Spatio-Temporal Correlation Analysis of Global Temperature Based on the Correlation Matrix Theory

Based on the NCEP/NCAR reanalysis daily mean temperature data from 1948 to 2005 and random time series of the same size, temperature correlation matrixes (TCMs) and random correlation matrixes (RCMs) are constructed and compared. The results show that there are meaningful true correlations as well as correlation "noises" in the TCMs. The true correlations contain short range correlations (SRCs) among temperature series of neighboring grid points as well as long range correlations (LRCs) among temperature series of different regions, such as the El Nieno area and the warm pool areas of the Pacific, the Indian Ocean,the Atlantic, etc. At different time scales, these two kinds of correlations show different features: at 1-10-day scale, SRCs are more important than LRCs; while at 15-day-or-more scale, the importance of SRCs and LRCs decreases and increases respectively, compared with the case of 1-10-day scale. It is found from the analyses of eigenvalues and eigenvectors of TCMs and corresponding RCMs that most correlation information is contained in several eigenvectors of TCMs with relatively larger eigenvalues, and the projections of global temperature series onto these eigenvectors are able to reflect the overall characteristics of global temperature changes to some extent. Besides, the correlation coefficients (CCs) of grid point temperature series show significant temporal and spatial variations. The average CCs over 1950-1956, 1972-1977, and 1996-2000 are significantly higher than average while that over the periods 1978-1982 and 1991-1996 are opposite, suggesting a distinctive oscillation of quasi-10-20 yr. Spatially, the CCs at 1- and 15-day scales both show band-like zonal distributions; the zonally averaged CCs at 1-day scale display a better latitudinal symmetry,while they are relatively worse at 15-day scale because of sea-land contrast of the Northern and Southern Hemisphere. However, the meridionally averaged CCs at 15-day scale display a longitudinal quasi-symmetry.