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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 I, 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 a 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 gridscale adjustment process not only includes traditional warming by large-scale descent but also captures the spread of the convective cold top. The formulation also illustrates the possibility of multihour time lag before the transition to deep convection and remote initiation by small vertical velocities in the gridcell environment. Comparing 1-, 2-, 4-, and 8-ACE instances suggests promise as a potential convective-parameterization class between traditional and superparameterization, while providing a sandbox to aid understanding of convective and adjustment processes. 

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 II. 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. 

Moist heatwaves in the tropics and subtropics pose substantial risks to society, yet the dynamics governing their intensity are not fully understood. The onset of deep convection arising from hot, moist near-surface air has been thought to limit the magnitude of moist heatwaves. Here we use reanalysis data, output from the Coupled Model Intercomparison Project Phase 6 and model entrainment perturbation experiments to show that entrainment of unsaturated air in the lower-free troposphere (roughly 1–3 km above the surface) limits deep convection, thereby allowing much higher near-surface moist heat. Regions with large-scale subsidence and a dry lower-free troposphere, such as coastal areas adjacent to hot and arid land, are thus particularly susceptible to moist heatwaves. Even in convective regions such as the northern Indian Plain, Southeast Asia and interior South America, the lower-free tropospheric dryness strongly afects the maximum surface wet-bulb temperature. As the climate warms, the dryness (relative to saturation) of the lower-free tropospheric air increases and this allows for a larger increase of extreme moist heat, further elevating the likelihood of moist heatwaves. 

Abstract Daily precipitation extremes are projected to intensify with increasing moisture under global warming following the Clausius-Clapeyron (CC) relationship at about $$ 7\% /^\circ {\text{C}} $$ 7 % / ∘ C . However, this increase is not spatially homogeneous. Projections in individual models exhibit regions with substantially larger increases than expected from the CC scaling. Here, we leverage theory and observations of the form of the precipitation probability distribution to substantially improve intermodel agreement in the medium to high precipitation intensity regime, and to interpret projected changes in frequency in the Coupled Model Intercomparison Project Phase 6. Besides particular regions where models consistently display super-CC behavior, we find substantial occurrence of super-CC behavior within a given latitude band when the multi-model average does not require that the models agree point-wise on location within that band. About 13% of the globe and almost 25% of the tropics (30% for tropical land) display increases exceeding 2CC. Over 40% of tropical land points exceed 1.5CC. Risk-ratio analysis shows that even small increases above CC scaling can have disproportionately large effects in the frequency of the most extreme events. Risk due to regional enhancement of precipitation scale increase by dynamical effects must thus be included in vulnerability assessment even if locations are imprecise. 

Abstract Tropical areas with mean upward motion—and as such the zonal-mean intertropical convergence zone (ITCZ)—are projected to contract under global warming. To understand this process, a simple model based on dry static energy and moisture equations is introduced for zonally symmetric overturning driven by sea surface temperature (SST). Processes governing ascent area fraction and zonal mean precipitation are examined for insight into Atmospheric Model Intercomparison Project (AMIP) simulations. Bulk parameters governing radiative feedbacks and moist static energy transport in the simple model are estimated from the AMIP ensemble. Uniform warming in the simple model produces ascent area contraction and precipitation intensification—similar to observations and climate models. Contributing effects include stronger water vapor radiative feedbacks, weaker cloud-radiative feedbacks, stronger convection-circulation feedbacks, and greater poleward moisture export. The simple model identifies parameters consequential for the inter-AMIP-model spread; an ensemble generated by perturbing parameters governing shortwave water vapor feedbacks and gross moist stability changes under warming tracks inter-AMIP-model variations with a correlation coefficient ∼0.46. The simple model also predicts the multimodel mean changes in tropical ascent area and precipitation with reasonable accuracy. Furthermore, the simple model reproduces relationships among ascent area precipitation, ascent strength, and ascent area fraction observed in AMIP models. A substantial portion of the inter-AMIP-model spread is traced to the spread in how moist static energy and vertical velocity profiles change under warming, which in turn impact the gross moist stability in deep convective regions—highlighting the need for observational constraints on these quantities. Significance Statement A large rainband straddles Earth’s tropics. Most, but not all, climate models predict that this rainband will shrink under global warming; a few models predict an expansion of the rainband. To mitigate some of this uncertainty among climate models, we build a simpler model that only contains the essential physics of rainband narrowing. We find several interconnected processes that are important. For climate models, the most important process is the efficiency with which clouds move heat and humidity out of rainy regions. This efficiency varies among climate models and appears to be a primary reason for why climate models do not agree on the rate of rainband narrowing. 

Projecting climate change is a generalization problem: We extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations but tend to extrapolate poorly to climate regimes that they were not trained on. To get the best of the physical and statistical worlds, we propose a framework, termed “climate-invariant” ML, incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes. 

Abstract The performance of GCMs in simulating daily precipitation probability distributions is investigated by comparing 35 CMIP6 models against observational datasets (TRMM-3B42 and GPCP). In these observational datasets, PDFs on wet days follow a power-law range for low and moderate intensities below a characteristic precipitation cutoff scale. Beyond the cutoff scale, the probability drops much faster, hence controlling the size of extremes in a given climate. In the satellite products analyzed, PDFs have no interior peak. Contributions to the first and second moments tend to be single-peaked, implying a single dominant precipitation scale; the relationship to the cutoff scale and log-precipitation coordinate and normalization of frequency density are outlined. Key metrics investigated include the fraction of wet days, PDF power-law exponent, cutoff scale, shape of probability distributions, and number of probability peaks. The simulated power-law exponent and cutoff scale generally fall within observational bounds, although these bounds are large; GPCP systematically displays a smaller exponent and cutoff scale than TRMM-3B42. Most models simulate a more complex PDF shape than these observational datasets, with both PDFs and contributions exhibiting additional peaks in many regions. In most of these instances, one peak can be attributed to large-scale precipitation and the other to convective precipitation. Similar to previous CMIP phases, most models also rain too often and too lightly. These differences in wet-day fraction and PDF shape occur primarily over oceans and may relate to deterministic scales in precipitation parameterizations. It is argued that stochastic parameterizations may contribute to simplifying simulated distributions. 

Abstract A set of diagnostics based on simple, statistical relationships between precipitation and the thermodynamic environment in observations is implemented to assess phase 6 of the Coupled Model Intercomparison Project (CMIP6) model behavior with respect to precipitation. Observational data from the Atmospheric Radiation Measurement (ARM) permanent field observational sites are augmented with satellite observations of precipitation and temperature as an observational baseline. A robust relationship across observational datasets between column water vapor (CWV) and precipitation, in which conditionally averaged precipitation exhibits a sharp pickup at some critical CWV value, provides a useful convective onset diagnostic for climate model comparison. While a few models reproduce an appropriate precipitation pickup, most models begin their pickup at too low CWV and the increase in precipitation with increasing CWV is too weak. Convective transition statistics compiled in column relative humidity (CRH) partially compensate for model temperature biases—although imperfectly since the temperature dependence is more complex than that of column saturation. Significant errors remain in individual models and weak pickups are generally not improved. The conditional-average precipitation as a function of CRH can be decomposed into the product of the probability of raining and mean precipitation during raining times (conditional intensity). The pickup behavior is primarily dependent on the probability of raining near the transition and on the conditional intensity at higher CRH. Most models roughly capture the CRH dependence of these two factors. However, compensating biases often occur: model conditional intensity that is too low at a given CRH is compensated in part by excessive probability of precipitation.