Evaluating two methods of estimating error variances from multiple data sets using an error model

Abstract

Abstract. In this paper we compare two different methods of estimating the error variances of two or more independent data sets. One method, called the "three-cornered hat" (3CH) or "triple co-location" method, requires three data sets. Another method, which we call the "two-cornered hat" (2CH) method, requires only two data sets. Both methods assume that the errors of the data sets are not correlated and are unbiased. The 3CH method has been used in previous studies to estimate the error 10 variances associated with a number of physical and geophysical data sets. Braun et al. (2001) used the two-cornered hat (2CH) method to estimate the error variances associated with two observational data sets of total atmospheric water vapor.In this paper we compare the 3CH and 2CH methods using a simple error model to simulate three and two data sets with various error correlations and biases. With this error model, we know the exact error variances and covariances, which we use 15 to assess the accuracy of the 3CH and 2CH estimates. We examine the sensitivity of the estimated error variances to the degree of error correlation between two of the data sets as well as the sample size. We find that the 3CH method is less sensitive to these factors than the 2CH method and hence is more accurate. We also find that biases in one of the data sets has a minimal effect on the 3CH method, but can produce large errors in the 2CH method.