Principal components (alternatively empirical orthogonal functions) are widely used to study modes of dependence in meteorological phenomena. However PCA/EOFs arise by decomposing the covariance matrix, and therefore are not well-suited for describing extremal dependence. Characterizing extreme dependence in high dimensions is difficult for most existing multivariate extreme modeling frameworks.
Using recently developed methods, we summarize extremal dependence via the tail pairwise dependence matrix (TPDM), which can be seen as an extreme analog to the covariance matrix. An eigendecomposition of the TPDM results in an ordered orthonormal basis through which the modes of extremal dependence can be studied.
Applying these methods to US precipitation data, we investigate relationships between the extremes of the time series of basis coefficients and climatological drivers such as ENSO.