Isotopic evidence for dominant secondary production of HONO in Isotopic evidence for dominant secondary production of HONO in near-ground wildfire plumes near-ground wildfire plumes

. Nitrous acid (HONO) is an important precursor to hydroxyl radical (OH) that determines atmospheric oxidative capacity and thus impacts climate and air quality. Wildﬁre is not only a major direct source of HONO, it also results in highly polluted conditions that favor the heterogeneous formation of HONO from nitrogen oxides (NO x = NO + NO 2 ) and nitrate on both ground and particle surfaces. However, these processes remain poorly constrained. To quantitatively constrain the HONO budget under various ﬁre and/or smoke conditions, we combine a unique dataset of ﬁeld concentrations and isotopic ratios ( 15 N / 14 N and 18 O / 16 O) of NO x and HONO with an isotopic box model. Here we report the ﬁrst isotopic evidence of secondary HONO production in near-ground wildﬁre plumes (over a sample integration time of hours) and the subsequent quantiﬁcation of the relative importance of each pathway to total HONO production. Most importantly, our results reveal that nitrate photolysis plays a minor role ( < 5 %) in HONO formation in daytime aged smoke, while NO 2 -to-HONO heterogeneous conversion contributes 85 %–95 % to total HONO production, followed by OH + NO (5 %–15 %). At nighttime, heterogeneous reduction of NO 2 catalyzed by redox active species (e.g., iron oxide and/or quinone) is essential ( ≥ 75 %) for HONO production in addition to surface NO 2 hydrolysis. Additionally, the 18 O / 16 O of HONO is used for the ﬁrst time to constrain the NO-to-NO 2 oxidation branching ratio between ozone and peroxy radicals. Our approach provides a new and critical way to mechanistically constrain atmospheric chemistry and/or air quality models on a diurnal timescale.

Abstract. Nitrous acid (HONO) is an important precursor to hydroxyl radical (OH) that determines atmospheric oxidative capacity and thus impacts climate and air quality. Wildfire is not only a major direct source of HONO, it also results in highly polluted conditions that favor the heterogeneous formation of HONO from nitrogen oxides (NO x = NO + NO 2 ) and nitrate on both ground and particle surfaces. However, these processes remain poorly constrained. To quantitatively constrain the HONO budget under various fire and/or smoke conditions, we combine a unique dataset of field concentrations and isotopic ratios ( 15 N / 14 N and 18 O / 16 O) of NO x and HONO with an isotopic box model. Here we report the first isotopic evidence of secondary HONO production in near-ground wildfire plumes (over a sample integration time of hours) and the subsequent quantification of the relative importance of each pathway to total HONO production. Most importantly, our results reveal that nitrate photolysis plays a minor role (<5 %) in HONO formation in daytime aged smoke, while NO 2 -to-HONO heterogeneous conversion contributes 85 %-95 % to total HONO production, followed by OH + NO (5 %-15 %). At nighttime, heterogeneous reduction of NO 2 catalyzed by redox active species (e.g., iron oxide and/or quinone) is essential (≥ 75 %) for HONO production in addition to surface NO 2 hydrolysis. Additionally, the 18 O / 16 O of HONO is used for the first time to constrain the NO-to-NO 2 oxidation branching ratio between ozone and peroxy radicals. Our approach provides a new and critical way to mechanistically constrain atmospheric chemistry and/or air quality models on a diurnal timescale.

Introduction
Vastly increased wildfire activity and intensity is a challenging issue in many parts of the world including the western US, and it is strongly linked to warming surface temperatures and earlier spring snowmelt (Westerling, 2016). Wildfire is a significant source of nitrogen oxides (NO x = NO + NO 2 ) and nitrous acid (HONO), as well as other important trace gases and particulate matter. NO x serves as a key precursor to atmospheric ozone (O 3 ) and secondary aerosols in the presence of organic compounds; in wildfire plumes NO x can be a limiting factor to O 3 production owing to high emission molar ratios of non-methane organic carbon (NMOC) to NO x (Akagi et al., 2011;Jaffe and Briggs, 2012). HONO is a major daytime photolytic precursor of hydroxyl radical (OH) via Reaction (R1) that determines the atmospheric oxidative capacity and therefore the lifetimes of many other species in the atmosphere. Wildfire-emitted HONO supplies the majority of OH in the first few hours after smoke emission in the day-time, and it greatly counteracts reduced OH production from O 3 photolysis caused by high particle loading reducing actinic flux (Jaffe and Briggs, 2012;Peng et al., 2020;Theys et al., 2020). Wildfire-emitted NO x and HONO not only greatly impact the atmospheric chemistry in local regions close to the fire but also contribute significantly to the reactive nitrogen (RN) burden thousands of kilometers downwind via transport and RN cycling, especially when mixed with fossil fuel combustion emissions (Jaffe et al., 2013;McClure and Jaffe, 2018;Westerling et al., 2006;Westerling, 2016).
Despite their important impacts on air quality, climate, and human and ecosystem health, the budgets of wildfire-derived NO x and HONO are poorly constrained due to limited field measurements, high reactivity and large spatiotemporal heterogeneity. Bottom-up approaches rely on limited emission factor measurements with uncertainty in HONO sources and chemistry; top-down approaches (i.e., satellite observations) have limited sensitivity in the lower troposphere and boundary layer and again are limited by large uncertainties in HONO sources and chemistry to interpret the satellite measurements. Although gas-phase reaction between OH and NO (Reaction R2) ubiquitously produces HONO, it is far from sufficient to explain the observed HONO levels in numerous studies given the fast photolysis during the day (Su et al., 2011). HONO, along with NO x , can be directly emitted from various sources including vehicle exhaust, biomass burning (BB) and microbially driven soil emissions. In addition, it has been proposed that HONO can be produced from other RN species (e.g., NO 2 and nitrate) via various heterogeneous pathways (Fig. 1). Major secondary HONO production pathways during the day include heterogeneous NO 2 conversion on photoactive surfaces (Reaction R3) (Ammann et al., 1998;George et al., 2005;Stemmler et al., 2006) and heterogeneous photolysis of nitrate including particulate nitrate (p-NO − 3 ) and nitric acid (HNO 3 ) via Reaction (R4) (Ye et al., 2016;Zhou et al., 2011). In past studies, heterogeneous conversion of NO 2 to HONO on photoactive surfaces such as organic surfaces (Reaction R3) has been proposed to explain a missing HONO source (Ammann et al., 1998;George et al., 2005;Stemmler et al., 2006;Wong et al., 2012). Organic surfaces exist in both aerosol particles and soils at the surface (e.g., humic acids), but there is major uncertainty associated with quantifying available surface area and the NO 2 uptake coefficient. During the night, surface (soils and aerosols) uptake is the predominant sink for HONO (Reaction R5), and heterogeneous conversion of NO 2 to HONO has been widely accepted as the major secondary HONO production source during the night (Reaction R6 and/or Reaction R7). Although it is clear that heterogeneous NO 2 hydrolysis (Reaction R6) can be a major pathway for nighttime HONO production (Finlayson-Pitts et al., 2003), recent work has also shown compelling evidence for faster HONO formation via reduction of NO 2 on inorganic surfaces (e.g., iron-bearing minerals) and organic surfaces (e.g., quinonerich humic acid) in soils and particulate matter (Reaction R7) (Scharko et al., 2017;Kebede et al., 2016;Martins-Costa et al., 2020). While the emission sources and heterogeneous pathways were hypothetically used to account for missing HONO sources (Stemmler et al., 2006;Su et al., 2011;Ye et al., 2016;VandenBoer et al., 2014;Donaldson et al., 2014a;Kebede et al., 2016;Scharko et al., 2017), their relative importance is poorly quantified due to large uncertainties associated with emission heterogeneity, surface area and composition, environmental condition (day versus night, temperature, relative humidity), quantification of heterogeneous reaction rate, and knowledge gaps in detailed mechanisms. As a result, the HONO budget in the atmospheric boundary layer remains poorly constrained.
HO + NO + M → HONO + M (M = third body gas molecules, e.g., nitrogen) (R2) Stable isotopes hold unique promise to provide rigorous constraints on sources, chemical processing pathways and sinks of RN species as they reflect isotopic signatures associated with these processes. δ 15 N (= [( 15 N / 14 N) sample / ( 15 N / 14 N) air−N 2 − 1] × 1000 ‰) has shown great potential to trace the atmospheric origin of NO x and its fate as nitrate (Hastings et al., 2009) (Thiemens, 2006). In particular, O 3 has an exclusively high δ 18 O as a result of mass-independent fractionation associated with its formation in the atmosphere, and this anomaly is transferred to oxidized products such as NO 2 , HONO and HNO 3 (Thiemens, 2006).
Using our recently developed and validated sampling techniques in combination with offline isotopic composition analyses , we characterized for the first time δ 15 N of NO x and HONO, as well as δ 18 O-HONO, in ground-level wildfire plumes in the western US as part of two major field campaigns: Western Wildfire Experiment for Cloud Chemistry, Aerosol Absorption and Nitrogen (WE-CAN) in summer 2018 and Fire Influence on Regional and Figure 1. The schematics of loss and secondary production of HONO in areas impacted by wildfire smoke in daytime (Reactions R1-R4) and nighttime (Reactions R5-R7). We conducted our sample collection <30 km from the edge of the wildfires, with smoke ages ranging from a few minutes to half a day. M is bath gas including N 2 , O 2 , CO 2 , etc. DSS is daytime substrate surface including terrestrial surfaces and aerosol particles that incorporate photoactive metal oxides (e.g., TiO 2 ), humic-like organics (e.g., quinone), etc. In essence, solar radiation induces reduction of these substrates with H, and this facilitates H abstraction by NO 2 (or H transfer). NSS is nighttime substrate surface (terrestrial and aerosol surfaces) containing iron-bearing minerals and/or humic acid (quinone). Note other sinks during both day and night (e.g., OH + HONO) are negligible compared to the major sinks shown here. Isotopic enrichment factors for N and O result from kinetic isotopic effects associated with each reaction and are calculated and expressed as 15 ε i and 18 ε i , where the subscript i indicates the reaction number, and the superscripts 15 and 18 denote the isotopic composition 15 N/ 14 N and 18 O/ 16 O, respectively. Global Environments Experiment -Air Quality (FIREX-AQ) in summer 2019. Here we report our findings based on samples collected in a mobile laboratory platform from three different wildfires; Rabbit Foot fire (RF) in eastern Idaho, Williams Flats fire (WF) in central Washington, and Nethker fire (NF) in northern Idaho (Figs. S1 and S2 in the Supplement). Surface-based mobile sampling allowed us to characterize young nighttime (YN), young daytime (YD), mixed daytime (MD), aged nighttime (AN) and aged daytime (AD) smoke. Physical smoke age determination using meteorological parameters near the ground is challenging due to large variations in wind speed and direction. Proxies involving total RN, NO y and ammonia (NH 3 ) relative to carbon monoxide (CO) can only be used to qualitatively evaluate smoke age due to large uncertainties in source emission factors and complexity caused by photochemistry Kleinman et al., 2007). In contrast, the concentration ratio between PM 2.5 and CO (PM 2.5 / CO) has shown potential for estimating smoke age (Yokelson et al., 2009;Selimovic et al., 2020). In this work, we determined the smoke condi-tions (young versus aged) primarily by comparing the field δ 18 O-HONO results with those obtained in our previous lab study that represents fresh emissions, with additional evaluation involving δ 15 N-HONO and relative concentration of HONO and NO 2 (Fig. 2). Note young and aged smoke refers to negligible and large proportions of secondarily produced HONO, respectively. We also take into account smoke sampling locations (i.e., approximate distance from the wildfire) to confirm the smoke age estimate. In brief, largely elevated δ 18 O-HONO in field samples compared with those from the lab-controlled fires signifies significant atmospheric processing, and this will be discussed in detail below. Our grouping method using δ 18 O-HONO shows fairly consistent results with those suggested by PM 2.5 / CO for WF and NF fire plumes (Kaspari et al., 2021). In addition to distinguishing aged smoke from young smoke, the grouped δ 18 O and δ 15 N also allow us to characterize potential mechanisms of secondary HONO formation in the aged smoke, as well as NOto-NO 2 oxidation pathways, with the HONO budget evalu- Figure 2. Box-whisker plots for concentration of NO 2 (left) and HONO (right) (a), δ 18 O-HONO (b) and δ 15 N-HONO (c) for each sample. Individual data points are plotted within each box grouped by various field smoke conditions including young nighttime smoke (YN), young daytime smoke (YD), mixed daytime smoke (M) that contains smoke contributed by either night smoke or fresh smoke, aged nighttime smoke (AN) and aged daytime smoke (AD). Data from three wildfires are shown here, including Rabbit Foot (RF) fire during the 2018 WE-CAN campaign, Williams Flats (WF) fire and Nethker fire during the 2019 FIREX-AQ campaign. N is sample number measured for each condition. Each box-whisker presents the 5th, 25th, 50th, 75th and 95th percentile of sample values in each group. ated using the synergistic measurement of HONO, NO and NO 2 concentrations in the field. During the WE-CAN campaign in August 2018, we conducted our measurements and sampling using the NOAA Chemical Science Division mobile laboratory (Molab), which was a cargo van with all instruments mounted on it. Meteorological instrumentation on the roof of the Molab provides temperature, relative humidity, wind speed, wind direction, altitude and GPS coordinates. All additional instruments were mounted onto the interior floor, and ambient air is sampled through 1 or 2 m Teflon inlets that exit the roof of the Molab via boreholes. NO and NO x concentrations were measured with a Thermo Scientific Model 42i chemiluminescence NO / NO x analyzer owned by Brown University, with ± 0.4 ppbv precision and 0.2 ppbv zero noise at 1 min time resolution. Note the NO x concentration measured using the chemiluminescence analyzer can be falsely elevated due to known interferences from NO y species, e.g., HONO and PAN. However, these data provide an upper limit of NO x level that supports the isotopic collections of NO x , HONO and nitrate. HONO and HNO 3 concentrations were measured using the University of New Hampshire's dual mist chamber and ion chromatograph (MC/IC) system with an uncertainty of 3 % at 5 min resolution Scheuer et al., 2003). During the FIREX-AQ field campaign in July-August 2019, we mounted our sampling instruments onto the NASA Langley mobile aerosol characterization platform (MACH-2) (Kaspari et al., 2021).

Description of sampling location and strategy
While our sampling strategy was similar in both years, the actual sampling approach differed in response to fire condition and accessibility to fresh smoke from the mobile platforms. During the 2018 WE-CAN campaign, our ground measurements and sampling targeted smoke from Rabbit Foot (RF) fire in the Challis area of Salmon-Challis National Forest in central Idaho, from 9 to 18 August 2018 (Salmon-Challis National Forest, 2018). Measurements were made at various locations around the Challis area of Idaho impacted by the RF fire, consisting of five different conditions: young smoke during nighttime (YN), young smoke during daytime (YD), aged smoke during nighttime (AN), aged smoke during daytime (AD) and mixed daytime smoke (M) that contains smoke contributed by either night smoke or fresh smoke. To sample the young smoke, we drove the Molab to Morgan Creek Road (MCR), which extends into a valley that was several kilometers away from the edge of the fire. We observed heavy smoke that based on distance and wind speed was expected to transport from the RF fire burning locations to the valley within a few hours or less. Three night trips and two day trips were made to MCR. While the nighttime measurements were conducted while driving, the daytime work was carried out while parked at a spike camp (i.e., a campsite for firefighters and support personnel) at the upper end of MCR; the spike camp was about 2 km from the fire, which we were able to see while conducting the measurements. The aged smoke was sampled at three stationary sites located around the Challis area, each less than 30 km away from the RF fire. All of these sites were recreational vehicle parks that allowed for power plugins. A total of 7 nights and 4 d were measured. The sampling locations and driving map are shown in Fig. S1 with detailed information on the measurements listed in Table 1.
During 2019 FIREX-AQ, we investigated five wildfires in the western US including Shady fire (Idaho), Black Diamond fire (Montana), Williams Flats fire (Washington), Nethker fire (Idaho) and Little Bear fire (Utah) from 24 July to 22 August 2019. We intensively sampled the emissions from Williams Flats fire and Nethker fire based on the large size and easy access to sampling locations (Fig. S2). Similar to

Collection of HONO, NO x and nitrate for isotopic analysis
Nitrogen oxides (NO x = NO + NO 2 ), nitrous acid (HONO), particulate nitrate (p-NO − 3 ) and nitric acid (HNO 3 ) were captured in the field using recently developed methods and sent to Brown University for analyses of isotopic composition Fibiger and Hastings, 2016;Chai and Hastings, 2018;Fibiger et al., 2014). In brief, HONO was completely captured at a pumping flow rate of ∼ 10 L min −1 with an annular denuder system (ADS), comprised (in order) of a Teflon particulate filter to re-move p-NO − 3 and a Nylasorb filter to remove HNO 3 , followed by two annular denuders, each coated with a premixed Na 2 CO 3 −glycerol−methanol−H 2 O solution following a standard Environmental Protection Agency (EPA) method (Chai and Hastings, 2018). Within 24 h after each collection, the coating was extracted in 10 mL of ultrapure water (18.2 M ) in two sequential 5 mL extractions. Particulate nitrate on the upstream Millipore filters and HNO 3 from the Nylasorb filters, if there was any, were extracted by sonicating the filters in ∼ 30 mL ultrapure H 2 O (18.2 M ). Samples with [NO − 3 ] >1 µM were analyzed for isotopic composition (concentration techniques detailed below).
The denuder-extracted solution with a pH of ∼ 10 was frozen and transported to Brown University for concentration and isotopic analysis, which was completed within 2 months after the sampling. The timescales for sample extraction and isotopic analysis preserve both the solution concentration and isotopic composition of HONO in the form of nitrite (Chai and Hastings, 2018). The two-denuder setup allows for the minimization of the interference for both concentration and isotopic analysis from other N-containing species that could be trapped and form nitrite in residual amounts on the denuders, especially NO 2 . Note that HONO levels were above the minimum detection limit (0.07 µM in extraction solution) and that the breakthrough amount of HONO threshold is far from being reached given the concentrations (Table 1), flow rate (∼ 8 L min −1 ) and collection times. Isotopic analysis of nitrite required the collection of a minimum amount of 10 nmol. NO x was completely collected in an impinging solution containing 0.25 M KMnO 4 and 0.5 M NaOH which oxidizes NO and NO 2 to NO − 3 by pumping sampled air through a gas washing bottle at a flow rate of ∼ 4 L min −1 . Collection time for HONO ranged from 2 to 12 h and that for NO x ranged from 0.75 to 2.5 h depending on their mixing ratios to make sure sufficient samples were captured against blanks for isotopic analysis (Fibiger et al., 2014;Fibiger and Hastings, 2016;Wojtal et al., 2016). Particulate filters and Nylasorb filters were collected over 7-12 h due to the low concentration of particulate nitrate and HNO 3 .
The samples from each collection system were retrieved and processed following the procedures described in . All treated samples from NO x , HONO, p-NO − 3 and HNO 3 collection and their corresponding blanks were analyzed offline for concentrations of NO − 2 and NO − 3 with a WestCo SmartChem 200 discrete analyzer colorimetric system. The reproducibility of the concentration measurements was ± 0.3 µmol L −1 (1σ ) for NO − 2 and ± 0.4 µmol L −1 for NO − 3 when a sample was repeatedly measured (n = 30). A detection limit of 0.07 µmol L −1 for NO − 2 and 0.1 µmol L −1 for NO − 3 was determined, and no detectable nitrite or nitrate was found in the blank denuder coating solution, whereas blank NO − 3 concentrations of ∼ 5 µM are typical for the NO x collection method (Fibiger et al., 2014;Wojtal et al., 2016). We only report the samples whose concentrations were at least 30 % above NO − 3 present in the blank KMnO 4 solution upon purchase to avoid increasing the error associated with the isotopic composition (Fibiger et al., 2014). Note that NO − 3 concentration was measured on the ADS solutions to verify whether and to what extent NO − 2 was oxidized to NO − 3 on denuder walls because the denitrifier method will convert both NO − 3 and NO − 2 to N 2 O for isotopic analysis (see below). Note that the complete collection of HONO and NO x have been verified in various environments including biomass burning emissions. During the FIREX fire lab experiment, we applied the same method to quantify the HONO and NO x isotopic composition . The concentrations of HONO captured with our ADS compared well with four other high-time-resolution concentration measurement techniques, including mist chamber and ion chromatography (MC/IC), open-path Fourier transform infrared spec-troscopy, cavity-enhanced spectroscopy, and proton-transferreaction time-of-flight mass spectrometer. In the same work, the NO x concentrations collected in the permanganate impinger were verified by real-time measurement with a chemiluminescence NO x analyzer. In addition, our NO x collection technique has been verified with real-time NO x concentrations in on-road, near-road and urban background environments (Wojtal et al., 2016;Miller et al., 2017). These agreements verify complete capture of HONO and NO x associated with biomass burning emissions using our techniques, which preserve the isotopic signatures without isotopic fractionation during the sampling process.

Isotopic analysis
The denitrifier method was used to complete nitrogen ( 15 N / 14 N) and oxygen ( 18 O / 16 O) isotope analyses of separate NO − 3 samples converted from NO x and NO − 2 samples converted from HONO by quantitative conversion to N 2 O by denitrifying bacteria P. aureofaciens (Casciotti et al., 2002;Sigman et al., 2001). The isotopic composition of N 2 O is then determined by a Thermo Finnigan Delta V Plus isotope ratio mass spectrometer at m/z 44, 45 and 46 for 14 N 14 N 16 O, 14 N 15 N 16 O and 14 N 14 N 18 O, respectively. Sample analyses were corrected against replicate measurements of the NO − 3 isotopic reference materials USGS34, USGS35 and IAEA-NO-3 (Böhlke et al., 2003) and that of the NO − 2 isotopic reference materials N7373 and N10219. Precisions for δ 15 N-NO x , δ 15 N-HONO and δ 18 O-HONO isotopic analysis across each of the entire methods are ± 1.3 ‰, ± 0.6 ‰ and ± 0.5 ‰, respectively (Chai and Hastings, 2018;Fibiger et al., 2014).

Concentrations of HONO and NO x
Among the three fires, increased HONO concentrations were observed in young smoke during both night (0.2-2.0 ppbv) and day (2.5 ppbv), while HONO level is significantly lower in aged smoke during both night (0.06-1.0 ppbv) and day (0.05-0.6 ppbv) as shown in Fig. 2a. Although median values show young night and day are significantly higher than aged smoke day and night, there is significant overlap between young nighttime and aged day and night for WF and Nethker fires. These parts per billion volume to sub-parts per billion volume HONO concentrations can be a major OH source in areas that are impacted by wildfire. We also determined the molar ratio HONO / NO 2 from the concentrations for each sample (Fig. 3) (Yokelson et al., 2009;Selimovic et al., 2020, and references therein). Our results for YN are also in agreement with airborne measurements (0.34 ± 0.08) from the BB-Flux campaign that occurred in parallel with WE-CAN but are lower than the WE-CAN airborne observation of 0.72 ± 0.34 during the day (Theys et al., 2020;Peng et al., 2020). It is worth noting that the majority of the WE-CAN airborne data overlap with the BB-Flux results and our measurements, and Peng et al. (2020) associate very high ratios with different transport dynamics of fresh plumes. The concentration results for the ADS collected [HONO] agree well with that measured via MC/IC in real time and averaged over the ADS sampling periods (Fig. S3). The good agreement between these techniques sampling the same plumes near the ground and previous agreement with other HONO and NO x observation methods suggest the concentrations are accurate (see also Sect. 2.3). It is important to also consider possible interference of peroxyacetyl nitrate (PAN) with NO x collected in the alkaline permanganate solution for biomass burning conditions (Jaffe and Briggs, 2012). There is minimum PAN formed in fresh biomass burning (BB) emissions and young smoke of less than half an hour, based upon previous lab and field measurements, as well as modeling studies (Stockwell et al., 2014;Yokelson et al., 2009;Alvarado et al., 2010Alvarado et al., , 2015. In aged BB plumes in the upper troposphere, PAN can form rapidly at low temperatures and act as a temporary NO x reservoir, reaching a maximum PAN / NO y ratio of 0.3 (comparable to NO x / NO y ) within ∼ 2 to 4 h of aging after emission (Yokelson et al., 2009;Liu et al., 2016;Akagi et al., 2012). Though we note that these results are all from airborne measurements. There are no ground-level measurements for PAN in BB plumes during WE-CAN or FIREX-AQ, nor from other field studies to the best of our knowledge. PAN is thermally unstable in the boundary layer during summertime, and its main loss process in the atmosphere is thermal decomposition to release NO 2 . The lifetime of PAN is on the order of 1 h or less at 20 • C and above (Talukdar et al., 1995;Fischer et al., 2010). We therefore expected PAN in near-ground air to maintain low levels or less due to photochemistry and thermal decomposition. Thus, given the short lifetime and the sample integration time of over 40 min to 2 h timescale, PAN is unlikely to interfere with our NO x results.
In the aged smoke, [HONO] / [NO 2 ] are greatly reduced to median values of 0.05 and 0.07 observed for AN and AD, respectively, lower than the lab-derived range (Fig. 3). Wildfire plumes near ground level are expected to be more diluted than those directly injected upwards during the day, and the loss of HONO due to photolysis in the plume and/or surface reactions would be expected to be much faster than that in higher altitude dense plumes. The very low ratios indicate that HONO was lost faster than NO x ; however, given the 10-20 min lifetime of HONO against photolysis during the day and up to a couple of hours during the night (Nie et al., 2015), and considering aged smoke was sampled tens of kilome- ters from the fire, HONO levels may be maintained via secondary chemistry due to the high particle loadings and other terrestrial surface reactions in wildfire plumes (Alvarado and Prinn, 2009). While the concentration data are valuable for the ground-based setting near the fires, considerable uncertainty exists in the rate coefficients of the heterogeneous processes in daytime, as well as the HONO and NO 2 uptake coefficient and surface area densities (Appendix A). This makes it challenging to quantify the relative contribution of each potential pathway to the observed HONO budget.

Isotopic signatures of HONO and NO x
In the 2016 FIREX fire laboratory experiment, we obtained δ 15 N of NO x and HONO, as well as δ 18 O of HONO, in direct emissions from controlled burning of various vegetation biomasses representative of the western US . The lab-based δ 15 N and δ 18 O results serve as source signatures of biomass burning (BB) emissions: δ 15 N-NO x (−4.3 ‰ to +7.0 ‰) and δ 15 N-HONO (−5.3 ‰ to +5.8 ‰) are derived from biomass N and the transformation in the combustion process, and δ 18 O-HONO (5.2 ‰ to 15.2 ‰) incorporates δ 18 O of molecular oxygen and water via combustion reactions . In the field, we expect that once NO x and HONO are released and transported, atmospheric processing including photochemistry and nighttime chemistry would cause the isotopic composition of emitted NO x and HONO to change.
By directly comparing the field-measured δ 18 O-HONO with that measured from lab-controlled burning, we separate the data observed in young smoke from those in aged smoke. Very young smoke largely reflects fresh wildfire emissions without significant atmospheric processing, while aged smoke δ 18 O-HONO should deviate from the lab values due to the influence of secondary chemistry involving RN cycling. The δ 18 O-HONO of young nighttime smoke ranged from 4.8 ‰ to 32.3 ‰ with a median value of 19.0 ‰, while the value in a single young daytime sample was 25.6 ‰ (Fig. 2b). There is a major overlap between the lab results and young nighttime smoke but with some higher δ 18 O-HONO values in the field observations. These results suggest the HONO sampled in young smoke was dominated by primary BB emissions from the nearby wildfire but included contributions of secondarily produced HONO. By contrast, δ 18 O-HONO is greatly elevated in aged smoke from all three fires both day and night. In addition, two aged smoke samples are labeled as mixed smoke because the collection interval included both sunlit and dark periods. The enrichment of δ 18 O-HONO (up to 78 ‰), regardless of location and time, suggests that HONO in these conditions is produced by secondary chemistry involving NO, NO 2 and nitrate, which transfer high δ 18 O values due to O 3 influence via photochemistry (Appendix B) (Thiemens, 2006;Michalski et al., 2003). The varying δ 18 O-HONO values reflect different oxidizing environments, i.e., NO-to-NO 2 conversion via RO 2 versus O 3. These branching ratios can be determined if we resolve the dominant pathways for HONO production.
The δ 15 N-HONO in the young smoke ranges from −0.3 ‰ to +7.4 ‰ with a median value of 2.8 ‰ for YN and +3.4 ‰ for YD, whereas that in the aged smoke shows decreased median values of −2.9 ‰ and −1.8 ‰ for AN and AD, respectively. In addition, the daytime aged smoke exhibits the largest variability (Fig. 2c), and this likely reflects daytime HONO secondary chemistry. It is noted that δ 15 N-NO x and δ 15 N-HONO measured across the entire period of all three fires at ground level ranges from −4.3 ‰ to +8.7 ‰ and −6.7 ‰ to +7.4 ‰, respectively, with the majority overlapping with the corresponding ranges found in the fire laboratory experiment and no significant difference in mean values (p value >0.5) Fibiger and Hastings, 2016). This consistency suggests δ 15 N is a reliable tracker generally for BB-derived NO x and HONO, although there is clear variability between the different smoke conditions that can refine our understanding of reactive N cycling. We note again that, although no near-ground PAN measurements in BB plumes are available, the isotopic results also suggest that PAN interference is not important to the δ 15 N-NO x results. For aged smoke, we would expect δ 15 N-NO x to decrease from that in fresh emissions due to partial transformation of NO x to additional oxidized N products (e.g., PAN), as well as isotopic exchange between NO x and these oxidized species; both processes will leave 15 N depleted in NO x and 15 N enriched in PAN (Walters and Michalski, 2015). If PAN existed at significant concentrations that were (1) comparable with NO x in the atmosphere and (2) completely collected in the permanganate solution, then the δ 15 N would reflect the overall δ 15 N of NO x + PAN in the final reduced per-manganate solution. In this case, we would expect that aged smoke would not shift from the δ 15 N-NO x range of young smoke because δ 15 N shifts in both PAN and NO x could offset each other. However, our observed δ 15 N-NO x mean values for both aged daytime and nighttime smoke are significantly (p<0.05) lower than that of the young smoke, a good indicator of a lack of PAN interference on the isotopic results (see also Miller et al., 2017).
Our prior lab-controlled burning study revealed a linear relationship between δ 15 N-HONO and δ 15 N-NO x , with δ 15 N-HONO slightly more negative than δ 15 N-NO x in fresh BB emissions . This δ 15 N relationship is plotted as a solid line, together with all field observations, to illustrate the potential influence of atmospheric processing on the δ 15 N-HONO and δ 15 N-NO x (Fig. 4). The plot can be sub-divided into three regimes. In regime I, we find all of the δ 15 N of NO x and HONO in young smoke from both daytime and nighttime. In this young smoke regime, more positive δ 15 N than that of the rest of our samples is found for both species, and all samples concur with the δ 15 N relationship found for fresh emissions (Fig. 4). This, along with the low δ 18 O-HONO associated with these samples (Fig. 2b), confirms HONO is not significantly affected by secondary chemical processing in the air mass captured from fresh smoke. Regime II is filled with the results of daytime aged smoke ∼ 30 km away from the RF fire; these results exhibited much more positive δ 15 N-HONO than δ 15 N-NO x by 3 ‰ to 6 ‰, as well as the largest (positive) discrepancy from the BB δ 15 N relationship line, as shown in the upper left region of Fig. 4. The daytime aged smoke also exhibited the highest values of δ 18 O-HONO observed (Fig. 2). All samples of aged nighttime smoke that were collected fall in regime III. While the majority of the regime III data fall within the 95 % confidence interval for the lab-based δ 15 N relationship, there is a tendency for these samples to have δ 15 N-HONO that was more negative than δ 15 N-NO x to different degrees of up to −8.7 ‰. In particular, we hypothesize that the combination of more negative δ 15 N-HONO values and elevated δ 18 O-HONO indicate secondary production of HONO. We next explore quantitative use of δ 15 N-NO x , δ 15 N-HONO and δ 18 O-HONO to understand the isotopic shifts in terms of secondary chemistry involving RN cycling.

Isotopic mass balance modeling
In aged smoke, the observed δ 18 O-HONO enhancement and shift of δ 15 N values away from the δ 15 N NO x -HONO line, as a result of RN cycling, would be expected to be derived from the integrated kinetic isotopic fractionation (expressed as enrichment factor 18 ε and 15 ε) associated with each of the loss/production processes (Fig. 1) weighted by their relative contribution to the budget. By definition, ε = (α − 1) × 1000 ‰, with fractionation factor α referring to the rate coefficient ratio between the heavy isotopologue and the light isotopologue. For δ 18 O-HONO, we also took into account the transferring effect of oxygen from different Ocontaining reactants that produce HONO (as explained in Appendix B). In order to elucidate the relative role each process plays in the HONO budget, we constructed an isotopic mass balance model for δ 15 N and for δ 18 O.
In aged smoke, a deviation in δ 15 N, represented as δ 15 N HONO−NO x (= δ 15 N-HONO − δ 15 N-NO x ), is simulated following Eq. (1), where f is the fraction of reaction i (reaction numbering in Sect. 1) to total loss (L) or production (P) of HONO. δ 18 O-HONO is simulated following Eq. (2), in which the change in δ 18 O-HONO i,P arises from, in addition to kinetic isotopic fractionation, the transferring of δ 18 O i,t (Eq. 3) in the reactant (OH, NO, NO 2 , H 2 O and NO − 3 ) to the product HONO as HONO contains two O atoms that may stem from more than one reactant (Appendix B). The δ 18 O values of all possible reactions that produce HONO are evaluated, as tabulated in Table S1 in the Supplement, to help determine δ 18 O of NO, NO 2 and HONO. The isotopic enrichment factors 15 ε and 18 ε associated with each of Reactions (R1)-(R7) are computed via theoretical principles as none of these key parameters are currently available in the literature (Appendix B).
3.3.1 Modeling of δ 15 N of HONO and NO x in aged daytime and nighttime smoke We first simulated δ 15 N HONO−NO x for both daytime and nighttime aged conditions using this model. According to the potential HONO-NO x chemistry in ground areas impacted by wildfire smoke plumes (Fig. 1), HONO is expected to be predominantly lost to photolysis (Reaction R1) during the day. It is well known that HONO can be produced via a gas-phase radical recombination reaction between NO and OH (Reaction R2) (Platt et al., 1980). However, the rate of Reaction (R2), calculated from the rate coefficient, the typical daytime OH concentration (1-2 × 10 6 molecule cm −3 ) (de Gouw et al., 2006) in biomass burning plumes and our measured mean NO x concentration, can only account for up to 15 % of the HONO production rate (Appendix A and Table A1). Under a typical pseudo-steady-state approximation (PSSA) (d[HONO]/dt ≈ 0), additional sources of HONO must be included to balance the HONO budget. Thus, we modeled three scenarios varying the relative contribution of Reaction (R2) as 5 %, 10 % and 15 %. With rapid photolytic loss, HONO has a lifetime nearly 2 orders of magnitude shorter than the lifetime of NO in Reaction (R2), as well as that of NO 2 in Reaction (R3) and nitrate in Reaction (R4); thus, the δ 15 N HONO−NO x is mostly sensitive to the change in δ 15 N HONO immediately upon photolysis but overall remains constant, associated with Reactions (R2)-(R4) within the timescale of HONO photolysis. We quantify the remaining HONO fraction from secondary production, f rp , to represent HONO that has been produced but not yet photolyzed. Thus, the daytime δ 15 N HONO−NO x for aged smoke was simulated as a function of f rp following a Rayleigh-type isotopic fractionation scheme ( Fig. 5 and Sect. B2.1). Generally, δ 15 N HONO−NO x follows an exponential increase as f rp decreases. In other words, as more photolysis occurs the difference in the remaining δ 15 N-HONO and the δ 15 N-NO x increases, and this is driven by the negative value of 15 ε 1 which tends to enrich 15 N in the HONO reactant (Reaction R1). The simulation was carried out for two different sets of HONO production mechanisms, with HONO photolysis being the dominant loss pathway. With mechanism M1 (solid lines in Fig. 5), photo-induced surface NO 2 -to-HONO conversion (Reaction R3) is the major pathway in addition to gas-phase OH + NO (Reaction R2) to produce HONO. As 15 ε 2 has a positive value, a larger Reaction (R2) contribution leads to higher δ 15 N HONO−NO x . With mechanism M2 (dashed line in Fig. 5), nitrate photolysis (Reaction R4) is included in addition to Reactions (R2) and (R3) in the HONO production mechanism. Taking the contribution of Reaction (R2) of 10 % as a constant, three scenarios were modeled by varying the relative contribution of Reaction (R3) (75 %-85 %) and Reaction (R4) (5 %-15 %). The results suggest larger Reaction (R4) contribution yields lower δ 15 N HONO−NO x due to severe 15 N depletion associated with nitrate photolysis ( 15 ε 4 ≤ −47.9 ‰) (Appendix B). Importantly, the addition of Reaction (R4) in M2 also lowers δ 15 N HONO−NO x compared to M1. By applying the fieldobserved δ 15 N HONO−NO x for the aged daytime smoke to the model, we solved f rp for all scenarios and plotted these as circles in Fig. 5. All five aged daytime datasets from RF can be reproduced by M1 under all three scenarios; by contrast, via M2, none of the three scenarios can explain the two highest δ 15 N HONO−NO x values observed in the field. As such, we conclude that Reaction (R4) plays a minor role (<5 %) in the secondary HONO production in the aged daytime smoke during our sampling periods. Rather, HONO forms primarily via Reactions (R2) and (R3) during the day in the areas impacted by aged wildfire smoke. However, there are two limitations to the modeling results. First, as the 15 N / 14 N fractionation associated with Reactions (R3), (R6) and (R7) are not distinguishable with our current parameterization (Appendix B1.2 and B2.2), we cannot rule out the potential importance of heterogeneous NO 2 -to-HONO conversions (Reactions R6 and R7) in daytime. Second, it should be noted that the results represent our best estimate of the average relative importance of Reactions (R2)-(R4) for HONO production during our HONO sampling periods (2-10 h) for the aged daytime plume. Due to the long sample integration time, our samples were influenced by both aged smoke and near-background air when the smoke was very diluted. Under the NO x -limited condition (low NO x <1 ppbv) in remote background air, nitrate photolysis is expected to be the major secondary HONO source (Ye et al., 2016;Zhou et al., 2011), which cannot be ruled out by our results. Isotopic measurement techniques with higher time resolution will be required to achieve real-time quantification of the HONO budget.
For the nighttime smoke, we simulated that the HONO budget is maintained by Reactions (R5)-(R7).
δ 15 N HONO−NO x reflects the combination of kinetic isotopic fractionation 15 ε 5 associated with the HONO loss (Reaction R5) and production reactions (Reactions R6 and R7 in proportion). With our calculated uptake 15 ε 5 (−2 ‰) and estimated 15 ε 6 or 15 ε 7 (ranging from −2.9 ‰ to −4.5 ‰), we obtained δ 15 N HONO−NO x ranging from −0.9 ‰ to −2.5 ‰ when uptake and production occur at a similar timescale (rate coefficient), and this can explain the majority of observed aged nighttime results (regime III; Fig. 4). Two aged nighttime points sampled for RF (16 and 17 Au- In the first mechanism (M1, solid lines), Reaction (R3) is the major HONO production pathway with a varying relative contribution from Reaction (R2), which is constrained as producing no more than 15 % of the observed HONO concentrations. In the second mechanism (M2, dashed lines), nitrate photolysis (Reaction R4) is included in addition to Reactions (R2) and (R3) for HONO production. Taking the contribution of Reaction (R2) of 10 % as a constant, three scenarios were modeled by varying the relative contribution of Reaction (R3) (75 %-85 %) and (R4) (5 %-15 %). gust 2018) fall outside of the predicted range, with much lower δ 15 N HONO−NO x (−8.7 ‰ and −5.5 ‰, respectively). These two samples were associated with 2-10 times elevated NO x concentration compared to the previous 4 nights and likely higher concentrations of particulate matter (Figs. 2a; Fig. S4 in the Supplement). This could cause an accelerated conversion of NO 2 -to-HONO, which is not accounted for in the steady state estimation above, leading to the much lower δ 15 N HONO−NO x values that were observed.

Modeling of δ 18 O of HONO in aged daytime and nighttime smoke
The  (Thiemens, 2006), while OH and RO 2 have very low δ 18 O values (Thiemens, 2006). O 3 participation in reactive N cycling involving NO x (Reaction R8) results in high δ 18 O of NO 2 (Michalski et al., 2003;Walters et al., 2018 The δ 18 O signature is subsequently passed to HONO when it is produced from NO (Reaction R2) and NO 2 (Reaction R3) during the day and from NO 2 (Reactions R6 and R7) during the night, and thus δ 18 O-HONO is a positive linear function if kinetic isotopic fractionation ( 18 ε) associated with these processes are fixed values (as calculated in Appendix B). Given that HONO is predominantly produced via Reactions (R2) and (R3) in aged daytime smoke (Fig. 5), δ 18 O-HONO was simulated following the three M1 scenarios with the contribution of Reaction (R2) varying from 5 % to 15 %. All three scenarios reproduced the range of our field results for aged daytime smoke, further pointing to M1 as explaining the HONO in this environment. In addition, the variation in δ 18 O was driven by differing oxidation that is determined by f NO O 3 /(O 3 +RO 2 ) , which depends on the relative concentration of O 3 to RO 2 (Figs. S5 and S6). The f NO corresponding to each observed δ 18 O-HONO were solved and plotted in Fig. 6a. We found f NO O 3 /(O 3 +RO 2 ) decreased by less than 0.02 as the contribution of Reaction (R2) to total HONO production decreased from 15 % to 5 %. On the other hand, δ 18 O-HONO changes sensitively with varying f NO O 3 /(O 3 +RO 2 ) , increasing from 50.2 ‰ to 78.0 ‰ as the fraction of NO oxidized by O 3 rather than RO 2 increases from 0.34 to 0.65.
The δ 18 O-HONO of nighttime aged smoke was modeled following the nighttime chemistry (Reactions R5-R7), i.e., taking NO 2 conversion as the source and surface uptake as the sink. In areas impacted by nighttime aged smoke, HONO forms from wildfire-derived NO 2 residing in the nocturnal boundary layer. As the two pathways (Reactions R6 and R7) for heterogeneous NO 2 conversion lead to very different δ 18 O-HONO stemming from different δ 18 O transfer (Appendix B), we examined the relative importance of the two  Table S3 in the Supplement. During the night (b), three scenarios with various contributions of Reactions (R6) and (R7) are modeled ( Fig. S6 and Table S4) is predicted to be over unity for the last four observed δ 18 O-HONO values if Reaction (R6) is assumed as the only nighttime pathway. pathways for HONO production by varying the relative contribution between the two pathways and comparing it to the observed δ 18 O-HONO (Fig. 6b). If HONO is constrained to exclusively form via Reaction (R6) (surface hydrolysis), the model would require an unrealistic f NO O 3 /(O 3 +RO 2 ) >100 % to explain δ 18 O-HONO >55 ‰. Even for samples with lower δ 18 O-HONO values (34 ‰ to 52 ‰), the high branching ratio f NO O 3 /(O 3 +RO 2 ) (>0.6) required to create such large enrichment is unrealistic for BB environments. In particular, solved under this mechanism is at least twice as large as values derived from the previous field measurement of aged wildfire smoke (Baylon et al., 2018). By contrast, the inclusion of Reaction (R7) in addition to Reaction (R6) in rate ratios 3 : 1 and 20 : 1 based on previous lab studies (Kebede et al., 2016;Scharko et al., 2017) can elevate the modeled δ 18 O-HONO and explain all observed δ 18 O-HONO values. This suggests NO 2to-HONO heterogeneous conversion catalyzed by surfacehosted iron oxides and quinone (Reaction R7) in the nighttime aged smoke proceeds significantly faster than NO 2 hydrolysis (Reaction R6). Our isotopic analyses provide evidence for the participation of such a pathway in BB environments and also shows the capability to constrain the relative importance between these two pathways. Although the daytime δ 18 O-HONO can be larger than that of nighttime aged smoke, similar [O 3 ] / [RO 2 ] ratios are derived from our solved f NO O 3 /(O 3 +RO 2 ) and are consistent with the limited field measurements (Parrington et al., 2013;Baylon et al., 2018), and they further indicate the important role peroxy radicals play as an oxidant in wildfire-smoke-impacted environments.

Conclusions
As wildfire has enormously impacted climate, air quality and ecosystems in the past and is expected to worsen (Westerling, 2016), accurately tracking wildfire-derived reactive nitrogen species (i.e., NO x and HONO) and their cycling is extremely important for quantifying and mitigating key pollutants such as O 3 in wildfire-impacted areas both close to the fire and thousands of kilometers downwind. We show δ 15 N-HONO and δ 15 N-NO x can serve as a powerful tool to track BB sources and constrain secondary HONO production pathways. With the help of field-observed δ 18 O-HONO, we grouped our measured relationship between the δ 15 N-HONO and δ 15 N-NO x into three different regimes, which clearly distinguish between young wildfire plumes, aged daytime plumes and aged nighttime plumes. The δ 15 N results allow for constraining the daytime HONO budget and particularly secondary production mechanisms via the isotope mass balance simulation. The use of excess δ 15 N ( δ 15 N HONO−NO x ) also provides an approach for constraining HONO budgets in other environmental settings, such as urban ambient areas and remote areas including forest and polar regions. Furthermore, by combining δ 15 N emission source signatures and chemical fractionation characteristics, we could potentially track the impact and relative role of wildfire-derived reactive nitrogen more extensively when the plume transfers thousands of kilometers downwind and mixes with other air such as urban plumes. In addition, the δ 18 O-HONO results not only offer direct evidence for secondary production of HONO that allows for the determination of the NO oxidizing branching ratio between O 3 and RO 2 but also constrains nighttime HONO production mechanisms. We expect to apply the δ 18 O-HONO approach to a variety of atmospheric settings for constraining the HONO budget and its cycling with other reactive nitrogen species, as well as O 3 . As such, online isotopic measurement techniques with higher time resolution will benefit the use of stable isotopes and broaden its application in atmospheric chemistry. In the meantime, in order to more accurately quantify the relative contribution of these potential pathways, further experimental and theoretical investigations on isotopic fractionation characteristics of each pathway under various environmental conditions are required.

Appendix A: Overview of HONO budget quantification under different conditions based upon concentrations
A common approach to quantitatively understand the wildfire-derived HONO budget -its direct emissions, secondary productions and sinks -is to use concentration-based mass balance calculation. Ideally, if we know the rate coefficients and reactant concentrations for each of the pathways, we would be able to quantify the relative contribution of each pathway to the total HONO concentration measured in the field under the assumption of pseudo-steady-state approximation (PSSA) as described in Eq. (A1), where R emission , R production and R loss are rate of emission, production and loss, respectively. In aged smoke, we expect HONO is almost exclusively produced from secondary formation. During the day, HONO is predominantly lost to photolysis with a coefficient depending on solar zenith angle differing with time of the day, while one or more reactions of Reactions (R2)-(R4) may be responsible for producing HONO. Under PSSA, using the well quantified rate coefficient k 2 , observed NO and HONO concentrations, estimated OH concentration, and TUV-model-calculated (tropospheric ultraviolet and visible) HONO photolysis coefficient j HONO , we estimated the ratio of Reaction (R2) to the total HONO production (P OH+NO ) via Eq. (A2) and found Reaction (R2) can only contribute 2 %-15 % (Table A1) of the total HONO production under the ambient conditions when the five aged daytime samples were collected. This suggests at least 85 % of HONO was produced from heterogeneous HONO formation via Reaction (R3) and/or Reaction (R4).

d[HONO]
dt = R emission + R production − R loss ≈ 0 (A1) HONO production from photo-enhanced NO 2 conversion has been proposed to take place on various types of surfaces. However, the uptake coefficient (γ hν NO 2 →HONO ), which indicates the probability of NO 2 collisions with a surface that results in the formation of a HONO molecule, varies by at least 3 orders of magnitude depending on the specific type of surface materials. For instance, γ hν NO 2 →HONO on soot particles was found to range from 3.7 × 10 −4 to 1.1 × 10 −3 s −1 (Ammann et al., 1998), while that on surfaces comprised of humic acid was measured as 2-8×10 −5 s −1 in several lab studies (Stemmler et al., 2006;Scharko et al., 2017). The latter is consistent with daytime modeling results of 6 × 10 −5 s −1 (Wong et al., 2013). Additionally, a much smaller (10 −7 -10 −6 s −1 ) γ hν NO 2 →HONO value was obtained for metal oxide surfaces such as TiO 2 and SiO 2 (Ndour et al., 2008).
Daytime photolysis of nitrate (HNO 3 and pNO − 3 ) via Reaction (R4) has also been proposed as an important renoxification pathway that produces HONO and NO 2 in low NO x remote environments (Zhou et al., 2011), as well as high NO x urban settings with abundant urban grime (Baergen andDonaldson, 2016, 2013). The p-NO − 3 and surface-adsorbed HNO 3 were found to be photolyzed with rate coefficients 2-3 orders of magnitude larger than gas-phase HNO 3 and possess lifetimes as short as a few hours (Ye et al., 2017). However, the rate coefficient of Reaction (R4) is poorly constrained. Not only have the branching ratios between the NO x -producing channel and HONO-forming channel been poorly known (Baergen and Donaldson, 2016), but previous laboratory-measured nitrate photolysis rate coefficients also vary by up to 3 orders of magnitude (Ye et al., 2017). The uncertainty is even greater because it is complicated by dependence on relative humidity, particle composition and pH.
During the night, HONO is primarily lost to uptake on surfaces including aerosols and soils, and the uptake coefficient can be expressed by Eq. (A3).
In this equation, ω HONO is the mean thermal HONO molecular velocity calculated by ω HONO = √ 8RT /π M, where R, T and M are the gas constant, absolute temperature and molecular weight. S/V is the surface-to-volume ratio (cm 2 cm −3 ). The uptake coefficient γ HONO was measured to be 10 −5 for soil surface and in the range of 10 −5 -10 −3 for aerosol particle surface (Donaldson et al., 2014b;Wong et al., 2012). In addition, OH + HONO occurs at rates 1-2 orders of magnitude smaller than the uptake and therefore plays a minor role. The combined loss processes lead to a HONO lifetime of about 4 h during the night.
HONO is generally assumed to be produced via heterogeneous NO 2 hydrolysis disproportionation (Reaction R6) (Finlayson-Pitts et al., 2003), and the production rate of HONO is estimated by Eq. (A4), expressed in the unit of ppbv-HONO ppbv −1 -NO 2 s −1 .
where ω NO 2 is the mean NO 2 molecular velocity, and S/V is the surface-to-volume ratio of particles, which could range from 9.0 × 10 −6 to 3.0 × 10 −4 cm 2 cm −3 for normally polluted areas and highly polluted areas, respectively (Spataro and Ianniello, 2014). The S/V in biomass burning smoke plumes has huge uncertainty; additionally, ground surface is also expected to play an important role in nighttime HONO production given our ground sampling location (Tuite et al., 2021;Scharko et al., 2017;Kebede et al., 2016;Stemmler et al., 2006); however, its S/V is not well defined/quantified. Overall, considerable uncertainty remains regarding the rate coefficient of the heterogeneous processes in the daytime, as well as the HONO and NO 2 uptake coefficients and S/V ratio. This uncertainty, complicated further with large variability in fire behavior and emissions, make the HONO budget quantification extremely challenging. Surface uptake is the major sink for HONO during the night. Surface uptake of HONO has been found to be kinetically limited by bulk diffusion in particles containing viscous organic-water matrices, and it incorporates two simultaneous processes: (1) reactive uptake of HONO on the bare particle/mineral surface and (2) accommodation and reaction of HONO in the bulk aqueous layer that is affected by pH and diffusion in the organic-water matrix (Donaldson et al., 2014b). The uptake coefficient of HONO is determined by the competition between these two processes as a function of fraction of water coverage on the surfaces, θ H 2 O , ranging from 0 to 1 in Eq. (B1), where γ 0 and γ 1 are the reactive uptake coefficients of HONO onto particle (mineral/soil) surfaces at dry (θ H 2 O = 0) and wet (θ H 2 O = 1) conditions, respectively. Under completely dry conditions (θ H 2 O = 0 or relative humidity (RH) = 0 %), the former process is dominant, and the isotopic fractionation can be estimated by the ratio of the square root of inverse mass, which is caused by different thermal velocities (ω HONO ) of two isotopologues following Eq. (B2), where R is the gas constant, T is absolute temperature, and M is the molecular weight. Thus, heavier isotopes are depleted in HONO, resulting in −10 ‰ and −20 ‰ for 15 ε and 18 ε, respectively. By contrast, under wet conditions when RH is 30 % which results in a monolayer water coverage on particle surfaces (θ H 2 O = 1), the aqueous layer uptake becomes dominant, and the wet uptake coefficient γ 1 can be mechanistically simulated with a resistor model simplified as Eq. (B3) (Hanson, 1997;Pöschl et al., 2007). In Eq. (B3), α is the accommodation coefficient describing the probability that a HONO molecule striking a water-coated particle enters into the bulk liquid phase, and b is the solubility of HONO in the bulk water in the particles or soils. b can be calculated with Eq. (B4), where D a is the apparent diffusion coefficient of HONO in the particle-water (soil (organics)water) matrix, and τ is the exposure time. H eff is the effective Henry's law constant that depends on the absolute Henry's law constant for HONO, pH, and acid dissociation constants for HONO (K a1 ) and H 2 NO + 2 (K a2 ).
Taking the previously measured HONO γ 1 of 2 × 10 −5 as that for the light isotopologue and α of 5.8 × 10 −5 as a constant (Donaldson et al., 2014b), b (H 16 O 14 N 16 O) is calculated to be 1.36 × 10 −5 following Eq. (B3). As derived from Eqs. (B2) and (B4), b ratio between two isotopologues equals the ratio between the two molecular weights, and therefore b (H 16 O 15 N 16 O) and b (H 16 O 15 N 16 O) were calculated and used to derive the corresponding γ 1 values. The fractionation factor associated with HONO uptake (α u-HONO ), defined as the ratio between heavy and light rate coefficients (k H /k L ), was calculated following the relationship determined by Eq. (B5). On the basis of this model, we estimate that the isotopic fractionation associated with the wet uptake process is −2 ‰ and −4 ‰ for 15 ε and 18 ε, respectively. From our calculation, RH clearly influences isotopic fractionation in the range of 0 %-30 %, with the wet uptake of HONO favoring a smaller kinetic isotope effect than dry uptake.

B1.2 Isotopic fractionation of N and O associated with each nighttime HONO production pathway
Heterogeneous conversion of NO 2 to HONO has been widely accepted as the major secondary HONO production source during the night. However, the mechanism via which the conversion occurs remains disputed. Additionally, the kinetic isotopic fractionation factor (KIF) associated with this pro-  (3) desorption of HONO from aqueous to gas phase. Recently it was shown that reduction of NO 2 on iron-bearing minerals and quinone-rich humic acid in soils and particulate matter (Reaction R7) leads to faster HONO production than NO 2 hydrolysis. Although differing in reaction mechanism, the two possible pathways (Reactions R6 and R7) proceed in three steps including uptake of NO 2 into the surface aqueous layer, reactions in aqueous phase and desorption of HONO from aqueous to gas phase. The first two steps are limited by aqueous diffusion, and it is reasonable to assume diffusionlimited processes in the aqueous phase create no KIF. As HONO desorption may involve hydrogen bond breaking of complex HONO-(H 2 O) n , this process likely determines the KIF associated with the heterogeneous NO 2 -to-HONO conversion (α d ), as calculated by Eq. (B6), where µ l and µ h are the reduced mass for the light and heavy isotope containing pair, respectively (Shi et al., 2019). As a result, 15 ε and 18 ε are estimated to be −2.9 ‰ (n = 1) to −4.5 ‰ (n = 2) and −5.7 ‰ (n = 1) to −8.9 ‰ (n = 2), respectively. For the isotope mass balance modeling, mean values of 15 ε (3.7 ‰) and 18 ε (7.4 ‰) were generally used for steady-state Reactions (R3), (R6) and (R7) under steady-state conditions, and the low (n = 2) and high (n = 1) values were used to evaluate the lower and upper bound.

B2.1 HONO photolysis
The isotopic effect associated with photolysis (PIE) of HONO is calculated for the first time following the ZPE approach proposed by Yung and Miller (1997) to determine the PIE of N 2 O photolysis. In principle, the absorption spectrum for the same kind of electronic transition is expected to be similar in shape and intensity upon isotopic substitution, based on the assumption that the electronic potential energy surface is constant for each isotopologue. This assures the continuum levels (leading to photolysis) of the excited state are not significantly changed, while the vibrational levels of the ground state vary with isotopic substitutions due to mass difference. The latter results in a lower ground state zero point energy (ZPE) for a heavy isotopologue than a light one and causes blue shift in the absorption spectrum of the heavy isotopologue relative to the light one (Miller and Yung, 2000). When exposed to sunlight in the troposphere (>290 nm), HONO is known to feature a set of progressive absorption bands between 310 and 370 nm arising from electronic excitation ( X 1 A → A 1 A ), which results in HONO photolysis to OH and NO with nearly unity quantum yield (Cox et al., 1980;Suter and Huber, 1989). Under the aforementioned assumptions, we calculate the spectra blue shift of all three heavy isotopologues (HO 15 NO, H 18 ONO or HON 18 O) relative to that of HONO using the ZPE approach as shown in Fig. B1 and Tables B1 and B2. We calculated ZPE from 1/2 ν i , where ν i is the ground state vibrational frequency difference between the normal isotopologue (HONO) and the heavier isotopologue (HO 15 NO, H 18 ONO or HON 18 O) for each vibrational mode calculated via forced field by Monse et al. (1969). Note only HO 15 NO UV absorption was measured in a previous study that reported an average blue shift of ∼ 20 cm −1 (8-40 cm −1 ) relative to HONO, and this is consistent with our calculation (Table B1). Note trans-HONO / cis-HONO abundance ratio is 2.5 at room temperature (Suter and Huber, 1989), and the difference of ZPE for trans-HONO and cis-HONO is less than 0.5 % for 15 N and 2 % for 18 O (Ta- The negative values of 15 ε and 18 ε suggest both 15 N and 18 O will be enriched in the remaining HONO upon photolysis. Applying a Rayleigh fractionation model described by equation Eq. (B9), we obtain δ 15 N and δ 18 O of HONO (δ f ) as a function of the fraction of HONO left after photolysis (f ). The initial isotopic composition of HONO (δ 0 ) is taken from nighttime young smoke mean values in Table 1, as they are the best estimate of the fresh emission from the fires we investigated.
ln δ f + 1000 ‰ = ε ln (f ) + ln(δ 0 + 1000 ‰) (B9) B2.2 Isotopic fractionation of N and O associated with each daytime HONO production pathway OH + NO (Reaction R2) is a radical-radical recombination reaction, which is characteristic of the stabilization of activated complex HONO * via collisional energy transfer. This reaction type is characteristic of large KIF that enriches heavier isotopologues in the product at the low-pressure limit but almost no KIF at the high-pressure limit. The closer a reaction system is to the high-pressure limit, the less fractionation occurs (Chai and Dibble, 2014). Under the atmospheric pressure, the rate coefficient k 1 is in the fall-off region but close to the high-pressure limiting rate coefficient k atm = 1/3k ∞ (Forster et al., 1995). Therefore, we expect a moderate positive 15 ε (∼ 10 ‰) and 18 ε (∼ 15 ‰) (Chai and Dibble, 2014;Burkholder et al., 2019). Kinetic isotopic fractionation (KIF) associated with photo-enhanced NO 2 conversion is not known. Similar to the nighttime heterogeneous NO 2 conversion, Reaction (R3) is also expected to occur in the surface aqueous phase, and the overall KIF is largely determined by that associated with the desorption of HONO from aqueous to gas phase. Thus, 15 ε 3 and 18 ε 3 are the same as that of Reactions (R6) and (R7) (Appendix B1.2). KIF associated with HNO 3 and p-NO − 3 photolysis (Reaction R4) in the atmosphere has never been measured experimentally, and the lack of p-NO − 3 absorption spectroscopy hinders calculation. The 15 N enrichment factor ( 15 ε) for photolysis of snow-surface-adsorbed HNO 3 under natural sun-light was theoretically determined to be ≤ −47.9 ‰ following the ZPE approach Yung and Miller (1997), which explained well the laboratory-measured 15 ε for snow surface nitrate photolysis under the radiation of simulated sunlight (Berhanu et al., 2014;Frey et al., 2009). If we take this 15 ε value and the measured δ 15 N of nitrate (8 ‰ to 20 ‰), the HONO produced from surface nitrate photolysis will be very negative (−38.9 ‰ to −27.5 ‰) within 2 h of photolysis. The 18 O enrichment factor ( 18 ε) for photolysis of snow-surfaceadsorbed HNO 3 has been measured to range from 6.0 ‰ to 12.5 ‰ (Frey et al., 2009;Berhanu et al., 2015).  (Ammann et al., 1998;George et al., 2005;Stemmler et al., 2006;Scharko et al., 2017;Kebede et al., 2016). In Reaction (R6), the hydrolysis mechanism discussed in Appendix B suggests the H 2 O-derived OH − and NO 2derived NO + NO − 3 equally contribute their O atom to HONO (Finlayson-Pitts et al., 2003). During the day, NO-NO 2 equilibrium is maintained via NO 2 photolysis and NO oxidation by O 3 and/or RO 2 following Reactions (R8) and (R9), and NO and NO 2 are expected to possess similar δ 18 O, and this can be expressed as δ 18 O-NO x . During the night, due to increased sink of NO x and decreased O 3 concentration, δ 18 O-NO x is expected to be lower than during daytime. NO x resulting from Reactions (R8) and (R9) should carry δ 18 O of RO 2 and O 3 , respectively, via transfer; as RO 2 and O 3 have very different δ 18 O values ∼ +23 ‰ and +117 ‰, respectively, the competition between Reactions (R8) and (R9) critically affects δ 18 O-NO x , as described by equations Eqs. (11) and (12). OH radical in the troposphere has been calculated to be −35 ‰ depleted in 18 O relative to H 2 O as a result of isotopic exchange at 298 K (Walters and Michalski, 2016); by taking the 18 O values for summertime precipitation water in the western US (−10 ‰ to −5 ‰) (Welker, 2000) and the H 2 O liquidto-vapor enrichment factor ε g−l of +9 ‰ at 298 K derived from the literature with Eq. (B13) (Michalski et al., 2012), δ 18 O-OH is estimated in the range of −35 ‰ to −30 ‰ if we ignore the unknown KIF derived from OH oxidation reaction with the vast majority of atmospheric species. The overall δ 18 O-HONO is modeled using the isotope mass balance model. ε g−l = −7.68 + 6.71 10 3 T − 1.67 10 6 T 2 + 0.35 10 9 T 3 (B13)