This section analyzes how qc varies vertically in the convection cloud chamber. Since simulations reached quasi-equilibrium around 15 min, vertical profiles presented are averaged over the subsequent 15 min period (15–30 min). Figure 3 (top panels) shows the vertical profiles of domain-averaged qc for varying aerosol concentrations based on VOCALS and Seoul aerosol distributions. In general, qc increases with height; however, this increase with height weakens with increasing aerosol concentrations. At higher aerosol concentrations, the vertical distribution of qc becomes increasingly uniform, suggesting more spatially homogeneous droplet growth within the cloud chamber. To quantify the vertical variation in qc, a diagnostic metric, Δqc, was introduced. Δqc indicates the relative difference in qc between the upper and lower portions of the cloud chamber, capturing the degree of vertical inhomogeneity: 1Δqc=q‾cz=1.7m-q‾cz=0.3mq‾cz=0.3,1.7m×100%, where the numerator is the horizontal mean qc at z=1.7m minus the horizontal mean qc at z=0.3m, and the denominator is the mean qc at these two reference heights during the quasi-equilibrium period, which is used to normalize the vertical-contrast metric. These heights are chosen to be symmetrically offset from the lower and upper plates (0.3 m from each boundary) to reduce sensitivity to boundary-adjacent layers. Figure 3 (bottom panel) shows that Δqc decreases with increasing aerosol concentration for both VOCALS and Seoul aerosol distributions. At low aerosol concentrations (60–200 cm-3), Δqc typically ranges between approximately 9 %–15 %, indicating a relatively strong vertical increase in qc that reflects efficient droplet activation and condensational growth in the lower part of the chamber where mixing between warm, moist air from the bottom boundary and cooler air aloft generates enhanced supersaturation. Conversely, under high-aerosol conditions (≥1000cm-3), Δqc drops below 5 %, reaching approximately 2 % in certain Seoul cases, indicative of a vertically uniform cloud structure. The weakening vertical gradient in qc with increasing aerosol concentration implies underlying mechanisms: intensified competition for water vapor and therefore low values of supersaturation (S), which are examined further in the following section.

To elucidate the mechanisms behind the simulated reduction in Δqc at high aerosol concentrations, relationships between Δqc and key microphysical parameters were analyzed. Figure 4 shows a strong positive correlation (R2=0.82) between Δqc and the phase relaxation time, which is defined as τp=(4πDcNcrm)-1, where Dc is a modified molecular diffusion coefficient for water vapor. A longer τp, characteristic of low aerosol conditions, is linked to a relatively greater vertical increase in qc. Physically, τp represents the time required for cloud droplets to equilibrate with the surrounding vapor field. When aerosol concentrations are high, the number of droplets increases, leading to stronger competition for available water vapor. As a result, supersaturation is driven rapidly toward a low quasi-steady value, so individual droplets experience weaker supersaturation and grow more slowly, but the population equilibrates sooner and exhibits limited additional growth aloft, thereby weakening the vertical increase in qc. In the polluted cases, the enhanced condensational sink keeps supersaturation close to its low quasi-steady value during ascent, which limits additional condensational growth aloft and therefore reduces the vertical increase in qc. The suppression of vertical S gradients under high aerosol concentrations is clearly illustrated in Fig. 5a and b, which show vertical profiles of S for the VOCALS and Seoul cases, respectively. Notably, the near-bottom layer exhibits predominantly positive mean supersaturation, although both positive and negative values occur intermittently. This behavior is consistent with moist Rayleigh–Bénard convection results from a one-dimensional turbulence (ODT) framework (Chandrakar et al., 2020), supporting the role of the lower boundary layer as a plausible activation region. As aerosol loading increases, the vertical variation in S becomes gradually reduced, reflecting enhanced competition for water vapor and faster equilibration. In other words, higher Nc leaves insufficient vapor to sustain S during ascent, resulting in vertically almost uniform qc profiles.

The S histograms in Fig. 5c and d confirm this narrowing distribution, clearly illustrating the diminished variability and reduced magnitude of S in polluted cases. Figure 6 further demonstrates a systematic decline in the standard deviation of supersaturation (σS) with increasing aerosol concentrations, reflecting suppressed S fluctuations in more polluted environments. In addition, the domain-mean supersaturation (S‾) also shows a decreasing trend with increasing aerosols (Fig. 6; see symbol colors), indicating an overall reduction in the thermodynamic potential for droplet activation and growth. The minimum critical supersaturation (Scrit) in the prescribed aerosol spectrum is approximately 0.02 %, designated to the largest aerosol particles in the size distribution. As aerosol loading increases, S‾ steadily falls toward this value, often converging near 0.02 % (see Fig. 6). This behavior is qualitatively consistent with Yang et al. (2025), who found that mean supersaturation approached the critical value for their monodisperse aerosol. In our polydisperse case, S‾ does not collapse to a single value, but instead converges to a narrow range near the minimum Scrit set by the largest particles. When S‾ is near this threshold, particles with Scrit close to S‾ can repeatedly transition between weak activation and deactivation as turbulent S fluctuations move conditions slightly above or below their critical value, which effectively buffers S‾. This buffering helps explain why, beyond a certain aerosol concentration, the domain-mean qc no longer increases (Fig. 2): enhanced vapor competition limits additional net activation and condensational growth despite further increases in aerosol loading. This suppression of S variability parallels the weakening of the vertical qc gradient discussed earlier. That is, just as vertical differences in qc become less pronounced with increasing aerosol, so does the vertical structure of S. Figure 2 also shows that each microphysical variable, Nc, rm, or qc, exhibits distinct timescales to reach quasi-equilibrium conditions, with these timescales varying systematically with aerosol concentration (see Supplement Figs. S1 and S2 for a detailed analysis). Specifically, the increasing aerosol concentration reduces S‾ (Fig. 6), influencing these equilibrium timescales.

To better understand the dynamical origin of this suppressed variability, we examine how S interacts with vertical motion. Figure 7 illustrates a significant linear correlation (R2=0.93) between σS and the correlation coefficient between S and vertical velocity (W). This suggests that σS is closely tied to the interaction between W and S. Before interpreting this relationship, we address a potential concern raised by the mean supersaturation profiles in Fig. 5a and b, which exhibit oscillations near the lower and upper rigid boundaries. Two factors likely contribute to these near-wall oscillations. First, resolved transport and mixing are inefficient near rigid boundaries in ILES, which can allow sharp gradients to persist. Second, supersaturation is a diagnosed quantity, so small grid-scale perturbations in temperature and water vapor can translate into comparatively large fluctuations in S because of the nonlinear saturation relationship and advection–condensation coupling (Grabowski and Smolarkiewicz, 1990). Importantly, the W–S correlations reported in Fig. 7 are computed over the interior region away from the plates, and the aerosol-dependent trends in Fig. 7 remain unchanged when the boundary-adjacent layers are included (not shown). With this in mind, we interpret the aerosol dependence of W–S coupling as follows. In cleaner conditions, the longer phase relaxation time allows S to respond more directly to vertical motions, as vapor is not quickly depleted by condensation. However, in polluted conditions, the short phase relaxation time causes supersaturation to relax rapidly toward its quasi-steady value, so supersaturation responds only weakly to fluctuations in vertical velocity W. In other words, the rapid vapor consumption reduces S response to W variations, effectively decoupling S from W. This explains the weakened W–S coupling under high aerosol concentrations. To illustrate this W–S coupling more directly, Fig. 8 shows the scatterplot of supersaturation and vertical velocity. The scatterplots show that positive S values are preferentially associated with updrafts (W>0), whereas negative S occurs mainly in downdrafts (W<0), consistent with condensation being most effective during ascent. As aerosol concentration increases, both the positive and negative S tails contract toward zero, making the W–S relationship more symmetric and thereby weakening the W–S coupling. As noted by Grabowski et al. (2024), this positive correlation between S and W in the chamber arises not from adiabatic cooling driven by the updraft itself, but rather from the mixing of air volumes (parcels) with different thermodynamic properties originating from the lower and upper boundaries. Under constant-pressure conditions, upward motions near the lower boundary transport warmer and moister air there into the chamber, producing positive S perturbations. Conversely, downward motions transport air that is saturated at the cold upper boundary (low absolute qv) into the warmer chamber interior; as this air warms and mixes, saturation vapor mixing ratio increases faster than qv, so the local relative humidity decreases and subsaturation (S<0) can occur. This behavior is consistent with observations from laboratory chamber experiments, which report the most negative S in downdrafts (Anderson et al., 2021), accelerated vapor consumption reduces droplets' responsiveness to vertical S fluctuations, weakening the coupling between S and W (small W–S correlation) and reducing the variability of S (small σS). The physical explanation for this is: as aerosol concentration increases, the total droplet surface area also increases, facilitating faster water vapor consumption; Consequently, positive S in regions of upward motion is rapidly reduced toward zero; Meanwhile, in regions of downward vertical velocity, the increased droplet surface area accelerates evaporation, supplying water vapor efficiently and thereby driving negative S values toward zero fast. Notably, our simulations show clear sensitivity of both positive and negative S distributions to aerosol concentration (Fig. 8), whereas Grabowski et al. (2024) reported negligible sensitivity of negative S values to aerosol concentration. This discrepancy is likely attributable to differences in aerosol injection methodologies. Repeating the analysis over the full domain, including the boundary-adjacent layers, reduces the absolute magnitude of the W–S correlation but does not change the aerosol-dependent trends or the tight relationship between σS and the W–S correlation (not shown).

The simulated suppression of vertical gradients in qc under high aerosol concentrations is most plausibly explained by constraints imposed by τp. In polluted environments, the high number of activated droplets dramatically increases the total surface area available for condensation, which shortens τp and allows the condensational sink to balance the turbulent source of supersaturation over a short timescale. As a result, supersaturation remains small away from the production region near the lower boundary, and most condensational growth occurs there rather than being sustained throughout the full depth of the chamber. Consequently, droplets complete their growth before experiencing the full extent of vertical S variability typically encountered during upward transport. As a result, the effect of vertical motion on condensational growth is diminished, leading to a vertically uniform qc structure regardless of height within the convection chamber. This mechanism highlights how fast microphysical adjustment, rather than turbulent dynamics, primarily governs the vertical distribution of cloud condensate under polluted conditions. To further evaluate this interpretation, the next section presents a Lagrangian analysis that directly compares the characteristic timescales of condensation and turbulent mixing using parcel trajectories, providing a more quantitative framework for understanding the suppression of vertical microphysical variability.

To investigate how SDs near the chamber base are vertically transported and dispersed, we performed Lagrangian tracking of all SDs residing within the lowest 0–0.2 m layer of the chamber at a certain point of time. Rather than analyzing a single case, we repeated this tracking procedure across multiple start times during the quasi-equilibrium period, specifically from 900–1780 s at 20 s intervals, to ensure statistical robustness and account for temporal variability of the flow field. Figures 9 and 10 present representative results for two tracking initiation times: 900 and 1600 s, respectively. Panel (a) in each figure shows time–height histograms of SD counts, revealing how SDs rapidly ascend from near the chamber base toward the upper region, subsequently descending and ascending again, with the total count decreasing due to wall losses. Panel (b) in each figure illustrates the spatial distributions of SDs at the initial moments (t=900s for Fig. 9, and 1600 s for Fig. 10), while panel (c) depict their positions 20 s later (t=920 and 1620 s, respectively). These figures clearly illustrate that most SDs ascend to heights above 1.5 m within approximately 20 s (panel a), although the detailed spatial distribution and vertical extent differ depending on the tracking initiation time (panel c).

Given that most SDs ascend from the chamber base to the upper region (z>1.5m) within approximately 20 s, this ascent time serves as a proxy for the turbulent mixing timescale (τm), that is, the characteristic time over which the supersaturation field changes due to turbulent advection and mixing, in contrast to the phase relaxation time (τp), which characterizes changes in supersaturation due to condensational growth. The turbulent mixing timescale can also be independently estimated from the upper height of the chamber (1.5 m) and a characteristic turbulent velocity scale (U≈0.06ms-1), interpreted as the rms turbulent velocity, derived from the mean turbulent kinetic energy (TKE≈0.004m2s-2) as U=(2/3TKE)1/2. This calculation yields a mixing timescale of approximately 28 s, which is longer than the previously mentioned ascent timescale of ∼20s, likely because the 20 s estimate primarily considers SDs strongly influenced by ascending motion. In contrast, τp becomes significantly shorter under high aerosol concentrations, decreasing from about 14 s in clean cases to around 1 s in polluted conditions (Fig. 4). This disparity can be expressed by the Damköhler number (Da=τm/τp), which quantifies the relative pace of condensation versus turbulent mixing. In polluted environments, Da≫1, which indicates that condensation adjusts much faster than vertical mixing, so the condensational sink rapidly balances the turbulent source and maintains a low quasi-steady supersaturation. As a result, supersaturation fluctuations and additional condensational growth aloft are strongly reduced, and qc becomes nearly uniform with height. This behavior is consistent with the quasi-steady supersaturation framework of Chandrakar et al. (2018), in which both the mean supersaturation and its variance decrease as the system timescale τs=τmτp/(τm+τp) becomes smaller. This decoupling between vertical motion and S evolution explains the weakened vertical gradients of qc observed under high aerosol loading. To further investigate how vertical motion influences droplet behavior under these conditions, we analyzed the trajectories of SDs within the lowest 0–0.2 m layer based on their normalized vertical displacement, using the VOCALS (200, CTRL) case as a representative example. Normalized vertical displacement is quantified for each SD over the 20 s tracking interval by comparing its height at a certain second to that of the previous second. If the SD ascended, score of +1 was assigned; if it descended, -1; and if there was no change, 0. These 20 values were summed and divided by 20, yielding a normalized score between -1 (entirely descending) and +1 (entirely ascending). Figure 11a shows the evolution over time (0–20 s) of the mean height of all SDs grouped by their normalized vertical displacement bins: each line represents the mean height of SDs and shaded bands indicate the 25th–75th percentile range. The results demonstrate a clear trend that shows SDs with higher normalized vertical displacement tending to reach significantly higher heights. Despite this trend, turbulent motions in the convection chamber allow some SDs with lower normalized vertical displacement to reach relatively elevated heights. Figure 11b presents the results averaged over all tracking start times (900–1780 s). For each start time, the mean SD height was calculated for each normalized vertical displacement bin, and the shaded bands represent the 25th–75th percentile range of these mean height lines across all start times. The overall trend closely resembles that of the single case shown in Fig. 11a, confirming the robustness of the normalized vertical displacement metric in capturing vertical transport pathways in the convection chamber.

Building on the Lagrangian tracking framework introduced above, we further investigate how vertical motion influences droplet growth under varying aerosol conditions. Specifically, we analyze the size evolution of individual SDs over 20 s as a function of their normalized vertical displacement. Again, this analysis focuses on SDs initially located near the chamber base (0–0.2 m layer) and tracked upward through turbulent mixing. Tracking was initiated at multiple start times during the quasi-equilibrium period (from t=900 to 1780 s, every 20 s), and the results were averaged across these intervals. Figure 12a presents the mean normalized droplet growth (dr) of each SD as a function of its normalized vertical displacement. The droplet growth is calculated using: 2dr=rend-rstart(rend+rstart)/2, where rstart and rend are the radius of each SD at the beginning and end of the 20 s interval, respectively. It is clear that SDs with higher normalized vertical displacement generally exhibit larger dr compared to those in the lowest normalized vertical displacement bin (-1.0 to -0.78), particularly for normalized vertical displacement bins up to approximately -0.56 to -0.33, across most aerosol concentrations. This indicates that trajectories that spend more time moving upward within the supersaturation source region near the chamber base tend to experience enhanced condensational growth. Under such conditions, ascending SDs experience more favorable thermodynamic environments for condensational growth. However, as aerosol concentration increases, dr for ascending SDs becomes less pronounced. In particular, the VOCALS (10 K) and Seoul (10 K, CTRL) cases show significantly reduced differences in growth between ascending and descending SDs, suggesting that condensational growth becomes less sensitive to vertical motion because S is rapidly buffered near a low quasi-steady value set by the balance between the boundary-forced vapor supply (transport) and the enhanced condensational sink at high aerosol loading (short τp). Figure 12b presents the mean count of SDs in each normalized vertical displacement bin. SDs that were removed due to wall-loss were excluded from the count. Notably, the total SD count tends to increase with aerosol number concentration. This is because higher aerosol loading generally leads to smaller activated droplets with lower fall velocities, thereby reducing sedimentation-driven wall losses and allowing more SDs to remain within the domain throughout the tracking period.

A particularly notable feature in Fig. 12a is that the maximum dr does not occur at the highest normalized vertical displacement bin but instead peaks near -0.25, for polluted conditions. This counterintuitive result can be explained by the vertical structure of the S field within the chamber. As shown in Fig. 5a and b, S is high near the bottom boundary, where warm and moist air perturbations are introduced via wall forcing. Consequently, S is spatially confined to the lower region of the chamber and becomes progressively depleted with height. SDs with moderate normalized vertical displacement (around -0.25) tend to remain within this lower region (z≲0.5m; see Fig. 11) and are repeatedly exposed to grid cells containing higher S. In contrast, SDs with higher normalized vertical displacement ascend more rapidly and move beyond the S-generating layer, entering S-depleted regions where further growth is limited. This mechanism explains the turnover in dr (except VOCALS (60) and Seoul (60)) in Fig. 12a: droplets that ascend too quickly exit the favorable growth environment before maximizing condensational growth. This interpretation is further supported by the normalized vertical displacement-binned mean S values shown in Fig. 13a, which represent the average S encountered by SDs along their trajectories. In all cases, S reaches its maximum at a normalized vertical displacement near -0.25 and steadily declines at higher bins. This trend reflects the spatial confinement of the S production zone near the chamber base and the lack of its regeneration at higher heights. Under clean conditions, where vapor competition is weak and the S field persists longer due to slower depletion, dr continues to increase with normalized vertical displacement. In contrast, under polluted conditions, rapid vapor consumption depletes S more efficiently near the base, limiting droplet growth even for strongly ascending SDs. Figure 13b confirms the positive correlation between normalized vertical displacement and vertical velocity.

To further investigate how vertical dynamics influence cloud microphysical evolution, we analyze the activation behavior of unactivated SDs initially located near the chamber base (z=0-0.2m) under varying aerosol conditions. Rather than focusing on a single time, we apply this analysis across multiple start times during the quasi-equilibrium period (900–1780 s, every 20 s). The activation fraction is defined as the ratio of the number concentration of SDs that become activated during the 20 s tracking interval to the total number concentration of initially unactivated SDs located near the chamber base (z=0-0.2m). Figure 14a shows the activation fraction of SDs binned by normalized vertical displacement, averaged for all start times. Each SD was tracked for 20 s after its respective start time, and its activation status was evaluated. The activation fraction increases from the mostly descending trajectories toward moderately ascending ones and typically peaks near a normalized vertical displacement of about -0.25, then decreases or changes only weakly at higher normalized vertical displacements. This pattern closely resembles dr trends discussed earlier (Fig. 12), where SDs with moderate normalized vertical displacement experienced the largest size increase. In both the dr (Fig. 12) and activation fraction (Fig. 14) analyses, the key factor is that SDs whose normalized vertical displacement lies near -0.25 remain longer within the lower chamber layer (z≲0.5m), where S is locally enhanced by mixing of air parcels with contrasting temperature and humidity from the upper and lower boundaries. As shown in Fig. 5, horizontally averaged S tends to be the highest near the bottom boundary and decreases toward zero with height. Trajectories in this normalized vertical displacement range around -0.25 are repeatedly exposed to this supersaturation source region, which increases both their probability of activation and their condensational growth. In contrast, SDs with larger normalized vertical displacement ascend more quickly out of the lower layer and spend more time in regions where S has already been depleted, so both their activation fraction and dr are reduced. As aerosol concentration increases, the overall activation fraction declines due to intensified vapor competition. In highly polluted cases such as VOCALS (10 K) and Seoul (10 K, CTRL), even strongly ascending SDs show limited activation, and the difference between ascending and descending SDs becomes small. This suggests that condensational growth depletes vapor faster than it can be replenished by turbulent mixing, reducing S variability and diminishing the impact of vertical motion. Figure 14b shows the mean number of unactivated SDs near the chamber base that remained within the simulation domain and were fully tracked for 20 s after each start time (t=900-1780s, every 20 s), binned by normalized vertical displacement. Figure 15a and c show the three-dimensional locations of the first activation events for 50 000 SDs that were randomly selected from the population of unactivated SDs located between 0 and 0.2 m at 1600 s for VOCALS (200, CTRL) and VOCALS (10 K) cases, respectively. Figure 15b and d present the corresponding vertical histograms using 0.02 m height bins. For VOCALS (200, CTRL), 24 423 of the tracked SDs activate between 1600 and 1620 s, and a substantial fraction of these activation events occur well above the source layer near the lower boundary, with activation locations extending through much of the chamber depth. For VOCALS (10 K), only 6512 SDs activate, and these activation events are almost entirely confined to heights below about 0.3 m, with a weaker secondary maximum near the chamber top where S is also elevated, consistent with the vertical structure of S, as shown in Fig. 5a. As discussed in Sect. 3.2, the present simulations exhibit supersaturation oscillations near the lower and upper rigid boundaries, and in Fig. 15c and d much of the polluted-case activation occurs within the near-bottom layer where the positive supersaturation oscillation is the strongest. This indicates that activation in polluted conditions is indeed concentrated in a shallow near-bottom region in the chamber, although the local magnitude of activation in this boundary-adjacent layer may be enhanced by the numerical oscillation. We therefore interpret Fig. 15 primarily as evidence for the vertical confinement of activation under polluted conditions, rather than as a precise quantitative measure of the absolute activation magnitude near the boundary. Importantly, the main conclusions of this study do not rely on this near-wall feature alone, because the weakening of the dependence of droplet growth and activation on vertical motion is also supported by the interior W–S diagnostics and the trajectory-based statistics shown in Figs. 7, 12, and 14. Reducing these near-boundary supersaturation oscillations is an important priority for future chamber simulations.

These results collectively suggest that, under high aerosol loading, droplet activation becomes increasingly independent of vertical motion due to limited thermodynamic potential for nucleation. These Lagrangian findings reinforce the τm-τp perspective. Under polluted conditions (Da≫1), intensified vapor competition rapidly depletes available water vapor, leading to early saturation of condensational growth at lower heights. This process not only reduces the overall magnitude of droplet growth and activation fraction, as shown in Figs. 12 and 14, but also weakens the dependence of these microphysical processes on vertical transport, as quantified by normalized vertical displacement. As a result, the qc structure becomes increasingly uniform in the vertical. This highlights that the homogenization of cloud condensate in the vertical direction under polluted conditions might be primarily driven by microphysical timescale constraints

In comparing VOCALS and Seoul cases for the same aerosol concentrations, dr is greater for Seoul cases, whereas the activation fraction is higher for VOCALS cases (Figs. 12 and 14). This difference arises because VOCALS aerosols contain more large particles that readily activate, resulting in higher Nc and activation fractions. In contrast, Seoul aerosols include more small particles that activate less efficiently, leading to fewer activated droplets. Consequently, these fewer droplets face reduced competition for water vapor, promoting greater individual growth compared to VOCALS.

From a Lagrangian perspective, we interpret our diagnostics as follows. At a given time, the super droplets within the lowest 0.2 m can be viewed as originating from a common near-bottom air mass. Turbulent motions then disperse these droplets along trajectories that differ in their net ascent and in their residence time within the near-bottom supersaturation source region. These differences produce distinct time-integrated supersaturation exposures, and therefore distinct condensational growth histories, even for droplets that start from the same near-bottom layer. In the clean (low-CCN) cases, supersaturation fluctuations are relatively large, so growth becomes strongly history dependent and the normalized radius increment, dr, varies substantially across trajectories. In the polluted (high-CCN) cases, supersaturation fluctuations are damped, so droplets experience more similar effective supersaturation histories and dr becomes more uniform. In our simulations, this transition is accompanied by a weakening of the vertical gradient in qc, consistent with reduced contrasts between strongly ascending and weakly ascending trajectories as CCN increases.