Several different reconditioning methods are explored in our paper (Campbell et al., 2017). They can be used independently from, or in conjunction with the new method outlined here. We identify sets of channels that have very high mutual error correlation from the Desroziers-derived error matrices. The high error correlation means that there is significantly less information that can be extracted, and that what is there is significantly more difficult to extract.
In tests with IASI and CrIS in our Hybrid 4DVar DA system (NAVGEM), we replaced sets of channels with high error correlations by a single channel from each set. The resulting condition number of the error covariance matrices was significantly reduced, so the solver converged faster, and there was no negative impact on forecasts. The forecasts were significantly better than the control, which used a diagonal R with inflated variances.