Improving ensemble covariances in hybrid variational data assimilation without increasing ensemble size

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Abstract
Increasing the size of the ensemble used in hybrid‐variational assimilation methods has been shown to be beneficial, but is computationally expensive. This work sets out to see whether similar improvements can be obtained from a smaller ensemble by better estimation of ensemble covariances. Methods for improving these are described and illustrated using a toy model. The optimal settings depend on the ensemble size, the criterion used to measure error and the errors in ensemble generation. A hybrid covariance, filtered by spectral localization using wavebands and scale‐dependent spatial localization, is shown to perform well and robustly.In the cycled ensemble data‐assimilation scheme used for numerical weather prediction (NWP), another method of increasing the effective ensemble size in covariance estimates is the use of time‐lagged and time‐shifted perturbations. This is demonstrated to be effective in the Met Office's hybrid‐4DEnVar system, both on its own and with waveband and scale‐dependent localization. The best such combination performs nearly as well as an increase in ensemble size from 44 to 200.

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