New particle formation (NPF) comprises (1) the initial combination of molecules into clusters (of ∼ 1 nm diameter) and (2) their subsequent growth to larger diameters (Kulmala et al., 2013). Nucleation-mode aerosol particles with a diameter (dp) of at least 3 nm frequently form in considerable quantities from gaseous precursors. Once formed, the particles are subject to altering processes (e.g. coagulation, growth by condensation of water vapour and other gases, evaporation, and scavenging). Within the entire atmosphere, NPF seems ubiquitous as was demonstrated by various studies and observations of NPF's occurrence:

at or close to the surface (Kulmala et al., 2004; Nieminen et al., 2018)

Modelling studies suggest that the NPF process constitutes one of the most important contributions (up to 45 %) to global mean tropospheric concentrations of cloud condensation nuclei (CCN) activated at 0.2 % supersaturation (Merikanto et al., 2009). Uncertainties remain concerning the effectiveness of NPF, which complicates the implementation of the NPF mechanism in global-scale simulations of aerosol number densities (Yu et al., 2010; Zhang et al., 2010). Chamber experiments, conducted at temperatures similar to those prevailing in the UT, and also numerical simulations confirm that the UT constitutes an important source region for atmospheric particles (Kürten et al., 2016; Dunne et al., 2016).

Based on airborne in situ observations of high particle number concentrations together with high levels of particle volatility in the cloud-free tropical UT, the conditions of NPF occurrence were described for the first time by Brock et al. (1995). Between 7 and 20 km altitude, fields of recent NPF events were encountered in about 20 % of the probed flight segments (Lee et al., 2004). High NPF productivity with the largest nnm was observed particularly at the bottom TTL, as shown by airborne measurements during missions over Brazil and over northern Australia (Weigel et al., 2011). Recently, a survey of NPF occurrence in the free troposphere (∼ 0.2–12 km altitude) has suggested that the NPF-produced particles persist (zonally almost invariant) as a globally extending band within the tropical UT, thereby covering 40 % of the Earth's surface (Williamson et al., 2019). At altitudes between 12 and 20 km within the tropics, this had also been reported by Borrmann et al. (2010).

Between 27 July and 10 August 2017, during the Asian monsoon season, a total of eight scientific flights with the high-altitude research aircraft M-55 Geophysica over parts of the Indian subcontinent were performed from Kathmandu, Nepal (27∘42′3′′ N, 85∘21′42′′ E), during the StratoClim 2017 mission (see Fig. 1 and also Bucci et al., 2020). Some of these flights partly spanned out of Nepalese airspace to eastern India, Bangladesh, and the northern part of the Bay of Bengal. During StratoClim 2017, NPF was frequently observed in the presence of ice cloud particles within cirrus or in anvils of the convective outflow and is discussed in detail in the companion paper (Weigel et al., 2021). Based on these observations during StratoClim 2017, NPF turned out to be largely unaffected by faint ice clouds that typically occur in the TTL (Weigel et al., 2021). This study aims at discussing the NPF encounters in their entirety as observed during the StratoClim 2017 mission in the UT and TTL region at altitudes of up to 20 km in the Asian monsoon anticyclone.

The Asian monsoon anticyclone (AMA) represents one of the most important circulation systems in the UTLS associated with deep convection over the Indian subcontinent and beyond. From the beginning of June until about the end of August, the large-scale anticyclone persists at altitudes from the UT to the LS regions (e.g. Randel and Park, 2006; Park et al., 2007), extending over longitudes from East Asia to the Middle East and East Africa (e.g. Vogel et al., 2014, 2019). The anticyclonic rotation of the system induces confinement of air inside the AMA's interior (Ploeger et al., 2015). Air masses in the region of the Asian monsoon are rapidly lifted by convection up to the maximum level of convective outflow (∼ 360 K, corresponding to ∼ 13 km) followed by a slow diabatic lift superimposed on the anticyclonic motion (e.g. Vogel et al., 2019). Within the AMA, young air is transported to UTLS altitudes during boreal summer, and in this way various pollutants and other gaseous material (Glatthor et al., 2015; Chirkov et al., 2016; Pan et al., 2016; Santee et al., 2017) and in particular water vapour (Ploeger et al., 2013) are lifted into the UTLS region. Based on satellite studies, the existence of the aerosol layer at tropopause altitudes within the AMA region (Asian tropopause aerosol layer, ATAL) was demonstrated (Vernier et al., 2011a; Thomason and Vernier, 2013). The existence of the ATAL was further confirmed by in situ balloon-borne backscatter measurements between 2013 and 2017 at different locations near the AMA centre (Vernier et al., 2015, 2018; Brunamonti et al., 2018; Hanumanthu et al., 2020) and recent aircraft measurements of Mahnke et al. (2021) or Fujiwara et al. (2021).

Hence, the constituents of the rising young air also include precursor material from anthropogenic (Vernier et al., 2015; Yu et al., 2015) and other sources. The NPF process in the TTL region could contribute significantly to the formation and persistence of ATAL as a source of additional aerosol material (He et al., 2019). Once the boundary layer material has reached UTLS levels within the AMA, the elevated tropopause potential temperature during the monsoon season allows the material's isentropic dispersion into the “overworld” stratosphere (Pan et al., 2016). Three-dimensional simulations with the Chemical Lagrangian Model of the Stratosphere (CLaMS) and backward trajectory analyses show that by the end of August, during the 2008 monsoon season, air masses younger than 6 months reach the top of the AMA at about 460 K potential temperature (corresponding to ∼ 60 hPa). According to these simulations (Vogel et al., 2019), air masses are lifted due to diabatic (radiative) heating in an anticyclonic large-scale upward spiral with ascent rates of about 1 K potential temperature per day across the tropopause, consistent with the conclusions of previous works (Bergman et al., 2012; Garny and Randel, 2016; Ploeger et al., 2017).

Particle number concentrations were measured in situ in 1 Hz resolution by means of a four-channel condensation nuclei (CN) counter COPAS (COndensation PArticle counting System; see Weigel et al., 2009). For reduction in the statistical noise, the COPAS 1 Hz raw data (direct signal of the scattered-light detectors) are preprocessed by applying a 15 s running average. Three of the four COPAS channels operate with different 50 % detection particle diameters dp50 (i.e. 6, 10, and 15 nm). The fourth COPAS channel (with dp50 = 10 nm) detects particles downstream of a heated (270 ∘C) sample flow line, resulting in measured particle mixing ratios of non-volatile (nv) particle residues or refractory particles (e.g. soot, mineral dust, metallic particle material, etc.).

The sampling is carried out via the forward-facing aerosol inlet of COPAS well outside the boundary layer of the aircraft. For stratospheric particle concentrations, the COPAS measurement uncertainty in the StratoClim 2017 data discussed herein is about 15 %, which is due to particle counting statistics and uncertainties in the volume flow. The measurement properties of COPAS are described in detail by Weigel et al. (2009), and its performance has been demonstrated by several studies (Curtius et al., 2005; de Reus et al., 2009; Borrmann et al., 2010; Frey et al., 2011; Weigel et al., 2011, 2014).

For StratoClim 2017, a new inlet configuration was used, allowing both COPAS instruments to sample through a single aerosol inlet, resulting in an almost doubled flow velocity through the sample tubes and reduced diffusional particle loss. This set-up required the reanalysis of the corrections to account for particle loss (Table 1) using the method introduced by von der Weiden et al. (2009) with modifications for low-pressure application. One of the four COPAS channels detects particle number densities of non-volatile particle residues downstream of a heated stainless steel tube (at ∼ 270 ∘C) (Appendix A).

The measurements of the aerosol particle size distributions during StratoClim 2017 were performed with an in-house-modified airborne version of the ultra-high-sensitivity aerosol spectrometer (UHSAS-A; DMT Inc., Longmont, CO, USA). The modifications on the flow and pumping system of the UHSAS-A enabled the maintenance of constant system flows (sample, sheath, purge flow) through the instrument even under ambient pressures as low as 50 hPa. Details concerning the modified airflow system of the UHSAS-A, the characterisation of the instrument's particle sizing performance, and its calibration during the campaign period are provided by Mahnke et al. (2021). The uncertainty in the number concentration measured by the UHSAS-A with 1 Hz resolution was determined to be ∼ 10 % for the particle diameter range of 65 nm < dp < 1000 nm, based on laboratory characterisations of the sample flow measurement and of the counting efficiency of the instrument (Mahnke et al., 2021). Due to the unknown in-line temperature of the sample and the wide ambient temperature range throughout StratoClim 2017, a maximum uncertainty in the UHSAS-A measurements is estimated at 25 %. Some of the results from the measured particle size distributions and a comparison with other instruments and the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) are presented by Mahnke et al. (2021).

During the StratoClim 2017 mission, CO mixing ratios were determined by means of the tunable diode laser (TDL) detection principle, which the Carbon Oxide Laser Detector-2 (COLD-2) spectrometer is based on. According to comprehensive comparisons to the previous instrument version COLD (Cryogenically Operated Laser Diode; 4 s temporal resolution; Viciani et al., 2008), the new system implies several improvements (Viciani et al., 2018). The measurement's temporal resolution is improved by a factor of 4, the in-flight sensitivity of the COLD-2 spectrometer is about 2 nmolmol-1 at integration times of 1 s, and an accuracy of 3 % is specified for the CO measurement with COLD-2 (Viciani et al., 2018).

Atmospheric temperature and pressure data were taken from the Unit for Connection with the Scientific Equipment (UCSE; Sokolov and Lepuchov, 1998), which is a part of the avionic system of the M-55 Geophysica. UCSE data are available as 1 Hz resolved ambient pressure (accuracy: ± 1 hPa) and temperature (± 2 K accuracy). Based on these UCSE data, the potential temperature θ along the mission flight tracks is calculated in compliance with the definition by the World Meteorological Organization (WMO, 1966). For the given vertical temperature gradients and for the θ range over which the StratoClim 2017 flights extended (i.e. up to ∼ 477 K), the WMO-recommended calculation of θ differs at the most by up to ∼ 1 K from the values obtained when using the recently reappraised θ calculation (Baumgartner et al., 2020).

Meteorological data were also taken from ERA-Interim reanalyses by the European Centre of Medium-Range Weather Forecasts (ECMWF) (Dee et al., 2011). Hybrid reanalysis levels in the TTL are located at various pressure heights (i.e. around 177, 154, 133, 113, 96, 80, 67, and 55 hPa, respectively) representing a vertical resolution of about 1 km in this region.

The aircraft data are analysed in coordinates relative to the tropopause height and to the monsoon anticyclone centre, respectively. The height of the lapse-rate-based thermal tropopause was determined based on ERA-Interim data and following the WMO criterion (WMO, 1957). The potential temperature θ at tropopause level was interpolated to the 1 Hz resolved position along the flight track of the M-55 Geophysica, and the measurement data were sorted as a function of θ distance (Δθ) to the local tropopause as a vertical coordinate.

The centre of the AMA was determined based on the anomalous potential vorticity distribution within the monsoon region at the 380 K potential temperature level, where lowest values of the potential vorticity (PV) are found in the AMA centre. The AMA-centred equivalent latitude was calculated for a given closed PV contour as a projection onto polar coordinates (Ploeger et al., 2015). An equivalent latitude of 90∘ N corresponds to the centre of the anticyclone (lowest PV), and the equivalent latitude decreases with increasing distance from the centre, or rather, towards the anticyclone's edge. Note that the calculation of AMA-centred equivalent latitude is valid within a layer of about ± 10 K around 380 K potential temperature, where a clear negative PV anomaly occurs. The uncertainties in calculated equivalent latitude become significant at levels beyond the ± 30 K range above or below 380 K.

The model employed in this study numerically solves the discretised coagulation equation (e.g. Jacobson, 2005, and Eq. 15.2 therein) as formulated in the numerical chemistry–climate model SOCOL (SOlar Climate Ozone Links; Stenke et al., 2013). For the coagulation of nucleation-mode aerosol particles the Brownian coagulation kernel (Jacobson, 2005, Eq. 15.33 therein) is used. The particles are assumed to be spherical, and the model is based on a discretisation of the volume space, wherein the ratio of two subsequent volume size bins is constant, Vk+1Vk=1.4. The particle size range of the first volume size bin V1 corresponds to particle diameters of 7.5 nm < dp,1 < 8.5 nm. With a total number of 40 size bins, the largest particle size included in this investigation is about 635 nm (=dp,40=1.4393⋅dp,1).

The coagulation rate and thus the persistence of the nucleation-mode particles were simulated under given background conditions during observation. As input for the simulation, the aerosol size distribution detected by the UHSAS-A (nominally covering 65 nm < dp < 1000 nm; see Sect. 2.2 and Mahnke et al., 2021) was extended towards smaller diameters by further particle size bins obtained from the measurements with COPAS. For the simulation presented herein, the NPF event on 4 August 2017 (KTM 5) over 26 s between 04:04:40 and 04:05:06 UTC (pressure altitude: 110 hPa; ambient air temperature: 196 K) was selected. Each of the two size intervals of the COPAS measurements in the nucleation mode, i.e. 6 nm < dp < 10 nm and 10 nm < dp < 15 nm, is divided into three subintervals to adapt to the higher particle size resolution of the coagulation model. The three sub-bins within the size classes 6–10 and 10–15 nm were uniformly set to one-third of the respective concentrationN6-10 and N10-15. The difference between the total number concentrations N15 (COPAS) and N65 (UHSAS-A) yields the number concentration of N15-65. The number concentration N15-65 (∼ 5000 cm-3) was interpolated over 13 sub-bins (with exponential degradation on increasing particles size) such that the size distribution exhibits a continuous transition towards the detection size range of the UHSAS-A. The size-segregated aerosol concentrations measured with the UHSAS-A were interpolated (with respect to particle size) to the resolution of the remaining 21 sub-bins of the coagulation simulation. The particle concentrations N(dp) over the entire particle size range from the nucleation-mode sizes up to dp = 1 µm were converted into an aerosol size distribution dN/dlog⁡dp in cm-3 as a representation of an initial state and input for the coagulation simulation (for more details see the results in Sect. 4.5).

It is worth noting that for the coagulation simulation, the NPF event is considered to be expired; i.e. any fresh supply of nucleation-mode particles due to continuous or renascent NPF is excluded for the simulated runtime of the coagulation process over 24 h. Generally, constant conditions of atmospheric pressure (p) and temperature (T) are assumed over the 24 h period for the simulation as the air is lifted very slowly at TTL levels within the AMA (by ∼ 1 K potential temperature per day, corresponding to Δp ≈ 1–1.5 hPa and ΔT < 1 Kd-1; see Vogel et al. 2019).

Backward trajectories of 50 d were calculated for each sampling position along Geophysica's flight track in 1 Hz resolution during the StratoClim 2017 mission using the trajectory module of the Chemical Lagrangian Model of the Stratosphere (CLaMS; McKenna et al., 2002; Konopka et al., 2012; Pommrich et al., 2014) driven by horizontal winds from ERA5 reanalysis (Hersbach and Dee, 2016). With the vertical resolution of the ERA5 data, a much better representation of convective updraught and tropical cyclones is realised (Hoffmann et al., 2019) compared to earlier reanalyses (Dee et al., 2011), in particular in the region of the Asian summer monsoon (Li et al., 2020). Further detailed validation of the very new ERA5 products is required, so ERA interim reanalyses still represent the state of the art until ERA5 becomes the new standard.

For vertical air mass transport velocities, the diabatic approach was applied using the total diabatic heating rate to extract the vertical velocity, thereby including the release of latent heat (for details, see Ploeger et al., 2021).

The CLaMS backward trajectory calculations, which were initialised from each sampling position along the flight track in 1 Hz resolution, were used to allocate the air's latest contact with the model boundary layer at 2–3 km above the ground. This allows for the investigation of the location of sources which influence the mixing ratios in the air samples taken aboard the M-55 Geophysica.

The history of a convective air mass is analysed by making use of the TRACZILLA Lagrangian model (Pisso and Legras, 2008), which is a variation in FLEXPART (Stohl et al., 2005). The simulations were based on the release of a cluster of 1000 back trajectories, representative of a generic aerosol tracer, each launched from a 1 s resolved time step along the flight path. The trajectories were traced back over a period of 30 d in the geographical domain (between 10∘ W and 160∘ E and between the Equator and 50∘ N, respectively). The meteorological fields (horizontal winds and radiative heating rates) are taken from ERA5 reanalyses. The convective influence is then distinguished from uninfluenced cases by high-frequency images (one image per 10–15 min) of cloud top altitudes from the geostationary satellites MSG1 and Himawari (for details see Bucci et al., 2020).

Investigations by Weigelt et al. (2009) previously approached the influence of convective cloud processes on the number concentrations of aerosols and in particular of nucleation-mode particles in the upper troposphere. In the present study, the convective sources were identified as such if the course of a TRACZILLA-modelled trajectory within a certain geographical area is found below the cloud top level, as similarly done by Tzella and Legras (2011) and Tissier and Legras (2016). It is noteworthy that, while the adopted trajectory method bypasses the uncertainties related to the convective representation in the reanalysis by using observation-based information on the convective events, uncertainties still remain. Those arise mainly from uncertainties in the identification of the cloud top from image data of geostationary satellites, the impossibility of accounting for the entrainment–detrainment-processes, and reanalysis-related uncertainties concerning advection (for more details see Bucci et al., 2020). In the presented analysis, the air mass age is computed as the difference between the time of release of the cluster and the convective cloud crossing. Since the trajectory cluster can spread in space and bring different contributions from different regions, only the mean age from the dominant convective source (i.e. the mean age from the regions with the highest percentage of convective cloud crossings) is considered in this analysis.

Vertical profiles of the total particle number concentration obtained from various field campaigns in the tropics are shown as medians with percentiles in Fig. 2. The vertical CN profiles from tropical regions of South America and West Africa (TROCCINOX, 2005; SCOUT-AMMA, 2006; Fig. 2a and b) exhibit merged data of two independent CN detectors with individual dp50 (i.e. N6 for θ > 350 K and N4 for θ < 350 K), which were deployed on individual aircraft, the M-55 Geophysica and the DLR Falcon 20 Borrmann et al., 2010; Weigel et al., 2011). The dark shaded areas of the vertical profiles illustrate the scatter of number concentrations between the 90th and 99th percentiles. At tropopause altitudes around 380 K (indicated by vertical bars), or rather at the bottom TTL, the variability in detected concentration reaches a maximum between the 90th and 99th percentile. The increased data scatter indicates the influence of NPF on the class of sub-micrometre-sized particles at these TTL levels, resulting in increased and fluctuating particle number concentrations due to the variable production rate of particles by NPF (see Sect. 2.2.1). Exclusively above the tropopause within the AMA (Fig. 2c), the scatter of the concentration values of sub-micrometre-sized particles remains elevated up to heights of ∼ 400 K potential temperature. Up to this point within the AMA, the scatter of the peak number concentrations (90th to 99th percentile range) is significantly increased in reference to the median values, while in other regions above the tropopause (Fig. 2a and b) the profiles of aerosol concentrations show a smoother transition into the stratosphere.

For comparison (Fig. 2d), particle number concentrations N5.3 are compiled as a vertical median profile (with percentiles) obtained from airborne measurements with the nuclei-mode aerosol spectrometer (NMASS; Brock et al., 2000) during several years (2004–2007, including winter and summer season) over Central America. These observations differentiate the bottom TTL (here 350–379 K) as the region where NPF predominantly occurs with the largest impact on the fine-mode (sub-micrometre-sized) aerosol particle concentration (e.g. Borrmann et al., 2010; Weigel et al., 2011). However, this vertical profile (Fig. 2d) illustrates additional features at altitudes above the mean tropopause altitude (assumedly located at ∼ 380 K). The locally increased concentrations with respect to the median become apparent at ∼ 380–390 and at ∼ 400–410 K, respectively. Above tropopause levels, significantly increased number concentrations of fine-mode particles, potentially caused by local NPF, were observed over both Central America (Fig. 2d) and the Indian subcontinent within the AMA (Fig. 2c).

The entire StratoClim 2017 data set of measured (1 Hz resolved) particle mixing ratios n6 and n10 is summarised in Fig. 3a as a function of potential temperature. The resulting median profile n6 of the StratoClim 2017 measurements is shown with the 25th and 75th percentile (blue profile). This allows for a direct comparison with the corresponding median profiles from earlier COPAS measurements at tropical regions (in red: TROCCINOX, Brazil, 2005; in dark green: SCOUT-AMMA, West Africa, 2006; cf. Borrmann et al., 2010 and Weigel et al., 2011). Figure 3a also includes the median vertical profile of the mixing ratios of fine-mode particles (bright-green line), which was obtained from measurements over the central Pacific, at tropical latitudes (Brock et al., 1995).

The profiles (n6, n10, and nnm in Fig. 3a and b) are structured as

∼ 350–380 K – characterised by the largest scatter of the particle mixing ratios and the highest values of up to 5 × 104 mg-1, thus representing the height level of the profile's maximum;

The course of the median profiles exhibits similar characteristics. The common feature of all median profiles from the tropics is their maximum at about 350–360 K, while the AMA observations indicate a corresponding maximum at slightly higher altitudes (i.e. 355–365 K). Further aloft, the particle mixing ratios obtained from different locations decrease with altitude on a similar gradient. In the altitude range between 360 and 400 K, the tropical data obtained over South America (red) constitute the lowest particle mixing ratios (by median values), whereas all other profiles are almost in line with each other up to 400 K. The vertical median profile of particle mixing ratios determined in the AMA (blue) during StratoClim 2017 exhibits the highest mixing ratios at each height level up to ∼ 415 K. Additionally, the AMA profile features a substantial increase in the median mixing ratio at altitudes of ∼ 410–415 K, where the values exceed those from the tropical regions by about 35 %. Above 415 K, the continuation of the tropical profiles from West Africa and Central America (coloured green) with altitude is largely consistent with the particle mixing ratios measured throughout StratoClim 2017, while at these altitudes the measurements from South America (red) show comparatively increased values. Above 440 K, the particle mixing ratio over West Africa (dark green) significantly deviates from those of all other vertical profiles, as is visible from the gradual increase in the particle mixing ratio with altitude. This deviation was attributed to the influence of the high-reaching volcanic injections of the Soufrière Hills (Borrmann et al., 2010). The 1 Hz resolved StratoClim 2017 data (grey dots in Fig. 3a) are added to the graph to illustrate how the scatter of measured particle mixing ratios relates to corresponding median profiles.

Figure 3b shows the vertical distribution of the mixing ratio of the nucleation-mode particles nnm (see Sect. 2.2.1). The flight-by-flight colouration of the data points indicates that increased nnm values were observed during each of the eight StratoClim 2017 mission flights. In addition, Fig. 3b shows the wide range of altitudes over which the layers of increased nnm were observed during the individual flights. Remarkably increased values of nnm were detected up to altitudes as high as 400 K.

Figure 3c depicts the 1 Hz resolved mixing ratios of the non-volatile particles n10nv (see Appendix A) as well as the resulting median profile of n10nv with the 25th and 75th percentiles. Figure 3c additionally shows the median profile of n6 as in Fig. 3a, which illustrates the vertical progression of n10nv in direct relationship to the NPF-influenced total particle mixing ratio. Figure 3d illustrates the vertical distribution of the fraction f of non-volatile particles, i.e. the ratio n10nvn10 (see Sect. 2.1.2), which is presented in 1 Hz resolution, as well as the profiles of resulting median with the 25th and 75th percentiles. At lower altitudes (< 350 K), the mixing ratio of non-volatile particles appears low with a relatively large scatter. The local minima of the n10nv profile and of the fraction f coincide with the local maximum of n6 (i.e. ∼ 355–375 K). Above 370 K, the n10nv profile follows the general decline with height. Above 390 K, both mixing ratios (n6 and n10nv) decrease uniformly, and the fraction f remains almost constant at ∼ 45 %–50 % up to altitudes of 430 K. Towards 435 K, the total mixing ratio n6 nearly stagnates, whereas n10nv exhibits slightly dropping mixing ratios.

In essence, the vertical profiles of the total particle mixing ratio n6 and those of the non-volatile particles n10nv are divided into three ranges: A.

At the bottom TTL region (θ < 375 K), both n6 and n10nv are mainly characterised by NPF, as indicated by the high mixing ratios of nucleation-mode particles nnm. NPF causes a significant addition to the scatter of the total mixing ratios towards high values, which exceed the median by more than 1 order of magnitude. In this altitude range, a local deficit of the non-volatile particle compounds favours the occurrence of NPF.

The steeply dropping vertical profile of the total mixing ratio of the sub-micrometre-sized aerosols above ∼ 415 K subtly indicates the upper limit of the AMA's influence on the vertical mixing of the UTLS. From the CO, ozone, and nitrous oxide content in air samples taken throughout StratoClim 2017, von Hobe et al. (2021) concluded that the AMA's interior was largely isolated from stratospheric in-mixing up to altitudes of 10 to 20 K above the tropopause (i.e. θ ≈ 400 K). Moreover, they found that mixing processes with stratospheric air are of increasing significance at levels between 400 and 420 K (von Hobe et al., 2021). At altitudes above θ ≈ 440 K, the median mixing ratios n6 exhibit a vertically stable continuation after another sharp drop between 435 and 440 K (Fig. 3a and b). Brunamonti et al. (2018) specified the 440 K level as the top of confinement (TOC) of the AMA for the 2017 monsoon season. So, according to this TOC definition, above 440 K potential temperature (≳ 18.5–19 km), the median n6 (Fig. 3a and b) represents stratospheric background values.

The ATAL (Vernier et al., 2011a; and see also Höpfner et al., 2019; Mahnke et al., 2021) is mainly attributed to the uplift of pollution from the boundary layer as concluded from balloon-borne and satellite-based observations (Vernier et al., 2018). The described drop in the aerosol concentration (Vernier et al., 2018) at potential temperatures of ∼ 400–420 K (well above tropopause levels) coincides with the uppermost altitude limit of main NPF activity at ∼ 400 K (∼ 17.5 km) observed during StratoClim 2017 (see Fig. 3). Here, the most substantial decrease in both mixing ratios n6 and n10nv was observed in transit from ∼ 410 to ∼ 415 K (at ∼ 18 km).

Figure 4 shows the 130 individual NPF events sorted according to their duration. Based on the average flight speed (Sect. 2.2.1) and assuming a constant heading during flight, the mean horizontal distance per 10 s flight time spans about 1.5 km. The spatially most extended uninterrupted NPF signature throughout StratoClim 2017 spanned a mean horizontal distance of ∼ 110 km. The hitherto most extended NPF event observed with COPAS at TTL level over South America (Weigel et al., 2011) lasted over a continuous duration of 262 s (∼ 35.5 km of covered flight distance). Another three individual NPF events were observed above West Africa (Weigel et al., 2011) over 20, 83, and 98 s (∼ 3, ∼ 12, and ∼ 13 km), respectively. Approximately 45 % of 130 NPF events observed throughout StratoClim 2017 were of less than 20 s duration (∼ 3 km), while the majority (∼ 75 %) of NPF observations above the Indian subcontinent extended over less than 80 s (∼ 12 km; Fig. 4a). The vertical profile (Fig. 4b) shows that above 380 K, predominantly short events of less than 2 min duration with comparatively low mixing ratios nnm were encountered. Here, observed NPF events rarely lasted for several minutes (i.e. 5–6 min). In the lower TTL range, i.e. below the tropopause, the number of persistent NPF events was higher than above the tropopause, and the mixing ratio of nucleation-mode particles was also more often increased. The highest mixing ratios of nucleation-mode particles were measured in events lasting from 1 min to a few (up to about 7) minutes.

Figure 5 depicts the diurnal distribution of observed NPF events. The frequency of NPF event observations is analysed as a function of the local daytime (LT) at Kathmandu, Nepal (Fig. 5a). Apart from one exception, the occurrence frequency of the NPF events seems evenly distributed over the course of a day. The exception is a time window between 10:00 and 10:30 (LT), when recent particle formation was observed up to 2.5 times more often than at other times of the day. In this time window, about one-third of all NPF events (31 of 105 events with durations of more than 5 s) were observed, most of which (25 of 31 events) lasted for less than 80 s (< 12 km mean horizontal distance). The measurements in this time window occurred at two distinct altitude layers, ∼ 360–370 and ∼ 390–400 K. The majority of the StratoClim NPF events in this period (20 of 31 events) were from altitudes above 390 K, while ascertained mixing ratios nnm‾ were never outside ∼ 500–5000 mg-1 during this time of day. Throughout the StratoClim 2017 mission, no further NPF event was observed above 390 K at any earlier time of day, and only two single events were encountered at these heights during different flights at a later time of day (∼ 12:20 and ∼ 17:30 LT, respectively). Determining whether this pronounced frequency of NPF occurrence at a particular time of day is due to bias effects would require a larger database. Beyond this, preferred times of day when NPF was observed with particular frequency were not identified in the StratoClim observations, while instead, within the same region, a diurnal dependence of NPF was previously concluded based on a larger data set (Hermann et al., 2003). The diurnal dependence of NPF would be expected if H2SO4 is assumed to be the main nucleating compound whose production maximum (from the reaction SO2 + OH) at the local noon time correlates with the solar zenith (cf. Weigel et al., 2011).

Throughout StratoClim 2017, NPF was predominantly observed before local noontime during the mission flights KTM 2, KTM 3, KTM 5, and KTM 7, while all other observations were made mainly during the afternoon. All NPF events which lasted longer than 5 s were almost evenly distributed over the day. Furthermore, Fig. 5c indicates that the longest NPF events are not generally associated with the highest mean mixing ratios nnm‾. The duration of an event is therefore primarily an indicator of the spatial extent of a region where NPF takes place. The derivation of the spatial extent from the duration of individual events, however, bears significant uncertainties since changes in flight attitude, such as curve manoeuvres or changing flight levels during an event, are not taken into account.

The NPF events observed during StratoClim 2017 are among the most frequent and spatially most extended of all those which have been identified by means of COPAS measurements during previous missions (cf. Borrmann et al., 2010; Weigel et al., 2011). Only a few events which lasted more than 100 s were observed during StratoClim 2017, but it cannot be excluded that they were actually composed of individual events of smaller extent. Very short events (< 10 s) make up almost 40 % of all NPF events observed. Consequently, hereafter, all events shorter than 5 s (i.e. 25 out of 130 events) are discarded from further analyses. In this way, individual 1–2 s features are filtered from the data. In addition, for the evaluation of individual NPF events, the reliability of the results increases if the arithmetic averaging occurs over more than five data points. Finally, the accuracy of the specified event duration improves as the raw signal processing (Sect. 2.1.3) smooths the temporal salience of short events.

Figure 6 illustrates the mean mixing ratio of nucleation-mode particles nnm‾ measured during the individual NPF events as a function of (1) the vertical distance Δθ‾ to the lapse-rate tropopause (Fig. 6a and c) and (2) the mean equivalent latitude ϕequ‾ (Fig. 6b and d). NPF events above the lapse-rate tropopause (Fig. 6a; positive Δθ‾ and up to +30 K) were mainly observed during the first half of the StratoClim 2017 mission (KTM 2, KTM 3, and KTM 5 on 29 July, 31 July, and 4 August 2017, respectively, with a maximum ceiling > 475 K) or during the last mission flight (KTM 8, on 10 August 2017, with a maximum ceiling ∼ 435 K). All further observations up to θ > 425 K were located below the lapse-rate tropopause (negative Δθ‾, down to -35 K) or in its close vicinity (Δθ‾ ≈ 0 K; e.g. KTM 6, 6 August 2017, with a maximum ceiling ∼ 380 K), i.e. in or above the region of the main convective outflow. As indicated by Bucci et al. (2020) and von Hobe et al. (2021), the first half of the StratoClim 2017 mission was characterised by weak convection, while the convective activity increased as the campaign progressed.

With respect to the AMA centre, most NPF events were encountered north of 60∘ equivalent latitude (Fig. 6b). An exception is a flight segment of flight KTM 3 (on 31 July 2017), where weak NPF with mixing ratios nnm‾ of ∼ 500–1300 mg-1 was detected at the farthest distance from the AMA centre (near the turning point at about 21.5∘ N and 80∘ E geographic coordinates; see Fig. 1). These measurements (at ϕequ‾ < 60∘ N) were made well above the tropopause since at positive Δθ‾ (up to +10 K) mean CO mixing ratios of 45–50 nmolmol-1 (Fig. 6c and d) were found, in agreement with satellite-based CO observations for altitudes of ∼ 16–19 km within the AMA (Park et al., 2009).

Towards the AMA centre (ϕequ‾ > 60∘ N), the NPF events are distributed over the entire range of Δθ‾. Here, weak NPF with several hundreds of nucleation-mode particles per milligram was observed well above the lapse-rate tropopause (Δθ‾ ≈ +28 K). The vertical distribution of the NPF events indicates that those events with the highest nnm‾ and mainly elevated CO mixing ratios (65 to ∼ 137 nmolmol-1) were encountered exclusively below the lapse-rate tropopause (to minimum Δθ‾ of -35 K). Regarding a relationship between (a) the position relative to the AMA centre and (b) the effectiveness of vertical transport or the NPF rate, the StratoClim 2017 data show that between 60∘ N and 90∘ N equivalent latitude, there is no indication that the mixing ratios of nnm‾ and CO depend on the position with respect to the AMA centre. Close to the AMA centre (60∘–90∘ N) and in an altitude range of almost ± 30 K around tropopause heights, both the distribution of CO-enriched air masses and the occurrence of NPF appear to be largely independent from ϕequ‾.

Coagulation represents one of the main processes limiting the persistence of nucleation-mode particles, i.e. the duration during which freshly formed particles remain in the size range of the nucleation mode. At elevated number densities, the highly diffusive nucleation-mode particles collide and coagulate with each other and with the present background aerosols on short timescales. Gaseous precursors, which are saturated or supersaturated under NPF conditions, may condense and additionally contribute to the growth of particles out of the nucleation-mode size range, which is considered to be a secondary process.

The aerosol size distribution, which was compiled from the measurements during an NPF event as input for the coagulation simulation (see Sect. 3.2), is depicted in Fig. 7 (black circles with horizontal bars indicating the width of their respective particle size bins of the model). The simulated change in the initial aerosol size distribution due to coagulation is shown in 1 h steps in different colours and line types (Fig. 7a). From this simulation, the temporal decay of Nnm was derived (Fig. 7b, solid black line), whereby the gradient of this decay illustrates the coagulation rate. The sequence of the simulated size distributions indicates that the initial number of nucleation-mode particles is reduced by coagulation within a few hours. Within the first hour after an expired NPF event the nucleation mode is no longer predominant in the overall size distribution, as seen from the maximum of the distribution at dp > 15 nm after 1 h of simulated coagulation (solid red line in Fig. 7a). Hence, with adopted instruments for the detection of nucleation-mode particles, a clear NPF signature is identified only while NPF is just proceeding or for a very short time immediately after an expired NPF event.

The concentration of nucleation-mode particles Nnm decreases steeply over time (Fig. 7b). From initially ∼ 13 000 cm-3 of nucleation-mode particles (∼ 75 % of Ntotal) at the earliest stage, Nnm falls below 1000 cm-3 (∼ 20 % of Ntotal) within about 1 h (the grey shaded areas serve for reference). The detection of 1000 cm-3 of nucleation-mode particles, however, would be interpreted as an NPF event of intermediate strength (see Sect. 2.2.1). In addition, coagulation leads to Nnm below 100 cm-3 (< 5 % of Ntotal) during less than 4 h and to Nnm of less than 10 cm-3 within 9 h. The efficiently proceeding coagulation impedes the identification of NPF based on in situ detections, and it is required to be at the NPF site at the right time. This circumstance is corroborated by tests concerning the sensitivity of the simulation to varying input parameters. For these tests, the input in the nucleation mode was modified while keeping constant background aerosol conditions. In three further simulation runs, the initial Nnm was multiplied by the factors 0.1, 10, and 100, respectively (Nnm,0.1, Nnm,10, Nnm,100; dashed lines in Fig. 7b). Increased initial concentrations of nucleation-mode particles, Nnm,10 and Nnm,100, last only for about 15 min compared to the original Nnm (black line in Fig. 7b). The initial values ∼ 105 or ∼ 106 cm-3 drop very quickly due to elevated coagulation rates, and in both of these cases, Nnm,10 and Nnm,100 fall below 1000 cm-3 within less than 1 h. The threshold of 100 cm-3 is crossed after less than 2 h (Nnm,10) or after 30 min (Nnm,100). Therefore, NPF events, which produce much higher concentrations of nucleation-mode particles, require even shorter time periods for a successful detection (e.g. by COPAS) after their expiration. However, for the simulation of decreased concentrations (Nnm,0.1), the coagulation rates remain nearly constant, as indicated from the almost identical decays of Nnm,0.1 and Nnm (Fig. 7b). Simulated concentration of nucleation-mode particles falls below 100 cm-3 within almost the same time from the initial values Nnm,0.1 or Nnm,10, respectively. Further investigation on the sensitivity of the simulation to the pressure and temperature conditions that were assumed as simulation input did not reveal any significant dependence unless the input is varied by more than ± 10 hPa and ± 18 K from the used values of the respective parameter (not shown here).

Based on these estimations, the detection of elevated Nnm indicates that an event with high NPF rates is currently proceeding, or a recently expired NPF event was observed. Detections of lower values of Nnm could indicate (a) intermediate or weak (currently proceeding) NPF at low supersaturation of the NPF precursor or (b) an NPF event (e.g. of high particle productivity) that has phased out several hours before the observation. NPF is measured in situ, while the formation event is currently in progress or at most a few hours later. Therefore, the short periods of time available for a clear NPF detection and the still frequent NPF encounters on each measurement flight during StratoClim 2017 indicate the prevalence of such events within the AMA.

NPF events with moderate numbers of nucleation-mode particles (< 1000 cm-3) in the lower-TTL region were previously attributed to CO mixing ratios above ∼ 70 nmolmol-1 (60–70 nmolmol-1 was assumed to be a typical CO background in the pristine marine boundary layer; cf. Weigel et al., 2011). Elevated concentrations of nucleation-mode particles (of up to ∼ 6000 cm-3) at altitudes of 350 K < θ < 360 K were associated with significantly increased CO mixing ratios of more than 85 nmolmol-1 (Weigel et al., 2011). These results, mainly based on two single NPF events over West Africa (SCOUT AMMA, 2008), could have indicated a correlation between NPF rates and CO load from pollution. However, almost 100 individual event observations (Sect. 4.4 and Fig. 6c and d) indicate that the relationship between pollution level and NPF rates is less direct than expected. In Fig. 8, the 1 Hz resolved data of synchronous detections of CO and particle mixing ratio during the entire StratoClim 2017 mission are compared. To illustrate the relative scattering of both n6 and nnm, the total particle mixing ratio n6 is shown in the background (grey dots), and the mixing ratio of particles in nucleation mode nnm (dots coloured with respect to θ) is displayed in the foreground.

At altitudes below the tropopause (below ∼ 380 K), where NPF rates lead to the highest nnm, the relationship between the 1 Hz resolved n6 or nnm and the CO mixing ratio is highly variable. At CO levels of 80–100 nmolmol-1, the scatter of nnm ranges from 700 mg-1 to the absolute maximum of about 50 000 mg-1. This maximum nnm is exclusively reached at CO mixing ratios of 100 ± 2.5 nmolmol-1. At the maximum CO mixing ratio (i.e. ∼ 150 nmolmol-1), particle mixing ratios nnm of about 6000 mg-1 (median value) were detected. Within a range of CO content between 85 and 130 nmolmol-1, the nnm (median) mixing ratios ranged consistently between 2000 and 10 000 mg-1, apart from the notable exception at about 100 nmolmol-1. CO mixing ratios between 60 and 80 nmolmol-1 were detected just below or at tropopause levels (yellow to orange colours) coincidently with decreasing nnm from about 3000 mg-1 to values below 1000 mg-1. For CO mixing ratios below 60 nmolmol-1, nnm almost stagnates between 300 and 1300 mg-1. At tropopause levels and aloft, the decreasing CO mixing ratio as well as abating NPF (expressed in decreasing nnm values) likely results from both the degradation of CO (see von Hobe et al., 2021) and the lacking supply of NPF precursor material by direct transport. According to von Hobe et al. (2021) any indication is missing that convection penetrated the tropopause during the StratoClim 2017 period. However, Lee et al. (2019) investigated the TTL-hydrating influence of an overshooting event that occurred in the Sichuan Basin about 1.5 d before the StratoClim measurements southbound of Kathmandu over north-eastern India (M-55 Geophysica, KTM 7 on 8 August 2017). Hence, there is no clear indication for a direct relationship between CO-enriched (polluted) air and the NPF rate.

The assignment of certain measurement sections of elevated nnm to possible source regions of NPF precursors is carried out in two steps:

The backward trajectories were traced down to the boundary layer (BL) for each measurement point (see Sect. 3.3) at which NPF was detected (Fig. 9a and b). In this way, the geographical position of the last BL contact of the air before the observations (1 Hz resolution) of elevated nnm ( 300 mg-1) is obtained throughout the StratoClim 2017 mission (Fig. 9a). In addition, the geographical position of the trajectories' fastest uplift during their transport history was determined (Fig. 9b).

Locations of fastest vertical updraught are more compactly distributed (Fig. 9b, close-up views in Fig. 9b.ii and b.ii) and better reflect the contours of an area where efficient convection frequently occurs within the monsoon region. The fastest updraught with simultaneously increased nnm is found in the Kathiawar region on the Indian west coast towards the Arabian Sea or in the far north of India (in the areas around Ladakh, Himachal Pradesh, and eastern Punjab). In areas of the central Tibetan Plateau, some sites were identified with elevated nnm, where also the fastest vertical upward transport occurred. Finally, the shape of the Himalayas is traced by the locations with the fastest vertical air mass transport over a wide range of nnm.

Also the shortest transport times from the BL are found around the Himalayas and their foothills, whereas the transport times from locations of air's last BL contact, which fall south of 25∘ N, west of 72∘ W, or east of 96∘ W, are rarely shorter than 10 d. In Fig. 10 (Fig. 10a and b; see also respective close-up view), the contour of the Himalayas is clearly reproduced by the distribution of the data points (transport times of less than ∼ 5 d and fastest vertical updraught). Hence, for the duration of the StratoClim 2017 mission, the convective uplift mainly occurred within the AMA. This more compact regional distribution of vertical uplift (Fig. 10b) is possibly related to the occurrence of a vertical conduit for upward transport in the monsoon, as conjectured by Bergman et al. (2013). Figure 10 also indicates air masses of elevated nnm, which have experienced convective uplift over Tajikistan and northern Afghanistan as well as over regions around the Yellow Sea, the Korean Peninsula, or Japan, hence far away from the AMA system.

Figures 9 and 10 both finally show that the region of the air's last BL contact and the location of the fastest vertical uplift do not necessarily coincide. Similarly, the locations of the fastest updraught do not always match the shortest transport times, but for most cases in the immediate vicinity of the Himalayas this correlation is clearly visible from the StratClim 2017 data set. Ultimately, it cannot be excluded that, within the free troposphere, the air is subject to loading from various source regions (not exclusively from the location of the last BL contact) prior to its convective uplift. Of course, this finding complicates an unambiguous apportioning of NPF to specific source regions of precursors in the BL.

The vertical distribution of the nnm mixing ratios as a function of the air mass transport time from the BL is shown in Fig. 11:

Above 380 K, almost all observations of enhanced nnm are associated with air mass transport times of more than 12 d. At 380 ± 3 K, none of the detected nnm is connected to air mass transport times of less than 12 d. Values of nnm that were several times higher (with 103–104 mg-1) were detected below 380 K in air masses, which had experienced more than 25 d of transport time from the BL.

For the following analysis, which is summarised in Fig. 12, the vertical distribution of the mean mixing ratios nnm‾ of the respective NPF event (see Sects. 2.2.1 and 4.4) is juxtaposed with a.

a measure for the convective contribution to the composition of the probed air mass

Figure 12a broadly confirms the general understanding that the main outflow region of deep convection is well below the tropical tropopause (i.e. at 350–370 K), and aloft the air is still rising but at a much lower vertical velocity. At altitudes above ∼ 380 K, the observed NPF events with nnm‾ < 2000 mg-1 generally remain in the lower range of moderate intensity (see Sect. 2.2.1), although there was one of the rare observations of overshooting convection up to levels ∼ 385 K, where NPF was detected in coincidence with ice cloud elements (cf. Weigel et al., 2021). Hence, if in exceptional cases the outflow region of deep convection extends above the 380 K level, as indicated by the presence of ice cloud elements, then high NPF rates are not necessarily to be expected. Below 380 K, about two-thirds of all events are connected to convective influence by more than 75 %. However, a remarkable proportion of observations below 380 K indicate convective contributions of less than 60 % and down to 25 %. Below ∼ 375 K, mean mixing ratios nnm‾ of 1000–2000 mg-1 were associated with 100 % convective contribution, and mixing ratios of more than 10 000 mg-1 were sometimes observed in air masses with ∼ 30 % convective contribution.

For the observed NPF events, Fig. 12b shows the mean age of the probed air masses since their release from the top of individual convective cells. Above ∼ 380 K, the air escaped the convection top mainly 12 d (or more) prior to its probing. Two events at ∼ 382 and at ∼ 385 K, respectively, indicate a more recent convective uplift within 5 d before the air was sampled. Despite the comparatively short transport times, here, the observed nnm‾ remained below 2000 mg-1. At altitudes below ∼ 380 K, the air predominantly resided within the TTL region for less than 5 d prior to the observation. Nevertheless, some of the comparatively intensive NPF events (with nnm‾ ≈ 7000–15 000 mg-1 at ∼ 360–375 K) were observed in air, which has been released from associated clouds' top more than a week (and up to 2 weeks) prior to the measurements. It should be considered, however, that short air mass transport times within the TTL are indicated also for NPF events with minor convective contribution (< 50 %).

From the StratoClim 2017 database emerges that NPF occurs at the lower TTL (i.e. below the tropopause) of the AMA in air masses that have been lifted by convection in time intervals ranging from 5 d to about 2 weeks. However, it remains unclear whether in some of the observed events the air samples were taken at a very advanced stage of NPF. Therefore, it can only be surmised whether or how often the short time period was missed during which NPF is detectable by aircraft-based measurements. Potential uncertainties remain to be considered in connection with the uncertainty in the reanalysis data and the representation of the transport history of the air masses.