2.1 Cloud and drizzle properties

The in situ measurements of MBL cloud properties are temporally synchronized to 1 Hz resolution, corresponding to approximately 100 m (5 m) of the horizontal (vertical) sampling. The sampling locations of the selected cases are indicated by the white dots in Fig. S1. The Fast Cloud Droplet Probe (FCDP) on board the aircraft during ACE-ENA can detect droplets with diameter (D_p) ranging from 1.5 to 50 µm, with the size bins of the probe between 1 and 3 µm (Glienke and Mei, 2020). SOCRATES used a similar cloud droplet probe (CDP) to measure droplets from 2 to 50 µm at a 2 µm probe size bin width. Both ACE-ENA and SOCRATES leverage the 2D-S Stereo Probe (2DS) to discern droplets with diameters from 5 to 1280 µm (Lawson et al., 2006; Glienke and Mei, 2019). The 2DS in situ measurements are used as additional screening to eliminate the ice particles with diameters larger than 200 µm. Moreover, the University of Washington Ice–Liquid Discriminator product, which is a machine-learning-based single-particle-phase classification of the 2DS images (Atlas et al., 2021), is used to identify small ice crystals when available. Through these three datasets, we can tease out the ice-dominated period to the highest extent possible and focus on the liquid cloud processes and ACI during SOCRATES (Y. Wang et al., 2021).

Although these in situ measurements can provide “ground-truth” datasets, their uncertainties must be properly analyzed, and the data quality must be controlled before being applied to scientific studies. The uncertainties in the FCDP in sizing and concentration are approximately 30 % and 20 %, respectively (Baumgardner et al., 2017). Considering the significant uncertainty in the concentration of smaller particles from a photodiode probe such as 2DS (Baumgardner and Korolev, 1997; Wang et al., 2021), a diameter of 40 µm is used as the demarcation line between cloud droplets and drizzle drops (Wood, 2005). Then the droplet number concentrations in the overlapping size bin between FCDP and 2DS are redistributed, assuming a gamma distribution, and thereby a complete size spectrum of cloud and drizzle can be merged from FCDP and 2DS measurements. Hence, the cloud and drizzle microphysical properties can be calculated.

The cloud droplet number concentration (N_c) is given by

The cloud droplet effective radius (r_c; Hansen and Travis, 1974) is given by

The cloud liquid water content (LWC_c) can be calculated by

where ρ_w is water density.

Similarly, the drizzle drop number concentration (N_d) and liquid water content (LWC_d) can be calculated using the size distribution from 40 to 1280 µm. Particularly, the drizzle mean mass diameter (D_mmd) is given by

This quantity is chosen because the D_mmd denotes the diameter of average mass (the third-moment average) of the drizzle size distribution, which provides the link between the number concentration and the mass concentration of drizzle droplets in a sample (Hinds, 1999).

Adapting the method in Zheng et al. (2022b), the cloud base precipitation rate (R_CB) is given by

In order to match the unit conversion, the D_p,mm is the diameter in units of millimeters; n(D_p,mm) is the drizzle number concentration in every size bin with a unit of m³ mm⁻¹; and U_∞(D_p,mm) is the terminal velocity in a given size bin, which is calculated from the full Reynolds number theory as in Pruppacher and Klett (2010).

The combined threshold of N_c>5 cm⁻³ and LWC_c>0.01 g m⁻³ is used for determining the valid cloud samples and cloud boundaries (Wood, 2005; Zheng et al., 2022b). The complete cloud vertical profiles from sub-cloud to the above-cloud are selected during the ACE-ENA and SOCRATES IOPs, in which the flight strategy includes sawtooth and spiral cloud transects and ramping cloud sampling. The precipitation conditions are determined by whether samples of N_d>0.001 cm⁻³ exist below the cloud base height. In total, the selected numbers of cloud (precipitating cloud) profiles are 18 (13), 26 (13), and 28 (24) for ACE-ENA Sum, ACE-ENA Win, and SOCRATES, respectively. The detailed selected cloud profiles, with their cloud-base heights (z_t), cloud-top heights (z_b), and cloud thicknesses ($H_{\mathrm{c}}=z_{\mathrm{t}}-z_{\mathrm{b}}$), are listed in Table S1 in the Supplement, along with the cloud profile macrophysics.

Furthermore, the assessments of ACI are significantly impacted by the MBL dynamic and thermodynamic conditions. Jones et al. (2011) suggested that the MBL would be in a well-mixed and coupled condition when the difference in the liquid water potential temperature (θ_L) and total water mixing ratio (q_t) between the bottom of MBL and the inversion layer is less than 0.5 K and 0.5 g kg⁻¹, respectively. The cases selected for this study feature both coupled and decoupled MBL conditions, particularly during ACE-ENA Sum, which is characterized by anomalously low MBL heights and substantial MBL decoupling. Previous studies found that under decoupled conditions the aerosols, CCN, and moisture sources near the surface are disconnected from the cloud layer aloft, hence exerting a much less effective impact on cloud microphysics (Zheng et al., 2022a; Christensen et al., 2023; Su et al., 2024). Therefore, we adapt and modify the metric in Jones et al. (2011) to calculate the sub-cloud coupled layer in order to quantify the degree to which aerosols and CCN-measured sub-cloud are in a well-mixed state and can represent the actual interaction (or contact) with the cloud layer. In this study, the q_t and θ_L at the cloud base are calculated, and then their vertical variations are examined, starting from the altitude of the cloud base (z_b) and looking downward. As such, the coupled point height (z_cp) is defined as the altitude where the downward vertical changes in q_t and θ_L exceed 0.5 K and 0.5 g kg⁻¹, respectively. Hence, the coupled layer thickness ($H_{\text{cp}}=z_{\mathrm{t}}-z_{\text{cp}}$) is defined as the layer between the cloud-top height (z_t) and coupled point height (z_cp); hence, the selection of the aerosols and CCN within the below-cloud part of the coupled layer can be viewed as being in contact with the cloud. An example of the coupled layer identification is shown in Fig. S2. Therefore, the degree of MBL decoupling (D_cp) can be quantified as the ratio of the coupled point height (z_cp) to the cloud base height (z_b), where $D_{\text{cp}}=z_{\text{cp}}/z_{\mathrm{b}}$. As shown in Table S1, the ACE-ENA Sum features, with the highest degree of decoupling (averaged D_cp=0.504) compared to the ACE-ENA Win (D_cp=0.370) and SOCRATES (D_cp=0.277).

2.2 Aerosol properties

The total aerosol number concentrations (N_a) from ACE-ENA and SOCRATES are measured by the airborne condensation particle counter (CPC) models 3772 and 3760A, which count the number of aerosols with a diameter (D_p) larger than 3 and 11 nm, respectively (Kuang and Mei, 2020; UCAR/NCAR, 2022). Additionally, the Passive Cavity Aerosol Spectrometer Probe (PCASP) on board the ACE-ENA aircraft is capable of sizing the aerosol with D_p, ranging from 0.1 to 3.2 µm (Goldberger, 2020). The ultra-high-sensitivity aerosol spectrometer (UHSAS) measures the size-resolved aerosol distribution from 0.06 to 1.0 µm during SOCRATES (Uin and Goldberger, 2020). Therefore, the number concentrations of accumulation mode aerosols (N_ACC; 0.1–1 µm) can be discerned from the PCASP and UHSAS aerosol size distributions. Aitken mode aerosols (N_Ait, <0.1 µm) from ACE-ENA are retrieved by the Fast Integrated Mobility Spectrometer (FIMS), which can size the aerosol down to 9 nm (Olfert et al., 2008), while the N_Ait from SOCRATES is limited to 0.06–0.1 µm due to the limitation of UHSAS. As for the CCN measurements, the ACE-ENA utilized the dual-column CCN counter at two constant supersaturation levels of 0.15 % and 0.35 % (Uin and Mei, 2019), while the CCN number concentration (N_CCN) during SOCRATES was measured under various supersaturation levels from 0.06 % to 0.87 %, using a scanning CCN counter (Roberts and Nenes, 2005). In this study, N_CCN at 0.35 % supersaturation (N_{CCN 0.35 %}) is used to ensure a direct comparison between ACE-ENA and SOCRATES. The aerosol measurements are in the temporal resolution of 1 Hz. Note that the aerosol and CCN data are quality-controlled by removing the data point where the N_c+N_d value is greater than 5 cm⁻³ or N_d value is greater than 0.01 cm⁻³ to filter out the contamination of the cloud droplets and drizzle water splashing.

The sub-cloud aerosols and CCN are selected within the below-cloud-base part of the coupled layer, which is described in Sect. 2.1, in order to better assess aerosol–cloud interactions. The above-cloud aerosols and CCN are selected between the cloud top and 200 m above. Note that the selection criteria of 200 m above the cloud top would inevitably induce uncertainty in the cloud-top ACI assessment, depending on the vertical trend of the individual aerosol profile. Over the southeastern Atlantic, Gupta et al. (2021) conducted an analysis focusing particularly on the differing impacts when biomass-burning aerosols are in contact with marine stratocumulus cloud tops, using 100 m above as the demarcation, compared to when they are separated by various distances and found that significant differences were observed in cloud microphysics, owing to different droplet evaporation and nucleation, compared to profiles in which aerosols and cloud layer are separated. That result is in agreement with the modeling sensitivity study over the eastern North Atlantic by Wang et al. (2020), who found that aerosol plumes can exert impacts on the cloud-top microphysics only when they are in close contact with the cloud layer. During much of the ACE-ENA campaign, nearly constant (and sometimes decreasing) vertical atmospheric profiles of aerosol concentration were observed within a few hundred meters above the cloud top. Aerosol intrusions due to long-range transport, particularly during the summer season, were observed to induce an elevated aerosol layer in higher altitudes that was not in contact with the cloud layer. The frequent new-particle-formation events during SOCRATES significantly alter the free-troposphere Aitken mode aerosol budget, but the aerosols would need to further subside to impact the cloud (McCoy et al., 2021; Zhang et al., 2023). Note that from previous studies on ACE-ENA and SOCRATES, the aerosol vertical profiles within ∼200 m above the cloud layers are typically found to have less variation (Wang et al., 2020; Wang et al., 2021; McCoy et al., 2021; Zhang et al., 2023), hence representing the aerosol layers in contact with the cloud. Hence, the 200 m criterion used in this study provides a sufficient sample size population for statistical analysis.

3.1 Aerosols and CCN in above- and sub-cloud regimes

The probability density functions (PDFs) of aerosols, CCN, and cloud microphysical properties from selected cases during the ACE-ENA and SOCRATES field campaigns are presented in Fig. 1. Notably, the N_a, N_Acc, and N_{CCN 0.35 %} values from SOCRATES are the highest among the three IOPs, followed by the ACE-ENA Sum and ACE-ENA Win, as illustrated in both the above-cloud (Fig. 1a–c) and sub-cloud regimes (Fig. 1d–f). Such variations can be linked to the different aerosol sources in the ACE-ENA and SOCRATES regions, especially during the summer and winter seasons over the Azores.

Figure 1Probability density functions (PDFs) of N_a, N_ACC, and N_{CCN 0.35 %} in the above-cloud (a–c) and sub-cloud (d–f) regimes and the cloud microphysical properties of N_c (g), r_c (h), and LWC_c (f) within the cloud layer. The statistical metrics in the legends denote the mean and standard deviation values for all samples in three IOPs. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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In the SOCRATES region, according to the previous studies involving back-trajectory analyses, dominant air masses within the MBL primarily originate from the south or from the west, skirting the Antarctic coast (Zhang et al., 2023). While the air masses above the MBL follow a similar transport pathway, they can also originate from the tip of southern Africa and be transported southeast along the warm conveyor belt (McCoy et al., 2021). Above-cloud aerosol N_{CCN 0.35 %} values analyzed during SOCRATES (674.6 cm⁻³) are primarily constituted by the Aitken mode aerosols because the mean N_Acc is only 62.5 cm⁻³. Previously, McCoy et al. (2021) reported average N_{CCN 0.35 %} values of 680.69, 546.28, and 465.05 cm⁻³ for the mid-troposphere and above- and below-cloud for the multiple SOCRATES cases, respectively. For individual cases, the above-cloud aerosols vary from 200 to over 1000 particles per cubic centimeter (McCoy et al., 2021; Zhang et al., 2023). These aerosols are predominantly produced from the oxidation of biogenic gases, notably dimethyl sulfide (DMS) emitted by marine biological productivity (Sanchez et al., 2021; McCoy et al., 2020). The rising air currents in the MBL transport these particles into the free troposphere with dominant aerosol population over the SO (McCoy et al., 2021; Sanchez et al., 2021). Hence, it reinforces the notion that the SO represents a pre-industrial marine environment, where the influence of anthropogenic and biomass-burning aerosols is mostly negligible (McCoy et al., 2020, 2021).

Conversely, the ENA region experiences aerosols of varied origins, spanning maritime air masses to those heavily influenced by continental emissions from North America or northern Europe, especially during the summer season (Logan et al., 2014; Wang et al., 2020). The summer air mass back-trajectories within the MBL strongly feature recirculating flow around the Azores High. During the wintertime, however, the air masses predominantly originate in the free troposphere, are transported above the MBL, and are then further entrained to the MBL by large-scale subsidence, indicating less influence from continental pollution (Y. Wang et al., 2021b). During the ACE-ENA Sum, the MBL is enriched by sulfate and carbonaceous particles (Y. Wang et al., 2021b; Zawadowicz et al., 2021). This enhancement is attributed both to local generation from DMS and to the long-range transport from the continental air masses, resulting in the mean N_a of 312.6 cm⁻³ and 301.5 cm⁻³ for above- and sub-cloud regimes, respectively. The ACE-ENA Win exhibits the lowest aerosol and CCN concentrations, which are predominantly sourced from local maritime influences and coupled with reduced continental air mass intrusions (Zheng et al., 2018; Y. Wang et al., 2021b).

Figure 2Aerosol size distributions (D_p=0.06–3 µm) for above-cloud (a) and sub-cloud (b) regimes. The vertical dashed line at D_p=0.1 µm and at D_p=1 µm denotes the demarcations between accumulation mode, Aitken mode, and coarse mode aerosols. The inner plots denote a smaller range of Aitken mode size distribution (D_p=0.01–0.06 µm) available from ACE-ENA. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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Figure 1a and d reveal that there are more above-cloud N_a values during the three IOPs than sub-cloud values, especially during SOCRATES. The higher above-cloud N_a values from the three IOPs are primarily contributed by Aitken mode aerosols because their corresponding N_Acc values are much lower (Fig. 1a and b). It is interesting to note that the above-cloud N_{CCN 0.35 %} values exceed the N_Acc values for all three IOPs (Fig. 1b and c), implying that a significant fraction of Aitken mode aerosols can be activated to become CCN, corroborating findings from earlier studies (McCoy et al., 2021; Zheng et al., 2021). For the sub-cloud regime, the N_a values for SOCRATES and ACE-ENA Win are ∼70 %–80 % of their corresponding above-cloud values, and the N_a during ACE-ENA Sum is almost identical to its above-cloud value. Notice that the sub-cloud N_Acc values from the three IOPs are more than double the above-cloud N_Acc values, and most of the sub-cloud accumulation mode aerosol can be activated to become CCN at supersaturation (SS) of 0.35 %. It is interesting to note that the higher N_{CCN 0.35 %} at the sub-cloud layer during SOCRATES may partially be a result of aerosols being positively impacted by cloud dynamic processes (Fig. 1e and f), which is suggested by previous studies (McCoy et al., 2021; Zhang et al., 2023) and will be further discussed in the following paragraphs.

To further investigate the above- and sub-cloud aerosol properties from the three IOPs, the aerosol droplet size distributions are analyzed in Fig. 2. It is evident that SOCRATES aerosols have the highest concentrations of Aitken mode particles (D_p=0.06–0.1 µm, given that the <0.06 µm is not available from UHSAS) for the above- and sub-cloud regimes. McCoy et al. (2021) and Zheng et al. (2021) identified analogous origins and formations of the above-cloud Aitken mode aerosols over the SO and ENA regions and concluded that these aerosols primarily originate from the nucleation of photo-oxidation products of DMS, notably H₂SO₄ and methanesulfonic acid (MSA), in the free troposphere. The differential concentrations can be ascribed to the fact that sea surface DMS concentrations in the SO are generally higher than those in the ENA region (Aumont et al., 2002; Zhang et al., 2023). Moreover, DMS emissions in the ENA during the summer season surpass those during winter (Zawadowicz et al., 2021). For the accumulation mode aerosols (0.1–1 µm), the N_Acc values for both above- and sub-cloud regimes during SOCRATES decrease monotonically with particle size. The results in Fig. 2 further support the finding that Aitken mode aerosols are dominant over the SO. The N_Acc values during ACE-ENA show slight uplifts for the small accumulation mode aerosols (<0.3 µm), particularly during the summer, reflecting the signal of potential long-range transport of fine-mode aerosols (Wang et al., 2020; Y. Wang et al., 2021b). Consequently, such a comparison reinforces the notion that the SO represents a largely pre-industrial marine environment for which the influence of anthropogenic and biomass-burning aerosols is minimal (McCoy et al., 2020, 2021; Zhang et al., 2023).

When contrasting the aerosol size distributions in the sub-cloud regime (Fig. 2b) with those in the above-cloud regime, the influence of cloud processing on aerosols is discernibly non-trivial, particularly under the cloud-topped MBL conditions examined in this study. The free tropospheric aerosols can be entrained and contribute to the population of Aitken mode aerosols within the MBL, and the sub-cloud aerosols can also be subject to the influence of new particle formation in the upper MBL, though they are arguably less effective than those within the free troposphere (Zheng et al., 2021). Additionally, in-cloud Brownian capture can lead to a substantial reduction in Aitken mode aerosols (Hudson et al., 2015; Wyant et al., 2022), providing the rationale for the observed decrease in Aitken mode aerosols from the above- to sub-cloud regime, especially for particles smaller than 0.07 µm. In addition, cloud chemical processing, such as the aqueous-phase condensation of sulfuric gas onto the aerosol cores inside the cloud droplets, is particularly pronounced during the transitioning of Aitken mode aerosols to accumulation mode aerosols (Hudson et al., 2015; Zhang et al., 2023).

The larger Aitken mode aerosols (>0.07 µm) in the above- and sub-cloud regimes can effectively grow to accumulation mode aerosols through coagulation and water vapor diffusional growth (Covert et al., 1996), contributing to the elevated accumulation mode aerosol distribution and increased N_Acc in the sub-cloud regime. These processes are evident by the decrease in the critical supersaturations from above-cloud (between 0.35 %–0.4 %) to sub-cloud regimes (between 0.3 %–0.35 %) during SOCRATES (Fig. S3) because the aerosol droplet sizes are enlarged and more readily become CCN. Furthermore, the collision–coalescence combines mixtures of large and small cloud droplets and results in the sub-cloud aerosol residuals shifting towards the larger size upon the drizzle droplet evaporation below the cloud. This partially elucidates the observed increase in the tail-end of the accumulation mode aerosol distribution for all three IOPs. The elevation in the sub-cloud coarse mode aerosols observed for both ACE-ENA IOPs (as seen in Fig. 2) can be attributed to the evaporation of collision–coalescence-enlarged drizzle droplets and the intrusion of sea spray aerosols (e.g., sea salt), as illustrated and analyzed based on a summertime case study that exhibits the signal of cloud-processing aerosols (Zheng et al., 2022b), and the long-term aerosol physicochemical properties over the ARM-ENA ground-based observatory (Zheng et al., 2018), particularly during the winter season where the production of sea spray aerosol is prevalent.

3.2 Distribution of bulk cloud microphysical properties

The PDFs of MBL cloud microphysical properties (N_c,r_c, and LWC_c) derived from aircraft in situ measurements from the three IOPs are shown in Fig. 1g–i. The mean microphysical properties for the individual cloud profiles are listed in Table S2. SOCRATES has the highest sub-cloud aerosols and CCN and subsequently feature a larger number of smaller cloud droplets, given the highest N_c (148.3 cm⁻³) and smallest r_c (8 µm) values among the three IOPs. These results have further confirmed and reassured our understanding of the aerosol first indirect effect in which a larger population of aerosols induces a higher number concentration of small cloud droplets under constrained liquid water content conditions, and thus, the MBL clouds reflect more incoming solar radiation (Twomey, 1977). The ACE-ENA Win clouds feature the fewest N_c (70.6 cm⁻³) and largest r_c (9.8 µm) values, while the N_c and r_c (89.4 cm⁻³ and 9 µm) during ACE-ENA Sum fall between the SOCRATES and ACE-ENA Win values. Considering the aerosol competing effect against the available water vapor, the relatively abundant aerosols in SOCRATES might account for the observed narrower r_c distribution, which peaks between 6–10 µm. SOCRATES has a lower-cloud layer water vapor mixing ratio (figure not shown) compared to ACE-ENA because the SO region has been observed to contain less precipitable water vapor than the ENA region due to the colder sea surface temperatures (Marcovecchio et al., 2023). Therefore, the aerosol and cloud properties in Fig. 1 promise a further examination of the different cloud microphysical responses to aerosols via the ACI process. Note that the N_{CCN 0.35 %} values are lower than N_c values during the ACE-ENA Win, which is also confirmed in previous studies (J. Wang et al., 2022; Wang et al., 2023). This interesting phenomenon can potentially be attributed to a combination of factors, including lower MBL aerosol sources, stronger in-cloud coalescence-scavenging depletion of sub-cloud aerosols, and the aircraft snapshots capturing the equilibrium states of aerosols and cloud due to enhanced aerosol activations induced by stronger updrafts during the ACE-ENA Win (J. Wang et al., 2022). This thereby compels further investigation into the potential impacts of precipitation on the MBL CCN budget, which is further discussed in Sect. 4.

3.3 Vertical distributions of cloud and drizzle microphysics

The vertical distributions of the cloud and drizzle microphysical properties within the cloud layer from the three IOPs are shown in Fig. 3. To ensure the representativeness of the vertical profiles, all of the in-cloud samples are vertically smoothed using a triangular moving average method and are inverse-distance-weighted in every 50 m moving altitude window. Furthermore, the altitude is then normalized by $z_{\mathrm{i}}=\frac{Z-Z_{\text{base}}}{Z_{\text{top}}-Z_{\text{base}}}$, where z_i=0 denotes the cloud base, and z_i=1 denotes the cloud top. Consistent with previous discussions on the bulk microphysics distribution, the mean N_c values from SOCRATES are consistently higher than ACE-ENA Sum and ACE-ENA Win for the entire cloud layer, with a slight increase ranging from the cloud base to the upper–middle part (z_i≈0.85) and then decreasing toward the cloud top (Fig. 3a). All r_c values from the three IOPs show a near-linear increase from cloud base to top, with the smallest values observed during SOCRATES and the largest values observed during ACE-ENA Win (Fig. 3b).

Figure 3Vertical distributions of N_c (a), r_c (b), LWC_c (c), N_d (d), D_mmd (e), and LWC_d (f). Here the z_i=0 denotes the cloud base, and z_i=1 denotes the cloud top. Shaded areas denote the inter-cloud-case standard deviations. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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The warmer and drier air near the cloud top entrains into the cloud layer and further mixes downward, often resulting in the evaporation of small cloud droplets and the shrinking of droplet sizes, which oppose condensational growth (Desai et al., 2021). Decreases in both N_c and LWC_c and the reduced growth of r_c near the cloud-top (z_i>0.85) support signals of cloud-top entrainment mixing during all three IOPs. It is interesting to note that the r_c values from SOCRATES increase monotonically from the cloud base to the top, while the r_c values from both ACE-ENA Sum and ACE-ENA Win increase until z_i≈0.8 and then remain nearly constant, although all of their N_c values (at z_i≈0.8) decrease towards the cloud top. When dry air entrainment occurs at the cloud top, some of the upper-level smaller cloud droplets will evaporate, leading to decreases in N_c (Fig. 3a). As a result, the nearly constant r_c  values (at z_i>0.8) might represent the equilibrium balance between two competing processes, namely cloud droplet condensational and collision–coalescence growths and the entrainment-mixing evaporation effects.

Carrying the distinct discrepancies in the mean values for all layers, the N_c and r_c values from ACE-ENA Sum and ACE-ENA Win clouds experienced similar vertical evolutions to SOCRATES. The increases in r_c (δr_c) from cloud base to cloud top are 4.03, 4.78, and 5.85 µm, with percentage increases of 66 %, 68 %, and 79 %, for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively. Even though, theoretically, the condensational growth effect would be more pronounced on smaller cloud droplets due to their smaller surface area (Wallace and Hobbs, 2006), SOCRATES exhibits the thickest mean cloud thickness but experienced the least r_c increase among the three IOPs. This suggests that high-aerosol loading limits the overall growth of the cloud droplet size distribution (DSD) in SOCRATES clouds, while in contrast, the ACE-ENA Win clouds show the strongest r_c increase. This comparison indicates different cloud microphysical responses to aerosol perturbations in the three IOPs, which will be further discussed in Sect. 4.1. The LWC_c values from the three IOPs are comparable to each other. The vertical distributions of MBL cloud microphysical properties examined in this study are in good agreement with the previous studies conducted on these two field campaigns (Wu et al., 2020a; Y. Wang et al., 2021a; Wang et al., 2022, 2023). Cloud adiabaticity is a key parameter as it provides insight into the degree of mixing and microphysical processes occurring within clouds. The sub-adiabatic conditions indicate that the LWC_c is less than what would be expected in an adiabatic scenario, often due to processes such as in-cloud collision–coalescence and entrainment mixing (Hill et al., 2009; Braun et al., 2018; Gao et al., 2020; Wu et al., 2020b). In addition, the cloud adiabaticity is defined as f_ad= LWC_c/LWC_ad, where LWC_ad denotes adiabatic LWC (Wu et al., 2020b). As shown in Fig. S4, the clouds from all three IOPs feature certain levels of sub-adiabaticity above the cloud base. Considering the inter-cloud-layer mean f_ad, the campaign mean f_ad values are 0.689±0.229, 0.542±0.143, and 0.490±0.207 for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively.

To quantitatively evaluate the impact of the cloud-top entrainment-mixing rate on cloud droplets, we adapt the method of Albrecht et al. (2016), where the cloud-top entrainment rate (w_e) can be expressed as

where the turbulence kinetic energy (TKE) dissipation coefficient A_σ is empirically taken as 26 as in Albrecht et al. (2016), and the R_iσ is the buoyancy Richardson number calculated by $(g/{\mathit{\theta }}_{\mathrm{0}})\cdot (\mathrm{\Delta }{\mathit{\theta }}_{\mathrm{v}}h/{\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}})$. σ_w denotes the standard deviation of the vertical velocities taken near the cloud top (z_i>0.9), and h is the MBL height. θ₀ is the reference potential temperature, and Δθ_v is the virtual potential temperature difference across the temperature inversion layer above the cloud. Given the valid cloud-top virtual potential temperature and vertical velocity measurements for the selected cloud cases, the averaged w_e values are 0.570±0.834, 0.581±0.560, and 0.960±1.127 cm s⁻¹ for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively. The stronger w_e during ACE-ENA Win might be induced by the generally weaker cloud-top inversions and stronger near-cloud-top turbulence (Fig. 5a), compared to the summertime when the ENA is dominated by the large-scale high-pressure system (Ghate et al., 2021). Within the above-cloud inversion layer, the temperature (water vapor mixing ratio) differences ΔT (Δq) are 1.76 K (−1.75 g kg⁻¹), 1.54 K (−1.66 g kg⁻¹), and 1.48 K (−1.09 g kg⁻¹) for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively. The virtual potential temperature differences Δθ_v are 4.90, 5.16, and 3.82 K, for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively, indicating relatively drier entrained air masses during SOCRATES and ACE-ENA Sum. Considering the near-cloud-top proportion of cloud where the LWC_c experienced decrease, the difference in LWC_c (between the cloud-top value and the upper–middle cloud maximum for the mean profiles) for the ACE-ENA Sum (−0.032 g m⁻³) is higher than the reductions in ACE-ENA Win (−0.018 g m⁻³) and SOCRATES (−0.009 g m⁻³), although the w_e for ACE-ENA Sum is comparable to SOCRATES and much lower than ACE-ENA Win values. The warmer and drier entrained air can partially contribute to the greater LWC_c reduction and the lower f_ad (0.39) during the ACE-ENA Sum than those during the ACE-ENA Win (f_ad=0.45) and SOCRATES (f_ad=0.66) near the cloud top (Fig. S4). For the three IOPs, the N_c and LWC_c values exhibit stable trends from the cloud base, followed by noticeable decreases near the cloud-top mixing zone, while the changes in r_c trends near the cloud top were not as dramatic as the others. Such characteristics of the cloud microphysics vertical profiles indicate the signal of inhomogeneous mixing, which occurs when dry and warm air mixes unevenly and slowly with the cloud air, hence partially evaporating the cloud droplets (Lehmann et al., 2009; Lu et al., 2011). The results are consistent with previous research results regarding stratocumulus clouds over multiple field campaigns (Brenguier et al., 2011; Jia et al., 2019) and with the findings for selected cases during ACE-ENA (Yeom et al., 2021) and SOCRATES (Sanchez et al., 2020). The near-cloud-top r_c profiles (z_i>0.8) for the ACE-ENA cases exhibit fewer increases compared to SOCRATES, which could possibly be attributed to more effective mixing due to the stronger entrainment rate, particularly during ACE-ENA Win, eventually reaching a smaller equilibrium in terms of mean sizes.

Figure 3d–f illustrate the normalized profiles of MBL drizzle microphysical properties. The N_d values from the three IOPs mimic each other, which all maximize at the cloud top and then monotonically decrease toward the cloud base (Fig. 3d), while their LWC_d values follow a similar trend, albeit with relatively large differences (Fig. 3f). In contrast to the N_d and LWC_d trends, the D_mmd values gradually increase from cloud top to cloud base (Fig. 3e), making physical sense since the drizzle droplets are typically formed near the cloud top and continuously grow via a collision–coalescence process while falling. The ACE-ENA Win drizzle D_mmd and LWC_d values are distinctively larger than those in ACE-ENA Sum and SOCRATES. It is interesting to note that near the cloud top (z_i>0.9), ACE-ENA Win has comparable N_d but much larger D_mmd than the other two IOPs, suggesting that there were more larger drizzle embryos formed from large cloud droplets (Fig. 3b) during ACE-ENA Win. It is noteworthy that the D_mmd in the region in the lower-half of the ACE-ENA Win clouds experienced rapid growth from ∼80 to ∼105 µm (Fig. 3e), and this increment of ∼25 µm contributed to most of theD_mmd growth from cloud top to cloud base (33.5 µm), indicating a stronger warm-rain process during the winter.

Figure 4Cloud and drizzle size distributions for (a) upper cloud (z_i>0.8), (b) upper–middle cloud ($\mathrm{0.5}\le z_{\mathrm{i}}<\mathrm{0.8}$), (c) lower–middle cloud ($\mathrm{0.2}\le z_{\mathrm{i}}<\mathrm{0.5}$), and (d) lower cloud (z_i<0.2). The vertical dashed line at D_p=40 µm denotes the demarcation between cloud droplets and drizzle drops. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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In order to further analyze the cloud-to-drizzle conversion processes, the cloud and drizzle DSDs are categorized into four segments, based on their relative position within the cloud layer, as follows (Fig. 4): upper cloud (z_i>0.8; Fig. 4a), upper–middle cloud ($\mathrm{0.5}\le z_{\mathrm{i}}<\mathrm{0.8}$; Fig. 4b), lower–middle cloud ($\mathrm{0.2}\le z_{\mathrm{i}}<\mathrm{0.5}$; Fig. 4c), and lower cloud (z_i<0.2, Fig. 4d). The cloud DSDs (D_p<40 µm) from the three IOPs gradually shift towards larger sizes, moving from the lower- to the upper-cloud regions. This is accompanied by the narrowing of the cloud DSD ranges, as evidenced by the decline in the relative dispersion of cloud droplets (ϵ), which is defined as the ratio between the standard deviation and the mean radius of the distribution. At the lower portion of the cloud (Fig. 4d), the relatively greater value of ϵ represents the co-existence of the newly formed small cloud droplets from recently activated CCN and the sedimentation of larger droplets from the upper sections of the cloud. In addition, the discrepancies in ϵ between the three IOPs may be attributed to the sub-cloud aerosol differences, which essentially resided in different microphysical regimes. Y. Wang et al. (2021a) stated that higher aerosol loading would lead to increased ϵ due to the water vapor competition effect, supporting the discrepancy between SOCRATES and ACE-ENA Sum, which can be categorized as a water-vapor-limited regime. Meanwhile, ACE-ENA Win exhibits the characteristics of an aerosol-limited regime in which the cloud DSDs tend to be narrower than in the water-limited regime, due to enhanced droplet growth, and the ϵ values further decrease with height via the condensational narrowing effect (J. Chen et al., 2018).

Notably, for the four cloud portions from cloud base to cloud top, the skewness of summer (winter) cloud DSDs is 0.627 (0.271), 0.358 (0.175), 0.098 (−0.063), and −0.362 (−0.554), respectively. The cloud DSDs during ACE-ENA Win exhibit a more pronounced negative skew (to the left) than those during ACE-ENA Sum, which can be partially attributed to the activation of more sub-cloud coarse mode aerosols becoming larger cloud embryos, as demonstrated in Fig. 2. These coarse mode aerosols, whether from the primary production of sea spray or the residuals of evaporated drizzle drops, are more easily activated (or re-activated) into larger cloud droplets when they intrude (or recirculate) into the cloud layer (Hudson and Noble, 2020; Hoffmann and Feingold, 2023). Nevertheless, it is challenging to pinpoint the actual origins of coarse mode aerosols from the perspective of aircraft observational snapshots, thus requiring further numerical modeling work. Ascending within the cloud, the process of water vapor condensation perpetually pushes the DSD towards larger sizes, culminating in a more negatively skewed DSD. Concurrently, the cloud-top entrainment mixing plays a pivotal role in minimizing ϵ in the upper-cloud region, as elaborated by Lu et al. (2023).

In the upper region of the cloud (Fig. 4a), the ACE-ENA Win clouds contain more cloud droplets close to 40 µm, although the mean N_c is lower. This scenario is conducive to the formation of larger drizzle embryos compared to summertime clouds, as depicted in Fig. 3e. In comparison, the SOCRATES clouds feature a pronounced log-normal DSD compared to during ACE-ENA, as the DSDs peak at D_p∼15 µm throughout the cloud, and subsequently, the lack of larger cloud droplets results in the smaller drizzle embryos near the cloud top. As the newly formed drizzle drops descend and continuously grow through the collision–coalescence process, the drizzle DSDs (D_p> 40 µm) are noticeably broadened. From upper- to lower-cloud regions, the longer tails of the drizzle DSDs expand at the cost of smaller drizzle drops and cloud droplets via the collision–coalescence process. The clouds observed during ACE-ENA, especially in wintertime, contain more larger drizzle drops (D_p>200 µm) than SOCRATES, which is reflected in the distinct differences in the vertical D_mmd, as shown in Fig. 3e.

It has been intensively studied that in-cloud turbulence can stimulate collision–coalescence and consequently enhance the drizzle evolution processes (Pinsky et al., 2007; Grabowski and Wang, 2013; Wu et al., 2017; S. Chen et al., 2018). The turbulence strength is characterized by the turbulence kinetic energy (TKE), which is calculated as

where the turbulent perturbations of vertical ($\stackrel{\mathrm{‾}}{{w^{\prime }}^{\mathrm{2}}}$) and horizontal ($\stackrel{\mathrm{‾}}{{u^{\prime }}^{\mathrm{2}}}$ and $\stackrel{\mathrm{‾}}{{v^{\prime }}^{\mathrm{2}}}$) components are calculated as the simple moving variance in a 10 s window centered at the measurement time, without window weighting function, using 1 Hz data for all three IOPs. The w data are confined to an absolute aircraft roll angle of less than 5° (Cooper et al., 2016). Given the average aircraft ground speed of ∼140 m s⁻¹ and vertical speed of ∼5 m s⁻¹ (Atlas et al., 2020), the smallest resolved wavelength is 140 m. Hence, within the 10 s moving window, the ∼50 m in the integral vertical range is able to resolve the eddies up to ∼1400 m in size and preserve the potential of capturing the inertial subrange.

Figure 5Vertical distributions of in-cloud TKE (a), ${w^{\prime }}^{\mathrm{2}}$ (b), ${u^{\prime }}^{\mathrm{2}}$ (c), and ${v^{\prime }}^{\mathrm{2}}$ (d). Shaded areas denote the inter-cloud-case standard deviations. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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As shown in Fig. 5, the vertical wind variances (Fig. 5b) in ACE-ENA Win (layer mean of 0.244 m² s⁻²) are generally higher than those in ACE-ENA Sum (0.153 m² s⁻²) and SOCRATES (0.147 m² s⁻²), while the horizontal wind variances (Fig. 5c and d) are comparable between ACE-ENA Sum and ACE-ENA Win but much higher than SOCRATES, resulting in higher TKE during ACE-ENA. Note that the higher ${w^{\prime }}^{\mathrm{2}}$ near the cloud top corresponds to the stronger entrainment rate in ACE-ENA Win. Near the cloud top, turbulence effectively enhances coalescence between the larger cloud droplets, primarily by increasing the relative velocities between droplets (Magaritz-Ronen et al., 2016; Ghate and Cadeddu, 2019), and this is especially true for the vertical component ${w^{\prime }}^{\mathrm{2}}$ of TKE. The horizontal turbulence components, the ${u^{\prime }}^{\mathrm{2}}$ and ${v^{\prime }}^{\mathrm{2}}$, can also play a role in mixing the ambient air masses and contribute to the broadening of DSD (Wu et al., 2017). The use of TKE provides an illustration of how the in-cloud turbulence during ACE-ENA is stronger than that observed during SOCRATES. That being said, the quantitative evaluation of the turbulent enhancement of collision–coalescence requires access to the eddy dissipation rate, as typically used in model parameterizations (Grabowski and Wang, 2013; Witte et al., 2019). The smallest scales resolvable with the 1 Hz measurement used in this study are on the order of 140 m, thus capturing only the larger-scale end of the inertial subrange and larger turbulent motions. Consequently, the ability to resolve smaller eddies and turbulent structures, crucial for understanding the energy cascade within the inertial subrange, is limited by coarse spatial and temporal resolutions and aliasing issues (Siebert et al., 2010; Muñoz-Esparza et al., 2018; Kim et al., 2022). Therefore, to fully resolve the spectrum of turbulence and quantitatively examine the energy dissipation and mixing processes, access to higher-frequency measurements is required to capture smaller eddies within the inertial subrange (Siebert et al., 2010; Lu et al., 2011; Wacławczyk et al., 2017). Additionally, further quantifying the entrainment-mixing mechanisms also requires high-frequency eddy dissipation and accurate examination of the mixing timescale (Lehmann et al., 2009; Lu et al., 2011) for individual profiles. Though currently beyond the scope of this study, utilizing the high-rate measurements of velocities available from SOCRATES (at 25 Hz) and ACE-ENA (at 20 Hz) to explore those mechanisms further will be of interest to future investigations.

Drizzle formation and evolution in the ACE-ENA Win clouds are noticeably stronger than in the other two IOPs, which could be attributed to multiple factors. First, the ambient aerosols and CCN during winter are substantially fewer, featuring clean environments that promote the formation of generally larger cloud droplets due to the availability of more water content per droplet. Larger cloud droplets are more likely to collide and coalesce into drizzle drops, leading to relatively heavier precipitation (Chen et al., 2011; Duong et al., 2011; Mann et al., 2014). Furthermore, deeper cloud layers with a mean thickness of (392.4 m) during ACE-ENA Win were observed when compared to the ACE-ENA Sum clouds (336.3 m). In a thicker cloud layer with sufficient turbulence, the residence times of large cloud droplets and drizzle drops would become longer, and the chance of collision–coalescence growth could be effectively increased by recirculating the drizzle drops (Brost et al., 1982; Feingold et al., 1996; Magaritz et al., 2009; Ghate et al., 2021). Additionally, the prevalence of winter season precipitation–evaporation-induced MBL cold pools disturbs the MBL thermodynamics and contributes to turbulent mixing (Zuidema et al., 2017) and can provide a strong dynamical forcing perturbation to the warm-rain process (Jenson et al., 2021; J. Wang et al., 2022; Smalley et al., 2024). The physical hypotheses from previous studies could potentially serve as the explanation for the phenomena that the ACE-ENA Win drizzle DSD is sufficiently broadened, and the D_mmd is enlarged toward the cloud base. In comparison, although SOCRATES exhibits even thicker clouds (487.4 m), the drizzle processes are seemingly suppressed by the much higher ambient aerosol and CCN concentrations.

4.1 Cloud microphysical responses on aerosols

The impacts of aerosol loading on cloud microphysical properties can be assessed by the aerosol–cloud interaction (ACI) index, which can be quantified as both

and

which emphasizes the cloud microphysical responses to CCN via the relative logarithmic change in N_c and r_c to the change in N_{CCN 0.35 %} (Feingold et al., 2003; McComiskey et al., 2009). Physically, the ACI process involves aerosols intruding into the cloud layer, activating as cloud droplets, and subsequently altering cloud DSD and dispersion (Zheng et al., 2022a, b) under varying water vapor conditions. Therefore, the cloud microphysical responses within the lower region of the cloud are assessed, which is the first stage in which the sub-cloud CCN can directly interact with the cloud droplets. Furthermore, the similarity in the vertical integral of LWC_c (as shown in Fig. 3c) provides comparable liquid water between three IOPs for the assessment of newly generated cloud embryos from activated CCN because the ACI_r is normally assessed under a fixed liquid water (Zheng et al., 2020).

Figure 6Scatterplots of the (a) N_c and (b) r_c at the lower cloud (z_i<0.2) against the sub-cloud N_{CCN 0.35 %} and the (c) N_c and (d) r_c at the upper cloud (z_i>0.8) against the above-cloud N_{CCN 0.35 %}. The statistical metrics in the legends denote the ACI values and standard errors and the absolute values of correlation coefficients (in parentheses). The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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Considering all the cases from three IOPs with available CCN measurements (some cases without CCN measurements during SOCRATES), the N_c and r_c values at the lower cloud (z_i<0.2) are plotted against the sub-cloud N_{CCN 0.35 %} in Fig. 6a and b, and the ACI indices are calculated as ACI_N,CB and ACI_r,CB (CB denoting the assessment near the cloud base). The ACI indices from three IOPs are in the ACI range of the previous studies in MBL clouds (Twohy et al., 2005; Lu et al., 2009; Diamond et al., 2018) using aircraft in situ measurements. Note that the availability of valid sub-cloud measurements inevitably limits the sample size, especially for SOCRATES, as shown in Table S2. As shown in Fig. 6a, the ACI_N,CB for ACE-ENA Win (0.748) is higher than ACE-ENA Sum (0.617), indicating that N_c is more sensitive to the sub-cloud N_{CCN 0.35 %} during the winter. In other words, aerosols intruding into the cloud layer are easily activated to become cloud droplets. The N_c sensitivity for the SOCRATES cloud (0.692) lies between the two ACE-ENA IOPs. The ACI_N,CB values from three IOPs are generally higher than the ACI_N values from the layer mean N_c against the sub-cloud N_{CCN 0.35 %} (not shown). Previous studies have shown that the enhanced vertical turbulence (updraft velocity) can effectively facilitate CCN replenishment into the cloud layer (Hu et al., 2021; Zheng et al., 2022a, b) and increase the actual in-cloud supersaturation (Brunke et al., 2022), thus leading to a more efficient cloud droplet formation, enhancing the ACI_N,CB. By correlating the mean TKE values with the CCN activation ratio ($N_{\mathrm{c}}/N_{\text{CCN}\mathrm{0.35}\mathit{\%}}$) for all individual cloud cases, the three IOPs show moderate but statistically significant correlation coefficients of 0.36, 0.55, and 0.51 for ACE-ENA Sum, ACE-ENA Win, and SOCRATES, respectively. This result reinforces the notion that the CCN activation fractions, particularly during the ACE-ENA Win, are significantly correlated with in-cloud turbulence intensities. Furthermore, more coarse mode aerosols during ACE-ENA Win are also favorable to the activation efficiency (Dusek et al., 2006).

As for the r_c responses to CCN (Fig. 6b), the typical Twomey effect, where more CCN compete against available water vapor and result in smaller cloud droplets, is evident by different cloud susceptibility between the three IOPs. SOCRATES features a higher ACI_r,CB (0.311), suggesting that an increase in N_{CCN 0.35 %} can result in a significant decrease in r_c compared to ACE-ENA Sum (0.206) and ACE-ENA Win (0.263). Although the absolute range of variation for r_c during SOCRATES is smaller, the slope is much deeper (Fig. 6b). Recall that the sub-cloud N_{CCN 0.35 %} during SOCRATES is generally higher than ACE-ENA and contains more small-sized aerosols (as indicated in Fig. 2b). Consequently, after activation, the lower part of the cloud exhibits a higher number of smaller cloud droplets for SOCRATES, as shown in Fig. 4d. Therefore, as more CCN intrudes into the cloud, the competition for water vapor among newly activated cloud droplets becomes more pronounced, given the similar water availability. In contrast, the presence of larger cloud droplets near the cloud base, whether activated from coarse-mode aerosols or remaining as residuals from collision–coalescence, would elevate the r_c, especially under the relatively lesser CCN condition, hence inevitably dampening the ACI_r,CB during ACE-ENA. However, a more comprehensive investigation into the cloud microphysical responses to CCN intrusions under a larger range of various water supply conditions, and further untangling the ACI from the meteorological influences, will require additional aircraft cases from more field campaigns. Examples include the VAMOS Ocean–Cloud–Atmosphere–Land Study (VOCALS; Wood et al., 2011), the Cloud System Evolution in the Trades (CSET; Albrecht et al., 2019), the ObseRvations of CLouds above Aerosols and their intEractionS (ORACLES; Redemann et al., 2021), and the Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE; Sorooshian et al., 2019). Note that the ACI_r,CB values in Fig. 6b are also larger than the results from the layer mean r_c against sub-cloud N_{CCN 0.35 %}, since the layer mean microphysics is more subject to the cloud droplet evolution processes such as condensational growth and collision–coalescence.

To investigate the ACI indices at the upper level of the cloud, the N_c and r_c values at the upper cloud (z_i>0.8) are plotted against the above-cloud N_{CCN 0.35 %} in Fig. 6c and d, and the ACI indices are calculated as ACI_N,CT and ACI_r,CT (denoting the assessments near the cloud top). Compared to the ACI_N,CB and ACI_r,CB, the ACI_N,CT and ACI_r,CT  are much weaker, especially for ACI_r,CT, as the near-cloud-top droplets are too large for above-cloud aerosols to exert a significant influence on r_c (Diamond et al., 2018; Gupta et al., 2022). The weaker cloud-top N_c dependence on the N_{CCN 0.35 %} could be due to the legacy of the sub-cloud CCN impacts on N_c being conveyed to the cloud top. This occurs because free-tropospheric aerosols and CCN can be entrained into the MBL before and during the cloud process, as observed in the assessment of inter-cloud cases. Note that the LWC_c values near the cloud top for the three IOPs are not comparable to each other, which might also induce uncertainty in the near-cloud-top ACI assessment. These weaker relationships support the notion that although the aerosols entrained into the upper-cloud region can affect the cloud microphysics to a certain degree, the effects are less pronounced than those from the sub-cloud aerosols (Diamond et al., 2018; Wang et al., 2020) because the MBL cloud N_c and r_c variations are dominated by the condensational growth, collision–coalescence, and entrainment-mixing processes near the cloud top.

4.2 Precipitation susceptibility

The precipitation susceptibility relies on the assessment of relative responses in the precipitation rate to the change in N_c (Feingold and Seibert, 2009; Sorooshian et al., 2009), which is defined as

where the R_CB is the cloud base precipitation rate calculated in Sect. 2 (Eq. 5). By incorporating all the cloud cases, including both precipitating and non-precipitating clouds (the R_CB can also be calculated based on the drizzle DSD near the cloud base), the S_o value accounts for the impact of cloud droplets on the potential precipitation ability of the cloud (Terai et al., 2012).

Figure 7Scatterplots of the cloud base precipitation rate R_CB against the (a) layer mean N_c and (b) $H_{\mathrm{c}}^{\mathrm{3}}/N_{\mathrm{c}}$. The ACE-ENA Sum, ACE-ENA Win, and SOCRATES values are color-coded in pink, purple, and green, respectively.

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As shown in Fig. 7a, the R_CB values generally have a negative correlation with increased layer mean N_c for all three IOPs. The S_o values are 0.979, 1.229, and 1.638, with the absolute values of correlation coefficients being 0.33, 0.29, and 0.45 for SOCRATES, ACE-ENA Sum, and ACE-ENA Win, respectively. The regression relationships are statistically significant, with p<0.05 for all three IOPs. These correlation coefficient values fall within the reasonable range found in previous studies on precipitation susceptibility in the MBL stratus and stratocumulus clouds (Jung et al., 2016; Gupta et al., 2022) and indicate statistically significant dependences of R_CB on N_c. A previous study by Terai et al. (2012) found that the S_o values decrease with the increasing cloud thickness over the southeastern Pacific, and Jung et al. (2016) found that the S_o is more pronounced within the medium deep clouds with thicknesses of ∼300–400 m in the MBL stratocumulus over the eastern Pacific. Gupta et al. (2022) found that the S_o values are generally higher under low ambient N_a conditions in the southeastern Atlantic MBL. In this study, R_CB for the ACE-ENA Win is more susceptible to the layer mean N_c than the ACE-ENA Sum and SOCRATES, which can be partially attributed to the existence of more larger drizzle drops (as shown in Fig. 4d) near the cloud base in ACE-ENA Win. As previously discussed, the ACE-ENA Win featured enhanced collision–coalescence, suggested by the stronger in-cloud turbulence, and a possible drizzle-recirculating process, as indicated by the previous study. And such mechanisms might explain the low N_c conditions with more larger drizzle drops, leading to the increase in S_o values during ACE-ENA Win. In comparison, the aerosol of SOCRATES is largely composed of fine Aitken mode aerosol, which results in smaller cloud droplets. Thus, collision–coalescence is ineffective during SOCRATES, which leads to the relatively narrower drizzle DSDs, where the warm-rain processes are suppressed, and, in turn, diminishing the sensitivity of R_CB to N_c (Stevens and Feingold, 2009; Fan et al., 2020; Gupta et al., 2022).

It is well known that the R_CB values can be parameterized or predicted by assuming an approximate relation with N_c and cloud thickness (H_c), which is usually parameterized in the form of $R_{\text{CB}}\propto c{H}_{\mathrm{c}}^{\mathrm{3}}{N}_{\mathrm{c}}^{-\mathrm{1}}$ (Lu et al., 2009; Kang et al., 2024). Following the same method, we derive the relationships from three IOPs in Fig. 7b, where the R_CB are positively (negatively) proportional to the H_c (N_c), with the exponential parameters in the range of the typical values in the MBL clouds (Comstock et al., 2004; van Zanten et al., 2005; Lu et al., 2009). The statistical coefficient of determination (R²) values of R_CB against H_c (N_c) are 0.696 (0.177), 0.419 (0.212), and 0.165 (0.295) for the ACE-ENA Sum, ACE-ENA Win, and SOCRATES, respectively, suggesting that the R_CB  in ACE-ENA clouds may be more determined by H_c, while the R_CB  in SOCRATES clouds could be less dependent on both H_c and N_c. Note that the relationship for the SOCRATES values in this study reveals a similar R_CB dependence on N_c but a smaller dependence on the cloud thickness than the study by Kang et al. (2024), who concluded a relationship of $R_{\text{CB}}=\mathrm{1.41}\times {\mathrm{10}}^{-\mathrm{9}}{H}_{\mathrm{c}}^{\mathrm{3.1}}{N}_{\mathrm{a}}^{-\mathrm{0.8}}$, based on the rain rate retrieved from radar and lidar measurements and the aerosol concentration also from SOCRATES. The discrepancies are possibly due to the different sample selections and different methods in the R_CB calculation. Note that the mean cloud thicknesses of ACE-ENA Sum (336.3 m), ACE-ENA Win (392.4 m), and SOCRATES (487.4 m), are within the thickness range found to exhibit stronger S_o (Terai et al., 2012; Jung et al., 2016; Gupta et al., 2022).

4.3 Drizzle impacts on sub-cloud CCN and implication to ACI

Multiple studies on the MBL clouds have concluded that the in-cloud drizzle formation and evolution processes can effectively impact the sub-cloud CCN budgets via the coalescence-scavenging effect (Wood, 2006; Diamond et al., 2018; Zheng et al., 2022b; Zhang et al., 2023). Drizzle drops are formed and grow via the collision–coalescence process by collecting cloud droplets and small drizzle drops, resulting in the consumption of CCN (the precursor of cloud droplet), but in the meantime, the in-cloud N_c can be continuously buffered by the sub-cloud CCN replenishment. Although the sub-cloud aerosols (especially in large size) would be added if the drizzle fell and evaporated outside the cloud, the increment cannot compensate for the loss. Therefore, the net result of the whole process is usually presented as the depletion of sub-cloud CCN residuals, and such a drizzle modulation on the CCN budget could be substantial in moderate-to-light drizzles or even non-precipitating clouds, depending on the collision–coalescence efficiency (Feingold et al., 1996; Wood, 2006; Kang et al., 2022).

Figure 8ACI_r,CB as a function of the sub-cloud N_{CCN 0.35 %} retrospective time for (a) all clouds and (b) precipitating clouds.

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The CCN loss rate due to the coalescence-scavenging effect can be calculated as

where the constant K (2.25 m² kg⁻¹) denotes the drizzle collection efficiency (Wood, 2006; Diamond et al., 2018). H_c is cloud thickness, and H_cp is the coupled layer thickness to ensure that the change in the cloud layer can be sufficiently conveyed throughout the layer. The calculated CCN loss rate for individual cases is listed in Table S2. Considering all cloud (precipitating cloud) scenarios, the mean CCN loss rates are $-\mathrm{7.69}\pm \mathrm{13.96}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$ ($-\mathrm{10.45}\pm \mathrm{15.56}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$), $-\mathrm{6.29}\pm \mathrm{11.65}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$ ($-\mathrm{12.11}\pm \mathrm{14.64}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$), and $-\mathrm{4.94}\pm \mathrm{7.96}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$ ($-\mathrm{5.58}\pm \mathrm{8.43}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}$) for ACE-ENA Sum, ACE-ENA Win, and SOCRATES, respectively. As the results indicate, the ACE-ENA clouds experience a more substantial sub-cloud CCN loss than SOCRATES, especially in wintertime-precipitating clouds. Recall that the assessment of ACI_r,CB relies on the relative changes in r_c and N_CCN, while the different L_CCN for individual cases can result in the shrinking of the N_CCN variation ranges (imagine the abundant CCN are depleted by the coalescence scavenging). In other words, the given change in r_c corresponds to a narrowed change in N_CCN. Mathematically speaking, the assessment of ACI_r,CB depends on the ratio of the numerator (change in r_c) and the denominator (change in N_CCN). Under the circumstances of substantial cloud-processing to the aerosols, the altered sub-cloud CCN budgets are reflected as a smaller denominator, versus the less altered numerator, and are hence mathematically presented as an enlarged ACI_r,CB. Therefore, the coalescence-scavenging effect can not only deplete the sub-cloud CCN but also quantitatively amplify the assessment of cloud microphysics susceptibilities (Feingold et al., 1999; Duong et al., 2011; Jung et al., 2016; Zheng et al., 2022b). In order to examine the potential impact of the aforementioned processes on the ACI assessment, a sensitivity analysis is conducted by simply retrospecting the sub-cloud N_{CCN 0.35 %} according to their L_CCN. For each retrospective time step ΔT, the r_c values are held unchanged, and the retrospective N_{CCN 0.35 %} values for individual cloud cases are given by $N_{\text{CCN}\mathrm{0.35}\mathit{\%}}-L_{\text{CCN}}\cdot \mathrm{\Delta }T$, and then the ACI_r,CB can be recalculated. Note that assuming a constant r_c value over time inevitably induces uncertainty and biases, as it does not consider the microphysical processes affecting the cloud droplet mean size. However, previous numerical experiments show that the noticeable impact on the cloud mean radius through collision–coalescence necessitates a high degree of CCN depletion, and the quantified percentage changes in droplet mean sizes are several times smaller than the changes in CCN depletion (Feingold et al., 1996). Hence, the retrospective method, from an observational snapshot point of view, provides a direction that enables the assessment of ACI_r,CB as if before the sub-cloud aerosols and CCN are scavenged by in-cloud coalescence-scavenging and precipitation-scavenging processes.

As shown in Fig. 8, the ACI_r,CB values tend to decrease with the retrospective time, which indicates the retrospective CCN variation range is enlarged and counteracting the coalescence-scavenging amplification. The detailed illustration of the different ACI_r,CB calculated from the scattered r_c and sub-cloud N_{CCN 0.35 %} is shown in Fig. S5. Note that the ACI_r,CB decreasing rates for the precipitating clouds (Fig. 8b) are not as strong as for all clouds because the non-precipitating clouds have smaller L_CCN largely due to weaker collision–coalescence. Hence, the retrospective period used here might quickly exceed the actual time of cloud-processing to become effective on aerosol and CCN. In other words, the actual time needed to trace back to the sub-cloud CCN concentration before they were cloud-processed is shorter than the retrospective time tested here in Fig. 8. This results in the faster decrease in ACI_r,CB in the non-precipitating cloud. The retrospective of the sub-cloud CCN budget will yield an alternative assessment of ACI, assuming that the drizzle processes have not yet significantly impacted the sub-cloud CCN budget, especially for the assessment under the precipitating clouds. However, examining the exact precipitating timing is challenging since the aircraft provides a snapshot of the cloud and aerosol information. Thus, this retrospective study only provides a possible direction, and the result should be interpreted with caution.