Diagnosis and formulation of heterogeneous background-error covariances at the mesoscale

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 Meteo-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 (C) 2010 Royal Meteorological Society