'Balance' and Ensemble Localization
Bannister, R.N.1; Migliorini, S.2; Baker, L.H.3; Rudd, A.C.3

Ensemble data assimilation would help to bypass many of the problems encountered in variational data assimilation (namely the need to model background error covariances) were it not for the sampling errors that inevitably arise from the application of a finite number of ensemble members. Sampling errors lead to rank deficiency (and hence poor conditioning) of the data assimilation problem and can be seen as artifacts in the background error structure functions derived from the finite ensemble. Methods, like covariance localization, have been used for some time to depress these artifacts. Although they have been reasonably effective at this, they do have the negative side effect of affecting the 'balance' properties (hydrostatic, geostrophic, anelastic) of the ensemble. These properties are valuable in order to minimize initialization problems in post-assimilation forecasts and so localization methods are sought that preserve (as far as possible) the degree of balance.

This work reports on a range of balance diagnostics found from an ensemble of Met Office high-resolution forecasts with and without the application of the Schur-product style localization. Of special interest is the investigation of new flow-adaptive localization methods introduced by Bishop and Hodyss in 2007 and 2009 whose effect on balance is not well studied.