Regression model for the 22-year Hale solar cycle derived from high altitude tree-ring data

Initially some simple analytical properties based on the annual Zurich relative sunspot number are established for the 22-year Hale solar magnetic cycle. Since about AD1850, successive maximum sunspot numbers in a Hale cycle are highly correlated. Also, a regression model for the reconstruction of the 22-year Hale cycle has been formulated from proxy tree-ring data, obtained from spruce trees growing at a high altitude site in White River National Forest in Colorado. Over a considerable fraction of the past 300 years to AD1986, the ring-index time series power spectrum exhibits a strong 22-year periodicity, and more recently a significant spectral peak (at the 95% confidence level) at approximately 11 years. The model shows that the greatest variation in 'amplitude' in the magnetic cycle occurs over the early decades of the eighteenth century, when the sample size is small. Thereafter, a nearly constant amplitude is maintained until about AD1880 when a break occurs in both phase correspondence and amplitude, extending over the next three cycles. From AD1950 the signal recovers phase with the solar cycle, with reduced but increasing amplitude.