• ensemble data assimilation;
  • background error variances;
  • flow dependency;
  • a posteriori diagnostics;
  • model error;
  • multiplicative inflation


Since July 2008, a variational ensemble data assimilation system has been used operationally at Météo-France to provide background error variances ‘of the day’ to the operational 4D-Var assimilation of the global Arpège model. The current ensemble is run in a perfect model framework and estimated variances are inflated ‘offline’ (i.e. after the ensemble has been completed) to account for model errors. The inflation coefficient is tuned according to a posteriori diagnostics relative to the minimum of the cost function. In this study, the ‘offline’ variance inflation is replaced by an ‘online’ multiplicative inflation of 6 h forecast perturbations after each step of 6 h model integration. This allows the inflation information to be accounted for in the production of background perturbations with realistic amplitudes for the perturbed analysis steps.

In the case of a perfect model approach, background error standard deviations are underestimated by a factor of approximately two. When using online inflation to avoid this kind of mismatch, background perturbations after 6 h of model integration are inflated by around 10%. Examination of error spectra and of standard deviation maps indicates that the increase of variance is somewhat larger for synoptic scales and in data-sparse regions with dynamically active systems such as in the extratropical part of the Southern Hemisphere. Moreover, the reduction of background perturbation amplitude during the analysis step is more pronounced, especially for large-scale variables such as temperature and surface pressure.

Parallel analysis and forecast experiments indicate that the covariance estimates provided by the inflated background perturbations have a neutral to positive impact on the forecast quality, in addition to being more consistent with innovation-based estimates. Copyright © 2011 Royal Meteorological Society