A Simple Parameterization for Detrainment in Shallow Cumulus

Abstract

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-sortingbased mixing schemes, and can be easily incorporated in current mass flux schemes.

Analytical expressions for entrainment and detrainment in cumulus convection

“…Figure 2 reveals that it is only the massive detrainment that regulates the shape of the cloud layer mass flux profile and consequently determines primarily where the updraught properties are deposited in the environment. This picture is consistent with de Rooy and Siebesma (2008) who use only the detrainment to describe variations in the shape of the shallow convection mass flux profile.…”

“…Besides the depth of the cloud layer, the shape of the mass flux profile, and therewith δ, is also influenced by environmental conditions (e.g. Derbyshire et al, 2004) as well as properties of the updraught itself (de Rooy and Siebesma, 2008). The above-mentioned arguments support the approach of de Rooy and Siebesma (2008) Table I.…”

“…In shallow convection cases, the mass flux in the cloud layer will usually decrease (e.g. Siebesma and Cuijpers, 1995;de Rooy and Siebesma, 2008). Consequently, Eqs.…”

“…Because the ARM case is non-steady, it is pre-eminently suited as a thorough test of our expressions. For all cases, precipitation is turned off in the LES model (only RICO observations show some light rain) and cloud base level is defined as the height where the mass flux is at its maximum (de Rooy and Siebesma, 2008). For BOMEX and RICO the first hour is excluded for spin-up reasons.…”

“…If resulting mixtures are positively buoyant, they remain in the updraught and are part of the entrainment process while negatively buoyant mixtures are rejected from the updraught and are part of the detrainment process. A number of recently proposed shallow cumulus convection schemes (Bretherton et al, 2004;de Rooy and Siebesma, 2008;Neggers et al, 2009) are based on this buoyancy sorting concept. Finally a large number of parametrizations for and (sometimes) δ have been published that are directly or indirectly inspired on large-eddy simulation (LES) results of shallow cumulus convection (e.g.…”