The Three-Cornered Hat Method for Estimating Error Variances of Three or More Atmospheric Datasets. Part I: Overview and Evaluation

Abstract

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 data sets. 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 data sets. 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 data sets, biases, and unknown error correlations. Using simulated data sets for which the errors and their correlations among the data sets 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 data sets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the data sets, and the impact of this source of errors can be reduced by appropriate filtering.

Improving global gross primary productivity estimation by fusing multi-source data products

“…The weight values of different products are defined as: in the formula is obtained by the three-cornered hat method ( Premoli and Tavella, 1993 ; Sjoberg et al., 2021 ).…”

The relationship between two methods for estimating uncertainties in data assimilation

“…This work does not aim to provide a comprehensive review of the literature on either of the methods investigated here. Sjoberg et al (2021) give a review of 3CH, its history, intricacies, and limitations, including its relationship with the triple-collocation method of Stoffelen (1998). Tandeo et al (2020) give a review of what the authors refer to as "innovation-based methods" but which should more generally be referred to as "residual-based methods" of which DBCP is one example.…”

“…Still, perhaps for clarity, it might be worthwhile to look briefly into how the known limitations affecting each of these methods compare when viewed from the light of the present work. Sjoberg et al (2021) lists the following factors limiting the accuracy of 3CH estimates: (i) sample size; (ii) outliers in the relevant data sets; (iii) relative magnitude of cross-covariance (random) errors among data sets; (iv) biases; and (v) unknown cross-covariances. Put in the context of 3CH's relationship with DBCP, the following can be stated.…”

Evaluation and Assimilation of the COSMIC‐2 Radio Occultation Constellation Observed Atmospheric Refractivity in the WRF Data Assimilation System

“…10.1029/2021JD034935 4 of 21 in the RMS (root-mean-square) and standard deviation (Std.Dev) of the differences between the two profiles, in addition to the different errors of the two observations (Anthes & Rieckh, 2018;Kitchen, 1989;Sjoberg et al, 2021).…”

“…RO observations represent horizontal scales of ∼150 km and vertical scales of ∼100 m, while RS observations are essentially point measurements. These representativeness differences manifest as differences in the RMS (root-mean-square) and standard deviation (Std.Dev) of the differences between the two profiles, in addition to the different errors of the two observations (Anthes & Rieckh, 2018;Kitchen, 1989;Sjoberg et al, 2021).…”