Comparison of Desroziers and Three-Cornered Hat Methods for Estimating COSMIC-2 Bending Angle Uncertainties

Abstract

Abstract We compare two seemingly different methods of estimating random error statistics (uncertainties) of observations, the three-cornered hat (3CH) method and Desroziers method, and show several examples of estimated uncertainties of COSMIC-2 (C2) radio occultation (RO) observations. The two methods yield similar results, attesting to the validity of both. The small differences provide insight into the sensitivity of the methods to the assumptions and computational details. These estimates of RO error statistics differ considerably from several RO error models used by operational weather forecast centers, suggesting that the impact of RO observations on forecasts can be improved by adjusting the RO error models to agree more closely with the RO error statistics. Both methods show RO uncertainty estimates that vary with latitude. In the troposphere, uncertainties are higher in the tropics than in the subtropics and middle latitudes. In the upper stratosphere–lower mesosphere, we find the reverse, with tropical uncertainties slightly less than in the subtropics and higher latitudes. The uncertainty estimates from the two techniques also show similar variations between a 31-day period during Northern Hemisphere tropical cyclone season (16 August–15 September 2020) and a month near the vernal equinox (April 2021). Finally, we find a relationship between the vertical variation of the C2 estimated uncertainties and atmospheric variability, as measured by the standard deviation of the C2 sample. The convergence of the error estimates and the standard deviations above 40 km indicates a lessening impact of assimilating RO above this level. Significance Statement Uncertainties of observations are of general interest and their knowledge is important for assimilation in numerical weather prediction models. This paper compares two methods of estimating these uncertainties and shows that they give nearly identical results under certain conditions. The estimation of the COSMIC-2 bending angle uncertainties and how they compare to the assumed bending angle error models in several operational weather centers suggests that there is an opportunity for obtaining improved impact of RO observations in numerical model forecasts. Finally, the relationship between the COSMIC-2 bending angle errors and atmospheric variability provides insight into the sources of RO observational uncertainties.