In the activation regime, the drm/dt–ddr/dt correlation is primarily positive (region A in Fig. c and d), especially when rm<2µm. This regime is associated with droplet activation occurring in updrafts (Fig. b) near the cloud base (Fig. c), as indicated by high net activation rates (Fig. i). The corresponding increase in droplet number concentration (Fig. c) marks cloud formation. In Fig. b, most particle trajectories initiate within this regime (black dots). During this phase, condensational growth increases rm, while the time-dependent activation of aerosols with different critical supersaturations leads to an increase in dr. This results in a transient broadening of the DSD, prior to narrowing due to subsequent condensational growth.

Following the activation regime, droplets enter the adiabatic growth regime (region B in Fig. c and d), particularly when dr<0.1. In this regime, cloud droplets grow by condensation within regions of high supersaturation (Fig. g), strong updrafts (Fig. b), and low mixing fraction χ (Fig. h). Activation and deactivation are negligible (Fig. i), resulting in an almost constant droplet number concentration, Nc (Fig. c). The turbulent kinetic energy dissipation rate (ε) remains low (Fig. g), indicating weak turbulence. In addition, the small standard deviation of supersaturation, σS (Fig. h), indicates a highly homogeneous supersaturation field, implying minimal entrainment and mixing-driven dilution of the cloudy air.

In this regime, the rates of change of rm (drm/dt) and dr (ddr/dt) exhibit a negative correlation, reflecting classical condensational growth behavior: the radius of small droplets grows faster, narrowing the DSD as its mean size increases. This behavior aligns with parcel theory and is typically observed within the adiabatic cores of stratocumulus clouds .

After the adiabatic growth regime, droplets enter the entrainment and descent regime (region C in Fig. e and f). In this regime, the drm/dt–ddr/dt correlation becomes negative: rm decreases and dr increases due to evaporation caused either by mixing with entrained free-tropospheric air or by adiabatic heating during descent. Unlike in the previous regimes, where most droplets follow similar evolution pathways, droplet pathways diverge significantly in this regime (Fig. b). Notably, for rare cases of very high dr, rm increases while dr decreases (Fig. e and f). These represent cases of narrowing mixing , wherein an extremely wide DSD narrows after mixing due to the substantial evaporation of small droplets, causing the average droplet size to increase.

While some droplets experience rapid altitude changes, following the STBL vertical circulation (indicated by the p50 line in Fig. ), others remain near the cloud top, close to the p90 line (Fig. f). These latter droplets exhibit weak vertical velocity W (Fig. e) within negatively buoyant air (Fig. d) and are subject to stronger entrainment-driven dilution. This is indicated by high ε (Fig. j), high σS (Fig. k), low S (Fig. j), and high χ (Fig. k). Consequently, droplets in more diluted regions (near the p90 line in Fig. k) undergo more abrupt evaporation and deactivation (Fig. l) compared to those following the STBL vertical circulation (near the p50 line in Fig. b), which experience more gradual evaporation (Fig. l) and lower χ (Fig. k).

To determine whether certain droplets escape the strong effects of entrainment and mixing (i.e. those following the downdrafts of the STBL vertical circulation with minimal dilution), we analyze the density distribution of maximum χ values along individual droplet trajectories (Fig. ). The maximum χ, calculated over each droplet's lifetime from activation to deactivation, serves as a proxy for the droplet's entrainment history, representing the maximum fraction of environmental air the parcel has experienced. Trajectories with a maximum χ<0.1 indicate a relatively minor impact from entrainment. As shown in Fig. , a notable fraction of parcels exhibit low maximum χ values, suggesting that these are not substantially diluted by entrainment and mixing events near the cloud top. This is consistent with Fig. , where some droplets descend without a significant decrease in supersaturation S or increase in χ (Fig. j and k) despite strong downdrafts (Fig. e).

The diversity of pathways in the evaporation regime contrasts with the adiabatic growth regime, where droplets follow nearly uniform growth paths. In the entrainment and descent regime, trajectories diverge: some parcels are strongly diluted by entrainment (near the p90 line in Fig. e), while others experience minimal dilution, following the strong downdraft circulation (near the p50 line in Fig. e). To better understand the evolution of these diverse pathways and how microphysical properties diverge, we show changes in mixing-related properties for individual particle trajectories in the χ–z phase space (Figs.  and ). We categorized droplets based on the 25th (χ=0.08) and 75th (χ=0.14) percentiles of their maximum lifetime χ values (Fig. ). Droplets within parcels subject to strong entrainment-driven dilution experience high maximum χ>0.14 (first row), while the second and third rows show droplets with intermediate (0.08≤χ≤0.14) and low (χ<0.08) maximum values, respectively. In all cases, dr remains below 0.1 during ascent and increases when W<0, particularly for parcels with higher χ (Fig. c, f, and i).

While most droplets descend without experiencing a substantial decrease in S, only a fraction are strongly diluted by entrainment, where S decreases as χ increases (Fig. e). For these droplets, S increases and χ decreases again after reaching its peak, indicating the restoration of S following turbulent mixing and evaporation, as well as further homogenization within the cloud. Notably, supersaturation fluctuation (σS) reaches a maximum at the cloud top while χ increases, further indicating entrainment and mixing. As rm decreases and dr increases rapidly during mixing and evaporation (Fig. b and c), these droplets descend and evaporate in a new state characterized by modified rm and dr. Conversely, droplets that do not experience high χ descend with a continuous state obtained at the end of the adiabatic growth regime, characterized by maximum rm and minimum dr (Fig. h and i).

Thus, for droplets within parcels subject to minimal dilution, rm is primarily a function of altitude (Fig. h). At the same altitude, rm is only slightly smaller at higher χ, regardless of whether the droplets are ascending or descending (Fig. g). Meanwhile, dr is larger during descent (Fig. i), reflecting the broadening of the droplet size distribution due to evaporation in the absence of the collision-coalescence process. Along these trajectories, S remains high, while χ and σS remain low, suggesting that these droplets likely ascend and descend with negligible influence from entrainment. Furthermore, while both droplet groups undergo evaporation during descent, their initial rm and dr differ based on whether they reached a new state after mixing. This divergence leads to distinct evolution paths in the rm–dr phase space.

Another difference between the ascending and descending pathways is the evolution of droplet number concentration. To separate the decrease in Nc caused by simple entrainment dilution from that caused by mixing-induced evaporation, we examine the dilution-corrected number concentration, defined as Nad=Nc/(1-χ). Here, the subscript “ad” denotes the adiabatic value, representing the concentration expected in an undiluted parcel. Specifically, Nad is substantially lower at higher altitudes when parcels are strongly diluted by entrainment (Fig. a) compared to those experiencing minimal dilution (Fig. g). This distinct reduction is also evident in the rm–dr phase space, where parcels subject to strong entrainment-driven dilution exhibit a rapid decrease in Nad (Fig. a). This decrease, representing droplet loss beyond simple dilution, is consistent with inhomogeneous mixing, wherein some droplets completely evaporate in locally subsaturated environments while others remain relatively unaltered. The localized increase in σS further supports the conclusion that SGS supersaturation variability, as resolved by the LEM, drives this selective evaporation. These findings align with recent observational studies suggesting that inhomogeneous mixing signals are prevalent near the top of Sc clouds .

However, we cannot ensure that Nc/(1-χ) has fully isolated the effects of evaporation from entrainment-driven dilution. While the spatial distribution of the mixing signal indicates stronger inhomogeneous characteristics near the cloud top and homogeneous-like features below, it is questionable whether changes observed in the lower cloud should be interpreted as a result of active entrainment, especially since the majority of parcels descending with the STBL vertical circulation experience minimal dilution through entrainment. These uncertainties highlight a fundamental ambiguity in interpreting in situ observations of rm and Nc as indicators of mixing type, particularly when a precise estimation of χ is unavailable.

To resolve this ambiguity, the maps of Daphase, Daevap, and the ratio τphase/τevap in the χ–z phase space (Fig. ) quantify the varying inhomogeneous and homogeneous mixing signals at the same height. Here, the Damköhler number is defined generally as 7Da=τmixτmicro, where the mixing timescale is 8τmix=l2ε13. Here, l represents the length scale of scalar inhomogeneity caused by entrainment, which breaks down to the Kolmogorov length scale through turbulent motion. Since the entrainment length scale l varies with the size of the entrained blobs, we estimate the mixing length using χ as l=(χ⋅Δx⋅Δy⋅Δz)1/3. Notably, using the equivalent geometric LES grid lengthscale (≈7.9m) as a proxy for l results in a larger τmix but does not alter the conclusions. The relevant microphysical timescales are the phase relaxation time 9τphase=14πDvrmNc and the evaporation timescale 10τevap=-rm22GS, defined only in subsaturated regions with S<0 . Here, Dv is the molecular diffusion coefficient for water vapor, and G=Fd+Fk-1 is the condensational growth parameter that summarizes the effects of vapor diffusion and heat conduction on condensation, with Fd, a coefficient associated with vapor diffusion, and Fk, associated with heat conduction . Theoretically, when Da≫1, turbulent mixing is slower than the microphysical response, favoring inhomogeneous mixing. Conversely, when Da≪1, turbulent mixing is fast enough to homogenize the subsaturated entrained air with the saturated cloud air before droplets respond, leading to homogeneous mixing.

While mixing scenarios have often been characterized using a single Damköhler number constructed from one microphysical response time e.g., recent work has highlighted the limitations of such single-parameter descriptions and the need to consider multiple thermodynamic timescales . Therefore, we define two Damköhler numbers: 11Daphase=τmixτphase and Daevap=τmixτevap, which represent the supersaturation relaxation-based and evaporation-based Damköhler numbers, respectively. Here, Daphase measures how efficiently phase relaxation can restore supersaturation relative to turbulent mixing, whereas Daevap measures how efficiently droplets can evaporate before the mixed air is re-saturated. In addition, we use the ratio between the two Damköhler numbers, τphase/τevap, which is closely related to the parameter suggested by and corresponds to the potential evaporation parameter of .

In the high-χ regime (first row of Fig. ), parcels subject to strong entrainment-driven dilution frequently exhibit Daphase>1 (Fig. a) and Daevap>1 (Fig. b), alongside a ratio of τphase/τevap≳1 (Fig. c). This combination is consistent with an inhomogeneous mixing scenario, in which a subset of droplets evaporates completely while the remaining droplets maintain a relatively large rm. As these parcels descend, Daphase tends to decrease (Fig. a), whereas Daevap remains greater than unity (Fig. b). Consequently, reliance on Daphase alone might falsely indicate a transition toward homogeneous mixing during descent. The persistently high Daevap, however, contradicts this interpretation. These parcels retain the signature of inhomogeneous mixing (depleted Nc, high Daevap) well below the cloud top, even as a consistent decrease in χ indicates no further active entrainment dilution but mixing with boundary layer air. This occurs because they descend through air that remains incompletely homogenized, creating an environment more subsaturated than would be expected from adiabatic descent alone.

In contrast, trajectories that remain in the low-χ regime throughout their lifetime (third row of Fig. ) tend to occupy regions with smaller Daevap (Fig. h) but relatively large Daphase (Fig. g), and with τphase/τevap<1 (Fig. i). In this regime, phase relaxation is fast compared to both turbulent mixing and evaporation. This implies that adiabatic warming during descent is the primary source of droplet evaporation, without additional subsaturation caused by entrainment and dilution. These signatures are consistent with a homogeneous mixing-like response during descent, in which droplets gradually adjust rm under a comparatively uniform supersaturation field without a substantial decrease in Nc, aside from weak entrainment-driven dilution at the cloud top. Moreover, as χ generally decreases during the descent, this implies no further strong effect of entrainment dilution during the descent. Crucially, this implies that the homogeneous-mixing-like signature often observed deeper in the cloud is not necessarily due to active entrainment and mixing at that level. Instead, it reflects droplet evaporation in weakly diluted, near-adiabatic parcels descending via the STBL vertical circulation .

The corresponding maps of the absolute timescales τmix, τphase, and τevap (Fig. ) clarify why these diagnostics separate the regimes. The mixing timescale τmix varies relatively modestly across the χ–z phase space (Fig. a and g), whereas τphase and τevap exhibit much stronger spatial contrasts. Therefore, changes in Daphase and Daevap are driven mainly by the two microphysical timescales. The phase relaxation time τphase is strongly related to Nc: regions with strongly reduced Nc after complete evaporation events exhibit larger τphase (Fig. b), while most other regions show much shorter τphase (Fig. h). The evaporation timescale τevap behaves inversely, being large in nearly saturated regions and decreasing rapidly with increasing subsaturation (Fig. c and i). Consequently, the ratio τphase/τevap serves as a direct indicator of where complete droplet evaporation is likely. This ratio is significantly higher for high maximum-χ parcels, reflecting their tendency toward complete evaporation, and remains much lower for low maximum-χ parcels until they reach the cloud base. Taken together, using τphase/τevap provides a natural separation between regimes where droplets are prone to complete evaporation due to entrainment-induced dilution and regimes where supersaturation is restored quickly enough to prevent substantial droplet loss.

These results highlight a contrast based on Lagrangian history. Parcels strongly diluted by entrainment near the cloud top are dominated by the inhomogeneous mixing signature. During descent, these parcels undergo gradual evaporation by adiabatic warming. Because of their greater subsaturation and decreased Nc, the droplets evaporate completely at a higher location in the cloud (Figs. l and f). Conversely, weakly diluted parcels descending near-adiabatically via the STBL circulation show a homogeneous-mixing-like signature driven solely by evaporation in the adiabatically descending parcel, rather than by active mixing events. These distinct Lagrangian histories explain why snapshots of rm and Nc at a given altitude can simultaneously contain the imprints of both inhomogeneous and homogeneous mixing signatures, even without active entrainment events.

Droplets transition into the deactivation regime at the end of their life cycle near the cloud base (Fig. f). In this regime, the relationship between drm/dt and ddr/dt is complex, as rm decreases while dr increases for larger rm, but decreases for smaller rm. The decrease in rm is due to the evaporation of droplets. For larger rm, dr initially increases, as observed in the entrainment and descent regime. However, as the droplets approach complete evaporation, dr decreases since only a small number of droplets remain. Therefore, this regime is opposite to the activation regime with substantial deactivation (Fig. l). Note that this regime does not overlap with the activation regime, because rm and dr are generally larger in the deactivation regime compared to the activation regime, indicating a stronger spatial variability in deactivation. Moreover, since particle trajectories are only tracked for qc>0, an abrupt loss of liquid water near the point of complete evaporation may result in a bias toward retaining large rm values as the final recorded state.