Heterogeneous convective-scale background error covariances with the inclusion of hydrometeor variables

Convective scale models used in NWP nowadays include detailed realistic parametrisation for the representation of cloud and precipitation processes. They however still lack advanced data assimilation schemes able to efficiently use observations to initialize hydrometeor fields. This challenging task may benefit from a better understanding of the statistical structure of background errors in precipitating areas for both traditional and hydrometeor variables, which is the goal of this study. A special binning has been devised to compute separate background error covariances matrices for precipitating and non-precipitating areas. This binning is based on bi-dimensional geographical masks defined by the vertical averaged rain content of the background error perturbations. The sample for computing the covariances is taken from an ensemble of short range forecasts run at 3-km resolution for the prediction of two specific cases of convective storms over the US. The covariance matrices and associated diagnostics are built on the Control Variable Transform formulation typical of variational data assimilation. The comparison especially highlights the strong coupling of specific humidity, cloud and rain content with divergence. Shorter horizontal correlations have been obtained in precipitating areas. Vertical correlations mostly reflect the cloud vertical extension due to the convective processes. The statistics for hydrometeor variables show physically meaningful auto-covariances and statistical couplings with other variables. Issues for data assimilation of radar reflectivity or more generally of observations linked to cloud and rain content with this kind of background error matrix formulation are thereon briefly discussed.