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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 rate ε are also obtained. These expressions indicate rather complicated entrainment behavior of ascending updrafts, with local enhancement of ε up 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.

Intense thunderstorms produce rapid cloud updrafts and may be associated with a range of destructive weather events. An important ingredient in measures of the potential for intense thunderstorms is the convective available potential energy (CAPE). Climate models project increases in summertime mean CAPE in the tropics and subtropics in response to global warming, but the physical mechanisms responsible for such increases and the implications for future thunderstorm activity remain uncertain. Here, we show that high percentiles of the CAPE distribution (CAPE extremes) also increase robustly with warming across the tropics and subtropics in an ensemble of state-of-the-art climate models, implying strong increases in the frequency of occurrence of environments conducive to intense thunderstorms in future climate projections. The increase in CAPE extremes is consistent with a recently proposed theoretical model in which CAPE depends on the influence of convective entrainment on the tropospheric lapse rate, and we demonstrate the importance of this influence for simulated CAPE extremes using a climate model in which the convective entrainment rate is varied. We further show that the theoretical model is able to account for the climatological relationship between CAPE and a measure of lower-tropospheric humidity in simulations and in observations. Our results provide a physical basis on which to understand projected future increases in intense thunderstorm potential, and they suggest that an important mechanism that contributes to such increases may be present in Earth’s atmosphere.

The sensitivity of a simulated Madden–Julian oscillation (MJO) was investigated in the NCAR Community Atmosphere Model 3.1 with the relaxed Arakawa–Schubert convection scheme by analyzing the model’s response to varying the strength of two moisture sensitivity parameters. A higher value of either the minimum entrainment rate or rain evaporation fraction results in increased intraseasonal variability, a more coherent MJO, and enhanced moisture–convection feedbacks in the model. Changes to the mean state are inconsistent between the two methods. Increasing the minimum entrainment leads to a cooler and drier troposphere, whereas increasing the rain evaporation fraction causes warming and moistening. These results suggest that no straightforward correspondence exists between the MJO and the mean humidity, contrary to previous studies. Analysis of the mean column-integrated and normalized moist static energy (MSE) budget reveals a substantial reduction of gross moist stability (GMS) for increased minimum entrainment, while no significant changes are found for an increased evaporation fraction. However, when considering fluctuations of the normalized MSE budget terms during MJO events, both methods result in negative GMS prior to the deep convective phase of the MJO. Intraseasonal fluctuations of GMS, rather than the mean, appear to be a better diagnostic quantity for testing a model’s ability to produce an MJO.

Previous studies have shown that atmospheric models with a spectral element grid can benefit from putting physics calculations on a relatively coarse finite volume grid. Here we demonstrate an alternative high‐order, element‐based mapping approach used to implement a quasi‐equal‐area, finite volume physics grid in E3SM. Unlike similar methods, the new method in E3SM requires topology data purely local to each spectral element, which trivially allows for regional mesh refinement. Simulations with physics grids defined by 2 × 2, 3 × 3, and 4 × 4 divisions of each element are shown to verify that the alternative physics grid does not qualitatively alter the model solution. The model performance is substantially affected by the reduction of physics columns when using the 2 × 2 grid, which can increase the throughput of physics calculations by roughly 60%–120% depending on whether the computational resources are configured to maximize throughput or efficiency. A pair of regionally refined cases are also shown to highlight the refinement capability. Plain Language Summary Most atmospheric models use the same grid for dynamics (e.g., advection) and physics (e.g., clouds). For spectral element models the grid uses irregularly spaced points and the treatment of element edges can lead to grid imprinting bias. Previous studies have shown that using a regularly spaced physics grid in a spectral element model can alleviate the grid imprinting biases. This alternative physics grid can also reduce the computational cost of the model if the physics grid is coarser than the dynamics grid. This study presents a new approach for using a regularly spaced physics grid in a global spectral element model that additionally allows mesh refinement for regionally focused simulations. The use of a relatively coarse physics grid is shown to make the model faster without qualitatively degrading the simulated climate. Key Points A method is presented for defining a finite volume physics grid in a spectral element model that allows for regional refinement The new method is shown to qualitatively preserve the model solution and effective resolution A relatively coarse physics grid increases the speed of physics by roughly 60%–120% depending on how the computational resources are configured

Convective momentum transport (CMT) is the process of vertical redistribution of horizontal momentum by small‐scale turbulent flows from moist convection. Traditional general circulation models (GCMs) and their multiscale modeling framework (MMF) versions poorly represent CMT due to insufficient information of subgrid‐scale flows at each GCM grid. Here the explicit scalar momentum transport (ESMT) scheme for representing CMT is implemented in the Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) with embedded 2‐D cloud‐resolving models (CRMs), and verified against E3SM‐MMF simulations with 3‐D CRMs and observations. The results show that representing CMT by ESMT helps reduce climatological mean precipitation model bias over the western Pacific and the ITCZ regions, which is attributed to the weakened mean easterlies over the Pacific. Also, CMT from simulations with 2‐D and 3‐D CRMs impose a similar impact on Kelvin waves by reducing their variability and slowing down their phase speed, but opposite impacts on the Madden‐Julian Oscillation (MJO) variability. The ESMT scheme readily captures the climatological mean spatial patterns of the zonal and meridional components of CMT and their variability across multiple time scales, but shows some differences in estimating its magnitude. CMT mainly affects the MJO by decelerating its winds in the free troposphere, but accelerates its near‐surface winds. This study serves as a prototype for implementing CMT scheme in the MMF simulations, highlighting its crucial role in reducing model bias in mean state and spatiotemporal variability. Plain Language Summary Small‐scale turbulent flows from moist convection typically lead to the vertical redistribution of large‐scale winds (referred to as convective momentum transport [CMT]). Due to the coarse grids that are too large to resolve small‐scale flows, traditional earth system models poorly represent the CMT, and thus rely on parameterizations that empirically describe the magnitude and vertical profiles of the CMT. In contrast, the default Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) is an earth system model with a 2‐D (one horizontal dimension and one vertical dimension) cloud‐resolving model embedded within each coarse grid so as to better resolve small‐scale flows, although it still lacks the necessary information to fully calculate CMT due to the lack of the third dimension. Here we implemented the explicit scalar momentum transport (ESMT) scheme to represent CMT in the E3SM‐MMF associated with 2‐D small‐scale flows at each coarse grid. The results show that in general CMT helps reduce model biases in predicting time‐mean precipitation and winds as well as the spatiotemporal variability of tropical convection. The ESMT scheme reproduces the spatial patterns of CMT as simulated by the E3SM‐MMF model with 3‐D small‐scale flows. Lastly, we focused on the Madden‐Julian Oscillation, the dominant intraseasonal variability in the tropics, as an example to investigate the impact of CMT. Key Points Convective momentum transport (CMT) affects large‐scale circulation and convective organization, and representing CMT reduces model biases in Energy Exascale Earth System Model‐Multiscale Modeling Framework simulations Explicit scalar momentum transport scheme captures the spatial pattern of CMT comparable to 3‐D cloud‐resolving models that explicitly model CMT CMT damps the free tropospheric circulation associated with the Madden‐Julian oscillation, but accelerates its near‐surface winds

Column water vapor (CWV) is studied using data from the Dynamics of the Madden–Julian Oscillation (DYNAMO) field experiment. A distinctive moist mode in tropical CWV probability distributions motivates the work. The Lagrangian CWV tendency (LCT) leaves together the compensating tendencies from phase change and vertical advection, quantities that cannot be measured accurately by themselves, to emphasize their small residual, which governs evolution. The slope of LCT versus CWV suggests that the combined effects of phase changes and vertical advection act as a robust positive feedback on CWV variations, while evaporation adds a broadscale positive tendency. Analyzed diabatic heating profiles become deeper and stronger as CWV increases. Stratiform heating is found to accompany Lagrangian drying at high CWV, but its association with deep convection makes the mean LCT positive at high CWV. Lower-tropospheric wind convergence is found in high-CWV air masses, acting to shrink their area in time. When ECMWF heating profile indices and S-Pol and TRMM radar data are binned jointly by CWV and LCT, bottom-heavy heating associated with shallow and congestus convection is found in columns transitioning through Lagrangian moistening into the humid, high-rain-rate mode of the CWV distribution near 50–55 mm, while nonraining columns and columns with widespread stratiform precipitation are preferentially associated with Lagrangian drying. Interpolated sounding-array data produce substantial errors in LCT budgets, because horizontal advection is inaccurate without satellite input to constrain horizontal gradients.

The Dynamics of the MJO (DYNAMO) field campaign took place in the Indian Ocean during boreal fall and winter of 2011–2012 to collect observations of Madden‐Julian Oscillation (MJO) initiation. Hindcast experiments are conducted with an atmospheric general circulation model with varying values of a dilute CAPE entrainment rate parameter for the first two MJO events of DYNAMO from 1 October 2011 to 15 December 2011. Higher entrainment rates better reproduce MJO precipitation and zonal wind, with RMM skill up to 20 days. Simulations with lower entrainment rapidly diverge from observations with no coherent MJO convective signal after 5 days, and no MJO predictive skill beyond 12 days. Analysis of the tropical Indian Ocean column moist static energy (MSE) budget reveals that the simulations with superior MJO performance exhibit a mean positive MSE tendency by vertical advection; inconsistent with reanalysis that indicates a weak negative tendency. All simulations have weaker mean MSE source tendency and significantly weaker cloud‐radiative feedbacks. The vertical gross moist stability (VGMS) is used to interpret these MSE budget results in a normalized framework relevant to moisture mode theory. VGMS in the high entrainment runs is far too low compared to ERAi, indicating that it cannot be used in isolation as a measure of model success in producing a realistic MJO hindcast, contrary to previous studies. However, effective VGMS that includes radiative feedbacks is similar among the high entrainment runs and ERAi. We conclude that the MJO is erroneously improved by increasing the entrainment parameter because moistening by vertical MSE advection compensates for the overly weak cloud‐radiative feedbacks. Key Points Higher entrainment improves MJO DYNAMO Hindcasts for the wrong reason MSE import by vertical advection compensates for overly weak MSE sources Changes in the omega profile largely explain the differences in GMS among models

In this study, we compare the Energy Exascale Earth Systems Model (E3SM) multiscale modeling framework (MMF) with the cloud resolving model (CRM) configured in two (2dMMF) and three (3dMMF) dimensions. We explore how CRM dimensionality impacts the representation of mean and extreme precipitation characteristics. Our results show that tropical mean precipitation patterns are better represented in 3dMMF compared to observations (Integrated Multi‐satellitE Retrivals for GPM and Global Precipitation Climatology Project One Degree Daily products), while 2dMMF better captures extreme precipitation intensity, with systematic land‐ocean differences in precipitation and cloud‐associated variables. These differences are attributed to the co‐occurrence of CRM throttling (i.e., suppressed convection in due to smaller numbers of CRM columns and domain size) and dilution (i.e., 3‐D cloud circulations with increased entrainment and lower precipitation efficiency) effects. Overall, throttling results in more low‐level humidity in 2dMMF and dilution contributes to more high clouds with less precipitation efficiency in 3dMMF. Since throttling occurs more strongly over the ocean than land, the 3dMMF tends to have less cloud liquid and precipitation over the ocean and more cloud ice and precipitation over land. These results may serve as a guide for choosing the CRM structure to reduce precipitation and cloud‐related biases. Plain Language Summary Global cloud‐resolving models (CRMs) are compulationally prohibitive for climate length simulations, but an alternate approach that embeds independent kilometer‐scale CRMs in each column of a low‐resolution (∼100 km) global grid can permit convection with lower computational expanse. Such an approach allows cloud‐scale motions to be represented in multi‐year global climate simulations, though at the expense of a disconnection between the global model and CRM grids. In this study we compare two different ways of configuring the embedded CRMs: two‐dimensions (2‐D) aligned in north‐south direction versus three‐dimensions (3‐D) including both north‐south and west‐east directions. The results demonstrate a strong land‐ocean contrast in precipitation, cloud properties, and radiation in the difference between the 2‐D and 3‐D CRM simulations. And the differences are generated by the co‐occurrence of a throttling effect associated with a smaller number of CRM columns in 2‐D, which constrains deep convection, and a dilution effect associated with 3‐D cloud circulations, which enhances mixing and reduces precipitation efficiency. While the dilution effect impacts most of the tropics, the throttling effect is more influential over the ocean. This information can be used to inform the best configuration of the CRM approach for simulating precipitation and related processes in a global climate model. Key Points E3SM MMF with a 3‐D CRM reduces mean precipitation pattern biases relative to IMERG, but weakens overall intensity compared to a 2‐D CRM Weaker throttling with dilution effects in 3dMMF result in less low‐level humidity, more high clouds, and lower precipitation efficiency The impacts of dilution and throttling differ over land and ocean, which leads to an overall shift of precipitation toward land in 3dMMF

Modern climate projections often suffer from inadequate spatial and temporal resolution due to computational limitations, resulting in inaccurate representations of sub‐grid processes. A promising technique to address this is the multiscale modeling framework (MMF), which embeds a kilometer‐resolution cloud‐resolving model (CRM) within each atmospheric column of a host climate model to replace traditional convection and cloud parameterizations. Machine learning offers a unique opportunity to make MMF more accessible by emulating the embedded CRM and reducing its substantial computational cost. Although many studies have demonstrated proof‐of‐concept success of achieving stable hybrid simulations, it remains a challenge to achieve near operational‐level success with real geography and comprehensive variable emulation that includes, for example, explicit cloud condensate coupling. In this study, we present a stable hybrid model capable of integrating for at least 5 years with near operational‐level complexity, including coarse‐grid geography, seasonality, explicit cloud condensate and wind predictions, and land coupling. Our model demonstrates skillful online performance, achieving a 5‐year zonal mean tropospheric temperature bias within 2 K, water vapor bias within 1 g/kg, and a precipitation root mean square error of 0.96 mm/day. Key factors contributing to our online performance include an expressive U‐Net architecture and physical thermodynamic constraints for microphysics. With microphysical constraints mitigating unrealistic cloud formation, our work is the first to demonstrate realistic multi‐year cloud condensate climatology under the MMF framework. Despite these advances, online diagnostics reveal persistent biases in certain regions, highlighting the need for innovative strategies to further optimize online performance. Plain Language Summary Traditional climate models often struggle to accurately simulate small‐scale processes like thunderstorms due to compute limitations, leading to less reliable climate predictions. Machine learning (ML) offers a promising solution by efficiently modeling these processes and integrating them into hybrid ML‐physics simulations within a host climate model. While previous studies have shown success in simplified setups, such as all‐ocean planets, achieving accurate and stable hybrid simulations in complex, real‐world settings remains challenging. In this study, we developed a stable hybrid model capable of simulating the climate for 5 years using real geographic features and explicitly predicting the time evolution of temperature, moisture, cloud, and wind. Our model achieves skillful accuracy in long‐term mean atmospheric states. This success is due to several key improvements: an advanced architecture and the incorporation of cloud physics constraints. Key Points Stable hybrid climate simulations are achieved with a data‐driven emulator of subgrid physics coupled with a comprehensive atmosphere model Online performance benefits from a U‐Net architecture and microphysical constraints A realistic cloud climatology with explicit cloud condensate coupling is achieved in a hybrid multi‐scale modeling framework

High‐Resolution Multi‐scale Modeling Frameworks (HR)—global climate models that embed separate, convection‐resolving models with high enough resolution to resolve boundary layer eddies—have exciting potential for investigating low cloud feedback dynamics due to reduced parameterization and ability for multidecadal throughput on modern computing hardware. However low clouds in past HR have suffered a stubborn problem of over‐entrainment due to an uncontrolled source of mixing across the marine subtropical inversion manifesting as stratocumulus dim biases in present‐day climate, limiting their scientific utility. We report new results showing that this over‐entrainment can be partly offset by using hyperviscosity and cloud droplet sedimentation. Hyperviscosity damps small‐scale momentum fluctuations associated with the formulation of the momentum solver of the embedded large eddy simulation. By considering the sedimentation process adjacent to default one‐moment microphysics in HR, condensed phase particles can be removed from the entrainment zone, which further reduces entrainment efficiency. The result is an HR that can produce more low clouds with a higher liquid water path and a reduced stratocumulus dim bias. Associated improvements in the explicitly simulated sub‐cloud eddy spectrum are observed. We report these sensitivities in multi‐week tests and then explore their operational potential alongside microphysical retuning in decadal simulations at operational 1.5° exterior resolution. The result is a new HR having desired improvements in the baseline present‐day low cloud climatology, and a reduced global mean bias and root mean squared error of absorbed shortwave radiation. We suggest it should be promising for examining low cloud feedbacks with minimal approximation. Plain Language Summary Stratocumulus clouds cover a large fraction of the globe but are very challenging to reproduce in computer simulations of Earth's atmosphere because of their unique complexity. Previous studies find the model produces too few Stratocumulus clouds as we increase the model resolution, which, in theory, should improve the simulation of important motions for the clouds. This is because the clouds are exposed to more conditions that make them evaporate away. On Earth, stratocumulus clouds reflect a lot of sunlight. In the computer model of Earth, too much sunlight reaches the surface because of too few stratocumulus clouds, which makes it warmer. This study tests two methods to thicken Stratocumulus clouds in the computer model Earth. The first method smooths out some winds, which helps reduce the exposure of clouds to the conditions that make them evaporate. The second method moves water droplets in the cloud away from the conditions that would otherwise make them evaporate. In long simulations, combining these methods helps the model produce thicker stratocumulus clouds with more water. Key Points We improve a long‐standing stratocumulus (Sc) dim bias in a high‐resolution Multiscale Modeling Framework Incorporating intra‐CRM hyperviscosity hedges against the numerics of its momentum solver, reducing entrainment vicinity Further adding sedimentation boosts Sc brightness close to observed, opening path to more faithful low cloud feedback analysis