An estimate of some analysis-error statistics using the Global Modeling and Assimilation Office observing-system simulation framework

The observing-system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration (NASA), Global Modeling and Assimilation Office (GMAO) is used to estimate some characteristics of analysis error. This is possible because, within the framework, the true state of the simulated atmosphere is known and, after suitable interpolation to a common grid, can be simply differenced with the analysis to compute errors explicitly. The only assumption is that the OSSE is sufficiently realistic so that error statistics derived from it adequately describe those obtained when analyzing observations of the real atmosphere. Attention here is restricted to the troposphere during the months of July and August at 0000 and 1200 UTC using an observation data set from 2011. Analysis-error statistics presented here include geographical distributions of temporal variances, power spectra of spherical harmonics and correlations in meridional, latitudinal and vertical directions. Our most noteworthy results include the revelation through spectral analysis that only synoptic scales are well analyzed and that horizontal correlation lengths in the extratropics are short, with little vertical variation, and the dominance of rotational wind errors in contrast to divergent ones. Also examined are fractional reductions in background-error variances due to analysis of observations. These reveal that in most geographical regions throughout the troposphere, errors are reduced by analyzing observations, as intended. The reductions are typically small, however (-10% in most regions), as should be expected from consideration of the equilibration of errors implied by the Kalman-filter equations.