Scale-dependent background-error covariance localisation

A new approach is presented and evaluated for efficiently applying scale-dependent spatial localisation to ensemble background-error covariances within an ensemble-variational data assimilation system. The approach is primarily motivated by the requirements of future data assimilation systems for global numerical weather prediction that will be capable of resolving the convective scale. Such systems must estimate the global and synoptic scales at least as well as current global systems while also effectively making use of information from frequent and spatially dense observation networks to constrain convective-scale features. Scale-dependent covariance localisation allows a wider range of scales to be efficiently estimated while simultaneously assimilating all available observations. In the context of an idealised numerical experiment, it is shown that using scale-dependent localisation produces an improved ensemble-based estimate of spatially varying covariances as compared with standard spatial localisation. When applied to an ensemble of Arctic sea-ice concentration, it is demonstrated that strong spatial gradients in the relative contribution of different spatial scales in the ensemble covariances result in strong spatial variations in the overall amount of spatial localisation. This feature is qualitatively similar to what might be expected when applying an adaptive localisation approach that estimates a spatially varying localisation function from the ensemble itself. When compared with standard spatial localisation, scale-dependent localisation also results in a lower analysis error for sea-ice concentration over all spatial scales.