This study focuses on diagnosing variations of background-error covariances between precipitating and non-precipitating areas, and on presenting a heterogeneous covariance formulation to represent these variations in a variational framework. The context of this work is the assimilation of observations linked to precipitation (radar data especially) in the AROME model, which has been running operationally at Météo-France since December 2008 over French territory with a 2.5 km horizontal resolution. This system uses multivariate background-error covariances deduced from an ensemble-based method. At first, such statistics have been computed for 17 precipitating cases using an ensemble of AROME forecasts coupled with an ALADIN ensemble assimilation. Results, obtained from 3 h forecast differences performed separately for non-precipitating and precipitating columns, display large discrepancies in error variances, correlation lengths and the correlations between humidity, temperature and divergence errors.
These results argue in favour of including heterogeneous background-error covariances in AROME incremental 3D-Var, allowing different covariances to be used in regions with different meteorological patterns. Such a method enables us to get increments more adequately structured in those regions, and thus potentially to make better use of observations in a data assimilation system. The implementation consists of expressing the analysis increment as the sum of two terms, one for precipitating areas and the other for non-precipitating areas, making use of a mask that defines rainy regions. This implies a doubling in the size of the control variable and of the gradient of the cost function. The feasibility of this method is shown through experiments with four isolated observations. Copyright © 2010 Royal Meteorological Society