Physical significance of TKE penetration not scaled by the model time step ?

[jchanut]

Context

On TKE additional source term (e.g. nn_etau>0 in namzdf_tke)

Analysis

The additional TKE source term in zdftke is not scaled by the model time step:

      IF( nn_etau == 1 ) THEN           !* penetration below the mixed layer (rn_efr fraction)
         DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
            en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -gdepw(ji,jj,jk,Kmm) / htau(ji,jj) )   &
               &                                 * MAX( 0._wp, 1._wp - zice_fra(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)

As expected, this leads to a dependency of the tke profiles, hence of viscosities/diffusivities on the chosen time step. This may well be on purpose, but I have trouble to see the physical motivation behind that. I would rather have seen a kind of time scale associated with that process (in place of the surface tke fraction) and then multiplied by the time step.

Recommendation

At this point, I would like to be convinced :)