Development and validation of a NO_x⁺ ratio method for the quantitative separation of inorganic and organic nitrate aerosol using a unit-mass-resolution time-of-flight aerosol chemical speciation monitor equipped with a capture vaporizer (CV-UMR-ToF-ACSM)

Particulate nitrate is a major component of ambient aerosol around the world, present in inorganic form, mainly as ammonium nitrate, and also as organic nitrate. It is of increasing importance to monitor ambient particulate nitrate, a reservoir of urban nitrogen oxides that can be transported downwind and harm ecosystems. The unit-mass-resolution time-of-flight aerosol chemical speciation monitor equipped with capture vaporizer (CV-UMR-ToF-ACSM) is designed to quantitatively monitor ambient PM_2.5 composition. In this paper, we describe a method for separating the organic and ammonium nitrate components measured by CV-UMR-ToF-ACSM based on evaluating the ${\mathrm{NO}}_{\mathrm{2}}^{+}/{\mathrm{NO}}^{+}$ ratio (${\mathrm{NO}}_x^{+}$ ratio). This method includes modifying the ACSM fragmentation table, time averaging, and data filtering. By using the measured ${\mathrm{NO}}_x^{+}$ ratio of NH₄NO₃ and a plausible range of ${\mathrm{NO}}_x^{+}$ ratio for organic nitrate aerosol, the measured particulate nitrate can be split into inorganic and organic fractions. Data pre-treatment filters concentrations of particulate nitrate below 0.6–2.0 µg m⁻³, depending on the time averaging. The method detection limit, when considering ±10 % absolute uncertainty of organic nitrate fraction, is found to be 2 µg m⁻³ (120 min averaging) to 10 µg m⁻³ (10 min averaging) for total particulate nitrate concentration and 10 % (120 min) to 20 % (10 min) for organic nitrate fraction. We show that this method is able to distinguish periods with inorganic or organic nitrate as major components at a rural site in the Netherlands. A comparison to a high-resolution time-of-flight aerosol mass spectrometer equipped with a standard vaporizer (SV-HR-ToF-AMS) and positive matrix factorization (PMF) method shows similar response of increasing particulate organic nitrate fraction with uncertainties mainly from sensitivity to fragmentation table correction when obtaining the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal. We propose that researchers use this ${\mathrm{NO}}_x^{+}$ ratio method for CV-UMR-ToF-ACSM (adapting the appropriate fragmentation table and data pre-treatment for each specific application) to quantify the particulate organic nitrate fraction at existing monitoring sites in order to improve understanding of nitrate formation and speciation.

1 Introduction

In the current age of decreasing sulfur emissions, nitrate is becoming a principal aerosol component globally and regionally (Adams et al., 1999; Metzger, 2002; Liao et al., 2003; Rodriguez and Dabdub, 2004; Feng and Penner, 2007; Bauer et al., 2007; Paulot et al., 2016; Bian et al., 2017; Vasilakos et al., 2018; Drugé et al., 2019; Lu et al., 2021). In addition to an increasing aerosol fraction of ammonium nitrate (NH₄NO₃), ambient organic nitrates (ONs) produced through the oxidation of volatile organic compounds (VOCs) in the presence of nitrogen oxides (NO_x) can condense into the particulate phase or grow new particles (Huang et al., 2019a, b; Song et al., 2024). The particulate organic nitrate (pON) contribution to total particulate nitrate mass (pNO₃) is substantial (Ng et al., 2017), with an average fraction of 17 %–31 % in China (Yu et al., 2024) and 34 %–44 % in Europe (Kiendler-Scharr et al., 2016), with large differences between urban and rural areas (Fisher et al., 2016; Schlag et al., 2016; Romer Present et al., 2020; Yu et al., 2024). Improved understanding of pON fraction in different regions can provide insight into chemical mechanisms of secondary aerosol formation (Pye et al., 2015; Lee et al., 2016; Ng et al., 2017; Zare et al., 2018).

ON flux worldwide accounts for ∼25 % of the total nitrogen deposition (Jickells et al., 2013). Zare et al. (2018) estimated, via WRF-Chem simulations in the southeast United States, that 60 % of NO_x loss is related to ON chemistry. Similar to inorganic nitrate, ON also can be regarded as a NO_x reservoir, because thermal or photolysis processes can re-release NO_x. The partitioning between gas-phase and particulate ON (Zare et al., 2018) can affect this reservoir lifetime and, thus, the spatial scale of transport of urban nitrogen emissions from their source, determining how far downwind these emissions can harm natural habitats (Fields, 2004; Bobbink and Hicks, 2014; Erisman et al., 2015; Melillo, 2021).

The ${\mathrm{NO}}_x^{+}$ ratio method, first described by Farmer et al. (2010), is a robust method to separate the total pNO₃ signal measured by high-resolution aerosol mass spectrometer (AMS) into particulate ammonium nitrate (pAmN) and particulate organic nitrate (pON) using the variation of ${\mathrm{NO}}_{\mathrm{2}}^{+}/{\mathrm{NO}}^{+}$ ion ratios (subsequently referred to as ${\mathrm{NO}}_x^{+}$ ratios) in the mass spectra observed. This method has been successfully used to analyze pON composition in several studies (Fry et al., 2013, 2018; Pye et al., 2015; Kiendler-Scharr et al., 2016; Ng et al., 2017; Huang et al., 2019a, b; Brownwood et al., 2021; Day et al., 2022a).

The basis of the ${\mathrm{NO}}_x^{+}$ ratio method comes from the different fragmentation patterns of chemical species due to the interaction of the mass spectrometer's vaporizer and ionizer with the analytes. The empirical observation shows that nitrates attached to an organic moiety have different fragmentation patterns compared to nitrate in the form of NH₄NO₃, as well as other less-volatile inorganic nitrates. Thus, each nitrate will have different ${\mathrm{NO}}_x^{+}$ ratios, R_ν, as shown below in Eq. (1) (Day et al., 2002; Francisco and Krylowski, 2005; Farmer et al., 2010; Drewnick et al., 2015; Hu et al., 2016; Day et al., 2022a).

$$\begin{array}{}\text{(1)}& R_{\mathit{\nu }}={\displaystyle \frac{(C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}{)}_{\mathit{\nu }}}{(C_{{\mathrm{NO}}^{+}}{)}_{\mathit{\nu }}}}\end{array}$$

ν: nitrate compound or mixture measured,
$C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$: signal intensity of ${\mathrm{NO}}_{\mathrm{2}}^{+}$,
$C_{{\mathrm{NO}}^{+}}$: signal intensity of NO⁺.

The ${\mathrm{NO}}_x^{+}$ ratio of the observed air (R_obs) falls between the ${\mathrm{NO}}_x^{+}$ ratios of pure pAmN (R_pAmN) and pure pON (R_pON). The time-varying mass fraction of particulate organic nitrate (f_pON, referring to pNO₃ existing as pON) and particulate ammonium nitrate (f_pAmN, referring to pNO₃ existing as pAmN) can be extracted from this time-varying R_obs using Eqs. (2) and (3) (Farmer et al., 2010).

$$\begin{array}{}\text{(2)}& {\displaystyle }& {\displaystyle }{f}_{\text{pON}}={\displaystyle \frac{(R_{\text{obs}}-R_{\text{pAmN}})(\mathrm{1}+R_{\text{pON}})}{(R_{\text{pON}}-R_{\text{pAmN}})(\mathrm{1}+R_{\text{obs}})}}\text{(3)}& {\displaystyle }& {\displaystyle }{f}_{\text{pAmN}}=\mathrm{1}-f_{\text{pON}}\end{array}$$

The aerosol chemical speciation monitor (ACSM, Aerodyne Inc.) is a unit-mass-resolution (UMR) mass spectrometry instrument intended for continuous ambient aerosol monitoring (Ng et al., 2011; Fröhlich et al., 2013), unlike its predecessor the aerosol mass spectrometer (AMS, Aerodyne Inc.) which is designed primarily for research (Drewnick et al., 2005). In this work, we explored whether the ACSM can be used to determine pAmN and pON in the same way as has been successfully demonstrated for the AMS. ACSMs are used extensively in monitoring networks, such as the sites in the Aerosol, Clouds and Trace Gases Research Infrastructure (ACTRIS) network in Europe (https://www.psi.ch/en/acsm-stations/overview-full-period, last access: 6 November 2024) and the Atmospheric Science and Chemistry mEasurement NeTwork (ASCENT) network in the USA (https://ascent.research.gatech.edu, last access: 6 November 2024).

For monitoring purposes, a capture vaporizer (CV) and an intermediate pressure lens (IPL) are recommended by Aerodyne for improved quantification of the PM_2.5 fraction, relative to a standard vaporizer (SV) and standard lens (Zheng et al., 2020). Almost half of the ACSMs in the ACTRIS network in Europe use a CV. The CV is designed to increase particle collision events with the vaporizer surface by having a narrow entrance, resulting in a particle collection efficiency (CE) of 1 and better mass closure of PM_2.5 monitoring (Jayne and Worsnop, 2016; Hu et al., 2017a; Xu et al., 2017; Liu et al., 2024). The enhanced thermal decomposition, however, shifts the fragmentation pattern toward smaller ion fragments (Hu et al., 2017a, 2018a; Xu et al., 2017; Zheng et al., 2020). Therefore, the ${\mathrm{NO}}_x^{+}$ ratio is substantially lower with CV compared to SV due to favored NO⁺ formation. As a consequence, the ${\mathrm{NO}}_x^{+}$ ratio method's applicability in CV-based measurements is limited by the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ detection limit (<0.1 µg m⁻³; Hu et al., 2017a).

While high-resolution mass spectrometers can separate non-${\mathrm{NO}}_x^{+}$ peaks which are detected at the same nominal $m/z$ (mass-to-charge ratio) as ${\mathrm{NO}}_x^{+}$ peaks (30 for NO⁺ and 46 for ${\mathrm{NO}}_{\mathrm{2}}^{+}$), UMR analysis requires estimations based on related ions at other $m/z$. These estimations are incorporated into data workup by the implementation of a fragmentation table, which subtracts an estimated amount of organic at $m/z$ 30 and $m/z$ 46, based on the signal at another related organic-only $m/z$ values. The default fragmentation table typically applied for the analysis of UMR spectra is based on generalized fragment mass composition of ambient aerosol composition measured using SV-based instruments (Allan et al., 2004; Ulbrich et al., 2009) and, thus, is not suitable for CV-UMR-ToF spectra that have different fragmentation patterns. Using a CV-HR-ToF-AMS, Hu et al. (2017a) determined the organic fragment interference with NO⁺ at $m/z$ 30 and with ${\mathrm{NO}}_{\mathrm{2}}^{+}$ at $m/z$ 46 for CV-UMR measurements in a biogenically dominated dataset, but no study has yet shown this calculation adapted to general ambient aerosol composition.

This work aims to adapt the ${\mathrm{NO}}_x^{+}$ method to separate pAmN and pON signals for CV-UMR-ToF-ACSM measurements. We first provide a revised fragmentation table for $m/z$ 30 and $m/z$ 46 that is compatible with CV-UMR-ToF-ACSM measurements with varying composition to better calculate NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal contributions. Second, we show the variation of experimental ${\mathrm{NO}}_x^{+}$ ratio for pAmN in CV-UMR-ToF-ACSM instruments and determine the ${\mathrm{NO}}_x^{+}$ ratio for pON. Third, we demonstrate the capability of data pre-treatments (filtering and time averaging) to overcome the low and noisy ratio signals produced by CV in ambient measurements. Fourth, the proposed ${\mathrm{NO}}_x^{+}$ ratio method is applied to an extended ambient dataset (at the Cabauw site of the Ruisdael Observatory network) to test its robustness for changing ambient aerosol mixtures. Lastly, the formation of pAmN and pON in a chamber experiment measured using CV-UMR-ToF-ACSM is used for method validation by comparing results with SV-HR-ToF-AMS.

2 Instrumentation

2.1 Description of ToF-ACSM

A ToF-ACSM (Aerodyne Inc.) is the main instrument used in this study, allowing for the chemical analysis of non-refractory organics (Org), ammonium (NH₄), nitrate (NO₃), sulfate (SO₄), and chloride (Chl) in the aerosol phase (Ng et al., 2011; Fröhlich et al., 2013). In comparison to compact time-of-flight (cToF)-AMS (Drewnick et al., 2005) and HR-ToF-AMS (DeCarlo et al., 2006), ToF-ACSM is more compact in size, lower in price and operational cost, simpler in analysis, and requires less user intervention, which makes this instrument practical for long-term monitoring but still comparable to the AMS (Fröhlich et al., 2013). ToF-ACSM uses a three-way valve system that allows automatic switching between the sample and filter mode, unlike ToF-AMS, which has a mechanical chopper that physically blocks the particle beam. The lack of a chopper (but with the use of particle time-of-flight chamber) in the ToF-ACSM, however, removes the particle sizing feature, which makes it similar to the quadrupole-ACSM (Q-ACSM) but with better mass resolution and detection limits.

To conduct the various analyses in this paper, we primarily use data from two ToF-ACSM instruments with identical setups. The instruments are managed by Utrecht University (UU) and University of Groningen (RUG), part of a larger monitoring network of Ruisdael Observatory in the Netherlands (https://ruisdael-observatory.nl, last access: 6 November 2024). We label the instruments as ACSM-UU and ACSM-RUG. The instrument setup for ambient measurements uses a combination of a PM_2.5 size-cut cyclone, an intermediate-pressure lens (PM_2.5 aerodynamic lens), and a capture vaporizer (CV, temperature ∼525 °C; Jayne and Worsnop, 2016) that has been aligned with the particle beam. Together, they configure the ToF-ACSM as a PM_2.5 monitor (Xu et al., 2017) with unit mass resolution. The instrument provides UMR mass spectra with default 10 min time resolution, analyzed using Tofware v3.3 in Igor Pro 8. The fractions of the UMR signal are assigned to different aerosol species using the fragmentation table.

2.2 Ambient measurements with ACSM

We use an ambient dataset measured using ACSM-UU deployed in Cabauw, the Netherlands, for method development and case studies. The ambient data were measured between 18 April 2023 and 15 April 2024 with some gaps (net 205 d of data) as part of the continuous monitoring of the Ruisdael Observatory network. Aerosol measurements were carried out with an inlet height of 4.5 m above the ground at the Cabauw tower (51.97° N, 4.93° E), an infrastructure of the Royal Netherlands Meteorological Institute (KNMI, the Netherlands, https://www.knmi.nl/home, last access: 9 November 2024). The site is surrounded by agricultural lands in the province of Utrecht, the Netherlands, a relatively nitrogen-polluted rural site.

Ambient air is sampled through a stainless-steel inlet system with a PM_2.5 size-cut cyclone (URG-2000-30ED) and a Nafion dryer with a sampling flow rate of ∼2 L min⁻¹, of which on average 1.23 cm³ s⁻¹ (0.07 L min⁻¹) is sampled by the ACSM. The calibrations of ionization efficiency (IE) and relative IE (RIE) were performed using 300 nm particles from ammonium nitrate (NH₄NO₃) and ammonium sulfate ((NH₄)₂SO₄) solutions (size-selected with a differential mobility analyzer, model TSI 3081, and co-sampled with a condensation particle counter, model TSI 3750). The average IE value for the instrument is 169 ions pg⁻¹ for NO₃, and RIE values are 1.40, 1.58, 1.30, and 3.37 for Org, SO₄, Chl, and NH₄, respectively. RIE values used for Org and Chl were not measured and were instead applied as default values, as is common practice. The detection limits at 10 min time resolution are 0.38 µg m⁻³ for Org, 0.12 µg m⁻³ for NH₄, 0.07 µg m⁻³ for NO₃, 0.07 µg m⁻³ for NO⁺ ($m/z$ 30), 0.04 µg m⁻³ for ${\mathrm{NO}}_{\mathrm{2}}^{+}$ ($m/z$ 46), 0.11 µg m⁻³ for SO₄, and 0.09 µg m⁻³ for Chl.

2.3 Chamber measurements with ACSM and AMS

ACSM-RUG was deployed to measure aerosol in chamber experiments conducted in the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) chamber, a facility maintained by Karlsruhe Institute of Technology (KIT), Germany. Chamber experiments were conducted in 2023 and 2024 as part of the Cloud-Aerosol Interactions in a Nitrogen-dominated Atmosphere (CAINA) project (https://sites.google.com/view/cainaproject/, last access: 6 November 2024).

Chamber air is sampled using stainless-steel tubing equipped with a Nafion dryer and a sampling flow of ∼2 L min⁻¹ of which on average 1.44 cm³ s⁻¹ (0.09 L min⁻¹) is sampled by the ACSM. The average IE value for the instrument is 152 ions pg⁻¹ for NO₃. The ACSM instrument is run with 2 min time resolution unlike the default setting to capture more variation in the aerosol composition. The detection limits at 2 min time resolution for the ACSM-RUG instrument are 0.20 µg m⁻³ for Org, 0.19 µg m⁻³ for NH₄, 0.17 µg m⁻³ for NO₃, 0.17 µg m⁻³ for NO⁺ ($m/z$ 30), 0.03 µg m⁻³ for ${\mathrm{NO}}_{\mathrm{2}}^{+}$ ($m/z$ 46), 0.02 µg m⁻³ for SO₄, and 0.05 µg m⁻³ for Chl.

In addition, a high-resolution time-of-flight aerosol mass spectrometer (HR-AMS, Aerodyne Research Inc.) from KIT is connected to the chamber via a 6 mm (4 mm internal diameter) stainless-steel tube. The instrument is equipped with a PM_2.5 aerodynamic lens to measure the non-refractory PM_2.5 components, at a time resolution of 1 min (DeCarlo et al., 2006; Canagaratna et al., 2007; Williams et al., 2013), averaged to 2 min for this comparison. The operation of the AMS is explained in previous publications (Huang et al., 2019a; Song et al., 2022). Briefly, chamber air is sampled with a flow of 1.08 L min⁻¹, of which on average 84 cm³ min⁻¹ is sampled by the AMS (Gao et al., 2022). The aerosol particles are then focused into a narrow beam by a PM_2.5 aerodynamic lens with an effective complete transmission for particle sizes ranging from 70 to 2500 nm (vacuum aerodynamic diameter, D_va) and heated by a standard vaporizer at 600 °C. The resulting vapors are ionized by electron impact (70 eV) and characterized by a time-of-flight mass spectrometer. The AMS ionization efficiency is calibrated using 300 nm dried NH₄NO₃ aerosol particles to give an average IE for NO₃ of 185.0 ions pg⁻¹. The AMS data are analyzed using the software packages Squirrel 1.66E and PIKA 1.26E in Igor Pro 8. To account for the effect of particle bouncing loss, chemical-composition-based collection efficiency (0.5) was applied to calculate the particle mass concentration (Middlebrook et al., 2012).

3 Development of a fragmentation table for CV-UMR-ToF-ACSM from the AMS spectral database and ACSM chamber experiment spectra

3.1 General fragmentation table for typical ambient dataset

In the UMR-ACSM instruments, ions detected at $m/z$ 30 and $m/z$ 46 can originate from both nitrate (NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$) and organic fragments. However, it is known that some fragments produced by processes in the vaporizer and ionizer can be related to one another (Allan et al., 2004). For instance, UMR peaks at $m/z$ 29, $m/z$ 42, $m/z$ 43, and $m/z$ 45 are mainly the product of further fragmentation of fragments at $m/z$ 30 and $m/z$ 46 and assumed to be exclusively of organic origin. The aim of the fragmentation table, with respect to the ${\mathrm{NO}}_x^{+}$ species, is to predict the signal contribution of organic fragments at $m/z$ 30 and $m/z$ 46 based on the masses measured at $m/z$ 29, $m/z$ 42, $m/z$ 43, and $m/z$ 45 and subsequently to extract the signal that can be attributed to NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$.

Our starting point is the default fragmentation table from Allan et al. (2004) (see Table 1). A fragmentation table consists of columns dividing the raw mass spectra into chemical species, with rows denoting entries for different UMR nominal masses. Thus, each entry consists of components which are added up to obtain the species concentration at a specific nominal mass. These components can be the whole peak of an $m/z$ x, referred to as an integer number (with square brackets in this paper, “[x]”), or the contribution of a certain species to $m/z$ x in the fragmentation table, denoted as “frag_species[x].” A multiplier a (positive or negative) is included if the addition or subtraction of the component is fractional. The fragmentation table for ToF-AMS and ToF-ACSM are identical, except that gas-phase species contribution must also be removed in ToF-AMS. For the ACSM, due to the automatic filter sampling cycle and subtraction, gas-phase species are already removed. The fragmentation table developed in this paper, therefore, is applicable to a CV-UMR aerosol mass spectrometer. Because the training dataset incorporated multiple chamber and ambient measurements with different instruments, it should be applicable for a range of typical measurement configurations, but users should be aware of the potential effects of the instrument condition (e.g., vaporizer temperature, particle beam alignment, measurement history).

Allan et al. (2004)

Table 1 Excerpt of fragmentation table for Org and NO₃ species at $m/z$ 30 and $m/z$ 46. The second and third columns show entries originated from the default fragmentation table of Allan et al. (2004) (used in Tofware v3.3). The fourth and fifth columns show entries proposed to develop a revised CV-UMR-ToF-ACSM fragmentation table in this study.

i represents UMR masses tested against $m/z$ 30 and $m/z$ 46 in this study, which includes frag_Org[29], frag_Org[42], frag_Org[43], and frag_Org[45]. See the list in the footnote of Table S3 in the Supplement.
^a a_Org[30],[i] is the multiplier for frag_Org[30] component, obtained from the slope of ODR fit between frag_Org[30] and frag_Org[i].
^b a_Org[46],[i] is the multiplier for frag_Org[46] component, obtained from the slope of ODR fit between frag_Org[46] and frag_Org[i].

In the default fragmentation table (which was developed using an SV-based instrument), the signal at $m/z$ 46 is assigned exclusively to ${\mathrm{NO}}_{\mathrm{2}}^{+}$, and the relationship of organic signal at $m/z$ 30 is found to be only 0.022 times the magnitude of organic signal at $m/z$ 29. Switching from SV to CV modifies the signal ratio between organic and inorganic fragments at $m/z$ 30 and $m/z$ 46 because of greater organic fragmentation in CV (Hu et al., 2018a). It also leads to greater nitrate fragmentation and consequently smaller ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal, which makes the organic contribution at $m/z$ 46 more important. For instance, Fry et al. (2018) found larger contributions of organic fragments at $m/z$ 30 and $m/z$ 46 than the default fragmentation table in a semi-polluted biogenically influenced air analyzed with an SV-HR-ToF-AMS. Therefore, modifications to frag_NO₃[46] and frag_NO₃[30] entries (later referred to as $C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$ and $C_{{\mathrm{NO}}^{+}}$ to calculate ${\mathrm{NO}}_x^{+}$ ratio outside fragmentation table context) must be established for CV-based instruments.

To make a revised fragmentation table applicable for general ambient organic aerosol (OA) mixtures, a variety of organic aerosol profiles is necessary. We use 25 CV-HR-ToF-AMS spectra (including both nitrates and non-nitrate organics) from the AMS spectral database (http://cires1.colorado.edu/jimenez-group/AMSsd_CV, last access: 6 November 2024) and 6 CV-UMR-ToF-ACSM spectra from chamber experiments. The CV-HR-ToF-AMS database mass spectra include 3 chamber experiments, 7 factors of positive matrix factorization (PMF) analysis from ambient measurements, and 15 laboratory standards measurements (Hu et al., 2025, 2017a, 2018a, b; Carlton et al., 2018), summarized in Table S1 in the Supplement. The CV-UMR-ToF-ACSM mass spectra were measured from experiments conducted in the AIDA chamber (see Sect. 2.3). These spectra were obtained using vaporizer temperature ranging from 525 to 600 °C (see Tables S1 and S2 in the Supplement). Therefore, the revised fragmentation table should be valid for CV-based instruments run in this temperature range.

Using these data, we determine the multipliers a used in a revised calculation of frag_Org[30] and frag_Org[46] (see Table 1, fourth and fifth columns, and Table S1, third and fourth column). The new multipliers are determined by performing orthogonal distance regression (ODR) constrained to a zero intercept of mass spectra in UMR. For HR-AMS spectra, the dataset is “degraded” from HR into UMR spectra by summing HR Org fragments to their respective nominal mass in each AMS spectrum. Note that for UMR-ACSM spectra, because we cannot separate species at the same nominal $m/z$, we only use chamber experiments that are assumed nitrate-free or to contain negligible nitrate (no seed or precursor for inorganic and organic nitrate). Therefore, all signals at $m/z$ 30 and $m/z$ 46 are exclusively organic fragments. We perform ODR fits of frag_Org[30] and frag_Org[46] against a list of chemically related masses (frag_Org[i]). The slope of the ODR fits to determine the multiplier a_Org[30],[i] and a_Org[46],[i] are summarized in Table S3, alongside the list of fragments of i that contribute to each nominal mass, in the footnote. It is found that frag_Org[30] is best correlated with frag_Org[29] (see Table S3), where a_Org[30],[29]=0.311 ± 0.016 (mean ± uncertainty, r²=0.88; see Fig. 1a). On the other hand, frag_Org[46] has the best correlation with frag_Org[45] (see Table S3), where a_Org[46],[45]=0.305 ± 0.037 (mean ± uncertainty, r²=0.43; see Fig. 1b). The final revised fragmentation table in CV-UMR-ToF-ACSM is summarized in the conclusions (see Table 4).

Figure 1 The left-hand panels (a and b) show the best ODR fits (set to zero intercept) which are found in the relationship between the signal contributions of (a) frag_Org[30] vs. frag_Org[29] and (b) frag_Org[46] vs. frag_Org[45]. The correlations of all mass pairs are summarized in Table S3. The right-hand panels (c and d) show the predicted organic contributions (based on the new multipliers) at each $m/z$ versus the measured amount. Plot (c) shows the predicted UMR frag_Org[30] against the measured total Org fragments at $m/z$ 30, and plot (d) shows the predicted UMR frag_Org[46] against the measured total Org fragments at $m/z$ 46. The figure demonstrates that the predicted frag_Org[x] slightly underestimates (slope=0.83) but approached the measured frag_Org[x].

We apply these new multiplier values to the full dataset and compare the results with those from multipliers described in Allan et al. (2004), the SI of Fry et al. (2018), and the Supplement of Hu et al. (2017a) (see Table S4 in the Supplement). The result suggests that the multiplier a_Org[46],[45] determined here gives the best predicted frag_Org[46] over multipliers from other studies (see Table S4, third and seventh columns, in the Supplement). Meanwhile, the multiplier a_Org[30],[29] determined here performs similarly with the multipliers obtained from Hu et al. (2017a) (SV and CV) for a dataset dominated by biogenic secondary organic aerosol (SOA). The plot of predicted UMR frag_Org[30] against the measured total Org fragments at $m/z$ 30 (see Fig. 1c) shows that the multiplier determined here is able to estimate on average 96.9 % ± 4.9 % of the measured frag_Org[30]. Meanwhile, the similar plot for frag_Org[46] against the measured total Org fragments at $m/z$ 46 (see Fig. 1d) shows that the multiplier determined here estimates on average 82.5 % ± 9.5 % of the measured frag_Org[46]. The low signal intensity of both $m/z$ 46 and $m/z$ 45 may cause this underestimation and suggests that frag_Org[46] and frag_Org[45] may have a more complicated relationship; their correlation may vary substantially depending on the aerosol mixture. Therefore, it may be appropriate to modify the entry for frag_NO₃[46] according to the type of aerosol mixture analyzed. On the other hand, for complex ambient mixtures, the ensemble composition may produce spectra that are more similar to the average determined here. Analysis of CV-HR spectra from a variety of ambient samples would be required to determine the actual variation of organic contributions at $m/z$ 46.

3.2 Composition-specific fragmentation table

The multipliers determined in Sect. 3.1 are designated for typical ambient aerosol composition. In some cases, a composition-specific fragmentation table may be more appropriate to use. For instance, from a field study with biogenically dominated composition, Hu et al. (2017a) reported a_Org[30],[29]=0.32 and a_Org[46],[45]=0.68. By using selected chamber experiments in the same dataset, we can explore different multipliers that are compatible for different composition profiles. For chamber experiments that involve glyoxal (and its oligomers), we obtain a_Org[30],[29]=0.291 ± 0.022 (mean ± uncertainty, n=4, r²=0.90) and a_Org[46],[45]=0.082 ± 0.036 (mean ± standard deviation, n=4, r²=0.35). For chamber experiments that involve only terpenes (e.g., isoprene, α-pinene), we obtain a_Org[30],[29]=0.476 ± 0.067 (mean ± uncertainty, n=5, r²=0.82) and a_Org[46],[45]=0.204 ± 0.055 (mean ± uncertainty, n=5, r²=0.33), which can be applied for chamber experiments with terpene as precursor. The ODR fit plots are given in Fig. S1 in the Supplement. The multipliers to revise the fragmentation table in CV-UMR-ToF-ACSM for specific aerosol composition subsets are summarized in the conclusions (see Table 4).

4 Determination of ${\mathrm{NO}}_x^{+}$ ratios for the CV-UMR-ToF-ACSM

4.1 ${\mathrm{NO}}_x^{+}$ ratio of pure pAmN

To quantify the inorganic ${\mathrm{NO}}_x^{+}$ ratio typical value and variability produced by the CV, we use repeated measurements from regular pAmN calibration from the two ACSM instruments described in Sect. 2. The R_pAmN of ACSM-UU is found to be 0.0237 ± 0.0009 (mean ± uncertainty, n=5), and R_pAmN of ACSM-RUG is 0.0115 ± 0.0002 (mean ± uncertainty, n=3). The values are similar but lower than other studies where R_pAmN with CV was found to be 0.04–0.07 (Hu et al., 2017b), and all are ∼10 times lower than the typical R_pAmN measured with the SV, i.e., 0.3–0.7 (Day et al., 2022b). We found that R_pAmN values are very consistent for each instrument over time. A summary of R_pAmN values and regression fit parameters from each measurement can be found in Table S5 in the Supplement.

Hu et al. (2017a) found that the ${\mathrm{NO}}_x^{+}$ ratio is affected by the aerodynamic lens alignment. The influence is greater in the CV since the vaporizer opening diameter is ∼2.5 mm (SI of Hu et al., 2018b), smaller than that of SV, which is ∼3.8 mm (Drewnick et al., 2005). For optimum particle detection, the aerodynamic lens must point the particle beam at the center of the vaporizer. Directed into the center, the particles enter the CV cavity and experience augmented thermal decomposition, at which the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal intensity is at its minimum, while the NO⁺ signal intensity is highest. The ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal intensity increases as the particle beam moves closer to the edge of the vaporizer, where the thermal decomposition is not as extensive as in the center, resembling how the SV works. Thus, it is important to consider performing lens alignment to obtain the correct result for the ${\mathrm{NO}}_x^{+}$ ratio method. Monitoring the behavior of $m/z$ 30 and $m/z$ 46 during pAmN calibration is a good way to determine whether the aerodynamic lens is aligned well. Combining the result of this study and the R_pAmN range in Hu et al. (2017a), a value of R_pAmN in the range of 0.01–0.07 can be used as reference to indicate properly aligned lens. Plotting the profile of the ${\mathrm{NO}}_x^{+}$ ratio with movement in both the vertical and horizontal directions obtained during the alignment is the best diagnostic.

4.2 ${\mathrm{NO}}_x^{+}$ ratio of pure pON

To obtain a ${\mathrm{NO}}_x^{+}$ ratio for pON, one would ideally measure pure atmospherically relevant ON, prepared through synthesis or in a chamber experiment. Often, such standards are not available; therefore, experimental R_pON cannot be easily determined for each instrument. To overcome this challenge, Day et al. (2022a) used the strategy of a “ratio of ratios” ($\text{RoR}=R_{\text{pAmN}}/R_{\text{pON}}$), which can be used to calculate R_pON for any arbitrary instrument from its routinely measured R_pAmN, and an average value for the RoR measured across many instruments under varying conditions. Day et al. (2022a) found that based on the relationship between R_pAmN and R_pON over a large range of measurement conditions, SV produces RoR of 2.75 ± 0.70 (mean ±25 % uncertainty).

There have not yet been enough studies that determined R_pON values in CV-based instruments in order to determine a robust RoR estimate for CV instruments. In the work of Hu et al. (2017a), a chamber experiment producing pure pON yielded R_pON=0.0045; with comparison to R_pAmN=0.06 for their instrument, the value RoR=13.3 is obtained. With R_pAmN being 0.01 in CV as found in this study, using this RoR of 13.3 means that R_pON would be 0.0008 (approaching zero).

Similar to the approach of Kiendler-Scharr et al. (2016) that used the minimum measured value of ${\mathrm{NO}}_x^{+}$ ratio to set a fixed R_pON value, to estimate R_pON, we use the lowest measured ${\mathrm{NO}}_x^{+}$ ratio from a chamber experiment in which we expected to produce pON, with no inorganic nitrate present. The selected experiment used glyoxal as SOA precursor, NO₂ and O₃ to produce NO₃ radical as the major oxidant, and sodium chloride (NaCl) seed to form SOA containing organic nitrates at 90 % relative humidity. This experiment was conducted in the AIDA chamber at IMK KIT, Germany, as part of CAINA project. For the spectrum analysis, we use the fragmentation table specific for glyoxal-related chamber experiment, as described in Sect. 3.2.

While this experiment should produce pure organic nitrate aerosol, during pON formation, we observe an increase in NH₄ which could happen for two reasons. First, ammonium nitrate impurities can be formed from reactions or chamber wall repartitioning. Second, particulate water can be incorrectly assigned as NH₄ through fragmentation table correction at $m/z$ 16 and $m/z$ 17 (see complete fragmentation table in Allan et al., 2004). Both can result in a higher ${\mathrm{NO}}_x^{+}$ ratio than we would have if the total nitrate were purely pON. Therefore, we derive two bounding R_pON values from the glyoxal chamber experiment. First, we determine the R_pON value from the experiment by assuming pure pON formation to obtain an upper limit. Second, to obtain the lower limit of R_pON, we assume all observed NH₄ increase is NH₄NO₃ aerosol, and we subtract this equivalent amount of inorganic nitrate, with the inorganic ${\mathrm{NO}}_x^{+}$ ratio, from the total NO₃, in order to obtain a lower limit of pON time series and calculate the R_pON. This strategy has been described as the “excess NH₄” method in Takeuchi and Ng (2019). By rearranging Eq. (2) to Eq. (S2) in the Supplement, we can obtain R_pON using f_pON, R_pAmN, and R_obs for the lower limit experiment (see details in Sect. S3 in the Supplement).

The upper limit experiment gives R_pON=0.0035 (see Fig. 2a). If we compare to R_pAmN=0.0115 ± 0.0002 (measured separately with pure AmN), R_pON=0.0035 obtained from the upper limit experiment gives RoR=3.29 (see Fig. 2a). This value is higher than RoR for SV-AMS but lower than RoR obtained from Hu et al. (2017a).

Figure 2 The time series of (a, b) R_obs, (c, d) ACSM species concentration (in µg m⁻³, left bottom axis), and f_pON (right bottom axis) of glyoxal + NO₃ chamber experiment at 15 min time averaging. The UMR fragmentation table specific for glyoxal is used to obtain $C_{{\mathrm{NO}}^{+}}$ and $C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$. Panels (c) and (d) show the progression of NO₃ concentration compared to panels (a) and (b) for the ${\mathrm{NO}}_x^{+}$ ratio during the formation of pON. By averaging R_obs after pON formation started, the left-hand panel shows that R_pON=0.0035 is obtained when assuming f_pON=1. When possible inorganic impurity is removed by assuming “excess” NH₄ species are NH₄NO₃, the average f_pON is found to be 0.75. The excess NH₄ concentration is obtained by subtracting total NH₄ concentration by the average NH₄ concentration before the addition of NO₂ and O₃ (to exclude any possible NH₄Cl contribution). By calculating R_pON using the obtained f_pON from the “excess NH₄” method, R_pAmN, and R_obs, the value $R_{\text{pON}}=-\mathrm{0.0033}$ is obtained, suggesting an overcorrection (see text). The value R_pON=0.0035 from the lower limit experiment and R_pAmN=0.0115 ± 0.0002 (mean ± uncertainty) give a ratio of ratios ($\text{RoR}=R_{\text{pAmN}}/R_{\text{pON}}$) of 3.29.

On the other hand, the lower limit experiment gives $R_{\text{pON}}=-\mathrm{0.0033}$ (see Fig. 2b). A negative (or below zero) R_pON value is not chemically possible for the ratio. This value indicates an overcorrection, or that R_pON is varying around the zero value (small positive and negative) when the air mixture is strictly inorganic nitrate free. Thus, for calculation purposes, we use R_pON=0.0001 to represent the smallest possible ${\mathrm{NO}}_x^{+}$ ratio for CV-ACSM measurements.

As the RoR from the experiments (including Hu et al., 2017a, RoR=13.3) are very different, we set the upper limit of R_pON to be R_pON obtained using RoR=3.29, and we set the lower limit to be R_pON=0.0001 in CV. The calculated R_pON values for two CV-ToF-ACSMs deployed in this study are summarized in Table 2. These limits are used to determine the uncertainty of the f_pON calculation. Since we see a tendency for the $m/z$ 46 signal intensity (and thus ${\mathrm{NO}}_{\mathrm{2}}^{+}$) to be produced in the vaporizer in relatively small quantities compared to NO⁺, the tendency of R_pON, therefore, is also to approach zero (non-normal distribution). With only limited information about R_pON in CV unlike SV, we use the geometric mean instead of arithmetic mean to establish the expected central value of R_pON. We note that it is common to use geometric means to estimate averages of ratios.

Table 2 Summary of measured R_pAmN (including uncertainties) and calculated R_pON (upper and lower limits as determined from pON in glyoxal + NO₃ chamber experiment). The geometric mean is considered as the central value since R_pON is likely approaching zero. Values are for ACSM-UU (employed for ambient measurements in Cabauw) and the ACSM-RUG (employed for AIDA chamber experiments).

^a Calculated using RoR=3.29. The RoR is obtained using R_pON from the upper limit experiment of glyoxal + NO₃ and measured R_pAmN, using ACSM-RUG (see Fig. 2).
^b Experimental ${\mathrm{NO}}_x^{+}$ ratio value from the lower limit experiment of glyoxal + NO₃ using ACSM-RUG (see Fig. 2a).
^c Geometric mean of the upper and lower limit of R_pON.
^d Set as the lowest possible ${\mathrm{NO}}_x^{+}$ ratio in CV-based instruments, approaching zero.

Since the R_pAmN values are quite different for the two ACSMs used in this study (as we see in Table 2), the upper limit R_pON values are also different by almost a factor of 2. However, since the lower limit of R_pON approaches zero, the geometric means of the upper and lower limits for the two instruments differ by only 25 %. While calibrating every instrument with a pure organic nitrate aerosol standard would be a preferable way to establish R_pON, we recognize the unlikeliness of that for all monitoring ACSMs. Therefore, we recommend this RoR-based approach. As will be shown in the following section, despite the uncertainties outlined here based on potential impurities in our “pure pON” chamber experiment, the nitrate splitting performs encouragingly well, with both ACSMs.

5 Development of the ${\mathrm{NO}}_x^{+}$ ratio method for CV-UMR-ToF-ACSM

5.1 Challenges in the ${\mathrm{NO}}_x^{+}$ ratio method application to the CV-UMR-ToF-ACSM dataset

Applying the ${\mathrm{NO}}_x^{+}$ ratio method to separate pAmN and pON in CV-UMR-ToF-ACSM datasets is a greater challenge than with SV, due primarily to the higher detection limit of NO₃. The detection limit of pNO₃ in CV-UMR-ToF-ACSM is 0.01–0.08 µg m⁻³ (from this work and Zheng et al., 2020, converted), which is around 10–100 times higher compared to those in SV-cToF-AMS (∼0.6 ng m⁻³ from Drewnick et al., 2009) and SV-HR-ToF-AMS (0.1–4.0 ng m⁻³ from DeCarlo et al., 2006), all converted to 10 min time resolution.

The poor detection limit for ${\mathrm{NO}}_x^{+}$ ratios in CV-ToF-ACSM results from the low signal for $m/z$ 46 relative to $m/z$ 30 that are used to calculate frag_NO₃[30] ($C_{{\mathrm{NO}}^{+}}$) and frag_NO₃[46] ($C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$). For instance, using ACSM-UU, the detection limit of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ is comparable to the detection limit of NO⁺ at pNO₃ concentration near the detection limit of pNO₃ ($C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}=\mathrm{0.044}$ µg m⁻³; $C_{\text{DL},{\mathrm{NO}}^{+}}=\mathrm{0.066}$ µg m⁻³; for $C_{\text{DL},\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}=\mathrm{0.075}$ µg m⁻³; all in 10 min time resolution). However, the magnitude of observed ${\mathrm{NO}}_{\mathrm{2}}^{+}$ from ambient measurements is 25–500 times lower than NO⁺ in CV-ToF-ACSM. This means the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal intensity is regularly close to the detection limit, particularly when the total pNO₃ concentration is low. This behavior also leads to noisy R_obs, due to a computation of very low or negative ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signals, poor baseline, or both.

5.2 Data pre-treatment: time averaging and data filtering

To determine which data points are reliable for R_obs calculation in the dataset, we could discard observed ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal intensities that are below the detection limit. However, this would result in removing nearly all the data, including data that, while low and noisy, can still provide quantitative information with adequate averaging. Therefore, we use observed NO⁺ signals as the filtering parameter. The NO⁺ signal accounts for ∼95 % of the total concentration of NO₃ species measured by ToF-ACSM (no RIE applied) and thus is a good indicator of when both NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signals are too uncertain.

Equation (4) describes the NO⁺ signal limit ($C_{{\mathrm{NO}}^{+},\text{lim}}$) which assures reliable separation of f_pON and f_pAmN calculated using the detection limit of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ ($C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}$) and R_pAmN as filter ${\mathrm{NO}}_x^{+}$ ratio. We choose the larger R_pAmN value, which is a less strict limit relative to the R_pON value but still keeps any data with sufficiently good signal-to-noise ratio. The measured data points with observed NO⁺ signal intensity below these criteria are replaced with “nan” (not a number).

$$\begin{array}{}\text{(4)}& {\displaystyle }{\displaystyle }{C}_{{\mathrm{NO}}^{+},\text{lim}}={\displaystyle \frac{C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}}{R_{\text{pAmN}}}}\end{array}$$

On this basis, we recommend data pre-treatments by time averaging and data filtering using observed NO⁺ signal contribution as parameter. Time averaging over longer time periods allows for the reduction of the electronic noise coming from the instrument response and low counting statistics associated with sampling ambient air. Meanwhile, the data filtering serves to determine the minimum pNO₃ concentration at which reliable R_obs can be obtained to calculate f_pON and f_pAmN.

The values of $C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}$ and $C_{{\mathrm{NO}}^{+},\text{lim}}$ with different time averaging are evaluated in Table 3 for the CV-ToF-ACSM deployed for ambient measurements in Cabauw, the Netherlands. The signal limit is lower as the time resolution increases due to the improvement of detection limit with better statistics. For measurements in this study, the minimum reliable $C_{{\mathrm{NO}}^{+}}$ values for 10, 30, 60, and 120 min time resolutions are 1.88, 1.08, 0.77, and 0.54 µg m⁻³, respectively.

Table 3 Detection limits of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ and signal limits for NO⁺ across different time averaging with R_pAmN as filter ${\mathrm{NO}}_x^{+}$ ratio for the CV-UMR-ToF-ACSM deployed for ambient measurements in the rural site of Cabauw, the Netherlands (ACSM-UU).

With these $C_{{\mathrm{NO}}^{+},\text{lim}}$ values, we performed data filtering to the ambient measurement time series from Cabauw with different averaging of the time series. The time averaging (generated by Tofware v3.3) is applied first before the data filtering to maximize retained data in the concentration average.

Chemical coordinate plots of R_obs and f_pON against the total concentration of particulate nitrate ($C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$) are shown in Fig. 3. These plots show the quantile average of the output variable on the y axis (i.e. R_obs or f_pON) as a function of concentration bins in the x axis ($C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$). Figure 3a and b show that data filtering removes extreme R_obs and f_pON values near the detection limit level. The fact that the chemical coordinate trends are consistent across different averaging times indicates that filtering to remove noisy data will not bias the interpretation of the ensemble dataset. The value of treating the data as a chemical coordinate plot is to allow for a robust characterization of the average trend, even using a method with substantial uncertainties. Importantly, the standard errors represent how well the averages are known. Their small uncertainty ranges support the result that the characterized trend is robust.

Figure 3 Chemical coordinate plots (a) for R_obs against $C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$ in Cabauw (net 205 d of data) and (b) for the f_pON calculated using geometric mean of R_pON (R_pON=0.0008) against $C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$. The revised fragmentation table for the typical ambient dataset is used to obtain $C_{{\mathrm{NO}}^{+}}$ and $C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$. The line and marker traces represent the quantile average. The colored shading represents the standard deviation of each quantile, while the whisker is the standard error. The standard deviation and standard error both include the uncertainty of ion counting statistics from measurements and the uncertainty from ODR fit slope of fragmentation table correction. For f_pON (plot b), the standard deviation and standard error also include the uncertainty from the lower and upper limit of R_pON (R_pON=0.0001; R_pON=0.0072). All analyses were done using the 10, 30, 60, and 120 min averaging of the time series, with data filtering. The original 10 min data without pre-treatment are also included for comparison. The combination of data filtering and time averaging reduces the noise compared to original data and improves the minimum concentration reliable for apportionment calculation (pNO₃ concentration limit for each time average, as indicated with vertical dashed lines).

The combination of data filtering and time averaging shows different concentration cut-offs for calculation of the ${\mathrm{NO}}_x^{+}$ ratio. The concentration cut-off is lower for longer averaging times due to the improvement of $C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}$. For measurements in this study, the $C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$ cut-offs for 10, 30, 60, and 120 min time averaging are 2.0, 1.2, 0.9, and 0.6 µg m⁻³, respectively. Because there is a trade-off between time resolution and the concentration cut-off, for a given dataset, the timescale of typical variations should be assessed in order to determine the appropriate averaging time.

5.3 Propagation of uncertainty

We propagated uncertainties from the variables in f_pON using simplified propagation of uncertainties using standard error (Day et al., 2023; see Sect. S4.3 in the Supplement for details). The uncertainty of the final function (s_f) is calculated using the standard error ($s_{x_i}$) and partial derivative of the function ($\frac{\partial f}{\partial x_i}$) of each measurand (x_i) using Eq. (5).

$$\begin{array}{}\text{(5)}& {\displaystyle }{\displaystyle }{s}_{f(x_i,x_{i+\mathrm{1}},\mathrm{\dots })}=\sqrt{\sum _{i=\mathrm{1}}^N{\left({\displaystyle \frac{\partial f(x_i,x_{i+\mathrm{1}},\mathrm{\dots })}{\partial x_i}}\right)}^{\mathrm{2}}\cdot s_{x_i}^{\mathrm{2}}}\end{array}$$

The uncertainty of f_pON arises from three terms: R_obs, R_pAmN, and R_pON. For R_obs, the uncertainty is further composed of six components that make up NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signals (the uncertainties of $m/z$ 29, $m/z$ 30, $m/z$ 45, and $m/z$ 46 related to precision uncertainty from electronic noise and ion counting statistics and the uncertainties of the fragmentation table multipliers, represented by the uncertainty of ODR fit slope). For R_pAmN, we propagate the uncertainty of the mean ${\mathrm{NO}}_x^{+}$ ratio from repeated NH₄NO₃ measurements using ODR fit to consider the instrument stability in acquiring the ${\mathrm{NO}}_x^{+}$ ratio over time. For R_pON, the uncertainty is set to zero. Instead, the lower and upper limits of R_pON (see Table 2) serve to give a range of final propagated uncertainty, which includes R_obs, R_pAmN, and R_pON.

Figure 4a shows that low pNO₃ concentrations produce larger uncertainties in f_pON ($s_{f_{\text{pON}}}$) compared to higher concentrations. If we compare the analysis with and without data filtering, we observe that filtering targets data points with high absolute $s_{f_{\text{pON}}}$ (above ±0.5). We avoid removing many data points in the low concentration range by performing time averaging, where the average uncertainty decreases by $\sim \sqrt{N}$ for each N-fold of averaging from 10 min. Meanwhile, the uncertainties from R_pAmN and R_pON (RoR) remain unaffected by time averaging because the values remain constant in the time series.

Figure 4 The chemical coordinate plot (quantile average) between (a) $s_{f_{\text{pON}}}$ and $C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$ (logarithmic scale) and between (b) $s_{f_{\text{pON}}}$ and f_pON (linear scale), with R_pAmN=0.0237 as filter ${\mathrm{NO}}_x^{+}$ ratio at various averaging times of the time series. The line and marker trace represent the average uncertainty produced from the geometric mean of f_pON. The uncertainty consists of uncertainties of ion counting statistics from measurements, uncertainty from ODR fit slope of fragmentation table correction, and uncertainty of R_pAmN. The colored shading represents the standard deviation of each quantile, while the whisker is the standard error. The shading and whisker both include the uncertainty of R_pON coming from the lower and upper limit of R_pON (R_pON=0.0001 and R_pON=0.0072), as well as the uncertainty of the average quantile. Uncertainties of f_pON<0.1 (absolute value) are reached at pNO₃ concentration >10 µg m⁻³ for 10 min time averaging, while at 60 min it is reached already at ∼4 µg m⁻³. In terms of fraction, uncertainties of f_pON below the calculated f_pON ($s_{f_{\text{pON}}}<f_{\text{pON}}$) is reached at f_pON∼0.2 for 10 min averaging, while at 60 min it is reached at f_pON∼0.17.

Several studies reported f_pON lower than 20 %, which occur mainly in urban areas and during a colder period. Yu et al. (2024) observed a lower range of annual average of urban f_pON in China to be ∼17 %, while Mohr et al. (2012) and Pandolfi et al. (2014) reported ∼13 % fraction in Barcelona, Spain, and Xu et al. (2021) reported 9.8 % fraction in wintertime Beijing, China. If we use the lower range of f_pON of ∼10 % as reference for the minimum uncertainty needed to report reliable f_pON, we can observe that the lowest pNO₃ where we obtain below 0.1 absolute uncertainty in f_pON decreases along with time averaging as well. Uncertainties below ±0.1 can only be reached at pNO₃ concentrations higher than 10, 7, 4, and 2 µg m⁻³ at 10, 30, 60, and 120 min time averaging, respectively.

Figure 4b shows the relationship between the absolute $s_{f_{\text{pON}}}$ and f_pON. The limit at which the absolute value of $s_{f_{\text{pON}}}$ is below or equal to f_pON (minimum uncertainty) is found to be 20 %, 15 %, 14 %, and 12 % at 10, 30, 60, and 120 min time averaging, respectively. This result suggests that the ${\mathrm{NO}}_x^{+}$ ratio method in CV-UMR-ToF-ACSM is more reliable to analyze nitrate pollution episodes or chamber experiments and not for low background pNO₃ concentrations. By combining both the concentration limit and the fraction limit, we suggest that in the region where pNO₃ concentration is <10 µg m⁻³ and/or f_pON<12 %, the method requires a longer time average to calculate f_pON to achieve minimum uncertainty.

6 Case studies demonstrating the ${\mathrm{NO}}_x^{+}$ ratio method for CV-ToF-ACSM

6.1 Ambient measurements at a rural site

In order to demonstrate the efficacy of this method, we investigate the trend of f_pON and f_pAmN in the dataset observed at Cabauw. The ambient concentration time series of pAmN and pON (using R_pAmN=0.0237 and R_pON=0.0008) are compared with the ACSM-measured Org and NH₄ fractions, shown in Fig. 5. The time series are averaged to 60 min and filtered using R_pAmN=0.0237 (values of $C_{{\mathrm{NO}}^{+}}<C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}/R_{\text{pAmN}}$ are discarded). We observe that f_pON increases with increasing fraction of organic aerosol concentration in total ACSM PM_2.5 ($C_{\text{OA}}/C_{{\text{PM}}_{\mathrm{2.5}}}$, from 48 % to 64 %), whereas the f_pAmN increases with increasing fraction of particulate ammonium concentration in total ACSM PM_2.5 ($C_{\mathrm{p}{\mathrm{NH}}_{\mathrm{4}}}/C_{{\text{PM}}_{\mathrm{2.5}}}$, from 8 % to 15 %). This shows that the organic nitrate fraction is correlated with availability of organics (particularly at high organic fraction), while the inorganic fraction increases with available NH₄ (particularly at low ammonium fraction).

Figure 5 (a) The chemical coordinate plot (quantile average) of f_pON against $C_{\text{OA}}/C_{{\text{PM}}_{\mathrm{2.5}}}$ shows an average increase in f_pON as OA fraction increases from 48 % to 64 %, where the f_pON varies from 33 % to 66 %. (b) The chemical coordinate plot (quantile average) of f_pAmN against $C_{\mathrm{p}{\mathrm{NH}}_{\mathrm{4}}}/C_{{\text{PM}}_{\mathrm{2.5}}}$ shows an average increase in f_pAmN as pNH₄ fraction increases from 8 % to 15 %, where f_pAmN varies from 30 % to 74 %. Note that all quantile averages were calculated using the 60 min averaging of the time series. The colored shading is the standard deviation of each quantile average, while the whiskers represent the standard error. They include the uncertainties of ion counting statistics from measurements, uncertainty from ODR fit slope of fragmentation table correction, and the R_pON range value.

We also investigate specific nitrate episodes to show the composition of pON and pAmN in ambient pollution events. The time series of the ${\mathrm{NO}}_x^{+}$ ratios, ACSM species concentrations (OA, pNH₄, pNO₃), and pAmN and pON concentrations are shown in Fig. 6. Four nitrate episodes from spring (15 May 2023), summer (23 June 2023), autumn (5–6 September 2023), and winter (11 January 2024) are shown. The uncertainty of the concentration is obtained by combining the uncertainty from the nitrate fraction (f_pON or f_pAmN), the total ACSM NO₃, and the R_pON value range (see Eqs. S14 and S15 in the Supplement). Note that the reported uncertainties are only related to precision uncertainty and not to concentration quantification (e.g., ionization efficiency) like the one described by Bahreini et al. (2009) (see details in Sect. S4.3). We observe that the adapted ${\mathrm{NO}}_x^{+}$ ratio method is able to separate contributions of pON and pAmN to the total pNO₃ concentration. In Fig. 6i, ii, and iv, we can see that the time series of pON tracks with total OA, while pAmN tracks with pNH₄ in the rural site. In Fig. 6iii, no significant trend is observed for pON due to lower mass loading of pNO₃.

Figure 6 The time series for select periods of (a) R_obs, with horizontal lines indicating the values for R_pAmN and R_pON, and (b) mass concentration of ACSM-measured total OA, pNH₄, and pNO₃, as well as pAmN and pON. The separation of pAmN and pON is calculated using R_pAmN=0.0237 and R_pON=0.0008. The whiskers represent the uncertainty from nitrate fraction (f_pON or f_pAmN), precision uncertainty of total ACSM NO₃ from Tofware v3.3, and the R_pON value range. The time series (i), (ii), (iii), and (iv) represent representative compositions in spring, summer, autumn, and winter, respectively, all with 60 min time averaging.

Unless there are co-located ambient measurements of UMR and HR instruments, the reported concentration of NO₃ in pON depends on the value of R_pON and multipliers used to calculate NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal contribution in the fragmentation table. The sensitivity of these variables needs to be assessed to understand which parameter is the most critical in the separation of the inorganic and organic nitrate signal from ACSM.

In Fig. 7, we show the sensitivity analysis of R_pON, a_Org[30],[29], and a_Org[46],[45]. We varied R_pON from zero to R_pON=0.0072 (calculated using RoR=3.29). Figure 7a suggests that for $R_{\text{pON}}\le {\mathrm{10}}^{-\mathrm{3}}$ the reported pON concentrations are not significantly different and therefore confirm the lower limit of R_pON approaching zero, as established in Table 2. The value of R_pON calculated using RoR (in this case R_pON=0.0072) shows relatively higher pON concentration, which is consistent with its use as the upper limit of R_pON.

Figure 7 Sensitivity analysis of (a) R_pON, (b) a_Org[30],[29], and (c) a_Org[46],[45] to the pON concentration (NO₃ in pON) calculated using adapted ${\mathrm{NO}}_x^{+}$ ratio method. The time series in each case is an ambient pollution episode in Cabauw, the Netherlands, during spring, summer, autumn, and winter period (i–iv). The results show that (a) $R_{\text{pON}}\le {\mathrm{10}}^{-\mathrm{3}}$ does not show significant differences in reported pON concentration, and (b) the reported pON concentration is not sensitive to the change in a_Org[30],[29]. In contrast, the results (c) show a significant change in reported pON concentration when a_Org[46],[45] is varied, showing that this correction is the primary limitation of the ${\mathrm{NO}}_x^{+}$ ratio method in CV-ACSM, as it can be highly dependent on the calculation of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal contributions to $m/z$ 46.

We also varied a_Org[30],[29] and a_Org[46],[45] using the values listed in Table S4 and Fig. S1c and d. Figure 7b shows that the calculated pON concentration is sensitive to a_Org[46],[45], which is not the case for a_Org[30],[29]. It further demonstrates that the limitation of this adapted ${\mathrm{NO}}_x^{+}$ ratio method is its sensitivity towards a_Org[46],[45] to obtain the ${\mathrm{NO}}_{\mathrm{2}}^{+}$ signal contribution. Chemically, this suggests that the organic contribution at $m/z$ 46 can vary and comprises a substantial portion of the total $m/z$ 46 signal. Therefore, an average correction for $m/z$ 46 may result in a high uncertainty of calculated f_pON using the ${\mathrm{NO}}_x^{+}$ ratio method. This was considered in the propagation of uncertainty, where we take into account the changing a_Org[46],[45] in the reported f_pON, therefore representing a range of the observed organic nitrate contribution.

6.2 pAmN and pON formation in a chamber experiment

We investigated the pAmN and pON formation in a chamber experiment using limonene precursor, NO₃ oxidant, and AmN seed aerosol. The experiment was carried out in the AIDA chamber. Alongside CV-UMR-ToF-ACSM (ACSM-RUG), an SV-HR-ToF-AMS managed by IMK KIT was also deployed.

The ACSM data are analyzed using the revised fragmentation table specific for terpene chamber experiments (see Sect. 3.2), while the AMS data are analyzed using Squirrel 1.66E and PIKA 1.26E with the default ion list. Although the time resolution is 2 min, time averaging and data filtering are not necessary since the experiment involves high concentrations. The lower limit, geometric mean, and upper limit of R_pON (R_pON=0.0001; 0.0006; 0.0035, respectively) are employed to estimate the uncertainty of f_pON, alongside R_pAmN=0.0115 (see Table 2). For the AMS instrument, the measurements of pure pAmN give R_pAmN=0.61 ± 0.05, and the R_pON value is calculated using RoR=2.75 ± 0.70 (Day et al., 2022a), which gives R_pON=0.18, 0.22, and 0.30 as lower limit, mean, and upper limit, respectively.

We also performed PMF analysis using the ACSM data including OA, ${\mathrm{NO}}_x^{+}$, and ${\mathrm{NH}}_x^{+}$ ions, which has been similarly done in other studies (e.g., Day et al., 2022a, and references therein). The 2 min average matrices of UMR organic fragment mass spectra with an $m/z$ of 12 to 120, fragments of ammonium (NH₄_16 and NH₄_17, two main signals of NH₄ which are ${\mathrm{NH}}_{\mathrm{2}}^{+}$ and ${\mathrm{NH}}_{\mathrm{3}}^{+}$), and fragments of nitrate (NO₃_30 and NO₃_46, two main signals of NO₃ which are NO⁺, ${\mathrm{NO}}_{\mathrm{2}}^{+}$) are used as variables in the PMF input matrix. Fragment contributions are calculated using the terpene-related fragmentation table (see Sect. 3.2). We choose a two-factor solution (see Fig. S2 in the Supplement) as we are interested in splitting the aerosol mass only into inorganic aerosol (pAmN) and organic aerosol (OA mixture, containing pON). From the organic aerosol factor, we calculate the f_pON from the factor concentration time series. The details of the PMF method are described in Sect. S5 in the Supplement, including the statistical summary and the diagnostic plots of the PMF analysis.

The ${\mathrm{NO}}_x^{+}$ ratio and f_pON time series for the limonene SOA experiment are shown in Fig. 8. The whiskers around the mean f_pON represent the uncertainties coming from the value range of R_pON combined with the uncertainties from ion counting statistics, electronic noise, fragmentation table (for UMR), and R_pAmN (see Sect. 5.3). The initial mixture of NH₄NO₃ seed and NO₃ radical from NO₂ and O₃ gives a ratio that matches R_pAmN from an offline calibration, where f_pON is close to zero for both instruments. Although nitric acid (HNO₃) can be formed by nitrogen pentoxide (N₂O₅) hydrolysis under these humid conditions, experiments were run in excess NH₃; therefore, we expect no substantial increase in HNO₃ that can affect the ${\mathrm{NO}}_x^{+}$ ratio. After the limonene injection, the R_obs rose to values in between R_pAmN and R_pON, indicating the formation of a mixture of pAmN and pON inside the chamber.

Figure 8 (a, b) The time series with 2 min time averaging of R_obs, R_pAmN, and R_pON measured by CV-UMR-ToF-ACSM (top) and SV-HR-ToF-AMS (middle). The fragmentation table specific for terpene is used to obtain the $C_{{\mathrm{NO}}^{+}}$ and $C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$ of the chamber experiment. (c) The time series with 2 min time averaging of f_pON from ${\mathrm{NO}}_x^{+}$ ratio method applied to SV-HR-ToF-AMS and CV-UMR-ToF-ACSM, as well as the PMF method applied to CV-UMR-ToF-ACSM. The markers represent geometric mean for the ${\mathrm{NO}}_x^{+}$ ratio method applied to CV-UMR-ToF-ACSM (circle), mean for ${\mathrm{NO}}_x^{+}$ ratio method of SV-HR-ToF-AMS (square), and for the PMF method of CV-UMR-ToF-ACSM (cross). The whiskers represent the uncertainties from the value range of R_pON combined with the uncertainties from electronic noise, ion counting statistics, fragmentation table (for UMR), and R_pAmN. The uncertainty from the PMF analysis is not shown for simplicity.

Based on observations of Takeuchi et al. (2024), pON measured with the SV-AMS is only quantitatively detected as −NO₂ moiety, not −ONO₂. The reasoning for this difference in detection of alkyl nitrate (RONO₂) and NH₄NO₃ is thought to be due to thermal decomposition of pON producing NO₂ gas in the vaporizer, while NH₄NO₃ would more likely decompose to HNO₃ and thus dominantly ionizing gases of different molecular weights. The “missing oxygen” is generally retained bound to the carbon and thus accounted as an organic moiety. Thus, f_pON needs to be corrected for this phenomenon using molar mass ratio of ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{NO}}_{\mathrm{2}}$ (62 g mol⁻¹$/$46 g mol⁻¹) to recalculate the pON mass. There is no study yet assessing the necessity of correcting f_pON in CV, and we suggest that it is likely unnecessary due to the more complete thermal decomposition that shifts the fragmentation pattern of both NH₄NO₃ and RONO₂ to NO₂ and NO.

Both ${\mathrm{NO}}_x^{+}$ ratio methods (SV-AMS and CV-ACSM) and the PMF method (CV-ACSM) show a similar response to the injection of limonene, whereupon f_pON increases rapidly from ∼0 to 0.3–0.5. The agreement between the two instruments on this initial pON production is encouraging. However, after this initial jump, the trend of f_pON seems to vary. While mean f_pON calculated using the ${\mathrm{NO}}_x^{+}$ ratio method from CV-ACSM remains steady after the injection, the other two results show a gradual decrease in f_pON as the chamber dilutes.

The ${\mathrm{NO}}_x^{+}$ ratio method on CV-ACSM data shows a similar change in f_pON relative to the PMF method immediately after limonene injection but then continues to decrease over time (see Fig. 8). The PMF method combines the variations of Org, ${\mathrm{NO}}_x^{+}$, and ${\mathrm{NH}}_x^{+}$ ions to obtain the factor profiles, therefore allowing a more subtle change in the chamber composition to be taken into account. The ${\mathrm{NO}}_x^{+}$ ratio method in CV-UMR, in contrast, only takes into account fragments that are at $m/z$ 30 and $m/z$ 46 using a constant fragmentation table relationship.

Similarly, the SV-AMS also shows a gradual decrease in mean f_pON unlike the ${\mathrm{NO}}_x^{+}$ ratio method from CV-ACSM (see Fig. 8). This suggests that changing contributions of organics at $m/z$ 30 and $m/z$ 46 may be taken into account by HR peak fitting and not by the UMR fragmentation table, causing a divergence as the chamber aerosol dilutes. Based on the sensitivity analysis in Fig. 7, the signal contribution of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ ($m/z$ 46) is the largest source of uncertainty in the CV-ACSM, since the adapted method is sensitive to the change in a_Org[46],[45]. On the other hand, the uncertainty of RoR used to calculate R_pON accounts for the largest contribution to the uncertainty calculated for SV-AMS. Since the RoR in Day et al. (2022a) relies on the average value of a broad range of organic nitrate, a chamber experiment that uses a specific precursor is likely to have R_pON further away from the average value than, for instance, a complex ambient mixture.

Nevertheless, we are encouraged by the match in responses upon formation of organic nitrate, indicating that the ${\mathrm{NO}}_x^{+}$ ratio method is similarly sensitive to changing nitrate speciation in both instruments. When considering the propagation of uncertainty, we observe overlaps between the results of CV-ACSM and SV-AMS. Therefore, by considering the uncertainty from a_Org[46],[45] in CV-UMR and uncertainty from RoR in SV-AMS, the results for both instruments are comparable. Further investigation of the detailed response of each instrument to changing aerosol composition would be valuable.

7 Conclusions and recommendations

We have shown the separation of particulate ammonium nitrate (pAmN) and particulate organic nitrate (pON) signals from the total particulate nitrate (pNO₃) signal measured using a time-of-flight aerosol chemical speciation monitor equipped with a capture vaporizer with unit mass resolution (CV-UMR-ToF-ACSM), using an adapted ${\mathrm{NO}}_x^{+}$ ratio method with a revised fragmentation table and data pre-treatment. The shift of fragmentation pattern towards smaller ion fragments in the capture vaporizer (CV) compared to the standard vaporizer (SV) affects the signals of NO⁺ and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ fragments and interferences by Org fragments used to calculate the ${\mathrm{NO}}_x^{+}$ ratio in UMR. Therefore, we recommend updating the default fragmentation table from Allan et al. (2004) for entries shown in Table 4 before applying the ${\mathrm{NO}}_x^{+}$ ratio method, according to the aerosol composition. As noted previously, substantial corrections to the fragmentation table for these terms have been shown to be needed for measurements using the SV under some conditions (Fry et al., 2018).

Table 4 Proposed $m/z$ 30 and 46 entries for Org and NO₃ in the revised fragmentation table adapted for the ${\mathrm{NO}}_x^{+}$ ratio method in CV-UMR-ToF-ACSM. The multipliers (a_Org[x],[i]) are applied according to the aerosol composition. The entries that are not included in this table should follow the fragmentation table of Allan et al. (2004) for AMS and adapted without gas-phase corrections (frag_air) for ACSM.

^a Retrieved from Hu et al. (2017a).

The shift of fragmentation pattern in the CV towards more formation of NO⁺ fragments and less of ${\mathrm{NO}}_{\mathrm{2}}^{+}$ fragments changes the magnitude of the ${\mathrm{NO}}_x^{+}$ ratio for both pure pAmN and pure pON. The ${\mathrm{NO}}_x^{+}$ ratio in CV is affected by the aerodynamic lens alignment; therefore, we recommend users to align their aerodynamic lens to obtain the correct ${\mathrm{NO}}_x^{+}$ ratio.

To separate the pAmN and pON signal from total pNO₃ and calculate the particulate organic nitrate fraction (f_pON), the regular ammonium nitrate calibration should be used to obtain the ${\mathrm{NO}}_x^{+}$ ratio for pure ammonium nitrate (R_pAmN), where a value of 0.01–0.07 is expected. On the other hand, we observed from a chamber experiment that the R_pON value approaches zero in the CV. Therefore, we recommend analyzing using three R_pON values, to describe the upper limit (R_pON calculated using RoR=3.29), geometric mean, and lower limit (R_pON=0.0001), which also provides the f_pON uncertainty. If possible, we recommend constraining the RoR for more accurate results (e.g., performing a chamber experiment to form pure organic nitrate). Through this study, we hope to inspire more research regarding R_pON measurements in CV-based instruments to obtain more precision in analyzing organic nitrate concentrations.

The observed ${\mathrm{NO}}_x^{+}$ ratio (R_obs) tends to have more noise in CV-based measurements compared to SV. Data filtering using the instrument's R_pAmN and ${\mathrm{NO}}_{\mathrm{2}}^{+}$ detection limit has shown that the adapted ${\mathrm{NO}}_x^{+}$ ratio method in the CV-UMR-ToF-ACSM is able to filter unreliable measurements with a concentration cut-off ranging from 0.6 to 2.0 µg m⁻³, depending on time averaging. This data pre-treatment filters data points with high fraction uncertainty (above ±0.5) and decreases the average uncertainty by $\sqrt{N}$ for each N-fold of averaging from 10 min.

With a longer time averaging, the concentration limit and fraction limit improve, which allows more reliable determination of f_pON and f_pAmN. The method reports absolute uncertainty of particulate organic nitrate <10 % at the total particulate nitrate concentrations of 2 µg m⁻³ (120 min time averaging) to 10 µg m⁻³ (10 min time averaging) and organic nitrate fraction of 10 % (120 min time averaging) to 20 % (10 min time averaging). We recommend users to average the time series to 30 or 60 min to retain information about real ambient variation, while improving the reliable nitrate concentration limit. This may also be convenient when comparing to auxiliary data that are typically reported half-hourly or hourly. In the region where pNO₃ concentration is <10 µg m⁻³ and/or f_pON<12 %, longer time averaging may be necessary to achieve the absolute uncertainty <10 %. In studies where noise is not a problem (e.g., chamber experiments with high particle concentration), time averaging may be unnecessary. With a similar approach, this method could be used for SV-UMR-ToF-ACSM observations as well, with a fragmentation table suited for SV-based measurements.

The adapted ${\mathrm{NO}}_x^{+}$ ratio method on rural nitrate episodes can distinguish periods with pAmN or pON as the major component, confirmed by relation to the ammonium and organic aerosol composition, respectively. The adapted ${\mathrm{NO}}_x^{+}$ ratio method applied to CV-UMR-ToF-ACSM measurements in a chamber experiment is able to replicate the response to precursor injection observed from PMF analysis of the same measurements, as well as a co-located high-resolution time-of-flight aerosol mass spectrometer equipped with standard vaporizer (SV-HR-ToF-AMS). The largest uncertainties in this comparison come from a_Org[46],[45] (CV-UMR-ToF-ACSM) and RoR (SV-HR-ToF-AMS). The adapted ${\mathrm{NO}}_x^{+}$ ratio method for CV-UMR-ToF-ACSM demonstrated in this study can be used at monitoring sites to monitor regional f_pON and improve understanding of particulate nitrate sources and evolution.

Appendix A: List of terms and abbreviations

Terms	Name
ACSM	aerosol chemical speciation monitor
ACTRIS	Aerosol, Clouds and Trace Gases Research Infrastructure
AIDA	Aerosol Interaction and Dynamics in the Atmosphere
AmN	ammonium nitrate
AMS	aerosol mass spectrometer
AmS	ammonium sulfate
aOrg[x],[i]	multiplier for calculating frag_Org[x] based on the relationship between frag_Org[x] and frag_Org[i]
Cν	concentration or signal of species ν
$C_{\text{DL},{\mathrm{NO}}^{+}}$	detection limit of NO+
$C_{\text{DL},{\mathrm{NO}}_{\mathrm{2}}^{+}}$	detection limit of ${\mathrm{NO}}_{\mathrm{2}}^{+}$
$C_{\text{DL},\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$	detection limit of pNO3
$C_{{\mathrm{NO}}^{+}}$	signal of NO+
$C_{{\mathrm{NO}}^{+},\text{lim}}$	signal limit of NO+ for reliable organic nitrate and ammonium nitrate separation
$C_{{\mathrm{NO}}_{\mathrm{2}}^{+}}$	signal of ${\mathrm{NO}}_{\mathrm{2}}^{+}$
COA	concentration of total organic aerosol
$C_{{\text{PM}}_{\mathrm{2.5}}}$	concentration of total PM2.5
$C_{\mathrm{p}{\mathrm{NH}}_{\mathrm{4}}}$	concentration of total particulate ammonium
$C_{\mathrm{p}{\mathrm{NO}}_{\mathrm{3}}}$	concentration of total particulate nitrate
CAINA	Cloud-Aerosol Interactions in a Nitrogen- dominated Atmosphere
CE	collection efficiency
Chl	chloride species in AMS/ACSM
cToF	compact time-of-flight
CV	capture vaporizer
fpAmN	fraction of particulate ammonium nitrate to the total nitrate
fpON	fraction of particulate organic nitrate to the total nitrate
frag_NO3[x]	total nitrate fragments in nominal $m/z$ x
frag_Org[x]	total organic fragments in nominal $m/z$ x
HR	high resolution
IE	ionization efficiency
IMK	Institute for Meteorology and Climate Research
IPL	intermediate pressure lens
KIT	Karlsruhe Institute of Technology
KNMI	Royal Netherlands Meteorological Institute
$m/z$	mass-to-charge ratio
n	number of data
${\mathrm{NO}}_x^{+}$ ratio	${\mathrm{NO}}_{\mathrm{2}}^{+}$-to-NO+ signal ratio
obs	observed data (ambient or chamber)
OA	organic aerosol
ODR	orthogonal distance regression
ON	organic nitrate

Terms	Name
Org	total organic aerosol in AMS/ACSM
pAmN	particulate ammonium nitrate
PIKA	Peak Integration by Key Analysis
PM2.5	particulate matter with size <2.5 µm
PMF	positive matrix factorization
pNH4	particulate ammonium
pNO3	particulate nitrate
pON	particulate organic nitrate
Q-ACSM	quadrupole ACSM
Rν	${\mathrm{NO}}_x^{+}$ ratio of ν
Robs	${\mathrm{NO}}_x^{+}$ ratio of observed data
RpAmN	${\mathrm{NO}}_x^{+}$ ratio of particulate ammonium nitrate
RpON	${\mathrm{NO}}_x^{+}$ ratio of particulate organic nitrate
r2	coefficient of determination
RIE	relative ionization efficiency
RONO2	alkyl nitrate
RoR	ratio of ratios
RUG	University of Groningen
sf	uncertainty of function f
$s_{f_{\text{pON}}}$	uncertainty of particulate organic nitrate fraction to the total nitrate
$s_{x_i}$	standard error
SI	supplementary information
SOA	secondary organic aerosol
Squirrel	Sequential Igor Data Retrieval
SV	standard vaporizer
ToF	time of flight
UMR	unit mass resolution
UU	Utrecht University
VOCs	volatile organic compounds
WRF-Chem	Weather Research and Forecasting model coupled with Chemistry
xi	measurand or measured value
${\displaystyle \frac{\mathit{\delta }f}{\mathit{\delta }{x}_i}}$	partial derivative of the function f