Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling
27 May 2020

Principal Component Analysis for Extremes and Application to US Precipitation


We propose a method for analyzing extremal behavior through the lens of a most-efficient basis of vectors. The method is analogous to principal component analysis but is based on methods from extreme value analysis. Specifically, rather than decomposing a covariance or correlation matrix, we obtain our basis vectors by performing an eigendecomposition of a matrix that describes pairwise extremal dependence. We apply the method to precipitation observations over the contiguous US. We find that the time series of large coefficients associated with the leading eigenvector shows very strong evidence of a positive trend, and there is evidence that large coefficients of other eigenvectors have relationships with the El Nino-Southern Oscillation.


The standard eigenfunctions used for Principal Component Analysis (PCA) or Empirical Orthogonal Function (EOF) analyses are not applicable for application to the tails of distributions. This new statistical method, using the tail dependence concept of Coles, presents a new set of eigenfunctions tailored to extreme values. We demonstrate that these functions have the same properties as standard EOFs and can reconstruct the variability of extreme precipitation. This new method opens up possibilities to develop more rigorous detection and attribution methods for extreme temperature and precipitation as well as explore the effect of natural modes of variability.


A new mathematical formalism, tailored to extreme values, is developed to permit eigenfunction analyses of extreme temperature and precipitation analogous to Principal Component Analyses of means.

William D. Collins
Lawrence Berkeley National Laboratory
Jiang, Y, D Cooley, and MF Wehner.  2020.  "Principal Component Analysis for Extremes and Application to US Precipitation."  Journal of Climate.