Identification of Multi-Station Extreme-Most Daily Maximum/Minimum Historical Temperatures Patterns Using Principal Components Analysis

Floating-bar or Hi-Lo charts are a widely used visual means of conveying the character of changes over time of variables such as market prices or temperature, to name a few. In the case of calendar year daily max/min temperatures, the depictions of the varied diurnal, synoptic, long-wave, and seasonal influences over time can be quite interesting to inspect, both from physical interpretative and pure pattern standpoints, and the notion may arise on how typical or unusual a given arrangement of bars is, especially if it appears irregular or in some other way abnormal. Along with the more conventional statistics like means, extremes and ranges, it should be worthwhile to have statistics calculable that can characterize and compare in an objective way the year-to-year configurations relative to each other.

Utilizing daily data for a single station (Downtown Los Angeles), a previous exploratory analysis delved into this question (Fisk, 2004), employing two properties (“shape”, i.e., the correlation coefficient) and (“spread”, i.e., the covariance coefficient). These were an adaptation of concepts originally described by Yarnal (1993) which involved Linear Principal Components Analysis. It turned out that the above calculations could be conducted as a Principal Components Analysis problem, a somewhat unconventional, labor-saving, but valid application of a PCA. The approach identified years that qualified as the most “extreme” in pattern, through referencing of first component correlation and covariance loadings’ statistics, both individually and in the 2-D sense. Follow-up studies, also using the PCA approach, examined Downtown Los Angeles daily mean temperature modes for selected calendar months (Fisk, 2007), and extreme patterns in LAX hourly temperatures, also for a specified calendar months (Fisk, 2012).

Returning to daily max/min calendar year data, this investigation expands the scope to multiple stations in the Western U.S., identifying and comparing the most extreme calendar year patterns in the combined 2-D shape/spread sense (as evaluated by their relative point positions on 2-D confidence ellipsoids). In a typical calendar year max/min application, first component PCA results, as indicated by the very high eigenvalue magnitudes and percent of variance explained, describe an overwhelming portion of the variance, but for a few select stations, recently identified, second and even third component results display eigenvalue confidence interval bands that include the eigenvalue magnitude of one, the minimum threshold for “original variable” status - these examples could not have been identified by a means other than PCA. In a daily max/min temperature application, first components’ statistics describe adherence to patterns that are first harmonic in form. Second and third component patterns, in those few significant cases, conform in a general sort of way to second and third harmonic forms, the agreement most visible for certain sub-portions of the year. Results will include floating-bar graphs, by station, for those years that qualified as the most “extreme" in the first component sense, and also, when applicable, of those second and third component cases.