Unbiased Estimation of Autocorrelations of Daily Meteorological Variables

Abstract

A new method is proposed for estimation of autocorrelations from daily values of a continuous meteorological variable (e.g., temperature) over a selected period for many years. It has the following two advantages over the two existing time domain nonparametric methods. First, the proposed method is asymptotically unbiased in the sense that the probability mean of an estimate tends to the true value as the number of periods tends to infinity, whereas the two existing methods are biased. Second, the proposed method can handle the annual cycle of daily variances, which is exhibited in some datasets but that cannot be handled by the two existing methods. Simulations show that the variances of the estimates for all the methods are about the same. As a result, autocorrelations estimated by the proposed method are more theoretically sound and, therefore, may be more accurate than those estimated by the two existing methods. Improved estimates of autocorrelations can be used to improve the analysis of natural variability of daily meteorological variables and other estimates that are important to meteorological or climatological research, such as potential predictability, effective sample sizes, and total degrees of freedom.