[8-2]

Objective localization of ensemble covariances: theory and applications

Yann MICHEL (1), Benjamin Menetrier (2) and Thibaut Montmerle (1)

(1) Meteo-France, CNRM-GAME/GMAP, Toulouse, France
(2) NCAR, Boulder, CO, USA

Data assimilation schemes rely more and more on ensembles to estimate flow-dependent background error covariances. The ensemble size is much smaller than the number of model coordinates or the (unknown) dimension of the dynamical system. Thus, the sampled covariances suffer from sampling noise as well as rank deficiency. This sampling noise is more pronounced at long distance ranges, where spurious correlations appear. These problems are usually alleviated though localization. Most localization schemes are highly empirical and may require extensive tuning to give best performance. Moreover, the prescribed localization is quite often the same for all control variables and does not depend on space nor time.

The goal of this work is to present a theory that achieves objective estimation of localization. We first show that localizing covariances can be understood as a linear filter, for which optimality criteria may be defined. Second, we highlight that sampling noise has known statistical properties. Merging these two theories allows to compute an optimal localization that best filters out the sampling noise. The main result of this work is that it is possible to estimate the objective localization using the ensemble only.

The computation of these objective localizations is possible on every ensemble. We use it on ensembles of variationnal assimilations that are running at Meteo-France. We illustrate the dependency of vertical and horizontal localizations on the ensemble size, on the variable considered and with the vertical. Results are shown both at global scale and at convective scale with the non-hydrostatic AROME model. These diagnosed localizations may be used in future ensemble variational assimilations (EnVar) that are developed at Meteo-France to possibly replace traditional 3D/4D-Var schemes.