Main

Nitrogen oxides (NOx = NO and NO2) are essential in the formation of secondary aerosol and atmospheric oxidants, such as ozone (O3) and hydroxyl radicals (OH)1. Nitric acid (HNO3) is a major oxidation product of NOx. The formation of HNO3 has traditionally been considered to be a permanent sink of NOx owing to the small photolysis frequency of gaseous HNO3 and to its rapid removal from the troposphere by wet and dry deposition1. However, this traditional view has recently been challenged by laboratory studies demonstrating that photolysis of surface-adsorbed HNO3 is enhanced by one to four orders of magnitude, compared to gaseous HNO3 and aqueous nitrate, with NOx and nitrous acid (HONO) as products5,6,7,8. Field observations have provided further evidence that photolysis of HNO3 adsorbed on the forest canopy surfaces is the primary daytime HONO source for the overlying atmosphere9. Model simulations that include HONO observations or photolytic HONO formation mechanisms have substantially improved estimates of atmospheric oxidant formation12,13. However, it remains unknown whether photolysis of particulate nitrate (pNO3) contributes to the HONO and NOx budgets and affects the formation of oxidants and secondary aerosol.

The Nitrogen, Oxidants, Mercury and Aerosol Distributions, Sources and Sinks (NOMADSS) field study was conducted in the summer of 2013 aboard the NSF/NCAR C-130 aircraft. One objective was to investigate the role of pNO3 photolysis in reactive nitrogen cycling. Two research flights in particular, RF14 on 5 July 2013 and RF16 on 8 July 2013, involved similar flight tracks in the marine boundary layer (MBL) and the free troposphere over the North Atlantic Ocean (flight tracks from 33° 39′ N, 77° 42′ W to 32° 11′ N, 77° 41′ W). The flight periods in the MBL and the free troposphere over the Atlantic Ocean took place between 12:00 and 15:00 Eastern Standard Time (equivalent to Coordinated Universal Time (utc) minus 5 h). The solar elevation angle during the flight legs in the MBL for both research flights was between 17° and 31°. A comprehensive suite of parameters relevant to the research objective were simultaneously measured, including HONO, NOx, pNO3, HNO3, aerosol surface area density (for particle diameters <1 μm), OH, hydroperoxyl (HO2) and alkylperoxyl (RO2) radicals, bromine oxide (BrO), iodine oxide (IO), O3, volatile organic compounds (VOCs), and photolysis frequencies J (see Extended Data Table 1). The air masses encountered in the MBL consisted mostly of aged marine air circulating over the North Atlantic Ocean under a Bermuda high-pressure system as indicated by back-trajectories, with slight influence from coastal emissions in RF16 (Extended Data Fig. 1).

The observed mixing ratios of HONO, NOx and pNO3 versus altitude are shown in Fig. 1. The mixing ratios of NOx ranged from 10 to 40 parts per trillion by volume (p.p.t.v.), and were comparable to previous observations in the clean MBL14. The mean mixing ratios of HONO (±1 s.d., standard deviation) within the MBL were 11.3 ± 1.6 p.p.t.v. for RF14 and 8.8 ± 2.3 p.p.t.v. for RF16. These HONO values are substantially lower than other airborne observations in the continental boundary layer over Northern Michigan (8–70 p.p.t.v.)15 and in the morning residual layer over an industrial region of Northern Italy (up to 150 p.p.t.v.)16. These low HONO values are consistent with the lower levels of its precursors, such as NOx, in this clean MBL compared to the other two locations. In addition, the ocean surface is likely to be a net HONO sink given the slight alkalinity of sea water, while the land surface is typically a net HONO source for the overlying atmosphere9,15.

Figure 1: Vertical profiles of HONO, NOx and pNO3 in marine air off the coast of North and South Carolina on 5 July 2013 (RF 14) and 8 July 2013 (RF 16).
figure 1

a, HONO; b, NOx; c, pNO3. Each error bar represents ±1 s.d. of the measurements. The height of the MBL is about 1 km.

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The photolysis lifetime of HONO during the flight legs discussed here was approximately 12 min. To balance the photolytic loss and maintain a nearly steady-state HONO concentration, there must be an in situ HONO source well distributed in the MBL. NOx is a well known HONO precursor, especially in urban environments17. However, there was no significant and positive correlation (r2 < 0.1) between the concentrations of HONO and NOx, suggesting that NOx was not an important HONO precursor in the marine atmosphere. On the other hand, HONO and pNO3 concentrations were much higher in the MBL than in the free troposphere (Fig. 1) and were significantly correlated (r2 = 0.62 for RF14 and r2 = 0.61 for RF16), suggesting that pNO3 was a potential HONO precursor in the marine atmosphere. Indeed, the HONO source required to sustain the observed HONO concentration correlated well with the product of the pNO3 concentration and HNO3 photolysis frequency (r2 = 0.82 for RF14 and r2 = 0.80 for RF16) (Fig. 2). An enhancement factor of about 300 can be calculated from the slopes of linear least-squares fits for the photolysis rate constant of pNO3 relative to that of gaseous HNO3, if pNO3 photolysis is the in situ HONO source sustaining the observed HONO concentrations after removing the minor contributions from NOx-related reactions. A normalized photolysis rate constant for pNO3, , of ~2.0 × 10−4 s−1 can be derived from the enhancement factor, scaled to the typical tropical summer conditions on the ground (solar elevation angle θ = 0°), corresponding to a gaseous HNO3 photolysis rate constant of ~7.0 × 10−7 s−1 (refs 1 and 18).

Figure 2: Correlation between the required in situ HONO source and the product of the pNO3 concentration and the photolysis frequency of gaseous HNO3.
figure 2

The lines are the linear least-squares fits to the data. The correlation coefficients (r2) are 0.82 and 0.80 for RF14 and RF16, respectively. The relative uncertainty (±1 s.d.) is within 25% for the required in situ HONO source and within 35% for  × [pNO3] in the MBL, and is within ~50% and ~70% in the free troposphere.

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To confirm the role of pNO3 photolysis as a HONO source, aerosol samples were collected on board the C-130 aircraft using Teflon filters for the laboratory determination of the photolysis rate constants of pNO3. A value of 1.0 × 10−4 s−1 was determined from one aerosol sample collected during the MBL flight RF16. In addition, photolysis rate constants were determined to be in the range 1.3 × 10−5 s−1 to 3.1 × 10−4 s−1, with a median of 1.3 × 10−4 s−1 and a mean ± 1 s.d. of (1.7 ± 1.1) × 10−4 s−1, from seven filter samples collected in various air masses during the NOMADSS flights, including one over the ocean (RF 16) and six over terrestrial environments in the southern and southeastern USA. HONO was the major product of pNO3 photolysis under the experimental conditions, with an average HONO/NOx production ratio of ~2. The laboratory-determined values are in reasonably good agreement with the value of ~2.0 × 10−4 s−1 inferred from the field observations (Fig. 2).

Both the field-inferred and the laboratory-determined values are also well within a reported range for the surface HNO3 photolysis rate constant, from 2.2 × 10−5 s−1 on glass surfaces5,19 to 1.2 × 10−3 s−1on urban grime6. Similar to surface-adsorbed HNO3, the high photolysis rate of pNO3 may be due in part to its enhanced absorption cross-section, compared to that of gaseous HNO3 (refs 7 and 8). The photolysis rate of pNO3 associated with sea-salt aerosol may also be enhanced in the unique chemical environment of the MBL. Organic matter is ubiquitous and highly enriched in sea-salt aerosols20 and may serve as a photosensitizer for the photolysis of pNO3. Furthermore, the relative humidity was measured to be mostly higher than the deliquescence point of sea-salt particles, and thus sea-salt particles were in the form of liquid droplets in the MBL. The light intensity is enhanced in sea-salt droplets owing to resonance and refraction21, and the nitrate ion is attracted by Br− to the air–water interface, where it becomes more photochemically reactive22.

All the evidence from the field and the laboratory indicate that fast photolysis of pNO3 in sea-salt aerosol sustains a majority of the observed HONO level in the MBL. Since HONO is readily photolysed to NO and OH during the day, the photolysis of pNO3 becomes a ‘renoxification’ pathway. Sea-salt particles scavenge HNO3 in the MBL, converting photochemically inert HNO3 into photochemically reactive pNO3 and thus accelerating the photochemical recycling of nitric acid/nitrate to NOx in the MBL. Figure 3 shows diurnal cycling of the pNO3–HONO–NOx system, simulated by a box model based on the Master Chemical Mechanism (MCM v3.2)10,11. The observed and the predicted values during the early afternoon are in good agreement, within the measurement and model uncertainties. The simulated HONO and NOx diurnal profiles were similar to those observed in the polar regions, where the photolysis of snowpack nitrate was the dominant HONO and NOx source23 and to that of NOx in the clean MBL, where a photolytic NOx source was proposed24,25.

Figure 3: Simulated diurnal profiles of mixing ratios and budgets for HONO, NOx and total nitrate in the MBL.
figure 3

a, HONO; b, NOx; c, total nitrate (HNO3+ pNO3). HONO sources include reactions of excited NO2 with H2O (refs 26 and 27), of H2O·HO2 with NO2 (refs 16 and 28), of OH with NO, the heterogeneous reaction of NO2 on aerosols, and the photolysis of pNO3. NOx sinks consist mainly of reactions of RO2 with NO (ref. 30), of XO (primarily BrO and IO) with NO2 (ref. 29) and of OH with NO2. The error bar represents ±1 s.d. of the model calculations and field observations.

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The predicted daytime HONO maximum is due to the strong HONO source from pNO3 photolysis (Extended Data Fig. 2a). Other HONO sources included in our box model are the gas-phase reactions of OH with NO, of excited NO2 with H2O (refs 26 and 27), and of HO2·H2O with NO2 (refs 16 and 28), and heterogeneous reactions of NO2 on sea-salt aerosol particles, but all of these have been found to be insignificant. The predicted daytime NOx maximum is also due to the strong NOx source from pNO3 photolysis, partly though HONO as an intermediate (Extended Data Fig. 2b). Other known ‘renoxification’ processes in the gas phase, such as the HNO3 + OH reaction and HNO3 photolysis, are negligible NOx sources in the clean MBL. NOx is effectively oxidized to HNO3 and pNO3 via several mechanisms at comparable rates (Extended Data Fig. 2b). Of these mechanisms, the gas-phase reactions of NO2 with OH and XO (X is primarily Br and I) are important HNO3 and pNO3 sources in the MBL29; the gas-phase reactions of NO with RO2 radicals leading to organic nitrates have recently been reported to be the main sink of NOx in low-NOx forested environments30. The total nitrate (that is, HNO3 + pNO3) shows a net loss in the morning and a net gain from the mid-afternoon to early evening, with a balanced daily budget (Fig. 3). Model simulation results indicate that the pNO3–NOx cycling occurs on a scale of a few hours during the day, and is capable of sustaining the observed midday levels of HONO and NOx in the MBL.

The rapid pNO3–HONO–NOx cycling suggests that the total nitrate in the troposphere is a NOx reservoir instead of the permanent NOx sink. The traditional view of the reactive nitrogen budget needs revision. Oceans account for over 70% of Earth’s surface, so this recycling NOx could contribute substantially to the global NOx source. Moreover, this recycling source of NOx occurs in the MBL, where direct NOx emissions are negligible, and thus it could have profound impacts on global tropospheric chemistry, such as oxidant and secondary aerosol formation.

Methods

Field measurements

Measurements on board the C-130 aircraft during the NOMADSS field campaign included HONO, pNO3, NOx, O3, BrO, IO, OH radicals, HO2 radicals, RO2 radicals, aerosol surface area densities (for particle diameter <1 μm), VOCs, photolysis frequencies, and other meteorology parameters. Extended Data Table 1 summarizes the instrumentation, time resolution, detection limit, accuracy and references31,32,33,34,35,36,37,38,39,40 for our measurements.

HONO was measured by two long-path absorption photometric (LPAP) systems based on the Griess–Saltzman reaction31. Briefly, ambient HONO was scrubbed by deionized water in a 10-turn glass coil sampler. The scrubbed nitrite was then derivatized with 5 mM sulfanilamide (SA) and 0.5 mM N-(1-naphthyl)-ethylene-diamine (NED) in 40 mM HCl, to form an azo dye within 5 min. The azo dye was detected by light absorbance at 540 nm using a fibre optic spectrometer (LEDSPEC-4, World Precision Instruments) with a 1-m liquid waveguide capillary flow cell (World Precision Instruments). ‘Zero-HONO’ air was generated by pulling ambient air through a Na2CO3-coated denuder to remove HONO and was sampled by the systems periodically to establish measurement baselines. Interference from NOx, peroxyacetyl nitrate (PAN) and particulate nitrite, if any, was corrected by subtracting the baseline from the ambient air signal. Owing to the low collection efficiency of these interfering species in the sampling coil and their low concentrations, the combined interference signal was estimated to be less than 10% of the total signal in the clean MBL. Potential interference from peroxynitric acid (HO2NO2) was suppressed by heating the Teflon perfluoroalkoxy alkanes (PFA) sampling line to 50 °C with a residence time of 0.8 s. The HO2NO2 steady-state concentration in the MBL was estimated to be less than 1 p.p.t.v. at a temperature of 23–26 °C in both flights, and thus interference from HO2NO2 was negligible41. Overall, the instrument baseline in the clean MBL was stable and low, and clear and strong ambient air signals (approximately ten times the detection limit) were observed. The accuracy of HONO measurements was confirmed by comparison with limb-scanning differential optical absorption spectroscopy (DOAS)36. The agreement between these two instruments was very good in wide power plant plumes, where HONO mixing ratios exceeded the lower detection limits of both instruments (Extended Data Fig. 3). HNO3 and pNO3 were quantitatively collected with a coil sampler and a frited glass disk sampler, respectively. The collected nitrate in the two channels were reduced to nitrite by two cadmium (Cd) columns, and determined using two LPAP systems31,32. Zero air was generated to establish measurement baselines: for HNO3 by passing the ambient air through a NaCl-coated denuder to remove HNO3, and for pNO3 through a Teflon filter and a NaCl-coated denuder to remove aerosol particles and HNO3. Potential interference from HONO, NOx and PAN was corrected by subtracting the baselines from the ambient air signals.

Ozone measurements were unavailable on 8 July 2013 and OH radical measurements were unavailable on 5 July 2013 owing to instrument malfunction. Steady-state OH radical concentrations were calculated and used in the budget analysis when OH radical measurements were not available42. Most of the parameters were observed at similar values during both flights, indicating that both flights captured the primary features of the local chemical environment. The lack of OH and O3 measurements on the different flights had a negligible impact on our analysis. Several spikes in NOx and aerosol surface area density detected from ship exhaust were excluded from the analysis.

Seventy-two-hour back-trajectories were calculated for both flights (Extended Data Fig. 1) with the Lagrangian particle dispersion model FLEXPART43, version 9.02 (http://flexpart.eu), using six-hourly meteorological analysis data of the Global Forecasting System of the National Centers for Environmental Prediction (http://nomads.ncep.noaa.gov/txt_descriptions/GFS_half_degree_doc.shtml), interlaced with 3-h forecasts (0:00 utc, 3:00 utc, 6:00 utc, 9:00 utc, 12:00 utc, 15:00 utc, 18:00 utc and 21:00 utc), at a horizontal resolution of 0.5°. Every 5 min during the research flight 10,000 particles were released at the then-current position of the NSF/NCAR C-130 and followed back in time for 72 h. A ‘particle’ here refers to an infinitesimally small parcel of air, which is only affected by three-dimensional transport, turbulence and convection, and does not have any removal processes (no deposition, washout, sedimentation, chemical losses). Centroids shown in the figures are based on an algorithm44 that reduces the residence probability distribution resulting from the locations of the 10,000 particles into five probable locations at each time interval.

Particulate nitrate photolysis experiment

One aerosol sample was collected using a Teflon filter (Sartorius, pore size 0.45 μm, diameter 47 mm) on-board the NSF/NCAR C-130 aircraft during every research flight from 30 min after takeoff to 30 min before landing. The total sampling volume ranged from 1.1 m3 to 1.5 m3 depending on the flight length (ranging from 6 h to 8 h). The filter sample was wrapped in aluminium foil and stored in a refrigerator until use. The pNO3 photolysis rate constant was determined using the filter sample in the laboratory.

The photochemical experiments were conducted using a cylindrical flow reactor (inner diameter 10 cm, depth 1.5 cm) with a quartz window on the top, at a temperature of 21.0 ± 1.0 °C and a relative humidity of (50 ± 2)%. The filter sample was moved into the flow cell directly from the freezer for the photochemical experiment. Compressed air was purified by flowing through an activated charcoal and Purafil chemisorbant column (Purafil) to remove NOx, VOCs, H2S, SO2, HNO3 and HONO and was used as carrier gas. Gaseous products, HONO and NO2, released during the experiment were flushed out of the reactor by the carrier gas, and were sampled by two coil samplers connected in series. The first 10-turn coil sampler scrubbed HONO with purified water at a collection efficiency of 100% (ref. 31), and the second 32-turn coil sampler was to scrub NO2 with an acetic acid modified SA/NED solution at a collection efficiency of 60% (ref. 45). The scrubbed nitrite and NO2 were converted to an azo dye with SA/NED reagents and analysed by two separate LPAP systems31,45. The filter sample was exposed to the solar simulator radiation for 10 min; baselines were established for both HONO and NO2 before and after the light exposure. Photochemical production rates of HONO and NO2 were calculated from their time-integrated signals above the baselines over the period of light exposure. To correct for HONO and NO2 production from photolysis of HNO3 deposited on the flow reactor wall surface, a control experiment was conducted by irradiating the empty flow reactor. The control signals were subtracted from the sample exposure signals when calculating the production rates of HONO and NO2 from pNO3 photolysis. After 10 min of light exposure, nitrate in the filter sample was extracted with 15 ml 1% NH4Cl buffer solution (pH = 8.5), reduced to nitrite by a Cd column and determined by LPAP. A 300-W Ceramic xenon arc lamp (Perkin Elmer, model PE300BUV) was used as a light source. The ultraviolet light below 290 nm and the heat-generating infrared light were removed by a Pyrex glass filter and a water filter, respectively. The parabolic light beam irradiated only a circular area of a 1-inch (2.54 cm) diameter in the centre of the flow reactor. The shape of the spectrum of the filtered light source is similar to that of the solar actinic spectrum in the MBL (Extended Data Fig. 4). The effective light intensity in the centre of the flow reactor under direct irradiation was measured to be about 3.5 times higher than that at tropical noon on the ground (solar elevation angle θ = 0°)1,18, using a nitrate actinometer18. The production rates of HONO and NO2 were normalized by the amount of pNO3 exposed and the effective ultraviolet light intensity, to obtain the normalized photolysis rate constants of pNO3, (ref. 5).

where PHONO and are the production rates of HONO and NO2, respectively; Nnitrate is the light-exposed pNO3 amount determined in the extraction solution; Jnitrate is the photolysis rate constant of nitrate in the actinometer solution exposed to the experimental light source; and the ‘standard’ photolysis rate constant of aqueous nitrate (Jnitrate,0° ≈ 3.0 × 10−7 s−1) is assumed for typical tropical summer conditions on the ground (solar elevation angle θ = 0°)1,18, corresponding to a gas-phase HNO3 photolysis rate constant () of ~7.0 × 10−7 s−1. HONO is the major product from pNO3 photolysis, with an average production ratio of HONO to NO2 of 2.0. It should be noted that the value is calculated from the production rates of HONO and NO2, and thus it may underestimate the photolysis rate constant of pNO3 if other products, such as NO, are produced. However, NO was only a minor secondary product from the photolysis of HONO and NO2, and accounted for ~1% of the total production of HONO and NO2 in the flow reactor in a resident time of 8 s. Therefore, lack of NO measurement in this study would not affect the measurement. The overall uncertainty in the photolysis rate constant measurement is about 50%, taking into account the measurement uncertainties in production rates of HONO and NO2, nitrate loading and effective ultraviolet light intensity.

It should be pointed out that the laboratory-determined represents merely an average photolysis rate constant of pNO3 collected during the entire flight covering a wide geographic area, and thus does not reflect the possible temporal and spatial variability in the actual during the flight. In addition, the photochemical reactivity of bulk aerosol sample collected on the filter may be altered during sampling and handling, and thus the laboratory-determined using the bulk aerosol sample might be different from that under the ambient conditions. Nevertheless, the laboratory-determined is still the first and best estimate of the pNO3 photolysis rate constant in the ambient atmosphere so far, and is in reasonable agreement with the values inferred from field observations (Fig. 2).

To evaluate the global recycling NOx source from particulate nitrate photolysis, more aerosol samples need to be collected from different atmospheric environments all over the world, and better-designed experiments need to be conducted using these samples to more accurately determine the photolysis rates constants of particulate nitrate under conditions similar to those of ambient atmosphere.

Model simulations

The air masses encountered consisted mostly of aged air masses circulating within the boundary layer of the North Atlantic Ocean under a Bermuda high-pressure system for several days before reaching the measurement locations (Extended Data Fig. 1). Within this relatively isolated air mass in the MBL, the cycling of pNO3–HONO–NOx was occurring much more rapidly, of the order of hours during the day, than dry deposition, which was of the order of days. Therefore, the diurnal chemistry of pNO3–HONO–NOx in the MBL can be simulated by a zero-dimensional box model.

Model simulations were conducted using the MCM v3.2 updated with the Jet Propulsion Laboratory’s latest recommended kinetics10,11,46, and constrained by the field-measured long-lived species, such as O3, VOCs and total NOy. The model was initiated from 00:00 local time and was allowed to run for three diurnal cycles (72 h). The diurnal concentration profiles of short-lived species, including OH, HO2, HONO and NOx, were affected by their initial concentrations only during the first diurnal cycle of simulation. The results presented here (Fig. 3, Extended Data Figs 2 and 5) were from the second diurnal cycle of the simulation run. To simulate the time-varying cycling of pNO3–HONO–NOx, the diurnal profiles of photolysis frequencies were also calculated by the MCM v3.2 and scaled by the measured values in the early afternoon. The time-dependent photolysis rate constant of particulate nitrate () at certain times of the day was calculated as follows:

where is the photolysis rate constant of gas-phase HNO3 measured in the MBL. The ratio of pNO3 to HNO3 was set to 1, as observed in the MBL during the early afternoon.

The photolysis of pNO3 is considered a source of both HONO and NOx. To include all the possible HONO sources in the model, the following reactions are also considered: the gas-phase reactions of OH with NO, of excited NO2 with H2O (refs 26 and 27), and of HO2·H2O with NO2 (refs 16 and 28), and the heterogeneous reactions of NO2 on sea-salt aerosol particles. Upper-limit HONO formation rates from reactions of excited NO2 with H2O and of HO2·H2O with NO2 are calculated using the latest recommendations27,28. An upper-limit uptake coefficient of 10−4 was assumed for NO2 uptake on sea-salt aerosol47. HONO sinks in the model include its photolysis and the gas-phase reaction with OH radicals.

The photolysis of pNO3 is a NOx source mainly through HONO as an intermediate. Other NOx sources, such as the photolysis of gaseous HNO3 and the reaction of gaseous HNO3 with OH, are negligible, and are not included here. NOx sinks include the formation of bromine nitrate (BrONO2), iodine nitrate (IONO2) and organic nitrate (RONO2) as well as HNO3 through the reactions of NO2 with OH and of NO with HO2. The uptake of halogen nitrate and organic nitrates on the sea-salt aerosols and following hydrolysis provide effective pathways for conversion of NOx to particulate nitrate in addition to HNO3 uptake. The photolysis lifetime of BrONO2 in the gas phase was estimated to be ~12 min in the MBL, somewhat longer than the uptake and hydrolysis lifetime of ~6 min using an uptake coefficient of 0.8 on sea-salt aerosols46. Therefore, two-thirds of BrONO2 is converted to pNO3 through hydrolysis on the aerosol particle at midday. The photolysis lifetime of IONO2 in the gas phase was estimated to be ~5 min (ref. 48), comparable to its uptake and hydrolysis lifetime46,49. Therefore, half of IONO2 is converted to pNO3 via hydrolysis on the aerosol particles at midday. BrO was measured at 1.5 p.p.t.v. by the DOAS instrument. The IO level was below the detection limit and was assumed to be at the typical MBL concentration49,50 of 0.5 p.p.t.v.

To evaluate the impact of VOCs on reactive nitrogen chemistry, explicit methane chemistry is considered in the model. Higher VOCs are lumped into a single species, RH. The concentration of RH is adjusted by the sum of the abundance of individually measured VOCs (RiH) scaled by the ratio of their rate coefficients for OH+RiH to that for OH+CH4. The products of OH+RH reactions lead to the formation of RO2 radicals, carbonyls, peroxides, and organic nitrates. The yield of organic nitrate from the reaction of RO2 radical with NO (reaction 3) is calculated based on the reaction rate of CH3O2 radical with NO () and the effective branching ratio β.

The effective branching ratio is calculated:

where [RiO2] and [CH3O2] are the concentrations of various RiO2 radicals formed from oxidation of various VOCs and methane, respectively; ki and βi are the recommended rate constants and branching ratios (βi) for various RO2 radicals, respectively30,51. The effective branching ratio β is estimated to be ~7% for our model. The fate of RONO2 in the MBL is not well known; hydrolysis has been assumed to be an effective sink of organic nitrates in forested regions30. In our model, an uptake coefficient of 10−2 and a 100% nitrate yield from RONO2 uptake is assumed for organic nitrates on sea-salt aerosol.

The model is initialized with typically measured parameters and is run at 15-min time steps for three diurnal cycles. Multiple runs are used to constrain the model uncertainty by error propagation from the errors of all considered parameters. Gaussian error propagation is applied for the uncertainty calculation. Overall, a model uncertainty of 28% (±1 s.d.) is calculated. The reactive nitrogen species are found to be reproducible for multiple days without considering deposition and transport. Sensitivity studies with the model indicate that the calculated HONO concentrations are relatively insensitive (≤2%) to the following assumed parameters: the RONO2 branching ratio (varying from 1% to 7% to 14%), the uptake coefficients of RONO2 and XONO2 (changing up and down by a factor of two), the nitrate yield from RONO2 hydrolysis (varying from 5% to 100%), the initial concentration of non-methane hydrocarbons (changing up and down by a factor of two), and the RO2+NO reaction rate constant (changing up and down by a factor of two). Changing up and down by a factor of two in the initial concentrations of BrO or IO leads to a change of up to 4% in the calculated HONO. Finally, the sensitivity of the model output to the ratio of HNO3 to pNO3 was assessed by varying between 0.5 and 2.0, and the modelled HONO varied between 1.17 and 0.74 of the value for the ratio of unity. Despite the simplicity of this model approach, the good agreement between model calculations and field observations for key species (Fig. 3 and Extended Data Fig. 5) shows its feasibility and usefulness for assessing the chemistry of radicals and reactive nitrogen in the MBL.