Estimating Random Error Variances in Observations, NWP Analyses, and Reanalyses Using the Three-Cornered Hat Method

The Three-Cornered Hat (3CH) method for estimating random errors of multiple independent data sets, 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 (RO), to other data sets (such as radiosondes or model analyses or reanalyses, 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. These results can be used for diagnosing the errors and improving the accuracy of all the data sets, as well as providing useful information for operational numerical weather prediction modeling centers.

In this talk we present a brief summary of the three-cornered hat (3CH) method and 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 data set co-location interpolations.

We show a few examples of error estimates of temperature, specific humidity and refractivity for selected data sets, including COSMIC-1, COSMIC-2 (launched June 25, 2019), radiosondes, ECMWF and GFS forecasts, and a number of reanalyses, including ERA-Interim, ERA5, JRA-55, MERRA, MERRA-2, 20CR, and ERA-20C.

We show that different combinations of the 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 most of the data sets are small and the 3CH method yields realistic vertical profiles of error estimates. The estimated error variances of the ERA-Interim and ERA5 data sets are generally the smallest, a reasonable result considering the excellent model and data assimilation system and assimilation of high-quality observations.

References:

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

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