July 4, 2022

# Synergistic HNO3–H2SO4–NH3 upper tropospheric particle formation – Nature

### The CLOUD facility

We conducted our measurements at the CERN CLOUD facility, a 26.1-m3, electropolished, stainless-steel CLOUD chamber that allows new-particle-formation experiments under the full range of tropospheric conditions with scrupulous cleanliness and minimal contamination9,30. The CLOUD chamber is mounted in a thermal housing, capable of keeping the temperature constant in the range 208 K and 373 K with a precision of ±0.1 K (ref. 31). Photochemical processes are initiated by homogeneous illumination with a built-in UV fibre-optic system, including four 200-W Hamamatsu Hg-Xe lamps at wavelengths between 250 and 450 nm and a 4-W KrF excimer UV laser at 248 nm with adjustable power. New particle formation under different ionization levels is simulated with and without the electric fields (±30 kV), which can artificially scavenge or preserve small ions produced from ground-level GCR. Uniform spatial mixing is achieved with magnetically coupled stainless-steel fans mounted at the top and bottom of the chamber. The characteristic gas mixing time in the chamber during experiments is a few minutes. The loss rate of condensable vapours and particles onto the chamber walls is comparable with the ambient condensation sink. To avoid contamination, the chamber is periodically cleaned by rinsing the walls with ultra-pure water and heating to 373 K for at least 24 h, ensuring extremely low contaminant levels of sulfuric acid <5 × 104 cm−3 and total organics <50 pptv (refs. 32,33). The CLOUD gas system is also built to the highest technical standards of cleanliness and performance. The dry air supply for the chamber is provided by boil-off oxygen (Messer, 99.999%) and boil-off nitrogen (Messer, 99.999%) mixed at the atmospheric ratio of 79:21. Highly pure water vapour, ozone and other trace gases such as nitric acid and ammonia can be precisely added at the pptv level from ultra-pure sources.

### Instrumentation

Gas-phase sulfuric acid was measured using a nitrate chemical ionization APi-TOF (nitrate-CI-APi-TOF) mass spectrometer34,35 and an iodide chemical ionization time-of-flight mass spectrometer equipped with a Filter Inlet for Gases and Aerosols (I-FIGAERO-CIMS)36,37. The nitrate-CI-APi-TOF mass spectrometer is equipped with an electrostatic filter in front of the inlet to remove ions and charged clusters formed in the chamber. A corona charger is used to ionize the reagent nitric acid vapour in a nitrogen flow38. Nitrate ions are then guided in an atmospheric pressure drift tube by an electric field to react with the analyte molecules in the sample flow. Sulfuric acid is quantified for the nitrate-CI-APi-TOF with a detection limit of about 5 × 104 cm−3, following the same calibration and loss correction procedures described previously9,32,39. FIGAERO is a manifold inlet for a CIMS with two operating modes. In the sampling mode, a coaxial core sampling is used to minimize the vapour wall loss in the sampling line. The total flow is maintained at 18.0 slpm and the core flow at 4.5 slpm; the CIMS samples at the centre of the core flow with a flow rate of 1.6 slpm. Analyte molecules are introduced into a 150-mbar ion-molecule reactor, chemically ionized by iodide ions that are formed in a Po-210 radioactive source and extracted into the mass spectrometer. The sulfuric acid calibration coefficient for the I-FIGAERO-CIMS is derived using the absolute sulfuric acid concentrations measured with the pre-calibrated nitrate-CI-APi-TOF.

Gas-phase nitric acid was also measured using the I-FIGAERO-CIMS. Nitric acid concentration was quantified by measuring HNO3/N2 mixtures with known nitric acid concentrations, following similar procedures described previously16. The HNO3/N2 mixture was sourced from flowing 2 slpm ultra-pure nitrogen through a portable nitric acid permeation tube, at constant 40 °C. The permeation rate of nitric acid was determined by passing the outflow of the permeation tube through an impinger containing deionized water and analysing the resulting nitric acid solution through spectrophotometry.

Gas-phase ammonia was either measured or calculated. We measured ammonia using a proton transfer reaction time-of-flight mass spectrometer (PTR3-TOF-MS, or PTR3 for short)40. As a carrier gas for the primary ions, we used argon (ultra-high purity 5.0) to ensure that ammonium ions could not be artificially formed in the region of the corona discharge. Although the theoretical detection limit from peak height and width would be even smaller, the lowest concentration we were able to measure during the first fully ammonia-free runs of the beginning of the campaign was 109 cm−3. An explanation for this is that, when concentrations of ammonia are low, effects of wall interaction of the highly soluble ammonia become important and the decay of ammonia in the inlet line becomes very slow. To reduce inlet wall contacts, we used a core-sampling technique directly in front of the instrument to sample only the centre 2 slpm of the 10 slpm inlet flow, but owing to frequent necessary on-site calibrations of volatile organic compounds, a Teflon ball valve was placed within the sample line that probably influenced measurements during times of low ammonia concentrations. At concentrations above about 2 × 109 cm−3 ammonia, however, the response of the instrument was very fast, so that, for example, changes in the chamber ammonia flow rate were easily detectable. Off-site calibrations showed a humidity-independent calibration factor of 0.0017 ncps/ppb. Calibrated data from the PTR3 agree very well with the Picarro above 1010 cm−3 (detection limit of the Picarro). The PTR3 also provides information about the overall cleanliness of the volatile organic compounds in the chamber. The technique was extensively described previously40.

For ammonia concentrations below 109 cm−3, we calculated concentration using the calibrated ammonia injection flow and an estimated first-order wall-loss rate. The wall-loss rate (kwall) for ammonia inside the CLOUD chamber is confirmed to be faster than for sulfuric acid41, and can be determined from the following expression42:

$${k}_{{rm{wall}}}=frac{A}{V},frac{2}{{rm{pi }}},sqrt{{k}_{{rm{e}}},{D}_{i}}={C}_{{rm{wall}}},sqrt{{D}_{i}}$$

(1)

in which A/V is the surface-to-volume ratio of the chamber, ke is the eddy diffusion constant (determined by the turbulent mixing intensity, not the transport properties of the gases) and Di is the diffusion coefficient for each gas. Cwall is thus referred to as an empirical parameter of experiment conditions in the chamber. Here we first determine the kwall for sulfuric acid and nitric acid to be 1.7 × 10−3 and 1.9 × 10−3 s−3, respectively, by measuring their passive decay rates and subtracting the loss rate of chamber dilution for both (1.2 × 10−3 s−1), as well as the loss rate of dimer formation for sulfuric acid (around 1.6 × 10−3 s−1 for 5 × 106 cm−3 H2SO4). The kwall for sulfuric acid agrees with our measurements from previous campaigns43. We then derive the Cwall for sulfuric acid and nitric acid both to be 2.0 × 10−4 torr−0.5 cm−1 s−0.5, with ({D}_{{{rm{H}}}_{2}{{rm{SO}}}_{4}}) of 74 torr cm2 s−1 and ({D}_{{{rm{HNO}}}_{3}}) of 87 torr cm2 s−1 (ref. 44). Finally, we calculate the kwall for ammonia to be 2.7 × 10−3 s−1, with ({D}_{{{rm{NH}}}_{3}}) of 176 torr cm2 s−1 (ref. 44). Ammonia desorption from the chamber surface is a strong function of the temperature and is believed to be negligible at low temperatures30. Even after a long time exposure, ammonia desorption should be less than 1.6 × 106 cm−3, according to previous parameterization of ammonia background contamination in the CLOUD chamber41.

The composition of negatively charged ions and clusters were determined using an APi-TOF mass spectrometer45. The APi-TOF mass spectrometer is connected to the CLOUD chamber by means of a 1-inch (21.7-mm inner diameter) sampling probe, with coaxial core sampling to minimize the wall losses in the sampling line. The total sample flow is maintained at 20 slpm and the core sample flow for the APi-TOF mass spectrometer at 0.8 slpm. Because this instrument only measures charged clusters, the measurements were made during GCR conditions. Owing to a large temperature difference between the cold chamber (223 K) and the warm APi-TOF mass spectrometer (around 293 K), HNO3–H2SO4–NH3 clusters probably lose relatively weakly bonded HNO3 and NH3 molecules. This resembles the chemical ionization process of detecting ammonia with the nitrate-CI-APi-TOF, in which HNO3 and NH3 molecules rapidly evaporate from the resulting ammonia nitrate cluster in the CI-APi-TOF vacuum regions46.

Gas monitors were used to measure ozone (O3, Thermo Environmental Instruments TEI 49C), sulfur dioxide (SO2, Thermo Fisher Scientific Inc. 42i-TLE) and nitric oxide (NO, ECO Physics, CLD 780TR). Nitrogen dioxide (NO2) was measured by a cavity attenuated phase shift nitrogen dioxide monitor (CAPS NO2, Aerodyne Research Inc.) and a home-made cavity enhanced differential optical absorption spectroscopy (CE-DOAS) instrument. The relative humidity of the chamber was determined by dew point mirrors (EdgeTech).

Particle number concentrations were monitored by condensation particle counters (CPCs), including an Airmodus A11 nano Condensation Nucleus Counter (nCNC), consisting of a particle size magnifier (PSM) and a laminar-flow butanol-based CPC47, as well as a butanol TSI 3776 CPC. Particle size distributions between 1.8 nm and 500 nm were measured by a nano-scanning electrical mobility spectrometer (nSEMS), a nano-scanning mobility particle sizer (nano-SMPS) and a long-SMPS. The nSEMS used a new, radial opposed migration ion and aerosol classifier (ROMIAC), which is less sensitive to diffusional resolution degradation than the DMAs48, and a soft X-ray charge conditioner. After leaving the classifier, particles were first activated in a fast-mixing diethylene glycol stage49 and then counted with a butanol-based CPC. The nSEMS transfer function that was used to invert the data to obtain the particle size distribution was derived using 3D finite element modelling of the flows, electric field and particle trajectories50,51. The two commercial mobility particle size spectrometers, nano-SMPS and long-SMPS, have been fully characterized, calibrated and validated in several previous studies52,53,54.

Particle-phase chemical composition was quantified using a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS, Aerodyne Research). The working principles of the HR-ToF-AMS have been explained in detail previously55,56. In brief, particles are focused by an aerodynamic lens and flash-vaporized by impact onto a hot surface at 600 °C under a high vacuum. The vapours are then ionized by 70-eV electrons and the ions are detected with a ToF mass spectrometer. Ionization efficiency calibrations were conducted before and after the campaign and the variation is within 30%. The particle collection efficiency was considered constant during the experiments because temperature and relative humidity in the chamber were fixed and the particle composition was dominated by ammonium nitrate.

INP were measured in real time at 215 K, as a function of ice saturation ratio (Sice), by the mobile ice nucleation instrument of the Karlsruhe Institute of Technology (mINKA). mINKA is a continuous flow diffusion chamber with vertical cylindrical geometry57, on the basis of the design of INKA58,59. A detailed description of the continuous flow diffusion chamber working principle is presented elsewhere57. Here, predefined scans of the water vapour saturation ratios were performed in the diffusion chamber every 30 min. For each scan, Sice steadily increased from 1.2 to 1.8 while the temperature was kept constant. The errors associated to temperature and Sice inside the diffusion chamber were derived from the uncertainty of the thermocouples attached to the instrument walls (±0.5 K)59.

### Determination of particle formation rate

The particle formation rate, J1.7, is determined at 1.7-nm mobility diameter (1.4-nm physical diameter), here using a PSM. At 1.7 nm, a particle is normally considered to be above its critical size and, therefore, thermodynamically stable. J1.7 is calculated using the flux of the total concentration of particles growing past a specific diameter (here at 1.7 nm), as well as correction terms accounting for aerosol losses owing to dilution in the chamber, wall losses and coagulation. Details were described previously47.

### Nucleation model

The nucleation model is on the basis of the thermodynamic model for H2SO4–NH3 nucleation described in detail previously18,19. It is developed from the general dynamic equations60, to calculate the production and losses for each cluster/particle size to determine the formation rates of the acid–base clusters. For HNO3–H2SO4–NH3 nucleation, we simplify the model simulations by extrapolating nano-Köhler-type activation by nitric acid and ammonia to clusters down to sulfuric acid trimers. Eighty size bins, ranging from one ammonium sulfate cluster to 300 nm, are used to capture the evolution of the size and composition of polydisperse particles.

In brief, we calculate the equimolar condensation flux of nitric acid and ammonia on the basis of the supersaturation of gas-phase nitric acid and ammonia over particle-phase ammonium nitrate39,60:

$${Phi }_{i}^{v}={k}_{{rm{c}}},[{C}_{i}^{v}-{a}_{i},{C}_{i}^{0}]$$

(2)

in which ({Phi }_{i}^{v}) is the net condensation flux of nitric acid or ammonia, with vapour concentration ({C}_{i}^{v}) and saturation concentration ({C}_{i}^{0}). The term ai is the activity of species i at the condensed-phase surface of the particle and kc is the condensation sink for vapours resulting from interaction with particles. The saturation concentrations of nitric acid and ammonia are estimated on the basis of the dissociation constant Kp (ref. 60). When the vapours are unsaturated, particle-phase ammonium nitrate will evaporate to nitric acid and ammonia to reach the equilibrium.

We also include the Kelvin term (Ki,p) in the simulation to account for the increased activity (({a}_{i}={a{prime} }_{i},{K}_{i,p})) of a small curved cluster/particle:

$${K}_{i,p}={10}^{({d}_{{rm{K}}10}/{d}_{{rm{p}}})}$$

(3)

in which Ki,p scales with a ‘Kelvin diameter’ (dK10) for decadal change and dp is the diameter of the small cluster/particle. The Kelvin diameter for ammonium nitrate is estimated to be 5.3 nm by fitting the data from previous CLOUD experiments according to:

$$S={10}^{({d}_{{rm{K10}}}/{d}_{{rm{act}}})}$$

(4)

in which S is the saturation ratio, calculated by means of dividing the product of measured concentrations of nitric acid and ammonia by the dissociation constant Kp and dact is the activation diameter, at which the thermodynamic energy barrier for condensation is overcome and particles start to grow rapidly.

### Determination of ice nucleation ability

During the experiments, aerosol particles were continuously sampled from the CLOUD chamber into the mINKA ice nucleation instrument, using an actively cooled sampling line for a consistent temperature profile. Particles were then subject to well-controlled ice supersaturated conditions; the ones that nucleated ice were selectively detected and counted by an optical particle counter (custom-modified Climet CI-3100, lower detection limit of about 1 μm) located at the outlet of the instrument. Background ice crystals were quantified before each saturation scan (for 2 min) and subtracted from the total ice number concentration of the corresponding measurement. The fraction of INP (fice) was calculated as the ratio of ice crystals number concentration to the total number of particles larger than 10 nm in diameter. The ice nucleation active surface site density (ns)61 was calculated as the ratio of ice number concentration to the total surface area of particles larger than 10 nm in diameter. The overall uncertainty of ns is estimated to be ±40% (ref. 24). Particle number and surface area concentrations were measured by the SMPS described in the ‘Instrumentation’ section.

In Extended Data Fig. 4, we provide a detailed summary of the measurement data recorded during the ‘hotspot condition’ experiment shown in Fig. 4a, in which we investigated the heterogeneous crystallization and ice nucleation ability of ammonium nitrate/sulfate particles produced directly from new particle formation. We first formed pure ammonium nitrate particles through nucleation of nitric acid and ammonia vapours at 223 K and 15–30% relative humidity (over liquid water). When the evolution of the particle size distribution (Extended Data Fig. 4a) levelled off at a median diameter of around 100 nm, we turned on the UV lights and progressively injected SO2 at 03:33 to gradually increase sulfuric acid concentration (Extended Data Fig. 4b). Consequently, in Extended Data Fig. 4c, aerosol mass spectrometer measurements show that particle composition was dominated by ammonium nitrate over the course of the experiment, whereas sulfate appeared approximately 1 h after the injection of SO2. Finally, we show ice nucleation measurements in Extended Data Fig. 4d. Each vertical trajectory represents a saturation ratio scan in mINKA, colour-coded by the measured ice active fraction (fice). In each scan, we use a horizontal black dash to indicate an ice onset threshold corresponding to fice of 10−3. Circles indicate the corresponding scans shown in Fig. 4a.

When the particulate sulfate-to-nitrate molar ratio is smaller than 0.0001, the ice nucleation threshold is detected at an ice saturation ratio (Sice) of about 1.6, consistent with the homogeneous freezing threshold of aqueous solution droplets62. This finding shows that, if particles presented as absolutely pure ammonium nitrate (NH4NO3), they would exist as supercooled liquid droplets even at very low relative humidity, consistent with previous studies22,63. As the particulate sulfate-to-nitrate molar ratio gradually increases to about 0.017, the ice nucleation onset shifts to a lower Sice of 1.2, caused by heterogeneous ice nucleation on crystalline ammonium nitrate particles23. Crystalline salts are known to be efficient INP at low temperatures when their deliquescence occurs at higher relative humidity compared with the humidity range of their heterogeneous ice nucleation activity64. The fact that the addition of sulfate can promote the crystallization of ammonium nitrate has already been observed in previous studies with particles nebulized in large sizes (around 1 μm) from bulk solutions of ammonium nitrate/sulfate6,23,65. But it is evidenced here for the first time in an in situ particle nucleation and crystallization experiment representative of upper tropospheric conditions.

### Particle formation rate parameterization

According to the first nucleation theorem for multicomponent systems25, we parameterize the particle formation rates (J1.7) for the HNO3–H2SO4–NH3 nucleation scheme with the empirical formula:

$${J}_{1.7}=k,{[{{rm{H}}}_{2}{{rm{SO}}}_{4}]}^{a},{[{{rm{HNO}}}_{3}]}^{b}{[{{rm{NH}}}_{3}]}^{c}$$

(5)

in which vapour concentrations are in units of cm−3 and k, a, b and c are free parameters. This method has been validated by previous observations that the particle formation rates (J1.7) vary as a product of power-law functions of nucleating vapours. For example, J1.7 for ternary sulfuric acid, ammonia (and water) nucleation follows a cubic dependency on sulfuric acid8 and a linear8 or quadratic19 dependency on ammonia; J1.7 for multicomponent nucleation of sulfuric acid, biogenic oxidized organics and ammonia follows a quadratic dependency on sulfuric acid, a linear dependency on both organics66 and ammonia11. The prefactor k accounts for effects of external conditions, such as temperature and relative humidity, thus differs in different environments.

To isolate variables, here we fit the power-law exponents for sulfuric acid, nitric acid and ammonia, respectively, to the dataset of experiments in which only the corresponding vapour concentration was varied. The red triangles, blue circles and yellow squares in Extended Data Fig. 5a–c (same experiments in Extended Data Fig. 1, Fig. 1 and Extended Data Fig. 2), respectively, show that J1.7 depends on [H2SO4]3 for sulfuric acid between 2.6 × 105 and 2.9 × 106 cm−3 (or 0.008 and 0.09 pptv), on [HNO3]2 for nitric acid between 2.3 × 108 and 1.7 × 109 cm−3 (or 7 and 52 pptv) and on [NH3]4 for ammonia between 1.7 × 108 and 4.9 × 108 cm−3 (or 5 and 15 pptv). The third power exponent for sulfuric acid is consistent with previously reported parameterizations for ternary H2SO4–NH3 nucleation8,19. The fourth power exponent for ammonia, however, is larger than those in ternary8,19 or multicomponent systems11, which emphasizes the critical role of ammonia and suggests further bonding between ammonia and nitric acid molecules in the nucleating clusters. Next, we verify the exponents by refitting the product of [H2SO4]3, [HNO3]2 and [NH3]4 to the full dataset. Extended Data Fig. 5d shows good consistency (R2 = 0.9) of the parameterization among the three experiments, with a slope of 3.4 × 10−71 s−1 cm24 being the prefactor k:

$${J}_{1.7}=3.4times {10}^{-71}{[{{rm{H}}}_{2}{{rm{SO}}}_{4}]}^{3}{[{{rm{HNO}}}_{3}]}^{2}{[{{rm{NH}}}_{3}]}^{4}$$

(6)

This parameterization is representative of new particle formation in the Asian monsoon upper troposphere because our experimental conditions of 223 K and 25% relative humidity, as well as concentrations of sulfuric acid67,68 and nitric acid69,70, are within the upper tropospheric range, with ammonia5,6 typical of Asian monsoon regions. One caveat, however, is that the cosmic radiation was at the ground level in our chamber, as shown with grey dot-dashed horizontal line in Extended Data Fig. 5d. The ion-pair production rate can be up to ten times higher in the ambient upper troposphere71, potentially leading to further enhancement of J1.7 by ion-induced nucleation, although the neutral channel dominates in our experiments.

### Estimated temperature dependence of the particle formation rate

We did not cover the full temperature range in the upper troposphere, instead focusing on 223 K. However, to make the parameterization in the previous section more applicable for model simulations while not overstating the role of this mechanism, we provide some constraints on the temperature dependence of J1.7 for HNO3–H2SO4–NH3 nucleation. Broadly, it is certain that particle formation involving HNO3 will have a strong temperature dependence, becoming much slower as T increases.

We first present the temperature dependence of J1.7 for pure HNO3–NH3 nucleation with the expression:

$${J}_{1.7}=k(T)f([{{rm{HNO}}}_{3}],[{{rm{NH}}}_{3}])$$

(7)

in which k(T) is an empirical temperature-dependent rate constant and has the Arrhenius form

$$k(T)={{rm{e}}}^{left(-frac{1}{T}frac{E}{R}right)},$$

(8)

in which T is the absolute temperature (in Kelvin), E is the activation energy and R is the universal gas constant. f([HNO3],[NH3]) is a function of the ammonia and nitric acid concentrations (including the pre-exponential factor and free-fitting parameters). This expression is then fitted to the dataset in Fig. 3c in our previous study16, in which J1.7 were measured with only nitric acid, ammonia and water vapours added to the chamber, and the temperature was progressively decreased from 258 K to 249 K. Because the ammonia and nitric acid concentrations were kept almost constant during the temperature transition, we treat the f([HNO3],[NH3]) term as a constant to reduce the degrees of freedom. This expression with its two free parameters leads to a good agreement with the data, R2 = 0.96. And the fitted −E/R and f([HNO3],[NH3]) are 14,000 K and 3.2 × 10−26, respectively.

Next, we apply the same k(T) term to the HNO3–H2SO4–NH3 parameterization (equation (9)), assuming that the multicomponent nucleation follows a similar temperature dependence:

$${J}_{1.7}=2.9times {10}^{-98}{{rm{e}}}^{left(frac{14,000}{T}right)}{[{{rm{H}}}_{2}{{rm{SO}}}_{4}]}^{3}{[{{rm{HNO}}}_{3}]}^{2}{[{{rm{NH}}}_{3}]}^{4}$$

(9)

Although this temperature-dependent parameterization may not be the final description of this process, it tracks the trend of J1.7 well. In the event of 4 × 106 cm−3 H2SO4, 1.5 × 109 cm−3 HNO3 and 5 × 108 cm−3 NH3, the multicomponent nucleation is quenched (J1.7 < 0.01 cm−3 s−1) above 268 K. This is consistent with the observations that nitric acid and ammonia only contribute to the growth of ammonium sulfate particles at 278 K (ref. 16). At 223 K, the parameterized J1.7 is 306 cm−3 s−1, matching our measurement in Fig. 2. And for the temperature in the upper troposphere and lower stratosphere (198 K), the parameterized J1.7 is 8 × 105 cm−3 s−1, which is still much slower than its kinetic limit of about 109–1010 cm−3 s−1.

### The EMAC global model

The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and climate simulation system that includes sub-models describing tropospheric and middle atmosphere processes and their interaction with oceans, land and human influences72. It uses the second version of the Modular Earth Submodel System (MESSy2) to link multi-institutional computer codes. Atmospheric circulation is calculated by the 5th generation of the European Centre Hamburg general circulation model (ECHAM5 (ref. 73)) and atmospheric chemical kinetics are solved for every model time step. For the present study, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.54.0) in the T42L31ECMWF-resolution, for example, with a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of approximately 2.8° by 2.8° in latitude and longitude) with 31 vertical hybrid pressure levels up to 10 hPa. EMAC uses a modal representation of aerosols dynamics (GMXe) that describes the aerosol size distribution as seven interacting log-normal distributions, of which four modes are soluble and three modes are insoluble. New particles are added directly to the nucleation mode. The applied model setup comprises the sub-model New Aerosol Nucleation (NAN) that includes new parameterizations of aerosol particle formation rates published in recent years74. These parameterizations include ion-induced nucleation. The ion-pair production rate, needed to calculate the ion-induced or ion-mediated nucleation, is described using the sub-model IONS, which provides ion-pair production rates74.

### The TOMCAT global model

The TOMCAT model is a global 3D offline chemical transport model75,76. It is run at approximately 2.8° spatial resolution, such as EMAC on a T42 grid, driven by ECMWF ERA-Interim reanalysis meteorological fields for the year 2008. We also used 31 hybrid sigma-pressure levels from the surface to 10 hPa. The dissolved fraction of gases in cloud water is calculated by means of an equilibrium Henry’s law approach and set to zero for temperatures below −20 °C. The model includes GLOMAP aerosol microphysics77 with nitrate and ammonium from the HyDIS solver78 and the representation of new particle formation used by Gordon et al.3. The HyDIS solver adopts a sophisticated approach to the dissolution of nitric acid and ammonia into the aerosol phase that is a hybrid between a dynamic representation of the process, which accounts for the time needed for mass transport, and an equilibrium representation, which does not78. The main limitation of the solver is that it assumes all aerosol particles are liquid, which is probably a poor approximation in cold, dry conditions frequently found in the upper troposphere.

### The cloud trajectories framework

We conducted a sensitivity study on ammonia transport processes and estimated the fraction remaining of ammonia vapour after convection from the boundary layer to the upper troposphere, using a cloud trajectories framework described in detail in Bardakov et al.79,80. In brief, trajectories from a convective system simulated with the large-eddy simulation (LES) model MIMICA81 were extracted and a parcel representing the cloud outflow was selected for further analysis (Extended Data Fig. 8a). The meteorological profiles and clouds microphysics scheme used here were the same as in Bardakov et al.80, producing altitude-dependent distributions of water and ice hydrometeors depicted in Extended Data Fig. 8. Partitioning of gas between vapour and aqueous phase along the trajectory was calculated on the basis of Henry’s law constant adjusted to a cloud pH, H* = H × 1.7 × 10(9−pH) following the expression for ammonia from Seinfeld and Pandis60.

We then investigated the factors governing ammonia transport through the simulated convective system by varying: (1) the pH for the liquid water hydrometeors (Extended Data Fig. 8c); (2) the total amount of water in the system (Extended Data Fig. 8d); (3) the retention of ammonia molecules by the ice hydrometeors (Extended Data Fig. 8e). In our base-case simulation, the pH was assumed to have an altitude-dependent profile, reflecting the higher abundance of acids close to the surface and ranging from 4.5 to 5, in accordance with the representative pH values in the EMAC simulation. The base-case water content was as in Bardakov et al.80 and the ice retention coefficient 0.05 in accordance with Ge et al.13, with no further uptake on ice.

### Atmospheric interpretation

This work focuses on the Asian monsoon region in part because this region is fairly extensive, but also because ammonia concentrations measured in this region are by far the highest in the upper troposphere. Although we frame this synergistic HNO3–H2SO4–NH3 nucleation in a scenario that suits the Asian monsoon upper troposphere, the physics applies more broadly — the colder the conditions are, the more important this mechanism is likely to be. To explore the importance of this synergistic nucleation to the atmosphere, we combine our experimental results, cloud resolving modelling and global-scale chemical transport modelling. On the basis of these constraints, the rate-limiting elements of new particle formation seem to be convective transport of ammonia and the production rate of particles in the mixing zone between convective outflow and the background upper free troposphere; however, confirmation of this will require extensive field and modelling studies.

Generally, nitric acid ranges between about 108 and 109 cm−3 (refs. 14,15) and sulfuric acid between about 105 and 106 cm−3 (refs. 82,83) in the tropical upper troposphere. The typical acid-excess conditions leave the principal uncertainty being ammonia levels, which are not yet well constrained. Although satellite-based ammonia measurements have provided a spatial distribution on a global scale, they are limited to cloud-free areas owing to blockage of the ammonia signal by optically thick clouds. However, deep convection followed by cloud glaciation may be a major source of upper tropospheric ammonia. This process may then not be captured by satellites as it occurs near clouds, with short time duration and high spatial heterogeneity. This may also explain why the in situ-measured ammonia concentrations are up to 40 times higher than those from satellite measurements6.

Ammonia has no known chemical source in the atmosphere but is instead transported by cloud processes from the surface, whereas nitric acid and sulfuric acid vapours are formed primarily by out-of-cloud oxidation. Consequently, it is probable that this synergistic nucleation occurs initially in the outflow of convective clouds, in which the released ammonia mixes with pre-existing (background) nitric acid and sulfuric acid. Subsequently, as ammonia is titrated over several e-folding times (governed by the condensation sink in this mixing zone) and the outflow air fully mixes with the background air, nucleation conditions will shift from the ammonia-rich regime to the ammonia-limited regime. These highly dynamic processes are thus the key to constraining the climatic effects of this synergistic nucleation in Asian monsoon and potentially other convective regions. Nevertheless, current ambient measurements confirm the presence of ample ammonia, as well as particles comprised largely of ammonium nitrate4, and our experiments show that synergistic HNO3–H2SO4–NH3 nucleation is a viable mechanism for new particle formation in the Asian monsoon upper troposphere. As global ammonia emissions continue to increase owing to agricultural growth and the warmer climate84,85, the importance of this particle formation mechanism will increase.

Further, as there is almost no in situ composition measurement of clusters or newly formed particles in the upper troposphere, we can only infer the major particle formation pathway from indirect evidence such as composition of precursor vapours or larger particles. Previously established mechanisms include binary and ternary sulfuric acid nucleation, which drive new particle formation over marine or anthropogenically influenced regions1,4,86,87, nucleation by oxygenated organics, which dominates over pristine vegetated areas such as the Amazon basin2,10,88, and nucleation by iodine oxidation products, which may be especially important in marine convection89,90. Over the Asian monsoon regions, however, mixed emissions of both inorganic and organic vapours may well complicate the particle formation mechanism. However, it has been demonstrated that ammonium nitrate can often explain more than half of the particulate volume in the upper troposphere6. This means that the HNO3–NH3 concentration is probably higher than the sum of all other condensable vapours (that is, sulfuric acid and oxygenated organics). And given that HNO3–H2SO4–NH3 nucleation is orders of magnitude faster than binary and ternary sulfuric acid nucleation at observed ammonia levels, we therefore infer that synergistic HNO3–H2SO4–NH3 nucleation is a major particle formation pathway in the Asian monsoon upper troposphere. It seems unlikely that this inorganic pathway and the organic pathways are antagonistic in growth, and without strong indications otherwise, it seems probable that they are more or less additive for nucleation itself. However, to further investigate interactions between different nucleation schemes, we would rely on further information on the source and identity of organic vapours that are present in the Asian monsoon upper troposphere.