# William Campbell, Naval Research Laboratory, Monterey, CA

## Accounting for Correlated Satellite Observation Error in Variational Data Assimilation

##### Coauthors

Elizabeth Satterfield and Benjamin Ruston#### Abstract:

We will show results from the inclusion of vertical (interchannel) correlation terms in the observation error covariance matrix (denoted R) for the ATMS, IASI, and CrIS instruments in the Navy’s Global 4D-Var model and data assimilation system (NAVGEM). Until recently, most operational NWP centers assumed that observation errors were uncorrelated. Typically, when observation errors are actually correlated, techniques such as thinning (discarding) or averaging data, and/or inflation of the assigned observation error variance, must be used to compensate. Such techniques are suboptimal and can be rendered unnecessary by correctly accounting for correlated error.
The vertical observation error covariance matrices estimated using the Desroziers method (Desroziers et al., 2005) and an archive of satellite data and NAVGEM model data. The results suggest lowering the error variance (diagonal of R) and introducing strong correlations (off-diagonal terms), especially in the moisture-sensitive channels. Because of the dual formulation of our data assimilation scheme, the inverse of the R matrix is not required, which has benefits both in reduced computation time and in solver convergence.
The convergence rate of the solver depends on the condition number of the R matrix derived from the Desroziers method, which can be quite large. We used a procedure that optimizes the approximation to a poorly conditioned matrix in a given norm and allows the user to choose any condition number required.
Full cycling data assimilation experiments using standard forecast metrics for two-month boreal winter and summer cases were run with approximate interchannel correlation matrices. In addition, we ran the same experiments with reduced observation error variances, which are suggested by the Desroziers diagnostic. The inclusion of correlation terms leads to statistically significant positive results vs. both ECMWF analyses and radiosondes at most levels and lead times.