The 4-D Var method is 2-sided, like a smoother.  To do the backwards pass, you need an adjoint.  But since one of the big advantages of the EnKF is not needing an adjoint, you might as well use the varational method at that point.  There _is_ the fixed-lag smoother; this does not require an adjoint since it always moves forward in time, but requires more storage to store multiple time steps in the state.