A Systematic Re-evaluation of Methods for Quantification of Bulk Particle-phase Organic Nitrates Using Real-time Aerosol Mass Spectrometry

Organic nitrate (RONO 2 ) formation in the atmosphere represents a sink of NO x (NO x = NO + NO 2 ) and termination of the NO x /HO x (HO x = HO 2 + OH) ozone formation and radical propagation cycles, can act as a NO x reservoir transporting reactive nitrogen, and contributes to secondary organic aerosol formation. While some fraction of RONO 2 is thought to reside in the particle phase, particle-phase organic nitrates 25 (pRONO 2 ) are infrequently The and matrix effects of and show


Introduction 50
Organic nitrate (RONO2) formation in the atmosphere, through oxidation of VOCs (volatile organic compounds) in the presence of NOx (NOx = NO + NO2), represents a sink of NOx and termination of the catalytic NOx/HOx (HOx = OH + HO2) ozone formation and radical propagation cycles, can act as a NOx reservoir transporting (or removing) reactive nitrogen, and contribute to secondary organic aerosol formation (Zare et al., 2018 and references therein). Particle-phase organic nitrates (pRONO2) have been 55 shown to contribute substantial mass to organic aerosol (OA) (Ng et al., 2017 and references therein), can provide insight into the chemistry controlling SOA formation (e.g., Pye et al., 2015;Xu et al., 2015b;Lee et al., 2016;Ng et al., 2017), may constitute a semivolatile component of OA and dynamically partition between the gas-and particle-phases (e.g., Fry et al., 2013;Rollins et al., 2013;Pye et al., 2015), and represent a loss mechanism for RONO2 or reactive nitrogen oxides (e.g., via hydrolysis or deposition) 60 (Fisher et al., 2016;Lee et al., 2016;Zare et al., 2018). However, pRONO2 have infrequently been measured in ambient air until recently and thus are still poorly understood (Ng et al., 2017).
The recent emergence of a variety of online and offline methods of both speciated and bulk pRONO2 and their applications to ambient aerosol measurements are summarized in Ng et al. (2017). Instrumentation and methods include: (online bulk) aerosol mass spectrometry (AMS; (Jayne et al., 65 2000)) and its monitoring versions (known as Aerosol Chemical Speciation Monitors, ACSM; (Ng et al., 2011;Fröhlich et al., 2013)); thermal dissociation -laser induced fluorescence (TD-LIF; (Day et al., 2002)); (online speciated) filter inlet for gases and aerosols (FIGAERO) -chemical ionization mass spectrometry (CIMS) (Lopez-Hilfiker et al., 2014); (offline speciated) high-pressure liquid chromatography -mass spectrometry (HPLC/MS) often with electrospray ionization (ESI) (Surratt et al., 70 2006); (offline bulk) Fourier Transform InfraRed (FTIR) spectroscopy (Maria et al., 2002). While speciated methods can provide more detailed source or mechanistic information, they are slow and, to date, none (online nor offline) has demonstrated quantitative measurement of the bulk of pRONO2 for ambient measurements. Therefore, bulk measurements provide useful constraints on the budgets, formation and loss rates of gas-and aerosol-phase RONO2 in the atmosphere; and fast online methods are 75 essential when ambient concentrations are rapidly changing, especially for aircraft sampling.
For most field applications of the AMS, typically aerosol nitrate concentrations have been reported as a single total (organic plus inorganic) concentration, due to the fact that nearly all of the signal of the nitrate functional group for any nitrate type (or nitrite) is measured at a couple of common ion peaks (NO + and NO2 + in high-resolution (HR) instruments or m/z 30 and m/z 46 in unit mass resolution (UMR) 80 instruments) (Farmer et al., 2010). Early on in the application of the AMS, an implicit assumption was often made that ammonium nitrate (NH4NO3) typically dominated aerosol nitrate, based on early urban studies that showed semivolatile behavior consistent with NH4NO3 (e.g., Jimenez et al., 2003;Hogrefe et al., 2004;Zhang et al., 2004). However, a few early reports on field measurements using UMR AMS (Allan et al., 2004b(Allan et al., , 2006 showed that the m/z 46 -to -m/z 30 ratio (hereinafter "46/30 ratio") was too 85 low to be associated with only NH4NO3, suggesting substantial contributions from mineral nitrates (NaNO3, Ca(NO3)2), pRONO2, or possibly other reduced organo-nitrogen, or organic ion interferences. In a study focusing on cluster analysis of ambient (UMR) AMS spectra, Marcolli et al. (2006) also reported 46/30 ratios substantially smaller than NH4NO3 and found several spectra cluster categories with dominant m/z 30 peaks (but not m/z 46) and suggested that these signals may be associated with organic 90 nitrates. Similarly, Alfarra et al. (2006) reported 46/30 ratios from chamber-generated SOA (photooxidation of trimethyl benzene and α-pinene) ~2-4 times lower than NH4NO3, which they attributed to pRONO2 or nitro-compounds. A few years later, reports from chamber studies where pRONO2-rich SOA was generated (β-pinene or isoprene +NO3 radicals), using an HR-AMS, showed NO2 + /NO + ratios (hereafter "NOx + ratio") ~2-4 times lower than pure NH4NO3 (Fry et al., 2009;Rollins 95 et al., 2009).
Subsequently, broader surveys of the fragmentation patterns of aerosol nitrates (and nitrites) in the AMS were reported, including consistently low NOx + ratios for pRONO2 (Bruns et al., 2010;Farmer et al., 2010). Farmer et al. (2010) evaluated the fragmentation patterns of single-component pRONO2 isolated from SOA, and showed that ~95% the nitrogen-containing signal was observed as NOx + ions with 100 the balance as HNO3 + and very little signal at CxHyOzN + ions. Farmer et al. evaluated several methods for constraining pRONO2 contribution to AMS nitrate signal including using: 1) NOx + ratios, 2) HNO3 + ions, 3) CxHyOzN + ions, 4) "ammonium balance", and 5) AMS total nitrate comparison to inorganic nitrateonly measured with another instrument (typically ion chromatography-based). For the urban dataset evaluated in that study, all methods appeared to be associated with relatively large uncertainties. Bruns et 105 al. (2010) reported NOx + ratios for SOA formed from several monoterpenes and isoprene (with NO3 radicals) as well as NaNO3 and NaNO2 (with the sodium salts showing greatly reduced NOx + ratios).
Other studies have used the ammonium balance (hereafter NH4_Bal) of AMS data, or comparisons to other instruments to estimate pRONO2 content (Aiken et al., 2009;Zaveri et al., 2010;Docherty et al., 2011;Häkkinen et al., 2012;Xu et al., 2015a); however, in most cases, uncertainties were large or not assessed. 110 Since the Farmer et al. study, several other laboratory studies reported NOx + ratios for pRONO2containing SOA, which are summarized in Sect. 3. Additionally, a number of analyses of field studies have used the NOx + ratios (or its 46/30 UMR equivalent) to support qualitative or semi-quantitative statements about the presence (or low contribution) of pRONO2 (Setyan et al., 2012;Brown et al., 2013;Schneider et al., 2017;Bottenus et al., 2018) or to quantify pRONO2 (Fry et al., 2013, 115 2018; Ayres et al., 2015;Kostenidou et al., 2015;Xu et al., 2015aXu et al., , 2021Fisher et al., 2016;Kiendler-Scharr et al., 2016;Lee et al., 2016Lee et al., , 2019Nault et al., 2016;Zhou et al., 2016;Zhu et al., 2016Zhu et al., , 2021Florou et al., 2017;Palm et al., 2017;Brito et al., 2018;de Sá et al., 2018de Sá et al., , 2019Reyes-Villegas et al., 2018;Schulz et al., 2018;Avery et al., 2019;Dai et al., 2019;Huang et al., 2019aHuang et al., , 2019bYu et al., 2019;Chen et al., 2020Chen et al., , 2021Lin et al., 2021). Yu et al. (2019) also used the particle size dependence of the 120 46/30 ratio to investigate particle size and temporal (diurnal and seasonal) trends in pRONO2. Other studies have used positive matrix factorization (PMF) of AMS spectra including both the OA and NOx + signals to quantify pRONO2 (Sun et al., 2012;Hao et al., 2014;Xu et al., 2015a;Zhang et al., 2016;Kortelainen et al., 2017;Yu et al., 2019;Lin et al., 2021;Zhu et al., 2021). Recently, Xu et al., (2021) demonstrated another method, using AMS thermal denuder measurements. Thus there is promising use of 125 AMS measurements for quantifying bulk pRONO2 functional group contribution to ambient aerosols (and in addition, providing higher quality NH4NO3 concentrations). However, the methods have not been standardized and uncertainties of the different methods have not been well-characterized, and were reported to be large by at least some studies. Together with the increasing prevalence of AMS (and ACSM) field measurements, a detailed evaluation of pRONO2 quantification methods is timely. 130 Here we explore the application of the AMS NOx + ratio method to separate and quantify inorganic and organic nitrate and discuss the methods in detail, as well as comparison to other methods, and some scientific applications. In addition to drawing from available literature whenever possible, new analyses for several field and laboratory datasets are used extensively throughout this manuscript to explore and support findings. Descriptions of those datasets and data processing methods can be found in Supp. Info. 135 Sect. S1 (including Fig. S1). All data, analysis, and recommendations presented here is for use with the standard AMS vaporizer; while in practice, similar methods could be applied to explore the possibility of using data from an AMS equipped with the capture vaporizer to apportion nitrate, although it would likely have higher detection limits (Hu et al., 2017a).

Previous use and methods for pRONOquantification using AMS NOx + ratios 140
An equation for quantitative apportionment of the AMS nitrate signal into pRONO2 and NH4NO3 using the NOx + ratio was first presented by Farmer et al. (2010) (equation 1 from Farmer et al., and derived in their supporting information, here substituting different notation for some terms for consistency with this manuscript): where fpRONO2 is the fraction of total AMS nitrate (hereafter pNO3) that is pRONO2, and RNH4NO3, RpRONO2, and Rambient are the NOx + ratios (NO2 + /NO + ) for pure NH4NO3, pure pRONO2, and the ambient aerosol nitrate mixture measured, respectively. Note that here we use the NO2 + /NO + ratio for all terms, while Farmer et al. and some others have used NO + /NO2 + . This formulation is preferred since NO2 + tends to be lower than NO + for all nitrates, and thus using NO2 + /NO + avoids ratios trending toward infinity as 150 detection limits are approached. This usage has been applied in several publications, such as Fry et al. (2013) and Kiendler-Scharr et al. (2016), as presented in equations 11 and 1 in those papers, respectively. The equation is identical regardless of the inversion of the NOx + ratio. That can be shown by simply swapping all the instances of NO and NO2 in the definitions and derivation shown in Farmer et al. or by substituting 1/Rx for each ratio term in Eq. 1 above, multiplying all parenthetical terms by 155 RambientRNH4NO3RpRONO2, factoring out the same term in the numerator and denominator then canceling, and finally multiplying the first parenthetical terms in the numerator and denominator by -1. While typically RNH4NO3 is measured frequently as pure NH4NO3 is periodically sampled by the AMS as a primary calibrant for sensitivity (Canagaratna et al., 2007), regular calibration using pRONO2 is generally not practical. Moreover, it is not immediately clear that all pRONO2 produce the same RpRONO2 in the AMS.

160
Values reported in the literature for RNH4NO3 and RpRONO2 both appear to have a substantial range (factor of ~3) and generally RpRONO2 is 2-4 times lower than RNH4NO3 (see Sects. 1 and 3).
Several studies have applied Eq. 1 to quantify pRONO2 and NH4NO3, using different assumptions regarding RpRONO2. Farmer et al. (2010) applied their measurements of RpRONO2 from their lab study to estimate an upper limit of 50% for the pRONO2 contribution to pNO3 for the urban SOAR campaign, 165 substantially higher than with other methods they applied. They considered that method to be a high upper limit, due to the possible influence of non-refractory nitrates. However, we note that the RpRONO2 used in that early study was nearly a factor of two different than we suggest in this study, in the direction favorable to higher pRONO2 fractions. For calculation of pRONO2 for the BEACHON-RoMBAS campaign, Fry et al. (2013) assert that RNH4NO3 and RpRONO2 likely co-vary for an instrument and therefore 170 define the term "ratio-of-ratios" (hereafter RoR = RNH4NO3/RpRONO2) in order to estimate RpRONO2 from infield RNH4NO3 measurements and literature reports of RpRONO2 and RNH4NO3. The RoR value applied by Fry et al. (2013)  ambient datasets examined (noting that "such low ratios of NO2 + /NO + were also detected in some data sets where RNH4NO3 was reported high"). Those authors state that their approach represents a lower limit of pRONO2. Similarly, Brito et al. (2018), Schulz et al. (2018), Huang et al. (2019aHuang et al. ( , 2019b, and Avery et al. (2019), applied a fixed RpRONO2 of 0.1 (citing Kiendler-Sharr et al. (2016)) for aircraft measurements in West Africa, aircraft measurements in the Amazon, rural forest and urban sites in Germany, and seasonal 180 variations of indoor/outdoor air, respectively. The same method has been applied to laboratory studies of biomass burning aging (Tiitta et al., 2016), composition from photooxidation of terpenes (Zhao et al., 2018;Pullinen et al., 2020), and the composition, optical properties, and aging of particles from a wide variety of biomass burning fuel sources McClure et al., 2020). However, in the latter study, the organic component is classified as "organonitrogen", assuming it includes contributions from 185 both organic nitrate and nitro-organic (i.e. nitroaromatics) functional groups (and assumed to have the same NOx + ratio).

Survey of NOx + ratios for particle-phase nitrates 220
Given the numerous applications of NOx + ratios to separate pRONO2 and NH4NO3 in AMS measurements, yet many variations in methods and the numerical values used within each method, we have conducted a systematic survey of literature values and trends of NOx + ratios for different nitrates. Such data compilation is aimed at evaluating the evidence that supports using a fixed RoR to estimate RpRONO2 from the calibration RNH4NO3 and to investigate the variability in RpRONO2 produced from different 225 sources. Figure 1 shows a compilation of RoR values for pRONO2 derived for chamber-generated SOA, isolated compounds (from chamber SOA or standards), and ambient measurements (using instrument comparisons or PMF separation). Figure 1 also shows the RoR for the same data as a histogram and average, as well as the correlations of the pRONO2 vs NH4NO3 (inverse) NOx + ratios. Details of the values used to compute the ratios and uncertainties, data sources, and any additional calculations for the 230 information included in Fig. 1, are provided in Table S1.
The correlation between the RpRONO2 and RNH4NO3 is fairly strong (R 2 =0.54), considering the variety of data sources and substantial measurement uncertainties. It provides strong evidence that, to first order, the RoR method is consistent and supported by various methods, species/mixtures, instruments and operating conditions. The slopes of the linear regression constrained to a zero intercept using an ODR fit 235 (2.66±0.11; assuming both variables contribute comparable uncertainty) is equivalent to an overall RoR and is similar to the average of the individual RoR datapoints (mean±standard error: 2.75±0.11). Highlighted in the scatterplot in Fig. 1 are a couple of pairs of datapoints that are averages from several experiments conducted in our laboratory with two different AMS during two different years, with substantially different measured calibration RNH4NO3 while sampling the same chamber SOA (see S1.2). 240 The trends in those points are similar to the overall trend and provide an example of the validity of the RoR method when only differences in instrument / operating conditions are present. Fig. S2 shows a complementary histogram to that in Fig. 1 for the RpRONO2, without normalizing to RNH4NO3. Compared to the normalized values shown in Fig. 1 (i.e., RoRs), a factor of two larger relative variability is apparent, with a relative standard deviation of 49% compared to 25%. Also of note is that the average value is 245 0.21±0.10, twice as high as used in several literature studies. Finally, Fig. S3 shows a complementary plot to the scatter plot in Fig. 1, with the inverse NOx + ratios and axes swapped, which emphasizes different data and outliers, and yields similar but slightly higher (<10%), RoR slopes and the same degree of correlation. While the representation in Fig. S3 uses the inverse NOx + ratio of that used throughout this manuscript, it places the RNH4NO3 on the x-axis, and thus a non-ODR fit may be appropriate under the 250 assumption that most uncertainty is contributed by the pRONO2 ratios. The ODR and non-ODR fits (2.83±0.12, 2.66±0.12, respectively) bracket the simple average value (2.75).
The compilation shown in Fig. 1 allows for consideration of dependencies of the RoR on species/mixtures or methods. Generally, the RoRs cluster around 1.5-4 for most studies. The variability within duplicated VOC-oxidant pairs (e.g., β-pinene+NO3 SOA), similar compound classes (e.g., 255 monoterpenes, isoprene, aromatics, long-chain alkanes or alkenes), or measurement methods (SOA mixtures, isolated compounds, ambient measurements) is similar to the variability between such groupings. Therefore, given the data currently available, there does not appear to be any strong evidence to support any general chemical-dependence of the pRONO2 RoR. While such a dependence may in fact exist, evaluation likely would require comparison of several organic nitrate molecules and/or mixtures 260 systematically with the same instrumentation, operation conditions, and analysis methods, together with duplication by different instruments.
Therefore, for applications and further evaluation described in this manuscript, we use the average and variability of the RoR determined from data highlighted in Fig. 1: 2.75 (mean) and standard deviation (±0.70, 25%) or standard error (±0.11, 4.0%). The 25 th /50 th /75 th percentiles are 2.12, 2.73, 3.12 265 (interquartile range / median +14%/-22%). Given the approximate symmetry for the limited statistics available, we treat the variability and uncertainty of the RoR as approximately a normal distribution. The standard deviation should be considered an upper limit of the uncertainty of the applicable RoR and corresponds to the assumption that the variability in reported values is primarily attributable to true differences in ratios for different types of pRONO2. The lack of clear differences among different sources 270 suggests that some of the variability may instead be instrument/operator related, and that the std. error may be a more relevant characterization of the uncertainty. Complex mixtures of pRONO2 in the atmosphere would likely represent an ensemble of those ratios, and thus result in values closer to the average. In fact, for the limited (7) examples of ambient-derived RoRs, the average is similar and the variability somewhat smaller (2.99±0.51, ±17%) compared to the overall survey data. The standard error 275 of the overall survey can be considered a measure of the uncertainty under the assumption that the RoR is invariable with source/type and the RNH4NO3 for an instrument is a perfect predictor of RpRONO2. A separate manuscript will include further discussions on the RoR uncertainty and applications to estimation of the overall nitrate apportionment and concentrations uncertainties.
We recommend the use of the average RoR value computed here for future separations of pRONO2 280 and NH4NO3 in ambient aerosol with AMS until there is additional information available to support a different or more complex formulation. On the other hand, where additional constraints on the expected pRONO2 ratio response may be available, a more specific value may be applied. For example, Takeuchi and Ng (2019) measured RoRs during dry chamber experiments for different SOA types where only pRONO2 nitrate was generated, and then used those system-specific RoRs to separate pRONO2 and 285 NH4NO3 during wet experiments where substantial NH4NO3 was also formed. We note that in a recent study, Xu et al. (2021) inferred a substantial variability in RpRONO2 for ambient measurements on diurnal timescales and with varying pollution levels; however, that relied on comparison of the NOx + ratio method to a newly-proposed method using thermal denuder profiles, which they acknowledge has several potentially large uncertainties or biases that were not quantified. 290 It is important to emphasize that under strong influence of particle-phase nitrites or semi/nonrefractory nitrates (e.g., NaNO3, Ca(NO3)2), quantitative separation of nitrate types may be hindered or simply not feasible (Schroder et al., 2018). As a few studies have reported, nitrites and mineral nitrates produce substantially lower NO2 + /NO + ratios (thus higher RoR) in the AMS. For example, RoRs of ~10-60 for NaNO3 (Alfarra, 2004;Bruns et al., 2010;Hu et al., 2017b), 17 for Ca(NO3)2 (Alfarra, 2004), 3.9 295 for Mg(NO3)2 (Alfarra, 2004), 9.7 for KNO3 (Drewnick et al., 2015), and ~300 for NaNO2 (Alfarra, 2004) have been previously reported. We report additional measurements from our laboratory for NaNO3, KNO3, and KNO2 showing similarly high values. Table S2 provides additional details and Fig. S4 shows a graphical representation and comparison to pRONO2 for literature reports and our new data. Consequently, even if the expected ratios of other compounds were accurately known, apportioning the 300 different nitrates or nitrites using a formulation like Eq. 1 would be under-constrained, as there would be more unknowns than equations. Therefore, care must be taken to screen for measurements that may be substantially influenced by such interferences (e.g., seasalt, dust). Additionally, during a recent aircraft campaign focused on biomass burning, we conducted regular calibrations with 4-nitrocatechol, a nitroaromatic (Pagonis et al., 2021). The RoR was relatively similar to pRONO2 at 3.35 ± 0.81 (1σ, 305 standard deviation) (Table S2, Figs. S4, S5).

Evaluation of calibration RNH4NO3 and RoR using ambient data
A survey of NOx + ratios for multiple field studies is explored here in order to assess the framework of using measured calibration RNH4NO3 and a RoR to apportion NH4NO3 and pRONO2 concentrations. See Sect. S1.1 and Table S3 for details and a summary of all field campaigns for which data is used within 310 this manuscript. Figure 2 shows frequency distributions of Rambient for ambient aerosol from two aircraftbased remote continental (SEAC 4 RS, DC3) and two ground-based forest campaigns (SOAS, BEACHON-RoMBAS). The data is shown as the calibration RNH4NO3 divided by Rambient, so that all data is comparable. For all campaigns, the large majority of the data fall between the RNH4NO3 (1 on Fig. 2, indicating all NH4NO3) and the RoR-determined RpRONO2 (2.75 on Fig. 2, indicating all pRONO2). The small fraction of 315 data outside that range may be due to a combination of instrument noise, drifts in the instrument NOx + ratio response not captured by periodic calibrations, and/or the inability of the fixed RoR to perfectly capture the RpRONO2 response. However, these results show that under a large range of chemical conditions and instrument RNH4NO3 (spanning a factor of 2.4 for these campaign averages), the data are generally consistent with the RoR apportionment model. Figure S6 shows the same distributions as Fig. 2, except as 320 simple frequency distributions, rather than weighted by mass concentration as in Fig. 2. The broadening and shift to the right for simple frequency distributions (compared to those weighted by mass concentration), reflect the typical trend that pRONO2 tends to constitute higher fractions of pNO3 when pNO3 is lower. Distributions are similar for other campaigns (not shown in Figs. 2, S6), as can be inferred from Figs. 5 and S9, which are discussed below. 325 The effects of estimating RpRONO2 using time-variant vs constant RNH4NO3 is explored in Fig. S7. For the SEAC 4 RS campaign, the flight-to-flight calibration RNH4NO3 were highly variable due to some instrument instability (range: 0.40-1.49, mean±stdev: 0.80±0.31; Figs. S8, S9e), compared to the very stable ratios measured during the other campaigns (see Fig. 2 caption). Therefore, two histograms are shown overlaid in Fig. S7, one normalized to flight-dependent calibration RNH4NO3 and the other 330 normalized to the campaign-averaged RNH4NO3. For the standard frequency distributions (Fig. S7a), there is substantial narrowing when using the flight-dependent ratios, indicating that application of the timevariant ratios provides better constraints on the instrument response to the NH4NO3 -pRONO2 mixture. Conversely, normalizing to arbitrary RNH4NO3 would be expected to broaden the distribution. The most prominent differences for the mass concentration-weighted distributions (Fig. S7b) are largely due to data 335 with high NH4NO3 concentrations where the measured Rambient were beyond the campaign-averaged RNH4NO3 (resulting in a substantial fraction of the distribution <1). There is also subtle broadening toward the pRONO2 portion of the distribution. These comparisons support that using the variable calibration RNH4NO3 better represents ambient NH4NO3 ratios (left side of plots) and tying RpRONO2 to RNH4NO3 (i.e. using the RoR method, rather than fixed RpRONO2) better represents pRONO2 ratios (right side of plot). 340 Additional support for the practice of using the measured calibration RNH4NO3 and anchoring the RpRONO2 to those calibrations with a fixed RoR can be drawn from the Rambient vs pNO3 plots shown in 0.10, 0.40, respectively; range of 4.0). If assuming that the low-pNO3 observed Rambient approximate pure pRONO2 ratios, a relatively narrower range is computed for an inferred RoR (1.6-3.0, factor of 1.9; 2.36±0.63), which is also similar to expected RoRs (albeit low possibly due to urban ground studies never sampling pure pRONO2).
Further evidence supporting the use of calibration RNH4NO3 and the RoR using ambient data is 355 presented in Sect. S2 using campaign datasets where the calibration RNH4NO3 showed large variability (DAURE, SEAC 4 RS campaigns). Exploration of the NOx + ratios vs pNO3 relationships showed similar relationships to those discussed above for campaigns where RNH4NO3 was constant or changed little, but with the curves shifting with the measured RNH4NO3. Similar values of RoR to those presented in the literature survey in Sect. 3 were also inferred from the SEAC 4 RS dataset. Finally, both datasets were used 360 to evaluate biases when using a fixed value of RpRONO2 vs estimation of a dynamic value using the RoR method. Additional evidence from ambient measurements supporting use of calibration RNH4NO3 and the RoR is presented in Sect. 5.2 where applications of PMF separation are discussed.

pRONO2 -NH4NO3 separation compared to total (gas+particle) RONO2 (Tot-RONO2) 365
Figure 3 shows time series of AMS pRONO2 and NH4NO3 concentrations for a SEAC 4 RS flight (RF16) in the Southeast US. The nitrate components were apportioned according to Eq. 1 and a RoR of 2.75. "Total RONO2" (gas+particle; hereafter Tot-RONO2) concentrations, as measured by thermal dissociation -laser induced fluorescence (TD-LIF) (Day et al., 2002;Perring et al., 2009), are shown for comparison. A wide range of sources were sampled including (and indicated by) biogenic (monoterpenes and/or 370 isoprene and photochemical products such as IEPOX, MVK), anthropogenic (e.g., NOx, NOy, aromatics), biomass burning (e.g., acetonitrile and f60, an AMS tracer (Cubison et al., 2011)), likely agricultural, as well as mixtures of these sources or relatively clean free tropospheric air. Flight tracks are shown in Fig.  S10 and approximate periods and corresponding source influences are listed in the caption. A large and variable range of pNO3 was observed (<10 ng m -3 or <4 ppt up to ~5 μg m -3 or ~1800 ppt) and ranging 375 from pRONO2-dominated to NH4NO3-dominated. The pRONO2 and Tot-RONO2 tracked remarkably closely. NH4NO3 concentrations exhibited more plume-like behavior, rapidly increasing and decreasing, often while both pRONO2 and Tot-RONO2 remained relatively constant or in some cases showed moderate and similar increases. Overall, pRONO2 was correlated with Tot-RONO2 (R 2 =0.49 for all data, R 2 =0.69 for data with fpRONO2 >0.3) with a regression slope of 0.029 (0.033), indicating that on average 380 ~3% of RONO2 was in the particle phase (Fig. 3, bottom left). NH4NO3 showed little overall relationship to Tot-RONO2 beyond the trend that at higher altitudes, well above the boundary layer and outside of plumes, both concentrations tended to be low (Fig. 3 Taken together, these observations indicate that the AMS nitrate apportionment method effectively separated pRONO3 and NH4NO3 over a large range of concentrations, relative contributions, and source influences. However, it is clear that there are limitations when the fpRONO2 is very low (see Sect. 5.2). It would not be surprising if the pRONO2 and Tot-RONO2 showed large variability in relative ratios for 395 different sources and locations, since: 1) pRONO2 is only a small subset of Tot-RONO2 and 2) changes in chemical composition and ambient conditions (e.g., OA concentration, temperature) could have large impacts on gas-particle partitioning. However, in this case those effects do not appear to be large factors (or fortuitously cancel out), which in part may be due to relatively similar temperatures and OA concentrations combined with regionally consistent biogenic chemical sources of RONO2 compounds. 400 Regardless of the exact reasons for the relatively invariant partitioning, it provides an excellent test case, since it would be very unlikely that the strong temporal/spatial correlation would be observed if there were major artifacts in either or both the AMS and TD-LIF methods.
There were no measurements of inorganic nitrate onboard the aircraft with fast enough time resolution to compare with the rapidly changing NH4NO3 concentrations calculated from the AMS. 405 Therefore, as a rough indicator of possible changes in the NH4 related to NH4NO3, "Excess NH4" was calculated as the AMS-measured NH4 -1.2 x SO4 (as molar concentrations). A molar ratio of 1.2 was roughly consistent with the observed ratio when no indications of NH4NO3 were present (NH4=1.2 x SO4) and substantial concentrations of SO4 were present, as shown in Fig. S11. That ratio represents a mixture of (NH4)2SO4 and ammonium bisulfate or an ammonium balance (NH4_Bal) of ~0.7 (NH4_Bal = molar ratio 410 of NH4/(NO3+2SO4)). During periods of elevated NH4NO3 concentrations, the measured NH4NO3 tracked the estimated "Excess NH4" very closely with roughly half the concentration (Fig. S11). As suggested by some negative "Excess NH4" values and the factor of two between NH4NO3 and "Excess NH4", the assumption of constant NH4/SO4 ratios based on composition in the absence of NH4NO3 is not always valid (and not surprising) and clearly a more sophisticated thermodynamic model would be required to 415 accurately predict NH4NO3 concentrations. Nonetheless, the similar features suggest the assignment of NH4NO3 is consistent with variations in the other AMS-measured inorganic compounds. The factor of two suggests that ~half of the "Excess NH4" was associated with sulfate and half with nitrate. During this flight, with the exception of the large biomass burning plume, the elevated NH4NO3 concentrations were observed when the aircraft flew at altitudes of ~2000-4000 m and never during the low-altitude (~300-420 400 m) legs (S20 bottom left/middle). This effect may have been due to the substantially cooler temperatures (0-15°C vs 25-30°C) at those altitudes, favoring partitioning to the particle-phase, since there did not appear to be any clear relationship between NH4NO3 and gas-phase HNO3 (Fig. S11, bottom right). Increases in available NH3 gas (not measured) could also be a factor (and consistent with both more sulfate-and nitrate-associated ammonium). 425 Another example for a different flight (RF18) during the SEAC 4 RS aircraft campaign is shown in Fig.  S12, and was also selected due to large relative and absolute variability in calculated pRONO2 and NH4NO3 concentrations and diverse source types sampled (see Fig. S13 for flight track and description). Similarly, the pRONO2 and Tot-RONO2 track remarkably well during periods when NH4NO3 concentrations are low or elevated and variable, and there is little correlation between NH4NO3 and Tot-430 RONO2. Overall, pRONO2 was correlated with Tot-RONO2 (R 2 =0.51 for all data, R 2 =0.71 for data with fpRONO2>0.3) with a regression slope of 0.050 (0.068), indicating that on average ~5-7% of RONO2 was in the particle phase (Fig. S12a, bottom left). The measured NH4NO3 tracked the estimated "Excess NH4" reasonably well and showing similar sharp features (and roughly half the concentration; Fig. S12b, top).
In contrast to RF16 discussed above, for RF18 most of the elevated NH4NO3 was observed in the warm 435 boundary layer and often coincident with elevated pRONO2 (Fig. S12a,b).

Prior studies using PMF for pRONO2 separation
For the vast majority of analyses of AMS data using PMF, only traditional OA ions have been included in the input data matrices. Ions typically associated with nitrate, sulfate, ammonium, and chloride have 440 generally been excluded, with the mindset that they are already separated as unambiguous inorganic species using the standard AMS analyses. However, since organic molecules (e.g., organic nitrates, organosulfates, reduced organic nitrogen) can in fact produce some of the same ions as those inorganic species, inclusion with the OA ions in PMF analysis may allow for separation of inorganic and organic components, as well help identify associations with more well-established source factors. 445 A few studies have reported results for using PMF of ambient AMS spectra including both the OA and NOx + signals to quantify pRONO2 (and sometimes NH4NO3), with mixed results (Sun et al., 2012;Hao et al., 2014;Xu et al., 2015aXu et al., , 2021Zhang et al., 2016;Kortelainen et al., 2017;Yu et al., 2019;Zhu et al., 2021). Additionally, a couple other studies have reported results where NOx + ions or calculated pRONO2 (using the NOx + ratio method) are included in PMF analysis, while not explicitly apportioning 450 the inorganic-organic nitrate directly with the PMF results in the laboratory (Tiitta et al., 2016) and field Reyes-Villegas et al., 2018). Lin et al. (2021) conducted PMF using only the NOx + ions and nitro-polycyclic aromatic hydrocarbon (NPAH) ions. Details and discussions of those studies are presented in Sect. S3 and key results are summarized in Table S4, as related to the PMF analyses.

New results for PMF separation of pRONO2 and comparison to RoR method 455
We conducted PMF on the combined OA and NOx + ion time series for the same two flights from the SEAC 4 RS campaign (as discussed above in Sect. 5.1; RF16, RF18) to test PMF separation of nitrates and the information it can provide, explore strategies, and compare to the RoR method. Details and an extended discussion of that analysis is documented in Sect. S4 and key results are summarized in Table  S4 alongside previous published analyses. A brief summary is provided here. 460 As discussed in Sect. 5.1, those two flights included sampling of a wide range of source types and concentrations. PMF was conducted initially on 1-s data; however, although robust overall factors were separated, results suggested that the S/N was not adequate to apportion the NOx + ions to secondary factors at ratios that reflected pRONO2 ratios. Therefore, all analyses discussed here are from 1-min measurements (which were more effective). Several strategies were used to explore the separation of OA, 465 nitrate, and the NOx + ratios (in separate and combined factors), including: number of factors, rotations (varying FPEAK), upweighting and downweighting NOx + ions, bootstrapping, seeding, constraining NOx + ratios, and removing large biomass burning plumes. For both flights, five factors were robustly separated: NH4NO3, BBOA (biomass burning OA), IEPOX-SOA (IEPOX-derived SOA), LO-OOA (less-oxidized oxygenated OA), and MO-OOA (more-oxidized OOA) (Figs. S14-S28). See the Glossary and Sects.

470
S3/S4 for more details on factor types. Generally, the best separations with the most information were for FPEAK at or near 0, using standard NOx + ion S/N (no downweighting/upweighting), not constraining NOx + ratios, not removing any plume data, and using bootstrapping to extract averages and assess uncertainty/robustness.
The NH4NO3 factors and the BBOA factors had very similar NOx + ratios that were consistent with 475 calibration RNH4NO3, with little variability across the 100 bootstrapping runs (Figs. S17, S25). While the apportionment of nitrate between the NH4NO3 and BBOA factors was very consistent across bootstrapping runs, changes in FPEAK had large effects on that relative apportionment as well as the amount of OA ions in the NH4NO3 factor spectrum. For the OOA/SOA factors (IEPOX-SOA, LO-OOA, and MO-OOA) the NOx + ratios for LO-OOA and the combination of all three factors were consistent with 480 expected pRONO2 NOx + ratios using the RoR (Figs. S17, S25). Across bootstrapping runs, there was modest variability for those ratios (Figs. S17, S25), including some solutions where the LO-OOA had only NO + (but not for the combined OAA/SOA factor). The averages and standard deviations of the NOx + ratios for the combined OOA/SOA factor are included in the survey of pRONO2 RoRs (Fig. 1, Table S1). For calculation of NH4NO3 and pRONO2 concentrations, the nitrate contributions from the NH4NO3 and 485 BBOA factors were summed as were the three OOA/SOA factors, respectively. The majority of the pRONO2 was contributed by the LO-OOA factor, followed by MO-OOA and then IEPOX-SOA (Figs. S18, S27). The variability in the factor spectra NOx + ratios and nitrate concentration apportionment across bootstrapping tended to follow the same trend (higher variability for factors with lower pRONO2 contribution; e.g., Figs. S17, S18a, S25, S27). Additionally, substantial trends were observed between 490 factor spectra NOx + ratios and the amount of nitrate apportioned to that factor for some OOA/SOA factors. Bootstrapping and exploration of FPEAK was useful to investigate those dependencies.
Comparisons of NH4NO3 and pRONO2 concentrations using the RoR and PMF methods are shown for each flight in Figs. 4 and S12a as time series and scatter plots. For both flights there is very good agreement (near unity slope, 0.99-1.04, and R 2 >0.99) between methods for NH4NO3, certainly in part due 495 to the dominance of NH4NO3 during higher concentrations periods. There is reasonable agreement for pRONO2 (slopes of 0.86-1.50, R 2 of 0.51-0.65 depending of the flight and fitting method; and improved to slopes of 1.04-1.42, R 2 of 0.68-0.84 for fpRONO2>0.3) but with notable differences. pRONO2 concentrations tended to be noisier for the RoR method compared to the PMF method when nitrate was dominated by NH4NO3 or when pNO3 was very low. This may be due to the additional S/N and 500 constraints that the inclusion of the other OA ions provide, as well as the sensitivity (for both precision and accuracy) of apportionment for the RoR method when ratios approach the RNH4NO3 limit. On the other hand, the PMF method may dampen some real variability due to the fact that the factor spectra are fixed and cannot chemically evolve in the PMF model. In order to assess the true accuracy of either method, an independent and reliable determination of pRONO2 would be required. Finally, the comparison between 505 the PMF-determined pRONO2 and the TD-LIF Tot-RONO2 showed substantially-improved correlation (compared to using the RoR method) for one of the two flights ( Fig. 4 vs 3).

Summary of PMF method for nitrate separation
The results from our investigation of PMF and analyses described in the literature summarized above highlight some general aspects, as well as some potential advantages and disadvantages of using PMF to 510 apportion nitrate between organic and inorganic. One major potential advantage is that with PMF, the nitrates can be immediately associated with different source factors. On the other hand, the NOx + ratio method can be used first and then correlations of nitrates with OA-only factors can be explored and even apportioned. PMF may provide additional resolving power and S/N by inclusion of associated OA ions, potentially more precisely separating nitrate concentrations, especially when either pRONO2 or NH4NO3 515 dominate the nitrate. Also, prior knowledge of the NOx + ratio for NH4NO3 (or pRONO2) may not be necessary if the ratios are robustly resolved with PMF. Additionally, the NOx + ratios resolved for PMF factors is a product for exploring ratios for ambient aerosol response, and validating application of offline calibration RNH4NO3 and RoRs derived largely from laboratory studies. PMF may also be useful in separating other species that produce NOx + ions (e.g. nitrites, nitro-organics, mineral nitrates), from just 520 NH4NO3 and pRONO2, when they are present and have a unique NOx + ratio.
Some potential drawbacks or cautionary aspects are as follows. Since the PMF model requires fixed profile spectra, this means that nitrate-to-OA ratios are fixed for each factor. Therefore, if this ratio is in fact substantially variable over the period/space of analysis, for example driven by processes such as pRONO2 hydrolysis or gas-particle partitioning, substantial biases or uncertainties in nitrate 525 apportionment can be introduced. While consideration of additional factors could help mitigate such effects, PMF is not designed to concisely separate profiles that are a continuum. Sometimes factors with clear NH4NO3 or pRONO2 NOx + ratio signatures are not resolved. We suspect that datasets where neither type of nitrate is dominant for some periods may be more susceptible to that issue; however, those issues may sometimes be resolvable with more extensive investigation with available PMF exploration tools 530 (e.g., seeding, bootstrapping, FPEAK, constraining a NH4NO3 factor from offline calibrations). Otherwise, apportioning nitrate using results with profile spectra that do not have clear nitrate signatures may introduce large uncertainties which are difficult to estimate. Variable NOx + ratios due to instrument drifts or changes (e.g., vaporizer bias voltage drifts or tuning) may lead to uncertainty in nitrate apportionment since PMF computes fixed factor spectra. In practice, for using the NOx + ratio method this 535 is not problematic, as long as regular offline NH4NO3 calibrations were performed. For PMF, separating the dataset into periods where the NOx + ratio was stable/constant and performing PMF separately for each period is one option to mitigate instrument drift issues; however, this can be very laborious if the dataset requires separate analysis of multiple periods. Another option may be to apply the "rolling method" recently made available with ME-2/SoFi, where a sub-window is moved across the PMF input along the 540 time coordinate, allowing factor profiles to vary with each sub-window shift (Canonaco et al., 2021). Theoretically, offline calibration ratios of NH4NO3 may not be necessary for such application, although they would be preferable to have for validation.
A few other notable trends and observations are as follows (with details provided in Sect. S3, S4). PMF-resolved pRONO2 often tends to have the largest contribution from (and association with) LO-545 OOA/SV-OOA, followed by MO-OOA/LV-OOA, especially for biogenically-influenced locations (Sun et al., 2012;Hao et al., 2014;Xu et al., 2015a;Zhang et al., 2016;Kortelainen et al., 2017;Yu et al., 2019; Sect. S3, Table S4). That is consistent with pRONO2 forming in fresh SOA (i.e. LO-OOA/SV-OOA) and being partly lost as the OA ages and/or MO-OOA/LV-OOA consisting of a mix of aged OA, some of which was not associated with pRONO2. Nitrate associated with aged ambient BBOA can be 550 dominated by NH4NO3 (shown with aircraft data with PMF in this study, and discussed more broadly in Nault et al. (2021)); however, primary and secondary pRONO2 (or other oxidized organic nitrogen) associated with BBOA emission has been reported in the laboratory and field, sometimes as large contributions (Tiitta et al., 2016;Reyes-Villegas et al., 2018;McClure et al., 2020;Lin et al., 2021). When NH4NO3 factors are resolved, they tend to contain substantial contributions (~15-80%) of OA 555 (non-NOx + ) ions (Sun et al., 2012;Hao et al., 2014;Xu et al., 2015a;Zhang et al., 2016;Kortelainen et al., 2017). Generally, those non-NOx + contributions seem to be higher for strongly biogenicallyinfluenced measurements and less so during cooler wintertime periods when NH4NO3 comprises a larger fraction of nitrates (Xu et al., 2015a;this study). Our experience through exploration of various approaches (e.g., upweighting the NOx + ions, increasingly positive FPEAK, increasing number of factors) 560 suggests that efforts at "cleaning" the NH4NO3 factor tends to be ineffective and/or lead to degradation of the overall PMF solutions. Since the OA contained in the NH4NO3 tends to not be a large overall fraction of the OA, this does not appear to be a major issue. Finally, evidence suggests that inclusion of NOx + ions in PMF does not tend to have much influence on overall OA-dominated factors (factor spectra nor concentration time series), which is not surprising given that their overall contribution to the S/N among 565 the many OA ions is fairly small. Consequently, there does not appear to be any drawbacks or complications associated with also including NOx + ions when running PMF on AMS data.
Overall, PMF appears to be a useful tool for apportioning nitrates and investigating their associations with sources. The case for quantitative apportionment of nitrate with PMF is strongly bolstered when the NOx + ratios resolved for both the NH4NO3 factor and separate or combined pRONO2-associated factors 570 are similar to NH4NO3 calibration and expected pRONO2 NOx + ratios. When those criteria are not met, using the NOx + ratio method may be better, as it is likely less prone to such biases or ambiguities, and uncertainties can be better defined.

Comparison of pRONO2 quantification with AMS and other instruments in the lab and field
Several studies have reported quantitative comparisons of pRONO2 concentrations, as measured by AMS 575 vs other instrumental methods (alternate AMS-based methods, FTIR, TD-(LIF/CRDS/CAPS), and FIGAERO-CIMS). Section S5 provides details and discussions and Table S5 presents a summary of key aspects of those comparisons. Overall, those comparisons show good agreement in most cases (1:1 within known uncertainties) and substantial differences in a few cases (factors up to 2-4). In some of the cases where substantial differences were observed, possible explanations were discussed and sometimes 580 explored. There do not appear to be any consistent reasons for the differences. In some of the field comparisons and all of the laboratory experiments, the nitrate sampled was dominated by (or exclusively) pRONO2, and thus largely serve as a test of pRONO2 quantification (general calibration/quantification factors, RIE, collection efficiency, etc.). Consequently, taken together the evidence available does not support use of an RIE for pRONO2 quantification with AMS that is significantly different from that 585 measured for (and regularly calibrated with) NH4NO3. In order to narrow the uncertainties in pRONO2 quantification (in the field and laboratory), controlled laboratory-based intercomparisons of total and speciated organic nitrates using AMS and other methods are needed.

Physical basis for NOx + ratios observed for nitrate types and variability among instruments
As Farmer et al. (2010) points out, it is probable that a large fraction of RONO2 molecules thermally 590 decompose to RO and NO2 at the AMS vaporizer after which NO2 gas is ionized. For example, the TD-LIF technique (and CRDS/CAPS equivalent methods) rely on quantitative thermal dissociation of RONO2 to NO2 in the gas phase, which occurs at ~350 °C in ~50 ms at near ambient pressures (Day et al., 2002). The timescale of evaporation/decomposition/ionization/detection for the AMS are on order tens of µs (Drewnick et al., 2015;Jimenez et al., 2016); however, at 600°C the dissociation rate coefficient for 595 pRONO2 is ~4 orders of magnitude larger (compared to 350 °C). That said, it is not clear what the pressures or temperatures of the gases are in the evaporation plume. Nevertheless, Farmer et al. note that thermal decomposition of pRONO2 to NO2 in the AMS would be consistent with the higher NO + /NO2 + ratios observed for pRONO2 than NH4NO3. Their reasoning is that reported ratios of NO2 gas ionization (3.0) are substantially higher than those reported for HNO3 (0.5) gas as well as their measurements of 600 particle-phase NH4NO3. Using the simplest assumption that only NO2 (from RONO2 thermal decomposition) and HNO3 (from NH4NO3 evaporation) are ionized would yield a RoR of 6, which is double that observed. Moreover, fixed values would be expected for pRONO2 and NH4NO3 rather than the observed range of ~4. Clearly, the behavior is more complicated than this simple model. Given that mass discrimination (ion transmission or detector efficiency differences) for the m/z range of the NO + and 605 NO2 + ions is expected to be minor for the AMS (Hu et al., 2017b), the values and variability in NOx + ratios likely originate in the vaporizer and/or ionizer region. As discussed in Hu et al. (2017b), the values and range of NOx + ratios observed for NH4NO3 (combined with other observations) are consistent with EI from a combination of HNO3, NO2, and NO gases that are formed through thermal decomposition. They show the greatly-enhanced importance of such neutral gas-phase decomposition for measurements where 610 a "capture vaporizer" is substituted for the standard AMS vaporizer. The capture vaporizer has a different geometry (optimized for limiting particle bounce) that results in longer gas-phase residence time near the hot vaporizer surfaces. Consequently, an order of magnitude lower NO2 + /NO + ratio is observed for NH4NO3 (0.04-0.07), likely due to a shift in ionization toward primarily NO gas. Similar thermal decomposition processes would be expected for RONO2. However, thermal decomposition to RO and 615 NO2 may occur much faster and always to near completion, given the thermal instability of the O-NO2 bond and near absence of CxHyOzN + fragments in AMS pRONO2 spectra (Farmer et al., 2010). Hu et al. (2017a) report a large reduction in the NO2 + /NO + ratios for pRONO2 when using the capture vaporizer compared to the standard vaporizer (with a pRONO2 ratio ten times lower than for NH4NO3 with the capture vaporizer). 620 As shown in Drewnick et al. (2015) and Jimenez et al. (2016), single-particle detection timescales for ions when sampling NH4NO3 show a range of a factor of two (and ~25 μs differences), primarily with NO + being longer than NO2 + and NHx + ions. Those observations are interpreted as evidence for additional processes occurring at longer timescales than flash vaporization at the nominal temperature such as vaporization at lower effective temperatures, slower vaporization or thermal decomposition, and 625 adsorption/desorption from ionizer surfaces. They also showed that the signal-particle detection timescales were insensitive to vaporizer temperatures above 300°C. On the other hand, Hu et al. (2017b) showed a small dependence of the RNH4NO3 on vaporizer temperature decreasing by 25% from 200°C to 800°C, consistent with more thermal decomposition to NO2 and NO gases. Other studies have reported no dependence of NOx + ratios on vaporizer temperature (~200-600°C) for pRONO2-containing chamber 630 SOA (Fry et al., 2009) or ambient (mixed nitrate) aerosol (Docherty et al., 2015). Overall, these observations point toward the timescales of interaction, and effects of spatial distribution of competing processes, playing a more important role in affecting observed ion ratios, rather than vaporizer temperature. In part, this relative insensitivity to vaporizer temperature may be because the physical process of particle vaporization occurs at lower temperature than the nominal vaporizer temperature due 635 to evaporative cooling (Saleh et al., 2017). Another observation that Hu et al. reported for using the capture vaporizer was that the vaporization timescales (based on UMR PToF distributions) for NO + was much longer than for NO2 + for NH4NO3, but the reverse for pRONO2. Such apparent spatiotemporal differences in thermal decomposition and ionization could potentially be used as another method for differentiating nitrates. However, low S/N of NO2 + , differences in sizes and broader distributions for 640 ambient aerosol nitrates, and the possibility that some of the differences Hu et al. observed were from CH2Ox + , may seriously limit such approach and would require further evaluation (using HR-PToF).
A few other evaluations of RNH4NO3, described in Hu et al., (2017b) (using the standard vaporizer), showed dependencies of NOx + ratios of only <20% including varying the location on which particles impact the vaporizer (by horizontally translating the aerodynamic lens position) and varying the vaporizer 645 bias voltage over ranges expected for typical AMS operation. On the other hand, varying the vaporizer bias voltage over a wider range, such as slightly beyond the settings where the aerosol signal peaks and where the gaseous "airbeam" signal peaks, can result in nearly a factor of two shift in the RNH4NO3 (Fig.  S29). This behavior reflects the ability of the vaporizer bias voltage tuning to preferentially sample ions produced in different regions of the ionizer. It has also been shown for the signals of other ions, such as 650 CO2 + (Jayne et al., 2015). While proper tuning of the AMS vaporizer bias voltage typically aims at optimizing the aerosol signal, that may not always be performed by AMS operators and likely in some cases the airbeam signal may be optimized instead (which can be different than the particle signal peak as in Fig. S29, although not always). Therefore, variability in this tuning parameter may explain a substantial fraction of the range in NH4NO3 (and possibly pRONO2) NOx + ratios shown in Fig. 1. Another effect that 655 appears to be able to substantially alter the NOx + ratios is related to exposure to high concentrations of OA for extended periods, possibly coating the vaporizer (and is possibly related to the "Pieber Effect" where nitrate aerosol produces CO2 + signal from interactions at the vaporizer surface), and will be discussed in a future publication. Taking all the evidence available at present, the range in NOx + ratios for NH4NO3 and pRONO2 among instruments, settings, and operating conditions appears to be driven by 660 changes in the amount of chemical decomposition and the overlap of those products with the ionizing electron beam. This aspect highlights the importance of periodic measurement of the NOx + ratios with a standard (i.e., NH4NO3), especially after making significant instrument changes, when quantifying pRONO2 and NH4NO3 with the AMS.

Multisite survey of inorganic/organic nitrate fractionation 665
An overview of the inorganic vs organic nitrate apportionment for all of the campaigns discussed in this manuscript is shown in Fig. 5. The apportionment was conducted using the RoR method. The campaigns span: late-winter to summer across the northern hemisphere and wet/dry seasons near the equator; from ground level to the upper troposphere; and urban to remote locations. Overall, the fpRONO2 shows an inverse relationship with the pNO3, approaching 100% at low pNO3, primarily at rural/remote locations.

670
At high pNO3 and strongly urban-influenced locations, the nitrate is dominantly NH4NO3. However, urban and urban-influenced locations can often exceed 50% contributions from pRONO2, when pNO3 is lower (<1-2 μg m -3 ). At the urban ground sites (MILAGRO, SOAR), the modulation of the variability in pNO3 tended to be driven by large increases in NH4NO3 from photochemical production of HNO3 during morning to early afternoon, followed by evaporation at higher temperatures during afternoon driving 675 concentrations to minima that were generally sustained through nighttime (Aiken et al., 2009;Docherty et al., 2011). At the rural/remote sites, nitrate is nearly always dominated by pRONO2 and with low concentrations. At the mid-latitude sites (BEACHON, SOAS), a large contribution to the variability in concentrations was attributed to nighttime production of pRONO2 from BVOC (Fry et al., 2013;Xu et al., 2015b). For the Amazon studies, substantial variability was observed on sub-day and synoptic timescales, 680 especially during the lower-concentration wet season measurements, with episodic elevated inorganic contributions (de Sá et al., 2018(de Sá et al., , 2019. Thus, variability may have largely been driven by transport changes and large-scale regional processes; however, the factors controlling particle-phase nitrate for those studies have not been thoroughly explored. For DAURE, an urban-downwind site with high pNO3, consistent diurnal patterns were not observed, and pNO3 variability was likely dominantly driven by 685 variability in transport (Minguillon´ et al., 2011;Zhang and Jimenez, 2021).
The aircraft campaigns span the entire range of the urban and rural/remote sites combined, since they include urban and biomass burning sampling, as well as rural/remote and free tropospheric sampling. However, there are notable differences among them and compared to ground-based studies. A major difference is the shift toward lower fpRONO2 or pNO3 in the intermediate ranges by factors of ~2 or ~10, 690 respectively. The large divergence as pNO3 decreases from ~2 to ~0.2 μg m -3 coincides with the range where the aircraft measurements show NH4_Bal transitions from balanced (NH4_Bal ~ 1) to a modest deficit in ammonium (NH4_Bal ~ 0.75-0.9) (see Fig. S30). Lower NH4_Bal can be indicative of more acidic aerosol (Nault et al., 2021;Schueneman et al., 2021), making particle-phase NH4NO3 less thermodynamically stable. In comparison, the NH4_Bal for the ground-based urban-influenced studies, (SOAR, MILAGRO, 695 DAURE) were consistently near unity (Aiken et al., 2009;Docherty et al., 2011; this work for DAURE, not shown). However, such effects alone would result in higher fpRONO2 in the aircraft studies, not lower as observed, due to sulfate not balanced by ammonium and acidity making ammonium nitrate thermodynamically unstable. Therefore, other factors must be at play, such as very different sources being sampled, lower temperatures and higher RH for the aircraft measurements (making NH4NO3 more 700 thermodynamically stable; see Sect. 5.1, Fig. S11), dilution shifting the curves, or higher acidity shortening the lifetime of pRONO2 (such as accelerating hydrolysis). At the lower range of pNO3 (<0.2 μg m -3 ) the fpRONO2 is substantially different following the order KORUS < DC3 < SEAC 4 RS. Considering again the NH4_Bal (Fig. S30), for SEAC 4 RS the aerosol inorganics are much less balanced by ammonium (NH4_Bal ~ 0.08-0.75) compared to DC3 (NH4_Bal ~ 0.5-0.8) and KORUS (NH4_Bal ~ 0.5-0.9) at the lower 705 pNO3 range, suggesting a possible role of acidity and NH3 availability. On the other hand, it does not appear that acidity plays a dominant role in favoring the high fpRONO2 at the rural/remote ground-based studies, as BEACHON tended to be fully balanced (NH4_Bal ≥ 0.9) while SOAS was not (NH4_Bal ~ 0.5-0.7) (Fry et al., 2013;Hu et al., 2016).
Many different chemical and physicochemical processes interplay to control the concentrations and 710 relative proportions of NH4NO3 and pRONO2 in the atmosphere. Fig. 6 shows a schematic of those key processes. The differentiation can be viewed as effectively beginning with the branching of the radicalradical reaction of NOx with OH vs RO2 or VOCs (NO+RO2, NO2+RC(O)O2, NO3+RC=CR´) to produce gas-phase HNO3 vs RONO2. The relative amount of these pathways can vary widely, in large part controlled by relative amounts of NOx concentrations compared to VOC reactivity; the RONO2 formation 715 pathway can become dominant below modest NOx concentrations, particularly at biogenically-influenced rural sites (e.g., Browne and Cohen, 2012;Romer, 2018). However, the partitioning of HNO3 and RONO2 into the particle phase can depend on numerous factors such as NH3 availability, RH, temperature, particle acidity, RONO2 volatility, or OA concentrations. Subsequent chemical, photochemical, evaporation, and deposition losses of gas and particle components will also exert controls on 720 concentrations and lifetimes. In large part, the general trend shown in Fig. 5, over more than three orders of magnitude pNO3, may be driven by the ability of HNO3 formation in the presence of sufficient NH3 at increasing pollutions levels (i.e., NOx) to overwhelm more modest pRONO2 formation, combined with the high volatility of NH4NO3 prone to evaporation upon dilution. In contrast, at rural and remote locations, the formation of RONO2 becomes more favorable, producing pRONO2 of which a substantial 725 portion is not prone to rapid chemical or evaporative loss, thus dominating widespread background nitrate composition. However, this is a very simplified picture of the complex processes at play and more detailed investigations combining corresponding measurements with modeling to better understand the dominant processes controlling the trends shown in Fig. 5 are needed. In a recent study of eleven aircraft campaigns from throughout the globe, Nault et al. (2021) showed overall trends of decreasing pH and 730 NH4_Bal with remoteness (as indicated by decreasing total inorganic PM1), which was not well-represented in many current models. While there may be some connections between that phenomena and the one shown in Fig. 5 (e.g., via acidity and NH3 availability), inorganic PM1 concentration is more closely related to remoteness than pNO3, as it is often dominated by sulfate, which is less chemically reactive and less volatile than pRONO2 and NH4NO3, and its formation is less coupled to VOC conditions. For a 735 ground-based study in a Chinese megacity during fall, a strong trend of increasing inorganic fraction of pNO3 with increasing calculated aerosol pH (pH=1.5-3.5) was observed, which was attributed to numerous coincident factors during pollution episodes favoring NH4NO3 precursor availability and gasto-particle partitioning (Chen et al., 2021).
We note that the data included in Fig. 5 are generally weighted toward warmer periods or regions. Xu 740 et al. (2015a) reported wintertime (within Nov-Feb) measurements of organic and inorganic nitrate at two urban and one rural site in the southeast US. Campaign averages of pNO3 ranged 0.8-1.4 μg m -3 (with 1σ variability of ±90-100%) and average fpRONO2 was 0-30% across the sites and the apportionment methods considered. pNO3 and inorganic nitrate showed strong diurnal cycles, peaking mid-morning with minima mid-to-late afternoon. Nitrate apportionment vs pNO3 was not reported, so it is unclear if similar trends to 745 those in Fig. 5 were present (e.g., if fpRONO2 increased during afternoon pNO3 minima). However, on average all three campaigns fell in the chemical coordinate space of the urban-influenced studies shown in Fig. 5. The fact that the rural site was similar to the urban sites may be due to the cooler winter temperature (and higher RH) as well as reduced biogenic influences, compared to warm rural studies shown in Fig. 5. A few other studies have shown AMS data as supplementary material, that suggest 750 similar relationships to those in Fig. 5 for individual studies. Those include plots of NO + vs NO2 + ions which appear to have higher ratios of NO + /NO2 + at lower signals (Docherty et al., 2015;Zhou et al., 2016) or decreasing NO2 + /NO + ratios with decreasing pNO3 (Kiendler-Scharr et al., 2016). Additionally, a recent analysis of three datasets in the North China Plain (urban summer/winter, rural winter), showed a strong decreasing trend in fpRONO2 vs PM1 during the urban summer measurements and weak trends for the 755 wintertime measurements (and lower overall fpRONO2) . Those observations are generally consistent with the trends with pNO3 during summer and with seasonality discussed above.

Further discussion of the efficacy and support for NOx + ratio apportionment
From simply inspecting the relationships of fpRONO2 and NOx + ratios vs pNO3 in Figs. 5 and S9, or the variability of ratios shown in Fig. 2, it could be postulated that such trends could simply be driven by 760 changing pNO3 concentrations or some other confounding factor such as matrix effects. Thus, here we review several pieces of evidence presented in this manuscript and prior literature that, taken together, provide overwhelming support that the variability of measured Rambient between the calibrated RNH4NO3 and the RoR-derived RpRONO2 values is dominantly controlled by the continuum of inorganic/organic nitrate contributions. We emphasize that this discussion is relevant only to conditions where refractory nitrates 765 (NaNO3, Ca(NO3)2, e.g., from dust or seasalt) or nitrites are not substantial components of the aerosol, since they produce different NOx + ratios and the apportionment equation becomes underconstrained.
Kiendler-Sharr et al. (2016) present laboratory data of NOx + ratios for over a range of NH4NO3 concentrations and mixtures (Sect. S1, Fig. S1 in that paper). They conclude that "fragmentation behaviour as a function of mass concentration, composition of the particles and particle size of NH4NO3 770 and mixtures of NH4NO3 with (NH4)2SO4 and glutaric acid, were observed to be constant, independent of mass concentration down to 0.1 μg/m 3 in the laboratory aerosol". We regularly generate scatterplots of the two NOx + ions over a range of NH4NO3 concentrations recorded during calibrations. This is the typical method we use and recommend for quantifying the RNH4NO3 and inspecting for any irregularity in the relationships (such as non-linearity). The insensitivity of RNH4NO3 with concentration is a consistent 775 feature. We have systematically explored concentration and matrix effects of NH4NO3 and pRONO2 in the laboratory and with field data and show that under typical ambient conditions, effects, if present, are small. This will be presented as part of a future manuscript exploring the uncertainties of these apportionment and quantifications methods. We note that this result contrasts with a similar study that assessed the viability of apportioning inorganic and organic sulfate using HySOx + and SOx + ion ratios 780 (Schueneman et al., 2021). Strong dependencies on aerosol composition (i.e. acidity and nitrate mass fraction, but generally not OA concentration) were found for those ions, making sulfate apportionment not possible under a substantial fraction of conditions found in the atmosphere.
Inspection of the NOx + ratios vs pNO3 shown in Fig. S9a for the three urban field studies shows that ratios generally plateau at RNH4NO3 when the nitrate is only ~30% of the bulk aerosol -and thus still 785 dominated by other compounds -supporting that mixing with other complex ambient components does not alter the NOx + ratio produced from NH4NO3. Furthermore, at lower pNO3, NOx + ratios for all campaigns generally approach expected pRONO2 ratios. While this certainly does not prove that at the lower pNO3 range, the nitrates are primarily organic, and primarily NH4NO3 at the higher pNO3 range, such consistent behavior would be highly coincidental. We also point to the comparisons of AMS-790 apportioned pRONO2 with independent measurements of total RONO2, shown in Figs. 3, S12a. There is a high level of tracking between the two independent organic nitrate components, while flying through intermittent plumes with elevated inorganic nitrate, which were sometimes correlated with elevated OA while in other cases not (Figs. S11, S12b). This provides strong evidence that the use of NOx + ratios are indeed effectively apportioning nitrate, and changing non-nitrate fractions are not hindering the method.

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Similarly, the apportioned NH4NO3 tracks well with estimates of NH4 not associated with sulfate for those same aircraft flights (Figs. S11, S12b).
Finally, the exploration of NOx + ratio apportionment with PMF, shows the distinct signature of pRONO2 NOx + ratios for secondary OA factors and that of NH4NO3 for the other components (Figs. S17, S25). That result would be highly unlikely if the continuum of NOx + ratios in the total aerosol were 800 dominantly controlled by concentration or matrix artifacts. While this preponderance of evidence strongly supports the effectiveness of this method, further laboratory and field data studies and analyses, including instrument comparisons, should be conducted to better constrain uncertainties and improve the method.

Conclusions
We have explored the viability of using the NOx + ion ratios produced in the AMS spectrum from nitrates 805 to separate and quantify NH4NO3 and pRONO2 concentrations in ambient aerosols. The use of NH4NO3 calibration NOx + ratios and an inferred NOx + ratio for pRONO2 that tracks the NH4NO3 ratio ("Ratio-of-Ratios") is investigated and tested. An extensive range of data and approaches are utilized for this investigation including: a diverse collection of ambient field datasets, chamber studies, oxidation flow reactors, pure compounds, comparisons to AMS PMF methods and other pRONO2 or related 810 measurements, and a compilation of a broad literature survey.
It is shown that the method is robust and effective under typical ambient sampling conditions. Methods and practical considerations for calculating concentrations are described. The Ratio-of-Ratios NOx + ratio method produced similar results to conducting PMF on the expanded mass spectra series (including both OA and NOx + ions) to apportion nitrates. While using the PMF method may have 815 advantages of improved signal-to-noise and can provide connections between pRONO2 and OA sources, it is much more labor-intensive and can lead to substantial biases if not explored and applied carefully.
A broad survey of nitrate apportionment shows a pervasive relationship of increasing (decreasing) pRONO2 relative contributions to nitrate with decreasing (increasing) total nitrate concentrations. Those trends generally follow from urban-influenced to rural/remote regions. However, there are some clear 820 differences in those trends between different sampling regions and conditions. Further investigation of the processes that control particle nitrate composition is required to understand the factors responsible for these observed trends and differences.
Previous studies reporting nitrate quantification using AMS NOx + ratios (or PMF using NOx + ions) have employed a range different approaches and assumptions, based on generally limited information. In 825 some instances, likely substantial biases were present and rarely has the accuracy of the results been considered. This investigation will help provide a more consistent, accurate and transparent approach to quantification and exploration of bulk particle-phase nitrates in the atmosphere with AMS (and related instrumentation). Comparisons of this method to other instrumentation capable of quantifying bulk or speciated particle-phase organic nitrates, in the laboratory and field, should be an ongoing focus to help 830 better constrain uncertainties, identify biases, and improve this method (and others).

Data availability
Data from the field campaigns are archived as follows: for the NASA airborne campaigns (DC3, SEAC 4 RS, KORUS-AQ) at https://www-air.larc.nasa.gov/index.html (see "missions"); for SOAS at 835 https://data.eol.ucar.edu/project/SAS; for BEACHON-RoMBAS at http://manitou.acom.ucar.edu/#data; for DAURE (and also for AMS data from other ground-based campaigns) at https://sites.google.com/site/amsglobaldatabase; for SOAR at http://cires.colorado.edu/jimenezgroup/Field_Data/SOAR_1/SOAR%20data; for MILAGRO at https://www.eol.ucar.edu/field_projects/milagro; and for GoAmazon at 840 https://www.arm.gov/research/campaigns/amf2014goamazon. All figures presented in the manuscript and data used to construct them are archived at http://cires1.colorado.edu/jimenez/group_pubs.html. Additional data used for or generated during intermediate stages of the analysis are archived on a data server at the University of Colorado and can be provided upon request by the corresponding authors.

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Author contributions DAD, PCJ, and JLJ designed the analysis; DAD, BAN, PCJ, and JLJ wrote the paper; All authors collected and analyzed data; All authors reviewed and provided comments for the paper. Figure 1. (a) Survey of "Ratio-of-Ratios" (RoR) computed from NO2 + /NO + ratios reported for chamber studies, pure organic nitrates, and field observations (using instrument comparisons or PMF separation). The mean (2.75) and standard deviation (±0.70, ±25%) are also shown (standard error for n=41: ±0.11, ±4.0%). The light grey shading ( "+" markers) indicates data that were not used in the average here, nor in 865 the fits below (see Table S1 for rationale). Details of the values used to compute the ratios and uncertainties, data source, and any additional calculations for the information included in Figure 1 are provided in Table S1. (b) Histogram and statistics of RoR. (c) scatter plot of RNH4NO3 vs. RpRONO2. Linear least-squares lines are shown with orthogonal distance regression (ODR) fit (with intercept constrained through the origin, since offsets from unconstrained fits were not significant and for consistency with the 870 apportionment equation). The data connected by cyan and green lines are averages from experiments conducted in our lab with two different AMSs (with substantially different calibration RNH4NO3) while sampling the same type of SOA particles produced using the same two precursors mixtures. See Fig. S3 for the equivalent scatter plot, instead using NO + /NO2 + ratios and swapping the axes (RpRONO2 vs RNH4NO3). Figure 2. Histograms of ambient NOx + ratios for aircraft and ground-based campaigns. The data is shown as the calibration RNH4NO3 divided by Rambient, so that all data are on the same reference coordinates. The histograms are weighted by pNO3 concentration. Cumulative distributions are shown in all plots and an additional curve only on the SOAS panel shows the fpRONO2 (pRONO2/pNO3) for these coordinates (would be identical on all panels). The data used were 1-minute averages and screened for pNO3 detection limits 880

Figures 860
for the aircraft campaigns (SEAC 4 RS, DC3), and 1-hour averages for the ground-based campaign (SOAS, BEACHON-RoMBAS). Measured RNH4NO3 for these studies were as follows: time series (a) and scatterplots of pRONO2 (b) or NH4NO3 (c) vs Tot-RONO2 are shown. Measured calibration RNH4NO3 (consistent with PMF results in Sect. 5.2.2), a RoR of 2.75, and Eq. 1 was used to apportion the AMS nitrate. Linear least-squares lines are orthogonal distance regression (ODR). For the pRONO2 vs Tot-RONO2 plot (b), an additional line (dotted) and fits (parentheses) are shown for data including only when fpRONO2 (pRONO2/pNO3) is greater than 0.3 (and datapoints with fpRONO2<0.3 are 895 greyed). Figure S10 shows the flight track and timing of different source types sampled. using the RoR method (as well as the measured NOx + signals and ratios) are shown for all data as well as only when above the Rambient detection limit (DL; approximated as when both NOx + ions are above standard AMS detection limits (Drewnick et al., 2009)). (e) PMF pRONO2 vs TD-LIF Tot-RONO2 (equivalent to Fig. 3b, which instead shows pRONO2 from RoR method). pRONO2 in scatterplots are colored by the fpRONO2 (pRONO2/pNO3) as computed using the PMF method. Regression line 905 fits/slopes/offsets and correlation coefficients are shown using different fitting methods and criterion as indicated in legends (including where data is limited to fpRONO2>0.3). All PMF-derived concentrations are averages (and standard deviations) of 100 bootstrapping runs (similar results using seeding runs are shown in Fig. S21).

Figure 5.
Fraction of total non-refractory submicron nitrate that is organic (fpRONO2) vs. total nitrate concentration (pNO3) for several ground and aircraft campaigns. Campaigns span: late-winter to summer across the northern hemisphere and wet/dry seasons near the equator; from ground level to the upper troposphere; and urban to remote locations. NOx + ion signals were first averaged and then data was 915 conservatively screened for detection limits (S/N>1-3) using both NOx + ions (small circles). Quantile averages (means, 7-15 bins) are also shown for each campaign. Additionally, for all campaigns, one additional average was calculated and included with the quantile averages for the highest 1% (3%) of pNO3 for urban/aircraft (rural/remote) campaigns in order to extend the pNO3 by a factor of ~1.3-3 (undersampled chemical regime, but with sufficiently high S/N). The average of the lowest 3% of pNO3 920 for the MILAGRO campaign is also included. Shaded swaths indicate the standard error for the quantile averages. Many are no larger than the markers and thus may not be very apparent. See Fig. S31 for a simplified version, showing only binned averages and standard error bars.