2.1 NAPS database and chosen study sites

All the PM_2.5 composition and trace gas data used in this study were downloaded from the NAPS program website (http://maps-cartes.ec.gc.ca/rnspa-naps/data.aspx, last access: 4 December 2018). The NAPS program provides long-term monitoring of air-quality-relevant pollutants at various sites across Canada. Altogether, there are 12 sites with comprehensive gas phase and particle phase composition measurements, including 4 coastal sites (Halifax, Saint John, Burnaby and Abbotsford), 1 central site (Edmonton) and 7 eastern sites (Toronto, Simcoe, Hamilton, Windsor, Ottawa, Montreal and St Anicet). Ambient samples of gaseous components (including NH₃ and HNO₃) and the dominant inorganic components of PM_2.5 were taken over 24 h from 00:00 to 24:00, generally every 3 d.

Six sites in the provinces of Ontario and Quebec were chosen for this study (Fig. 1), including Toronto (the largest city in Canada), Ottawa, two other metropolitan cities (Windsor and Montreal) and two sites in rural regions (Simcoe and St Anicet). The details of these monitoring sites including their longitudes and latitudes, NAPS monitoring station codes, and duration of the data record used for this study can be found in Table S1 in the Supplement. These sites were chosen because (1) they have long-term (at least 8-year) records of gaseous and PM_2.5 chemical components concentrations, and (2) they are located in the central region of North America with little influence of sea salt (Vet et al., 2014) and therefore the acidity of PM_2.5 is mainly dominated by the chemistry of sulfate, total nitrate and total ammonia (Young et al., 2013; Allen et al., 2015; Hennigan et al., 2015).

Figure 1Six NAPS monitoring sites chosen for this study: Toronto, Ottawa, Windsor, Montreal, Simcoe and St Anicet.

Measurements of 24 h average concentrations between 2007 and 2016 of alkaline and acidic gaseous components and major water-soluble inorganic ions in PM_2.5 were used in this study for pH calculation. Citric acid-coated denuders were used to collect gas phase NH₃ samples. Na₂CO₃-coated denuders were used to collect gas phase HNO₃ samples. After alkaline and acidic gases were removed by passing through the two denuders, PM_2.5 samples were captured by a filter pack consisting of a front Teflon filter and a back-up Nylon filter. The benefit of a nylon filter is that it captures volatized nitrate during sampling as the artefact of the evaporation ammonium nitrate and corrects the data accordingly (Yu et al., 2006; Babich et al., 2011). All the extracts were measured by ion chromatography. Field blanks were routinely performed as the background corrections. The detailed protocol for ambient constituent measurements for the NAPS database can be seen in Dabek-Zlotorzynska et al. (2011). In total, there are 1067, 851, 711, 840, 713 and 742 sets of valid data used at the sites of Toronto, Ottawa, Windsor, Montreal, Simcoe and St Anicet, respectively.

Relevant historical meteorological data including hourly average temperature, relative humidity and atmospheric pressure were downloaded from http://climate.weather.gc.ca (last access: 22 April 2019). The closest stations with complete data recordings were chosen as the meteorological data source. The 24 h average values of meteorological parameters during each sampling time period were calculated and used as the input for E-AIM thermodynamic calculation. Specifically, the St Clair meteorological station was chosen as the meteorological data source for the Toronto NAPS site (0.9 km from sampling site), the Delhi CS station for the Simcoe site (21 km), the Windsor A station for the Windsor site (9 km), the Ottawa CDA RCS station for the Ottawa site (6 km), the McTavish station for the Montreal site (16 km) and the St-Anicet 1 station for the St Anicet site (0.1 km).

2.2 E-AIM thermodynamic modelling

The Extended AIM thermodynamic model (http://www.aim.env.uea.ac.uk/aim/aim.php, last access: 29 August 2018) was applied for the calculation of aerosol acidity as E-AIM relies on few assumptions during the calculation of aerosol inorganic components' behaviour and it can also calculate the activity coefficient of each ion, which is crucial for aerosol pH calculation (Wexler, 2002). Specifically, model II, which mainly focuses on the thermodynamic calculations of the H⁺-${\mathrm{NH}}_{\mathrm{4}}^{+}$-${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$-${\mathrm{NO}}_{\mathrm{3}}^{-}$-H₂O system (Clegg et al., 1998), was used in this study. Model II was chosen rather than model III or IV because it can deal with a wider range of relative humidity and temperature, which gives more reliable information on the seasonal variation of aerosol acidity. The SNA (sulfate, nitrate and ammonium) components in PM_2.5 generally contributed more than 80 % of total measured charges in the particles. Temperature, relative humidity, total ammonia (summation of gas phase ammonia and ammonium in PM_2.5), total nitrate (summation of gas phase nitrate acid and nitrate in PM_2.5) and sulfate were used as the inputs for this model. Partitioning of both ${\mathrm{NH}}_{\mathrm{3}}/{\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{HNO}}_{\mathrm{3}}/{\mathrm{NO}}_{\mathrm{3}}^{-}$ allows for a strong constraint on the aerosol pH calculation (Murphy et al., 2017). Particles were forced to be metastable without any formation of salts or ice precipitation. Aerosol pH was calculated according to the following formula (Robinson and Stokes, 2002):

where $a_{\mathrm{H}}^{+}$ is the activity of the hydrogen ion in aerosol liquid water, $f_{\mathrm{H}}^{+}$ is the hydrogen ion's mole-fraction-based activity coefficient, ${\mathit{\chi }}_{\mathrm{H}}^{+}$ is the mole fraction of the hydrogen ion, and 55.509 is the conversion factor from a mole-based activity coefficient to a molality-based one. Model IV was also used to assess the influence from non-volatile cations.

Figure 2The time series of PM_2.5 pH at six sites coloured by ambient temperature.

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3.1 Time series of pH at six Canadian sites

The 10-year time series of PM_2.5 pH values at the six sites is illustrated in Fig. 2. To our knowledge, this is the first long-term study of aerosol pH in Canada and provides one of the longest records for the evaluation of trends anywhere in the world. The reliability of the pH calculations depends on several assumptions, including that daily average values are appropriate for the calculations, and that the gas and particle phases are equilibrated. The limitations of using the E-AIM II model also include the lack of consideration of non-volatile cations, aerosol liquid water contributed by organic species or possible phase separation etc. One rigorous method to evaluate the reliability of the calculated pH is to compare the input (measured) and output (modelled) gas-particle partitioning of semi-volatile species. The comparisons of modelled and measured gas phase fractions of total ammonia, denoted as $\mathrm{Frac}\left({\mathrm{NH}}_{\mathrm{3}}\right)=n\left({\mathrm{NH}}_{\mathrm{3}}\right)/\left[n\right({\mathrm{NH}}_{\mathrm{3}})+n({\mathrm{NH}}_{\mathrm{4}}^{+}\left)\right]$, are plotted in Fig. S2 in the Supplement, where the linear regressions were all close to 1:1 line with high R² (>0.88), indicating that the E-AIM modelling results are consistent with the observed phase partitioning characteristics of ${\mathrm{NH}}_{\mathrm{3}}/{\mathrm{NH}}_{\mathrm{4}}^{+}$. The use of the phase partitioning of both ${\mathrm{NH}}_{\mathrm{3}}/{\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{HNO}}_{\mathrm{3}}/{\mathrm{NO}}_{\mathrm{3}}^{-}$ to constrain the aerosol pH helps to avoid significant over- or underpredictions (Murphy et al., 2017).

In Fig. 2, all the time series of aerosol pH show a strong seasonal oscillation pattern between 1.5 and 4.0. By colouring the pH values by ambient temperature, we can clearly see that particles were generally more acidic when ambient temperature was higher. This variation pattern is consistent in both spatial (six sites) and temporal (10-year) terms. In the long term, the seasonal variation of aerosol pH fits well with the variation of ambient temperature. However, larger variation of aerosol pH can be identified during wintertime. In some cases, the aerosol is very acidic, with pH < 2, even when temperature < 0 ^∘C. This variation pattern is more clearly illustrated in the box-and-whisker plots of pH in each month at six sites shown in Fig. 3. The pH values are lowest in the summer (July and August averages <2) and highest in the winter (January and February averages >2.5). The aerosol was consistently more acidic and had smaller pH variation in warmer months, and showed higher average (and median) pH values but exhibited larger variation in wintertime.

Figure 3The box-and-whisker plot of aerosol pH in each month at six sites. In each box, the top, middle and bottom lines represent the 75th, 50th and 25th percentiles of statistical data, the upper and lower whiskers represent 90th and 10th percentiles, and the square marks represent the mean value.

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To assess the potential influence of non-volatile cations including Na⁺, K⁺, Mg²⁺ and Ca²⁺ on the seasonal variation pattern of aerosol pH, aerosol pH was also calculated using the E-AIM model IV (Friese and Ebel, 2010) with the input of a Na⁺ concentration representing the contributions of all non-volatile cations ($\left[{\mathrm{Na}}^{+}\right]+\left[{\mathrm{K}}^{+}\right]+\mathrm{2}\left[{\mathrm{Mg}}^{\mathrm{2}+}\right]+\mathrm{2}\left[{\mathrm{Ca}}^{\mathrm{2}+}\right]$). The pH calculation results are illustrated in Fig. S3. Because E-AIM IV deals with a narrower range of meteorological conditions (T≥263.15 K, RH ≥ 60 %), E-AIM IV calculations were only possible for a limited part of the data sets. However, shown in Fig. S3, E-AIM IV modelling results show similar time series compared to E-AIM II results. These results confirm that the aerosol pH seasonal variation pattern was not significantly affected by the non-volatile cations. The involvement of non-volatile cations typically increases pH values by less than 0.1, and the change is less than 0.4 for more than 90 % of data (shown in Fig. S4). Using Na⁺ to replace other non-volatile cations does not account for the precipitation of CaSO₄, which has the same effect on aerosol pH of reducing sulfate. The substitution also does not perfectly reflect the impact on aerosol liquid water content, which may indirectly affect the pH. In general, the gas fraction of NH_x calculated from the output of the thermodynamic model matches very closely with the measured gas fraction of NH_x (Fig. S2), suggesting that we are not missing substantial contributions to the ion balance in the particles by only considering ammonium sulfate.

The factors influencing aerosol pH can be roughly classified into two categories: meteorological parameters (including ambient temperature and relative humidity) and chemical composition (including gas phase and particle phase components). The following discussion will focus on the conceptual modelling of aerosol pH sensitivity to meteorological conditions in comparison to the impacts of changes in chemical composition.

3.2 Seasonal cycle of aerosol pH

To assess the sensitivity of aerosol pH to meteorological conditions and chemical composition changes individually, we first examine the pH of aerosol with chemical composition held fixed at representative values under different meteorological conditions. Then we study the aerosol pH sensitivity to chemical composition changes under fixed typical meteorological conditions of each of the four seasons. Figure 4 displays the aerosol pH calculated under every combination of relative humidity from 30 % to 95 % and temperature from −10 to 30 ^∘C with fixed chemical composition. The chosen concentrations for sulfate, ${\mathrm{TNO}}_{\mathrm{3}}(={\mathrm{HNO}}_{\mathrm{3}}+p{\mathrm{NO}}_{\mathrm{3}})$ and NH_x are 15, 30 and 180 nmol m⁻³, respectively, which are close to the 10-year average concentrations of chemical composition in the Toronto atmosphere (which were 17.6 nmol m⁻³ of sulfate, 34.2 nmol m⁻³ of TNO₃ and 188 nmol m⁻³ of NH_x).

Figure 4Plot of E-AIM calculated pH under different combinations of relative humidity (from 30 % to 95 %) and temperature (from −10 to 30 ^∘C) with the fixed input chemical compositions (15 nmol m⁻³ sulfate, 30 nmol m⁻³ TNO₃ and 180 nmol m⁻³ NH_x). The square plots on the graph represent monthly averages of meteorological parameters in Toronto from 2007 to 2016 with standard deviations as error bars.

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It can be seen in Fig. 4 that particles tend to become more acidic at higher temperatures and lower relative humidity and become more neutralized when the temperature is lower or RH is higher. The square symbols in Fig. 4 are the monthly average values of ambient temperature and relative humidity in Toronto from 2007 to 2016 with standard deviations as error bars. The seasonal cycles of meteorological conditions at five other sites are listed in Table S2 and generally show similar seasonal cycling of RH and temperature. Even excluding changes in chemical composition, we find from Fig. 4 that we can explain the summer minimum and winter maximum in pH from Fig. 3. Temperature is the main factor driving the seasonal variation of aerosol pH while the changes due to RH variation are much smaller. This result suggests the central role of meteorological conditions, especially temperature, in the determination of aerosol pH seasonal cycle in mid- and high-latitude regions with NH_x ≫ sulfate in chemical composition.

The temperature dependence of aerosol pH can be theoretically derived from the phase partitioning ${\mathrm{NH}}_{\mathrm{3}}/{\mathrm{NH}}_{\mathrm{4}}^{+}$ based on the equilibria NH₃(g)↔NH₃(aq) and ${\mathrm{NH}}_{\mathrm{4}}^{+}\leftrightarrow {\mathrm{NH}}_{\mathrm{3}}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}$, which are governed by K_H and pKa, respectively (Hennigan et al., 2015). Under equilibrium, aerosol pH can be theoretically derived from the observed gas or particle concentration ratio of NH_x and aerosol liquid water [ALW] as follows:

which Hennigan et al. (2015) showed as having good agreement with E-AIM modelling results. Because both K_H and pKa have strong temperature dependencies (Chameides, 1984; Bell et al., 2007), aerosol pH is going to be temperature-dependent even if liquid water content or ${\mathrm{NH}}_{\mathrm{3}}/{\mathrm{NH}}_{\mathrm{4}}^{+}$ partitioning behaviour does not change. The partial derivative of aerosol pH dependence on temperature will give $\partial \mathrm{pH}/\partial T=\partial (\mathrm{pKa}+\log K_{\mathrm{H}})/\partial T\approx -\mathrm{0.05}$ (K⁻¹), which corresponds to 0.1 unit increase (decrease) of aerosol pH if temperature decreases (increases) by 2 ^∘C. The pH gradient shown in Fig. 4 also illustrated that an approximately 10 ^∘C increase of temperature is required for a 0.5 unit decrease in aerosol pH under the same chemical composition and RH, which is consistent with the temperature sensitivity derived through the NH_x phase partitioning method.

It is possible that the sensitivity of aerosol pH to chemical composition is different in different seasons. As a result, the sensitivity of aerosol pH to composition changes in each season is further studied through the conceptual modelling. In Fig. 5a–d the pH calculated under different combinations of NH_x and sulfate concentrations under typical temperature and RH conditions in spring (April; T=10 ^∘C, RH = 60 %), summer (July and August; T=25 ^∘C, RH = 70 %), fall (October; T=10 ^∘C, RH = 75 %) and winter (January and February; $T=-\mathrm{5}$ ^∘C, RH = 75 %) in the Toronto atmosphere are shown. Total nitrate concentrations were set to be 2 times larger than sulfate concentrations. This assumption is representative of the Toronto atmosphere as a 10-year average of sulfate concentration (17.6 nmol m⁻³) is approximately half of the total nitrate molar concentration (34.2 nmol m⁻³), though for any given day the ratio could be different. The corresponding calculation results of the particle phase fraction of nitrate $\mathit{\epsilon }\left({\mathrm{NO}}_{\mathrm{3}}^{-}\right)$ in four seasons is shown in Fig. S5. During summer ammonium nitrate formation is unfavourable, while in wintertime ammonium nitrate can form very efficiently. As a result, in summertime, the aerosol liquid water content was mainly contributed by ammonium sulfate while in wintertime it was affected by both sulfate and nitrate. The effect of nitrate formation to aerosol pH will be further discussed in Sect. 3.4.

Figure 5Aerosol pH calculated with fixed meteorological parameters (temperature and RH) under different combinations of NH_x and sulfate concentrations. Total nitrate concentrations are set to be 2 times that of sulfate. The markers on the graph represent median summertime concentrations of NH_x and sulfate at six sites from year 2007 to 2016 with error bars indicating the 10th percentile to 90th percentile. The fixed meteorological parameters chosen in panels (a)–(d) are representative of the conditions in spring (April), summer (July and August), fall (October) and winter (January and February) shown in Fig. 4.

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The markers in Fig. 5 represent the median and the range (from 10th percentile to 90th percentile) of NH_x and sulfate concentrations in four seasons at six monitoring sites from 2007 to 2016. The three more westerly sites (Toronto, Windsor and Simcoe) tend to have higher sulfate in all seasons and Toronto has slightly higher NH_x. However, overall all six sites occupy regions of similar chemical sensitivity in the plots. The conceptual modelling of aerosol pH under summertime conditions, shown in Fig. 5b, suggests that the relatively low variability in summertime pH, shown in Fig. 3, results from the aerosol pH being insensitive to chemical composition changes under the corresponding meteorological conditions. Specifically, in summertime, pH was very constrained to the small range around 2 with little influence from the variation of chemical composition, even though the sulfate loadings were the most variable in the summer. Judging from the concentration ranges of sulfate and NH_x shown in all six sites, in summertime even decreasing sulfate concentration by 1 order of magnitude does not significantly change the pH values, and this effect became more obvious with a higher NH_x:sulfate molar ratio.

By comparison, the pH calculated under spring and fall temperatures (10 ^∘C) shown in Fig. 5a and c showed that pH became more sensitive to NH_x variation but still remain quite insensitive to sulfate concentration changes within the relevant concentration range. In spring, the median concentrations of NH_x at the sites of Toronto, Simcoe and Windsor were higher compared to the other three sites, leading to average April pH values in Toronto, Simcoe and Windsor (2.40–2.69) that were consistently higher than the other three sites (2.15–2.31). In October, NH_x and sulfate concentrations had wider ranges of concentration, but we can conclude from Fig. 5c that the pH changes due to chemical composition were mainly driven by the variation of NH_x. The effect of relative humidity changes can be seen from the comparison between Fig. 5a and c, where it is shown that with fixed chemical composition, aerosol will be slightly less acidic at higher RH.

By comparison, under wintertime meteorological conditions, aerosol pH was higher in the region ${\mathrm{NH}}_x:\mathrm{sulfate}>\mathrm{2}$. Apart from the effect of lower temperatures, a lower concentration of NH_x and lower NH_x-to-sulfate molar ratio also made aerosol pH much more sensitive to chemical composition changes than the other seasons because it will make the $\log \left(\right[{\mathrm{NH}}_{\mathrm{3}}]/[{\mathrm{NH}}_{\mathrm{4}}^{+}\left]\right)$ part in Eq. (2) more sensitive to chemical component changes. This could contribute to the larger variation of wintertime aerosol pH shown in Figs. 2 and 3. In Simcoe, Windsor and St Anicet, the sites with lower NH_x:sulfate molar ratios, wintertime pH values all exhibited significant variations. Under these conditions, not only the uncertainty in the SNA concentration measurements, but also the potential contributions from organic matter such as organic ammonium salts (Schlag et al., 2017; Tao and Murphy, 2018) or organosulfates (Vogel et al., 2016; Glasius et al., 2018), which current thermodynamic models do not fully consider, can contribute to uncertainty in aerosol pH calculation. These conceptual modelling results also provide insight into the challenges posed in the direct measurement of aerosol pH off-line as it is both strongly impacted by ambient environmental conditions and the NH₃ concentration equilibrated with the particle phase.

Figure 6Median of aerosol pH in summertime (data on July and August) from year 2007 to 2016 at six monitoring sites. The error bars with median pH values represent the range from the 25th to 75th percentiles. Average ambient temperature in summertime (July and August) at each site is also plotted on right axis to illustrate the reverse trend of temperature with pH inter-annual variation.

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One key assumption in the above conceptual modelling is forcing the total nitrate-to-sulfate molar ratio to be 2. To test the effect of this assumption on the aerosol pH, we calculate the pH of aerosol on each sampling day, assuming total nitrate-to-sulfate molar ratio to be 2, and compare with the pH calculated with the measured total nitrate. The results show that this assumption has a negligible influence on aerosol pH for samples from April to November but has a larger influence on wintertime aerosol, indicating that wintertime aerosol is more sensitive to nitrate concentration (the statistical summary is shown in Fig. S6). The influence of nitrate on wintertime aerosol pH will be further discussed in Sect. 3.4.

3.3 Long-term trends of pH in summertime

The above time series analysis and conceptual modelling of aerosol pH suggest that in the study region during summertime, aerosol pH is strongly impacted by ambient temperature with much weaker response to the other factors, while during wintertime aerosol pH is affected by both temperature and chemical composition. Figure 6 shows the summertime (data from July and August) median aerosol pH in each year at the six monitoring sites. A summertime average temperature was also plotted on the right axes in each graph. The clear anti-correlation indicates that interannual variability in summer temperatures causes interannual variability in aerosol pH. Another application of this result can be found in Battaglia et al. (2017), who showed that urban aerosol in US cities tended to be more acidic than rural aerosol due to the urban heat island effect, consistent with the important role of temperature in aerosol pH determination.

The study conducted by Weber et al. (2016) found that in summertime, aerosol remained highly acidic even with a significant reduction of sulfate in the US. A similar conclusion could be drawn for conditions in Canada, where we found the role of temperature to be more significant than variations in chemical composition for trends in aerosol pH. Significant changes in the particle phase sulfate have been observed during the summers of 2007–2016. Figure 7 displays the summertime average (data from July and August) concentrations of PM_2.5 sulfate at the six sites. Linear regressions are used to show the annual reductions in fine particulate sulfate. Significant decreasing trends (p value of linear regressions <0.05) of sulfate have been observed at five out of six sites (excluding the St Anicet site where large inter-annual variation was found). Specifically, sulfate concentrations have experienced 61 %, 56 %, 62 % and 67 % reductions in Toronto, Simcoe, Windsor and Ottawa, respectively, over the decade from 2007 to 2016. There is no statistically significant long-term trend in the NH_x values at any of these sites. Summertime aerosol pH is not decreasing with the decreasing trend of sulfate but is mainly influenced by the inter-annual variation of meteorological conditions.

Figure 710-year trends of summertime average concentrations of sulfate and NH_x at each site. Linear regressions of sulfate were illustrated on each graph to represent the reduction of particulate sulfate from 2007 to 2016.

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3.4 pH trends in wintertime

To assess the effect of chemical composition changes on aerosol pH in winter meteorological conditions, wintertime average concentrations of sulfate and NH_x in each year at each site were plotted in Fig. 8a with the colour representing the corresponding average pH values. The background colour in Fig. 8a represents pH calculated under different combinations of sulfate and NH_x concentrations with fixed temperature (−5 ^∘C), RH (75 %) and sulfate-to-TNO₃ molar ratio (1:2), the same as Fig. 5d but with a different scale and focused on a smaller range of chemical conditions. The figure clearly shows that changes in chemical composition under wintertime meteorological conditions can lead to significant changes in aerosol pH. Changes of 20 nmol m⁻³ in either NH_x or sulfate can change aerosol pH by more than 0.5 units for some cases. Also, although most of the wintertime average pH values calculated for the actual chemical composition at each site (colours of the markers) generally agree with the pH calculated as the conceptual model (colours of the same position in the background), some of the data points were slightly more acidic than the background value, and this is likely the result of our simplified assumption of a fixed sulfate-to-TNO₃ molar ratio during the calculation in the conceptual modelling.

Figure 8(a) The plot of aerosol pH under wintertime meteorological conditions (−5 ^∘C, RH = 75 %) under different combinations of sulfate and NH_x with more focused region compared to Fig. 5d. The markers on the graph represents the average wintertime (data from January and February) sulfate and NH_x concentrations in each year in each sampling site with colour indicating average pH value. (b) pH of aerosol with 10 nmol m⁻³ sulfate under different combinations of temperature and relative humidity as the function of TNO₃ in the system.

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Figure 8b shows the effects that temperature, relative humidity and TNO₃ concentrations can have on the pH of aerosol with 10 nmol m⁻³ sulfate under wintertime meteorological conditions. Generally, a lower temperature and higher relative humidity will make aerosol pH higher. However, the effect of the addition of total nitrate is more complicated. Based on Eq. (2), the added TNO₃ concentration can impact aerosol pH in two opposite ways. First, because ammonium nitrate is more hygroscopic than ammonium sulfate (Gysel et al., 2007), the particulate nitrate formation will raise the liquid water content [ALW] in aerosol, increasing the aerosol pH; however, nitrate formation will also scavenge NH₃ from the gas phase, and the smaller value of $\left[{\mathrm{NH}}_{\mathrm{3}}\right]/\left[{\mathrm{NH}}_{\mathrm{4}}^{+}\right]$ will make the aerosol more acidic. These two factors altogether contribute to the arc-shaped curve of the relationship between aerosol pH and nitrate shown in Fig. 8b. Figure S7 shows the box-and-whisker plots of wintertime average molar ratio of TNO₃ to sulfate concentration in each year at each sampling site, where it shows that the molar concentration of TNO₃ was generally more than 2 times higher than the sulfate concentration, which could contribute to wintertime aerosol being more acidic than the value calculated using the forcing $\mathrm{sulfate}:{\mathrm{TNO}}_{\mathrm{3}}=\mathrm{1}:\mathrm{2}$. As a result, during wintertime, both chemical composition and meteorological conditions can have significant impacts on aerosol pH without a clear dominant factor. As a corollary, the uncertainty in measurements of particle composition, the influence of non-volatile cations and the potential contribution from organic acids or organosulfates (the error caused by misrepresenting organosulfates as inorganic sulfate) will also have a more significant impact on the determination of aerosol pH in winter by potentially over- or underestimating the sulfate or nitrate that is balancing the ammonium.