Vertical aerosol particle exchange in the marine boundary layer estimated from helicopter-borne measurements in the Azores region

. Aerosol particles are important for radiation effects, cloud formation, and therefore, the climate system. A detailed understanding of the spatial distribution of aerosol particles within the atmospheric boundary layer, which depends on sources and sinks as well as long-range transport and vertical exchange, is important. Especially in marine regions, where the climate effect of clouds is comparable high, long-range transport with subsequent vertical mixing is dominating over local aerosol sources. 5 In this study, three different methods were applied to estimate the vertical aerosol particle ﬂux in the marine boundary layer (MBL) and the vertical exchange between the MBL and the free troposphere (FT): Eddy covariance (EC), ﬂux-gradient similarity (K-theory), and the mixed layer gradient method (MLG). For the ﬁrst time, MBL aerosol ﬂuxes derived from these three methods were compared in the framework of the "Azores stratoCumulus measurements Of Radiation, turbulEnce and aeroSols" (ACORES) ﬁeld campaign in the Azores region in the North-East Atlantic Ocean in July 2017. Meteorological parameters as 10 well as aerosol and cloud properties were measured in the marine troposphere using the helicopter-borne measurement platform ACTOS (Airborne Cloud Turbulence Observation System). All three methods were applied to estimate the net particle exchange between MBL and FT. In many cases, the entrainment ﬂuxes of the MLG method agreed within the range of uncertainty with the EC and K-theory ﬂux estimates close to the top of the MBL, while the surface ﬂux estimates of the different methods diverged. It was not possible to measure directly above the 15 surface with the helicopter-borne payload, which might be a source of uncertainty in the surface ﬂuxes. The observed particle ﬂuxes at the top of the MBL ranged from 0 to 10 · 10 6 m − 2 s − 1 both in the upward and the downward direction, and the associated uncertainties were on the same order of magnitude. Even though the uncertainties of all three methods are considerable, the results of this study contribute to an improved understanding of the transport of particles between the MBL and FT, and their distribution in the MBL. which is the ﬂight leg height in this study. In contrast, the K-theory ﬂux estimate F K represents the proﬁle segment between the concentration measurements used to calculate the gradient, and the MLG method yields two different estimates: (i) the surface ﬂux estimate F s , in this study at the interface between the ocean and the MBL, and the entrainment ﬂux estimate F e 245 at the interface between the MBL and the free troposphere. Due to these very different approaches and assumptions, variations between the results of the three methods for the same case study are expected.


Introduction
Aerosol particles influence the global climate in different ways: (i) they scatter and absorb the incoming solar radiation and (ii) they may act as cloud condensation nuclei (CCN) and affect cloud microphysical properties. These effects have been studied intensively over last few decades, however, there is still a large uncertainty in particular in the influence of the number size 25 distribution on cloud droplet number distribution (Stevens and Feingold, 2009) and the associated change in the shortwave albedo of clouds (Twomey, 1977;Ackerman et al., 2000;Werner et al., 2014).
Meanwhile, a comprehensive network of measurement stations for aerosol monitoring using in-situ and remote sensing methods in industrialized, continental regions has been established (e.g. ACTRIS, www.actris.net), but marine areas are still 30 poorly characterized. However, more than 70% of the earth's surface is covered with water, and these regions have a significant impact on the global climate. Furthermore, climate models indicate that a large fraction of the aerosol indirect radiative forcing is associated with marine low clouds (Quaas et al., 2009), while the simulation of these clouds is still very uncertain in climate models (Wyant et al., 2010). For the remote marine atmosphere, local anthropogenic emissions play a minor role. While the larger accumulation mode (diameter > 300 nm) is dominated by sea spray aerosol, sea spray contributes only a minor fraction 35 to the particle diameter range smaller than 300 nm (Zheng et al., 2018). The major fraction of aerosol particles in the marine boundary layer (MBL) originates in continental regions and is transported mainly in the free troposphere (FT) over long distances (Clarke et al., 2013;Logan et al., 2014) or is formed in the FT via new particle formation, e.g. in the outflow of deep convective clouds (e.g., Clarke et al., 2013). To become active as CCN in the MBL they need to be mixed downwards, i.e. they have to pass the inversion layer. The vertical mixing between these layers is the crucial process and needs to be quantified to 40 understand the vertical distribution of aerosol particles as well as the evolution of them in the marine boundary layer. This has been done for tropical regions by e.g. Clarke et al. (1996) resulting in entrainment rates of 0.6 cm s −1 into the MBL. This leads to an effective transport of potential CCN from FT to MBL (Clarke et al., 2013). However, these studies were performed in the Intertropical Convergence Zone where vertical exchange is very strong. For other regions such as the mid-latitudes, experimental studies investigating the vertical mixing of aerosol between FT and MBL have been lacking. Katoshevski et al. (1999) used 45 a box model to evaluate the influence of sources and sinks on the aerosol budget in remote marine regions and concluded that nucleation and further particle growth play a crucial role. The exchange between FT and MBL affects the aerosol dynamics in the subtropical MBL and thus also CCN concentrations (Raes, 1995). The influence of aerosol particles on dynamics and structure of marine stratocumulus clouds remains poorly understood and needs to be studied in more detail (Wood, 2012). This includes both the long-range transport as well as the vertical mixing into the MBL. 50 Aerosol in situ measurements in the MBL are limited to ship-or aircraft-based short-term campaigns and/or those performed on islands in the ocean. Previous studies were performed, for example, near Tasmania (e.g., Bates et al., 1998;Clarke et al., 1998), between the Canary Islands and Portugal (e.g., Raes et al., 2000), in the North-East Atlantic Ocean (e.g., Norris et al., 2012;Petelski and Piskozub, 2006), on Christmas Islands in the equatorial Pacific (e.g., Clarke et al., 2013), and over the 55 2 https://doi.org/10.5194/acp-2021-1071 Preprint. Discussion started: 16 February 2022 c Author(s) 2022. CC BY 4.0 License.
Azores (e.g., Dong et al., 2014Dong et al., , 2015Wood, 2012;Wood et al., 2015). The Azores are the only site located between the subtropics and the mid-latitudes in the North Atlantic Ocean and representative for a large fraction of marine areas.
In previous studies it turned out that the islands of Azores provide a perfect location for studying the MBL with low anthropogenic influence. For this purpose, the permanent ENA ARM (Eastern North Atlantic Atmospheric Radiation Measurement) 60 site has been established on the island of Graciosa (e.g., Dong et al., 2014;Wood et al., 2015). For a better understanding of vertical transport processes in the cloudy MBL as well as in the cloud-free MBL the "Azores stratoCumulus measurements Of Radiation, turbulEnce and aeroSols" (ACORES) project was initiated, and the intensive campaign was performed in July 2017.
One common method to estimate the vertical transport of aerosol particles is eddy covariance (EC) combined with conden-65 sation particle counters, which has been applied in earlier studies using fixed-point measurements (e.g., Buzorius et al., 1998). Buzorius et al. (2006) published a first pilot study estimating a vertical particle flux by the eddy covariance method, using an aircraft as the measurement platform.
One advantage of an airborne platform is the possibility of making measurements in different levels of the boundary layer or close to inversion layers. One challenge for estimating fluxes is to fulfill the criteria for stationarity and homogeneity, which 70 is often not full-filled for horizontal flight patterns. To our knowledge, until now only Buzorius et al. (2006) have used aircraft measurements to calculate particle fluxes via the EC method. Due to the relatively high flight speed and low time resolution of measurements the uncertainties were quite high.
In our study, we use a slow-flying helicopter in combination with highly resolved measurements under conditions with low anthropogenic influence. In addition to the EC method, two gradient-based methods are applied to calculate vertical turbulent 75 particle fluxes from profile measurements in the MBL above the North-East Atlantic Ocean.

ACORES 2017 campaign
In July 2017, the "Azores stratoCumulus measurements Of Radiation, turbulEnce and aeroSols" (ACORES) campaign was 80 performed in the North-East Atlantic Ocean at the islands of Azores. The archipelago is located approximately 1400 km west of the European continent. During the ACORES campaign ground-based measurements of aerosol particle number concentration and size distribution were performed at the ENA (Eastern North Atlantic) ARM site on the island of Graciosa at sea level and at the Pico Mountain Observatory (Observatorio da Montanha do Pico, OMP) in 2225 m above sea level. Helicopter-borne measurements of aerosol particle number concentration and meteorological parameters were performed from Graciosa airport 85 up to 3000 m covering the marine boundary layer (MBL) and free troposphere (FT). More details about the campaign are given by Siebert et al. (2021).
Graciosa is a small island (≈ 60 km 2 area) situated at 39.1°N, 28.0°W in the Azores Archipelago, at a latitude between the subtropics and the midlatitudes. As such, Graciosa is influenced by different meteorological conditions, including periods of relatively undisturbed trade wind flow, mid-latitude cyclonic systems and associated fronts, and periods of extensive low-level 90 cloudiness. The ACORES campaign took place from July 2 until July 23. According to meteorological conditions the campaign was divided into three periods: 1) until July 11, dominated by dry air with low cloud fraction, 2) July 12 -19, with warm and humid air masses and frequent precipitation, and 3) after July 20, again dry conditions with low cloud fraction (Siebert et al., 2021). The ACORES measurement strategy allowed for so-called aerosol flights focusing on the vertical stratification and transport of aerosol particles under conditions with no or few clouds. The airborne measurements were performed using 95 the helicopter-borne platform ACTOS (Airborne Cloud Turbulence Observation System) (Siebert et al., 2006) as external cargo hanging 170 m below a helicopter. The advantage of the system is the low true air speed of 20 m s −1 leading to a higher spatial resolution compared to fast flying aircraft. Furthermore, technical requirements such as inlet design and sampling issues are less serious compared with fast-flying aircraft.

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Each measurement flight started with a vertical profile up to a height well above the inversion layer followed by a specific flight pattern according to the meteorological conditions. Under low-cloud or cloud-free conditions e.g., horizontal legs in constant heights were flown. These vertical profiles as well as the horizontal legs are the main data base of this study.

Instruments and data
An overview over the instrumentation and specifications used on ACTOS is given in Siebert et al. (2021). Only parameters 105 used in this study will be explained here in more detail. ACTOS is equipped with instruments to measure basic meteorological parameters with high temporal resolution, such as the 3D-windvector (ultrasonic anemometer, Solent HS Gill), absolute humidity (Dew Point Mirror, TP3, MeteoLabor AG) and temperature (PT100, Rosemount Series 139 plus ultrafast airborne thermometer, UFT) as well as cloud properties such as liquid water content (LWC), which is not subject of this study.
The total particle number concentration is measured with a commercial Condensation Particle Counter (CPC Model 3762A, 110 TSI) (TSI, 1996) with a modified lower cut-off diameter of 8.5 nm, and a modified flow rate of 1 l min −1 . CPC data have been sampled and post-processed with a time resolution of 10 Hz. However, note that the typical response time of this CPC is approximately 1 s. Aerosol number concentrations are corrected for losses in the inlet system and for variations in the sample flow due to pressure changes. Furthermore, all aerosol data are transferred to standard conditions of T = 288 K and p = 1013.15 hPa.

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Although the wind vector measured in the ACTOS reference system has been transferred to an earth-fixed system using an inertial navigation system, the typical pendulum motion is still visible with a more or less sharp frequency around 0.04 Hz. To minimize this effect, a spectral band-stop filter has been applied in the range between 0.03 s −1 < f < 0.05 s −1 .

Flux estimation methods
Three different methods to calculate vertical turbulent exchange in the boundary layer (BL) are applied: The eddy covariance 120 (EC) method, the K-theory method and the mixed layer gradient method (MLG). In order to highlight advantages and limitations of each method, a brief introduction as well as specific assumptions and requirements pertinent to the methods will be given.

Eddy Covariance method
The EC method is a widely used micrometeorological method to directly measure turbulent vertical fluxes of atmospheric 125 constituents through a horizontal, homogeneous plane (Businger, 1986;Foken et al., 2012).
It is based on the mass balance equation which can be simplified due to the assumptions of stationarity and horizontal homogeneity. The vertical flux F EC of a scalar can be estimated by correlation of the fluctuation of the vertical wind component w and the fluctuation of a scalar concentration c , which is equal to the covariance of the vertical wind speed w and the scalar concentration c: The overbar indicates the mean over a certain averaging period, which is typically 30 min for atmospheric turbulent fluxes depending on the dominating scales at a fixed location (e.g., tower measurements). M is the number of data points in each averaging period, and k indicates the data point at time t k (Foken, 2016). The scalar c as well as the vertical wind speed have to be measured at high time resolution (typically at least 10 Hz for tower measurements), in order to cover high frequencies of 135 the turbulent spectrum and their contribution to the flux.
Even though the EC method was developed for ground-based measurements it has also been applied to airborne measurements before (e.g. Buzorius et al., 2006;Metzger et al., 2012;Yuan et al., 2015). Airborne sampling provides spatial averaging directly (Buzorius et al., 2006) if frozen turbulence (Taylor, 1938) is assumed, i.e. if the statistical properties of turbulence do not change. Thus, measuring at a fixed point at the ground, e.g. for 30 min at a wind speed of 2 m s −1 , probes the same air  Uncertainty ranges of EC particle fluxes based on counting statistics were calculated following Buzorius et al. (2003). In order to estimate whether the EC flux estimates are significantly different from zero, the random shuffle method by Billesbach (2011) was used. This method estimates the contribution of random instrument noise to the total uncertainty of the flux calcu- lation.

K-theory method
Vertical fluxes can also be estimated using the so-called gradient approach or K-theory assuming stationarity and horizontal homogeneity within the BL. In this K-theory, closure is accomplished when the flux is linearly proportional to the mean 155 gradient (flux-gradient similarity), and the proportionality constant K describes all properties influencing the vertical turbulent exchange: where F K is the vertical flux of a scalar c, and dc dz is the mean gradient of the scalar with height z. The vertical turbulent diffusivity K describes the efficiency of the vertical mixing. In this study, K is estimated following Hanna (1968): where σ w is the standard deviation of the vertical wind. The typical length scale l for the dominant eddies is defined as where v T AS is the true air speed and τ is the time lag when the auto-correlation function of the vertical wind drops to 1/e. In order to calculate σ w and τ , a horizontal flight leg within the MBL is needed to characterize turbulence. Due to the fact that not In order to estimate the uncertainty of the fluxes calculated by K-theory, Monte Carlo Simulation (MCS) (Anderson, 1976) was applied. For this purpose, the original calculation according to Eq. (2) is repeated 100 000 times with slightly changed input 170 values in order to take into account their uncertainty in a random fashion, and then the resulting flux estimates are statistically evaluated. For K-theory particle fluxes in this study, a 10% uncertainty was assumed for aerosol particle number concentration (N ± 0.1 N ). For σ w and τ , the ranges given above, which correspond to the standard deviation of the five available values, were used. For each of these parameters, a value was taken randomly from a uniform distribution between the minimum and maximum values, and combined in one simulation of the flux calculation. This procedure was repeated 100 000 times, which 175 led to a normal distribution of 100 000 simulations with a mean value and standard deviation of the flux estimate.
It should be noted that the vertical turbulent diffusivity according to Eq. (3) assumes similar K values of momentum and particle fluxes, which is a reasonable assumption (Siebert et al., 2004). In K-theory, it is assumed that there is one mean gradient across the layer of interest. In order to determine gradients, a linear model was fitted to median profiles of particle number 180 concentrations above the ocean within the MBL. It was applied for the whole MBL or for linear segments of the profile in cases were obvious gradient changes occurred. In these cases, the estimated fluxes are representative for the selected height ranges.

Mixed Layer Gradient method
The Mixed Layer Gradient (MLG) method is also based on flux-gradient similarity, and it is a specification of K-theory. It 185 relates vertical gradients of scalars ∂c ∂z to two fluxes, a surface flux F s and an entrainment flux F e (Lenschow et al., 1999;Wyngaard and Brost, 1984). Thus, MLG takes into account sources and sinks at two interfaces, the interface between the surface and the MBL and the interface between the MBL and the FT. Based on mixed layer scaling the turbulent equation of motion can be closed:

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A first assumption of MLG is mixed-layer similarity to find universal relationships between BL variables (Stull, 2012): z * = z zP is the ratio of the measurement height z and the particle mixing height z P , and w * is the convective velocity scale or Deardorff velocity. We use the particle mixing height z P as a proxy for the inversion height z i , which is used in the original MLG method.
The particle mixing height z P was determined using the profiles of the particle number concentration, the potential temperature, absolute humidity and the liquid water content, and z P is defined as the height where the gradients of the profiles clearly 195 change. If there are clouds, the height below the cloud layer is used as z P . The Deardorff velocity, characterizes the turbulent mixing due to free convection, with the gravitational constant g, the virtual potential temperature Θ v and the buoyancy flux at the surface w Θ v .
A second assumption in MLG is that top-down (TD) and bottom-up (BU) transport each obey separate flux-gradient relationships. The top-down and the bottom-up diffusivities are described by two dimensionless analytical functions g t and g b . In 200 contrast to K-theory, here the diffusivity is a function of height. In addition to turbulent exchange, the entrainment flux is influenced by mesoscale variability caused by small clusters of cumulus clouds, variation in horizontal wind or Kelvin-Helmholtz instabilities (Lenschow et al., 1999). Therefore, clear-sky conditions and a horizontal homogeneous surface are assumed. Topdown and bottom-up gradient functions above the ocean modelled by large eddy simulations (LES) were taken from Moeng and Wyngaard (1989): The gradient is calculated out of two measured concentrations from different heights. Thus, Eq. (5) must be integrated over height between the two heights of concentration measurements normalized with the particle mixing height, z * 1 and z * 2 . In order to calculate the two unknown fluxes F s and F e , at least three concentration measurements within the BL are needed to 210 have at least two equations for two different gradients.
For the MLG fluxes calculated in this study, the concentration difference was calculated between three different heights of the median profile of the particle number concentration. These heights were chosen close to the surface and inversion height as well as in the middle of the MBL profile. The resulting two equations were solved analytically after integration of Eq. (5). In order to calculate w * , a horizontal leg close to the ocean surface is needed. Thus, all available low horizontal flight legs were 215 used to estimate the median value and standard deviation of w * = 0.62 ± 0.17 m s −1 .
In order to estimate the uncertainty of the fluxes estimated by the MLG method, MCS was applied, similar to the MCS procedure for K-theory. Parameter values were taken randomly from uniform distributions, assuming a 10% uncertainty for aerosol particle number concentration (N ± 0.1N ), variation of w * ±0.17 m s −1 , and particle mixing height z P ±50 m.

Application and limitations of each method in comparison 220
All three methods used to estimate vertical particle fluxes in the MBL are suitable for different applications, they have different limitations, uncertainties, and underlying assumptions. Horizontal homogeneity and stationarity are assumed for all of them. 3-dimensional air-bone measurements cannot distinguish if variations occur due to temporal variations or spatial inhomogeneities. Fluctuations of particle number concentrations might be caused by turbulent mixing but also by variable sources or sinks such as new particle formation or coagulation. The assumption of horizontal homogeneity and stationarity was applied 225 due to generally low number concentrations, a homogeneous surface below and no obvious sources for aerosol particle. Tab. 1 summarizes additional requirements and challenges of the three methods. EC requires time series of vertical wind speed and particle number concentration at a reference height. Limited time resolution of the CPC measurement results in a loss of high frequency flux contributions, which can be spectrally corrected (Horst, 1997). In airborne EC flux measurements from a moving platform, the resolution of turbulent fluctuations is limited by the sampling frequency and the true air speed. In this study, the true air speed of the measurement platform was relatively slow, which is beneficial for the resolution of fast fluctuations in the EC method. Furthermore, particle fluxes can be calculated directly by EC without any additional parameter required.
In contrast to that, K-theory is using at least two, and MLG at least three, slow concentration measurements at different heights within the MBL and also additional parameters are required. In K-theory, the vertical turbulent diffusivity K has to be calculated to estimate the particle flux. For MLG, the particle mixing height z P and w * have to be calculated, and the top-down 235 and bottom-up functions have to be determined to estimate the particle surface and entrainment fluxes. K-theory as presented in Eq.
(2) is applied under neutral conditions, while in the surface layer non-neutral stability conditions can be taken into account with universal functions. The MLG approach is based on mixed layer scaling and requires a well-mixed MBL. Over the ocean, neutral conditions are typically expected but stable conditions and weakly unstable conditions may occur. In K-theory, nonlinear particle concentration profiles are only conditionally suitable to calculate a vertical gradient. Both in K-theory and the 240 MLG method, the smaller the vertical gradients of particle number concentration are, the stronger is the effect of measurement uncertainties on the flux estimate. Finally, it should be noted that EC estimates a particle flux F EC across a reference height, which is the flight leg height in this study. In contrast, the K-theory flux estimate F K represents the profile segment between the concentration measurements used to calculate the gradient, and the MLG method yields two different estimates: (i) the surface flux estimate F s , in this study at the interface between the ocean and the MBL, and the entrainment flux estimate F e 245 at the interface between the MBL and the free troposphere. Due to these very different approaches and assumptions, variations between the results of the three methods for the same case study are expected.

Results and discussion
Aerosol particle flux estimates of the three introduced methods will be shown and discussed focusing on case studies in order to demonstrate the main results and emerging challenges. Research flights #3, #4, #5 and #7 are chosen to highlight the main 250 results. During flights #3, #5 and #7 (see Siebert et al., 2021), the MBL was well-mixed, and the focus will be put on the comparison between the different methods. Flight #4 is chosen to introduce the methods for a case without well-mixed boundary layer conditions, illustrating special features of the profiles and their effects on flux estimates.

Particle flux estimates in well-mixed MBL: Comparison of different methods
255 Figure 2 shows vertical profiles observed in a clear-sky, well-mixed MBL on July 10, 2017. On that day, the particle mixing height z P was estimated from the temperature and humidity profiles (Fig. 2a) as well as from the particle number profile ( Particle fluxes plus uncertainties of the EC method (Fig. 2b) were calculated from data of horizontal flight legs within the MBL. K-theory fluxes (Fig. 2) as well as MLG fluxes (Fig. 2b) were calculated with median profile data shown in Fig. 2c.
In order to apply K-theory, the profile was split in three linear parts and fluxes for these three different height ranges were 265 calculated. The particle fluxes estimated by the different methods agree very well within the range of uncertainties for the MLG entrainment flux F e , F K in the layer close to the particle mixing height (450 -600 m), and F EC in the top segment of the mixing layer (530 m) (Fig. 2b). F EC represents a local balance at the measurement height, while F K represents the selected part of the profile while the flux estimated with MLG considers the whole profile.

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The amount of the MLG surface flux F s = −77 · 10 6 m −2 s −1 (off scale in Fig. 2b) was more than one order of magnitude larger than F K in the heights <300 m. Most of the uncertainty ranges of the flux estimates passed through zero, which means that in these cases even the sign of the flux cannot be unambiguously determined. Uncertainty ranges of the fluxes due to counting statistics were calculated following Buzorius et al. (2003) and Fairall (1984) for the EC fluxes, and by MCS for the fluxes estimated by K-theory and MLG. The random flux uncertainty due to limited particle counting statistics was estimated to range between 0.1 and 0.8 · 10 6 m −2 s −1 , 280 which is in the same order of magnitude as most flux estimates. However, with the random shuffle method by Billesbach values in N , ends within the cloud base explaining the drop of particle concentration in the upper part of the profile (Fig. 4c).
Just below z P , a weak particle concentration gradient is visible, and consequently, a slightly positive F K is estimated. The entrainment flux estimated by MLG shows the same tendency.
In all case studies shown here (flight #3, #5, #7), and also on other days, fluxes estimated by K-theory in the upper part of the 300 MBL and F e as well as their uncertainty ranges were comparable. Also, F EC in that height was within the uncertainty range of the gradient methods.
The surface fluxes estimated by the MLG method were in all cases much larger than the other estimated fluxes in the surface layer (e.g. flight #3 and #7), where the strongest gradients are expected due to the interface between ocean and atmosphere.
Fluxes calculated according to the EC or K-theory were not determined as close to the surface. On the other hand, the amount 305 of MLG surface fluxes often seem to be too large to be plausible. One reason for this could be that near-surface flights to determine the gradient were not possible for safety reasons. This could be one source of uncertainty for F s .

Particle flux estimates with complex aerosol layering 310
The cases shown in section 3.1 are based on aerosol concentration profiles with more or less monotonic gradients. However, estimating particle fluxes become more challenging for situations with more complex aerosol layering as shown in Fig. 5 for flight #4 on July 7, 2017. The particle mixing height z P = 1500 m was located at the cloud base. During the flight, stratocumulus clouds were dissipating over the ocean while some isolated convective cumulus clouds were observed close to the island.
Vertical profiles of particle number concentration were highly variable with an aerosol concentration peak above 500 m (Fig.   315 5c). Also, the potential temperature profile changed at this height (Fig. 5a) indicating a decoupling between surface and subcloud layer.
Fluxes estimated by MLG and K-theory near the inversion were opposite in direction, thus the results of the different methods were not comparable. F EC close to z P showed results comparable to F e estimated by the MLG method. For variable profiles, MLG is highly uncertain or even not applicable since the top-down and bottom-up functions are fixed, while K-theory can be 320 adapted to the profile by choosing linear parts of the profile.
One possible reason for profiles like the one shown in Fig. 5 are decoupled layers (Dong et al., 2015) within the MBL where different air masses lie on top of each other.

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Characteristic parameters of the 18 profiles flown during all research flights with the helicopter-borne platform ACTOS are shown in Tab. 2. In order to calculate and interpret these fluxes, the start time, the duration of the profile as well as the particle mixing height z P are important. Mean and standard deviation of aerosol particle number concentration as well as the mean and standard deviation of potential temperature within the whole MBL profile are useful to characterize different profiles and to assess the environmental conditions. A large standard deviation of the particle number concentration might be caused by 330 strong gradients within the MBL or by layers with particle concentration peaks due to poor mixing (e.g. flight #4).
An overview of particle fluxes and uncertainties estimated by all three methods is given in Tab Table 2. Overview of all profiles, where flux estimation methods were applied: start time and duration of profile,particle mixing height zP, mean and standard deviation of aerosol particle number concentration N as well as the mean and standard deviation of potential temperature Θ within the whole MBL profile and the cloud properties. NA means there was no horizontal flight leg in that region.

Summary and conclusions
Helicopter-borne measurements allow to quantify the vertical exchange of aerosol particles in the MBL by different methods.
In this study above the ocean in the Azores region, particle fluxes estimated by EC, K-theory, and MLG agreed reasonably well 345 in the upper part of the MBL, while flux estimates close to the surface differed considerably between the methods.
In this study, the observed particle fluxes at the top of the MBL ranged up to 10 · 10 6 m −2 s −1 both in the upward and the downward direction, but most flux values were significantly smaller. In order to illustrate the magnitude of this flux, assuming a well-mixed MBL with a mixing height of 1000 m, a net entrainment flux of F e = 10 · 10 6 m −2 s −1 would change the particle number concentration in the MBL by 30 to 40 cm −3 per hour. In many cases, the entrainment flux F e of the MLG method 350 agreed within the range of uncertainty with F EC and F K estimates close to the top of the MBL. This suggests that all three methods can be applied to estimate the net particle exchange at the interface between the MBL and the FT, depending on the flight track with respect to number, height and length of horizontal flight legs or profiles within the MBL.
When comparing these different results, the main differences between the methods must also be taken into account. In order to quantify the net particle exchange between MBL and FT, the EC method requires a horizontal flight leg at the top of the MBL, For this study, observations close to the surface are not available, which increases the uncertainties of the surface flux estimates of the MLG method. F s was typically much larger and in most cases unrealistically high compared to F EC and F K close to the surface.

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K-theory and MLG flux estimates are less sensitive to the selection of data from different heights if the MBL is well-mixed, however, the flux estimates are more robust for strong gradients. Fast measurements of vertical wind speed and particle number concentration and a relatively slow flight speed are beneficial to cover the entire turbulence spectrum when using EC. However, low particle number concentrations above the ocean cause poor counting statistics, which also increase uncertainties in particle number concentration gradients for the K-theory and MLG methods. A CPC with a larger sample flow rate would decrease the 365 error due to sampling statistics.
It is undisputed that the uncertainties in all three measurement methods are still quite large. Nevertheless, the results of this study contribute to a better understanding of the particle transport between MBL and FT and the distribution of particles within the MBL. In particular, they show the fundamental problems that still exist in flux determination despite the fact that the helicopter-borne ACTOS provides a slow-flying platform that minimizes the basic degradation of both turbulence and aerosol 370 measurements compared to fast-flying aircraft.
A promising approach for a more robust measurement of particle flux with the EC method would be a faster CPC as described in Wehner et al. (2011) however combined with a significantly increased volume flux to minimize statistical uncertainty. The latter is especially fundamentally important in environments with comparably lower particle number concentrations such as the Azores or Polar regions.
the two pilots Alwin Vollmer and Jürgen Schütz from the rotorflug GmbH, Germany. Technical support was provided by Astrid Hoffmann, Ralf Kaethner and Sebastian Duesing (TROPOS). We also thank all participants of the ACORES2017 Campaign, especially the 'Aerosol team' Silvia Henning and Kairne Chevalier (TROPOS). Table 3. Overview of the aerosol fluxes and their uncertainties for each profile of the CPC estimated by all three methods: K-theory, MLG, EC. The unit of all fluxes is 10 6 m −2 s −1 . Only the lowest and highest flux within the MBL estimated by the EC method is given here. If the EC flux is marked with *, it is not possible to distinguish if it is a random or actual flux (Billesbach, 2011