As reported previously by Hannah (JAS, 2017), we confirm the observation that the entrainment and detrainment rates calculated for the individual clouds do not correlate well with the corresponding dilution rates; that is, the rate of dilution due to entrainment cannot accurately be determined by the rate of entrainment for a cloud core due to the existence of a moist shell that mediates the turbulent mixing processes. Using these techniques, we can determine how the cloud cores are diluted and concentrated through entrainment and detrainment, and compare the dilution timescales with the traditional bulk-plume estimates of entrainment and detrainment rates. Using the shell correction method to faithfully translate the direct entrainment and detrainment rates to bulk-plume estimates, we show that the total dilution rate of the cloud core is equivalent to the traditionally-formulated entrainment rate, although the definition of entrainment in this traditional sense, however practical, remains unphysical. Based on these calculations, we find that although the entrainment rate (and dilution) of a cloud core decreases with increasing cloud size, it is not proportional to the inverse of the cloud radius, as assumed by many parameterization schemes.
These calculations also allow us to estimate the properties of entrained and detrained air (Dawe and Austin, JAS, 2011a; Moser and Lasher-Trapp, JAS, 2017), and compare them against the properties of the cloud core and its shell. We find preferential entrainment of moist air by the cloud core and weak concentration by detrainment. We also find that larger clouds exchange relatively dry air with their shells, while smaller clouds experience moderate dilution due to entrainment and weak concentration due to detrainment. The observed dilution tendencies of both shallow and deep clouds are in agreement with the individual cloud simulations of Hannah (JAS, 2017), although we observe that the properties of the moist shell are also strongly correlated with the cloud core properties. For example, we find that the shell remains consistently drier than the ascending cloud core, and that the size of the cloud core (and therefore of the shell surrounding the core) alters how entrainment and detrainment processes affect dilution of the ascending cloud.
We further examine the implications of the moist shell for turbulent momentum transport during moist convection in a large-scale atmosphere. Our direct calculations confirm other work (e.g. Jonker et al., GRL, 2008) that a simple mass-flux approximation of decomposing the atmosphere into ascending clouds and subsiding environment is unable to estimate the turbulent momentum transport by convective clouds.