The Department of Energy Atmospheric Radiation Measurement (DOE–ARM) Eastern North Atlantic (ENA) facility is positioned on Graciosa Island within the Azores archipelago, located in the northeastern Atlantic Ocean to the west of Portugal (Mather and Voyles, 2013). Air mass transport to this location follows four main pathways: (1) polluted outflow from North American sources, (2) continental emissions originating from northern European regions, (3) relatively clean Arctic air masses, and (4) air masses that recirculate within the Azores High pressure system (Wood et al., 2015; Zheng et al., 2018). The location is characterized by a low average annual aerosol optical depth (AOD) of 0.12 (Logan et al., 2014).

Data collection for this research occurred during the ACE-ENA field campaign, which included two intensive observation periods (IOPs): the initial period ran from 21 June to 20 July 2017, while the second period extended from 15 January to 18 February 2018 (Wang et al., 2019). All data from the ARM ENA site are publicly accessible through the ARM Data Discovery tool.

This study utilized datasets from the ARM Aerial Facility (Schmid et al., 2014). The G-1 research aircraft was equipped with over 50 instruments for comprehensive measurements of aerosols, clouds, and atmospheric processes. Detailed information regarding flight patterns executed during the campaign can be found in Wang et al. (2019).

Two Condensation Particle Counters (CPCs, models 3025A and 3772, TSI Inc.) with nominal 50 % counting efficiency cutoff diameters of 3 and 10 nm, respectively, sampled through an isokinetic inlet exhibiting >90 % efficiency for particles with aerodynamic diameters below 5 µm. The concentration of 3–10 nm sized particles was calculated as the difference between these CPC measurements and is denoted as N3-10 throughout this paper. Since the measurements did not extend to particle sizes small enough to directly identify nucleation events, we follow Islam et al. (2022) in using the term “small particle event” (SPE) to characterize these observations. The CPC 3772 operated at a constant 1 Lmin-1 flow rate maintained by an external pump and critical orifice (Fan and Pekour, 2018), while the CPC 3025A sample flow rate was not actively controlled. Both flow rates remained stable across the sampling altitude range (Zheng et al., 2021). The airborne CPC configuration was validated for operation up to 4000 m altitude and across ambient relative humidity conditions of 0 %–90 % RH. For a typical polluted environment (∼5000 cm-3), CPC concentration measurements had an accuracy of 0.3 % (Kuang and Mei, 2019). All data used in this study passed instrument mentor specified quality control filters, which are distributed alongside the data.

Vertical wind speed (w) was measured using the Aircraft Integrated Meteorological Measurement System probe (AIMMS-20, Aventech Research Inc.). The raw measurements define downward movement as positive; therefore, the sign was inverted to align with meteorological convention (positive values indicating updrafts and negative values indicating downdrafts). Although measurements were recorded at 20 Hz, they were downsampled to 1 Hz to match the temporal resolution of the CPC data acquisition.

Aerosol size distributions from 10 to 600 nm were characterized using a Fast Integrated Mobility Spectrometer (FIMS) (Kulkarni and Wang, 2006a, b). The FIMS provides size distribution measurements at 1 s temporal resolution suitable for detecting both remote continental and clean marine aerosol concentrations, as demonstrated in aircraft-based deployments (Kulkarni and Wang, 2006a, b; Olfert et al., 2008). Particles are charged within the instrument and separated by electrical mobility using an applied electric field. The separated particles are subsequently grown into supermicron droplets in a condenser and imaged with a high-speed camera. This approach enables the FIMS to deliver size distribution measurements comparable to those of Scanning Mobility Particle Sizers (SMPS), but at a significantly higher time resolution. This study employed an advanced FIMS configuration utilizing a spatially varying electric field that extends the measurement range from 10 to 600 nm (Wang et al., 2017b, a). Size distribution measurements were normalized to dry conditions; therefore, reported size distributions and number concentrations do not represent ambient humidity conditions. Cloud contamination filters were applied to prevent misclassification of cloud droplets as aerosol particles, with detailed filtering procedures described in the following section. FIMS-derived number concentration also served as a quality control flag for the CPC 3772. Since both instruments share an overlapping detection size range (10–600 nm for FIMS; >10 nm for CPC 3772), their total number concentrations should be broadly comparable, with CPC showing a higher total number concentration than FIMS under normal operating conditions, as the CPC detects all particles above 10 nm while FIMS is bounded at 600 nm. The histogram of differences between CPC and integral FIMS concentrations (Fig. S1 in the Supplement) shows a distribution sharply peaked near zero with a slight negative skew, confirming good agreement during normal operation. The dashed red line indicates zero difference, below which CPC concentrations are physically implausible given the instruments' overlapping but non-identical size ranges. The negative tail reflects episodic periods when the CPC concentration was found to be suspect, likely due to working fluid depletion or a change in flow rate controlled by a critical orifice, producing sustained negative deviations that are physically implausible given the instruments' overlapping size ranges. These episodic malfunctions are distinct from the instrument's typical 0.3 % measurement accuracy under stable conditions (Kuang and Mei, 2019). Hence, a conservative threshold was set with CPC concentrations falling below 10 % of the simultaneously measured FIMS concentration, indicating a physically implausible discrepancy inconsistent with real atmospheric variability, and were therefore excluded from analysis as likely instrument malfunctions.

A two-dimensional stereo probe (2D-S) was used to retrieve drizzle concentration. It uses shadowgraphy to measure size distribution of hydrometeor particles in the size range 15 µm to 2.5 mm (Glienke and Mei, 2019). All data products are publicly available through the ARM DOE website with citations in the data availability section and have undergone quality control by instrument mentors. Additional technical details are available in the corresponding citations.

Flux measurement methods were originally developed for tower-based platforms, and their application to aircraft measurements introduces fundamental differences in sampling characteristics that must be carefully considered. Tower measurements provide continuous observations at fixed heights, capturing the complete turbulent eddy spectrum including low-frequency contributions essential for accurate flux estimates (Helbig et al., 2021; Sakai et al., 2001). Aircraft measurements, by contrast, sample different air masses as the platform moves horizontally, effectively trading temporal for spatial averaging (Desjardins et al., 1989).

Three interconnected challenges arise specifically for aircraft-based flux measurements. First, turbulent intensity in convective boundary layers increases with height above the surface layer before decreasing above 0.3–0.4 zi (where zi is the boundary layer height). Maintaining flux variance within 10 % therefore requires measurement lengths of 100 to 104 times the boundary layer height (Lenschow and Stankov, 1986), a constraint that becomes increasingly difficult to satisfy at the higher altitudes routinely sampled by research aircraft. Second, high aircraft speeds impose strict constraints on sensor response times: for an aircraft traveling at 100 ms-1, a 1 Hz sampling system resolves eddies no smaller than 200 m, approaching the lower limit for capturing the dominant flux-carrying scales. The CPCs used in this study operate at 1 Hz, meaning that contributions from smaller eddies are not resolved and must be accounted for through flux loss corrections (Sect. 2.8). Third, and most critically for flux calculation, aircraft measurements are inherently non-stationary as the platform continuously moves through different air masses, meteorological conditions, and altitudes. Traditional eddy covariance methods assume stationarity over the averaging period, a condition that is difficult to maintain during aircraft sampling (Gioli et al., 2004).

To address this limitation, this study employs the continuous wavelet transform (CWT) method for flux derivation. The primary advantage of the CWT approach is that it does not require stationarity and eliminates the need for data detrending, thereby avoiding systematic errors that can arise from linear detrending procedures (Rannik and Vesala, 1999). This study follows CWT flux derivation method of Torrence and Compo (1998), described below.

The wavelet coefficient, WN(a,b), for a function x(z) which changes with height, is calculated as a function of both location (height for airborne measurements or time for ground-based measurements) and scale (frequency or wavenumber) through convolution with a wavelet function (ψ): 1WN(a,b)=∫-∞∞x(z)ψa,b(z)dz where ψa,b(z) represents the wavelet function, controlled by the scale parameter (a) and translation parameter (b). The scale parameter governs the wavelet frequency, while the translation parameter shifts it in the temporal domain. The wavelet function is defined as: 2ψa,b(z)=1aψ0z-ba. All wavelet functions are based on a “mother” wavelet, ψ0. For this study, the Morlet wavelet is chosen as the mother wavelet, which is the product of a plane wave with a Gaussian function (Torrence and Compo, 1998). Schaller et al. (2017) reported that the Morlet wavelet provides reliable results in flux analysis even when traditional eddy covariance methods fail. 3ψ0(η)=π-14eiω0ηe-η22 where ω0 is the non-dimensional frequency (set to 6 for this study), and η is the non-dimensional time parameter and, the first exponential term is the complex sinusoid, and the second exponential term is the Gaussian envelope. Using this methodology, the vertical turbulent particle flux can be calculated according to Schaller et al. (2017) and Torrence and Compo (1998) as: 4w′(z)N3-10′(z)‾=δtCδ×δjL×∑n=0L-1∑j=0JWN(a,b)×Ww∗(a,b)a(j). Cδ, the wavelet specific reconstruction factor is taken as 0.776, which is empirically derived for the chosen wavelet (Schaller et al., 2017; Torrence and Compo, 1998), L represents the number of elements in the time series with timestep δt which is the inverse of frequency (1 Hz for this study), J is the maximum number of scales with δj being the space between each discrete scale (Schaller et al., 2017; Torrence and Compo, 1998). 5J=δj-1×log⁡2L×δts0 δj was chosen to be 0.25 s (Schaller et al., 2017; Torrence and Compo, 1998), this value can be adjusted to get better scale resolution at the expense of higher computational cost, s0 is the smallest scale of the wavelet taken as 2δt, a(j) is the scale parameter for the discrete scale calculated as: 6a(j)=s0×2jδjj=0,1,…,J. WN(a,b) is the wavelet coefficient for the particle concentration signal, and Ww∗(a,b) is the complex conjugate of the wavelet coefficient for the vertical velocity signal. Under stationary conditions, fluxes calculated using both CWT and traditional eddy covariance methods should yield equivalent results, though agreement may vary in aircraft measurements due to the presence of non-stationarities (Misztal et al., 2014; Wolfe et al., 2018).

Spirig et al. (2005) demonstrated that calculating covariance at time ranges significantly larger than the integral time scale can quantify the precision of individual flux determinations. The integral time scale was calculated using the cross-correlation function between vertical wind w and 3–10 nm sized particle size concentration, using the method described by Lenschow et al. (2000) and Wulfmeyer et al. (2016). The cross covariance is given as: 7Ax,y(τ)=cov(xt,yt+τ) where xt and yt are the two signals of interest, with y shifted by the lag time. Now the cross covariance is fitted to a model of the form: 8Amodel(τ)=ν-kτ23 where ν and k are fitted parameters. The line is fitted till the first zero crossing of the cross covariance. And using this, the integral timescale, I is calculated as: 9I=25νk3/2. The median value of the integral timescale for the flux events was ∼11 s. The limit of detection (LoD) is defined as 1.96 times (95 % confidence interval) the standard deviation of covariance between w and N3-10 when one of the signals is temporally shifted with respect to the other. To estimate the precision of an individual flux determination, we followed Spirig et al. (2005) and examined fluctuation of the covariance function at time lags far away from the true lag. The standard deviations of the covariance function were calculated between 4500 to 5700 s (corresponding to 450 to 570 km spatial displacement) before and after the peak fluxes. These lag times were selected to be much higher than the integral timescale of turbulence at all measurement heights. Flux calculations are restricted to periods when the aircraft maintained horizontal, straight line flight segments to ensure reliable flux estimates and minimize the influence of aircraft maneuvers on turbulence measurements. The limit of detection is used as an absolute value and hence if a particular flux event is lower in absolute value compared to the LoD, they will not be considered for analysis.

Establishing appropriate threshold values for new particle formation over tropical oceanic regions presents significant challenges due to sparse observational datasets and the intricate interactions between meteorological and chemical processes in these environments. Earlier studies have typically used concentration thresholds of 103 to 104 particles cm-3 for ultrafine particles (3–25 nm) to distinguish nucleation events from background conditions. However, these criteria were primarily established based on observations from continental or mid-latitude marine environments (Dal Maso et al., 2005; Kulmala et al., 2012). Given that tropical marine regions are characterized by reduced background aerosol loadings and distinct precursor gas profiles relative to higher latitude zones, more conservative thresholds (500–1000 particles cm-3) may prove better suited for detecting nucleation phenomena in these relatively unpolluted environments (Modini et al., 2009; Weber et al., 1997). Additionally, the aircraft-based measurement method prevented the implementation of traditional nucleation event identification criteria, specifically the requirement for persistent concentration increases spanning 1–2 h to distinguish genuine nucleation from brief local source influences (Kulmala et al., 2012).

For this study, we modified the methodology established by Zheng et al. (2021) to detect small particle events (SPEs). Individual 1 s measurements were used to identify when N3-10 concentrations exceeded 150 cm-3, once identified the measurements that exceeded the threshold were grouped into 10 s intervals (equivalent to ∼1 km spatial resolution), and the average N3-10 for the group was checked to see if it achieved statistical significance using: 10N3-N10>3σD where σD represents the uncertainty in the concentration difference between N3 and N10, expressed as: 11σD=σ(N3-N10).

Momentum, enthalpy, and matter are transported in the atmosphere by eddies of different spatial scales. One-dimensional power spectral analysis is used to decompose the signal into components of different frequencies, which are associated with different eddy sizes. Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT) were used to calculate the power spectral density (PSD) of vertical wind speed and particle concentration.

Figure 1 shows the PSD for a flight leg on 21 June 2017 between 13:43 and 13:49 UTC at a height of 550 m above mean sea level. Dashed lines represent the theoretical slopes for the inertial subrange, which describe how energy cascades from larger to smaller eddies and finally dissipates as heat due to viscous friction (Pope, 2000). Both particle concentration spectra (Fig. 1a and b) and the flux spectrum (Fig. 1d) broadly follow the theoretical -5/3 and -7/3 Kolmogorov scaling across the resolved frequency range. The supplementary figure comparing 1 and 10 Hz vertical wind velocity spectra (Fig. S8) confirms that turbulent energy exists at scales beyond the 1 Hz Nyquist frequency. The absence of a visible noise floor in the particle concentration spectra at high frequencies reflects the band-limited response of the CPC, which acts as a low-pass filter that attenuates high-frequency concentration fluctuations, producing a steep spectral roll-off rather than a white noise floor. While this results in a cleaner spectrum visually, it still represents real flux loss at high frequencies that is accounted for through the correction described in Sect. 2.8.

Figure 1 also shows some differences between FFT and CWT flux calculations, especially for fluxes at high frequencies. These differences are attributable primarily to non-stationarity in the aircraft data, as the platform moves through different air masses, meteorological conditions, and altitudes. FFT assumes stationarity over the entire analysis window and can therefore introduce artifacts under such conditions, whereas CWT provides time-localized frequency information that is more robust for non-stationary signals (Schaller et al., 2017). Li et al. (2023) evaluated uncertainties of turbulent flux calculation using both methods, finding that biases can range from 50 %–100 % of the spectrally complete flux. We note that the high-frequency deviations visible in the particle concentration spectra are not a consequence of FFT limitations but reflect the band-limited response of the CPC, which attenuates concentration fluctuations at frequencies above ∼0.3 Hz, as discussed in Sect. 2.8. The CWT's more conservative high-frequency response may better represent the actual resolvable flux contributions (Misztal et al., 2014).

To assess whether the calculated fluxes adequately represent both low- and high-frequency turbulent contributions, we conducted ogive analysis using the approach described by Foken et al. (2006). Mobile measurement platforms necessitate modified considerations for flux averaging intervals. Standard 30 min averaging periods used in stationary tower observations are inappropriate for aircraft measurements. Considering the aircraft's ground speed, a 90 s sampling period covers an equivalent air mass to that sampled by a stationary sensor over 30 min at typical wind speeds of 5 ms-1. To enable direct comparison between ogives computed using FFT and CWT methods, normalization was applied according to Sun et al. (2018): 12Og^(f)=Og(f)sgn{max⁡(Og(f))+min⁡(Og(f))}max⁡(|Og(k)|) where sgn{x} represents the signum function, returning +1 for positive x, -1 for negative x, and zero when x equals zero. When the normalized ogive equals 1, the ogive value corresponds precisely to the covariance value for that averaging period. The advantage of this normalization approach is that it facilitates the identification of cases where low-frequency turbulence has an opposite sign to high-frequency turbulence. In such situations, large and small eddies transport material in opposing directions, indicating complex atmospheric processes such as counter-gradient transport. The normalized ogive plot visually reveals these opposing contributions through characteristic rise-and-fall patterns that might otherwise be obscured in non-normalized data.

Figure 2 illustrates the ogive as a function of distance covered by the aircraft for the same flight leg shown in Fig. 1. Signal frequency was converted to distance by dividing the aircraft speed (assumed to be constant at 100 ms-1) by the frequency obtained from the FFT or CWT analysis. This plot reveals that the particle flux for this flight leg can be resolved by averaging over 40 km. While both FFT and CWT ogives show agreement for this case, such consistency cannot be expected universally; therefore, CWT fluxes are used throughout this study for the reasons discussed in previous sections.

If the sensor used to measure fluxes are too slow to accurately capture the smaller eddies that contribute to the total flux, the turbulent fluxes will require correction. For micrometeorological flux measurements on towers at 10 m above the surface, instruments are typically operated at 10 Hz (Nyquist frequency = 5 Hz). Under typical wind speeds of 5 ms-1, this sampling rate can resolve eddies as small as ∼1 m, ensuring that most energy-containing and inertial subrange eddies are captured (Aubinet et al., 2012; Lee et al., 2005; Stull, 1988).

However, airborne flux measurements present different challenges. The integral length scales of turbulent eddies increase approximately linearly with height within the surface layer (roughly the bottom 10 % of the boundary layer), then remain approximately constant above this level, limited by the boundary layer height (Kaimal and Finnigan, 1994). In the mixed layer portion of a typical boundary layer (above ∼100 m surface layer), integral length scales are typically 100–200 m (Lenschow and Stankov, 1986). At an aircraft ground speed of 100 ms-1, the 1 Hz sampling provides 200 m spatial resolution, which approaches but does not fully resolve the integral length scale. Consequently, the sampling resolution approaches the lower limit for adequately resolving the dominant flux-carrying scales and may under sample contributions from smaller turbulent structures.

To address this limitation, we applied the approximations from Horst (1997) to estimate the ratio of measured flux (Fm) to spectrally complete flux (F) for different atmospheric stability conditions encountered during campaign flights: 13FmF=11+(2πnmτcu‾z)α where Fm is the measured flux, F is the spectrally completeflux, u‾ is the magnitude of average wind speed, z is the height of the airplane, τc is the response time constant of the CPC, which was taken as 3.0 s, α = seven-eights and nm=0.085 for neutral and unstable conditions (Pryor et al., 2007). Equation (13) was originally developed by Horst (1997) to estimate the attenuation of scalar flux measurements within the surface layer, but has been applied to aircraft measurements (Gioli et al., 2004), with corrected airborne fluxes showing good agreement with tower data when aircraft measurements were conducted over homogeneous surfaces at altitudes comparable to tower height.

To illustrate the practical importance of this correction, the FmF ratio varies substantially depending on measurement height and atmospheric stability conditions encountered during the campaign. For measurements conducted near the top of the marine boundary layer (∼1200–1400 m) under near-neutral to unstable conditions, FmF values approach unity (0.93–0.99), indicating that flux losses are modest at these heights where the dominant flux-carrying eddies are large relative to the CPC response limitation. However, for measurements conducted closer to the surface (∼30–550 m), FmF values range from 0.70 to 0.95, implying that uncorrected fluxes could underestimate the spectrally complete flux by up to 30 %. This highlights the importance of applying the flux loss correction, particularly for low-altitude flight legs where eddy sizes are smaller and the CPC response time constant becomes a more significant fraction of the dominant flux-carrying eddy turnover times.

Following the approach of Islam et al. (2022), we assessed the random uncertainty in particle flux due to counting statistics. We found it to be 2–3 orders of magnitude lower compared to the measured flux magnitudes reported in this study. Therefore, the correction due to discrete counting statistics of CPCs was not applied to this study.

Figures 3–5 present data collected on 29 January 2018 with an additional example from 10 February 2018, shown in Figs. S9–S11. Back-trajectory analysis (not shown) indicates that the sampled airmasses had been circulating around the Azores for the preceding three days and were therefore likely less polluted than North American outflow air masses. Figure 3 shows a multi-panel time series covering approximately 3.5 h of flight operations. The aircraft initially ascended to ∼2500 m but generally remained below ∼1500 m for most of the flight (Fig. 3a). The flight trajectory (Fig. 3b) reflects predominantly east–west movement across the Azores region, spanning latitudes from approximately 38.7 to 39.4° N and longitudes from -28.4 to -27.4° W. Drizzle number concentration measured by 2DS (purple and blue lines in Fig. 3b) was absent or low during the selected SPE periods. Elevated drizzle number concentration, together with high liquid water content regions (orange in Fig. 3d), mark frequent cloud encounters. Following our quality control procedures, all N3-10 concentration data with LWC ≥3×10-3 gm-3 were excluded from analysis to avoid contamination from cloud droplet shattering artifacts. Pink-shaded periods mark the intervals chosen for detailed analysis, which exhibited simultaneous increases in both N3 and N10 concentrations exceeding 104 cm-3 (indicating an SPE). Supermicron particle concentration (blue in Fig. 3c) as well as total particle surface area (green in Fig. 3c) were also low during the selected SPE periods, indicating the absence of particles such as sea spray aerosols.

Figure 4a shows the temporal evolution of particle concentration between ∼10:47–11:05 and ∼12:15–12:25 UTC. The colormap represents FIMS-derived, size-resolved aerosol number concentrations (10–600 nm diameter), varying across time and altitude, while the lower panel displays N3-10 concentrations. The two pink-highlighted intervals are the same as in Fig. 3. The high particle concentration spike observed ∼12:18 UTC coincides with elevated LWC and drizzle concentration (Fig. 3d) and was excluded from analysis following our quality control procedures (Sect. 2.3.1). Weber et al. (1998) documented that cloud droplet shattering can produce artifactual particle concentrations as small as 3 nm in airborne CPC measurements, making this the most plausible explanation for the observed spike. Aircraft exhaust contamination can be ruled out, as the nearest prior flight transect over this region occurred approximately half an hour earlier at an altitude ∼60 m lower, more than sufficient time and vertical separation for complete plume dispersal. This data point was therefore excluded from all flux calculations as the concurrent LWC exceeded the quality control threshold of 3×10-3 gm-3.

Figure 4b–d present vertical profiles of potential temperature, normalized vertical velocity variance (σw2w∗-2) i.e., (the vertical velocity variance normalized by the square of the convective velocity scale), total particle surface area, and the water vapor mixing ratio at three locations nearest to the pink-highlighted intervals. Sharp gradients in the potential temperature (orange) mark the top of the MBL, defining the capping inversion that suppresses vertical mixing between the boundary layer and the free troposphere. The co-occurrence of these temperature gradients with elevated normalized vertical velocity variance (σw2w∗-2) near the inversion level indicates the presence of an entrainment zone, where thermodynamic forcing (including cloud-top radiative cooling and wind shear) drives mixing between the free tropospheric air above and the convective boundary layer below (Boers and Eloranta, 1986). Figure 4b–d reveal a deep boundary layer with the entrainment zone between approximately 1200–1400 m, consistent with previous estimates that entrainment zones typically comprise 20 %–40 % of boundary layer depth (Martin et al., 2014).

Figure 4b–d present the profiles of (σw2w∗-2), a metric that characterizes the intensity of turbulent structures in convective boundary layers (Deardorff, 1974; Dewani et al., 2023). These profiles show elevated (σw2w∗-2) values near the ocean surface and within the entrainment zone, with minimal values in the free troposphere, where significant turbulence is absent.

The water vapor mixing ratio profiles in Fig. 4b–d reveal evolving boundary layer moisture structure during the flight. The early profile (Fig. 4b) shows a relatively well-mixed moisture distribution below the capping inversion at ∼1200 m, with a sharp decrease into the drier free troposphere above. The latter profiles (Fig. 4c and d) exhibit a two-step moisture structure, with a sharper gradient near ∼600 m suggesting progressive decoupling of the boundary layer during the course of the flight, separating a moister surface layer from a drier sub-cloud layer above. Despite some vertical variability shown in Fig. 4b–d, the total particle surface area (Stot) remained relatively low throughout the flight, falling well below the campaign averages of ∼30 µm2cm-3 in the surface mixed layer and ∼10 µm2cm-3 in the upper decoupled layer reported by Zheng et al. (2021). Figure 4c also shows a distinct Stot maximum at an altitude where small gradients in both potential temperature and mixing ratio suggest the presence of an entrainment layer. The pronounced Stot increase could indicate a nucleation occurring at this location (see Case 2 below), although this hypothesis could not be independently verified looking at the N3-10 data in this case. Figure 4c shows that the entrainment zone and free troposphere were characterized with extremely low Stot values.

Figure 5 presents the spatial distribution of N3-10 particle concentrations along the flight path at ∼1200 m altitude (dashed lines in Fig. 4b–d), with the calculated vertical turbulent fluxes labeled at their respective measurement locations. Concentrations up to 10 000 cm-3 were observed along the flight track, with the highest values concentrated within a horizontal extent of less than 10 km. The substantial downward fluxes of N3-10 particles (-41092 and -2975 cm-2s-1) at ∼1200 m both exceed their respective limits of detection (Table 1), confirming that the observed downward transport represents a statistically significant atmospheric signal rather than measurement noise. The downward flux direction indicates that the source of freshly nucleated particles was located above the measurement altitude, within the entrainment zone, while the large difference in flux magnitudes between the two events likely reflects spatial heterogeneity in source strength and the proximity of the aircraft to the nucleation zone during each transect. This interpretation is supported by the near-absence of N3-10 at ∼1600 m during 11:14–11:25 and 12:51–13:01 UTC (Fig. 3), with the exception of brief concentration spikes of uncertain origin retained in the record due to insufficient evidence for their removal. The small particle size (3–10 nm) and limited horizontal extent of less than 10 km further argue against a free tropospheric nucleation source, as particles originating in the free troposphere would be expected to have grown substantially and the plume to have diluted during descent to measurement altitude. Several mechanisms could promote nucleation specifically within the entrainment zone, adiabatic cooling in the rising convective plumes, turbulent fluctuation in temperature and vapor concentration generated by entrainment, and dilution of mixed-layer air by the entrained free tropospheric air, causing a sudden reduction in preexisting aerosol surface area (Nilsson et al., 2001). The extremely low Stot values observed in the entrainment zone and free troposphere (Fig. 4), falling well below the campaign averages, are consistent with this interpretation. These conditions are analogous to those identified in previous studies linking entrainment zone nucleation to reduced condensation sink environments (Größ et al., 2018; Meskhidze et al., 2019; Nilsson et al., 2001). Figures S10 and S11 provide additional support, showing a downward flux of N3-10 particles (-1195 cm-2s-1) at 1375 m with complete absence of N3-10 above ∼1400 m, consistent with SPE occurrence specifically within the entrainment zone between 1375–1400 m.

Figures 3–5 and the flux analysis (Table 1) demonstrate that the entrainment zone nucleation near the MBL top occurred on two days (29 January and 10 February 2018), representing nearly 5 % of flight days. Despite a relatively small horizontal extent (<10 km), these newly formed particles can be entrained in the boundary layer via vertical turbulent processes, potentially playing an important role in marine aerosol number budget and, given sufficient time for growth to CCN-relevant sizes, potentially influencing cloud condensation nuclei concentrations for marine stratocumulus clouds.

Figures 6–8 present data from 21 June 2017, with additional examples from 7 July 2017, 18 February 2018 and 12 February 2018, shown in Figs. S12–S14, S15–S17, and S18–S20. Back-trajectory analysis (not shown) indicates that the sampled airmasses originated from the Arctic and were therefore expected to be relatively clean. Figure 6 covers approximately 4 h of flight operations, during which the aircraft initially flew at very low altitudes (∼30 and 50 m) near 12:00 and 13:30 UTC before gradually ascending to ∼1000 m. Drizzle number concentration by 2DS (purple and blue lines in Fig. 6b) was absent or below the threshold during the selected SPE periods. Multiple events with N3-10 concentrations from 102 to 104 cm-3 were observed throughout the second half of the flight. The flight trajectory (Fig. 6b) reflects predominantly east-west movement, spanning latitudes from approximately 38.6 to 39.3° N and longitudes from -28.4 to -27.4° W. Pink-highlighted intervals show periods with concurrent increases in N3 and N10 concentrations exceeding 103 cm-3, indicating occurrences of SPEs. As in Case 1, supermicron particle concentrations (blue in Fig. 6c) and total particle surface area (green in Fig. 6c) remained low during the selected SPE periods, indicating the absence of coarse-mode particles such as sea spray.

Figure 7a shows size-resolved particle number concentration evolution during 13:30–14:20 UTC, encompassing the four pink-highlighted intervals from Fig. 6. The lower panel Fig. 7a displays N3-10 particle concentrations. High N3-10 concentrations were encountered at multiple altitudes, with maximum values exceeding 1800 cm-3 at ∼800 m.

The potential temperature and water vapor profiles (Fig. 7b and c) show the MBL structure consisting of a well mixed surface layer extending to ∼700 m and a decoupled upper boundary layer between ∼700–1300 m. Decoupled structures typically form from radiative heating of the cloud layer and evaporative cooling in the sub-cloud layer, which stabilize the boundary layer and suppress vertical mixing (Galewsky et al., 2022; Jones et al., 2011; Wood and Bretherton, 2004). Sharp gradients in both potential temperature and mixing ratio around 1300 m marking the entrainment zone, above which the free troposphere begins above 1400 m. The (σw2w∗-2) profiles show higher magnitudes in the mixed layer (indicating active turbulence) and low magnitudes in both the decoupled layer (due to stratification and suppressed vertical mixing) and free troposphere. Total particle surface area remained low in the mixed layer but increased considerably toward the top of the mixed layer before decreasing in the decoupled layer and reaching very low values in the free troposphere.

Figure 8 shows N3-10 particle concentrations along flight paths at varying altitudes: 30 m, 550 m, and two segments at 800 m. We separated the 800 m path to prevent the airplane sampling the same airmass because from 13:55–14:03 UTC the aircraft flew along the prevailing wind direction, then changed direction by 90° to fly perpendicular to the wind. The positive vertical turbulent fluxes at 800 m and negative values below suggest the SPE occurred between 550–800 m, likely at the top of the well mixed layer or the bottom of the decoupled layer.

The nucleation processes in the entrainment zone and at the base of the decoupled layer could be mechanistically similar. Both locations feature the convergence of distinct air masses, in this case, the well-mixed surface layer and the stratified decoupled layer above, which generates turbulent mixing and aerosol dilution effects. While less pronounced than at the boundary layer top, the interface between these layers exhibits comparable thermodynamic conditions: potential temperature gradients, contrasting vapor concentrations, and localized adiabatic cooling. Figure 7 demonstrates that the decoupled layer maintains significantly lower aerosol surface area concentrations relative to the well-mixed layer below, establishing conducive conditions for nucleation when air mass mixing occurs. A key distinction, however, lies in the spatial characteristics, whereas entrainment zone nucleation showed limited horizontal extent (<10 km), the decoupled layer event spanned at least 50–60 km, suggesting either more persistent favorable conditions or a fundamentally different source mechanism operating over regional scales.

Figure 8 reveals a strong negative flux of N3-10 (-2782 cm-2s-1) at 550 m that is nearly three times greater in magnitude than the flux at 30 m (-860 cm-2s-1), likely due to particle evolution through growth and coagulation, and dilution processes during vertical transport. The positive fluxes of N3-10 observed at 800 m (2929 and 1139 cm-2s-1) suggest that nucleation initiated either at the top of the well-mixed boundary layer or at the bottom of the overlying decoupled layer. This bidirectional flux structure suggests that newly formed particles were transported both upward and downward from the formation zone through turbulent mixing. The comprehensive analysis presented in Figs. 6–8, combined with the flux calculations in Table 1, provides some evidence that SPEs can originate within decoupled layer structures, constituting a significant source of secondary marine aerosols in stratified boundary layer conditions.

This work establishes aircraft-derived aerosol fluxes as a valuable tool for characterizing marine boundary layer aerosol sources. Several directions would advance understanding: Slower aircrafts:

unmanned aerial vehicles operating at 30–40 ms-1 would better resolve small-scale turbulence, particularly near the surface, where flux loss corrections are currently largest, improving flux accuracy and enabling more detailed vertical structure analysis.