On Sampling Errors in Empirical Orthogonal Functions

Abstract

Abstract A perturbation analysis is carried out to quantify the eigenvector errors due to the mixing with other eigenvectors that occur when empirical orthogonal functions (EOFs) are computed for a finite-size data sample. Explicit forms are provided for the second-order eigenvalue error and first-order eigenvector error. The eigenvector sampling error depends monotonically on the ratio of the lower to the higher eigenvalues that mix. The relationship to the eigenvalue separation criterion of North et al. is discussed. The eigenvector error formula is applied to quantify sampling errors for the leading EOF of the Northern Hemisphere wintertime geopotential height at various pressure levels, and it is found that the smallest sampling error in the troposphere occurs for the sea level pressure EOF. The errors in the 500-hPa height EOFs are almost twice as large.