The simple, commonly used turbulence closure schemes for the Atmospheric Boundary Layer (ABL) are those using equations for the turbulent kinetic energy (TKE) and a turbulent length scale. The length scale equation can either be diagonstic or prognostic and is often in the form of an equation for the TKE dissipation. These models are applied to simulate neutral, nocturnal and diurnal cycle situations in one-dimensional ABLs. There are problems with the robustness of several models. Adjustmens to limit the ABL depth are necessary in several models. Results obtained with the models are compared and discussed.