Spatial regression methods in dendroclimatology: A review and comparison of two techniques

Abstract

We review and compare two alternative spatial regression methods used in dendroclimatology to reconstruct climate from tree rings. These methods are orthogonal spatial regression (OSR) and canonical regression (CR). Both the OSR and CR methods have a common foundation in least-squares theory and converge to the same solution when all p candidate tree-ring predictors of climate are forced into the model. However, the perfomance of OSR and CR may differ when only subsets p′ < p predictors are used. Theory cannot predict how either method is likely to perform when best-subset selection is applied, especially with regards to reconstruction accuracy. Consequently, empirical comparisons of OSR and CR are made using three tree-ring and climate networks from western Europe and eastern North America that have been used in previous dendroclimatic studies. These comparisons rely on a suite of regression model verification statistics to validate the accuracy of the climatic reconstructions produced by the best-subset models. The results indicate little real difference between OSR and CR, with each performing equally good or bad depending on the amount of recoverable climatic information in the tree rings. Canonical regression may perform slightly better in high signal-to-noise cases; conversely, OSR may perform slightly better when the signal-to-noise ratio is low. None of these apparent differences are large enough to select one method in preference to the other, however, and many more comparisons would be needed to determine if such indications are generally valid.