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Estimating observation and model error variances using multiple data sets

Abstract. In this paper we show how multiple data sets, including observations and
models, can be combined using the “three-cornered hat” (3CH) method to
estimate vertical profiles of the errors of each system. Using data from
2007, we estimate the error variances of radio occultation (RO), radiosondes,
ERA-Interim, and Global Forecast System (GFS) model data sets at four radiosonde locations in the
tropics and subtropics. A key assumption is the neglect of error covariances
among the different data sets, and we examine the consequences of this
assumption on the resulting error estimates. Our results show that different
combinations of the four data sets yield similar relative and specific
humidity, temperature, and refractivity error variance profiles at the four
stations, 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 ∼ 100 km.
