Abstract: To quantify the turbulent transport at gray zone length scales between 1 and 10 km the Lagrangian evolution of the CONSTRAIN cold air outbreak (CAO) case was simulated with seven large eddy models. The case is characterized by rather large latent and sensible heat fluxes, and a rapid deepening rate of the boundary layer. In some models the entrainment velocity exceeds 4 cm/s. A significant fraction of this growth is attributed to a strong longwave radiative cooling of the inversion layer. The…