A well-mixed layer formed adjacent to the lower boundary in both simulations and gradually deepened through the 10 hours preceding our analysis window (not shown). Deepening of the boundary layer allowed for the widespread development of slow-moving convection by the start of the analysis period. Cloud and updraft depths in both simulations gradually deepened during the 10 h spin-up time period, eventually reaching quasi-steady heights in the 14–16 km range (Fig. ). Updraft top heights peaked in the 12–16 km range in both simulations, which is broadly consistent with echo top heights observed from GOAMAZON e.g., Fig. a, b in. Also consistent with the updraft observations analyzed in (their Fig. 5a–c), time-averaged maximum w was greater in the dry season simulation (∼ 31 m s⁻¹) than in the wet season simulation (∼ 27 m s⁻¹), and peak updraft intensities occurred lower in the atmosphere in the dry simulation than in the wet season simulation (Fig. c), though updrafts above roughly 10 km were stronger in the wet season simulation.

In addition to deep convection, congestus convection developed as well. Cloud properties of convection in the deep and congestus regime differ which, as shown in Sect. 3.3, has large implications on the behavior of accelerations driving subsiding shells. Deep convection is wider than that of congestus and is often characterized by multiple updraft thermals. The strongest surface-reaching downdrafts and heaviest precipitation are also associated with simulated deep convection. Though significant heterogeneity exists among cloud structures within each regime, examples of cloud structures in the deep and congestus regimes are shown in Fig. . Subsiding shells are present at cloud edge near cloud top in both the deep and congestus clouds in Fig. , as well as down the entire right side of the congestus cloud.

As will be shown later, differences in updraft intensity and vertical distribution between the dry and wet season simulations were important contributors to commensurate differences in shell intensities. We demonstrate the physical reasons for these differences by examining the temperature and moisture, the B of lifted surface parcels in the 10 h sounding, and by applying a simple updraft model. In this model, a surface parcel is lifted and diluted with a fractional entrainment rate ε calculated from the following formula:

6ε≡2k2LPrR2, where k2=0.18 is the squared Von-Karman constant, Pr=13 is the turbulent Prandtl number, L=200 m is a mixing length, and R is the updraft radius. This formula was derived in based on an eddy diffusivity approximation for lateral mixing. We set R to the lifting condensation level (LCL) height for a surface parcel calculated using the formula from , consistent with past studies that have shown correlations between the LCL height and updraft radius . The thermodynamic properties and B of the surface parcel were calculated using methods described in and , which include hydrometeor loading and ice processes. Using this B profile, w was calculated using the updraft plume model from (see their Appendix A).

Vertical profiles of ΔT0≡T0,wet-T0,dry (Fig. a), where the T0 variables are the horizontal averages of T shown in Fig. c, d, reveal warmer temperatures (i.e., positive ΔT0) at low-levels in the wet simulation than in the dry simulation at 10 h, particularly in the 2–7 km layer. This difference resulted in smaller undiluted adiabatic B in the 2–7 km layer in the wet simulation (blue dashed lines in Fig. b) than in the dry simulation (red dashed lines in Fig. b), which also translated to a commensurate difference in diluted B (solid lines in Fig. b). Using the profiles of diluted B, the updraft model (Fig. c) yields profiles of wet season (solid blue) and dry season (solid red) w that closely mimic the time averaged profiles from the simulations (see Fig. c). The larger low-level diluted B in the dry simulation partially explains the stronger low-level updraft strengths in the dry simulation than in the wet simulation.

The differences in moisture between the wet and dry simulation also influenced the differences in w among the simulations. For instance, vertical profiles of Δq0≡q0,wet-q0,dry reveal smaller surface and lower tropospheric moisture (green line is positive in Fig. a) in the dry simulation. Because of this, the dry simulation developed a higher LCL height (1285 m) than the wet simulation (1166 m), which contributed to wider updrafts and smaller ε in the dry simulation, resulting in strengthened updrafts relative to the wet simulation. We deduce this because neglecting this difference in ε in the updraft model (left-most dotted red line in Fig. c) results in weaker maximum w in the dry profile than in the wet profile, which is inconsistent with the simulations. On the other hand, a drier lower free troposphere enhanced dilution in the dry simulation relative to the wet, which moderated w in the dry simulation and resulted in stronger updrafts aloft in the wet simulation. We deduce this because replacing the moisture profile in the dry profile with that of the wet and re-running the updraft model results in a dry season w that is erroneously stronger than the wet season w at all levels (right-most dotted red line in Fig. c).

Utilizing parcel trajectories, subsiding shell properties were assessed in bulk. Dry and wet simulation shell parcel w are displayed in Fig. . The normalized downdraft time coordinate in Fig. a allows parcel properties to be compared based on downdraft start time and downdraft end time, whereas the normalized height coordinate in Fig. b is used to compare parcel properties based on downdraft origin height and termination height. Immediately, it is evident that use of the normalized height coordinate yields stronger shells. This is because the strongest shell subsidence may occur at different times in the downdraft but always occurs about halfway down the downdraft. For the remainder of this analysis, we choose to use the normalized time coordinate (Fig. a) because understanding time evolution of parcel properties such as acceleration is prioritized in this study. To avoid performing a temporal interpolation of trajectories, the first downdraft point for each parcel is the first time step in which w<0 m s⁻¹. As a result, trajectory w does not begin at 0 m s⁻¹, but rather at some value below it. Immediately, it is evident that dry shell downdrafts are stronger than those in the wet simulation, consistent with the RWP observations in . Mean wet simulation shell parcel w reached a mean minimum of -2.78 m s⁻¹, whereas dry shell parcels achieved a mean minimum w of -3.44 m s⁻¹. This equates to dry simulation downdrafts being 23.5 % stronger than their wet simulation counterparts. Statistical significance in the difference of the means was determined using a Welch's t-test with a significance level (α) of 0.05. Mean differences were statistically significant through the entire downdraft period, with dry simulation downdrafts on average being 26.5 % stronger than those in the wet simulation.

Mean accelerations acting on subsiding shell parcels are shown in Fig. . With regard to total accelerations, it is evident in both simulations that parcels that pass through shells are both negatively buoyant and are initially accelerated downward by VPG accelerations. Though not shown, parcels experienced minima in downward accelerations from both total VPG and B a few seconds to minutes before achieving a negative w. In Fig. a, subsiding shell parcels in the dry simulation are initially more negatively buoyant with a minimum average B of -0.021 m s⁻². B then increases through ≈ 55 % of the downdraft time, at which point B sign reversal occurs and B becomes positive due to parcels overshooting their level of neutral B. Wet simulation mean B, which is most negative at shell downdraft initialization with a value of -0.016 m s⁻², shares a similar increasing trend to that of the dry simulation. Like B, the VPG (Fig. b) is initially negative and decreases in magnitude as parcels descend. With an initial VPG of -0.023 m s⁻², dry simulation VPG acceleration becomes positive ≈ 60 % of the way through the downdraft before reaching a maximum of 0.027 m s⁻² at downdraft end. However, unlike B which increases continuously, dry simulation VPG accelerations plateau halfway through the downdraft. The wet simulation VPG undergoes the same behavior, albeit with both smaller downward accelerations initially, and smaller upward accelerations later on. Statistical significance of B and VPG acceleration behaviors was assessed as well. B differences were significant through the entirety of the downdraft, while VPG differences showed significance through the first and final ≈ 35 % of the downdraft. With this, differences in total acceleration means are significant in both the cloud-top region where the shells initiate and the shell terminus.

One acceleration that must also be addressed is that from subgrid scale processes such as turbulence. The subgrid scale acceleration, which does contribute to total acceleration within shells, is plotted in Fig. c. Though the acceleration is weak compared to B and VPG, it ultimately provides a dampening effect in both the dry and wet simulations. This subgrid term is likely physically representative of turbulent mixing. Because we see dampening, it is likely that, while shells are accelerated downward by B and VPG, turbulent mixing of updraft or environmental air into the shell acts to reduce net downward acceleration. This upward acceleration persists through the entirety of the downdraft. As for seasonal differences, dry season subgrid effects are larger than that of the wet season. Because turbulent mixing is tied to the horizontal shear at the interface of the updraft and shell, and since dry simulation updrafts and shells are stronger, the dampening effect from dry simulation turbulent mixing is greater as well.

The parcel buoyant VPGB=-cpθρ,0∂πB′∂z, dynamic linear VPGDL=-cpθρ,0∂πDL′∂z, and dynamic nonlinear VPGDN=-cpθρ,0∂πDN′∂z contributions to VPG accelerations in both simulations are plotted in Fig. . Effective buoyancy Beff; i.e., the net thermodynamic acceleration;, which is simply the sum of B and VPGB, is also plotted to show the effect that pressure perturbations have on modulating B. VPGDN has the largest magnitude of the three decomposed perturbation pressure accelerations. The temporal evolution of VPGDN closely mimics that of the total VPG. Initially VPGDN drives strong downward acceleration, but undergoes a sign reversal and drives strong upward acceleration by the end of the downdraft lifetimes. The magnitude of the initial downward VPGDN is considerably larger in the dry simulation than in the wet simulation, suggesting that this pressure contribution largely explains the differing total VPG magnitudes seen in Fig. c. Wet simulation VPGB begins as positive but quickly becomes negative 20 % into the downdraft, contributing downward acceleration thereafter. In contrast, the VPGB in the dry simulation remains positive for ≈ 55 % of the downdraft, becoming negative thereafter. Such VPGB accelerations partially counteract the strong negative B that arises from cloud edge evaporative cooling, while also opposing the positive B that decelerates downdraft parcels once they have descended below their levels of neutral B. Consequently, Beff shows a similar increasing trend like B itself, but magnitudes are reduced at the origin and termination points of the downdraft compared to B. In fact, Beff magnitudes are reduced from B to a greater extent in the dry simulation than in the wet because dry simulation VPGB is positive for more of the downdraft. This counteracts the difference in B between the simulations, leading to similar Beff magnitudes. VPGDL is very small relative to the other VPG contributions, which is likely a result of relatively weak vertical wind shear in both simulations (Fig. ). This pressure contribution does not contribute to the differing overall VPG magnitudes seen in Fig. c.

Previous subsiding shell studies have noted the presence of downward acceleration just within the cloud edge as well, where in-cloud negative B may be present e.g.,. To ensure that the accelerations shown in Figs. – are representative regardless of shell definition, we applied the same analysis to a new set of identified shell points, where w<0 m s⁻¹ and total cloud water mixing ratio was allowed to exceed 0.01 g kg⁻¹. Total non-cloud hydrometeor mixing ratio was also restricted to be less than 0.01 g kg⁻¹ in order to filter out any in-cloud hydrometeor-loaded downdrafts. However, as was done previously, points were only classified as shell points if they were in the vicinity of the cloud boundary. After identifying the parcels that passed through these new shell points, parcel w, VPG, B, and total acceleration were gathered (Fig. ).

With in-cloud points included as shell points, mean shell parcel w magnitude decreases, especially in the dry season (Fig. a). Such weakening of subsidence is due to a substantial decrease of the VPG contribution, specifically in the VPGDN term. Such decrease could arise due to the increased parcel sample size, but it is also possible that pressure gradients are slightly stronger on the outside of the cloud versus inside. Despite the VPG magnitudes de-amplifying, B becomes more negative throughout the downdraft. Aligned with previous literature mentioning negatively buoyant cloudy air, it appears as though many of the new points and parcels identified are cloudy and negatively buoyant, leading to the greater contribution to subsidence from B. This negative buoyancy arises from injection of environmental air into the cloud and the resulting evaporation/sublimation of a high volume of cloud water or ice. Despite the changes in subsiding shell w from the acceleration magnitude variation, the general behaviors of both resolved and subgrid accelerations are the same. Therefore, whether in-cloud downdraft points are included or not, the accelerations driving subsiding shells are the same, regardless of shell definition.

Following , we ascertain the net (i.e., integrated) contribution of each of these accelerations to downdrafts. This is accomplished by first considering the frictionless vertical velocity equation: 7dwdt=B+VPG+SG, where SG represents acceleration from subgrid scale processes. We may use the chain rule to re-write the left-hand-side term as dwdt=dwdzdzdt=wdwdz=ddzw22=dKEdt, where KE≡w22 is the kinetic energy. Upon vertically integrating from the downdraft start height zi to any arbitrary height below the start height z, we obtain:

8ΔKEB(z)=∫z∗=ziz∗=zBdz∗,9ΔKEVPG(z)=∫z∗=ziz∗=zVPGdz∗,10ΔKESG(z)=∫z∗=ziz∗=zSGdz∗,11ΔKEtot(z)=ΔKEB(z)+ΔKEVPG(z)+ΔKESG(z), where ΔKE is the change in kinetic energy between the parcel's starting location zi and a given height below the starting point z and z∗ is a dummy variable of integration. We similarly compute ΔKEVPG,B, ΔKEVPG,DL, ΔKEVPG,DN, and ΔKEBeff. Note that despite downward velocities within a downdraft, the absolute change in KE is positive since w is squared. Processes that accelerate the parcel downward will contribute positive ΔKE, whereas parcels that accelerate the parcel upward will contribute negative ΔKE. With the assumption that KE(zi)=0 at the downdraft start, all ΔKE terms can be expressed as KE. Throughout the downdraft, KEtot is larger in the dry simulation than the wet (Fig. c) because downdraft speeds are more negative in the dry than in the wet simulation. Both KEB and KEVPG contribute meaningfully to total KE, though KEB (Fig. a) is roughly double that of KEVPG (Fig. b) in both simulations. Hence, downdrafts in our simulations are both buoyantly and dynamically driven, though B is the predominant contributor. Both KEB and KEVPG are larger in the dry simulation by roughly equal magnitudes. This means that while B is the predominant overall driver of shell downdrafts, the environmental differences in downdraft strength are roughly equally driven by differences in B and differences in the VPG. The dampening of total KE from subgrid scale turbulence can also be seen in Fig. c where KESG is negative.

The results in Fig.  support both of the hypotheses proposed in the introduction that larger negative B and larger downward dynamic pressure accelerations drive stronger downdrafts in the dry season than in the wet season. However, an examination of KEBeff and KEVPG,B calls this conclusion to question. Specifically, the appreciably larger KEB in the dry season simulation is largely offset by smaller KEVPG,B in the dry season simulation, such that the difference in KEBeff between the wet and dry season simulations is small (Fig. c). This implies that while downdrafts are more negatively buoyant in the dry season, the atmosphere's thermodynamic response to these more negatively buoyant downdrafts induces an upward pressure gradient acceleration that nearly entirely offsets this larger negative B. Hence, the differences in downdraft strength between the wet season and dry season are predominately driven by larger KEVPG,DN in the dry season than in the wet season (Fig. a). In other words, there is stronger dynamic forcing for downdrafts in the dry season. Furthermore, KEBeff is now comparable in magnitude to KEVPG,DN, implying that shells are roughly equally thermodynamically and dynamically forced.

Exploration of shell origin and termination heights prompted a comparison between shells associated with shallow/congestus cumulus and deep convection (Fig. ). A bimodal distribution appeared in both the origin and termination heights, with a peak in origin heights centered about 9000 and 8000 m in the dry and wet season, respectively, but also at around 3000 m in both simulations. Termination height peaks in the distribution are shifted downward by about 500–1000 m, roughly matching the displacement magnitudes. Such displacement magnitudes are similar to those found in , who looked at ascending thermals with a limited displacement due to drag supplied by nonhydrostatic pressure perturbations. In the case of our descending motion within the shell, we believe displacement is limited partially by the overshooting of the level of neutral buoyancy by parcels, and primarily by the upward-directed VPGDN. We speculate that the bimodal distribution in shell origin/termination heights is associated with the congestus and deep regimes of cumulus. Given the large difference in the heights, it is possible that shell properties for congestus and deep convection may be different, especially since RH values are higher in the lower troposphere and the updrafts of congestus clouds are weaker. For this comparison, we assume cumulii that have a cloud top greater than 5 km are considered deep , whereas any cloud below this height and above 2 km is categorized as congestus. Mean w of parcels passing through (a) deep and (b) congestus shells is shown in Fig. . Unsurprisingly, the mean w magnitude of deep parcels is greater in the deep convection shells than it is in the congestus shells. Deep shell parcels attain minimum w of -3.66 and -2.96 m s⁻¹ in the dry and wet simulations, respectively. In the congestus regime, dry parcel subsidence is 1 m s⁻¹ weaker than in the deep and wet parcel subsidence is only slightly reduced to -2.44 m s⁻¹.

With differing w magnitudes between the two types of convection, we again perform an assessment of KE contributions to gauge the importance of thermodynamic and dynamic accelerations in shells. Figure  shows the comparison between deep and congestus contributions to KE from Beff and the VPGDN, as well as total acceleration with the subgrid contribution included. As was the case with w, maximum KE is greater in the deep shells versus the congestus shells (Fig. c, f). Additionally, in both convective regimes, dry simulation KE is greater at all times compared to the wet simulation. Given the larger number of parcels embedded within deep shell downdrafts, the behavior of KE in this regime is similar to that of all downdrafts combined (Fig. ). With this being the case, attention turns toward the congestus regime, where KE contributions from Beff and VPGDN differ from their deep counterparts. Maximum total KE in congestus shells is reduced from that in deep shells in both simulations, with dry and wet congestus shells on average having 43.9 % and 24.5 % less KE than deep shells, respectively. Despite KEBeff more than doubling in the dry simulation, total KE decreases. This is due to the overpowering effect of KEVPG,DN, which decreases significantly and is largely negative for much of the downdraft in the congestus regime. A large subgrid contribution exists in the dry simulation as well, again due to stronger updrafts in that simulation. Magnitudes of wet simulation differences in individual accelerations are reduced, with both KEBeff increasing and KEVPG,DN decreasing only minimally. With this, it is clear that VPGs are generally weaker (and potentially more detrimental) in congestus shells than they are in deep convection shells. Furthermore, KEVPG,DN is not statistically different between the dry season and wet season congestus shells, implying that the more intense downdrafts in dry congestus shells are primarily driven by these shells being more negatively buoyant in the dry season. This contrasts with deep convective shells, which were primarily stronger in the dry simulation because of a stronger downward VPGDN.

Visualization of the shell structures in both simulations and the two modes of convection was done via compositing of shells. The composites of subsiding shells allow us to physically interpret the processes driving the shells, and to understand how these processes differ between the two simulations. As shown in the previous section, differences may arise in the properties of shells associated with deep versus congestus convection. Shell width is one of those properties, and the widths of the shells that were used in the compositing process are shown in Fig. . Despite a mean deep convective shell width of 800 m identified in , the shells in the present study's simulations are much narrower. Dry simulation deep and congestus shells have mean widths of 480 and 420 m, respectively. Mean values are the same in the wet simulation, meaning shell width primarily depends on the depth of the convection. These low width values are surprising given that the updrafts in this study are deeper and stronger than those in . The congestus shell widths align with the findings of that study, but the deep shell widths are nearly half of their noted deep shell average. However, this reported average was specifically taken from cloud top, and noted that widths of shallow and deep shells were fairly similar away from the very top of the cloud. With this, shells in deeper convection are slightly wider, but the magnitude more closely matches the mean shell width found away from the very top of the cloud (see Fig. 4 in ).

Figure  displays composited deep convective shells and their associated accelerations. Though composites of w show shells of similar strength, the parcel trajectory analysis supports stronger shells in the dry simulation. One potential reason for not seeing a stronger shell in the dry composite is the asymmetrical nature of shells and potential smearing from that variability. Therefore, it is crucial that the composites are interpreted as a visual for general updraft-shell structure. Focusing on B in Fig. , a clear region of negative B encapsulates a strongly positively buoyant updraft core. Negative B exists both above the updraft and on the flank of the updraft where shells are present. Such negative B may arise in two ways. The negative B existing above the updraft arises from the adiabatic cooling of environmental air that is pushed upward by an ascending thermal. Here, negatively buoyant parcels are forced horizontally toward the flanks of the updraft and can begin to sink down the edges of the cloud in the shell. However, stronger negative B exists where shell subsidence is maximized. It is here that a strong positive perturbation of qv is present, likely owed to the evaporative cooling of cloud droplets at the edge of the updraft. The presence of this feature in the composite supports the evaporative cooling mechanism of formation of subsiding shells e.g.,. When comparing B to Beff, the region of downward acceleration that was located above the updraft is eliminated and only that which occurs in the shell remains. Because Beff accounts for the effects of VPGB, and with a high πB′ perturbation found in the upper portions of the updraft, almost all downward acceleration from negative B above the updraft is offset by upward VPGB, leading to no downward acceleration in this region. Therefore, all subsidence only will occur on the flanks of the updraft in the shell where negative thermal B arising from evaporative cooling dominates.

While a clear horizontal dipole in the B and Beff structure exists between the shell and the updraft, a vertical dipole is present in the VPGDN field and is maximized where vertical gradients of πDN′ are largest. The πDN′ field is structured so that a minimum in pressure is found embedded within the maximum horizontal gradient of w. This is also where the horizontal B gradient is maximized, allowing the minimum in pressure to arise in the center of the toroidal circulation associated with rising cloud thermals. As seen in both the composites and parcel trajectory accelerations, this VPGDN dipole structure leads to a downward acceleration above the shell core, and a positive acceleration below it. Additionally, the magnitude of VPGDN is much greater than that of B or Beff. This is especially the case where shell subsidence originates, about 500 m above the region of maximum subsidence. It is here that parcels are essentially “sling-shotted” down the side of the cloud by the downward branch of the toroidal circulation, which acts as the driver of shell subsidence e.g.,.

The dependence of downward shell accelerations on the toroidal low pressure regions explains why VPGDN is more intense in the dry simulation than in the wet simulation. That is, the magnitude of the toroidal low should scale with the magnitude of updraft w and the horizontal B gradient within the cloud core. This connection between w and πDN′ is evident in the analytic solutions of , and is further shown in simulations of moist thermals in (see Eq. 13 in that study). Hence, the dry simulations have stronger downdrafts than the wet because the dry simulations have stronger overall updrafts and consequently stronger downward accelerations driven by toroidal low pressure .

The structure of the w field in the congestus regime composite (Fig. ) is similar to that of the deep composite, aside from the congestus updrafts being weaker. The most notable differences between the deep and congestus composites is associated with the shell features. Congestus composite negative B and Beff wrap around the updraft in a bean-like shape, and negative values in these features extend further downward than they do in the deep convection composites. The trajectories support this, with negative buoyant accelerations persisting in the downdraft period longer than in the deep shells. Therefore, it is likely that the congestus regime exhibits more of the evaporative cooling processes that occur at cloud edge, which is supported by slightly stronger qv′ in the congestus shells than the deep shells. Though B variations are present between the two regimes, the most notable differences is embedded within the VPGDN fields. The composite structure of congestus VPGDN is nearly identical to that of deep convection, but magnitudes are reduced. This comes as no surprise as the strength of the VPGDN is proportional to horizontal B gradients and updraft strength, and such gradients and updrafts are weaker in the congestus convection. The weakened negative VPGDN prevents shells from being as strong as those in the deep regime.

To summarize (e.g., Fig. ) parcels near cloud top are first accelerated downward by the VPGDN induced by the toroidal circulation and by negative B driven by the evaporation of condensates. Because this circulation is proportional to updraft strength and horizontal B gradients, the VPGDN is stronger in deep convection versus shallow convection, and in stronger dry season simulations than in the wet season simulations. As soon as parcels within the shell pass below the height of minimum πDN′ in the toroidal circulation, they experience an upward VPGDN acceleration and only Beff and momentum can maintain the subsidence. Parcels will also become more positively buoyant as they overshoot their levels of neutral B. Once parcels are well below the height of minimum πDN′ and are positively buoyant, shell subsidence ceases. Based on both Fig.  and the composites, such processes yielded shells that were only about 500–1500 m in depth, depending on the strength of the convection. The authors note that individual cloud structures are much more complex than that shown in Fig. , as well as the composites of deep and congestus convection (see Fig. ). Heterogeneity among clouds will likely lead to inter-cloud differences in shell strength and behavior, likely due to the alteration of B and VPG magnitudes. However, given that shells are primarily driven by these two accelerations, the composites in Figs. – are an effective representation of the entire subsiding shell population. Additionally, shell downdrafts may not necessarily begin at cloud top, as depicted in Fig. . Investigation of individual parcels revealed most subsiding shell downdrafts originated above a thermal, whether it be at cloud top or potentially a rising thermal near the base of the cloud. Such thermals may be present at different stages of a cloud's lifetime, which may have implications on the relative contributions of each acceleration to shell subsidence. The link between subsiding shell properties and cloud life stage will be investigated in the future.