The Use of Eigenvectors for Climatic Estimates

Abstract

Eigenvectors may be used in the same way as orthogonal polynomials. They have an advantage over those orthogonal functions expressible by simple formulas, however, in that they are derived from the data being studied and strongly resemble the important features of the data, so that the first several eigenvectors contain a much higher percentage of ?variance? than would be contained in an equal number of ordinary orthogonal polynomials. This paper describes the process by which a matrix of eigenvectors was derived from the sets of 12 mean-monthly precipitation values for 60 stations in Nevada. The first three eigenvectors (in order of importance) were found to account for 93% of the ?variance? in the original 12 ? 60 matrix of raw data and they are also found to have features in common with three natural cycles of annual precipitation in Nevada. The effect of station elevation on each eigenvector is determined by linear correlation. The station multipliers, corrected to a mean elevation, are plotted and analyzed on three maps. These three maps plus the corresponding eigenvectors and elevation regressions supply all the information needed to estimate the mean monthly precipitation for any point or area in Nevada. The method is tested by using it to estimate long-term means for a period of time not included in the input data. Standard errors using the maps and eigenvectors are smaller than for estimates based directly on the short-term station means. Estimates for stations not used in the original input had standard errors small enough to be acceptable. Thus, it can be claimed that for a given point in Nevada, the eigenvector method will give as reliable an estimate of the 12 monthly average precipitation amounts as could be obtained from an actual 10-yr record.