Variational data assimilation is an advanced technique to provide correct and high quality initial fields for the numerical model. Digital filter is not restricted to initialization; it may also be implemented as a weak constraint penalizing the analysis towards a balanced state in a preoperational 4D-Var system. The constraint is imposed only on the analysis increments to damp spurious fast oscillations associated with gravity–inertia waves. The influence of DFI as a weak constraint on 4D-Var forecast is assessed by assimilation experiments with the recently occurring severe snow weather. It is shown that the weak constraint imposed only on the increments manages to control efficiently the emergence of fast oscillations in the resulting forecast while maintaining a closer fitting to the observations.