Comment on gmd-2022-3

Abstract

Hybrid ensemble-variational data assimilation (DA) methods have gained significant traction in recent years. These methods aim to alleviate the limitations and maximise the advantages offered by ensemble or variational methods. In this article, hybrid ensemble-variational DA is introduced to a simplified non-hydrostatic convective-scale atmospheric "toy model", the ABC model, and its corresponding existing variational framework, conveniently termed the ABC-DA system. The hybrid ensemble-variational DA algorithm is developed based on the alpha control variable approach, often used in numerical weather prediction. Aspects of the algorithm such as localisation (used to mitigate sampling error caused by finite ensemble sizes) and weighting parameters (used to weight the ensemble and climatological contributions to the background error covariance matrix) are implemented. To produce the flow-dependent error modes (ensemble perturbations) for the ensemble-variational DA algorithm, ensemble systems are also designed for the ABC model, which is run alongside the hybrid DA system. A random field perturbations method is used to generate an initial ensemble, which is then propagated using either the ensemble bred vectors method, or an approximate ensemble square-root filter method. This setup allows the ensemble to be centred on the hybrid control analysis. Visualisation software has been developed to focus on the diagnosis of the ensemble system. To demonstrate the hybrid ensemble-variational DA in the ABC-DA system, sensitivity tests using observing system simulation experiments are conducted within a tropical framework, which has not yet been explored in the ABC-DA system. A 30-member ensemble was used to generate the error modes for the experiments. In general, the best performing configuration (with respect to the "truth") for the hybrid ensemble-variational DA system used an 80 %/20 % weighting on the ensemble-derived/climatological background error covariance matrix contributions. For the horizontal wind variables though, full weight on the ensemble-derived background error covariance matrix (100 %/0 %) resulted in the smallest cycle-averaged analysis root-mean-square errors, mainly due to large errors in the meridional wind field when contributions from the climatological background error covariance matrix were involved, possibly related to a sub-optimal background error covariance model. The ensemble bred vectors method propagated a healthy-looking DA-centred ensemble without bimodalities or evidence of filter collapse. For some variables though, the ensemble was under-dispersive, but for other variables, the ensemble spread approximately matched the corresponding root-mean-square errors. Reducing the number of ensemble members led to slightly larger errors across all variables, due to the introduction of larger sampling errors into the system.