Wavelet-based multifractal analysis on a time series of solar activity and PDO climate index

There is increasing interest in finding the relation between solar activity and climate change. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigates the relations among solar activity, geomagnetic activity, and climatic regime shift by performing a multifractal analysis. To investigate the change in multifractality, we apply a wavelet transform to time series. The change in fractality of the sunspot number (SSN) correlates closely with that of the solar polar field strength. For the SSN and solar polar field strength, a weak multifractality or monofractality is present at the maximum SSN, minimum SSN, and maximum solar polar field strength. A strong multifractality is present two years before the maximum SSN. The climatic regime shift occurs when the SSN increases and the disturbance of the geomagnetic activity is large. At the climatic regime shift, the changes in the fractality of the Pacific Decadal Oscillation (PDO) index and changes in that of the solar activity indices corresponded with each other. From the fractals point of view, we clarify the relations among solar activity, geomagnetic activity, and climatic regime shift. The formation of the magnetic field of the sunspots is correlated with the solar polar field strength. The solar activity seems to influence the climatic regime shift. These findings will contribute to investigating the relation between solar activity and climate change.