An Alternative to PCA for Estimating Dominant Patterns of Climate Variability, with Application to US Rainfall

Floods and droughts are driven, in part, by patterns of extreme rainfall. Heat waves are driven, in part, by patterns of extreme temperature. The standard work-horse for understanding patterns of climate variability is Principal Component Analysis (PCA) and its variants. But PCA does not optimize for spatial extremes, and so there is no particular reason why the first PCA pattern should identify, or even approximate, the types of patterns that may drive these phenomena, even if the linear assumptions underlying PCA are correct. We present an alternative pattern identification algorithm that makes the same linear assumptions as PCA, but which can be used to explicitly optimize for spatial extremes. We call the method Directional Component Analysis (DCA), since it involves introducing a preferred direction, or metric, such as `sum of all points in the field'. We compare the first PCA and DCA patterns for US rainfall on a 6 month timescale, using the sum metric for the definition of DCA, and find that they are somewhat different. The definitions of PCA and DCA mean that the first PCA pattern has the larger explained variance of the two, while the first DCA pattern, when scaled appropriately, is both more likely and captures more rainfall. In combination these two patterns yield more insight into rainfall variability than either pattern on its own.