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

Abstract

A method is presented for making probability statements about past climatic conditions for the state of Arizona given the corresponding relative width of tree rings. The probability statements about periods of extreme climate from 1650 to 1899 are based upon the joint occurrence of the state-wide average seasonal climate and ring widths during 1899-1957. The ring-width values used are index chronologies selected from four different areas within Arizona. Spatial homogeneity among the four chronologies is evaluated by using digital filtering and correlation techniques. The chronologies are then normalized, averaged to form a state-wide series, and the values of state-wide growth for each year placed into one of nine equally probable classes. Similarly, seasonal temperatures and seasonal precipitation are placed into three equally probable classes and the joint occurrences between temperature and precipitation become nine climatic classes. Contingency tables are used to establish the joint occurrence of the nine climatic classes and the nine ring-width classes. A number of 10 and 20 year intervals since 1650 are identified as periods of unusually high or low probability of occurrence of above or below normal precipitation for any season of the year. The period 1880-1889 is of special interest as it was a period when downcutting was initiated in many Arizona streams and is also one of the periods in which the probability for below normal seasonal precipitation was unusually high (p = 0.48).