Empirical orthogonal functions of monthly precipitation and temperature over the United States and homogeneous stochastic models

The monthly mean precipitation and temperature at p = 62 stations over the United States and Canada for N = 91 years (1900-1990) are analyzed in terms of empirical orthogonal functions (EOFs) and their variances. The eigenvalues and eigenfunctions are compared with a succession of stochastic noise models: (1) uncorrelated noise, having eigenvalues depending on the ratio pin, with n = N - 1; (2) homogeneous noise having spatial correlations which are fit to the observations; and (3) homogeneous noise having both spatial and temporal correlations fit to the observations. Individual monthly data for January and July were analyzed as well as a combined data set of all months. The eigenvalue spectra of the homogeneous noise models are found to be in close agreement with the observed spectra even when time correlation is excluded from the model. Time correlations only slightly affect the results for temperature and have less impact for precipitation. The EOF patterns of the noise models contain inhomogeneities due only to the distribution of stations, the common correlation length, and the limited sample but are nevertheless in good agreement with the observed patterns, whose inhomogeneities may also be affected by secular trends and physical inhomogeneities such as orography. The observed EOF eigenvectors also show identifiable deviations from the homogeneous EOFs. Further work will be needed to see if these deviations can be convincingly associated with true physical inhomogeneities.