Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Meteo-France

In this paper, a weak constraint formulation of the digital filter based on the Dolph-Chebyshev window is introduced in a preoperational version of th e 4DVAR analysis of Meteo-France. The constraint is imposed only on the ana lysis increments to damp spurious fast oscillations associated with gravity -inertia waves. In the incremental formulation of 4DVAR, the analysis incre ments are obtained from a global model at a uniform low resolution with a s implified set of physical parameterizations, while the high-resolution fore cast is obtained with a model that uses a variable-resolution grid having a higher resolution over France and the complete set of physical parameteriz ations. Both models have the same vertical resolution. In a set of prelimin ary experiments using the same background field and the same set of observa tions, it is shown that the weak constraint imposed only on the low-resolut ion increments manages to control efficiently the emergence of fast oscilla tions in the resulting high-resolution forecast while maintaining a closer fit to the observations than is possible if the digital filter initializati on is applied externally on the final analysis increments. It is also shown that this weak constraint does not add any significant computer cost to th e 4DVAR analysis. Finally, 4DVAR has been cycled over a period of 2 weeks a nd the results show that, compared to 3DVAR, the initial dynamical imbalanc es are significantly less in 4DVAR even if no constraint is imposed at all. However, it has been noted that the innovation statistics show a positive impact when a constraint is applied.