Variable-dependent and selective multivariate localization for ensemble-variational data assimilation in the tropics

Two aspects of ensemble localization for data assimilation are explored using the simplified non-hydrostatic ABC model in a tropical setting. The first aspect (i) is the ability to prescribe different localization length-scales for different variables (variable-dependent localization). The second aspect (ii) is the ability to control (i.e., to knock-out by localization) multi-variate error covariances (selective multivariate localization). These aspects are explored in order to shed light on the cross-covariances that are important in the tropics and to help determine the most appropriate localization configuration for a tropical ensemble-variational (EnVar) data assimilation system. Two localization schemes are implemented within the EnVar framework to achieve (i) and (ii). One is called the isolated variable-dependent localization scheme (IVDL) and the other is called the symmetric variable-dependent localization (SVDL) scheme. Multi-cycle Observation System Simulation Experiments are conducted using IVDL or SVDL mainly with a 100-member ensemble, although other ensemble sizes are studied (between 10 and 1000 members). The results reveal that selective multivariate localization can reduce the cycle-averaged root-mean-square error (RMSE) in the experiments when cross-covariances associated with hydrostatic balance are retained and when zonal wind/mass error cross-covariances are knocked-out. When variable-dependent horizontal and vertical localization are incrementally introduced, the cycle-averaged RMSE is further reduced. Overall, the best performing experiment using both variable-dependent and selective multivariate localization leads to a 3-4% reduction in cycle-averaged RMSE compared to the traditional EnVar experiment. These results may inform the possible improvements to existing tropical numerical weather prediction systems which use EnVar data assimilation.