LETKF minimizes the errors of the day and thus provides an excellent first guess to the 3D-Var analysis
3DVar with the background provided from LETKF (forecast mean)
3DVar
3DVar with the background of the first 50 days provided from LETKF
LETKF
We conclude from this experiment that the errors of the day (and not just ensemble averaging) are important in LETKF and 3D-Var.