The three-cornered hat method for estimating error variances of three or more atmospheric datasets. Part I: Overview and evaluation

The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different datasets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three datasets. We discuss similarities and differences between these methods and the 3CH method. This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the datasets, biases, and unknown error correlations. Using simulated datasets for which the errors and their correlations among the datasets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of datasets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the datasets, and the impact of this source of errors can be reduced by appropriate filtering.