When you have a Data Assimilation Scheme implemented, e.g. a Variational DAS, you can simulate the time evolution of information thanks to this trick
This technics has been used to simulate the information's evolution with 4D-Var.
Dynamics of length-scale (in km) obtained thanks to the emulation of information's dynamics in 4D-Var DAS:
From the 20/01/2005 06 UTC to the 22/01/2005 06 UTC