A Statistical Study of the Relationship between the Solar Cycle Length and Tree-Ring Index Values

We have determined the correlation coefficient between tree-ring index values and the sunspot cycle length for 69 tree-ring data sets from around the world of greater than 594 years duration. A matrix of correlation coefficients is formed with varying delay and smoothing parameters. Similar matrices, formed from the same data, but randomly scrambled, provide a control against which we can draw conclusions about the influence of the solar cycle length on climate with a reasonable degree of confidence. We find that the data confirm an association between the sunspot cycle length and climate with a negative maximum correlation coefficient for 80% of the data sets considered. This implies that wider tree-rings (i.e. more optimum growth conditions) are associated with shorter sunspot cycles. Secondly, we find that the climatic effect of the solar cycle length is smoothed and delayed by several decades and the degree of smoothing and the amount of the delay is dependent on the elevation and the geographical location of the trees employed.