A formulation based on the anelastic approximation yields time-dependent simulations of convective updrafts, downdrafts and other aspects of convection, such as stratiform layers, under reasonably flexible geometry assumptions. Termed anelastic convective entities (ACEs), such realizations can aid understanding of convective processes, and potentially provide time-dependent building blocks for parameterization at a complexity between steady-plume models and cloud-resolving simulations. Formulation and behavior of single-ACE cases are addressed here, with multi-ACE cases in Part 2. Even for cases deliberately formulated to provide a comparison to a traditional convective plume, ACE behavior differs substantially because dynamic entrainment, detrainment and nonhydrostatic perturbation pressure are consistently included. Entrainment varies with the evolution of the entity but behavior akin to deep-inflow effects noted in observations emerges naturally. The magnitude of the mass flux with nonlocal pressure effects consistently included is smaller than for a corresponding traditional steady-plume model. ACE solutions do not necessarily approach a steady state even with a fixed environment but can exhibit chains of rising thermals, and even episodic deep convection. The inclusion of nonlocal dynamics allows a developing updraft to tunnel through layers with substantial convective inhibition (CIN). For cases of nighttime continental convection using GoAmazon soundings, this is found to greatly reduce the effect of surface-inversion CIN. The observed convective cold top is seen as an inherent property of the solution, both in a transient, rising phase and as a persistent feature in mature deep convection.

Seeking a family of models filling the hierarchy between steady plumes and cloud-resolving simulations, Part I of this study presented a formulation termed anelastic convective entities (ACEs). The solution includes pressure-mediated nonlocal effects in both vertical and horizontal and thus yields time-dependent simulations of convective updrafts, downdrafts and other aspects of convection even for a single column interacting with a fixed environment through dynamically determined inflow and outflow. Here we show how a straightforward iteration of that formulation can capture interactions among entities in a variety of choices for the geometry of the interactions. Using an oceanic sounding to contrast with land cases in Part 1, we first illustrate that a single ACE can exhibit ongoing time-dependent evolution depending, e.g., on choices in the parameterized turbulence. For a case in which a single ACE with fixed environment would yield a near-steady deep-convective state, we examine the adjustment process in a multi-ACE prototype for adjustment within a climate model grid cell. This embedded ACE configuration exhibits time-dependent stratiform cloud expansion through convective outflow modified by dynamic feedbacks. The grid-scale adjustment process includes not only traditional warming by large-scale descent, but also captures the spread of the convective cold top. The formulation also illustrates the possibility of multi-hour time lag before the transition to deep convection, and remote initiation by small vertical velocities in the grid-cell environment. Comparing 1-, 2-, 4-and 8-ACE instances suggests promise as a potential convective-parameterization class between traditional-and super-parameterization, while providing a sandbox to aid understanding of convective and adjustment processes.

The anelastic theory of effective buoyancy has been generalized to include the effects of momentum flux convergence. Mediated by the nonlocal perturbation pressure, the dynamics tends to average over details of the forcing, yielding acceleration robust to small-scale variations of the flow. Here we demonstrate in a large-eddy simulation (LES) with a 100-m horizontal grid spacing that including the anelastic nonlocal dynamics can help capture the mean evolution of convection without fully resolving the fine-scale coherent turbulent structures embedded in the flow. Instances of convection in the LES are identified. For these, the buoyancy and dynamic contributions to the vertical momentum tendency are separately diagnosed. The diagnoses show that buoyancy is the leading effect in the vertical acceleration while strongly interacting with the vertical momentum flux convergence. In comparison, the influence of the horizontal momentum flux convergence on the vertical motion are substantially weaker. The sensitivity resulting from averaging over fine-scale features are quantified. For deep-convective cases, these contributions at the cloud scale ($\sim8$ km) exhibit a robustness—as measured in a root-mean-square sense—to horizontally smoothing out turbulent features of scales $\lesssim3$ km. As expected, such scales depend on the size of the convective element of interest, while dynamic contributions tend to be more susceptible to horizontal smoothing than does the buoyancy contribution. By verifying a key attribute of the pressure-mediated dynamics in an LES, results here lend support to simplifying the representation of moist convection under the anelastic nonlocal framework for global climate models and storm-resolving simulations.

A formulation based on the anelastic approximation yields time-dependent simulations of convective updrafts, downdrafts and other aspects of convection-such as stratiform layers-under reasonably flexible geometry assumptions. Termed anelastic convective entities (ACEs), such realizations can aid understanding of convective processes, and potentially provide time-dependent building blocks for parameterization at a complexity between steady-plume models and cloud-resolving simulations. Even for cases deliberately formulated to provide a comparison to a traditional convective plume, ACE behavior differs substantially because dynamic entrainment, detrainment and nonhydrostatic perturbation pressure are consistently included. Entrainment varies with the evolution of the entity but behavior akin to deep-inflow effects noted in observations emerges naturally. The magnitude of mass flux with nonlocal pressure effects consistently included is smaller than for a corresponding traditional steady-plume model. ACE solutions do not necessarily approach a steady state even with fixed environment but can exhibit chains of rising thermals, and even episodic deep convection. The inclusion of nonlocal dynamics allows a developing updraft to tunnel through layers with substantial convective inhibition (CIN). For cases of nighttime continental convection using GoAmazon soundings, this is found to greatly reduce the effect of surface-inversion CIN. The observed convective cold top is seen as an inherent property of the solution, both in a transient, rising phase and as a persistent feature in mature deep convection. An embedded ACE configuration allows stratiform cloud formation by time-dependent detrainment modified by dynamic feedbacks during the grid-scale adjustment process. SIGNIFICANCE STATEMENT: Convective storms cause hazardous events such as flooding, often with economic losses. Forecasting such events and how they change in a warming climate for mitigation planning is hard. In modern numerical weather and climate models, one issue standing out is that model cannot satisfactorily simulate nighttime storms over land commonly observed over, for instance, the North American Great Plains or the Amazon basin. Here, we propose a new model-named anelastic convective entity (ACE)-with two purposes in mind: (i) to be useful for improving numerical models; and (ii) to help understand convective processes in general. Preliminary results covered here are promising, especially for the nighttime convection problem.

Observations and cloud-resolving simulations suggest that a convective updraft structure drawing mass from a deep lower-tropospheric layer occurs over a wide range of conditions. This occurs for both mesoscale convective systems (MCSs) and less-organized convection, raising the question: Is there a simple, universal characteristic governing the deep inflow? Here we argue that nonlocal dynamics of the response to buoyancy are key. For precipitating deep-convective features including horizontal scales comparable to a substantial fraction of the troposphere depth, the response to buoyancy tends to yield deep inflow into the updraft mass flux. Precipitation features in this range of scales are found to dominate contributions to observed convective precipitation for both MCS and less-organized convection. The importance of such nonlocal dynamics implies thinking beyond parcel models with small-scale turbulence for representation of convection in climate models. Solutions here lend support to investment in parameterizations at a complexity between conventional and superparameterization.