On the Accuracy of Monthly Means

Abstract

The errors involved in estimating mean values from data collected over the ocean have been considered in a number of recent papers. In these, errors have been investigated by taking a random sample, size n, many times, from hourly data collected by buoys and fitting curves to the empirical confidence limits obtained as a function of n. In this paper it is shown that this is unnecessary: an analytical solution can be obtained to this problem by considering the statistics. Because of the correlation structure these results, which assume independence, can be misleading; correct formulas are derived for the variance of the mean in the case of both short- and long-range dependence. Having given formulas for the variance of the mean in both the correlated and uncorrelated cases, the simulation results obtained previously are discussed. Finally, the problem of whether the mean for a particular month (e.g., June 1990) or the population mean (e.g., June) is required and how the answer to this question alters the amount of data needed to achieve a specified accuracy are discussed.