A simple closure scheme for nocturnal stratocumulus is proposed. The scheme is formulated in conserved variables. Cloud fraction and cloud waste amount are diagnosed assuming a top-hat distribution for total water. Conversion of cloud water into rain water is parameterized in terms of cloud water and the incoming rain flux. Turbulence transport in the cloud layer is accounted for by a first-order vertical diffusion scheme with a profile-type diffusivity. The length scale corresponds to the thickness of the cloud layer. The turbulent velocity scale is directly related to the long wave radiative flux divergence in the cloud. Entrainment at cloud top is implicitly treated by extending the in-cloud mixing profile slightly beyond cloud top. The excess height is derived from the buoyancy frequency at cloud top and a radiative-convective velocity scale. Thes cheme is capable of simulating realistic profiles of the conserved variables and cloud parameters for a case of nocturnal stratocumulus prepared on the basis of ASTEX data.
Van Meijgaard, E., & Van Ulden, A. P. (1998). A first order mixing-condensation scheme for nocturnal stratocumulus. Atmospheric Research, 45(4), 253–273. https://doi.org/10.1016/S0169-8095(97)00080-X