A caveat concerning singular value decomposition

Abstract

An assessment is made of the ability of the singular value decomposition (SVD) technique to recover the relationship between two variables x and y from a time series of their observations. It is shown that SVD is rigorously successful only in the special cases when either i) the transformation linking x and y is orthogonal or ii) the covariance matrix of either x or y is the identity matrix. The behavior of the method when these conditions are not met is also studied in a simple two-dimensional case. That this caveat can be relevant in a meteorological context is demonstrated by performing an SVD analysis of a time series of global upper-tropospheric streamfunction and vorticity fields. -from Authors