Methods of Calibration, Verification, and Reconstruction

Often tree-ring variations can be correlated with the variations in one or more environmental factors that are known to influence growth. In such cases, it should be possible to find a statistical growth-environment relationship that can be used to deduce or reconstruct the past variations in the environment from past variations in tree-ring growth. The procedure that estimates the statistical growth-environment relationship is called calibration. The word calibration was originally applied to the process of finding the caliber (area of cross section) of a tube, as in calibrating a thermometer. The word has been extended to include the determination of absolute values appropriate to selected fixed points of an instrument (McIntosh, 1972). In paleoclimatology, calibration involves the fitting of a statistical equation or model that can be applied to one or more predictors to estimate or reconstruct one or more predictands. One set of predictor and predictand data, called the dependent set, is used to estimate the coefficients of the calibration equation. The remaining data are outside of the interval used for calibration, so they are referred to as independent data. If climate is the predictor and tree-ring variation is the predictand, then the equation is referred to as a response function. In response functions, the magnitudes and the signs of the coeffficients of the statistical equation indicate the importance and signs of the tree-ring response to the calibrated variables of climate.