Formulation and use of 3D‐hybrid and 4D‐hybrid ensemble covariances in the Météo‐France global data assimilation system

Abstract The global data assimilation (DA) system at Météo‐France is currently based on a 4D‐Var formulation relying on wavelet‐based 3D background‐error covariances. These covariances are specified at the beginning of the DA window and are evolved implicitly in the DA window through tangent linear and adjoint model integrations. Further research and development steps on data assimilation at Météo‐France are conducted in the framework of the Object‐Oriented Prediction System (OOPS), which is developed in collaboration with the European Centre for Medium‐Range Weather Forecasts (ECMWF). For instance, 3D background‐error covariances can be made hybrid through a linear combination between wavelet‐based covariances and ensemble‐based covariances that are filtered through spatial localisation. This allows covariances to be made more anisotropic in a flow‐dependent way, and implementation of this hybridation in the OOPS framework is shown to have general positive impacts on the forecast quality. This 3D‐hybrid approach can also be extended to a 4D‐hybrid approach in the OOPS framework: this relies on a linear combination between 4D ensemble covariances on the one hand and 4D linearly propagated covariances on the other hand, corresponding to initial covariances that are evolved more explicitly by tangent linear and adjoint versions of the model. This provides a unifying framework for implementations of DA schemes that correspond to 4DEnVar, 4D‐Var, and new 4D‐hybrid formulations. This is thus considered as a novel way to combine the respective attractive features of 4D‐Var and 4DEnVar approaches, leading in particular to a new 4D‐hybrid formulation of 4DEnVar. Its properties and implementation in the OOPS framework are presented, and first experimental results show that this new formulation of 4DEnVar is competitive with 4D‐Var, in relation with the improved hybridisation.