Precipitation over Northern Italy: A Description by Means of Principal component Analysis

Abstract

Principal component analysis is used to study the rainfall distribution over northern Italy in the cold season (October-April). A spatial analysis is applied to the squares roots of daily data, recorded in 14 months, and of their 3- and 5-day means, working on cross-product matrices obtained from both standardized and nonstandardized values. Four principal components (PCs) can be selected: the first is an index of the mean rainfall; the second represents the longitudinal differences; the third and fourth are representative of orographic anomalies. For daily data, these 4 PCs account for more than 80% of the total variance (since cross-product matrices are used in the analysis the term variance must be interpreted as mean square value); this percentage is slightly higher working on nonstandardized values, but with standardized values the explained variance is distributed more uniformly among the 35 rainfall stations. Passing to 3- and 5-day means, the cumulative variance of the first 4 PCs increases: in particular, there is an increase for the first PC and a decrease for the others. These variations are compared with stability indices computed from the daily values of the PCs: the comparison shows that the properties of high rainfall cases are well described by the PCs of 3-day values, whereas 5-day values are excessively smoothed for this purpose. An orthogonal rotation, for which the criterion is based on physical considerations, is then applied to the first 4 PCs of nonstandardized daily values: the rotated rainfall patterns show a clear physical significance and can be related to different types of circulations in the lower troposphere over Europe.