Tuesday, 11 January 2005
Principal components analysis of month-to-month precipitation variability for Downtown Los Angeles (1877-8 through 2003-4 seasons)
Utilizing Principal Components Analysis (PCA), the existence and character of month-to-month modes in October-June precipitation variability are investigated for the Downtown Los Angeles, California station. Period of record is the 1877-78 through 2003-2004 seasons, a 127-year history. Preliminary processing of the data involving creation of combined October-November and April-June series (to go with December, January, February, and March), addition of an .01 constant ("start") to all series to accommodate zero observations, application of the Box-Cox Power transformation procedure, and standardizations enabled the analysis to be carried out with no compromises to the multivariate-normal assumption. Results resolved physically meaningful, but modest (as to eigenvalue magnitude and differentiation) components. The first three (out of six) components explained about 58% of the variance; these were the only three components whose eigenvalues were at 1 or greater magnitude after the data were subject to a Varimax rotation. The "primary" mode showed a contrast in eigenvector loadings' signs between the contiguous months January, February, and March (each significantly positively signed) with negligible magnitudes for the other periods. This pattern seemed to be associated frequently (but not exclusively) with major El Nino episodes. The "secondary" mode involved a contrast in signs between the contiguous periods October-November, December, and January (October-November and December each positively signed to a high degree, January moderately so), with undistinguished magnitudes for the other three periods. The "tertiary" mode showed a very high negative loading for April-June with minimal magnitudes for the other five periods. Time-series plots of the component scores are constructed, and identification of the most anomalous yearly month-to-month patterns are performed applying the concept of multivariate statistical distances on the scores.