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Abstract This study investigates how entrainment’s diluting effect on cumulonimbus updraft buoyancy is affected by the temperature of the troposphere, which is expected to increase by the end of the century. A parcel model framework is constructed that allows for independent variations in the temperature (T), the entrainment rateε, the free-tropospheric relative humidity (RH), and the convective available potential energy (CAPE). Using this framework, dilution of buoyancy is evaluated withTand RH independently varied and with CAPE either held constant or increased with temperature. When CAPE is held constant, buoyancy decreases asTincreases, with parcels in warmer environments realizing substantially smaller fractions of their CAPE as kinetic energy (KE). This occurs because the increased moisture difference between an updraft and its surroundings at warmer temperatures drives greater updraft dilution. Similar results are found in midlatitude and tropical conditions when CAPE is increased with temperature. With the expected 6%–7% increase in CAPE per kelvin of warming, KE only increases at 2%–4% K⁻¹in narrow updrafts but tracks more closely with CAPE at 4%–6% in wider updrafts. Interestingly, the rate of increase in the KE withTbecomes larger than that of CAPE when the later quantity increases at more than 10% K⁻¹. These findings emphasize the importance of considering entrainment in studies of moist convection’s response to climate change, as the entrainment-driven dilution of buoyancy may partially counteract the influence of increases in CAPE on updraft intensity. Significance StatementCumulonimbus clouds mix air with their surrounding environment through a process called entrainment, which controls how efficiently environmental energy is converted into upward speed in thunderstorm updrafts. Our research shows that warmer temperatures will exacerbate the moisture difference between cumulonimbus updrafts and their surroundings, leading to greater mixing and less efficient conversion of environmental energy into updraft speeds. This effect should be considered in future research that investigates how climate change will affect cumulonimbus clouds. 

Abstract Are the results of aerosol invigoration studies that neglect entrainment valid for diluted deep convective clouds? We address this question by applying an entraining parcel model to soundings from tropical and midlatitude convective environments, wherein pollution is assumed to increase parcel condensate retention. Invigoration of 5%–10% and <2% is possible in undiluted tropical and midlatitude parcels respectively when freezing is rapid. This occurs because the positive buoyancy contribution from freezing is larger than the negative buoyancy contribution from condensate loading, leading to positive net condensate contribution to buoyancy. However, aerosol‐induced weakening is more likely when realistic entrainment rates occur because water losses from entrainment more substantially reduce the latent heating relative to the loading contribution. This leads to larger net negative buoyancy contribution from condensates in polluted than in clean entraining parcels. Our results demonstrate that accounting for entrainment is critical in conceptual models of aerosol indirect effects in deep convection. 

Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm-relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocityw_maxin an updraft. Hence, these formulas are evaluated usingw_maxfrom past numerical modeling studies. Both of the new formulas improve predictions ofw_maxsubstantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance ofbyw_max, and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. Significance StatementSubstantial mixing occurs between the upward-moving air currents in thunderstorms (updrafts) and the surrounding comparatively dry environmental air, through a process called entrainment. Entrainment controls thunderstorm intensity via its diluting effect on the buoyancy of air within updrafts. A challenge to representing entrainment in forecasting and predictions of the intensity of updrafts in future climates is to determine how much entrainment will occur in a given thunderstorm environment without a computationally expensive high-resolution simulation. To address this gap, this article derives a new formula that computes entrainment from the properties of a single environmental profile. This formula is shown to predict updraft vertical velocity more accurately than past diagnostics, and can be used in forecasting and climate prediction to improve predictions of thunderstorm behavior and impacts.