Climatological daily mean temperatures are, of course, statistical idealizations, and considered as time-series for calendar month periods, their smoothed, linear-like form does not typlify “normal” patterns in day-to-day mean temperatures that actually occur (more likely quasi-sinusoidal). In this regard, a month-by-month pattern climatology of day-to-day mean temperatures might provide a better appreciation of the nature and relative frequencies of those that do in fact happen. These “modes” could be identified and characterized using Linear Principal Components Analysis.
Using a Correlation PCA with no rotations, the nature and hierarchy of daily mean temperature modes were explored, by month, for the 85-year Downtown Los Angeles daily temperature record (1921-2005). For eleven of the twelve months, results resolved 14 eigenvectors (or modes) with eigenvalues greater than equal to one (September had 13). Eigenvector one's standardized scores suggested propagation of long-waves and, occasionally, seasonal trend as the most important intra-month daily-mean temperature pattern. Highest percent-of-variance-explained statistic for Eigenvector one was 30.7% for June. Other modes, in descending rank order, seemed to describe progressively higher frequency quasi-sinusoidal patterns with phase shifts, suggestive of a gradation in relative importance from long-waves to short-waves.
For illustrative purposes, plots of selected months' eigenvector standard scores are provided along with samplings of actual months' temperature patterns that conformed particular well to certain modes.