Abstract. Cumulus entrainment, and its consequent dilution of buoyant cloud cores, strongly regulates the life cycle of shallow cumuli yet remains poorly understood. Herein, new insights into this problem are obtained through large-eddy simulations that systematically investigate the sensitivity of shallow-cumulus dilution to cloud-layer relative humidity (RH), cloud- and subcloud-layer depths, and continentality (i.e., the land–ocean contrast). The simulated cloud-core dilution is found to be strongly sensitive to continentality, with fractional dilution rates twice as large over the ocean as over land. Using a similarity theory based on the turbulent-kinetic-energy (TKE) budget, the reduced cloud-core dilution over land is attributed to larger cloud-base mass flux (mb), driven by stronger surface heating and subcloud turbulence. As mb increases, the fractional dilution rate must decrease to maintain energetic equilibrium. A positive sensitivity is also found to cloud-layer RH, with the core dilution increasing by 25 %–50 % for a 10 % enhancement in RH. This sensitivity is interpreted using the buoyancy-sorting hypothesis, in that mixtures of cloud and environmental air are more likely to become negatively buoyant and detrain (rather than diluting the cloud core) in drier cloud layers. By contrast, the sensitivities of (marine) shallow-cumulus dilution to cloud- and subcloud-layer depths are weak, with a 3 % decrease for a doubling for the former and a 4 % reduction in dilution for a 50 % deeper subcloud layer. These surprisingly weak sensitivities are readily explained by offsetting effects in the TKE similarity theory. Altogether, these experimental findings provide useful, though still incomplete, guidance for flow-dependent shallow-cumulus entrainment formulations in large-scale models.

A complete and quantitative understanding of cumulus entrainment remains elusive, in part due to the difficulty of directly observing cloud entrainment rates. Multiple approaches to ground‐based observational retrieval of bulk fractional entrainment rates (ε) within cumuli have been developed, such as the parcel model by Jensen and Del Genio (JDG, 2006, https://doi.org/10.1175/JCLI3722.1) and Entrainment Rate In Cumulus Algorithm (ERICA) by Wagner et al. (2013, https://doi.org/10.1175/JTECH-D-12-00187.1). In this paper, a new cumulus entrainment retrieval based on a turbulent kinetic energy (TKE) similarity theory is presented. This method estimates ε based on only the environmental and subcloud conditions. By conducting large‐eddy simulations of a range of continental and maritime shallow cumulus convection cases as Observing System Simulations Experiments, the first numerical verification of the three retrieval methods is produced. These simulations consider a broad range of shallow cumulus environments along with variations of the numerical configuration. The diagnosed ε from these simulations is found to be robustly larger in cumuli over the ocean than in cumuli over land. For continental cumuli, the experiments also reveal a diurnal cycle with increasing ε in the late afternoon. These diagnosed ε serve as the “truth” against which the pseudo‐retrieved entrainment rates from several different implementations of each retrieval are verified. Overall, the simpler JDG and TKE retrievals outperform the more sophisticated ERICA method and better capture the sensitivity to continentality. Only the TKE method reproduces the diurnal variations in ε within continental cumuli. The mean error in the ε retrievals are between 20% and 30% for the TKE and JDG methods, but 50% for ERICA.

Abstract. This second part of a numerical study on shallow-cumulus dilution focuses on the sensitivity of cloud dilution to changes in the vertical wind profile. Insights are obtained through large-eddy simulations of maritime and continental cloud fields. In these simulations, the speed of the initially uniform geostrophic wind and the strength of geostrophic vertical wind shear in the cloud and subcloud layer are varied. Increases in the cloud-layer vertical wind shear (up to 9 ms-1km-1) lead to 40 %–50 % larger cloud-core dilution rates compared to their respective unsheared counterparts. When the background wind speed, on the other hand, is enhanced by up to 10 m s−1 and subcloud-layer vertical wind shear develops or is initially prescribed, the dilution rate decreases by up to 25 %. The sensitivities of the dilution rate are linked to the updraft strength and the properties of the entrained air. Increases in the wind speed or vertical wind shear result in lower vertical velocities across all sets of experiments with stronger reductions in the cloud-layer wind shear simulation (27 %–47 %). Weaker updrafts are exposed to mixing with the drier surrounding air for a longer time period, allowing more entrainment to occur (i.e., the “core-exposure effect”). However, reduced vertical velocities, in concert with increased cloud-layer turbulence, also assist in widening the humid shell surrounding the cloud cores, leading to entrainment of more humid air (i.e., the “core–shell dilution effect”). In the experiments with cloud-layer vertical wind shear, the core-exposure effect dominates and the cloud-core dilution increases with increasing shear. Conversely, when the wind speed is increased and subcloud-layer vertical wind shear develops or is imposed, the core–shell dilution effect dominates to induce a buffering effect. The sensitivities are generally stronger in the maritime simulations, where weaker sensible heat fluxes lead to narrower, more tilted, and, therefore, more suppressed cumuli when cloud-layer shear is imposed. Moreover, in the experiments with subcloud wind shear, the weaker baseline turbulence in the maritime case allows for a larger turbulence enhancement, resulting in a widening of the transition zones between the cores and their environment, leading to the entrainment of more humid air.

We are very grateful to the two reviewers for their insightful and constructive comments, which have helped to substantially improve our analysis and physical interpretation. In the following, reviewer comments are written in black, author responses are written in blue, and passages of modified text in the manuscript are written in red. Referee 1 General comments: This paper discusses the sensitivity of dilution of shallow convec-C1 ACPD Interactive comment Printer-friendly version Discussion paper tion as a function of large scale state. While the paper is not unique, it does yield another piece in the puzzle of figuring out how to parameterize entrainment. The paper is generally well written, but sometimes also a little descriptive, with the theoretical interpretation mainly hypothesized. To enhance the paper, I have the following suggestions. I realize that not all of them may be feasible within the scope of this paper. We thank the reviewer for their insightful and valuable comments.

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