Use of an OSSE to evaluate background error covariances estimated by the "NMC method"

The "NMC method" has been proved useful for prescribing approximate background error covariances required by variational data assimilation systems. It begins by determining covariances of differences between 48 and 24-hour forecasts valid at the same time. Since these are not expected to characterize 6-hour forecasts, the statistics are rescaled in a tuning procedure. Here, these differences are computed in the context of an observing system simulation experiment (OSSE). Covariances of the true background errors are also calculated by exploiting the availability of the simulated truth in the OSSE. Corresponding statistics of the two data sets are then compared to determine how similar the statistics are and what kind of rescaling would be required to make them so.

Preliminary results have been produced for a global OSSE assimilating most of the observations used operationally during July-August 2011. Examination has been restricted to the atmospheric levels below 100 hPa. Ratios of the variances of background error versus those for 48 minus 24-hour forecasts vary between 0.2 near the extra-tropical tropopause and 2 near the surface in the tropics. Vertical correlation lengths are generally shorter for the background errors, especially for the wind in the extra-tropics, where they are half those of the corresponding forecast differences. Structures of the leading principal components of the covariances in the vertical direction are very similar for the forecast differences and corresponding errors but the explained variances differ. The leading PCs for wind are roughly barotropic through most of the troposphere. Horizontal correlations of the extra-tropical wind are 70% longer for the forecast differences. This is consistent with the change of vertical scale that occurs as revealed by the evolution of singular vectors. For tropical temperature, however, the change of horizontal scale is reversed. In the future we will attempt to use these results to provide a new background error covariance matrix to test within the OSSE and for an assimilation of real observations.