time interval. The availability of a physical, meaningful phase definition depends crucially on the appropriate choice of reference frequencies. At the coherent period scales, the leading role is found from those conditions where processes of sunspot formation in the northern hemisphere occur earlier than in the southern one (except some exceptions in several years around the year 1900) during the years of about 1874-1926 to those where the opposite is true during the years of about 1926-1966, and returning back again during the years of about 1966-2008. The mean phase synchronization values at the coherent timescales given by wavelet coherence represent the running trend of the line of synchronization given by a cross-recurrence plot.
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