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  1. Abstract

    Turbulent fluctuations of scalar and velocity fields are critical for cloud microphysical processes, e.g., droplet activation and size distribution evolution, and can therefore influence cloud radiative forcing and precipitation formation. Lagrangian and Eulerian water vapor, temperature, and supersaturation statistics are investigated in direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in the Pi Convection Cloud Chamber to provide a foundation for parameterizing subgrid-scale fluctuations in atmospheric models. A subgrid model for water vapor and temperature variances and covariance and supersaturation variance is proposed, valid for both clear and cloudy conditions. Evaluation of phase change contributions through an a priori test using DNS data shows good performance of the model. Supersaturation is a nonlinear function of temperature and water vapor, and relative external fluxes of water vapor and heat (e.g., during entrainment-mixing and phase change) influence turbulent supersaturation fluctuations. Although supersaturation has autocorrelation and structure functions similar to the independent scalars (temperature and water vapor), the autocorrelation time scale of supersaturation differs. Relative scalar fluxes in DNS without cloud make supersaturation PDFs less skewed than the adiabatic case, where they are highly negatively skewed. However, droplet condensation changes the PDF shape response: it becomes positively skewed for the adiabatic case and negatively skewed when the sidewall relative fluxes are large. Condensation also increases correlations between water vapor and temperature in the presence of relative scalar fluxes but decreases correlations for the adiabatic case. These changes in correlation suppress supersaturation variability for the nonadiabatic cases and increase it for the adiabatic case. Implications of this work for subgrid microphysics modeling using a Lagrangian stochastic scheme are also discussed.

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  2. 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 velocitywmaxin an updraft. Hence, these formulas are evaluated usingwmaxfrom past numerical modeling studies. Both of the new formulas improve predictions ofwmaxsubstantially 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 ofbywmax, 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 Statement

    Substantial 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.

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  3. Abstract

    A state‐of‐the‐art Lagrangian microphysics scheme is used in a large‐eddy simulation to investigate the stratocumulus transition from closed to open cell structure. Processes controlling precipitation development, which is a key to the transition, are analyzed by leveraging unique benefits of Lagrangian microphysics, particularly the ability to track computational drops in the flow. Sufficient time is needed for coalescence growth of cloud drops to drizzle within the updraft‐downdraft cycle of large eddies. This favors broad drop size distributions (DSDs) and drizzle growth in downdrafts, where drops are typically much older than in updrafts. During the closed cell stage, mean cloud drop radius is too small, and the DSDs are too narrow, so that the timescale for coalescence is much longer than the large eddy turnover time and drizzle growth is limited. The closed‐to‐open cell transition occurs when these timescales become comparable and the precipitation flux increases sharply.

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  4. Abstract. Secondary ice production (SIP) is an important physicalphenomenon that results in an increase in the ice particle concentration and cantherefore have a significant impact on the evolution of clouds. In thisstudy, idealized simulations of a mesoscale convective system (MCS) wereconducted using a high-resolution (250 m horizontal grid spacing) mesoscalemodel and a detailed bulk microphysics scheme in order to examine theimpacts of SIP on the microphysics and dynamics of a simulated tropical MCS.The simulations were compared to airborne in situ and remote sensing observationscollected during the “High Altitude Ice Crystals – High Ice Water Content”(HAIC-HIWC) field campaign in 2015. It was found that the observed high icenumber concentration can only be simulated by models that include SIPprocesses. The inclusion of SIP processes in the microphysics scheme is crucialfor the production and maintenance of the high ice water content observed intropical convection. It was shown that SIP can enhance the strength of theexisting convective updrafts and result in the initiation of new updraftsabove the melting layer. Agreement between the simulations and observationshighlights the impacts of SIP on the maintenance of tropical MCSs in natureand the importance of including SIP parameterizations in models. 
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  5. Abstract. High ice water content (HIWC) regions in tropical deep convective clouds, composed of high concentrations of small ice crystals, were not reproduced by Weather Research and Forecasting (WRF) model simulations at 1 km horizontal grid spacing using four different bulk microphysics schemes (i.e., the WRF single‐moment 6‐class microphysics scheme (WSM6), the Morrison scheme and the Predicted Particle Properties (P3) scheme with one- and two-ice options) for conditions encountered during the High Altitude Ice Crystals (HAIC) and HIWC experiment. Instead, overestimates of radar reflectivity and underestimates of ice number concentrations were realized. To explore formation mechanisms for large numbers of small ice crystals in tropical convection, a series of quasi-idealized WRF simulations varying the model resolution, aerosol profile, and representation of secondary ice production (SIP) processes are conducted based on an observed radiosonde released at Cayenne during the HAIC-HIWC field campaign. The P3 two-ice category configuration, which has two “free” ice categories to represent all ice-phase hydrometeors, is used. Regardless of the horizontal grid spacing or aerosol profile used, without including SIP processes the model produces total ice number concentrations about 2 orders of magnitude less than observed at −10 ∘C and about an order of magnitude less than observed at −30 ∘C but slightly overestimates the total ice number concentrations at −45 ∘C. Three simulations including one of three SIP mechanisms separately (i.e., the Hallett–Mossop mechanism, fragmentation during ice–ice collisions, and shattering of freezing droplets) also do not replicate observed HIWCs, with the results of the simulation including shattering of freezing droplets most closely resembling the observations. The simulation including all three SIP processes produces HIWC regions at all temperature levels, remarkably consistent with the observations in terms of ice number concentrations and radar reflectivity, which is not replicated using the original P3 two-ice category configuration. This simulation shows that primary ice production plays a key role in generating HIWC regions at temperatures <-40 ∘C, shattering of freezing droplets dominates ice particle production in HIWC regions at temperatures between −15 and 0 ∘C during the early stage of convection, and fragmentation during ice–ice collisions dominates at temperatures between −15 and 0 ∘C during the later stage of convection and at temperatures between −40 and −20 ∘C over the whole convection period. This study confirms the dominant role of SIP processes in the formation of numerous small crystals in HIWC regions. 
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  6. null (Ed.)
    Abstract Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided. 
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  7. Abstract

    This study evaluates a hypothesis for the role of vertical wind shear in deep convection initiation (DCI) that was introduced in Part I by examining behavior of a series of numerical simulations. The hypothesis states, “Initial moist updrafts that exceed a width and shear threshold will ‘root’ within a progressively deeper steering current with time, increase their low-level cloud-relative flow and inflow, widen, and subsequently reduce their susceptibility to entrainment-driven dilution, evolving toward a quasi-steady self-sustaining state.” A theoretical model that embodied key elements of the hypothesis was developed in Part I, and the behavior of this model was explored within a multidimensional environmental parameter space. Remarkably similar behavior is evident in the simulations studied here to that of the theoretical model, both in terms of the temporal evolution of DCI and in the sensitivity of DCI to environmental parameters. Notably, both the simulations and theoretical model experience a bifurcation in outcomes, whereby nascent clouds that are narrower than a given initial radiusR0threshold quickly decay and those above theR0threshold undergo DCI. An important assumption in the theoretical model, which states that the cloud-relative flow of the background environmentVCRdetermines cloud radiusR, is scrutinized in the simulations. It is shown that storm-induced inflow is small relative toVCRbeyond a few kilometers from the updraft edge, andVCRtherefore plays a predominant role in transporting conditionally unstable air to the updraft. Thus, the critical role ofVCRin determiningRis validated.

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  8. Abstract

    This article introduces a novel hypothesis for the role of vertical wind shear (“shear”) in deep convection initiation (DCI). In this hypothesis, initial moist updrafts that exceed a width and shear threshold will “root” within a progressively deeper steering current with time, increase their low-level cloud-relative flow and inflow, widen, and subsequently reduce their susceptibility to entrainment-driven dilution, evolving toward a quasi-steady self-sustaining state. In contrast, initial updrafts that do not exceed the aforementioned thresholds experience suppressed growth by shear-induced downward pressure gradient accelerations, will not root in a deep-enough steering current to increase their inflow, will narrow with time, and will succumb to entrainment-driven dilution. In the latter case, an externally driven lifting mechanism is required to sustain deep convection, and deep convection will not persist in the absence of such lifting mechanism. A theoretical model is developed from the equations of motion to further explore this hypothesis. The model indicates that shear generally suppresses DCI, raising the initial subcloud updraft width that is necessary for it to occur. However, there is a pronounced bifurcation in updraft growth in the model after the onset of convection. Sufficiently wide initial updrafts grow and eventually achieve a steady state. In contrast, insufficiently wide initial updrafts shrink with time and eventually decay completely without external support. A sharp initial updraft radius threshold discriminates between these two outcomes. Thus, consistent with our hypothesis and observations, shear inhibits DCI in some situations, but facilitates it in others.

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  9. null (Ed.)
    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. 
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  10. null (Ed.)
    Abstract In this study, processes that broaden drop size distributions (DSDs) in Eulerian models with two-moment bin microphysics are analyzed. Numerous tests are performed to isolate the effects of different physical mechanisms that broaden DSDs in two- and three-dimensional Weather Research and Forecasting Model simulations of an idealized ice-free cumulus cloud. Sensitivity of these effects to modifying horizontal and vertical model grid spacings is also examined. As expected, collision–coalescence is a key process broadening the modeled DSDs. In-cloud droplet activation also contributes substantially to DSD broadening, whereas evaporation has only a minor effect and sedimentation has little effect. Cloud dilution (mixing of cloud-free and cloudy air) also broadens the DSDs considerably, whether or not it is accompanied by evaporation. This mechanism involves the reduction of droplet concentration from dilution along the cloud’s lateral edges, leading to locally high supersaturation and enhanced drop growth when this air is subsequently lifted in the updraft. DSD broadening ensues when the DSDs are mixed with those from the cloud core. Decreasing the horizontal and vertical model grid spacings from 100 to 30 m has limited impact on the DSDs. However, when these physical broadening mechanisms (in-cloud activation, collision–coalescence, dilution, etc.) are turned off, there is a reduction of DSD width by up to ~20%–50% when the vertical grid spacing is decreased from 100 to 30 m, consistent with effects of artificial broadening from vertical numerical diffusion. Nonetheless, this artificial numerical broadening appears to be relatively unimportant overall for DSD broadening when physically based broadening mechanisms in the model are included for this cumulus case. 
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