In general, interannual tree growth in stressed environments varies according to changes in growth limiting climate variables. Where these growth limiting variables have been measured, the tree rings themselves can be used as predictors for past climate. The process of deriving a climate growth function and extending it beyond instrumental records is referred to as a calibration. The outcome is a chronology of climate as old as the oldest preserved tree in the tree ring series (Fritts 1976).
Because trees rarely respond to a single climate variable, it is desirable to use a combination of variables to derive a tree response function. An optimum combination of variables would be one in which the first derived variable described the largest proportion of variance in the data. Subsequent variables would be orthogonal and uncorrelated and would describe increasingly less variation in the data. The process of arranging the original variables in this fashion is called Principle Component Analysis. After deciding on a number of components to retain for analysis, one can then model the climate growth relationship using regression analysis with an optimum combination of variables. (Cook and Kairiukstis 1989)