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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 Sufficient low-level storm-relative flow is a necessary ingredient for sustained supercell thunderstorms and is connected to supercell updraft width. Assuming a supercell exists, the role of low-level storm-relative flow in regulating supercells’ low-level mesocyclone intensity is less clear. One possibility considered in this article is that storm-relative flow controls mesocyclone and tornado width via its modulation of overall updraft extent. This hypothesis relies on a previously postulated positive correspondence between updraft width, mesocyclone width, and tornado width. An alternative hypothesis is that mesocyclone characteristics are primarily regulated by horizontal streamwise vorticity irrespective of storm-relative flow. A matrix of supercell simulations was analyzed to address the aforementioned hypotheses, wherein horizontal streamwise vorticity and storm-relative flow were independently varied. Among these simulations, mesocyclone width and intensity were strongly correlated with horizontal streamwise vorticity, and comparatively weakly correlated with storm-relative flow, supporting the second hypothesis. Accompanying theory and trajectory analysis offers the physical explanation that, when storm-relative flow is large and updrafts are wide, vertically tilted streamwise vorticity is projected over a wider area but with a lesser average magnitude than when these parameters are small. These factors partially offset one another, degrading the correspondence of storm-relative flow with updraft circulation and rotational velocity, which are the mesocyclone attributes most closely tied to tornadoes. These results refute the previously purported connections between updraft width, mesocyclone width, and tornado width, and emphasize horizontal streamwise vorticity as the primary control on low-level mesocyclones in sustained supercells. Significance Statement The intensity of a supercell thunderstorm’s low-level rotation, known as the “mesocyclone,” is thought to influence tornado likelihood. Mesocyclone intensity depends on many environmental attributes that are often correlated with one another and difficult to disentangle. This study used a large body of numerical simulations to investigate the influence of the speed of low-level air entering a supercell (storm-relative flow), the horizontal spin of the ambient air entering the thunderstorm (streamwise vorticity), and the width of the storm’s updraft. Our results suggest that the rotation of the mesocyclone in supercells is primarily influenced by streamwise vorticity, with comparatively weaker connections to storm-relative flow and updraft width. These findings provide important clarification in our scientific understanding of how a storm’s environment influences the rate of rotation of its mesocyclone, and the associated tornado threat. 

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. 

Abstract Proper prediction of the inflow layer of deep convective storms is critical for understanding their potential updraft properties and likelihood of producing severe weather. In this study, an existing forecast metric known as the effective inflow layer (EIL) is evaluated with an emphasis on its performance for supercell thunderstorms, where both buoyancy and dynamic pressure accelerations are common. A total of 15 idealized simulations with a range of realistic base states are performed. Using an array of passive fluid tracers initialized at various vertical levels, the proportion of simulated updraft core air originating from the EIL is determined. Results suggest that the EIL metric performs well in forecasting peak updraft origin height, particularly for supercell updrafts. Moreover, the EIL metric displays consistent skill across a range of updraft core definitions. The EIL has a tendency to perform better as convective available potential energy, deep-layer shear, and EIL depth are increased in the near-storm environment. Modifications to further constrain the EIL based on the most-unstable parcel height or storm-relative flow may lead to marginal improvements for the most stringent updraft core definitions. Finally, effects of the near-storm environment on low-level and peak updraft forcing and intensity are discussed. 

Abstract In supercell environments, previous authors have shown strong connections between the vertical wind shear magnitude, updraft width, and entrainment. Based on these results, it is hypothesized that the influences of entrainment-driven dilution on buoyancy and maximum updraft vertical velocity w in supercell environments are a predictable function of the vertical wind shear profile. It is also hypothesized that the influences of pressure perturbation forces on maximum updraft w are small because of a nearly complete offset between upward dynamic pressure forces and downward buoyant pressure forces. To address these hypotheses, we derive a formula for the maximum updraft w that incorporates the effects of entrainment-driven dilution on buoyancy but neglects pressure gradient forces. Solutions to this formula are compared with output from previous numerical simulations. This formula substantially improves predictions of maximum updraft w over past CAPE-derived formulas for maximum updraft w , which supports the first hypothesis. Furthermore, integrated vertical accelerations along trajectories show substantial offsets between dynamic and buoyant pressure forces, supporting the second hypothesis. It is argued that the new formula should be used in addition to CAPE-derived measures for w in forecast and research applications when accurate diagnosis of updraft speed is required. 

Abstract The relationship between storm-relative helicity (SRH) and streamwise vorticity ωs is frequently invoked to explain the often robust connections between effective inflow layer (EIL) SRH and various supercell updraft properties. However, the definition of SRH also contains storm-relative (SR) flow, and the separate influences of SR flow and ωs on updraft dynamics are therefore convolved when SRH is used as a diagnostic tool. To clarify this issue, proximity soundings and numerical experiments are used to disentangle the separate influences of EIL SR flow and ωs on supercell updraft characteristics. Our results suggest that the magnitude of EIL ωs has little influence on whether supercellular storm mode occurs. Rather, the transition from nonsupercellular to supercellular storm mode is largely modulated by the magnitude of EIL SR flow. Furthermore, many updraft attributes such as updraft width, maximum vertical velocity, vertical mass flux at all levels, and maximum vertical vorticity at all levels are largely determined by EIL SR flow. For a constant EIL SR flow, storms with large EIL ωs have stronger low-level net rotation and vertical velocities, which affirms previously established connections between ωs and tornadogenesis. EIL ωs also influences storms’ precipitation and cold-pool patterns. Vertical nonlinear dynamic pressure acceleration (NLDPA) is larger at low levels when EIL ωs is large, but differences in NLDPA aloft become uncorrelated with EIL ωs because storms’ midlevel dynamic pressure perturbations are substantially influenced by the tilting of midlevel vorticity. Our results emphasize the importance of considering EIL SR flow in addition to EIL SRH in the research and forecasting of supercell properties. 

Abstract Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when nonequilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for nonequilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent. 

Abstract This study synthesizes the results of 13 high-resolution simulations of deep convective updrafts forming over idealized terrain using environments observed during the RELAMPAGO and CACTI field projects. Using composite soundings from multiple observed cases, and variations upon them, we explore the sensitivity of updraft properties (e.g., size, buoyancy, and vertical pressure gradient forces) to influences of environmental relative humidity, wind shear, and mesoscale orographic forcing that support or suppress deep convection initiation (CI). Emphasis is placed on differentiating physical processes affecting the development of updrafts (e.g., entrainment-driven dilution of updrafts) in environments typifying observed successful and null (i.e., no CI despite affirmative operational forecasts) CI events. Thermally induced mesoscale orographic lift favors the production of deep updrafts originating from ∼1- to 2-km-wide boundary layer thermals. Simulations without terrain forcing required much larger (∼5-km-wide) thermals to yield precipitating convection. CI outcome was quite sensitive to environmental relative humidity; updrafts with increased buoyancy, depth, and intensity thrived in otherwise inhospitable environments by simply increasing the free-tropospheric relative humidity. This implicates the entrainment of free-tropospheric air into updrafts as a prominent governor of CI, consistent with previous studies. Sensitivity of CI to the environmental wind is manifested by 1) low-level flow affecting the strength and depth of mesoscale convergence along the terrain, and 2) clouds encountering updraft-suppressing pressure gradient forces while interacting with vertical wind shear in the free troposphere. Among the ensemble of thermals occurring in each simulation, the widest deep updrafts in each simulation were the most sensitive to environmental influences. 

Abstract The response of severe local storms to environmental evolution across the early evening transition (EET) remains a forecasting challenge, particularly within the context of the Southeast U.S. storm climatology, which includes the increased presence of low-CAPE environments and tornadic nonsupercell modes. To disentangle these complex environmental interactions, Southeast severe convective reports spanning 2003–18 are temporally binned relative to local sunset. Sounding-derived data corresponding to each report are used to characterize how the near-storm environment evolves across the EET, and whether these changes influence the mode, frequency, and tornadic likelihood of their associated storms. High-shear, high-CAPE (HSHC) environments are contrasted with high-shear, low-CAPE (HSLC) environments to highlight physical processes governing storm maintenance and tornadogenesis in the absence of large instability. Last, statistical analysis is performed to determine which aspects of the near-storm environment most effectively discriminate between tornadic (or significantly tornadic) and nontornadic storms toward constructing new sounding-derived forecast guidance parameters for multiple modal and environmental combinations. Results indicate that HSLC environments evolve differently than HSHC environments, particularly for nonsupercell (e.g., quasi-linear convective system) modes. These low-CAPE environments sustain higher values of low-level shear and storm-relative helicity (SRH) and destabilize postsunset—potentially compensating for minimal buoyancy. Furthermore, the existence of HSLC storm environments presunset increases the likelihood of nonsupercellular tornadoes postsunset. Existing forecast guidance metrics such as the significant tornado parameter (STP) remain the most skillful predictors of HSHC tornadoes. However, HSLC tornado prediction can be improved by considering variables like precipitable water, downdraft CAPE, and effective inflow base. 

This research investigates a hypothesis posed by previous authors, which argues that the helical nature of the flow in supercell updrafts makes them more resistant to entrainment than nonsupercellular updrafts because of the suppressed turbulence in purely helical flows. It was further supposed that this entrainment resistance contributes to the steadiness and longevity of supercell updrafts. A series of idealized large-eddy simulations were run to address this idea, wherein the deep-layer shear and hodograph shape were varied, resulting in supercells in the strongly sheared runs, nonsupercells in the weakly sheared runs, and variations in the percentage of streamwise vorticity in updrafts among runs. Fourier energy spectrum analyses show well-developed inertial subranges in all simulations, which suggests that the percentages of streamwise and crosswise vorticity have little effect on turbulence in convective environments. Additional analyses find little evidence of updraft-scale centrifugally stable flow within updrafts, which has also been hypothesized to limit horizontal mass flux across supercell updrafts. Results suggest that supercells do have smaller fractional entrainment rates than nonsupercells, but these differences are consistent with theoretical dependencies of entrainment on updraft width, and with supercells being wider than nonsupercells. Thus, while supercells do experience reduced fractional entrainment rates and entrainment-driven dilution, this advantage is primarily attributable to increased supercell updraft width relative to ordinary convection, and has little to do with updraft helicity and rotation.