In this paper, spatial and temporal subsampling errors in estimating empirical orthogonal functions (EOFs) and the corresponding eigenvalues are studied. The subsampling errors are measured in terms of the minimum difference between an estimated eigenvalue and an exact one, and the minimum Euclidean norm of distance between an estimated eigenfunction and a linear space spanned by a certain number of exact eigenfunctions. This linear space represents a set of exact EOFs which admix into an estimated EOF. The extent of modal mixing, or variance split, is determined by the proximity of adjacent eigenvalues and the degree of subsampling error, and is estimated using one of the theorems of a posteriori error estimates for the eigenvalues and the eigenfunctions. Such a representation of the EOF errors allows a systematic approach to the sampling problems of EOFs. This methodology is applied to the surface air temperature field, in which errors in computing the EOFs and the corresponding eigenvalues are measured in terms of the sampling insufficiency spatially and temporally. To this end, different configurations of spatial sampling points, and different lengths of the temperature record have been used. This study addresses the spatial and temporal ''sampling theorem'' for the EOFs and the eigenvalues of the global surface temperature field. ¿ American Geophysical Union 1996