Estimating optimal localization for sampled background-error covariances of hydrometeor variables

Destouches, Mayeul ; Montmerle, Thibaut ; Michel, Yann ; Ménétrier, Benjamin

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<p align=justify>Kilometre-scale numerical weather prediction addresses the challenge of forecasting accurately clouds and precipitation. Ensemble-based data assimilation methods make use of background-error covariances that are sampled from an ensemble of forecasts. These methods can be considered in order to include hydrometeor variables and their flow-dependent error covariances in the data assimilation system. Yet, because of limited ensemble size, rank deficiency of the resulting covariances and sampling noise occur, which can be mitigated by a localization procedure. In order to optimally localize covariances for hydrometeor variables, previous work by the authors has been extended. This approach estimates localization as a linear filtering on covariances, optimal in the sense of minimizing sampling noise. The zero-variance and the high spatial variability issues met with hydrometeor variables are addressed by using an improved method for spatial sampling, based on geographical masks. Diagnosed optimal horizontal localization lengths appear to be much shorter for hydrometeors than for other classical thermodynamic variables. Conversely, we report optimal vertical localization to be very broad for precipitating species. Great variability between different meteorological situations has also been noticed, which reflects the high flow dependency of hydrometeor forecast errors. This suggests that ensemble-based data assimilation schemes that consider hydrometeors as control variables should adopt more refined localization schemes than the common "one-size-fits-all" approach.</p>
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