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 axe established for the 22-year Hale solar ma gnetic cycle. Since about AD1850, successive maximum sunspot numbers i n a Hale cycle are highly correlated. Also, a regression model for the reconstruction of the 22-year Hale cycle has been formulated from pro xy tree-ring data, obtained from spruce trees growing at a high altitu de site in White River National Forest in Colorado. Over a considerabl e fraction of the past 300 years to AD1986, the ring-index time series power spectrum exhibits a strong 22-year periodicity, and more recent ly a significant spectral peak (at the 95% confidence level) at approx imately 11 years. The model shows that the greatest variation in 'ampl itude' in the magnetic cycle occurs over the early decades of the eigh teenth century, when the sample size is small. Thereafter, a nearly co nstant amplitude is maintained until about AD1880 when a break occurs in both phase correspondence and amplitude, extending over the next th ree cycles. Rom AD1950 the signal recovers phase with the solar cycle, with reduced but increasing amplitude.