Local ensemble assimilation scheme with global constraints and conservation

Ensemble assimilation schemes applied in their original, global formulation respect linear conservation properties if the ensemble perturbations are set up accordingly. For realistic ocean systems, only a relatively small number of ensemble members can be calculated. A localization of the ensemble increment is therefore necessary to filter out spurious long-range correlations. The conservation of the global properties will be lost if the assimilation is performed locally, since the conservation requires a coupling between all model grid points which is removed by the localization. The distribution of ocean observations is often highly inhomogeneous. Systematic errors of the observed parts of the ocean state can lead to spurious adjustment of the non-observed parts via data assimilation and thus to a spurious increase or decrease in long-term simulations of global properties which should be conserved. In this paper, we propose a local assimilation scheme (with different variants and assumptions) which can satisfy global conservation properties. The proposed scheme can also be used for non-local observation operators. Different variants of the proposed scheme are tested in an idealized model and compared to the traditional covariance localization with an ad-hoc step enforcing conservation. It is shown that the inclusion of the conservation property reduces the total RMS error and that the presented stochastic and deterministic schemes avoiding error space rotation provide better results than the traditional covariance localization.