The Three-Cornered Hat Method for Estimating Random Error Variances in Multiple Data Sets
Presenter:
Richard A. Anthes
UCAR COSMIC Program
UCAR COSMIC Program
Poster
The Three-Cornered Hat (3CH) method, originally developed by physicists to estimate the errors of atomic clocks, has been shown by Anthes and Rieckh (2018) and Rieckh and Anthes (2018) to be a powerful tool for estimating vertical profiles of random error variances from multiple atmospheric data sets that are co-located in space and time. Unlike other methods of estimating errors that compare one data set such as radio occultation to other data sets (such as radiosondes or models, which also have errors), the 3CH method uses three or more data sets to estimate the actual random errors of all the data sets, not just the differences between data sets. We will use the 3CH method to compute vertical profiles of estimated errors of COSMIC-2 radio occultation (RO) retrievals and other satellite and in-situ observational and model data sets. This study will be valuable for diagnosing the errors and improving the accuracy of all the data sets, as well as providing useful information for operational modeling centers.
In this talk we present an overview of the three-cornered hat (3CH) method and discuss the factors that limit its accuracy. These include (1) sample size, (2) magnitude of the random errors, (3) bias errors, (4) correlation of errors among one or more data sets, and (5) effect of co-location interpolations. We test the 3CH method and estimate the effects of these factors using an error model to generate synthetic data sets with known bias and random errors.
We then show a few examples of error variance estimates for selected data sets. Using data from 2007, we estimate vertical profiles of the error variances of two versions of radio occultation (RO) retrievals, radiosondes, ERA-Interim, and Global Forecast System (GFS) model data sets at several radiosonde locations in the tropics and subtropics. We computed vertical profiles of estimated error variances for four variables (specific humidity, relative humidity, temperature, and refractivity for the five data sets using three linearly independent equations for each data set.
Our results show that different combinations of the five data sets yield similar error variance profiles for each data set, and these estimates are consistent with previous estimates where available. These results thus indicate that the correlations of the errors among all data sets are small and the 3CH method yields realistic error variance profiles. The estimated error variances of the ERA-Interim data set are smallest, a reasonable result considering the excellent model and data assimilation system and assimilation of high-quality observations. For the four locations studied, RO has smaller error variances than radiosondes, in agreement with previous studies. Part of the larger error variance of the radiosondes is associated with representativeness differences, because radiosondes are point measurements, while the other data sets represent horizontal averages over scales of approximately 100 km.
References:
Rieckh, T. and R.A. Anthes, 2018: Evaluating two methods of estimating error variances using simulated data sets with known errors. Atmos. Meas. Tech., 11, 4309-4325, https://doi.org/10.5194/amt-11-4309-2018
Anthes, R.A. and T. Rieckh, 2018: Estimating observation and model error variances using multiple data sets. Atmos. Meas. Tech., 11, 4239–4260, 2018. https://doi.org/10.5194/amt-11-4239-2018
Poster in PDF:
