Conditional Probability of Occurrence for Variations in Climate Based on Widths of Annual Tree Rings in Arizona

Abstract

Modern statistical innovations have been incorporated into several recent analyses of tree -ring growth as related to climate. For example, Fritts (1962) used stepwise multiple regression techniques to study the systematic relationship of ring widths to climatic parameters in the southwestern United States; Bryson and Dutton (1962) have utilized power and cross -power spectral analyses in analyzing tree-ring records for periodicities; Mitchell (1967) applied factorial analysis; and Julian and Fritts (1967) introduced digital filter techniques as a means of appraising the systematic relations of tree growth to climatic variables. None of these studies, however, has attempted to analyze the joint occurrence of specific ring widths with certain climatic types so that probability statements could be made about climate from ring widths. This present study analyzes the joint occurrence of climate and relative width of tree rings for the state of Arizona. Conditional probabilities of occurrence are used to establish quantitative relevance of state -wide tree -ring growth from 1900 through 1957 to recorded climate for 1899 through 1957. The results are then used to make probability estimates of climate for the period 1650 through 1899.