Alternative principal components regression procedures for dendrohydrologic reconstructions

Streamflow reconstruction using tree ring information (dendrohydrology) has traditionally used principal components analysis (PCA) and stepwise regression to form a transfer function. However, PCA has several procedural choices that may result in very different reconstructions. This study assesses the different procedures in PCA-based regression and suggests alternative procedures for selection of variables and principal components. Cross-validation statistics are presented as an alternative for independently testing and identifying the optimal model. The objective is to use these statistics as a measure of the model's performance to find a conceptually acceptable model with a low prediction error and the fewest number of variables. The results show that a parsimonious model with a low mean square error can be obtained by using strict rules for principal component selection and cross-validation statistics, Additionally, the procedure suggested in this study results in a model that is physically consistent with the relationship between the predictand and the predictor. The alternative PCA-based regression models presented here are applied to the reconstruction of the Upper Colorado River Basin streamflow and compared with results of a previous reconstruction using traditional procedures. The streamflow reconstruction proposed in this study shows more intense drought periods, which may influence the future allocation of water supply in the Colorado River Basin.