Maximum Supersaturation in the Marine Boundary Layer Clouds Over the North Atlantic

The maximum supersaturation (Sx) in clouds is a key parameter affecting the cloud's microphysical and radiative properties. We investigate the Sx of the marine boundary layer clouds by combining airborne and surface observations in the Eastern North Atlantic. The cloud droplet number concentration (Nc) in the least diluted cloud cores agrees well with the number concentration of particles larger than the Hoppel Minimum (HM) (N>HM) below clouds, indicating that the HM represents the average size threshold above which particles are activated to form cloud droplets. The Sx values derived from surface observations vary from 0.10% to 0.50% from June 2017 to June 2018, with a clear seasonal variation exhibiting higher values during winter. Most of the Sx variance (∼60%) can be explained by the cloud condensation nuclei (CCN) concentration and updraft velocity (w), with the CCN concentration playing a more important role than w in explaining the variation of Sx. The influence of CCN concentration on Sx leads to a buffered response of Nc to aerosol perturbations. The response of Nc to low aerosol concentration during winter is further buffered by the high w. The global Community Earth System Model (CESM) simulated Sx values in the Azores have a positive bias compared to measured Sx, likely due to overestimated w and underestimated CCN concentration. The CESM simulated Sx exhibits higher values further north over the North Atlantic Ocean, which is attributed to stronger w. The suppression of Sx by aerosol is also evident in regions with high CCN concentrations.

• Maximum cloud-base supersaturations are derived from 1-year measurements at a marine site in the North Atlantic • Maximum supersaturations are high in winter, consistent with the low aerosol loading and synoptic conditions • Variability in maximum supersaturation and updraft velocity lessens the sensitivity of clouds to seasonal changes in aerosol concentrations

Supporting Information:
Supporting Information may be found in the online version of this article.
GONG ET AL. 10.1029/2022AV000855 2 of 14 value near the cloud base.As aerosol particles are activated to cloud droplets when exposed to a supersaturation equal to or higher than their critical supersaturation, the maximum supersaturation (S x ) in clouds dictates the fraction of aerosol particles that can form cloud droplets, thereby strongly influencing cloud microphysical and radiative properties.
The value of S in clouds is difficult to measure directly, due to the challenges of precisely measuring water vapor pressure and temperature in clouds (Siebert & Shaw, 2017;Yang et al., 2019).There are a few different ways to estimate S indirectly.A number of studies have combined measured CCN spectrum (i.e., the variation of CCN concentration, N CCN , as a function of S) below the cloud base with droplet number concentration (N c ) in undiluted clouds (i.e., adiabatic cores).The S level at which N CCN matches N c represents the maximum value (S x ) in the cloud, which typically occurs near the cloud base (Hudson et al., 1998(Hudson et al., , 2010(Hudson et al., , 2015;;Martin et al., 1994;Russell et al., 2013;J. Wang et al., 2009).In a different method, S is estimated using an equation proposed by Politovich and Cooper (1988), based on a quasi-steady-state assumption whereby in a rising adiabatic cloud parcel, the saturation is determined by two competing processes, that is, the increase of saturation as a result of the decreasing air parcel temperature and the decrease of saturation as a result of the condensation of water vapor onto activating and activated aerosol particles.However, this assumption might not be valid in clean (low N c ) and/ or vigorous (large vertical air velocity) clouds for which clouds need a longer time to return to the quasi-steadystate following the change in environmental conditions.Recently, Yang et al. (2019) developed a new method to estimate S distribution in clouds using ground-based remote-sensing measurements.In the method, S is estimated from the gradient of liquid water content (LWC) with updraft velocity, assuming the difference in LWC between two cloud layers is the result of condensation or evaporation of cloud droplets.This method does not rely on the quasi-steady-state assumption and can provide a vertical profile of S.However, the uncertainties of derived S are relatively large (about 86%) due to large uncertainties of updraft velocity (about 43%), LWC (about 50%), and N c (100%) retrieved from surface-based remote-sensing (Yang et al., 2019).
Sub-micron particle number size distribution in the MBL is often bimodal (Gong et al., 2020;Modini et al., 2015;Y. Wang et al., 2021).The bimodal distribution consists of an Aitken and an accumulation mode, which are separated by a minimum in a size distribution often referred to as the Hoppel Minimum (HM, Hoppel et al., 1990).
The bimodal size distribution is considered a result of particle processing in non-precipitation clouds (Hoppel et al., 1986;O'Dowd et al., 1999).Therefore, the HM can be assumed as the average size threshold above which particles are activated into cloud droplets, and the critical supersaturation of particles at the HM size represents S x in boundary layer clouds.However, this assumption has not been validated, partially due to the challenges of conducting the appropriate measurements both in and out of the clouds.Nevertheless, with this assumption, Hoppel et al. (1996) estimated S x using HM by further assuming a fixed particle hygroscopicity (a mixture of ammonium sulfate and sulfuric acid).
In this study, we investigate the S x of MBL clouds by combining airborne and surface observations during the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign (J.Wang et al., 2022).We first present observational evidence that the HM is the result of cloud processing in the MBL and represents the average threshold above which particles are activated into cloud droplets.By combining the HM with N CCN or measured particle hygroscopicity, we derive S x in boundary layer clouds in the Azores from June 2017 to June 2018.We then investigate the seasonal variation of S x and its dependence on the CCN properties and synoptic conditions.Moreover, we evaluate the global Community Earth System Model (CESM) simulated S x using that derived from the measurements, and explore the implication of the measurements for the model representation of aerosol-cloud interactions.

Measurements and Model Simulation
Since late 2013, measurements are carried out continuously at the ENA observatory (39°5′30″ N, 28°1′32″ W, 30.48 m a.m.s.l.), which was set up on Graciosa Island in the Azores, Portugal, and operated by the Department of Energy Atmospheric Radiation Measurement (ARM) Climate Research Facility (Uin et al., 2019).During the ACE-ENA field campaign, airborne measurements of aerosol, cloud, and atmospheric states were carried out onboard the G-1 research aircraft in the Azores from June to July 2017 and January to February 2018 (J.Wang et al., 2022;Y. Wang et al., 2021).Additional aerosol measurements were carried out at the ENA observatory from June 2017 to June 2018 during the ACE-ENA campaign.The global CESM was used to simulate S x over the North Atlantic Ocean during the same 1-year period.In the following, we will introduce measurements relevant GONG ET AL. 10.1029/2022AV000855 3 of 14 to this study and review relevant aspects of the CESM and the simulation strategy.A summary of abbreviations, variable names, and definitions of variables is given in Appendix A. Aerosol size distribution from 10 to 600 nm and cloud droplet size distribution from 2 to 50 μm at 1 Hz were measured by a fast integrated mobility spectrometer (FIMS, J. Wang et al., 2017;Y. Wang et al., 2018) and a fast cloud droplet probe (FCDP, SPEC Inc., Boulder, CO), respectively.Cloud LWC was calculated by integrating the droplet size distribution measured by the droplet probe and agrees with direct measurements by a multi-element water content system (WCM-2000, SEI Inc., Tolland, CT).The total number concentration for particles larger than 10 nm (N 10 ) was measured by a condensation particle counter (CPC, 3772, TSI Inc., Shoreview, MN).The value of N 10 was also derived from the mobility spectrometer size distribution and agrees with the measurement by the CPC in cases when the size distribution shows a negligible contribution from nucleation mode particles.

Surface Measurements
During the ACE-ENA campaign, additional aerosol and meteorological measurements were carried out from June 2017 to June 2018 at the ENA observatory.Collectively, aerosol size distribution in the diameter range from 10 to 470 nm was measured by a scanning mobility particle sizer (SMPS, Model 3938, TSI Inc., Shoreview, MN) and the size distribution from 60 to 1,000 nm was measured by an ultra-high sensitivity aerosol spectrometer (UHSAS, DMT, Boulder, CO).SMPS-and UHSAS-measured aerosol size distributions were then combined to obtain a distribution from 10 to 1,000 nm (assume spherical particles) every 8 min.At the surface, the N 10 was measured by a CPC (model 3772, TSI Inc., Shoreview, MN).
N CCN was measured by a CCN counter (CCNC, DMT, Boulder, USA, Roberts & Nenes, 2005).The CCN counter was operated at a constant total flow rate of 0.5 L min −1 , with instrument supersaturation levels set at 0.10%, 0.20%, 0.50%, 0.80%, and 1.00%.Instrument supersaturation was stepped every 10 min, and an extra 10 min was used to ensure the CCN measurements reached a steady state when the supersaturation decreased from 1.00% to 0.10%.Therefore, a cycle of N CCN measurements at the five supersaturation levels took 1 hr.
The CCN activation spectrum (i.e., CCN activation fraction as a function of S) of size-selected particles was obtained using a differential mobility analyzer (DMA, Model 3081, TSI Inc., Shoreview, MN, USA), a CPC (Model 3010, TSI Inc., Shoreview, MN, USA), and a second CCN counter, a.k.a.size-resolved CCN (SCCN) measurement system (Mei et al., 2013;Thalman et al., 2017).The DMA stepped through five diameters of 40, 50, 75, 100, and 150 nm.At each diameter, the S level inside the CCN counter was varied by changing the temperature gradient (∆T, at values of 4, 6.5, and 10 K), the sampling flow rate (ranging from 0.3 to 1.0 L min −1 ), or both.The sampling time at each S was set from a minimum of 30 s to a maximum of 120 s, or until 1,500 particles had been detected by the CPC, resulting in roughly 10-20 min sampling time for each particle size.
From each set of measurements at a fixed particle diameter, we first generated a CCN activation spectrum.The impact of multiple-charging on the activation spectrum was corrected by using the method described in Thalman et al. (2017).The S value corresponding to a 50% maximum activation fraction was deemed as the critical S for this particle diameter (Rose et al., 2010).The critical S values at the five particle diameters (40, 50, 75, 100, or 150 nm) were obtained every hour.
Meteorological measurements at the ENA observatory include updraft velocity at the cloud base (w), which was retrieved from the Doppler Lidar (Borque et al., 2016;Ghate et al., 2021).For a few months during the ACE-ENA campaign, the Doppler Lidar was not operational, hence w was retrieved from the vertically pointing cloud radar measurements of non-precipitating clouds (Zhu et al., 2021).The cloud base updraft velocity retrieved from either the Doppler Lidar or the cloud radar has a 5-s temporal and 30 m range resolutions and was averaged to hourly intervals for further analysis.Inversion layer height (z i ) and lower tropospheric stability (Δθ) were derived from the vertical profile of the atmosphere thermodynamic state, which was measured by a balloon-borne sounding system (Holdridge, 2020).The temperature gradient over height was first calculated from the vertical profile.The strongest temperature gradient below 4 km was then determined, and the corresponding height is defined as z i .Lower tropospheric stability was calculated as the potential temperature (θ) difference between a nominal location in the free troposphere (700 hPa) and the surface (1,000 hPa) (Klein & Hartmann, 1993;Wood & Bretherton, 2006).Wind speed at 10 m (U 10 ) was measured by an RM Young 05106 sensor.

Community Earth System Model
We used CESM version 2.1 (CESM2.1)with the Community Atmosphere Model version 6 (CAM6) as the atmosphere component to simulate the aerosol size distributions, N CCN , and maximum supersaturation (Danabasoglu et al., 2020).A Morrison-Gettelman Version 2 (MG2) (Gettelman & Morrison, 2015) scheme was used in CAM6 for representing stratiform cloud microphysics.In addition, the Cloud Layers Unified by Binormals (CLUBB), a higher-order turbulence closure scheme, was used for a unified treatment of turbulence, shallow convection, and cloud macrophysics (Golaz et al., 2002a(Golaz et al., , 2002b;;Larson & Golaz, 2005).The aerosol processes were represented by the four-mode version of the Modal Aerosol Module (MAM4) (Liu et al., 2016), which adopts a modal approach and predicts mass mixing ratios of aerosol species including sulfate, primary particulate organic matter, secondary organic aerosol, black carbon, dust, sea salt, as well as number concentrations internally mixed within each of four externally mixed modes including Aitken, accumulation, coarse, and primary carbon modes.
In CAM6, aerosol activation is represented using the AG parameterization (Abdul-Razzak & Ghan, 2000).In the parameterization, the activated droplet number is calculated using Köhler theory from S x , which is a function of aerosol properties from MAM4 (e.g., aerosol size, concentration, and composition) and sub-grid scale w from CLUBB.Following Morrison and Pinto (2005), the characteristic subgrid w is diagnosed as a function of turbulence kinetic energy.The analytic expression for S x is obtained by solving an equation of the time rate of change of supersaturation with the two competing terms of adiabatically cooling rate and water condensation during the aerosol activation and subsequent growth (Abdul-Razzak et al., 1998).Once activated, both mass and number of aerosol species are transferred from the interstitial state to the cloud-borne state.Cloud-borne aerosol particles can be re-suspended to an interstitial state when droplets evaporate.
In this study, a 19-month simulation was conducted from 1 December 2016 to 30 June 2018, with the first 6 months as the spin-up period.The model simulation was configured with 0.9° × 1.25° horizontal grid spacing resolution and 56 vertical levels from the surface up to about 43 km.To better simulate the transport of aerosols, we nudged wind fields to 6-hourly reanalysis data of Modern-Era Retrospective analysis for Research and Applications, version 2 (Gelaro et al., 2017).To match observational frequency, we extracted w, N CCN , and S x (denoted by S x,CESM ) fields every model timestep (30 min) over the selected Northern Atlantic region (latitude: 0°-60°N; longitude: 80°-180°W) in addition to their monthly averages.Anthropogenic emissions for the medium scenario of the Shared Socioeconomic Pathway (SSP245) (Gidden et al., 2019) were used for model inputs.

Hoppel Minimum (HM) and Its Connection to CCN Concentration
The role of HM in aerosol-cloud interaction is examined by combining aerosol-and cloud-related measurements both on the ground and onboard the G-1 aircraft.Figures 1a-1c and 1d-1f show two cases of the time series measurements on 13 July 2017 and 3 July 2017, respectively.During the first case on 13 July 2017, LWC (blue line in Figure 1a) starts to increase at 09:24 UTC, indicating measurements in clouds.After ∼09:49 UTC, LWC suddenly decreases, indicating that the G-1 aircraft was again in cloud free air.
When the aircraft progressively ascended through the boundary layer (UTC from 09:06 to 09:18), N 10 aloft (green line in Figure 1b) is nearly constant and agrees with the N 10 measured on the ground (black line in Figure 1b), indicating a well-mixed boundary layer.The particle number concentration integrated from the FIMS size distribution (N FIMS ) also matches the N 10 aloft well.The ground-measured HM and FIMS-measured aerosol size distribution were used to derive N >HM aloft.The ground-measured, instead of FIMS-measured, HM was used to confirm that S x in the cloud can be derived from ground-measured HM, as the 1-year ground measurement enables us to examine the seasonal variation of S x .The resulting N >HM aloft and N >HM based on both the aerosol size distribution and HM measured on the ground are shown as magenta lines and black dots in Figure 1c, respectively.N >HM aloft agrees well with ground N >HM .The N c value in the least diluted clouds, which is defined here as the region where LWC is greater than the 90th percentile between 09:24 and 09:49 UTC, shows good agreement with the flight N >HM below the cloud (Figure 1c).The periods of the least diluted cloud cores are marked as black lines in LWC and N c .We note that the in-cloud aerosol concentration is not valid due to the shattering of droplets on the sampling inlet, and therefore excluded from the analysis.
The case on 3 July 2017 shows an example of when the MBL is decoupled (Figures 1d-1f).Again, N c in the least diluted cloud cores (13:16-13:24 UTC) matches N >HM out of the cloud (13:06-13:15 UTC) well.These periods for comparison are chosen because N 10 aloft remains the same both upstream and downstream of the cloud, suggesting the measurements were in the same air mass.The ground-and flight-measured N >HM show substantial differences as the MBL was decoupled.However, the flightand ground-measured HM diameters are in good agreement (Figure S1 in Supporting Information S1).
Overall, there were 18 below-cloud/out-of-cloud and in-cloud cases observed, including three decoupled and 15 well-mixed MBL cases.The well-mixed or decoupled boundary layers were characterized based on vertical profiles of potential temperature and water vapor mixing ratio (Jones et al., 2011;Y. Wang et al., 2021;Wood & Bretherton, 2004;Zheng et al., 2021).Figure 2 shows the comparison of N >HM aloft (below-cloud in well-mixed MBL in blue and out-of-cloud in decoupled MBL in red) with N c in the least diluted cloud cores.N c shows a strong positive correlation with N >HM (R = 0.95), and all data points are close to the 1:1 line, indicating that the ground-measured HM represents the average size threshold above which particles are activated to droplets in the clouds.

Derivation of Maximum Supersaturation in the Cloud
Figures 3b and 3c illustrates the approaches of deriving S x from the ground measurements.Aerosol size distributions measured at the ENA observatory are first averaged into 1-hr intervals.Roughly more than 93% of the hourly average distributions are bimodal.The HM was identified as the particle diameter corresponding to the local minimum of the number concentration between ∼40 and 150 nm.As discussed in Section 3.1, HM from the aerosol size distributions measured on the ground represents the average size threshold above which particles are activated into cloud droplets.Therefore, S x is essentially the same as the critical S of particles at the HM, which were derived using the following two approaches.In the first approach, the number concentration of particles larger than the HM (N >HM , shown as the green shaded area in Figure 3a) was first calculated by integrating from the HM to 1 μm.The critical S of particles at the HM (i.e., same as S x ) is given by the supersaturation level at which N CCN matches N >HM , and was derived from linear interpolation using the spectrum of S as a function of N CCN (Figure 3b).The S x derived from such interpolation is referred to as S x,NCCN .In the second approach, the critical S of particles at the HM size was derived by interpolating the size-resolved CCN measurements (i.e., variation of critical S as a function of particle diameter, Figure 3c).S x derived using the second approach is denoted as S x,SCCN .Both approaches explicitly take into account the variation of particle hygroscopicity instead of assuming a constant value as done by Hoppel et al. (1996).As S x represents the average maximum supersaturation in clouds, we did not consider the hygroscopicity heterogeneity among particles of the same size when estimating the uncertainty in the derived S x (Section 3.3).We also note that linear interpolation in both approaches may lead to additional minor uncertainties in derived S x , but these uncertainties are not considered in this study.

Measurement Uncertainty
The uncertainties in the measurements of aerosol size distribution, N CCN , and CCN activated fraction all contribute to the uncertainty in the derived S x values.The measurements have instrument-specific uncertainty levels.For example, the uncertainty in concentration is about 10% for the aerosol size distribution measurements (Wiedensohler et al., 2018).The uncertainty in measured particle size, originating from the uncertainties of the instrument's classifying voltage and sheath flow rate, is below 1% for sizes between 40 and 150 nm and was neglected in this study (Wiedensohler et al., 2018).The effective supersaturation in the CCN counter had a relative uncertainty of 3.5%, corresponding to 1 standard deviation.The counting uncertainty of the CCN counter is about 10% (Rose et al., 2008).To estimate the overall uncertainty of the derived S x , we employed a Monte Carlo simulation method similar to that described in Herenz et al. (2018).In the first step, the following general equation was applied to a measured quantity s:  reported in previous studies, for example, 0.02%-0.25%based on field measurements from February to April in the Pacific Ocean (Hoppel et al., 1996) and ∼0.20% in stratocumulus clouds from large eddy simulations (Stevens et al., 1996).
CCN concentrations at supersaturations of 0.20% and 0.50% (N CCN,0.20% and N CCN,0.50% ) exhibit similar seasonal variations, with low concentrations in winter and high concentrations in spring and summer (Figure 4b).Previous studies show that ocean biological activity and precipitation strongly influence N CCN at the ENA observatory (Wood et al., 2017;G Zheng et al., 2018).From late spring to summer, strong ocean biological activity leads to increased secondary aerosol formation and CCN concentration (Fu et al., 2013;Mayer et al., 2020;Zheng et al., 2020).In addition, low precipitation also contributes to the high N CCN observed during spring and summer (Y.Wang et al., 2021;Wood et al., 2017;Zheng et al., 2018).N CCN,0.20% is highly correlated with N CCN,0.50%(R = 0.95, see Figure S3 in Supporting Information S1).Here we use N CCN,0.50% to examine the relationship between S x and CCN concentration.S x is negatively correlated with N CCN,0.50%(R = −0.62, Figure 5a).Under the same updraft velocity, higher CCN concentration leads to more numerous cloud droplets, thus increased condensation sink for water vapor and decreased S x near the cloud base (Reutter et al., 2009).Whereas such a negative correlation is expected, to the best of our knowledge, this is the first time that the influence of CCN concentration on S x is demonstrated based on long-term field observations.We also examined the relationship between S x and meteorological parameters averaged over 6-day periods, including updraft velocity (w), lower tropospheric stability (Δθ), inversion layer height (z i ), and wind speed at 10 m (U 10 ).Supersaturation in clouds originates from the adiabatic cooling of rising air parcels, and the magnitude of the supersaturation is a function of the updraft velocity (Kabanov et al., 1971;Pinsky et al., 2013;Squires, 1952).Figure 4c shows the seasonal variation of w at the cloud base.As the value of w typically follows a log-normal distribution (Figure S5a in Supporting Information S1), the geometric means over 6-day periods are used for further analysis.w shows higher values and larger variations during winter and early spring.S x is positively correlated with w (R = 0.55, Figure 5b), in agreement with earlier studies showing higher S x under stronger w (Pinsky et al., 2013).When the w and N CCN,0.50%(6-day mean values) are included in a multi-linear regression (MLR) model, the modeled S x fits well to the measurement with an R 2 value of 0.60 (p-value < 0.05), indicating that 60% of the variance in S x can be explained by CCN concentration and w.Note that the correlation between N CCN,0.50% and S x (Figure 5a) is higher than that between w and S x (Figure 5b), suggesting CCN concentration is more important than w in explaining the variability of observed S x .
For cumulus clouds, a weak Δθ allows strong convection (i.e., high w), leading to increased z i .For stratocumulus clouds, strong updrafts are generally a result of strong radiative cooling at the cloud top, which is typically associated with thick clouds.A weak Δθ is associated with a deep z i (Wood & Hartmann, 2006) and cloud thickness tends to increase with z i .Therefore, for both cloud regimes, we expect a strong w and thus high S x associated with weak Δθ and deep z i .Indeed, both w and S x are negatively correlated with Δθ (R = −0.61 and −0.53, Figure S3 in Supporting Information S1 and Figure 5d) and positively correlated with z i (R = 0.44 and 0.41, Figure S3 in Supporting Information S1 and Figure 5e).High w and S x values are associated with increased U 10 (R = 0.40 and 0.42, Figure S3 in Supporting Information S1 and Figure 5c).This is likely because strong wind leads to increased surface heat and buoyancy fluxes.In addition, strong wind is more prevalent under postfrontal conditions, when the surface buoyancy flux is further increased by a larger temperature difference between the ocean surface and air.Including all variables (i.e., N CCN,0.50%, w, Δθ, z i , and U 10 ) only slightly increases the R 2 value of 10.1029/2022AV000855 9 of 14 MLR to 0.62 (p-value < 0.05).This is consistent with the discussion above that the influences of Δθ, z i , and U 10 on S x are mostly through their impact on w.The correlations among all relevant quantities are shown in Figure S3 in Supporting Information S1.The influences of Δθ, z i , and U 10 on w and S x should be further examined through a detailed modeling study.
The influence of N CCN on S x , as shown by the negative correlation between S x and N CCN,0.50%(Figure 5a), leads to a buffered response of N c to aerosol perturbations (Stevens & Feingold, 2009).In addition, high w during winter, such as that under post-frontal conditions, is often associated with thick clouds and strong precipitation, which lead to increased wet scavenging and thus low aerosol concentration.Therefore, in terms of the seasonal variation, the response of cloud droplet number concentration to low aerosol concentration during winter is further buffered by the high w.As a result, cloud droplet concentrations during summer and winter show similar ranges despite a strong seasonal variation in CCN concentration (J.Wang et al., 2022).N c were calculated using the AG parameterization (Abdul-Razzak & Ghan, 2000) from the measured aerosol size distribution, hygroscopicity, and w, to quantify the additional buffering effect on N c due to the variation in w.Assuming w in winter is the same as that during summer (i.e., a typical value of 0.26 m s −1 in summer), we calculated winter N c as 78 cm −3 , 46% lower than that in the summer (i.e., 144 cm −3 ).With the typical w value of 0.52 m s −1 in winter, the calculated winter N c increases by 34% from 78 cm −3 to 104 cm −3 and is only 27% lower than N c in summer.The increase of calculated winter N c demonstrates the additional buffering effect due to high w in winter.These results highlight the importance of accounting for the processes that buffer cloud response to aerosol perturbation when assessing aerosol indirect effects (Stevens & Feingold, 2009).

Modeling S x Over North Atlantic Ocean
The CESM simulated maximum supersaturation (S x,CESM ) at the cloud base below 2 km at the ENA observatory was evaluated using the derived S x,SCCN .While S x,CESM and S x,SCCN are in broad agreement with a correlation coefficient of 0.41, S x,CESM is statistically higher than S x,SCCN (Figure S4 in Supporting Information S1).To understand the bias in S x,CESM , we compared w and CCN populations simulated by CESM with the measurements at the ENA observatory.The CESM simulated w shows a narrow frequency distribution and higher frequencies at large values when compared with w retrieved from Doppler Lidar and cloud radar measurements (Figure S5a in Supporting Information S1).For 6-day geometric mean values, the model simulated w is well correlated with Doppler Lidar and cloud radar retrieved w (R = 0.63, Figure S5b in Supporting Information S1), but shows a nearly consistent positive bias.There is also a strong correlation between simulated and measured N CCN,0.50% and N CCN,0.20%(R = 0.62 and 0.65, Figure S6 in Supporting Information S1).However, CESM consistently underestimates the CCN population at the ENA observatory.Therefore, the positive bias in CESM simulated S x is likely due to a combination of overestimated w and underestimated CCN population.The bias in S x and CCN populations may lead to biases in simulated cloud properties.In addition, with higher S x , cloud droplet activation tends to be in the aerosol-limited regime, that is, the formation of cloud droplets is more limited by the availability of aerosol particles, and cloud droplet number concentration is more sensitive to changes in the aerosol concentration (Reutter et al., 2009).If aerosols during the present day (PD) and preindustrial era (PI) are accurately represented in the model, an artificial shift of cloud droplet formation toward a more aerosol-limited regime leads to an overestimate of the aerosol indirect forcing, that is, the difference in radiative fluxes between PD and PI.However, the combination of biases in both S x and CCN concentration makes it more challenging to evaluate model-simulated aerosol indirect forcing.If the low bias in simulated CCN concentration is mainly due to an underestimate of natural aerosols, the underestimation of natural aerosols and the artificial shift into a more aerosol-limited regime will lead to a further overestimation.On the other hand, if the bias in CCN concentration is mostly due to an underestimate of anthropogenic aerosols, the model may underestimate the aerosol indirect forcing.
The spatial variation of S x over the North Atlantic Ocean was examined using CESM simulation (Figure 6).Overall, S x,CESM is higher further north over the Atlantic Ocean and relatively low near the equator.The updraft velocity exhibits a similar spatial pattern as S x,CESM , that is, the further north, the higher the updraft velocity due to stronger storms (Figure S7 in Supporting Information S1).In a certain region, for example, the outflow of Sahara dust, the extremely high CCN concentrations (Figure S8 in Supporting Information S1) suppress S x .The modeled S x value over the North Atlantic also exhibits winter high and summer low variation (Figures 6a-6d).In winter, the zonal temperature between the warm ocean and cold continental is stronger and the surface temperature gradients can influence the baroclinicity of the atmosphere and the storm track (Brayshaw et al., 2009).Therefore, storms in winter usually are stronger than those in summer, leading to stronger updraft velocity and higher S x in the Northern Atlantic during winter.

Summary and Significance
In this study, we showed that cloud droplet number concentration (N c ) in the least diluted cloud cores agrees well with the number concentration of particles larger than the HM (i.e., the particle size corresponding to the minimum concentration between the Aitken and accumulation modes of aerosol size distribution), demonstrating that the HM measured on the ground represents the average size threshold above which particles are activated into cloud droplets.Therefore, the in-cloud S x is essentially the same as the critical supersaturation of particles at the HM size.The in-cloud S x over 1-year period from June 2017 to June 2018 was then derived from aerosol size distribution and CCN activity measured at the ENA observatory.The derived maximum supersaturation (S x ) reveals a clear seasonal variation, with low values in summer and higher values during winter.
The long-term S x data allow statistical analysis of the influences of CCN concentration (N CCN ), meteorological and synoptic parameters on S x .We found a negative correlation between S x and N CCN , which is attributed to the suppression of S x by increased condensation sink of water vapor at high N CCN .As expected, S x increases with updraft velocity (w).High w and S x values are associated with weak lower tropospheric stability (Δθ), increased inversion layer height (z i ), and strong wind speed at 10 m (U 10 ).An MLR model based on N CCN and w explains ∼60% of the variation in S x , and N CCN is more important than w in explaining the variability of observed S x .Including Δθ, z i , and U 10 as additional predictors in the MLR model only slightly increases the R 2 value to 0.62, because the influences of Δθ, z i , and U 10 on S x are mostly through their impact on w.
The influence of N CCN on S x leads to a buffered response of N c to aerosol perturbations.In addition, high w during winter, such as those under post-frontal conditions, are often associated with thick clouds and strong precipitation, which lead to increased wet scavenging and thus low aerosol concentration.Therefore, in terms of seasonal variation, the low aerosol concentration is associated with high w, and the response of N c to low aerosol concentration during winter is further buffered by the high w.
The long-term S x measurements also allow us to evaluate S x simulated by CESM (S x,CESM ).While S x,CESM is in broad agreement with the derived S x , S x,CESM is statistically higher than the derived S x .The positive bias in S x,CESM is attributed to a combination of overestimated updraft velocity and underestimated CCN population.Nevertheless, the CESM simulation was used to examine the spatial variation of S x over the North Atlantic Ocean.The S x,CESM over the North Atlantic Ocean clearly shows higher values further north and is relatively low near the equator.The variation of S x is correlated with the updraft velocity on a regional scale, while the suppression of S x by CCN is evident at locations of high CCN concentrations.Supersaturation in clouds is notoriously difficult to measure.At present, there have been few experimental studies of the S x in ambient clouds, despite its importance to cloud formation and the aerosol indirect effects.To the best of our knowledge, the S x derived from 1-year measurements in this study represents the first long-term data set, which allows for characterizing the seasonal variation and investigating the influences on S x by different factors, including CCN concentration, and meteorological and synoptic parameters.The long-term S x data set also allows for evaluating the representation of cloud activation in climate models and constraining simulated aerosol indirect forcing, which remains highly uncertain at present.Based on the model comparison of CCN, S x , and updraft velocity, we postulate that the CESM model can reasonably capture the relationship between changes in aerosol and cloud droplets.Further evaluations are needed to investigate the causes for the model biases in updraft velocity and CCN concentrations in CESM and to quantify the impacts of these biases on simulated aerosol indirect effects.

A2. Definitions
Least diluted cloud core: the region where LWC greater than the 90th percentile in a cloud HM: particle diameter corresponding to the local minimum of the number concentration between ∼40 and 150 nm z i : height of the strongest temperature inversion layer below 4 km Δθ: potential temperature (θ) difference between a nominal location in the free troposphere (typically 700 hPa) and the surface (1,000 hPa)

A
total of 39 flights (20 flights from 21 June to 21 July 2017 and 19 flights from 19 January to 18 February 2018) were conducted in the vicinity of Azores, out of the Lajes airport on Terceira Island.Most of the flights were conducted within 50 km of the ENA observatory to maximize the synergy between airborne and surface measurements.During each flight, 4 to 6 vertical profiles were taken, covering the altitude from 100 to ∼3,000 m a.m.s.l.Each flight also included multiple horizontal legs near the surface of the ocean (∼100 m a.m.s.l.), just below the cloud base, within the cloud, at the cloud top, and above the clouds in the lower free troposphere.Measurements conducted onboard the G-1 aircraft include meteorological parameters, trace gases, aerosol, and cloud properties (J.Wang et al., 2022).

Figure 1 .
Figure 1.(a-c) Measurements from the flight periods on 13 July 2017 (well-mixed marine boundary layer [MBL]).(a) Flight measurement data, including time series of liquid water content (LWC, blue line) and altitude of flight (red line).(b) Flight measurement data, including time series of number concentration of particles larger than 10 nm (N 10 aloft, green line) measured by a condensation particle counter (CPC), particle number concentration integrated from the fast integrated mobility spectrometer measured number size distribution (N FMIS aloft, brown line), and inlet status (orange line).Particles were sampled through an isokinetic inlet (Ambient), thermodenuder inlet (TD), or a counterflow virtual impactor inlet.Ground measurement data, including time series of number concentration of particles larger than 10 nm (N 10 ground, black line) measured by a CPC.(c) Flight measurement data, including time series of number concentration of particles larger than Hoppel Minimum (HM) (N >HM aloft, magenta line) and cloud droplet number concentration (N c , cyan line).Ground measurement data, including time series of number concentration of particles larger than the HM (N >HM ground, black dots).Periods of the least diluted clouds are marked as the black lines in LWC and N c .The periods when the flight is below-cloud and in-cloud are marked in black and purple dashed lines, respectively.(d-f) Measurement from the flight periods on 3 July 2017 (decoupled MBL), as in panels (a-c).

Figure 2 .
Figure 2. Comparison of the number concentration of particles larger than Hoppel Minimum (N >HM ) below-cloud in the well-mixed boundary layer (blue dots) or out-of-cloud in the decoupled boundary layer (red dots) with the cloud droplet number concentration (N c ) in the least diluted cloud cores.The dots are median values, and the error bars are the 25th and 75th percentiles.Each dot represents one case study and two cases on 3 and 13 July are marked in the figure.The linear fitting line and 1:1 line are shown using yellow solid and black dashed lines, respectively.

Figure 3 .
Figure 3. Illustration of the approaches of deriving S x,NCCN and S x,SCCN .(a) Particle number size distribution from 10 to 1,000 nm was measured by scanning mobility particle sizer and ultra-high sensitivity aerosol spectrometer at the ENA observatory.The red dot indicates the Hoppel Minimum (HM) and the green shaded area represents the number concentration of particles larger than HM (N >HM ).(b) Supersaturation (S) as a function of cloud condensation nuclei number concentration (N CCN ).S x calculated based on this spectrum is defined as S x,NCCN .(c) The critical S as a function of activation diameter.S x calculated based on this spectrum is defined as S x,SCCN .(d) One example of the distribution of 10,000 S values (S x,SCCN in blue and S x,NCCN in red) from the Monte Carlo simulations.The mean (μ) and the standard deviation (σ) values of the distributions are shown in the legend.

Figure 4 .
Figure 4. (a) The calculated maximum supersaturation in the clouds based on size-resolved cloud condensation nuclei (CCN) is shown in blue boxplots (S x,SCCN ).(b) Cloud condensation nuclei number concentration at a supersaturation of 0.50% (N CCN,0.50% ) is shown in purple boxplots.(c-g) Updraft velocity (w), wind speed at 10 m (U 10 ), lower tropospheric stability (Δθ), and inversion layer height (z i ) are shown in red, cyan, brown, and orange boxplots, respectively.In all panels, each boxplot is based on measurements over a 6-day period.Summer and winter mean values are marked by red and blue ticks on the y-axis.Whiskers show the 10th to 90th percentiles.Black triangles show the geometric mean values for updraft velocity and mean values for other parameters.

Figure 5 .
Figure 5. Scatter plot of S x,SCCN against (a) N CCN,0.50%, (b) updraft velocity (w) at cloud base, (c) wind speed at 10 m (U 10 ), (d) lower tropospheric stability (Δθ), and (e) inversion layer height (z i ).The linear regression lines are in black, and the correlation coefficient values are in the text boxes.
Δθ: Lower-tropospheric stability ENA: Eastern North Atlantic HM: Hoppel Minimum LWC: Liquid water content MBL: Marine boundary layer N c : Droplet number concentration N CCN : Cloud condensation nuclei concentration N 10 : Total number concentration for particles larger than 10 nm N >HM : Total number concentration for particles larger than Hoppel Minimum PD: Present day PI: Preindustrial era SCCN: Size-resolved CCN measurement S: Supersaturation S x : Maximum supersaturation S x,NCCN : Derived maximum supersaturation based on N CCN measurement S x,SCCN : Derived maximum supersaturation based on SCCN measurement S x,CESM : CESM simulated maximum supersaturation U 10 : Wind speed at 10 m w: Updraft velocity z i : Inversion layer height