Synthesizing evidence for the external cycling of NO_x in high- to low-NO_x atmospheres

Domain: earth_science
Published: 2023-12-02
Editorial outcome: minor_revision

Abstract
External cycling regenerating nitrogen oxides (NOx ≡ NO + NO2) from their oxidative reservoir, NOz, is proposed to reshape the temporal–spatial distribution of NOx and consequently hydroxyl radical (OH), the most important oxidant in the atmosphere. Here we verify the in situ external cycling of NOx in various environments with nitrous acid (HONO) as an intermediate based on synthesized field evidence collected on board aircraft platform at daytime. External cycling helps to reconcile stubborn underestimation on observed ratios of HONO/NO2 and NO2/NOy by current chemical model schemes and rationalize atypical diurnal concentration profiles of HONO and NO2 lacking noontime valleys specially observed in low-NOx atmospheres. Perturbation on the budget of HONO and NOx by external cycling is also found to increase as NOx concentration decreases. Consequently, model underestimation of OH observations by up to 41% in low NOx atmospheres is attributed to the omission of external cycling in models.

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)1–6. Field observations in high-NOx atmospheres highlight the primary production of OH (and NO) via HONO photolysis1,6–10. Across high- to low-NOx atmospheres, secondary production of OH via the HO2 plus NO reaction is another major source of OH.

HONO and NO2 are closely coupled in their NO2-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 cycle7–15. Since HONO photolyzes much faster, turnover routes of NO2 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 NO2/NOy ratio observations suggests unknown or underappreciated NOx regeneration pathways from NOz in low-NOx atmospheres4,16–28. 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.

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 surfaces4,20,24,27–38, nitrification/denitrification in the soil16,19 and the thermal decomposition of peroxyacetyl nitrate (PAN). Among these mechanisms, surface-catalyzed photolysis of nitrate 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 studies4,18,21–23,34,36,37,39. 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 studies18,21,22,30,33,34,36–39. 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
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 on board 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 NO2 (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 atmospheres5,21,26,38,40–42. 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 areas20,27–29, 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.

The GEOS-Chem model was used to provide a benchmark for the concentration ratios among reactive nitrogen species, such as the HONO/NO2 (≡NO + NO2) ratio, NO2/NOy ratio and HONO/NOy 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 photo steady 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 NO2 (Fig. 2). It was speculated that the relatively slow turnover rate of NO2 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 NO2 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 NO2 in the external cycling and presented HONO as an intermediate product. Nevertheless, direct regeneration of NO2 in the external cycling bypassing HONO intermediate could not be excluded.

The external cycling route of NOx with NO2 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 NO2 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 NO2 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 NOy 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 HNO3 and particulate nitrite, were not directly measured. PSS HNO3 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)46–48. Therefore, our HONO measurement had only been corrected for PSS HNO3 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 HNO3 interference since the interference was small relative to the signals. Similarly, reliable NO2 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, NO2, 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 NOx 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 air masses 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 observational 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.

As the GEOS-Chem did not compile detailed radical chemistry along the oxidation mechanism of VOCs51,52, an 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) rather than attempting to establish the kinetics or the dominant mechanism of the external cycling. 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 an NO2 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 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.

The counterbalancing role of NO2 regeneration in the external cycling extended the NO2 lifetime and sustained comparable NOx abundance in aged air masses or remote atmospheres. It also challenged the current chemical model scheme involving the continuous oxidative decay of NOx and a small NO2 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 HNO3, 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 (C external) to the budget of HONO and NOx as NOx decreased were observed (see Calculation of C internal and C external 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.

Frankly speaking, it is difficult to comprehend the observed trend of C external 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 NO2 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 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 that in LPAP57. Aerosol particle size distribution (SMPS) and aerosol surface density (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.

NO2 + surface → HONO + other products

HONO + hv (λ < 400 nm) → OH + NO

HONO + OH → H2O + NO2

The internal source of HONO (P internal) is calculated with the equation below:

P internal = k R1 [NO2] + k R2 [OH][NO] (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 R1 = 1/4 × v × s/v × γ (2)

where s/v represents the aerosol surface density, which is calculated from the particle number-sized distribution by the SMPS. v represents the average molecular speed of NO2. γ 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 [OH]) × [HONO] (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, C internal and C external, can be defined as follows:

C internal = P internal / (P internal + P external) (4)

C external = 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 pNO3) was expressed as follows:

P pNO3 = [pNO3] × j HNO3 × EF (6)

where j HNO3 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 HNO3. 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.

proxy mechanism in Model S1: pNO3 + hv → 150 × j HNO3 → HONO

proxy mechanism in Model S2: pNO3 + hv → 150 × j HNO3 → NO2

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/NO2 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 non-local 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.

Data availability
The field data used in this study have been deposited and are freely available in the SAS project data archive (http://data.eol.ucar.edu/master_list/?project=SAS).

Code availability
The full set of the MCM model mechanism can be extracted from the MCM website (https://mcm.york.ac.uk/MCM/) and the subset is also available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Ye et al. use aircraft measurements of nitrogen oxides (NOx), nitrous acid (HONO) and the sum of oxidized reactive nitrogen species (NOy=NOx + reservoirs) to show that recycling of NOx from the reservoir species is faster than what is commonly accounted for in atmospheric chemistry models and that it involves HONO as an intermediate species. The authors show that including the fast recycling of NOx in a model improves leads to a substantial increase in NO2 and HONO concentrations in free troposphere in the model, making it consistent with aircraft observations. This also leads to a substantial increase in the modeled OH concentration.\nPrevious studies have shown that recycling of NOx from its reservoirs is faster than what is predicted by established theory, but the mechanism and rate of the recycling reactions are not clear. In this study, the authors analyze the complete set of observations from a regional aircraft campaign to provide further evidence of NOx recycling. Previously, they had published similar results based on a smaller subset of the observations. The study uses high-quality observations, well-established models, and appropriate analysis to strengthen the evidence for NOx recycling.\nThe manuscript lacks clarity, key sections are missing, and is difficult to follow. Additionally, the results, as presented, do not constitute a significant advance on this topic. However, the study can be improved by considering the following revisions:\n1. The manuscript is missing a discussion of the results of this work in comparison to previous studies on this topic. Specifically, how does the recycling rate compare to what has been reported in the literature and can it be explained by mechanisms that have been proposed previously? The authors themselves have published several studies on particulate nitrate photolysis as the potential mechanism, but for some reason seem reluctant to discuss this in the main text, although it is discussed in the supplement. The significance of this study depends on whether it gives an insight on these questions.\n2. The modeling of the power plant plume (lines 226 onwards and fig. 4) is confusing. It is not clear how a “plume” would even be defined after 150-200 hours of transport and dilution with the background air. To avoid confusion, it would be clearer if only the results from the box model at steady-state were presented and compared to aircraft observations in Fig. 4.\n3. The analysis related to the effect of NOx recycling on OH concentrations (Lines 306-319 and Fig. 4) is inadequate. It is based on results of modeling an emission plume that has travelled 150-200 hours, which presents certain difficulties (as mentioned in point 2). In addition, it appears that not all of the OH production and loss terms were taken into account. For instance, the OH loss rate was set to a fixed value based on the measurements of the primary OH reactants, but this probably underestimates the OH reactivity (see Thames et al., 2020, 10.5194/acp-20-4013-2020).\n4. The section from lines 168 to 192 discusses the possibility of measurement artifacts for HONO, HNO3 and particulate nitrate. Additionally, there is a known positive interference in the NO2 chemiluminescence measurements used in this study. I recommend that this issue also be addressed within this section.\n5. The manuscript is lacking a crucial section - the “Methods” - which is only available in the supplement. This makes it challenging to interpret the results. Please add the “Methods” section to the main text. Specifically, the authors should provide a more detailed explanation of the box modeling approach and the different model configurations. The calculation of the C(external) source in configurations S1 and S2 is not clearly explained and needs to be addressed.\n6. The introduction could benefit from a more detailed and specific description of the problem addressed in the manuscript, including an explanation of the relevant chemistry. Fig. 1 may not be necessary and could potentially be removed.\n7. Minor/technical comments:\na. The title of the manuscript does not accurately reflect the main findings of the study, which focus on NOx recycling rather than the oxidative capacity of the atmosphere.\nb. Line 54: hydroxyl radical\nc. Line 74-75: NOx can also be recycled from alkyl nitrates, HNO4, CH3ONO2, and HNO3.\nd. Line 86: It is not obvious that a regional campaign in one season can provide a “global view”. Please clarify or consider rewording.\ne. Lines 91-99: Measurement details need to be included in the main text in the Methods section.\nf. Line 133: The GEOS-Chem model needs to be described in the main text in the Methods section.\ng. Lines 207 and 211: Atypical, With respect to what? Polluted conditions?\nh. Lines 214-216: This statement is not supported by the results presented in Fig. 3.\ni. Line 248: “traditional view involving continuous oxidative decay of NOx…”. Not accurate. The traditional view includes regeneration of NOx from HNO3, HNO4 and organic nitrates.\nj. Fig. 4: Please add GEOS-Chem results to the figure, too.\nk. Fig. 5: What does the dashed red line denote?", "reviewer_2": "Review of “External Cycling of NOx promotes the Oxidative Capacity of the Atmosphere” by Ye et al.\nThis paper presents an integrated view of the atmospheric chemical cycling of reactive and reservoir nitrogen species, drawing upon analyses of a collection of airborne atmospheric composition measurements. Cycling / recycling of NOx species such as NO and NO2 controls many atmospheric chemical processes, ranging from oxidative capacity (the abundance of OH, production rate of ozone) to formation and nature of secondary inorganic aerosol (affecting health and radiative transfer / climate). A number of recent studies, including the authors own, have presented evidence for external NOx cycling mechanisms – whereby NO / NO2 are regenerated from nominal reservoirs such as HNO3, in some cases through the intermediate HONO. Here, the authors present a more comprehensive synthesis from observations across a range of chemical environments, demonstrating that “non-traditional” (i.e., not considered in most atmospheric chemical models) mechanisms (external cycling pathways) are quantitatively necessary throughout atmospheric chemistry, further evidencing the need for critical revision of understanding.\nThe paper in essence provides a new and more comprehensive treatment of / demonstration of the evidence for external NOx cycling across chemical environments, considered in an integrated manner. The basic occurrence of these mechanisms has been demonstrated across specific environments previously, and published (including by the authors). The novelty here is the integrated systematic analysis across the environmental (chemical condition – specifically NOx abundance) parameter space.\nIt might be helpful for the authors to comment on the extent to which new data are presented here, vs that which has been used previously (eg as per comments around L102/L103)\nComments:\n-The paper would benefit from a much clearer explanation / definition of internal and external NOx cycling, both in the text and in Fig 1 (consider including the established and new reactions/processes) - and in the abstract (see below).\n-L81 the mechanism need not be heterogeneous (or indeed variable at all). However the flux or rate of recycling through new mechanism(s) will vary depending on the environmental conditions.\nL87/88 as above the rate of external cycling will vary with the chemical conditions. Is “account for” the right term ?\n-L97 Must define low NOx/high NOx etc.\n-L106/L107 – Distinguish between rate constants and reaction flux / process importance. The former will not change but their significance will, depending upon conditions. “expected environmental variability” – what does this mean ?\n-L115 – Fig 2 shows a distribution markedly different from the model (which is the point of course). How does this square with agreeing with accepted distribution – maybe need to be more quantitative here. Plotting these data in frequency space shows the distribution of conditions probed by the flights, but is subject to the airmasses probed by these. Are these distributions representative of the FT or BL overall (e.g. from GEOS-Chem) ?\n-L148/149 how can turnover of HONO produce HONO as a product – maybe this is terminology / phrasing\n-L160 there are a number of photosensitized NO2 reactions possible (L167: more than one thing may be happening so the inference only applies in isolation)\n-L203 isnt this (flat profiles) evident – I think has been noted in some of the previous papers presenting evidence for additional mechanisms\n-L226 – GEOS-Chem certainly includes radical chemistry…\n-L232-236 must include the mechanisms S1 and S2 with “reactions” in the main paper / figure\n-L248 the traditional view is challenged in the prior papers also (also L280)\n-L272 what does “agree on the environmental variability” mean ? If you mean “the data are consistent with the occurrence of external cycling mechanism(s) across the chemical parameter space explored” ?\n-L278 don’t the data indicate mechanistic consistency across environmental conditions ?\n-L282 define high NOx & contrast with the data here\n-L285 is this what fig 5 shows (slow change) ?\n-L310 why does that fact that (most) OH production is photochemical amplify the recycling mechanism ?\n-L322 …need for revision… *in models*\nMinor Comments\nAbstract is unclear esp around lines 44-46. 48 – is this really global, either geographically or in terms of chemical coordinates (NOx abundance) ?\n-L63 NOx catalysed processes – needs explanation. This section is not clear – even for the atmospheric chemistry expert\n-L99 and around check tenses\n-L115 what is the “middle free troposphere”\n-L141 simultaneous with what ?\n-L144 Not requires – is associated with\n-L172 sudden introduction of one possible interference issue – needs some background to explain why this is in the main text – may be better in SI ?\n-L176 DOAS typically more accurate (not precise or sensitive) than LPAP, and with uncertainties expected to be systematic wrt abundance (relating to NO2/HONO spectral cross-contamination in reference spectra). I don’t think you can argue the DOAS is wrong vs the LPAP without much more detail.\n-L198 NOx partitioning isn’t (directly) driven by JO(1D) – rather than correlation of j(NO2) with j(O1D) – be precise ! (neglecting O1D + H2O…)\n-L199 HONO appears three times in this sentence\n-L229 – Justify the power plant choice (as a perturbation to consider, not the chemical conditions of this specific one)\n-Fig 3 add red/blue labels to actual figure\n-Fg 4 suggest make all models red and all observations blue, in line with Figs 2 and 3\n-Fig 5 define Cexternal, Cinternal – not mentioned anywhere in the manuscript\n-L288-291 I don’t think this technical approach detail belongs in the main paper – suggest move to SI\n-L209 you mean most sensitive to small *absolute* changes in NOx abundance\n-L295 “limit thought” ?"}, "author_response": "Response to reviewer’s comments\nReviewer #1 (Remarks to the Author):\nYe et al. use aircraft measurements of nitrogen oxides (NOx), nitrous acid (HONO) and the sum of oxidized reactive nitrogen species (NOy=NOx + reservoirs) to show that recycling of NOx from the reservoir species is faster than what is commonly accounted for in atmospheric chemistry models and that it involves HONO as an intermediate species. The authors show that including the fast recycling of NOx in a model improves leads to a substantial increase in NO2 and HONO concentrations in free troposphere in the model, making it consistent with aircraft observations. This also leads to a substantial increase in the modeled OH concentration.\nPrevious studies have shown that recycling of NOx from its reservoirs is faster than what is predicted by established theory, but the mechanism and rate of the recycling reactions are not clear. In this study, the authors analyze the complete set of observations from a regional aircraft campaign to provide further evidence of NOx recycling. Previously, they had published similar results based on a smaller subset of the observations. The study uses high-quality observations, well-established models, and appropriate analysis to strengthen the evidence for NOx recycling.\nThe manuscript lacks clarity, key sections are missing, and is difficult to follow. Additionally, the results, as presented, do not constitute a significant advance on this topic. However, the study can be improved by considering the following revisions:\nResponse: A major revision has been made taking advantage of the comments and suggestions to improve the writing clarity and better summarize our analysis strategy and the innovation contribution on this topic.\n1. The manuscript is missing a discussion of the results of this work in comparison to previous studies on this topic. Specifically, how does the recycling rate compare to what has been reported in the literature and can it be explained by mechanisms that have been proposed previously? The authors themselves have published several studies on particulate nitrate photolysis as the potential mechanism, but for some reason seem reluctant to discuss this in the main text, although it is discussed in the supplement. The significance of this study depends on whether it gives an insight on these questions.\nResponse: Your comments truly inspire us to clarify our analysis strategy and summarize the innovation contribution on this topic. A major revision has been made accordingly. Many thanks!\nPrevious field studies obtained varied reaction rates of the external cycling by employment of a budget analysis for either HONO or NO2, for example in(YE et al. 2016; ROMER et al. 2018; YE et al. 2018; PENG et al. 2022; ANDERSEN et al. 2023). Those varied reaction rates were usually used to vote for/against a specific external cycling mechanism, and no consensus has been reached. Alternatively, those varied reaction rates might merely represent the environmental variability of the specific external cycling mechanism or analysis uncertainty concerning the specific external cycling mechanism. In such research background, it is meaningful to step back and not to focus on any specific mechanism (at least as merely field observations are discussed), but to synthesize critical field observational evidences, summarize the fundamental characteristics, and validate the impact of external cycling on the oxidative capacity of the atmosphere from high-NOx to low-NOx atmospheres.\nThrough such a broad lens, this manuscript takes advantage of high-quality aircraft observations and well-established models and gains meaningful insights on this topic. First, this manuscript integrated systematic analysis across high-NOx and low-NOx chemical coordinates to summarize two pieces of critical field evidences for the external cycling of NOx, i.e., unexpectedly high HONO/NO2 and NO2/NOy ratios and atypical diurnal profiles of HONO and NO2. Second, the external cycling features HONO as a photochemical intermediate and features increasing contribution of the external cycling to the budget of HONO and NO2 as NOx decreases. The former feature implies a amplified perturbation of the external cycling on the oxidative capacity of the atmosphere since photochemical external cycling and photochemical production of OH overlap temporally in the daytime. The latter feature further implies a amplified perturbation of the external cycling on the oxidative capacity of the low-NOx atmosphere since NOx impacts OH photochemistry in a more sensitive way in low-NOx regimes. Our data and analysis in low-NOx regimes also better represent the general tropospheric conditions than the conclusions obtained from high-NOx conditions in terms of chemical coordinates. Finally, external cycling largely accounted for the model underestimation of OH abundance in the low-NOx atmosphere, confirming its impact on the oxidative capacity of the atmosphere.\nPlease also refer to the discussion in the abstract (Lines 39-57) and the introduction (Lines 85-110).\n2. The modeling of the power plant plume (lines 226 onwards and fig. 4) is confusing. It is not clear how a “plume” would even be defined after 150-200 hours of transport and dilution with the background air. To avoid confusion, it would be clearer if only the results from the box model at steady-state were presented and compared to aircraft observations in Fig. 4.\nResponse: It has been rewritten in lines 265-276 as “As the GEOS-Chem does not compile detailed radical chemistry along the oxidation of VOCs (LELIEVELD et al. 2008; TARABORRELLI et al. 2012), a nearly explicit chemical model is adapted to evaluate the environmental variability of external cycling and its perturbation on OH photochemistry by simulating the photochemical evolution of a power plant plume under typical low-NOx conditions (Methods). Measurements in a random power plant plume are chosen to initialize our model, while chemical conditions in the low-NOx atmosphere are carefully summarized to constrain the model. The model was finally initialized with observed NO and HONO in the Fort Martin station power plant plume captured in RF10 and ran with typical background atmospheric conditions at noon. A conceptual photochemical evolution under solar noon conditions, rather than real-time plume diel evolution from photochemistry and dilution, was therefore simulated in our model.”\n3. The analysis related to the effect of NOx recycling on OH concentrations (Lines 306-319 and Fig. 4) is inadequate. It is based on results of modeling an emission plume that has travelled 150-200 hours, which presents certain difficulties (as mentioned in point 2). In addition, it appears that not all of the OH production and loss terms were taken into account. For instance, the OH loss rate was set to a fixed value based on the measurements of the primary OH reactants, but this probably underestimates the OH reactivity (see Thames et al., 2020, 10.5194/acp-20-4013-2020).\nResponse: We have to admit that modeling OH is always not easy. Our strategy (please also refer to the response to point 2) is to simulate the conceptual photochemical evolution of a power plant plume in low-NOx conditions. The chemical model is initialized by observed NO and HONO in the Fort Martin station power plant plume captured in RF10 and constrained with a typical background condition at noon. The total OH loss rate was set to approximately 5 s-1, which is much higher than the marine boundary layer condition as in (THAMES et al. 2020) or the free tropospheric condition(TRAVIS et al. 2020) but is representative of the terrestrial background atmosphere we mainly flew over during the field campaign. Reasonable agreement between OH modeling and OH observation in the low-NOx atmosphere was achieved. In addition, we try to compare OH simulations with/without the external cycling included in the model to illustrate the perturbation on OH photochemistry by external cycling. Such perturbation on OH photochemistry is also comparable to a previous chemical transport model evaluation(REED et al. 2017; KASIBHATLA et al. 2018). Hence, our modeling strategy and results further support our observational conclusion about external cycling and reasonably evaluate the impact on the OH photochemical budget.\nPlease also refer to the discussion Line 291-316 in the text.\n4. The section from lines 168 to 192 discusses the possibility of measurement artifacts for HONO, HNO3 and particulate nitrate. Additionally, there is a known positive interference in the NO2 chemiluminescence measurements used in this study. I recommend that this issue also be addressed within this section.\nResponse: This issue has also been addressed in lines 218-221 as follows: “Similarly, although reliable NOx measurements have been reported intensively in the literature(LEE et al. 2009), potential positive interference is not excluded(FUCHS et al. 2010). However, model underestimation on such as HONO/NO2 ratio would be even worse assuming potential positive interference for NO2.”\n5. The manuscript is lacking a crucial section - the “Methods” - which is only available in the supplement. This makes it challenging to interpret the results. Please add the “Methods” section to the main text. Specifically, the authors should provide a more detailed explanation of the box modeling approach and the different model configurations. The calculation of the C(external) source in configurations S1 and S2 is not clearly explained and needs to be addressed.\nResponse: The “Methods” section has been added to the main text (Lines 398-538). Calculation of the C internal and C external is explained in Lines 413-449. We adapted box modeling approach used in our previous modeling work, which is fully described in (YE et al. 2017). Specific model setup in this study is illustrated in Lines 469-510. Model configurations are illustrated in Table S3 and Table S4.\n6. The introduction could benefit from a more detailed and specific description of the problem addressed in the manuscript, including an explanation of the relevant chemistry. Fig. 1 may not be necessary and could potentially be removed.\nResponse: Please refer to our response to point 1. We have introduced proxy mechanisms of external cycling and the research dilemma of being unable to conclude on the rate of any specific mechanism in our society from previous field studies. Our analysis strategy is to step back and not to focus on any specific mechanism and its kinetics (at least as merely field observations are discussed), but to synthesize critical field observational evidences, summarize the fundamental characteristics, and validate the impact of external cycling on the oxidative capacity of the atmosphere in high-NOx and low-NOx atmospheres. The detailed kinetics and mechanisms of a specific external cycling mechanism are therefore not the topic of this manuscript.\n7. Minor/technical comments:\na. The title of the manuscript does not accurately reflect the main findings of the study, which focus on NOx recycling rather than the oxidative capacity of the atmosphere.\nResponse: The title has been rewritten as “Synthesizing evidence for the external cycling of NOx in high-to-low-NOx atmospheres”.\nb. Line 54: hydroxyl radical\nResponse\"It has been corrected.\nc. Line 74-75: NOx can also be recycled from alkyl nitrates, HNO4, CH3ONO2, and HNO3.\nResponse: These well-known reservoirs of NOx are included in the revised manuscript (Lines 306-310).\nd. Line 86: It is not obvious that a regional campaign in one season can provide a “global view”. Please clarify or consider rewording.\nResponse: It has been rewritten as “through broader lens” to avoid misunderstanding.\ne. Lines 91-99: Measurement details need to be included in the main text in the Methods section.\nResponse: The “Methods” section has been added to the main text.\nf. Line 133: The GEOS-Chem model needs to be described in the main text in the Methods section.\nResponse: The “Methods” section has been added to the main text and the description of GEOS-Chem model is included (Lines 511-534).\ng. Lines 207 and 211: Atypical, With respect to what? Polluted conditions?\nResponse: In this context, atypical diurnal is referred to as “the lack of expected daytime minima of NO2 and HONO, which is normally observed in a high-NOx atmosphere.”\nh. Line 214-216: This statement is not supported by the results presented in Fig. 3.\nResponse: The atypical diurnals of HONO and NO2 are evident, especially in the BL in Fig. 3.\ni. Line 248: “traditional view involving continuous oxidative decay of NOx…”. Not accurate. The traditional view includes regeneration of NOx from HNO3, HNO4 and organic nitrates.\nResponse: It has been written as “the current chemical model scheme involving the continuous oxidative decay of NOx and small NOx regeneration rate” (Lines 302-303).\nj. Fig. 4: Please add GEOS-Chem results to the figure, too.\nResponse: It has been added to the figure.\nk. Fig. 5: What does the dashed red line denote?\nResponse: It has been deleted.\nReferences\nAndersen, S. T., L. J. Carpenter, C. Reed, J. D. Lee, R. Chance et al., 2023 Extensive field evidence for the release of HONO from the photolysis of nitrate aerosols. Science Advances 9.\nFuchs, H., S. M. Ball, B. Bohn, T. Brauers, R. C. Cohen et al., 2010 Intercomparison of measurements of NO2 concentrations in the atmosphere simulation chamber SAPHIR during the NO3Comp campaign. Atmospheric Measurement Techniques 3: 21-37.\nKasibhatla, P., T. Sherwen, M. J. Evans, L. J. Carpenter, C. Reed et al., 2018 Global impact of nitrate photolysis in sea-salt aerosol on NOx, OH, and O-3 in the marine boundary layer. Atmospheric Chemistry and Physics 18: 11185-11203.\nLee, J. D., S. J. Moller, K. A. Read, A. C. Lewis, L. Mendes et al., 2009 Year-round measurements of nitrogen oxides and ozone in the tropical North Atlantic marine boundary layer. Journal of Geophysical Research-Atmospheres 114.\nLelieveld, J., T. M. Butler, J. N. Crowley, T. J. Dillon, H. Fischer et al., 2008 Atmospheric oxidation capacity sustained by a tropical forest. Nature 452: 737-740.\nPeng, Q. Y., B. B. Palm, C. D. Fredrickson, B. Lee, S. R. Hall et al., 2022 Direct Constraints on Secondary HONO Production in Aged Wildfire Smoke From Airborne Measurements Over the Western US. Geophysical Research Letters 49.\nReed, C., M. J. Evans, L. R. Crilley, W. J. Bloss, T. Sherwen et al., 2017 Evidence for renoxification in the tropical marine boundary layer. Atmospheric Chemistry and Physics 17: 4081-4092.\nRomer, P. S., P. J. Wooldridge, J. D. Crounse, M. J. Kim, P. O. Wennberg et al., 2018 Constraints on Aerosol Nitrate Photolysis as a Potential Source of HONO and NOx. Environmental Science & Technology 52: 13738-13746.\nTaraborrelli, D., M. G. Lawrence, J. N. Crowley, T. J. Dillon, S. Gromov et al., 2012 Hydroxyl radical buffered by isoprene oxidation over tropical forests (vol 5, pg 190, 2012). Nature Geoscience 5: 300-300.\nThames, A. B., W. H. Brune, D. O. Miller, H. M. Allen, E. C. Apel et al., 2020 Missing OH reactivity in the global marine boundary layer. Atmospheric Chemistry and Physics 20: 4013-4029.\nTravis, K. R., C. L. Heald, H. M. Allen, E. C. Apel, S. R. Arnold et al., 2020 Constraining remote oxidation capacity with ATom observations. Atmospheric Chemistry and Physics 20: 7753-7781.\nYe, C. X., D. E. Heard and L. K. Whalley, 2017 Evaluation of Novel Routes for NOx Formation in Remote Regions. Environmental Science & Technology 51: 7442-7449.\nYe, C. X., X. L. Zhou, D. Pu, J. Stutz, J. Festa et al., 2016 Rapid cycling of reactive nitrogen in the marine boundary layer. Nature 532: 489-491.\nYe, C. X., X. L. Zhou, D. Pu, J. Stutz, J. Festa et al., 2018 Tropospheric HONO distribution and chemistry in the southeastern US. Atmospheric Chemistry and Physics 18: 9107-9120.\nReviewer #2 (Remarks to the Author):\nReview of “External Cycling of NOx promotes the Oxidative Capacity of the Atmosphere” by Ye et al.\nThis paper presents an integrated view of the atmospheric chemical cycling of reactive and reservoir nitrogen species, drawing upon analyses of a collection of airborne atmospheric composition measurements. Cycling / recycling of NOx species such as NO and NO2 controls many atmospheric chemical processes, ranging from oxidative capacity (the abundance of OH, production rate of ozone) to formation and nature of secondary inorganic aerosol (affecting health and radiative transfer / climate). A number of recent studies, including the authors own, have presented evidence for external NOx cycling mechanisms – whereby NO / NO2 are regenerated from nominal reservoirs such as HNO3, in some cases through the intermediate HONO. Here, the authors present a more comprehensive synthesis from observations across a range of chemical environments, demonstrating that “non-traditional” (i.e., not considered in most atmospheric chemical models) mechanisms (external cycling pathways) are quantitatively necessary throughout atmospheric chemistry, further evidencing the need for critical revision of understanding.\nThe paper in essence provides a new and more comprehensive treatment of / demonstration of the evidence for external NOx cycling across chemical environments, considered in an integrated manner. The basic occurrence of these mechanisms has been demonstrated across specific environments previously, and published (including by the authors). The novelty here is the integrated systematic analysis across the environmental (chemical condition – specifically NOx abundance) parameter space.\nIt might be helpful for the authors to comment on the extent to which new data are presented here, vs that which has been used previously (eg as per comments around L102/L103)\nResponse: The review’s evaluation on our manuscript is enlightening. We revised our manuscript to summarize our analysis strategy and the innovation contribution in a more accurate way that the reviewer has helped to summarize here. We deeply appreciate the help. The suggestion to comment on the new data is also followed (Lines 124-127).\nComments:\n-The paper would benefit from a much clearer explanation / definition of internal and external NOx cycling, both in the text and in Fig 1 (consider including the established and new reactions/processes) - and in the abstract (see below).\nResponse: The suggestions are accepted.\n-L81 the mechanism need not be heterogeneous (or indeed variable at all). However, the flux or rate of recycling through new mechanism(s) will vary depending on the environmental conditions.\nResponse: The sentence has been rewritten in lines 95-99 as “However, the heterogeneous or multiphase nature of this reaction highlights its substantial environmental variability in both the kinetics and mechanisms, which does not allow us to simply extrapolate results from laboratory studies to field studies or compare results among field studies in various chemical regimes”\nL87/88 as above the rate of external cycling will vary with the chemical conditions. Is “account for” the right term ?\nResponse: The sentence has been rewritten in lines 102-109 as “To solve this dilemma, we suggest synthesizing critical observational and model evidence, summarizing the fundamental characteristics, and validating the impact of external cycling on the oxidative capacity of the atmosphere in high- to low-NOx atmospheres through broader lens, rather than attempting to establish the kinetics and mechanism for a specific mechanism of external cycling.”\n-L97 Must define low NOx/high NOx etc.\nResponse: The definition of low-NOx environments has been added (Line 119). Based on our observation, below 500 pptv appears to be good enough definition of low-NOx atmosphere in the context.\n-L106/L107 – Distinguish between rate constants and reaction flux / process importance. The former will not change but their significance will, depending upon conditions. “expected environmental variability” – what does this mean ?\nResponse: The sentence has been rewritten as “The reaction rate constant of the external cycling implied from the missing HONO source among these reports deviates by more than one order of magnitude, leading to conclusions on the environmental variability of the external cycling, or more likely different opinions on external cycling mechanisms.” (Lines 129-133)\n-L115 – Fig 2 shows a distribution markedly different from the model (which is the point of course). How does this square with agreeing with accepted distribution – maybe need to be more quantitative here. Plotting these data in frequency space shows the distribution of conditions probed by the flights, but is subject to the airmasses probed by these. Are these distributions representative of the FT or BL overall (e.g. from GEOS-Chem) ?\nResponse: We have reviewed the distributions observed in other remote boundary layer and free troposphere by other aircraft measurements, for example in remote Atlantic(ANDERSEN et al. 2023), remote forested region(ZHANG et al. 2009). Our distributions are comparable with those measured in previous research, with NOx distributing at hundreds pptv and HONO at tens pptv, suggesting that the aircraft measurements well represent the low-NOx atmosphere.\n-L148/149 how can turnover of HONO produce HONO as a product – maybe this is terminology / phrasing\nResponse: In the HONO-NOx internal cycling, the turnover rate of NOx to produce HONO should balance the turnover rate of HONO to produce NOx.\n-L160 there are a number of photosensitized NO2 reactions possible (L167: more than one thing may be happening so the inference only applies in isolation)\nResponse: Yes, there are various photosensitized reactions of NO2 with NO2 concentration, and the photosensitization reaction surface (i.e., organic aerosol) is the major variable in the reaction. Even with the upper limit evaluation of the photosensitization reaction of NO2, the observed HONO budget and high HONO/NO2 cannot be accounted for.\n-L203 isnt this (flat profiles) evident – I think has been noted in some of the previous papers presenting evidence for additional mechanisms\nResponse: Herein, we refer to the bell-shaped diel pattern and the higher-than-expected noontime concentration of HONO or NO2 observed in the background atmosphere as “atypical diel” of HONO and NO2 relative to the typical U-shaped diel observed in the high-NOx atmosphere. Atypical diels include flat ones and bell-shaped ones, probably depending on the strength of the external cycling. Such atypical diels, as a matter of fact, might be quite popular in the low-NOx background atmosphere. Previous papers summarize such atypical diurnal profiles in the clean marine boundary layer and snow-covered polar areas. In addition to previous papers, we find such atypical diurnal profiles in the low-NOx terrestrial boundary layer and the free troposphere. We have revised the paragraph to clarify these two points (Lines 226-240).\n-L226 – GEOS-Chem certainly includes radical chemistry…\nResponse: The sentence has been rewritten as “As GEOS-Chem does not compile detailed radical chemistry along the oxidation mechanism of VOCs (LELIEVELD et al. 2008; TARABORRELLI et al. 2012)”\n-L232-236 must include the mechanisms S1 and S2 with “reactions” in the main paper / figure\nResponse: It has been included in the revised manuscript (Lines 489-490).\n-L248 the traditional view is challenged in the prior papers also (also L280)\nResponse: It has been rephrased as “current chemical model scheme” (Line 302).\n-L272 what does “agree on the environmental variability” mean ? If you mean “the data are consistent with the occurrence of external cycling mechanism(s) across the chemical parameter space explored” ?\nResponse: The environmental variability pattern of the external cycling is “increasing perturbation by external cycling on atmospheric budget of NO2 and HONO as NOx decreases”. “Agree on” has been rephrased as “consistently reveal”. (Line 331)\n-L278 don’t the data indicate mechanistic consistency across environmental conditions ?\nResponse: The data do indicate mechanistic consistency across environmental conditions. However, variability in the rate of the external cycling and its perturbation on the chemical budget of HONO and NO2 are also expected. The environmental variability pattern mainly originates from the accumulation of NOz (the external cycling precursor) as NOx decreases. The environmental variability of the rate constant of external cycling, i.e., the high rate constant of pNO3 photolysis in a low NOx atmosphere, might also contribute (YE et al. 2017; ANDERSEN et al. 2023), but it is not considered in the chemical model.\n-L282 define high NOx & contrast with the data here\nResponse: Based on our observation, below 500 pptv appears to be good enough definition of low-NOx atmosphere, which above 500 pptv is high -NOx atmosphere. It has been defined in the revised manuscript.\n-L285 is this what fig 5 shows (slow change) ?\nResponse: It has been rephrased as “The shifting of the HONO/NO2 ratio as NOx decreases in the high-NOx atmosphere is so slow in a so narrow range of typically from 0.01 to 0.1 that it might have been mistaken to be unchanging (Fig. 4-5).”\n-L310 why does that fact that (most) OH production is photochemical amplify the recycling mechanism ?\nResponse: The perturbation of the external cycling on OH production depends on two features of the external cycling, i.e., the photochemical nature and increasing contribution to the budget of NOx as NOx decreases.This point has been clarified in the revised manuscript (Lines 331-366).\n-L322 …need for revision… *in models*\nResponse: This correction has been accepted.\nMinor Comments\nAbstract is unclear esp around lines 44-46. 48 – is this really global, either geographically or in terms of chemical coordinates (NOx abundance) ?\nResponse: It has been rephrased as “broader lens to view external cycling and its perturbations on the atmospheric oxidative capacity”. (Lines 53-54)\n-L63 NOx catalysed processes – needs explanation. This section is not clear – even for the atmospheric chemistry expert\nResponse: The paragraph has been rewritten. (Lines 63-65)\n-L99 and around check tenses\nResponse: It has been revised.\n-L115 what is the “middle free troposphere”\nResponse: “middle” has been deleted.\n-L141 simultaneous with what ?\nResponse: It has been rephrased as “moreover”.\n-L144 Not requires – is associated with\nResponse: It has been revised.\n-L172 sudden introduction of one possible interference issue – needs some background to explain why this is in the main text – may be better in SI ?\nResponse: Measurement interferences are challenged by other reviewers as an alternative reason for the model-observation discrepancies. This section is to carefully examine this alternative reason.\n-L176 DOAS typically more accurate (not precise or sensitive) than LPAP, and with uncertainties expected to be systematic wrt abundance (relating to NO2/HONO spectral cross-contamination in reference spectra). I don’t think you can argue the DOAS is wrong vs the LPAP without much more detail.\nResponse: Fair enough. It has been revised as “DOAS shows smaller value relative to LAPA in the lower concentration range”. (Line 204)\n-L198 NOx partitioning isn’t (directly) driven by JO(1D) – rather than correlation of j(NO2) with j(O1D) – be precise !\nResponse: It has been revised.\n-L199 HONO appears three times in this sentence\nResponse: It has been revised.\n-L229 – Justify the power plant choice (as a perturbation to consider, not the chemical conditions of this specific one)\nResponse: This is a nice suggestion. This point has been clarified. (Lines 265-276)\n-Fig 3 add red/blue labels to actual figure\nResponse: This has been stated in the figure caption. Red/blue labels make the figure quite busy.\n-Fg 4 suggest make all models red and all observations blue, in line with Figs 2 and 3\nResponse: This is the way we plot Figs. 2 and 3.\n-Fig 5 define Cexternal, Cinternal – not mentioned anywhere in the manuscript\nResponse: They have been defined at their first appearance. (Lines 335 & Line 348)\n-L288-291 I don’t think this technical approach detail belongs in the main paper – suggest move to SI\nResponse\"Other reviewer suggested to incorporate measurement interference and uncertainties into the analysis.\n-L209 you mean most sensitive to small *absolute* changes in NOx abundance\nResponse: Yes! This has been clarified.\n-L295 “limit thought” ?\nResponse: It has been revised to “An assumed extreme case”.\n-L306 increasing with respect to what ?\nResponse: It has been revised as “Both the photochemical nature and the increasing contribution of the external cycling to the budget of HONO and NOx as NOx decreases in the low-NOx atmosphere might have amplified its perturbation on OH photochemistry in the troposphere”. (Lines 377-379)\nReferences\nAndersen, S. T., L. J. Carpenter, C. Reed, J. D. Lee, R. Chance et al., 2023 Extensive field evidence for the release of HONO from the photolysis of nitrate aerosols. Science Advances 9.\nLelieveld, J., T. M. Butler, J. N. Crowley, T. J. Dillon, H. Fischer et al., 2008 Atmospheric oxidation capacity sustained by a tropical forest. Nature 452: 737-740.\nTaraborrelli, D., M. G. Lawrence, J. N. Crowley, T. J. Dillon, S. Gromov et al., 2012 Hydroxyl radical buffered by isoprene oxidation over tropical forests (vol 5, pg 190, 2012). Nature Geoscience 5: 300-300.\nYe, C. X., D. E. Heard and L. K. Whalley, 2017 Evaluation of Novel Routes for NOx Formation in Remote Regions. Environmental Science & Technology 51: 7442-7449.\nZhang, N., X. L. Zhou, P. B. Shepson, H. L. Gao, M. Alaghmand et al., 2009 Aircraft measurement of HONO vertical profiles over a forested region. Geophysical Research Letters 36."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors' response addresses some of my comments on the original submission. However, a discussion of how the results of this work relate to previous work on this topic in terms of the rates and mechanisms is still not included, although the authors have added some introductory text. Again, without this, I do not see this work as providing significant new insights.\nI also don't understand why there is a reluctance to discuss mechanisms, even though the study uses particulate nitrate photolysis as the \"external proxy mechanism\" (Lines 471-473 in the revision). If the intent is \"to step back and not to focus on any specific mechanism,\" it is not clear to me why to begin by assuming that the recycling will have characteristics of particulate nitrate photolysis, that is, driven by the UV flux, dependent on particulate nitrate concentrations, and produce either HONO or NO2.\nThe section on modeling the power plant plume in low-NOx conditions is still unclear.", "reviewer_3": "[Reviewer 2]\nThe authors have responded well to almost all the specific points I flagged in my initial review, and the manuscript is much improved, with all the science points addressed.\nI’m still troubled by how hard it is to follow the argument in the manuscript though – this is an issue of phrasing and precision, not science. Can I suggest the authors seek a “fresh pair of eyes” to look at the text throughout, but in particular the Introduction (L60-110) and final conclusions L377-L396 and really examine what each paragraph is trying to convey, and what precisely each sentence actually says.\nPhrasing Comments :\n-Introduction to / explanation of Fig 1 is lacking. Must include a really good concise definition of both internal and external cycling – this is critical – as the key terms used throughout the paper\nL92 the *effective* rate constant ? Needs some more words somewhere in the sentence\nL94 I don’t think a rate constant can vote. I know what you mean but be precise in the phrasing – what you mean is “the range of values for rate constants / fundamental parameters which describe the individual candidate mechanisms differ widely between studies, precluding (as yet) confident confirmation of one or more dominant mechanisms”\nL97 – the parameters/rate constants don’t vary with the chemical environment – if they are truly fundamental properties of a given reaction/mechanism – but the rate of the mechanism/reaction overall will. Again need to be much sharper between *parameters/rate constants* and reaction/process *rates*. Also L342\nL101 – tighten up what you mean by environmental variability. If fundamental parameters are obtained from the various literature studies – these should be independent of the NOx concentration (or H2O, j etc). If they vary with the chemical environment – then the mechanism is wrong/incomplete.\nL131 – leading to conclusions – what are they – make this clearer. Suggest avoid words like “opinions” – the point is that different mechanisms (or parameters/rate constants) lead to different predicted NOx/HONO/OH variation in the atmosphere, suggesting that the dominant mechanism(s) have yet to be identified (or correctly characterized) ?\nL252 – neither of the competing mechanism – interference is not a mechanism / you only mention one mechanism\nL265 – needs a new sentence to explain (big picture) why you are looking at the plume experiment. Start further “back” in the logic than the GEOS-Chem chemical scheme – what is the big picture aim/point of this ? “To explore the variation in NOx, HONO and OH with airmass age or extent of chemical processing, we examine one representative case – the evolution of chemical composition in a notional power plant plume, which covers a wider range of chemical conditions / NOx space, and relates <how ?> to the observation parameter space”\nL357-L362 I still think these specific technical details belong in the SI – they read very incongruously here\nHigh / Low NOx: from an atmospheric chemistry perspective these are often considered in terms of the fate of peroxy radicals HO2/RO2 (ie do they terminate together or propagate with NO) – which would put “low NOx” way below 500 ppt. ie 500 pptv is going to be “high” to some. Maybe address here as simply as “here, low NOx is taken to refer to measurements where NOx < 500 pptv, which accounts for xx% of our observations – although we note that the outflow of the continental US will show higher NOx levels than the global remote troposphere” or something"}, "author_response": "Response to reviewers’ comments\nReviewer #1 (Remarks to the Author):\nThe authors' response addresses some of my comments on the original submission. However, a discussion of how the results of this work relate to previous work on this topic in terms of the rates and mechanisms is still not included, although the authors have added some introductory text. Again, without this, I do not see this work as providing significant new insights.\nResponse: In this manuscript, we synthesized field evidence and fundamental characteristics of the external cycling rather than any specific or dominant mechanism of the external cycling, even though a specific mechanism, i.e., the photolysis of particulate nitrate, could potentially be responsible for the discussed external cycling. Currently, only limited data are available for pNO3 photolysis rate constants in a few atmospheric environments and with large uncertainties. It is therefore difficult to extrapolate results from laboratory studies to field studies or to directly compare results among field studies. It has 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 by exploring any specific mechanism in the atmosphere.\nOne natural step is to collect more data in the laboratory and field to explore the specific kinetics of a dominant external cycling mechanism. Alternatively, we synthesize field evidence, fundamental characteristics, and atmospheric impact of the external cycling through a broader lens. We explained this strategy and our contribution to this topic in the revised manuscript in lines 80-114.\nIn lines 80-114, “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 (nitrate abs) on snow/ice surfaces and possibly also on aerosol/ambient surfaces 4,20,24,27-38, nitrification/denitrification in the soil 16,19 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 studies 4,18,21-23,34,36,37,39. 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 size 30,38. Efforts in characterizing atmospheric aerosol properties and their photochemical reactivities are critical in quantitatively understanding the role of pNO3 photolysis in the 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 studies 18,21,22,30,33,34,36-39. 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.”\nI also don't understand why there is a reluctance to discuss mechanisms, even though the study uses particulate nitrate photolysis as the \"external proxy mechanism\" (Lines 471-473 in the revision). If the intent is \"to step back and not to focus on any specific mechanism,\" it is not clear to me why to begin by assuming that the recycling will have characteristics of particulate nitrate photolysis, that is, driven by the UV flux, dependent on particulate nitrate concentrations, and produce either HONO or NO2.\nResponse: Please also see the response to the previous question.\nWe have discussed the photolysis of particulate nitrate as a major daytime HONO source in our earlier papers (Ye et al., Nature, 2016). We also tried to provide the information relevant to this mechanism in the introduction section. However, a very wide range of pNO3 photolysis rate constants from relatively few measurements makes the extrapolation difficult. Instead, we chose to examine the external cycling in more general terms using the comprehensive dataset obtained from an aircraft measurement campaign. Our external cycling argument is based on our field observations and deductions that HONO was an intermediate in the external cycling of NOx, and that the external cycling compensates for the daytime oxidation loss of NO2 and HONO and that external cycling contributed more to the budget of HONO and NO2 in low-NOx atmospheres. Please see the related discussion in the revised manuscript.\nIn lines 173-182, we discuss HONO as an intermediate based on field observations, “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 photolyse 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 atmospheres 9) 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.”\nIn lines 249-257, we summarized the role of external cycling in compensate the daytime loss of HONO and NO2, “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.”\nThe section on modeling the power plant plume in low-NOx conditions is still unclear.\nResponse: Following the advice of other referees, we have added new sentences and explained why and how we construct the model in lines 271-299. The model setup and initialization conditions are briefly described in the Methods section (lines 480-500) and summarized in Table S4.\nLines 270-298, “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 NO2 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.”\nReference\nYe, C. X., X. L. Zhou, D. Pu, J. Stutz, J. Festa et al., 2016 Rapid cycling of reactive nitrogen in the marine boundary layer. Nature 532: 489-491.\nReviewer #3 (Remarks to the Author):\n[Reviewer 2]\nThe authors have responded well to almost all the specific points I flagged in my initial review, and the manuscript is much improved, with all the science points addressed.\nI’m still troubled by how hard it is to follow the argument in the manuscript though – this is an issue of phrasing and precision, not science. Can I suggest the authors seek a “fresh pair of eyes” to look at the text throughout, but in particular the Introduction (L60-110) and final conclusions L377-L396 and really examine what each paragraph is trying to convey, and what precisely each sentence actually says.\nResponse: We deeply appreciate the reviewer’s encouragement and help! We have revised our manuscript accordingly.\nPhrasing Comments :\n-Introduction to / explanation of Fig 1 is lacking. Must include a really good concise definition of both internal and external cycling – this is critical – as the key terms used throughout the paper\nResponse: Our revision is shown in lines 57-75 as “HONO and NO2 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 NO2 and OH have been intensively examined as major HONO formation routes in the internal cycle 7-15. Since HONO photolyzes much faster, turnover routes of NOx to recycle HONO are the rate-limiting steps of the internal cycling. OH is a net product in the 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 its more oxidized reservoirs, which are referred to as NOz, as airmasses are transported away from source regions. NOx aging processes suppress the internal cycling and diminish the role of HONO photolysis in OH budget. However, model underestimation of the NOx/NOz ratio observations suggests unknown or underappreciated NOx regeneration pathways from NOz in low-NOx atmospheres 4,16-28. 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 the external source of NOx. Consequently, secondary OH production via NOx regeneration, and net primary OH production via HONO regeneration could greatly perturb OH photochemical budget.”\nL92 the *effective* rate constant ? Needs some more words somewhere in the sentence\nResponse: The sentence has been rewritten as “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.” (Lines 91-94)\nL94 I don’t think a rate constant can vote. I know what you mean but be precise in the phrasing – what you mean is “the range of values for rate constants / fundamental parameters which describe the individual candidate mechanisms differ widely between studies, precluding (as yet) confident confirmation of one or more dominant mechanisms”\nResponse: The suggested phrasing is more precise. Our revision shown in lines 94-109 as “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 size 30,38. Efforts in characterizing atmospheric aerosol properties and their photochemical reactivities are critical in quantitatively understanding the role of pNO3 photolysis in the 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 studies 18,21,22,30,33,34,36-39. 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.”\nL97 – the parameters/rate constants don’t vary with the chemical environment – if they are truly fundamental properties of a given reaction/mechanism – but the rate of the mechanism/reaction overall will. Again need to be much sharper between *parameters/rate constants* and reaction/process *rates*. Also L342\nResponse: We have rephrased it. Please also refer to the last response.\nL101 – tighten up what you mean by environmental variability. If fundamental parameters are obtained from the various literature studies – these should be independent of the NOx concentration (or H2O, j etc). If they vary with the chemical environment – then the mechanism is wrong/incomplete.\nResponse: We have rephrased it as shown in the above response.\nL131 – leading to conclusions – what are they – make this clearer. Suggest avoid words like “opinions” – the point is that different mechanisms (or parameters/rate constants) lead to different predicted NOx/HONO/OH variation in the atmosphere, suggesting that the dominant mechanism(s) have yet to be identified (or correctly characterized) ?\nResponse: We have rephrased it in Lines 137-140 as “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 cycling 4,21,32,34,38.”\nL252 – neither of the competing mechanism – interference is not a mechanism / you only mention one mechanism\nResponse: We have rephrased it in Lines 257-260 as “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.\nL265 – needs a new sentence to explain (big picture) why you are looking at the plume experiment. Start further “back” in the logic than the GEOS-Chem chemical scheme – what is the big picture aim/point of this ? “To explore the variation in NOx, HONO and OH with airmass age or extent of chemical processing, we examine one representative case – the evolution of chemical composition in a notional power plant plume, which covers a wider range of chemical conditions / NOx space, and relates <how ?> to the observation parameter space”\nResponse: We have rephrased the sentence in Lines 270-279 as “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.”\nL357-L362 I still think these specific technical details belong in the SI – they read very incongruously here\nResponse: These technical details explain why NOy might be underestimated in our measurement, and they are removed to the Methods Section (Lines 498-506).\nHigh / Low NOx: from an atmospheric chemistry perspective these are often considered in terms of the fate of peroxy radicals HO2/RO2 (ie do they terminate together or propagate with NO) – which would put “low NOx” way below 500 ppt. ie 500 pptv is going to be “high” to some. Maybe address here as simply as “here, low NOx is taken to refer to measurements where NOx < 500 pptv, which accounts for xx% of our observations – although we note that the outflow of the continental US will show higher NOx levels than the global remote troposphere” or something\nResponse: We have rephrased the sentence in lines 124-128 as “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 NO2 (see below).”"}]

Decision letter