A comparison of hybrid variational data assimilation methods for global NWP

Variational data assimilation methods are reviewed and compared in the Met Office global numerical weather prediction system. This supports hybrid background-error covariances which are a weighted combination of modelled static climatological covariances with covariances calculated from a current ensemble of forecasts, in both three- and four-dimensional methods. For the latter, we compare the use of linear and adjoint models (hybrid-4DVar) with the direct use of ensemble forecast trajectories (hybrid-4DEnVar). Earlier studies had shown that hybrid-4DVar outperforms hybrid-4DEnVar, and 4DVar outperforms 3DVar. Improvements in the processing of ensemble covariances and computer enhancements mean we are now able to explore these comparisons for the full range of hybrid weights. We find that, using our operational 44-member ensemble, the static covariance is still beneficial in hybrid-4DVar, so that it significantly outperforms hybrid-4DEnVar. In schemes not using linear and adjoint models, the static covariance is less beneficial. It is shown that the time-propagated static covariance is the main cause of the better performance of 4DVar; when using pure ensemble covariances, 4DVar and 4DEnVar show similar skill. These results are consistent with nonlinear dynamics theory about assimilation in the unstable subspace.