Impact of the Digital Filter as a Weak Constraint in the Preoperational 4DVAR Assimilation System of Météo-France

Abstract

In this paper, a weak constraint formulation of the digital filter based on the Dolph–Chebyshev window is introduced in a preoperational version of the 4DVAR analysis of Météo-France. The constraint is imposed only on the analysis increments to damp spurious fast oscillations associated with gravity–inertia waves. In the incremental formulation of 4DVAR, the analysis increments are obtained from a global model at a uniform low resolution with a simplified set of physical parameterizations, while the high-resolution forecast is obtained with a model that uses a variable-resolution grid having a higher resolution over France and the complete set of physical parameterizations. Both models have the same vertical resolution. In a set of preliminary experiments using the same background field and the same set of observations, it is shown that the weak constraint imposed only on the low-resolution increments manages to control efficiently the emergence of fast oscillations in the resulting high-resolution forecast while maintaining a closer fit to the observations than is possible if the digital filter initialization is applied externally on the final analysis increments. It is also shown that this weak constraint does not add any significant computer cost to the 4DVAR analysis. Finally, 4DVAR has been cycled over a period of 2 weeks and the results show that, compared to 3DVAR, the initial dynamical imbalances 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.