Introduction

Nitrogen oxides (NOx ≡ NO + NO2) and gaseous nitrous acid (HONO) perturb the photochemical cycling of peroxy radicals (RO2 and HO2) and hydroxide radicals (OH)1,2,3,4,5,6. Field observations in high-NOx atmospheres highlight the primary production of OH (and NO) via HONO photolysis1,6,7,8,9,10. Across high- to low-NOx atmospheres, secondary production of OH via the HO2 plus NO reaction is another major source of OH.

HONO and NOx are closely coupled in their NOx-HONO internal cycling, referred to as internal cycling in this context (Fig. 1). Specifically, heterogeneous reactions of NO2 on ambient surfaces and gas-phase reactions between NO and OH have been intensively examined as major HONO formation routes in the internal cycle7,8,9,10,11,12,13,14,15. Since HONO photolyzes much faster, turnover routes of NOx to recycle HONO are the rate-limiting steps of internal cycling. OH is a net product in internal cycling even if only HONO production via heterogeneous reactions of NO2 is considered. Any external source (or sink) of HONO or NOx would promote (or suppress) the internal cycling. Apart from the internal cycling, NOx ages to form more oxidized reservoirs, which are referred to as NOz, as air masses are transported away from source regions. NOx aging processes suppress the internal cycling and diminish the role of HONO photolysis in the OH budget. However, model underestimation of the NOx/NOz ratio observations suggests unknown or underappreciated NOx regeneration pathways from NOz in low-NOx atmospheres4,16,17,18,19,20,21,22,23,24,25,26,27,28. NOx regeneration pathways, in contrast to the internal cycling, produce “new” NOx and hence are designated as the external cycling of NOx (Fig. 1). External cycling naturally promotes the internal cycling via at least an external source of NOx. Consequently, secondary OH production via NOx regeneration and net primary OH production via HONO regeneration could greatly perturb the OH photochemical budget. The current model omission of external cycling would lead to an underestimation of OH production and OH abundance, especially in low-NOx atmospheres.

Fig. 1: Schematic graph of internal cycling and external cycling of NO and HONO.
figure 1

The left reaction scheme describes internal cycling between nitrogen oxides (NO = NO + NO) and nitrous acid (HONO) in high- NO atmospheres. HONO photolysis is the major route producing OH radical (OH). The right reaction scheme describes external cycling among oxidative reservior species of NO (NO), NO, and HONO in low-NO atmospheres. NO -catalysed radical chain propagration takes over as the major route perturbing OH and ozone (O) chemical production.

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Identifying and exploring a specific mechanism is a natural step in characterizing external cycling and quantifying its impact on the oxidative capacity of the atmosphere. The external cycling pathways proposed in the literature include at least three mechanisms, i.e., surface-catalyzed photolysis of absorbed nitrate (nitrateabs) on snow/ice surfaces and possibly also on aerosol/ambient surfaces4,20,24,27,28,29,30,31,32,33,34,35,36,37,38, nitrification/denitrification in the soil16,19 and the thermal decomposition of peroxyacetyl nitrate (PAN). Among these mechanisms, surface-catalyzed photolysis of nitrateabs on aerosol surfaces, referred to as pNO3 photolysis, occurs in situ in the air column and therefore potentially perturbs the distribution of NOx and hence the oxidative capacity of the atmosphere from the lower troposphere to the upper troposphere35. pNO3 photolysis has been intensively explored in laboratory and field studies4,18,21,22,23,34,36,37,39. The reaction rate constant of pNO3 photolysis varies over at least two orders of magnitude in high-to low-NOx atmospheres by employing a budget analysis for either HONO or NO2 and by assuming that pNO3 photolysis fully accounts for the missing source of HONO or NO2 in the field4,21,32,34,38. Laboratory studies on a variety of pNO3 samples have confirmed that pNO3 photolysis is greatly enhanced compared to that of gaseous HNO3 and that the pNO3 photolysis rate constant is highly variable, over 3 orders of magnitude30,36,37 Based on these laboratory and field studies, Ye et al. and Andersen et al. have also revealed that pNO3 photolysis is surface-catalyzed in nature and is greatly affected by the physicochemical properties of aerosol particles, such as pNO3 loading, chemical composition and particle size30,38. Efforts in characterizing atmospheric aerosol properties and their photochemical reactivities are critical in quantitatively understanding the role of pNO3 photolysis in external cycling. However, the limited availability of the pNO3 photolysis rate constant in only a few atmospheric environments, its large variability, and potentially large uncertainties make it difficult to extrapolate results from laboratory studies to field studies or directly compare results among field studies18,21,22,30,33,34,36,37,38,39. The variability and potentially large uncertainties in the rate constant have also precluded as yet confident confirmation of pNO3 photolysis or other reactions as the dominant mechanism of the external cycling or direct characterization of the external cycling in the atmosphere. To solve this dilemma, we suggest synthesizing critical observational and model evidence, summarizing the fundamental characteristics, and quantifying the impact of the external cycling on the oxidative capacity of the atmosphere in high- to low-NOx atmospheres through a broader lens rather than attempting to establish the kinetics or the dominant mechanism of the external cycling.

Results and discussion

Synthesized field evidence for external cycling

A comprehensive dataset obtained from an aircraft measurement campaign provided excellent insight into the external cycling of NOx and its perturbation on the oxidative capacity of the atmosphere4,32. Nineteen research flights were conducted onboard NSF/NCAR C-130 to collect measurements of NOx, HONO, nitric acid (HNO3), particulate nitrate (pNO3), some alkyl nitrates, PAN, radicals (OH, HO2, RO2), ozone (O3), volatile organic compounds (VOCs), aerosol size distributions, photolysis frequencies, and other meteorological parameters, mostly in various locations in the low-NOx troposphere (Methods), i.e., from the pristine terrestrial and marine boundary layer (BL) to the FT (Fig. S1 and Table S1). Herein, we defined low-NOx and high-NOx regimes with a NOx concentration threshold of 500 pptv, given that 500 pptv represented the upper limit concentration of NOx in the remote troposphere. Furthermore, 500 pptv appeared to be a turning point for the external cycling to be key sources of HONO and NOx (see below). The data were collected from nineteen research flights without further screening and offered a more global representativity and atmospheric variability of the external cycling and therefore supported our analysis strategy for directly exploring the external cycling of NOx across high- to low-NOx atmospheres. In our previous publications, we exploited data from a limited number of research flights in forested areas (i.e., RF4-5, 11, 17-18) and clean marine boundary layers (i.e., RF14, 16) and discussed the budget of HONO and specific mechanism of the external cycling4,32. Several studies of this kind based on aircraft observations had generally employed the budget analysis methodology for HONO to conduct case studies in clean marine air or fire plumes21,34,38. The reaction rate constant of the specific external cycling route implied from the missing HONO source among these reports deviated by more than two orders of magnitude, reaching no consensus in the dominant external cycling route or atmospheric variability in the external cycling4,21,32,34,38.

The NO2 mixing ratios ranged from 10 pptv to 14.2 ppbv, with median values of approximately 30 pptv in the FT and 218 pptv in the BL (Fig. 2 and Table S2). While ppbv levels of NO2 were occasionally found as we flew through urban and industrial plumes, the median values of both HONO and NO2 were not affected by these high values and were still representative of the background troposphere. The median NO2 in the BL and the FT agreed with the established NO2 distribution in these background atmospheres5,21,26,38,40,41,42. The median HONO mixing ratio was approximately 7.0 pptv in the FT background and 12.1 pptv in the BL background (Fig. 2 and Table S2). Our data provided the first illustrations of the HONO distribution in such a variety of low-NOx atmospheres. The median HONO in the BL was among the lowest ever reported in specific low-NOx environments, such as in snow/ice-covered polar areas20,27,28,29, pristine terrestrial boundary layers32,43, and clean marine boundary layers4,23,25,38. The median HONO in the FT was slightly lower than values reported from other aircraft observations in low-NOx atmospheres41,43 but was one or two orders of magnitude lower than those observed in plumes34,44.

Fig. 2: Frequency distribution of concentrations and concentration ratios of the reactive nitrogen species as measured onboard the C-130 research aircraft and simulated by GEOS-Chem.
figure 2

a–e Distribution of NO2 concentration, the concentration ratio of NO2/NOy, HONO concentration, the concentration ratio of HONO/NOy, and the concentration ratio of HONO/NO2 in the free troposphere (FT), respectively. f–j Distribution of NO2 concentration, the concentration ratio of NO2/NOy, HONO concentration, the concentration ratio of HONO/NOy, and the concentration ratio of HONO/NO2 in the boundary layer (BL), respectively. The red lines with circles represent the GEOS-Chem model predictions. The blue lines with circles represent our aircraft observations. Open circles and solid circles represent data points from the FT and the BL, respectively. Dashed lines and solid lines connect adjacent data points.

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The GEOS-Chem model was used to provide a benchmark for the concentration ratios among reactive nitrogen species, such as the HONO/NOy (≡NOx + NOz) ratio, NO2/NOy ratio and HONO/NO2 ratio. The emission inventory applied in GEOS-Chem overestimated NOx emissions45. However, this drawback might not interfere with the model simulation of the HONO/NO2 ratio and NO2/NOy ratio in various low-NOx air masses since the reactive nitrogen species aged to reach their photosteady state (PSS) in the low-NOx atmosphere. Even with the anticipated model overestimation of NO2 and consequently overestimation of NOz (Fig. S2), the HONO concentration, HONO/NOy ratio and NO2/NOy ratio were substantially underestimated in the model (Fig. 2), indicating the external cycling of NOx. Moreover, model underestimation of the HONO/NO2 ratio and HONO/NOy further revealed that HONO might be an intermediate in the external cycling of NOx, as HONO regenerated in the external cycling would rapidly photolyze to produce NOx (Fig. 2). It was speculated that the relatively slow turnover rate of NOx to produce HONO was associated with a low HONO/NO2 ratio (<0.05, as commonly observed in high-NOx atmospheres9) to balance the rapid turnover rate of HONO to produce NOx via HONO photolysis and the Leighton cycle. Herein, a much higher HONO/NO2 ratio relative to the PSS prediction in GEOS-Chem indicated a net turnover of HONO to produce NOx in the external cycling and presented HONO as an intermediate product. Nevertheless, direct regeneration of NOx in the external cycling bypassing HONO intermediate could not be excluded.

The external cycling route of NOx with NOz as a precursor and HONO as an intermediate could be proposed based on the synthesized evidence from the concentration ratios of reactive nitrogen species. Anthropogenic emission perturbation, internal cycling mechanisms, and measurement interferences to reconcile the model–observation discrepancies could be safely excluded. First, anthropogenic emissions of HONO and NOx perturbed the distribution of HONO within a transport height of approximately 300 m while perturbing the distribution of NO2 within the boundary layer16,19,32. The nineteen research flights spent over 85% of the time 600 m above the ground surface in the BL and over 45% of the time in the FT. Hence, anthropogenic emissions of HONO and NOx could be excluded as the major reason for the model–observation discrepancies in the concentration ratio of reactive nitrogen species. Second, the photosensitization reactions of NO2 produced HONO, with photo-enhanced rates several-fold higher at noon in low-NOx conditions than at nighttime in high-NOx conditions;7,8,10 however, they were still too slow to account for the high HONO/NO2 ratio observed (Fig. 2). In fact, fully reconciling model–observation discrepancies in the HONO/NO2 ratio required a reactive uptake coefficient of NO2 to produce HONO to be in the order of magnitude of 10-3, which was nearly two orders of magnitude higher than the proposed photo–enhanced values at noon in low-NOx conditions7,10. In addition, such photosensitization reactions were not related to the model–observation discrepancy in the NO2/NOy ratio. Finally, a substantially positive measurement interference in HONO coupled with negative measurement interferences in NOz species, such as HNO3 and pNO3, might improve the model–observation agreement for both the HONO/NO2 ratio and NO2/NOy ratio. However, such species-dependent interference was not practical, as any positive (or negative) nitrite anion interference in HONO measurement would also result in a positive (or negative) interference in pNO3 and HNO3 measurements. A comparison of our LPAP HONO measurements with those by the DOAS instrument showed reasonable consistency in the concentration range beyond the detection limit of both instruments, but DOAS showed a smaller value relative to LPAP in the lower concentration range4. Potential chemical interferences for LPAP HONO, including HNO4 and particulate nitrite, were not directly measured. PSS HNO4 interference calculations suggested that it only caused minor interference (<15% of signal)32. The low partitioning ratio of particulate nitrite over HONO and low sampling efficiency of particulate nitrite in the LPAP system also suggested minor interferences (<1% of signal)46,47,48. Therefore, our HONO measurement had only been corrected for PSS HNO4 interference and therefore, the LPAP HONO measurement appeared to be reasonably reliable in our campaign. Measurements of pNO3 and HNO3 had not been corrected for PSS HNO4 interference since the interference was small relative to the signals. Similarly, reliable NOx measurements have been widely reported in the literature40. Although potential positive interference was not totally excluded49, model underestimation of such as the HONO/NO2 ratio would be even worse assuming potential positive interference of NO2. As such, although measurement interferences could not be completely excluded for HONO, NOx, pNO3, and HNO3 measurements, the potential interferences were either very small or did not show the species-dependent characteristics required to reconcile the model–observation discrepancies. These analyses further supported the external cycling as a proper cause to reconcile the model–observation discrepancies.

Helas and Warneck and Ye et al. deduced that the lack of expected daytime minima of NO2 and HONO might be additional critical evidence for the external cycling, at least for the low-NOx marine boundary layer4,26. Bell-shaped diurnals of HONO and NO2 were observed as critical evidence for the external cycling powered by snow photochemistry in polar areas29,50. Their deduction followed a budget analysis of NO2 and HONO. The oxidation of NO2 was a major sink for NO2, with the rate scaling with the radical concentration or photolysis frequency of O3 (jO1D). Additionally, partitioning of NO2 over NO was also promoted by fast photolysis of NO2 to produce NO at noon, as determined in the Leighton cycle40,42. Both chemical processes contributed to a noontime minimum of NO2. For HONO, daytime photolysis was the largest budget term and dominated the diurnal profile1,2. Therefore, typical U-shaped diurnal profiles for NO2 and HONO were expected and generally observed in high-NOx atmospheres1,2,40,42. External cycling of NO2 and HONO might compensate for their daytime losses and result in atypical diurnal profiles of HONO and NO2, including flat and even bell-shaped profiles depending on the rate of external cycling4,22,25.

Although the 19 research flights sampled various airmasses over a large geographic area across a variety of chemical regimes in the atmosphere during different hours of the day, typical photochemical peaks in radicals and jO1D were still observed (Fig. S3), and therefore the typical diurnals of HONO and NO2 were expected. However, we observed atypical diurnal profiles that lacked daytime minima of NO2 and HONO in more general BL, adding to the previous observation of the same kind in the clean marine boundary layer and polar boundary layer and first in the FT (Fig. 3). This observation also differed from the GEOS-Chem simulation which excluded external cycling and simulated the expected diurnal profiles of NO2 and HONO, especially in the BL (Fig. 3). Therefore, the atypical diurnal profiles of NO2 and HONO provided further observational evidence of the temporal distribution of reactive nitrogen to verify the external cycling of NOx and HONO. Notably, neither of the internal cycling mechanisms, such as the photosensitization reaction of NO2, nor potential measurement interferences of HONO or NO2, were able to reconcile model–observation discrepancies in the diurnal profiles of NO2 and HONO.

Fig. 3: Diurnal profiles of HONO and NO2 as measured onboard the C-130 research aircraft and simulated by GEOS-Chem.
figure 3

a, b Diurnal profiles of HONO in the free troposphere (FT) and boundary layer (BL), respectively. c, d Diurnal profile of NO2 in the FT and BL, respectively. The red dashed and solid lines represent the median values of the GEOS-Chem model predictions. The blue boxes represent, from top to bottom, the 75th, 50th, and 25th percentiles; the whiskers above and below the boxes represent the 90th and 10th percentiles; and the cross represents the mean value of our aircraft observations. Open boxes and solid boxes represent data points from the FT and the BL, respectively. The blue dashed lines and solid lines connect adjacent median values.

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Chemical model evaluation of external cycling

As the GEOS-Chem did not compile detailed radical chemistry along the oxidation mechanism of VOCs51,52, a nearly explicit chemical model (MCM version 3.3.1, http://mcm.leeds.ac.uk/MCM/) was adapted to simulate the photochemical evolution of a random power plant plume (Fort Martin station power plant plume captured in RF10, Methods) to represent nitrogen cycling photochemistry across various NOx regimes over a large geographic area. The objectives of the chemical model simulation were to explore the fundamental characteristics of external cycling (i.e., HONO being an intermediate, determinative role of external cycling in the observed high ratio of HONO/NO2 and NO2/NOy, and the perturbation of external cycling on OH photochemistry) along with the aging of the plume. To be more specific, measurements in the power plant plume were chosen to initialize our model, while chemical conditions in the low-NOx atmosphere were carefully summarized to constrain the model. To focus on the chemical evolution of composition in the plume, a conceptual photochemical evolution under solar noon conditions was simulated in our model. To avoid discussion on any specific external cycling mechanism and related arguments on the reaction rate of specific external cycling routes, a proxy mechanism for the external cycling employing pNO3 as a representative of NOz species and the precursor of HONO and NOx in the external cycling was included in the chemical model scheme. The pNO3 photolysis rate or the reaction rate of a general NOz species was set up based on the assumption that the external cycling could fully account for the unknown source of HONO or NO2. Previous field observations or laboratory measurements of the photolysis rate constant were not referred to or compared with, as only a proxy mechanism, rather than a specific mechanism, of the external cycling was the very core of the discussion. Three independent models were run: one excluded the external cycling of NOx and HONO (model S0), and the other two included external cycling, with/without HONO as a NOx intermediate (model S1-S2). Since the external cycling was verified and HONO was identified as an intermediate product based on our observations, chemical model S1 was expected to best represent our observations on the distribution of HONO and NO2 in varied NOx regimes.

The kinetic curve of reactive nitrogen species during the aging of the Fort Martin station power plant plume was shown in Fig. 4. NO2 went through quasi-exponential decay in the initial period and then approached a steady period with a stabilized NO2/NOy ratio and any other concentration ratios of reactive nitrogen species (Fig. 4). The initial period simulated reactive nitrogen photochemistry in a fresh plume or high-NOx atmosphere where the oxidation of NOx to form NOz species dominated the NOx budget, leading to rapid NO2 decay. The steady period mimicked reactive nitrogen photochemistry in aged plumes or in low-NOx atmospheres where the oxidation loss and regeneration of NO2 from the external cycling approached an equilibrium state, resulting in relatively consistent NO2 levels that had been persistently observed in various low-NOx atmospheres in our study and in the literature4,21,40.

Fig. 4: Distribution patterns of concentration and concentration ratios of reactive nitrogen species, and OH radicals during plume aging as simulated by the MCM model.
figure 4

a, b Concentrations of HONO and NO2, respectively. c–e Concentration ratio of HONO/NOy, NO2/NOy, and HONO/NO2, respectively. f Concentration of OH radicals. The red line represents the model S0, which excludes external cycling. The blue line and blue dashed line present the model S1 and S2, which include the proxy mechanism for external cycling with HONO yields of 100% (0% yield for NO2) and 0% (100% yield for NO2), respectively. The blue and red boxes represent the results of our aircraft observations and GEOS-Chem simulations, respectively. From top to bottom of the box, the 75th, 50th, and 25th percentiles are shown; the whiskers above and below the boxes represent the 90th and 10th percentiles; and the cross represents the mean values.

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The counterbalancing role of NOx regeneration in the external cycling extended the NOx lifetime and sustained comparable NOx abundance in aged airmasses or remote atmospheres. It also challenged the current chemical model scheme involving the continuous oxidative decay of NOx and a small NOx regeneration rate, leading to extremely low NOx abundance in the tropospheric background. In model S0, the NO2/NOy ratio was not negligible but was extremely low (Fig. 4) due to the low regeneration rate of NOx via transport and the thermal decomposition of PAN, even with higher PAN and higher rates of PAN decomposition applied in the model than those obtained from our aircraft observations (Fig. S4). The external cycling of NOx in model S1 or S2 better agreed with the observed NO2 concentrations and concentration ratios of NO2/NOy in low-NOx environments, confirming the determinative role of the external cycling in the distribution of NO2/NOy ratio especially in low-NOx atmospheres. Model S1 also better agreed with the HONO concentration, HONO/NOy ratio, and HONO/NO2 ratio, confirming HONO as an intermediate in the external cycling. Compared to other NOx regeneration mechanisms, such as thermal decomposition and photolysis of PAN (gaseous HNO4, organic nitrates, and nitric acid), the external cycling involving HONO as an intermediate proceeded far more rapidly, especially in low-NOx atmospheres.

To note, our observation and modeling consistently demonstrated the environmental variability pattern in the role of external cycling as the plume aged, and our modeling with the external cycling better captured the observed ratios of HONO/NO2, HONO/NOy, NO2/NOy as NOx decreased (Fig. 5). These environmental variability patterns were mainly rationalized by the accumulation of NOz (the external cycling precursor) as the plume aged. Consequently, an increasing trend in the HONO/NO2, HONO/NOy ratio and therefore a relatively strong external cycling contribution (Cexternal) to the budget of HONO and NOx as NOx decreased were observed (see Calculation of Cinternal and Cexternal in Method section). The environmental variability of the rate constant of the external cycling, i.e., the high rate constant of the external cycling in low NOx atmospheres, might also contribute to the environmental variability patterns30. Although the environmental variability in the rate constant of the external cycling was not considered in our box model scheme, our model reasonably captured the observations across NOx regimes. Therefore, both our observations and the model simulation illustrated increasing perturbations on atmospheric budgets of reactive nitrogen species by the external cycling as NOx decreased.

Fig. 5: Scatter plots of the concentration ratios of reactive nitrogen species, and contribution of external and internal cycling, against NO2, as measured onboard the C-130 research aircraft and simulated by the MCM model.
figure 5

a–c Concentration ratios of HONO/NO2, HONO/NOy, NO2/NOy, respectively. d, e External source contribution (Cexternal) and internal source contribution (Cinternal), respectively. Open circles and solid circles represent measured data points from the free troposphere (FT) and the boundary layer (BL), respectively. The red line represents model S0, which excludes external cycling. The blue line and blue dashed line present the model S1 and S2, which include the proxy mechanism for external cycling with HONO yields of 100% (0% yield for NO2) and 0% (100% yield for NO2), respectively.

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Frankly speaking, it is difficult to comprehend the observed trend of Cexternal as NOx decreases since it goes against the traditional theories in which internal cycling dominates the HONO budget. The shifting of the HONO/NO2 ratio as NOx decreased in the high-NOx atmosphere was so slow and limited in a narrow range, typically from 0.01 to 0.1 (Figs. 4, 5), that it might have been considered unchanged given the observational uncertainties. The relationship between HONO and NOx was strengthened by numerous observations in high-NOx atmospheres1,9,13, and the dominant role of the internal cycling tended to be mistakenly extrapolated to low-NOx chemical regimes as a consequence. Our characterization of the chemical-regime-dependent contribution of the external cycling better summarized the environmental variability feature of the external cycling and properly addressed the observational argument regarding missing HONO sources in high-NOx atmospheres and low-NOx atmospheres44.

The increasing contribution of the external cycling to the budget of HONO and NOx as NOx decreased might have amplified its perturbation on OH photochemistry because OH production was mostly sensitive to the abundance shifting of NOx in the low-NOx atmosphere. In addition, the daytime compensation of NOx by the external cycling might have further amplified its perturbation role because the photochemical production of OH overlapped with the external cycling of NOx and HONO during the daytime. This point was illustrated in the model underestimation of OH. Due to model S0 omission of the external cycling, the model underestimated OH, and this underestimation was more apparent in a low-NOx atmosphere than in a high-NOx atmosphere (Fig. 4). The model underestimation of OH was also confirmed to be more closely linked with primary OH production via photolysis of HONO (driven mainly by the internal cycling) in a high-NOx atmosphere but more closely associated with NOx-catalyzed secondary OH production driven by the external cycling of NOx in a low-NOx atmosphere. The S0 model underestimation of OH abundance reached approximately 41% in a low-NOx atmosphere (Fig. 4), comparable to a previous CTM evaluation, which showed a perturbation of the NOx budget and therefore the OH budget by approximately 40% via a proxy cycling mechanism in the marine boundary layer35.

Overall, the results of our analysis indicate the dominant role of external cycling in the chemical budget of reactive nitrogen in low-NOx atmospheres and its significant impact on oxidant photochemistry, thus calling for an urgent and significant revision in our understanding of the atmospheric chemistry of reactive nitrogen and oxidants. To advance this goal, extensive research efforts are needed, for example, laboratory work to better parameterize the kinetics and mechanisms of dominant external cycling routes, including but not limited to pNO3 photolysis, and field measurements to establish spatial and temporal distributions of reactive nitrogen species that are only sporadically available at this time, especially for low-NOx atmospheres5,17,34,53,54.

Methods

Aircraft observation

A total of 19 research flights were conducted, mostly from 8:00 to 18:00 local time, in various low-NOx troposphere environments. The raw data from the first 15 min after taking off and the last 15 min before landing were excluded from the analysis to avoid interference from pollution at the airport and were then averaged for 3 min for further analysis.

O3 and NOx were measured using chemiluminescence methods55,56. HONO, HNO3, and pNO3 were measured using a wet-chemistry method similar to LOPAP57. Aerosol number-size distributions were measured using a scanning mobility particle sizer (SMPS) and an ultrahigh sensitivity aerosol spectrometer (UHSAS)58. Alkyl nitrates, PANs, and VOCs were measured by a trace organic gas analyzer (TOGA)59. Free radicals were measured using a selected-ion chemical-ionization mass spectrometer (SICIMS)60. Photolysis frequencies were calculated from measurements of a scanning actinic flux spectroradiometer (SAFS)61.

Calculation of C internal and C external

The internal cycling included heterogeneous reactions of NO2 on ambient surfaces, gas-phase reaction between NO and OH radicals, HONO photolysis, and gas-phase reaction between HONO and OH radicals. The chemical reactions are listed as follows.

$${{{{{{\rm{NO}}}}}}}_{2}+{{{{{\rm{surface}}}}}}\to {{{{{\rm{HONO}}}}}}+{{{{{\rm{other\; products}}}}}}$$
$${{{{{\rm{HONO}}}}}}+{hv} \, ({{{{{\rm{\lambda }}}}}} \, < \, 400{{{{{\rm{nm}}}}}})\leftrightarrow {{{{{\rm{OH}}}}}}+{{{{{\rm{NO}}}}}}$$
$${{{{{\rm{HONO}}}}}}+{{{{{\rm{OH}}}}}}\to {{{{{{\rm{H}}}}}}}_{2}{{{{{\rm{O}}}}}}+{{{{{{\rm{NO}}}}}}}_{2}$$

The internal source of HONO (\({P}_{{internal}}\)) is calculated with the equation below:

$${P}_{{internal}}={k}_{R1}\left[{{{{{{\rm{NO}}}}}}}_{2}\right]+{k}_{R2}\left[{{{{{\rm{OH}}}}}}\right]\left[{{{{{\rm{NO}}}}}}\right]$$
(1)

where [X] represents the concentration of species X in molecule cm−3; \({k}_{R2}\) is the rate constant of NO with OH radicals; \({k}_{R1}\) is defined as the heterogeneous uptake rate constant of NO2 on the aerosol surface and is calculated with Eq. (2).

$${k}_{R2}=\frac{1}{4}\times s/v\times c\times \gamma$$
(2)

where s/v represents the aerosol surface density, which is calculated from the particle number-size distribution by the SMPS. c represents the average molecular speed of NO2. \(\gamma\) represents the uptake coefficient of NO2 on an aerosol particle surface. An upper limit of 10−4 was adopted to estimate the upper limit of internal sources of HONO62.

With a photolytic lifetime of approximately 10 min, the photosteady-state assumption is applicable for HONO. The external source of HONO (\({P}_{{external}}\)) is calculated according to the photosteady-state budget as follows.

$${P}_{{internal}}+{P}_{{external}}=({j}_{{HONO}}+{k}_{R3}\left[{{{{{\rm{OH}}}}}}\right])\times \left[{{{{{\rm{HONO}}}}}}\right]$$
(3)

where [X] represents the concentration of species X in molecule cm−3, \({j}_{{HONO}}\) represents the photolysis frequency of HONO, and \({k}_{R3}\) represents the rate constant of HONO with OH radicals. Soil and anthropogenic emissions of HONO are not included in the budget. The aircraft measurements were mostly taken ≥ 600 m above the ground in the boundary layer and up to 8000 m in the free troposphere. The air masses encountered were therefore decoupled from ground surface HONO sources such as soil emissions and heterogeneous reactions of NO2 at ground surfaces63. The high HONO/NO2 ratio observed here also excluded influences from primary HONO emissions except for occasional influences from power plant plumes or city plumes. Therefore, only in situ chemical reactions were considered for the internal and external cycling rate calculation in this study.

The relative contribution of the internal source and external source to the total HONO source, Cinternal and Cexternal, can be defined as follows:

$${C}_{{internal}}=\frac{{P}_{{internal}}}{{P}_{{internal}}+{P}_{{external}}}$$
(4)
$${C}_{{external}}=\frac{{P}_{{external}}}{{P}_{{internal}}+{P}_{{external}}}$$
(5)

Nearly explicit chemical model simulation

The master chemical mechanism (MCM v3.3.1) is adapted here to simulate nitrogen cycling photochemistry and its impacts on the oxidative capacity of the atmosphere. The specific objective of the model run was to test whether the external cycling proxy mechanism, i.e., particulate nitrate photolysis or reaction of a general NOz species, can reproduce the unique distribution patterns of OH, HONO, and NO2 in the low-NOx troposphere.

The chemical scheme extracted from the MCM website was employed. The initial mechanism revisions of the MCM model include the addition of the heterogeneous production of HONO from NO2 reactions, dry deposition-driven removal of model-calculated OVOC intermediates and reactive nitrogen species, and a transport source for HNO3 and PAN to compensate for dry deposition losses of NOy species22,25. The conversion rate of HONO from NO2 reactions is set to be 1.4 × 10−5 s−1 ( ~ 0.05 h−1). The dry deposition-driven removal of model-calculated OVOC intermediates and reactive nitrogen species are set to be 9.0 × 10−6 s−1 and 1.0 × 10−5 s−1, respectively. Both the transport source rate for HNO3 and PAN are 18 pptv h−1. This model mechanism setup is referred to as the baseline model, S0, which excludes the external cycling proxy mechanism. In further revised models (model S1 and S2), we added HONO production from the proxy mechanism of the external cycling (Table S3). The production rate of HONO or NO2 (\({P}_{{{pNO}}_{3}}\)) was expressed as follows:

$${P}_{{{pNO}}_{3}}={[{{{{{{\rm{pNO}}}}}}}_{3}]\times j}_{{HNO}3}\times {EF}$$
(6)

where\(\,{j}_{{HNO}3}\) is the photolysis frequency of HNO3 in its gaseous form, and the enhancement factor, EF, is the ratio of the photolysis rate constant of particulate nitrate relative to \({j}_{{HNO}3}\). A median EF of 150 and a pNO3/tHNO3 partitioning ratio of 0.5 were employed in the model to represent the average conditions for the background troposphere30. A HONO yield of 100% (S1, 0% yield for NO2) or 0% (S2, 100% yield for NO2) was adapted in models S1 and S2, respectively.

$$ {{{\rm{proxy}}}}\; {{{\rm{mechanism}}}}\; {{{\rm{in}}}}\; {{{\rm{Model}}}}\; {{{\rm{S}}}}1: \qquad {{{{\rm{pNO}}}}}_{3}+{hv}\mathop{\longrightarrow }\limits^{150\times {j}_{{HNO}3}}{{{\rm{HONO}}}}\\ \qquad\qquad \qquad \mathop{\longrightarrow }\limits^{{j}_{{HONO}}}{{{{\rm{NO}}}}}_{2}\\ {{{\rm{proxy}}}}\; {{{\rm{mechanism}}}}\; {{{\rm{in}}}}\; {{{\rm{Model}}}}\; {{{\rm{S}}}}2:\qquad{{{{\rm{pNO}}}}}_{3}+{hv}\mathop{\longrightarrow }\limits^{150\times {j}_{{HNO}3}}{{{{\rm{NO}}}}}_{2}$$

To mimic the photochemical evolution of reactive nitrogen species in the typical tropospheric background and represent external cycling and its perturbation on OH photochemistry across various NOx regimes over a large geographic area, the model was initialized with a NOx mixing ratio of 10 ppbv, as observed in the Fort Martin station power plant plume. Concentrations of O3 and OH were initialized at 30 ppbv and 1.7 × 106 cm−3, respectively, which were typically observed in our daytime measurements. To best represent the radical chemistry for the background troposphere, an OH reactivity of approximately 5 s−1 was used for the model based on our aircraft measurements of VOCs and other species that consume OH, such as O3, NOx, and CO. CO, CH4, HCHO, and CH3CHO were found to be the top four contributors to OH reactivity in the background troposphere. To simplify the model, all measured VOCs, except HCHO and CH3CHO, were grouped with CO to obtain an equivalent OH reactivity. The oxidative mechanism of these grouped VOCs was thus not included in our model. The photosteady state was established quickly in the model under these initial conditions. Because our focus was on the photochemical cycling of HONO and NO2, the models were run without day-night shifts and had constant photolysis frequencies under zero solar zenith angle conditions (Table S4) to mimic the continuous 400 hr photochemical aging of the power plant plume in the background troposphere. After approximately 100 hours, the model simulation reached a stable stage. Thus, only results for the first 200 hours are shown. The model settings and initialization conditions are summarized in Tables S3 and S4.

Our model generally reproduces the observation of reactive nitrogen in various atmospheric chemical regimes. The slightly lower modeling of the HONO/NOy ratio and NO2/NOy ratio might be partly accounted for by measurement underestimations in NOy species (Figs. 5 and S4). Air bubbles can deactivate the Cd columns in LPAPs, leading to potentially lower nitrate-to-nitrite conversion efficiencies; measurement underestimations in pNO3 and HNO3 from this phenomenon were recently estimated to reach twofold23. Incomplete NOy measurements in the aircraft platform, such as measurements of other alkyl nitrates, and uncertainties in the organic nitrogen formation mechanism might be other reasons17. An assumed extreme case of 100% HONO yield in model S1 might be another reason, as the direct yield of NO2 cannot be excluded4,25.

GEOS-Chem simulation

The GEOS-Chem model (version 9-02; www.geos-chem.org) regional simulations were conducted in a one-way nested grid formulation with the native GEOS-5 Forward Processing horizontal resolution of 0.25° × 0.3125° over the North America domain (130–60° W, 10–60° N). The initial and boundary conditions were obtained through a global GEOS-Chem model simulation with a coarser resolution of 2° × 2.5° (reduced from the native GEOS-5 forward processing grid). The GEOS-Chem meteorological fields were obtained from the assimilated products of the NASA Global Modeling and Assimilation Office Goddard Earth Observing System (http://gmao.gsfc.nasa.gov/products/). The model simulations had 47 vertical layers in the atmosphere. We used a nonlocal planetary boundary layer mixing scheme developed by Holtslag and Boville (1993) and implemented in GEOS-Chem by Lin and McElroy (2010)64,65. The tropospheric chemistry mechanism was described in Parrella et al. (2012)66. No further updates, including external cycling, were made. Emissions of atmospheric components included anthropogenic emissions from the Emissions Database for Global Atmospheric Research (https://edgar.jrc.ec.europa.eu), biogenic emissions of volatile organic carbons from the Model of Emissions of Gases and Aerosols from Nature inventory67, fire emissions from the Global Fire Emissions Database68, soil NOx emissions69, and lightning NOx sources70. The dry deposition scheme used a resistance in-series model based on Wesely (1989)71. The wet deposition scheme included the scavenging of soluble tracers in convective updrafts as well as the rainout and washout of soluble tracers72. Simulation results corresponding to the research flight track during the same period were extracted for measurement comparison.