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Cloud microphysics is critical for weather and climate prediction. In this work, we document updates and corrections to the cloud microphysical scheme used in the Community Earth System Model (CESM) and other models. These updates include a new nomenclature for the scheme, now called Parameterization of Unified Microphysics Across Scales (PUMAS), and the ability to run the scheme on graphics processing units (GPUs). The main science changes include refactoring an ice number limiter and associated changes to ice nucleation, adding vapor deposition onto snow, and introducing an implicit numerical treatment for sedimentation. We also detail the improvements in computational performance that can be achieved with GPU acceleration. We then show the impact of these scheme changes on the (a) mean state climate, (b) cloud feedback response to warming, and (c) aerosol forcing. We find that corrections are needed to the immersion freezing parameterization and that ice nucleation has important impacts on climate. We also find that the revised scheme produces less cloud liquid and ice but that this can be adjusted by changing the loss process for cloud liquid (autoconversion). Furthermore, there are few discernible effects of the PUMAS changes on cloud feedbacks but some reductions in the magnitude of aerosol–cloud interactions (ACIs). Small cloud feedback changes appear to be related to the implicit sedimentation scheme, with a number of factors affecting ACIs.

This study examines dynamic pressure drag on rising dry buoyant thermals. A theoretical expression for drag coefficient Cd as a function of several other nondimensional parameters governing thermal dynamics is derived based on combining the thermal momentum budget with the similarity theory of Scorer. Using values for these nondimensional parameters from previous studies, the theory suggests drag on thermals is small relative to that on solid spheres in laminar or turbulent flow. Two sets of numerical simulations of thermals in an unstratified, neutrally stable environment using an LES configuration of the Cloud Model 1 (CM1) are analyzed. One set has a relatively low effective Reynolds number Re and the other has an order-of-magnitude-higher Re; these produce laminar and turbulent resolved-scale flows, respectively. Consistent with the theoretical Cd, the magnitude of drag is small in all simulations. However, whereas the laminar thermals have Cd ≈ 0.01, the turbulent thermals have weakly negative drag (Cd ≈ −0.1). This difference is explained by the laminar thermals having near vertical symmetry but the turbulent thermals exhibiting considerable vertical asymmetry of their azimuthally averaged flows. In the laminar thermals, buoyancy rapidly becomes concentrated around the main centers of rotation located along the horizontal central axis, leading to expansion of thermals via baroclinic vorticity generation but doing little to break vertical symmetry of the flow. Vertical asymmetry of the azimuthally averaged flow of turbulent thermals is attributed mainly to small-scale resolved eddies that are concentrated in the upper part of the thermals.

This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ∼6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ∼13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ∼1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations. Significance Statement In nature, transporting several quantities through bulk motions of a fluid does not affect preexisting relationships between them. However, this is not always accomplished in numerical models of the atmosphere, because of intrinsic limitations in the transport algorithms employed. We aim to investigate how these errors behave in 3D realistic simulations of a cumulus cloud, where the turbulent flow constitutes a particular challenge. We show that relationships between quantities are significantly and frequently perturbed during bulk transport in the model. Moreover, our results suggest that increasing complexity of the bulk-transport algorithms (in a way that is conventionally employed for improving the representation of individual quantities) tends to worsen the representation of relationships between two or three quantities.

High ice water content (HIWC) regions with small ice crystals, where ice water contents (IWCs) are greater than 1.5 g m-3 and median mass diameters (MMDs) less than about 300 micrometers, occur above tropical mesoscale convective systems (MCSs) and can have detrimental impacts on aircraft engines. Data collected by the French Falcon aircraft and the National Research Council of Canada Convair-580 during the 2014 and 2015 High Altitude Ice Crystals and High Ice Water Content (HAIC/HIWC) projects are revisited here along with coordinated modeling studies to investigate processes that can produce such HIWCs. In particular, data collected from 2014 in the vicinity of Darwin Australia and from 2015 in the vicinity of Cayenne French Guyana are used to determine how bulk microphysical properties (e.g., number concentration, IWC, median volume diameter) and characteristics of ice crystal size distributions (i.e., multimodal nature, parameters fit to gamma distributions for each mode) vary with environmental conditions such as temperature, vertical velocity, MCS age, distance from MCS core, and surface characteristics. It is determined that temperature and vertical velocity are the biggest controls of small ice crystals, but younger cells, stronger convective strengths and closer proximity to convective cores also increase the relative importance of small crystals.Numerical simulations conducted using the Weather Research and Forecasting model with four different bulk microphysics schemes generally reproduce the observed temperature, dew-point, and wind structure. However, comparison of regime-specific observations against properties simulated over Cayenne using a variety of existing parameterization schemes show that although the coverage and evolution of convection is well predicted, simulations overestimate the intensity and spatial extent of observed airborne X-band radar reflectivity and do not well depict the peak of observed size distributions with maximum dimensions between 0.1 and 1 mm. To explore formation mechanisms for large numbers of small ice crystals, a series of simulations varying the representation of secondary ice production (SIP) processes were conducted. Simulations including one of three SIP mechanisms separately (i.e., the Hallett–Mossop mechanism, fragmentation during ice–ice collisions, and shattering of freezing droplets) did not replicate the observed ratio of number concentration divided by IWC. However, the simulation including all three SIP processes produced HIWC regions consistent with observations in terms of number concentration and radar reflectivity, which was not replicated using the original P3 two-ice category configuration that only included the Hallett-Mossop mechanism. In summary, observations and simulations show primary ice production plays a key role in generating HIWC regions at temperatures < -40 Celsius, shattering of freezing droplets dominates ice particle production in HIWC regions between -15 and 0 Celsius during the early stage of convection, and fragmentation during ice–ice collisions dominates between -15 and 0 Celsius during the later stage of convection and between -40 and -20 Celsius over the whole convection period. This study thus shows the dominant role of SIP processes in the formation of numerous small crystals in HIWC regions. Implications for future measurement and modeling needs are discussed.

Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

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.

Esme Cleall observes that for nineteenth-century British missionary families ill-health was constructed as being ‘reflexive of and contributory to a specifically missionary identity’. This article argues that while this was a persistent theme, a new and significantly different discourse emerged emphasizing missionary families’ health. Children were central to this discursive shift. The article focuses on missionary children's health, using selected Anglo-American cases. There was an uneasy overlap of religiously motivated rhetoric that still expected illness and death to be part of missionary childhood experience, and a professionalized discourse that redefined missionary families as sites of health and well-being. This culminated in medical and academic literature within religious and missionary circles that constructed missionaries’ children as a new category. Thus churches responded both to the development of the medical profession and to the development of modern child-centred thinking and practices, in the process developing a new missiological or theological response to childhood.

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 radius R0 threshold quickly decay and those above the R0 threshold undergo DCI. An important assumption in the theoretical model, which states that the cloud-relative flow of the background environment VCR determines cloud radius R, is scrutinized in the simulations. It is shown that storm-induced inflow is small relative to VCR beyond a few kilometers from the updraft edge, and VCR therefore plays a predominant role in transporting conditionally unstable air to the updraft. Thus, the critical role of VCR in determining R is validated.

Realistic simulation of the Earth's mean-state climate remains a major challenge, and yet it is crucial for predicting the climate system in transition. Deficiencies in models' process representations, propagation of errors from one process to another, and associated compensating errors can often confound the interpretation and improvement of model simulations. These errors and biases can also lead to unrealistic climate projections and incorrect attribution of the physical mechanisms governing past and future climate change. Here we show that a significantly improved global atmospheric simulation can be achieved by focusing on the realism of process assumptions in cloud calibration and subgrid effects using the Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1). The calibration of clouds and subgrid effects informed by our understanding of physical mechanisms leads to significant improvements in clouds and precipitation climatology, reducing common and long-standing biases across cloud regimes in the model. The improved cloud fidelity in turn reduces biases in other aspects of the system. Furthermore, even though the recalibration does not change the global mean aerosol and total anthropogenic effective radiative forcings (ERFs), the sensitivity of clouds, precipitation, and surface temperature to aerosol perturbations is significantly reduced. This suggests that it is possible to achieve improvements to the historical evolution of surface temperature over EAMv1 and that precise knowledge of global mean ERFs is not enough to constrain historical or future climate change. Cloud feedbacks are also significantly reduced in the recalibrated model, suggesting that there would be a lower climate sensitivity when it is run as part of the fully coupled E3SM. This study also compares results from incremental changes to cloud microphysics, turbulent mixing, deep convection, and subgrid effects to understand how assumptions in the representation of these processes affect different aspects of the simulated atmosphere as well as its response to forcings. We conclude that the spectral composition and geographical distribution of the ERFs and cloud feedback, as well as the fidelity of the simulated base climate state, are important for constraining the climate in the past and future.

Supersaturation fluctuations in the atmosphere are critical for cloud processes. A nonlinear dependence on two scalars—water vapor and temperature—leads to different behavior than single scalars in turbulent convection. For modeling such multiscalar processes at subgrid scales (SGS) in large-eddy simulations (LES) or convection-permitting models, a new SGS scheme is implemented in CM1 that solves equations for SGS water vapor and temperature fluctuations and their covariance. The SGS model is evaluated using benchmark direct-numerical simulations (DNS) of turbulent Rayleigh–Bénard convection with water vapor as in the Michigan Tech Pi Cloud Chamber. This idealized setup allows thorough evaluation of the SGS model without complications from other atmospheric processes. DNS results compare favorably with measurements from the chamber. Results from LES using the new SGS model compare well with DNS, including profiles of water vapor and temperature variances, their covariance, and supersaturation variance. SGS supersaturation fluctuations scale appropriately with changes to the LES grid spacing, with the magnitude of SGS fluctuations decreasing relative to those at the resolved scale as the grid spacing is decreased. Sensitivities of covariance and supersaturation statistics to changes in water vapor flux relative to thermal flux are also investigated by modifying the sidewall conditions. Relative changes in water vapor flux substantially decrease the covariance and increase supersaturation fluctuations even away from boundaries.

Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rainwater mixing ratios (qc and qr, respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large-eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulated qc closely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulated qr properties, though, with bulk simulated qr consistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produce qr that is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

The Predicted Particle Properties (P3) bulk microphysics scheme predicts cloud and microphysical processes in atmospheric models using the property-based approach to represent ice-phase hydrometeors. In most microphysics schemes, the representation of ice does not allow for mixed-phase particles. This is a notable deficiency in modelling important processes such as melting, refreezing, and wet growth and which ultimately is needed to simulate various types of precipitation (e.g., freezing rain, ice pellets, hail, wet snow).The P3 scheme has been recently modified to include prognostic variables for the mixing ratios of liquid in mixed-phase particles for each of the “free” ice categories. This is combined with the 3-moment representation of ice. The impacts of the predicted liquid fraction are examined for simulations of two real-case weather events: (1) a high-impact freezing rain storm, and (2) a mid-latitude squall line.The inclusion of the prognostic liquid fraction affects the following aspects of the microphysics and dynamics of the simulated storms: the cold pool depth, the propagation speed of the squall line, the precipitation, and the reflectivity structure. In addition to allowing for more detailed microphysical processes, the representation of mixed-phase particles in P3 has notable impacts on the prediction of high-impact weather elements., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Motivated by recent discussions concerning differences of convective dynamics in polluted and pristine environments, the so-called convective invigoration in particular, this paper provides an analysis of factors affecting convective updraft buoyancy, such as the in-cloud supersaturation, condensate and precipitation loading, and entrainment. We use the deep convective period from simulations of daytime convection development over land discussed in our previous publications. An entraining parcel framework is used in the theoretical analysis. We show that for the specific case considered here, finite (positive) supersaturation noticeably reduces pseudo-adiabatic parcel buoyancy and cumulative convective available potential energy (cCAPE) in the lower troposphere. This comes from keeping a small fraction of the water vapor in a supersaturated state and thus reducing the latent heating. Such a lower-tropospheric impact is comparable to the effects of condensate loading and entrainment in the idealized parcel framework. For the entire tropospheric depth, loading and entrainment have a much more significant impact on the total CAPE. For the cloud model results, we compare ensemble simulations applying either a bulk microphysics scheme with saturation adjustment or a more comprehensive double-moment scheme with supersaturation prediction. We compare deep convective updraft velocities, buoyancies, and supersaturations from all ensembles. In agreement with the parcel analysis, the saturation-adjustment scheme provides noticeably stronger updrafts in the lower troposphere. For the simulations predicting supersaturation, there are small differences between pristine and polluted conditions below the freezing level that are difficult to explain by standard analysis of the in-cloud buoyancy components. By applying the piggybacking technique, we show that the lower-tropospheric buoyancy differences between pristine and polluted simulations come from a combination of temperature (i.e., latent heating) and condensate loading differences that work together to make polluted buoyancies and updraft velocities slightly larger when compared to their pristine analogues. Overall, the effects are rather small and contradict previous claims of a significant invigoration of deep convection in polluted environments.

The British Protestant children’s missionary movement of the nineteenth and early- to mid-twentieth century was an educational movement, wherein philanthropy and pedagogy went hand in hand. Bringing an educational lens to bear on this group provides a more cohesive interpretive framework by which to make sense of the various elements than hitherto has been considered. As such, the Protestant children’s missionary movement emerges historically as a much more complex entity than simply a means of raising money or cramming heads full of knowledge. Across a range of geographic settings it acted as: a key site of juvenile religious and identity formation; a defining vehicle for the creation and maintenance of various types or scales of community (local, denominational, emotional, regional, national or global); a movement within which civic and religious messages were emphatically conflated (especially with respect to nation and empire); and in which children both participated in imperial or quasi-global networks of information exchange (especially as consumers of missionary periodicals) and became informed, active and responsive agents of missionary support in their own right.

Secondary ice production (SIP) is an important physical phenomenon that results in an increase in the ice particle concentration and can therefore have a significant impact on the evolution of clouds. In this study, idealized simulations of a mesoscale convective system (MCS) were conducted using a high-resolution (250 m horizontal grid spacing) mesoscale model and a detailed bulk microphysics scheme in order to examine the impacts of SIP on the microphysics and dynamics of a simulated tropical MCS. The simulations were compared to airborne in situ and remote sensing observations collected during the “High Altitude Ice Crystals – High Ice Water Content” (HAIC-HIWC) field campaign in 2015. It was found that the observed high ice number concentration can only be simulated by models that include SIP processes. The inclusion of SIP processes in the microphysics scheme is crucial for the production and maintenance of the high ice water content observed in tropical convection. It was shown that SIP can enhance the strength of the existing convective updrafts and result in the initiation of new updrafts above the melting layer. Agreement between the simulations and observations highlights the impacts of SIP on the maintenance of tropical MCSs in nature and the importance of including SIP parameterizations in models.

The spreading rates of convective thermals are linked to their net entrainment, and previous literature has suggested differences in spreading rates between moist and dry thermals. In this study, growth rates of idealized numerically simulated axisymmetric dry and moist convective thermals are directly compared. In an environment with dry-neutral stratification, the increase of thermal radius with height dR/dz is a larger by a factor of 1.7 for dry thermals relative to moist thermals. The fractional change in thermal volume ε is also greater for dry thermals within a distance of ~4 radii from the initial thermal height. Values of dR/dz are nearly constant with height for both moist and dry thermals consistent with classical theory based on dimensional analysis. The simulations are also consistent with theory relating impulse, circulation, and spreading rate for dry thermals proposed in previous papers and extended here to moist thermals, predicting they will spread less than dry thermals. Tests adding heating to dry thermals, either spread uniformly across the thermal volume or concentrated in the inner core, indicate that dR/dz and ε are smaller for moist thermals because latent heating is confined mostly to their cores. Additional axisymmetric moist simulations using modified lapse rates and large-eddy simulations support this analysis. Overall, these results indicate that slow spreading rates are a fundamental feature of moist thermals caused by latent heating that alters the spatial distribution of buoyancy within them relative to dry thermals.

In the original Predicted Particle Properties (P3) bulk microphysics scheme, all ice-phase hydrometeors are represented by one or more “free” ice categories, where the physical properties evolve smoothly through changes to the four prognostic variables (per category), and with a two-moment representation of the particle size distribution. As such, the spectral dispersion cannot evolve independently, which thus results in limitations in representation of ice—in particular, hail—due to necessary constraints in the scheme to prevent excessive gravitational size sorting. To overcome this, P3 has been modified to include a three-moment representation of the size distribution of each ice category through the addition of a fifth prognostic variable, the sixth moment of the size distribution. The details of the three-moment ice parameterization in P3 are provided. The behavior of the modified scheme, with the single-ice-category configuration, is illustrated through simulations in a simple 1D kinematic model framework as well as with near large-eddy-resolving (250-m grid spacing) 3D simulations of a hail-producing supercell. It is shown that the three-moment ice configuration controls size sorting in a physically based way and leads to an improved capacity to simulate large, heavily rimed ice (hail), including mean and maximum sizes and reflectivity, and thus an overall improvement in the representation of ice-phase particles in the P3 scheme.

This study applies an idealized modeling framework, alongside a Bayesian Markov chain Monte Carlo (MCMC) algorithm, to explore which combinations of upstream environmental conditions and cloud microphysical parameter values can produce a particular precipitation distribution over an idealized two-dimensional, bell-shaped mountain. Simulations focus on orographic precipitation produced when an atmospheric river interacts with topography. MCMC-based analysis reveals that different combinations of parameter values produce a similar precipitation distribution, with the most influential parameters being relative humidity (RH), horizontal wind speed (U), surface potential temperature (θsfc), and the snow fall speed coefficient (As). RH, U, and As exhibit interdependence: changes in one or more of these factors can be mitigated by compensating changes in the other(s) to produce similar orographic precipitation rates. The results also indicate that the parameter sensitivities and relationships can vary for spatial subregions and given different environmental conditions. In particular, high θsfc values are more likely to produce the target precipitation rate and spatial distribution, and thus the ensemble of simulations shows a preference for liquid precipitation at the surface. The results presented here highlight the complexity of orographic precipitation controls, and have implications for flood and water management, observational efforts, and climate change.

This is a rebuttal of Fan and Khain’s comments (hereafter FK21) on a 2020 paper by Grabowski and Morrison (hereafter GM20) that questions the impact of ultrafine cloud condensation nuclei (CCN) on deep convection. GM20 argues that “cold invigoration,” an increase of the updraft speed from lofting and freezing of additional cloud water in polluted environments, is unlikely because the latent heating from freezing of this cloud water approximately recovers the negative impact on the buoyancy from the weight of this water. FK21 suggest a variety of processes that could invalidate our claim. We maintain that our argument is valid and invite the authors to compare their microphysics scheme with ours in the same simplified modeling framework. However, pollution does affect the partitioning of latent heating within the column and likely leads to convection changes beyond a single diurnal cycle through larger-scale circulation changes. This argument explains impacts seen in our idealized mesoscale simulations and in convective–radiative equilibrium simulations by others. We agree with FK21 on the existence of a “warm invigoration” mechanism but question its interpretation. Consistent with the simulations in GM20, we argue that changes in the buoyancy can be explained by the response of the supersaturation to droplet microphysical changes induced by pollution. The buoyancy change is determined by supersaturation differences between pristine and polluted conditions, while condensation rate responds to these supersaturation changes. Finally, we agree with FK21 that the piggybacking modeling technique cannot prove or disprove invigoration; rather, it is a diagnostic technique that can be used to understand mechanisms driving simulation differences.

A parameterization for the subgrid-scale cloud and precipitation fractions has been incorporated into the Predicted Particle Properties (P3) microphysics scheme for use in atmospheric models with relatively coarse horizontal resolution. The modified scheme was tested in a simple 1D kinematic model and in the Canadian Global Environmental Multiscale (GEM) model using an operational global NWP configuration with a 25-km grid spacing. A series of 5-day forecast simulations was run using P3 and the much simpler operational Sundqvist condensation scheme as a benchmark for comparison. The effects of using P3 in a global GEM configuration, with and without the modifications, were explored through statistical metrics of common forecast fields against upper-air and surface observations. Diagnostics of state variable tendencies from various physics parameterizations were examined to identify possible sources of errors resulting from the use of the modified scheme. Sensitivity tests were performed on the coupling between the deep convection parameterization scheme and the microphysics, specifically regarding assumptions in the physical properties of detrained ice. It was found that even without recalibration of the suite of moist physical parameterizations, substituting the Sundqvist condensation scheme with the modified P3 microphysics resulted in some significant improvements to the temperature and geopotential height bias throughout the troposphere and out to day 5, but with degradation to error standard deviation toward the end of the integrations, as well as an increase in the positive bias of precipitation quantities. The modified P3 scheme was thus shown to hold promise for potential use in coarse-resolution NWP systems.

This study investigates impacts of altering subgrid-scale mixing in “convection-permitting” kilometer-scale horizontal-grid-spacing (Δh) simulations by applying either constant or stochastic multiplicative factors to the horizontal mixing coefficients within the Weather Research and Forecasting Model. In quasi-idealized 1-km Δh simulations of two observationally based squall-line cases, constant enhanced mixing produces larger updraft cores that are more dilute at upper levels, weakens the cold pool, rear-inflow jet, and front-to-rear flow of the squall line, and degrades the model’s effective resolution. Reducing mixing by a constant multiplicative factor has the opposite effect on all metrics. Completely turning off parameterized horizontal mixing produces bulk updraft statistics and squall-line mesoscale structure closest to an LES “benchmark” among all 1-km simulations, although the updraft cores are too undilute. The stochastic mixing scheme, which applies a multiplicative factor to the mixing coefficients that varies stochastically in time and space, is employed at 0.5-, 1-, and 2-km Δh. It generally reduces midlevel vertical velocities and enhances upper-level vertical velocities compared to simulations using the standard mixing scheme, with more substantial impacts at 1- and 2-km Δh compared to 0.5-km Δh. The stochastic scheme also increases updraft dilution to better agree with the LES for one case, but has less impact on the other case. Stochastic mixing acts to weaken the cold pool but without a significant impact on squall-line propagation. It also does not affect the model’s overall effective resolution unlike applying constant multiplicative factors to the mixing coefficients.

Recent studies have shown that cumulus updrafts often consist of a succession of discrete rising thermals with spherical vortex-like circulations. In this paper, a theory is developed for why this “thermal chain” structure occurs. Theoretical expressions are obtained for a passive tracer, buoyancy, and vertical velocity in axisymmetric moist updrafts. Analysis of these expressions suggests that the thermal chain structure arises from enhanced lateral mixing associated with intrusions of dry environmental air below an updraft’s vertical velocity maximum. This dry-air entrainment reduces buoyancy locally. Consequently, the updraft flow above levels of locally reduced buoyancy separates from below, leading to a breakdown of the updraft into successive discrete thermals. The range of conditions in which thermal chains exist is also analyzed from the theoretical expressions. A transition in updraft structure from isolated rising thermal, to thermal chain, to starting plume occurs with increases in updraft width, environmental relative humidity, and/or convective available potential energy. Corresponding expressions for the bulk fractional entrainment rateεare also obtained. These expressions indicate rather complicated entrainment behavior of ascending updrafts, with local enhancement ofεup to a factor of ~2 associated with the aforementioned environmental-air intrusions, consistent with recent large-eddy simulation (LES) studies. These locally large entrainment rates contribute significantly to overall updraft dilution in thermal chain-like updrafts, while other regions within the updraft can remain relatively undilute. Part II of this study compares results from the theoretical expressions to idealized numerical simulations and LES.

Research has suggested that the structure of deep convection often consists of a series of rising thermals, or “thermal chain,” which contrasts with existing conceptual models that are used to construct cumulus parameterizations. Simplified theoretical expressions for updraft properties obtained in Part I of this study are used to develop a hypothesis explaining why this structure occurs. In this hypothesis, cumulus updraft structure is strongly influenced by organized entrainment below the updraft’s vertical velocity maximum. In a dry environment, this enhanced entrainment can locally reduce condensation rates and increase evaporation, thus eroding buoyancy. For moderate-to-large initial cloud radius R, this breaks up the updraft into a succession of discrete pulses of rising motion (i.e., a thermal chain). For small R, this leads to the structure of a single, isolated rising thermal. In contrast, moist environments are hypothesized to favor plume-like updrafts for moderate-to-large R. In a series of axisymmetric numerical cloud simulations, R and environmental relative humidity (RH) are systematically varied to test this hypothesis. Vertical profiles of fractional entrainment rate, passive tracer concentration, buoyancy, and vertical velocity from these runs agree well with vertical profiles calculated from the theoretical expressions in Part I. Analysis of the simulations supports the hypothesized dependency of updraft structure on R and RH, that is, whether it consists of an isolated thermal, a thermal chain, or a plume, and the role of organized entrainment in driving this dependency. Additional three-dimensional (3D) turbulent cloud simulations are analyzed, and the behavior of these 3D runs is qualitatively consistent with the theoretical expressions and axisymmetric simulations.

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.