A Simple Parameterization for Detrainment in Shallow Cumulus

For a wide range of shallow cumulus convection cases, large-eddy simulation (LES) model results have been used to investigate lateral mixing as expressed by the fractional entrainment and fractional detrainment rates. It appears that the fractional entrainment rates show much less variation from hour to hour and case to case than the fractional detrainment rates. Therefore, in the parameterization proposed here, the fractional entrainment rates are assumed to be described as a fixed function of height, roughly following the LES results. Based on the LES results a new, more flexible parameterization for the detrainment process is developed that contains two important dependencies. First, based on cloud ensemble principles it can be understood that deeper cloud layers call for smaller detrainment rates. All current mass flux schemes ignore this cloud-height dependence, which evidently leads to large discrepancies with observed mass flux profiles. The new detrainment formulation deals with this dependence by considering the mass flux profile in a nondimensionalized way. Second, both relative humidity of the environmental air and the buoyancy excess of the updraft influence the detrainment rates and, therefore, the mass flux profiles. This influence can be taken into account by borrowing a parameter from the buoyancy-sorting concept and using it in a bulk sense. LES results show that with this bulk parameter, the effect of environmental conditions on the fractional detrainment rate can be accurately described. A simple, practical but flexible parameterization for the fractional detrainment rate is derived and evaluated in a single-column model (SCM) for three different shallow cumulus cases, which shows the clear potential of this parameterization. The proposed parameterization is an attractive and more robust alternative for existing, more complex, buoyancy-sorting-based mixing schemes, and can be easily incorporated in current mass flux schemes.