Isoprene nitrates drive new particle formation in Amazon’s upper troposphere

The CAFE-Brazil mission took place in Brazil between 30 November 2022 and 29 January 2023, which covers the end of the dry-to-wet season transition and the beginning of the wet season in the Amazon. The German High Altitude and Long Range Research Aircraft (HALO) was stationed at Manaus International Airport, conducting a total of 16 local research flights (143 flight hours), as well as the transfer flights between Germany and Brazil (26 flight hours). An overview of the flight tracks is shown in Extended Data Fig. 1a. The research flights, at altitudes between 0.3 and 13.8 km, covered the region from 11° 33′ S to 4° 40′ N and from 72° 33′ W to 33° 50′ W. The aircraft was equipped with instrumentation to measure the in situ concentration of trace gases, radicals, aerosol number concentration and several aerosol physical and chemical properties. Descriptions of the methods used for the detection of the gas compounds and aerosol properties are given here.

CI-APi-TOF mass spectrometer

The CI-APi-TOF mass spectrometer^56,57 measures gaseous molecules that can contribute to NPF (that is, aerosol nucleation and initial growth up to detectable particle size). Gases such as isoprene oxidation products (IP_0,1,2N), methanesulfonic acid (MSA) and sulfuric acid are detected. The instrument was specifically designed and certified for aircraft use and it is optimized for low inlet losses, a constant ionization pressure and minimal internal gas consumption.

The CI-API-TOF mass spectrometer uses a trace-gas inlet initially developed to measure OH radicals. It is almost identical to the inlet used for the HydrOxyl Radical measurement Unit based on fluorescence Spectroscopy (HORUS) instrument. The sampling location is placed at a sufficient distance from the fuselage to avoid the influence of the aircraft’s boundary layer. The inlet uses a set of shrouds and a flow restrictor to decelerate the air by a factor of 10 to around 25 m s⁻¹ before sampling into the inlet line to reduce turbulence⁵⁸. The flow restrictor, however, also causes a ram-pressure effect and thus adiabatic heating of the sample air depending on ambient pressure and air velocity, which will be discussed below in more detail.

The sampling line consists of a 20.5-mm inner diameter 1.8-m-long stainless-steel tube with an 8-mm orifice at the beginning (located in the centre part of the inlet). The sampling line has two bends with radii of about 120 and 500 mm, respectively, to enable installation close to the cabin wall. The inlet line is thermally insulated and has a temperature sensor 300 mm downstream of the sampling position inside the inlet. The sample flow is kept constant at 25.0 slpm for all altitudes to reduce wall losses, while still being in a laminar flow regime.

At the end of the sampling tube, the air reaches the SCORPION (Switchable Corona Powered Ion Source), which consists of a pressure-control and an ionization stage. The pressure-control stage comprises two sequentially placed and conically shaped orifices with 1.4 mm inner diameter each. Between these two orifices, a PID-controlled solenoid regulation valve allows for variable pumping, which provides a constant pressure of 200 hPa in the ionization region. The ionization region is located directly after the second orifice. It consists of a 20.5-mm inner diameter stainless-steel tube and two orthogonally attached ion source units, of which only one is used at any given time. The ion source uses a corona discharge to produce (HNO₃)_0,1,2NO₃⁻ reagent ions from gaseous HNO₃. Because a corona discharge also produces OH radicals, which could alter the chemical composition of the sample air, we implemented a counter-flow regime, such that the nitrate reagent ions are pushed towards the sample air by means of an electric field, whereas the gas flow, which also carries OH radicals, is directed away from the sample air towards the exhaust.

The nitrate reagent ions are mixed with the sample air and travel along the main drift tube (130 mm length) with a reaction time between 180 and 350 ms, depending on altitude. Although the ionization pressure is kept constant at 200 hPa, the flow along the drift region varies between 2.7 slpm at ground level and 1.4 slpm at 12 km altitude, causing different reaction times. The higher flow at lower altitudes is needed to maintain the ionization pressure at 200 hPa with the given orifice diameters. Although the reaction times are around 3–5 times longer than in an Eisele–Tanner-type ion source⁵⁹ (about 50 ms), the ionization pressure is also lower by a factor of 5, leading to a roughly comparable number of collisions between reagent ions and sample gas. However, because of the extra orifices in the pressure stage and a relatively long inlet line, the overall sensitivity of SCORPION is lower by about one order of magnitude compared with a nitrate reagent ion long time-of-flight (LTOF) mass spectrometer instrument as deployed, for example, at the CLOUD chamber^42,43. The detection limit for SCORPION is between 5 × 10⁵ and 5 × 10⁶ cm⁻³.

At the end of the SCORPION drift tube, the ions enter the Tofwerk time-of-flight mass spectrometer by means of a 350-µm inner diameter orifice. We use an HTOF with a resolution of around 4,000 at the m/z range 250–300 amu. The data are recorded at 1 Hz; however, it is averaged to 10 s resolution before post-processing and high-resolution peak fitting in Tofware (version 3.2.5, Aerodyne).

To derive the ambient concentrations of IP_0,1,2N, several pressure-dependent and temperature-dependent correction factors have to be applied to the fitted peak intensities as follows:

Here (IP_0,1,2N)_cps represents the fitted peak intensities in counts per second. Tr(m/z) is the m/z-dependent correction factor for the relative change in instrument transmission efficiency⁶⁰. For the IP_0,1,2N m/z range, this correction is about 10–20%, depending on the exact m/z ratio.

A pressure-dependent calibration factor is applied to the normalized signal (at 12.2 km altitude, C_230hPa = 6.5 × 10¹⁰ cm⁻³, whereas at ground level, C_1000hPa = 2.1 × 10¹¹ cm⁻³). This calibration factor was experimentally estimated for gaseous sulfuric acid by generating a known amount of gaseous sulfuric acid by means of ultraviolet (UV)-induced OH production (from photolysis of H₂O) and subsequent oxidation of sulfur dioxide⁶¹ to sulfuric acid⁶². We constructed a dedicated calibration rack for the CI-APi-TOF mass spectrometer, similar to that described in ref. ⁶². The calibration unit can be operated at pressures between 200 and 1,000 hPa.

After applying the calibration factor, a background correction of the signal is performed (BG). Background measurements were performed in flight by overflowing SCORPION with synthetic air from the internal gas bottle. This can, however, only be done above 9 km altitude, as at lower altitudes more gas would be needed to overflow the ion source than provided by the internal gas bottle. Typically, 2–3 background measurements are performed per flight, each lasting 10 min.

The factor I(p_i, T_i, F_i) represents the correction for losses to the wall in the 1.8-m-long sampling line and depends on inlet pressure p_i, inlet temperature T_i and inlet flow F_i. It is based on the parametrization for straight tube losses and thus ignores the two curves in our inlet tube. The inlet loss estimation uses the experimentally determined diffusion coefficient for gaseous sulfuric acid and its pressure-dependent and temperature-dependent parametrizations⁶¹. The inlet correction factor is about 1.65 for a typical high-altitude flight scenario (12 km altitude).

The correction factor A(p_a, p_i, T_a, T_i) scales the concentration levels from inlet temperature T_i and pressure p_i conditions to ambient temperature T_a and pressure p_a conditions. This scaling is necessary as the ram pressure caused by the flow restrictor increases the inlet pressure compared with ambient conditions (at 12.2 km altitude, at which most of research flight (RF) 19 was flown from 188 hPa ambient pressure to 268 hPa inlet pressure). This pressure increase also induces an adiabatic heating of the sampling air. Further heating comes from the limited thermal insulation of the inlet line. At 12.2 km altitude, we measure a temperature increase from −58 °C (ambient) to −13 °C (inlet), so ΔT = 45 °C. Although the inlet residence time at these conditions is rather short (0.38 s), this temperature increase could lead to the evaporation of molecules from the aerosol to the gas phase, which could enhance our measured gas-phase signals. At −58 °C, the main IP_0,1,2N products are ELVOCs, whereas they shift to the low-volatility organic compounds range at −13 °C (Fig. 3). Especially for freshly nucleated particles with diameters in the size range in which the Kelvin effect has a role, this could cause evaporation. Therefore, the measurements are considered to be a combination of pure gas-phase concentration and potentially re-evaporated aerosol-phase molecules. However, even if a large fraction of our signal would originate from evaporation of freshly nucleated particles, this still highlights the crucial role of isoprene-derived oxidation products for the NPF process in the upper troposphere over the Amazon.

The measurement of sulfuric acid was affected by a sulfur contamination inside the stainless-steel vessel containing the liquid HNO₃ supply of the ion source. This led to an increased instrumental background for sulfuric acid of about 2 × 10⁶ cm⁻³ for our measurements at altitudes above 8 km.

The overall uncertainty of the CI-APi-TOF measurements is ±62%. This consists mainly of the uncertainty of the sulfuric acid calibration factor of 55%, as well as the uncertainty of the mass-dependent transmission correction (20%) and the inlet loss correction (20%). No calibration standards are available for the measurement of ELVOCs from isoprene or monoterpenes. Therefore, we use the same calibration factor as determined for the sulfuric acid measurements. The sensitivity of the CI-APi-TOF instrument is high for the detection of highly oxidized organics with many functional groups, for example, HOMs from monoterpenes. For those, this approach is well established⁴², but the CI-APi-TOF instrument is expected to be less sensitive for the smaller IP-OOMs, especially when the molecules contain few oxygen atoms. This general dependence is confirmed by the comparison of nitrate reagent ions with, for example, bromide or iodide reagent ions⁴¹. The concentrations of the isoprene oxidation products detected by the CI-APi-TOF mass spectrometer should therefore be considered as lower limits. Compared with the IP_0N, IP_1N and IP_2N reported in ref. ⁴⁴, the CI-APi-TOF instrument will detect smaller fractions of these compound classes, as more mass spectrometers using other reagent ions are used in ref. ⁴⁴ to complement the IP_0,1,2N measurements. Nevertheless, the relative changes of individual compounds over time, as shown, for example, in Extended Data Fig. 5, are not affected by this effect.

We also apply the calibration factor estimated for sulfuric acid to derive the concentration of IP_0-2N, as a direct calibration for IP_0-2N is not possible. It was shown that HOMs with sufficient oxygen content, that is, a sufficient number of functional groups to cluster with NO₃⁻, are charged with nitrate reagent ions at the kinetic limit, similar to sulfuric acid^41,63. Riva et al.⁴¹ conducted a detailed comparison of various reagent ions and their respective sensitivities towards pure organic as well as nitrate HOMs derived from monoterpene oxidation. They found that both nitrate and non-nitrate HOMs can be charged by NO₃⁻ reagent ions at the kinetic limit as long as HOMs contain more than six oxygen atoms in the non-nitrate case and more than seven oxygen atoms in the nitrate case. Assuming that these results are transferable to IP_0-2N, this means that some of our reported IP_0-2N could be charged below the unit charging efficiency of the kinetic limit. This leads to an increase in calibration factor for these species and our reported concentrations represent a lower limit estimation, especially for low-oxygen-content IP_0-2N.

Aerosol number concentration and nucleation-mode particles

The Fast Aerosol Size Distribution (FASD) instrument is a compact multichannel system to detect newly formed particles. It was developed specifically for operation aboard the HALO aircraft. The system combines the concept of well-established commercial ultrafine condensation particle counters⁶⁴ (CPCs) with central temperature management, central butanol vapour supply, central pressure control and a new type of flow system. The prototype, designed and built at the Max Planck Institute for Chemistry (MPIC), simultaneously measures aerosol concentration in ten channels every second. The ten-channel device is about the size of two commercial ultrafine CPCs. Similar aircraft-based instruments use several CPCs^65,66,67.

For each CPC channel, the sample air is fed by means of a short (6 mm) capillary into a heated mixing chamber, surrounded by particle-free butanol-rich sheath air and fed into the cold condensation region. The supersaturated butanol condenses on the aerosol particles, causing them to grow sufficiently to be detected in a downstream optical particle counter. To minimize diffusional losses, all channels share a central sample line with a distance of only about 38 mm between adjacent inlets and the inlet capillaries protrude into the core sample flow.

The FASD instrument gradually reduces the butanol content of each sheath flow in a dilution chamber between the saturator and the channels. The exhaust air from each channel is collected and cleaned of particles by a HEPA filter and returned to the saturator and dilution stage by a central pump. There is a total of four pressure stages in the sheath flow loop, with the highest pressure in the saturator and the butanol dry air upstream of the dilution. Two valves control the saturated and dry air flow ratio into the dilution chamber. Although the saturated air is introduced at a single point, the dry air flow is split to replenish the air flowing to each channel. The mixing, condensation and detection areas of each channel are close to the ambient pressure level in the inlet and outlet lines. Finally, the lowest pressure is upstream of the sheath flow pump and also drives the removal of butanol that condenses on the walls of each condenser. This butanol is collected in a reservoir and can be reused as normally no water vapour condenses.

A valve controls the total sample flow. This valve allows some air to leave the sheath flow loop from the dilution stage to the exhaust line. In total, an equal amount of air enters through the short inlet capillary of each channel. Another valve sets the desired flow through the dilution stage and allows some air to flow directly from the end of the dilution stage to the sheath flow pump. Flow uniformity is achieved by carefully selecting the flow resistances, which results in pressure differentials between stages in the range 10–20 hPa. The condenser sections are cooled to a target temperature of 10 °C by a water cooling system. The waste heat is transferred from the cold water cycle to the hot water cycle through Peltier elements, in which the heat is eventually released to the ambient air through an external radiator. To avoid unwanted butanol condensation, it is essential that the dilution chamber and the individual sheath flow transfer lines and mixing chambers of each channel maintain temperatures above the saturator temperature. This is achieved by heating the saturator indirectly, while keeping the other parts actively warm, resulting in a permanent temperature gradient that prevents unwanted condensation.

The particle activation is determined by the temperature difference between condensation and saturation, the pressure differentials and the dilution factor. By measuring the activation curves under given conditions and comparing them with theoretical calculations, the activation behaviour can be derived for fluctuating measurement conditions⁶⁵. Initial measurements of selected particle sizes in the range 2–30 nm show that the performance of the first channel of the prototype is comparable with a commercial ultrafine CPC, whereas the measured values of the other channels fit to an effective dilution to around 75% per channel.

Although diffusional losses between the channels are not apparent, the final calibration requires further measurements^65,67. Therefore, for this study, the theoretical cut-off diameters are obtained using Kelvin’s equation⁶⁸ with a dilution of 75% per stage. For each measurement time step, the corresponding particle activation diameters can be calculated from the actual temperatures and pressure differences and are typically in the range 2–6 nm. Measurement periods without NPF events can be used to determine systematic deviations of sample flows owing to slight variations in flow resistances. To keep the measurement conditions of the channels stable, regardless of changes in ambient pressure, the FASD instrument is operated at a constant pressure of typically 200 hPa. The pressure control is achieved by continuously calculating the net flows in and out of the FASD instrument based on flow controller and pressure sensor data. The calculation results are used to drive two PID controllers that regulate the outflow by using a mass flow controller and the inflow by using a custom-made size-changing orifice⁶⁹.

Proton transfer reaction time-of-flight mass spectrometry

A proton transfer reaction time-of-flight mass spectrometer^46,70,71 (PTR-TOF-MS 8000, Ionicon Analytik) was used for the fast high-mass-resolution airborne measurements of VOCs (m/z < 500 amu). Isoprene, its oxidation products including methyl vinyl ketone, methacrolein and isoprene hydroxyhydroperoxide, and total monoterpenes reported in this study were measured at m/z = 69.069, 71.049 and 137.132 amu, respectively. In this technique, hydronium ions (H₃O⁺) are used as a reagent to ionize molecules in air that have a higher proton affinity than water (693 kJ mol⁻¹). The instrument was operated with a drift pressure of 2.2 mbar and an E/N of 137 Td. Air was drawn from outside the aircraft to the instrument through a fuselage-mounted inlet housing, in a heated 2-m-long, 0.64-cm outer diameter Teflon inlet line. Quantification of the detected compounds was performed by frequent in-flight background determinations with zero air and several ground-based calibrations using a gravimetrically prepared gas standard containing isoprene, methyl vinyl ketone and α-pinene (Apel-Riemer Environmental). At a time resolution of 1 min, the detection limit (3σ) was calculated to be 100, 41 and 25 pptv for isoprene, its oxidation products and total monoterpenes, respectively. An ozone correction for isoprene was applied on the basis of laboratory experiments and comparison with the gas chromatography–mass spectrometry data. The total uncertainty of measurement was usually below 25%. Further detailed information about the proton transfer reaction time-of-flight mass spectrometry used is given ref. ⁷², its response to atmospheric ozone in ref. ⁷³ and the configuration in the aircraft is described in ref. ⁷⁴.

Gas chromatography–mass spectrometry

VOCs were measured in situ using a customized gas chromatograph coupled to a commercial quadrupole mass spectrometer (Agilent Technologies 5973 MSD). The system has been described in detail previously⁷⁵ and its configuration in the aircraft payload for the CAFE-Brazil campaign is given elsewhere⁷⁴. In brief, ambient air is drawn at 200 scm³ through the Trace Gas Inlet (TGI, Enviscope) to the instrument by means of a heated 2-m-long Teflon line (0.6 cm outer diameter) equipped with a sodium thiosulfate ozone scrubber⁷³. Within a series of traps in a liquid-nitrogen-cooled cryo-concentrator, the sampled air is dried (−10 °C), enriched for VOCs (−160 °C) for 1 min and then concentrated into a small volume (−160 °C) before being rapidly heated to inject the sample into the gas chromatograph. The compounds are separated by a DB-624 UI, 10 m, 0.25 mm, 1.4 µm capillary column (Agilent Technologies). The temperature programme of the custom-built gas chromatograph oven is as follows: 30 °C for 50 s, then 30 °C to 200 °C at 1.8 °C s⁻¹ and constant 200 °C for the rest of the chromatogram. After separation, the compounds are electronically ionized (70 eV) and detected by the mass spectrometer in the selected ion mode. In the configuration used for the CAFE-Brazil campaign, more than 35 compounds could be resolved and quantified in a 2.4-min chromatogram, the overall measurement frequency being 3 min. Calibration was achieved using a gravimetrically prepared multicomponent pressurized standard (Apel-Riemer Environmental), with a stated accuracy of 5%, with calibrations being performed before, during and after each flight. Isoprene was detected at m/z = 67 amu and a retention time of 0.7 min with a detection limit of 5 pptv and an uncertainty of about 10%.

NO_x measurements

Nitrogen oxides were measured through photolysis chemiluminescence with the two-channel instrument Nitrogen Oxides Analyzer for HALO (NOAH). In one channel, nitric oxide (NO) is converted to excited-state nitrogen dioxide (NO₂*) by reaction with excess amounts of ozone (O₃). A photon is emitted during de-excitation of NO₂*, which is detected by a photomultiplier tube. The signal is converted to ambient NO mixing ratios using normal on-ground calibrations between the flights. The second channel is identical except for using a photolytic converter, in which NO₂ is photolysed to NO at a wavelength of around 395 nm before the addition of O₃. The conversion efficiency of the converter (the fractional conversion of NO₂ to NO) was 29% during the CAFE-Brazil campaign. Owing to enhanced temperatures in the instrument and the photolytic converter, NO₂ reservoir species, mostly methyl peroxy nitrate, can release NO₂. Therefore, the NO₂ measurement represents a sum of NO₂ and thermally labile nitrates and represents an upper limit of the NO₂ mixing ratios at night-time. For the day-time data, we use NO₂ derived from the photostationary state (inferred from NO, O₃ and j(NO₂)) in this study instead (Extended Data Fig. 2). The 1 Hz detection limit for NO is 8 pptv and the overall measurement uncertainty is 5%. A detailed description of the instrument is presented in refs. ⁷⁶,⁷⁷. Details on the thermal decomposition of NO₂ reservoir species in photolytic converters and resulting interferences can be found, for example, in refs. ^77,78,79.

HO_x measurements

The airborne HORUS instrument is based on the Fluorescence Assay by Gas Expansion–Laser-Induced Fluorescence of OH (FAGE-LIF) instrument as described in detail in ref. ⁸⁰. It was developed specifically for operation on the HALO research aircraft and combines an external inlet shroud with an in-flight calibration system, OH and HO₂ detection axes, a laser system and a vacuum system. The OH is drawn into the detection axis through a critical orifice at a pressure range of 300–1,300 Pa, depending on ambient pressure. It is selectively excited on the Q1(2) transition line (A2Σ +−X2Π, ν′ = 0, ν″ = 0) by a 3-kHz pulsed UV laser light around 308 nm. The UV laser emission wavelength is periodically tuned on and off resonance of the OH Q1(2) transition to quantify the fluorescence background. An inlet pre-injector (IPI) system is installed to remove atmospheric OH to measure the chemical OH background signal. The airborne IPI system has been redesigned to fit within the inlet shroud system, while maintaining similar operational features as the on-ground IPI installation⁸¹.

HO₂ is measured indirectly through the quantitative conversion of atmospheric HO₂ to OH by injection of NO within HORUS.

With excess amounts of NO used in the conversion of HO₂ to OH, subsequent HONO formation has to be taken into account.

The losses resulting from internal HONO formation are dependent on pressure and amount to less than 1% above 10 km and less than 2% at ground level.

We account for the reaction of RO₂ with NO leading to HO₂ formation, which then generates OH in the presence of NO. We reduce the NO addition to limit the contribution of RO₂ to the detected OH levels. The instrument operates in two modes during flights: one with a low NO addition, creating an internal NO concentration of 1.5 ± 0.1 × 10¹³ cm⁻³ and achieving a conversion rate of 20–40% depending on altitude, and another with a high NO addition of 7 ± 0.1 × 10¹³ cm⁻³, reaching a conversion rate of more than 95%. Furthermore, NO titrations are conducted at different altitudes to ensure accurate measurement of the HO₂ contribution. The HORUS instrument 1σ accuracy is ±22.6% for OH and ±22.1% for HO₂. Precision depends on ambient pressure and instrument performance.

Aerosol mass spectrometer

The composition of non-refractory aerosol particles in the diameter range approximately 50–800 nm was measured using a compact time-of-flight aerosol mass spectrometer (C-ToF-AMS)^82,83. The instrument samples the aerosol particles by means of a constant pressure inlet and an aerodynamic lens into the vacuum system. The particles are flash vaporized on a 600 °C surface and the resultant gas-phase molecules are ionized by electron ionization. The ions are analysed by a time-of-flight mass spectrometer. The C-ToF-AMS has been operated on HALO since the ACRIDICON-CHUVA campaign in 2014, which also took place over the Amazon rainforest³¹.

Other measurements

Carbon monoxide was measured with the quantum cascade laser absorption spectrometer TRISTAR with a mean total measurement uncertainty of 3.5% (refs. ^84,85).

Upward and downward spectral actinic flux densities in the range 280–650 nm are measured by combinations of two CCD spectroradiometers^86,87.

The Fast AIRborne Ozone (FAIRO) instrument measures ozone with high temporal resolution (10 Hz). It combines two independent techniques, UV photometry and chemiluminescence detection⁸⁸.

Data from the Basic HALO Measurement and Sensor System (BAHAMAS) are used for determination of the aircraft position, wind velocity and direction, humidity, temperature and pressure⁸⁹.

Trajectory calculations

Quasi-Lagrangian sampling periods during HALO flights were identified in Fig. 1 (marked by grey shading) using the flight measurements in combination with backward trajectories as described in the following.

The sampling period with the highest number of N_2–5 particles (light-red shading in Fig. 1 (T9)) was chosen as the reference period, with its limits defined as 10:05:46 and 10:10:30 local time. During this sampling period, HALO covered a distance of 62.2 km, which becomes relevant during the final computational step determining the quasi-Lagrangian sampling periods. To identify time intervals earlier during the flight in which approximately the same air mass as during the reference period was examined, backward trajectories were calculated for a set of ten parcels. These were initialized at HALO’s instantaneous location every 30 s (at 0 s and 30 s times) during the reference period. We used a simple Euler scheme with a 30-s time step to calculate the trajectories. We further assumed a constant wind velocity for each trajectory. The wind speed and direction were based on HALO measurements at the parcel initialization time. Vertical movements were not considered. These computations result in an m × 10 matrix containing the ten position vectors of the parcels initialized at HALO’s location during the reference period (p₁, p₂,…, p₁₀) at each historical time (t_i, t_i − Δt,…, t_i − (m − 1)Δt). We then calculated the Euclidean distance from each parcel to HALO’s location (in km), at each location along the trajectories. This distance is always computed with respect to HALO’s instantaneous position at the equivalent time. Finally, the quasi-Lagrangian intervals highlighted by the grey shading in Fig. 1 (T1–T8) were determined by selecting time periods along the backward trajectories for which the mean distance from the parcels to HALO was less than the sampling distance of the reference period (that is, 62.2 km).

The trajectories shown in Fig. 2 were computed using the above described method, but instead initializing 1-min-spaced parcels between 08:05 and 08:15 local time.

It should be noted that the calculated trajectories involve uncertainties, mainly because of the assumption of constant wind speed and the neglect of vertical velocity. However, tests, in which further backward trajectories were computed from each semi-Lagrangian time interval itself (not shown), indicate that the time-dependent changes in wind speed from one phase of the flight pattern loop to another did not substantially affect the estimates of the air-mass location. This indicates that we may use the approximation of constant horizontal wind speed on the spatio-temporal scales analysed for this specific flight. Also, convective clouds typically induce atmospheric gravity waves in their surroundings. Consequently, air parcels expelled by convective outflows may oscillate in the vertical dimension during horizontal displacements, remaining close to the outflow level for a few hours. Thus, vertical errors in parcel location are expected to be within a range smaller than the spatial extent of the air mass in which NPF was identified (about 62 km). We thus argue that neglecting the vertical velocity component serves as a reasonable proxy for the air-mass locations before the measurements in the near outflow proximity, in the absence of sufficiently accurate time-dependent vertical wind-speed data. This assumption also immediately breaks down when the backward trajectories come in contact with active convection.

Given the absence of a true value to evaluate parcel trajectories at this scale (note that atmospheric models provide time-dependent three-dimensional wind velocities, but these are highly sensitive to the representation of the location and structure of convective storms, making them unsuitable for this type of high-resolution analysis), the final validation should come from the tracer measurements themselves. The strong agreement between this trajectory analysis and the in situ measurements is reassuring and provides some validation of the conclusions presented here. Note that, during T8, only small amounts of N_2–5 particles and IP_0-2N were found, indicating that, at this time, the centre of the NPF air mass had probably moved north of section BC of the flight track (Fig. 2).

Identification of NPF

To identify a NPF event, we conservatively assumed a measurement uncertainty of 30% for each channel of the FASD instrument (including statistical uncertainty, drifts in the flows and other systematic uncertainties). The difference between N₂ and N₅ is classified as a NPF event if 0.7N₂ − 1.3N₅ > 0 cm⁻³ (refs. ^28,66).

Condensation sink

The condensation of a vapour to aerosol particles is described by the CS (ref. ⁹⁰). For vapours of ultralow or extremely low volatility, the condensation to pre-existing large particles competes with the NPF process. The size distribution of the aerosol is crucial for determining the CS. An Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) was generally used in combination with the FASD CPC measurements to determine the aerosol size distribution in the size range 60–1,000 nm, but for RF 19, the UHSAS was not operational. Therefore, we performed a rough estimation of the range of the upper limit of the CS by assuming that all aerosol particles measured by the 5-nm FASD channel N₅ have a size of 20, 50 or 100 nm. These three estimates are given in Extended Data Figs. 2 and 3. Before and outside the NPF events, the 50-nm or 100-nm assumptions give a reasonable range (compared with the other research flights when the UHSAS was operational), whereas during the NPF events, the <20-nm assumption is more likely to be correct.

Saturation vapour pressure

The SIMPOL model is used to obtain an estimate of the temperature-dependent saturation vapour pressures C_i* for the isoprene oxidation products⁴⁹ (Fig. 3). SIMPOL is based on the group-contribution method, in which the number of functional groups of an organic molecule determines its saturation vapour pressure. For the SIMPOL-derived saturation vapour pressures, an uncertainty of one order of magnitude in the volatility distribution is assumed⁴³. The saturation ratio S_i* of a compound can be determined by calculating S_i* = [c_i]m_i/(N_AC_i*), with [c_i] denoting the concentration of compound c_i and m_i its molecular mass. The saturation ratio, S_i*, of a compound can then be compared with estimates of the Kelvin diameters beyond which condensation is favoured over evaporation (Extended Data Fig. 3).

Comparison of CAFE-Brazil results to the CLOUD laboratory measurements of Shen et al.

Shen et al.⁴⁴ report laboratory measurements from the CLOUD chamber that investigate the role of isoprene for NPF at cold upper troposphere conditions (around −30 and −50 °C) with and without NO_x. For isoprene + NO_x conditions at −48 °C, they report an IP-OOMs distribution (Fig. 3d in ref. ⁴⁴) that is similar to the one we report for our atmospheric measurements (Fig. 3a and Extended Data Fig. 9). Note that the figure in ref. ⁴⁴ shows not only IP-OOMS data from a NO₃⁻ reagent ion CIMS similar to the CI-APi-TOF used in our study, but, in addition, data from IP-OOMs measured by further mass spectrometers using NH₄⁺ and Br⁻ reagent ions. This extends the range of detected compounds towards higher volatility compounds with lower oxygen content^41,44. These extra compounds are not expected to drive nucleation on their own but may contribute to the growth of newly formed particles after they have reached the respective Kelvin diameter. Comparing only the NO₃⁻ reagent ion data, the CLOUD data match our mass-defect plot (Extended Data Fig. 9). Nitrates, especially dinitrates, dominate the range in both cases. In ref. ⁴⁴, the NO₃⁻-CIMS measurement shows an even stronger dominance of nitrate IP-OOMs than our study. The highest peak in our study (C₅H₁₀N₂O₈) is the second highest peak in ref. ⁴⁴, whereas the highest peak found by Shen et al. is the closely related C₅H₁₀N₂O₉, which can be formed by low-temperature RO₂ reaction with NO₂ instead of NO (ref. ⁴⁴). This is more likely in CLOUD as it was operating at a higher NO₂/NO ratio owing to lower NO₂ photolysis rates in CLOUD compared with the upper troposphere over the Amazon during daytime (CLOUD: NO₂/NO ≈ 3.1; CAFE-Brazil, RF 19, T9, NO₂/NO ≈ 1.1; Extended Data Fig. 9 and Extended Data Table 1). Nevertheless, there is good overall agreement between the spectra recorded in CLOUD and our study.

Shen et al.⁴⁴ report that non-nitrate IP-OOMs are more effective for nucleation than nitrate IP-OOMs, which can be seen from lower nucleation rates at comparable concentration (extended data figure 5 in ref. ⁴⁴). Even with the lower nucleation efficiency for isoprene nitrates, the authors still measured notable nucleation rates at −48 °C in a nitrate-IP-OOMs-dominated experiment (J_1.7 ≈ 4 cm⁻³ s⁻¹ for 2 × 10⁸ cm⁻³ of IP_1-2N) with a gas-phase IP-OOMs spectrum similar to the one we report, as discussed above. Furthermore, figure 3c in ref. ⁴⁴ confirms that nitrate-IP-OOMs do participate in initial cluster formation. The authors also state that the role of nitrates for nucleation could increase at colder temperatures, as encountered during our flights (−58 °C for RF 19). They report a more than 100-fold increase in nucleation rate for isoprene + NO_x conditions when the temperature is reduced from about −30 to −50 °C. Given the observation that, at −50 °C, nitrate-IP-OOMs are weaker nucleators than non-nitrate-IP-OOMs, which means that they do not nucleate at the kinetic limit at −50 °C, it is plausible that the nitrate-IP-OOMs-driven nucleation rate increases when the temperature is reduced from −50 °C to −58 °C. Although the CLOUD experiment could only measure as cold as −50 °C, the expected increase in nucleation rate at colder temperatures leads to a good agreement with the NPF rate of 20 cm⁻³ s⁻¹ for a concentration of 2.7 × 10⁸ cm⁻³ of IP_1-2N reported here. We note that, even if nitrates dominate the IP-OOMs spectra, we do not rule out an important contribution of non-nitrates to the initial steps of cluster formation and nucleation.

Overall, the results of the Shen et al.⁴⁴ laboratory study agree with the nitrate-dominated IP-OOMs spectra that were measured in the upper troposphere over the Amazon. Taking into account the lower temperatures during our flights, the formation rates measured in the laboratory for isoprene + NO_x conditions are comparable with those estimated in our study.

The probable reason for why nitrate IP-OOMs are much more prevalent than non-nitrate-IP-OOMs is that the presence of isoprene and NO_x in the upper troposphere over the Amazon region is intrinsically coupled through deep convection, as isoprene is transported rapidly from the boundary layer to the upper troposphere, and NO_x is produced by lightning. Both isoprene and NO_x accumulate during the night. After sunrise, photolysis leads to the production of OH and NO (with NO presence enhancing OH recycling as well). OH and NO then trigger isoprene oxidation and the corresponding RO₂ termination reactions that lead to the reported nitrate-dominated IP-OOMs spectra and NPF events.