The present study utilized long-term data monitored at two urban sites in Edmonton (S-90132, Latitude: 53.486° N, Longitude: 113.465° W; and S-90130, Latitude: 53.544° N, Longitude: 113.499° W), as well as one urban site in each of the other six cities, including Winnipeg (49.898° N, 97.147° W), Victoria (48.442° N, 123.363° W), Vancouver (49.281° N, 122.849° W), Montreal (45.543° N, 73.572° W), Quebec City (46.821° N, 71.221° W), and Hamilton (43.258° N, 79.862° W) (Figs. S1 and S2). The first four cities are in western Canada with Edmonton in the province of Alberta, Winnipeg in the province of Manitoba, and Victoria and Vancouver in the province of British Columbia. The other three cities are in eastern Canada with Montreal and Quebec City in the province of Quebec and Hamilton in the province of Ontario.

In Edmonton, at the S-90132 site speciation PM_2.5 samplers have been used since 2007 to measure mass concentrations of PM_2.5, ionic concentrations in PM_2.5, and the levels of acidic and alkaline gases, with 24 h integrated sampling occurring one in every 3 d (Bari and Kindzierski, 2016a, b). At the S-90130 site, ionic species, including NO3-, SO42-, NH4+, Na⁺, and various elements in both PM_2.5 and PM_2.5–10 were collected using Dichotomous Air Samplers (Thermo, US), with 24 h integrated sampling occurring one in every 6 d during 1986–2005. Since no emission data were available before 1990, only the data after 1990 were included in this study. The ionic data were missing in 2006 at both sites. Note that the identical Dichotomous Air Samplers were also used at S-90132 for several years to collect PM_2.5, though no ionic data, for comparison purpose. Both datasets were included because neither alone covers the primary NO_x mitigation period in Edmonton.

In Hamilton, an identical speciation sampler has been used since 2013 to measure ionic components in PM_2.5 and gases, with sampling occurring one in every 3 d. In this city, only elements have been measured in samples collected by the Dichotomous Air Sampler since then. At the other five urban sites selected for this study, speciation PM_2.5 data were either unavailable (Winnipeg and Quebec City) or collected one in every six days after 2005 (Victoria, Vancouver, and Montreal). PM_2.5 air samplers (Thermo, US) were used in Victoria and Winnipeg after 2012, and PM_2.5 samplers (TISCH, US) were used in Vancouver and Montreal after 2016. Corresponding NO3- data in PM_2.5–10 were not available at these sites since then. In this study, NO3- in PM_2.5 collected by speciation samplers was also referred to as f-NO3-. The same definition is applied to f-SO42- and f-NH4+, which were used to facilitate the analysis of f-NO3-.

Hourly average mass concentrations of PM_2.5 and mixing ratios of NO₂ were also routinely measured at each site, except that no NO₂ mixing ratios were reported at S-90132. In this case, the values from S-90130 were used in this study. For certain parts of the year at the sites in Victoria and Quebec City, NO₂ mixing ratios were also unavailable. In these cases, the mixing ratios of NO₂ measured at different sites within a 1–2 km radius in the same city were used to facilitate the analysis. All the data are publicly available through the National Air Pollution Surveillance (NAPS) program network (https://data-donnees.ec.gc.ca/data/air/monitor/national-air-pollution-surveillance-naps-program/?lang=en, last access: 13 November 2025) and summarized in Table S1.

NO_x, SO₂, and NH₃ emissions data at the provincial level in Canada were obtained from https://www.canada.ca/en/environment-climate-change/services/environmental-indicators/air-pollutant-emissions.html (last access: 13 November 2025). The monthly average wind fields were downloaded from https://psl.noaa.gov/data/gridded/data.narr.html (last access: 13 November 2025, Figs. 1 and S1), and the Arctic Oscillation (AO) Indexes were obtained from https://www.ncdc.noaa.gov/teleconnections/ao/ (last access: 13 November 2025, Fig. S1d). Ground-level meteorological data from the airports of these cities were also downloaded from https://www.ncei.noaa.gov/products/land-based-station/integrated-surface-database (last access: 13 November 2025).

It should be noted that existing techniques for measuring ambient HNO_3gas are subject to certain artifacts. Specifically, the Na₂CO₃-coated denuder used in speciation samplers is designed to remove acidic gases upstream of PM_2.5 collection on a Teflon filter, thereby minimizing positive artifacts in the collected PM_2.5 (Dabek-Zlotorzynska et al., 2011, 2019). However, measurements obtained using the denuder technique do not exclusively represent HNO_3gas. Instead, they include HNO_3gas, N₂O_5gas, and other acidic gases that react with Na₂CO₃ to form NaNO₃. Consequently, the reported concentrations reflect an upper bound of (HNO_3gas + N₂O_5gas). To avoid ambiguity, the measured values are denoted as HNO3gas∗ rather than HNO_3gas throughout the following discussion. Importantly, this measurement uncertainty does not materially affect the conclusions of the present study, as HNO3gas∗ concentrations remain substantially lower than the corresponding particulate nitrate levels during the high-nitrate winter periods examined here (see Sect. 3.4). Nevertheless, the upper-bound nature of HNO3gas∗ may introduce bias in gas–particle equilibrium analyses, particularly during winter nighttime high-concentration episodes, when the true HNO_3gas mixing ratio may be considerably lower than HNO3gas∗ due to a potentially substantial contribution from N₂O_5gas.

Annual average mass concentrations of f-NO3- and c-NO3- were calculated from all available data in each calendar year. However, data loss was common in each city and year despite sampling occurring one in every three or 6 d. To minimize uncertainty from data loss and ensure sufficient data for trend analysis, data for trend analysis were excluded for any year when measurements for two consecutive months were unavailable. To analyze the time series of the annual average mass concentrations of each species, the Mann–Kendall (M–K) analysis was employed. The qualitative trend results determined by the M–K method include: (i) an increasing/decreasing trend with a P value of < 0.05, (ii) a probable increasing/decreasing trend with a P value between 0.05 and 0.1, (iii) a stable trend with a P value > 0.1, as well as a ratio of < 1.0 between the standard deviation and the mean of the dataset, and (iv) a no trend with a P > 0.1 and other conditions (Lin et al., 2022).

To quantify the overall effect of climate anomalies on the annual average f-NO3- between a pair of two years, our recently developed identical-percentile regression analysis was used (Lin et al., 2022; Yao and Zhang, 2024). In this method, the data sizes of the paired 2-year should be the same (e.g., with the same time resolution and filling up all the missing data). The two sets of data, originally in time series, are sorted separately from the smallest to the largest to generate two percentile-based data arrays, which were then used for regression analysis with the intercept being set to be zero. The regression analysis can also be conducted using data in any particular percentile range for exploring different research targets. If the data sizes of the paired two-year are different, the one with a larger size can be modified to match the one with a smaller size using the method presented by Lin et al. (2022) and Yao and Zhang (2024) before applying the regression analysis described above. Moreover, a Random Forest (RF) model was employed to evaluate the relative importance of meteorological and seasonal timing variables in driving f-NO3- formation (Sect. S2 in the Supplement), and the Flexible 0-D Atmospheric Model (F0AM) was applied to simulate secondary production of f-NO3- (Sect. S3 in the Supplement).

As mentioned in Sect. 2.1, two sites (S-90130 and S-90132) in Edmonton were selected for investigation due to the discontinued data coverage at both sites. Annual average mass concentrations of f-NO3- at S-90130 from 1990 to 2005 and at S-90132 from 2007 to 2019 were analyzed to illustrate the complexity of particulate nitrate trends in the urban atmosphere (Fig. 1a). As mentioned in Sect. 2.1, data in 2006 were missing at both sites. For comparison, annual average mass concentrations of c-NO3- at S-90130 from 1990 to 2005 are also shown in Fig. 1a and those of f-NH4+ and f-SO42- at S-90130 and S-90132 from 1990 to 2019 are shown in Fig. S3. To facilitate analysis, annual average mixing ratios of NO₂ at S-90130 from 1995 to 2019 are shown in Fig. 1b, and annual provincial total emissions of NO_x, SO₂, and NH₃ in Alberta are also presented (Figs. 1b, S3a and S3c, respectively). Correlation analyses between f-NO3- (or c-NO3-) and provincial total emissions of NO_x in 1990–2005 and between f-SO42- and provincial total emissions of SO₂ in 1990–2019 are conducted (Figs. 1c and S3b, respectively).

At S-90130, annual average f-NO3- and c-NO3- was 0.48 ± 0.25 µg m⁻³ (average ± standard deviation) and 0.15 ± 0.05 µg m⁻³, respectively, during 1990–2005. No trend or stable trend was found for these species (P > 0.10), likely due to a bell-shaped change in provincial total NO_x emissions from 1990 to 2005. In fact, a significant correlation was found between annual average c-NO3- and provincial total NO_x emissions during 1990–2005 (P < 0.01). However, a significant correlation between annual average f-NO3- and provincial NO_x emissions was obtained only during 1992–2005 (P < 0.01), but not for the entire period during 1990–2005 with the values in 1990–1991 being substantially deviating from the regression curve. Such a deviation is yet to be explained. Notably, f-NO3- and c-NO3- were not significantly correlated in any individual year during 1990–2005 (R2 < 0.1; P > 0.05). The same pattern was observed at the other six sites analyzed in this study. The lack of correlation between f-NO3- and c-NO3- is discussed in detail in Sect. 3.2.

At S-90132, annual average f-NO3- was 1.3 ± 0.40 µg m⁻³ during 2007–2019. f-NO3- exhibited a decreasing trend (P < 0.01), with a Sen's Slope of 0.063 µg m⁻³ yr⁻¹, resulting in an overall decrease of approximately 60 % during this period. In comparison, the monitored NO₂ mixing ratios at a different site (S-90130) decreased by approximately 20 %, while provincial total NO_x emissions in Alberta were reduced by only ∼ 10 % during the same period. Such disproportionate decreases were also identified for both f-NO3- and c-NO₃ at S-90130 in the selected period of 1997–2005, with a ∼ 60 % decrease in their annual average concentrations compared to a ∼ 20 % decrease in both the NO₂ mixing ratios and provincial NO_x total emissions. Notably, NO₂ mixing ratios at the urban site were significantly correlated with Alberta's total provincial NO_x emissions, with R2 = 0.81 over 1997–2019 (P < 0.01) and a slightly weaker correlation (R2 = 0.57) over the shorter period of 2007–2019 (P < 0.01). These results indicate broadly consistent NO_x mitigation signals at both the provincial and city scales. Thus, the disproportionate large decrease in the annual average f-NO3- at S-90132 relative to the reduction in provincial NO_x emissions is analyzed below by considering major driving factors (Sect. 3.4), primary and secondary sources (Sect. 3.5), and potential uncertainties in the data of the generated annual average f-NO3- (Sect. 3.6). It should be noted that the annual average f-NO3- measured at S-90132 in 2007–2019 were significantly higher than those recorded at S-90130 in 1990–2005 (P < 0.01), which could be attributed to an unexpected mitigation effect, as analyzed in Sect. 3.3 below.

Unlike f-NO3-, annual average f-SO42- exhibited a relatively smooth decreasing trend (P < 0.01), with a Sen's slope of 0.029 µg m⁻³ yr⁻¹ if combining data at S-90130 from 1990 to 2005 and at S-90132 from 2007 to 2019 together (Fig. S3a). This trend was mostly consistent with a 0.021 µg m⁻³ yr⁻¹ decrease in the provincial total SO₂ emissions from 1990 to 2019. Additionally, a moderately strong correlation was found between the annual average f-SO42- and the provincial total SO₂ emissions over the three decades (P < 0.01, Fig. S3b). The f-SO42- trend in the urban atmosphere reflects the mitigation effect, as has also been reported for rural atmospheres in Canada (Cheng and Zhang, 2017; Feng et al., 2020). f-SO42-, typically formed through in-cloud aqueous reactions and with non-volatile properties, is generally associated with regional sources, and thus tends to be spatially homogeneously distributed in urban scales (Bell et al., 2007; He et al., 2001; Park et al., 2004). This may explain the much smaller gaps in the annual average f-SO42- between the two nearby urban sites, as compared to the case of f-NO3-.

Annual average f-NH4+ exhibited a decreasing trend (P < 0.05) if combining data at S-90130 from 1990 to 2005 and at S-90132 from 2007 to 2019 (Fig. S3c). However, the trend was stable at both sites during the two separate periods (P > 0.10). From 1990 to 2019, the provincial total NH₃ emissions increased by approximately 40 % (Fig. S3c). The phenomenon of the decoupled trends between f-NH4+ and NH₃ emissions widely occurred in Canada and the U.S. in the recent decades, as reported in Yao and Zhang (2019). This is because the level of f-NH4+ was mainly controlled by those of SO42- and NO3- through neutralization reactions, especially under NH₃-rich conditions (Bari and Kindzierski, 2016b; Dabek-Zlotorzynska et al., 2011; Edgerton et al., 2020). The equivalent ratios of NH4+ to (SO42- + NO3-) in two selected years support this hypothesis (Fig. S4).

The annual average f-NO3- in Winnipeg varied within a range of 0.07–0.70 µg m⁻³, with a long-term average of 0.32 ± 0.15 µg m⁻³ from 1990 to 2018. A stable trend in annual average f-NO3- was identified by the M–K method (P = 0.51; Fig. 1d). The annual average c-NO3- varied within an even smaller range of 0.13–0.29 µg m⁻³, with a long-term average of 0.19 ± 0.04 µg m⁻³ during 1990–2012. A probable increasing trend in annual average c-NO3- was identified (P = 0.06). Over the same period, both the annual average mixing ratio of NO₂ at this site and provincial total NO_x emissions in Manitoba exhibited decreasing trends (P < 0.01) (Fig. 1e), and they correlated with each other strongly (R2 = 0.90, P < 0.01). The absence of a corresponding decrease in f-NO3- concentration compared to NO_x emissions is likely attributable to enhanced primary emissions of f-NO3--containing aerosols, as discussed in Sect. 3.3 and 3.5 below. This is clearly supported by the following evidence: from 1999 to 2004, annual average f-NO3- increased by approximately 200 %, even as provincial NO_x emissions and NO₂ mixing ratios declined by about 10 %. Accordingly, the trend in f-NO3- concentrations was analyzed in two separate periods: 1990–2002 and 2003–2018. The year of 2003 is allocated into the second rather than the first period based on the curve of annual variation shown in Fig. 1d. In the first period (1990–2002), f-NO3- showed a probable decreasing trend, with a Sen's Slope of 0.017 µg m⁻³ yr⁻¹ and a total decline of about 80 %. This sharp decrease cannot be explained by the relatively modest 10 %–20 % reductions in NO₂ and NO_x during the same period, suggesting that highly localized factors and/or uncertainties caused by coarse resolution data (1 in every 6 d) were likely the dominant contributors. The related uncertainty analysis is presented in Sect. 3.6 below. In the second period (2003–2018), f-NO3- exhibited a decreasing trend with a Sen's Slope of 0.018 µg m⁻³ yr⁻¹, amounting to an overall reduction of approximately 70 %, which also exceeded the ∼ 50 % reduction in NO₂ mixing ratios at the same site and the ∼ 30 % reduction in provincial NO_x emissions. The disproportionate trends between f-NO3- and NO_x emissions observed in Winnipeg are similar to the case in Edmonton discussed above.

When the time series of daily concentrations of f-NO3- and c-NO3- were examined for a low-concentration year (1996) and a high-concentration year (2007) (Fig. 1f–g), elevated concentrations of f-NO3- were predominantly observed during the cold months. High concentrations of f-NO3- were likely from primary sources, as discussed in Sect. 3.5 below, considering the similar climate in inland western Canada. This, however, needs to be confirmed using HNO3gas∗ data, which are not available at this site. In contrast, elevated concentrations of c-NO3- typically occurred during warmer months. Again, no significant correlation was observed between f-NO3- and c-NO3- in any year (R2 < 0.1, P > 0.05). Given the probable increasing trend in annual average c-NO3- despite decreasing NO_x emissions at both city and provincial scales, and considering the seasonal pattern of elevated levels, it is likely that the trend in c-NO3- was governed by the availability of alkali aerosols associated with suspended road dust and road-salt particles capable of neutralizing HNO3gas∗, rather than by changes in HNO3gas∗ itself. As further illustrated in Sect. 3.4 below for the case of Edmonton, stagnant winter meteorological conditions did not coincide with elevated HNO3gas∗ concentrations, likely due to the accompanying sub-freezing temperatures. Moreover, stagnant and freezing conditions are not conducive to the suspension of road dust and road-salt particles during winter. This interpretation is also supported by findings reported in literature at rural sites in Canada (Cheng and Zhang, 2017; Feng et al., 2020) and urban and rural sites in the U.S. (Sickles and Shadwick, 2015) and U.K. (Tang et al., 2018), where positive correlations between HNO3gas∗ and NO₂ have been observed, suggesting that a reduction in NO_x would not typically lead to enhanced HNO3gas∗ formation.

Long-term trends of f-NO3- could be distorted by unintentionally increased f-NO3- primary emissions resulted from certain NO_x mitigation measures. Such phenomena were repeatedly observed in urban atmospheres across Canada during a consistent time window from approximately 1998 to 2007, as illustrated in Figs. 1 and S5 as well as those aforementioned in Edmonton and Winnipeg. During this period, similar NO_x mitigation actions were taken in both Canada and the U.S., regulated by the Canada – U.S. Air Quality Agreement signed in 1991 and further expanded in 2000. Although mitigation policies were likely implemented independently in each province in Canada, and the exact timing may have varied slightly, a consistent pattern emerged. For example, in the province of Quebec, the annual average f-NO3- increased by approximately 150 % in Quebec City from 1998 to 2003 and by around 300 % in Montreal from 1998 to 2002. During the same period, annual average mixing ratio of NO₂ decreased by approximately 10 % in both cities, while provincial total NO_x emissions remained nearly unchanged. In the province of Ontario, annual average f-NO3- in Hamilton remained relatively low at 0.69 ± 0.09 µg m⁻³ during 1995–1999, but rose sharply to 1.6 µg m⁻³ in 2001, with a notable dip to 0.85 µg m⁻³ in 2002 possibly due to climate anomaly, bounced back to 1.7 µg m⁻³ in 2004 and stabilized at 1.6 µg m⁻³ in 2005. During the period from 1999–2005, both observed NO₂ mixing ratios in Hamilton and provincial NO_x emissions in Ontario began to decline by 20 %–30 %. A similar pattern was also found in western coastal urban areas such as Victoria and Vancouver, both located in British Columbia, between 1998 and 2002 (Fig. 2), where annual average f-NO3- increased by approximately 100 % while NO₂ mixing ratios and provincial NO_x emissions declined by 10 %–30 %. These widespread, disproportionate trends between f-NO3- and NO_x emissions across multiple cities strongly suggest that, during this early control window, NO_x mitigation measures may have been accompanied by an unintended increase in primary f-NO3- emissions, potentially associated with condensable particulate matter (CPM) and/or by-products of emission control technologies. However, no direct facility measurement data were made 20-year ago to verify this hypothesis. In fact, the USEPA only issued the method protocol for determining condensable particulate matter in 2017. Evidence from recent studies in developing countries further indicates that early-stage NO_x controls (e.g., NH₃-SCR operated at > 300 °C) can be susceptible to imperfect ammonia dosing and the formation of associated by-products (Yang et al., 2016). This provides a plausible mechanistic explanation, although the specific causes in Canada and the United States cannot be definitively determined in the absence of historical CPM measurements. Accordingly, trend analysis of particulate nitrate should treat this period separately, with a demarcation line drawn at approximately 2002 or later.

In contrast to this early-phase behavior, several lines of evidence suggest that primary f-NO3- emissions have likely declined in recent years. At the national scale, Canada's electricity supply has shifted markedly toward CO₂-emission-free sources (now exceeding 80 %), which are also largely free of NO_x emissions. This transition should reduce primary nitrate-related emissions from the power sector (Canada Electricity Advisory Council, 2024). In addition, the rapidly increasing share of zero-emission vehicles, accounting for 10.8 % of new vehicle registrations in 2023, is expected to further decrease primary f-NO3- emissions from the transportation sector (Statistics Canada, 2024). Consistent with these broader trends, observations in Edmonton show that the decline in annual mean f-NO3- concentrations over the past decade has been substantially larger than the corresponding decrease in NO₂. This divergence supports the interpretation that reductions in primary f-NO3- emissions have likely been an important contributing factor.

Setting the demarcation line at 2003 in Quebec City (noting the substantial data loss in 2002 for this city) and at 2002 in Montreal, the annual average f-NO3- decreased by more than 70 % over the subsequent 16- or 17-year period, largely agree with the 40 %–60 % reductions in NO₂ mixing ratios and provincial NO_x emissions during the same period. The slight differences in their decreasing rates could be attributed to unintended changes in primary emissions of f-NO₃ aerosols as discussed above, non-linear atmospheric chemistry process involving other chemical species, and data uncertainties, etc. Notably, the annual average c-NO3- showed no significant trend during these periods in either city, suggesting that c-NO3- levels may have been more strongly influenced by the presence of alkali aerosols capable of neutralizing HNO3gas∗ rather than by the availability of HNO3gas∗ itself. Data prior to 2002 (Montreal) or 2003 (Quebec City) were insufficient in duration to support robust trend analysis; nevertheless, the influence of unintended mitigation effects during this period was still evident. In comparison, if removing the demarcation line and considering the whole data record together, annual average f-NO3- would show no clear trend from 1995 to 2018 in Quebec City and a stable trend from 1997 to 2018 in Montreal. Over the full period, annual average f-NO3- and c-NO3- were 0.41 ± 0.19 and 0.19 ± 0.05 µg m⁻³, respectively, in Quebec City and 0.57 ± 0.38 and 0.28 ± 0.06 µg m⁻³, respectively, in Montreal.

Similarly, if setting a demarcation line at the year of 2002 for Victoria and Vancouver, f-NO3- would show either a significant decreasing trend or a probable decreasing trend, with a total decrease of around 40 % in both cities from 2002 to 2018. These declines were broadly consistent with the 30 %–40 % decreases in both NO₂ mixing ratios and provincial NO_x emissions during the same period. From 1990 to 2002, f-NO3- showed either no trend or a stable trend, which was consistent with the trend in the provincial NO_x emissions, but inconsistent with the observed decreasing trend in NO₂ mixing ratio during this period. If looking at the full data record of c-NO3- together (from 1990 to 2012 in Victoria or 2015 in Vancouver), either no trend or a stable trend was identified in either city, regardless of using the full data record or just data after the year 2002. The absence of a clear decreasing trend in c-NO3- concentration, despite significant NO_x emissions, appears to be a common feature across Canadian urban environments. Unlike the other cities aforementioned where annual average concentrations of f-NO3- were much higher than those of c-NO3-, in Victoria, annual average concentrations of f-NO3- and c-NO3- were similar, oscillating around 0.23 ± 0.06 µg m⁻³ (1990 to 2018) and 0.25 ± 0.05 µg m⁻³ (1990 to 2012), respectively. In contrast, annual average concentrations of f-NO3- (0.16 ± 0.05 µg m⁻³ in 1990–2018) were significantly smaller than that of c-NO3- (0.31 ± 0.05 µg m⁻³ in 1990–2015) (P < 0.01) in Vancouver, and the same conclusion can be generated if only using data in 1990–2015.

In Hamilton, no statistically significant trends were identified for f-NO3- and c-NO3-, whether considering the full time series or just the period post-2005. This is somewhat different than the cases in the other cities discussed above, suggesting potentially strong impact of local sources, besides the other main factors discussed above, considering that Hamilton is an industrial city with heavy density of industries. Annual average f-NO3- and c-NO3- in this city were 0.88 ± 0.35 and 0.46 ± 0.12 µg m⁻³, respectively, during the period of 1995 to 2019.

To explore key factors influencing the annual average f-NO3- and its trends in Edmonton, we selected data from two representative years (2010 and 2015) at site S-90132 for comparative analysis. The year 2010 was chosen because in this year abnormally high annual average f-NO3- was observed compared to all the other years during the period of 2007–2019, suggesting possible impact by climate anomaly in this year. The year 2015 was chosen because in this year annual average f-NO3- represents the median value of a five-year period of 2015–2019, likely reflecting the average climatic conditions, knowing that the annual average NO₂ mixing ratio observed at a nearby site (S-90130) and the provincial total NO_x emissions were nearly constant during 2015–2019. From 2010 to 2015, the decrease in NO₂ mixing ratios in Edmonton (11 %) was consistent with the decline in Alberta's provincial NO_x emissions (10 %). In contrast, the annual mean concentration of f-NO3- decreased much more sharply (by 58 %), falling from 2.1 µg m⁻³ in 2010 to 0.89 µg m⁻³ in 2015.

Through the comparative analysis, seasonal variations of f-NO3-, various single-factor effects on f-NO3-, and the impact of climate anomalies on f-NO3- were explored. As shown in Fig. 3a and b, higher concentrations of f-NO3- were predominantly observed during cold months, including January to March and November to December, in both 2010 and 2015. These higher concentrations during the five cold months contributed to 81 % and 88 % of the annual averages in 2015 and 2010, respectively. Thus, the annual trends in f-NO3- were mainly determined by higher concentrations of f-NO3- in cold months in Edmonton. Based on wind fields shown in Figs. S1 and S2, air masses reaching to this site in the cold winter should come from the remote northern areas with low pollution levels due to the strong northwest wind, which should have lowered concentrations of f-NO3- in the urban atmosphere. Thus, the high concentrations of f-NO3- observed at this site should be caused by local accumulation under stagnant weather conditions. Therefore, the emissions of f-NO3--contained aerosols related to mitigation measures, the precursors and formation pathways of f-NO3-, and meteorological conditions during the winter period should be considered as key factors determining the annual average f-NO3-.

We then correlated the 24 h integrated daily concentrations of f-NO3- with ambient T, wind speed (WS), RH, and HNO3gas∗ to explore various single-factor effects on f-NO3- (Fig. 3). A demarcation line was observed at -3 °C in 2010 and 0.5 °C in 2015, with substantially lower f-NO3- concentration at T on the right than left side of the line (Fig. 3a and e). Lower ambient T favored the gas-aerosol partitioning of NH₄NO₃ in PM_2.5 (Seinfeld and Pandis, 2016; Shah et al., 2018). However, lower ambient T also weakened photochemical reactions due to reduced amounts of intermediate volatility organic compounds or semi-volatile organic compounds in the gas phase (McDonald et al., 2018; Wernis et al., 2022). This reduction in photochemical activity subsequently lowered the concentration of HNO3gas∗ to some extent, e.g., the concentrations of HNO3gas∗ observed at T > 20 °C increased by over a factor of four relative to those at T < -10 °C in 2015 as shown in Fig. 3e. The sources of f-NO3- and its formation pathways during the winter period will be revisited in Sect. 3.5. The causes for the different T values of the demarcation line between 2010 and 2015 are not clear. The concentrations of f-NO3- decreased with increasing WS due to the dispersion effect, and no elevated concentrations were observed once WS is stronger than 5 m s⁻¹ (Fig. 3b and f). The concentrations of f-NO3- had little dependence on ambient RH (Fig. 3c and g), e.g., the highest concentrations in both years occurred at RH of 70 %–80 % instead of > 80 %. The lowest concentrations of f-NO3- appearing at RH < 60 % is because RH < 60 % typically occurred at ambient T greater than 0 °C in Edmonton. In addition, the relative importance of 15 major variables on f-NO3- concentration was examined using a Random Forest model, as detailed in Sect. S2 in the Supplement. The ambient T ranked as the dominant factor, followed by PM_2.5 mass concentration, NO₂ mixing ratio, boundary layer height, etc.

It should be noted that gas–particle equilibrium between HNO₃–NH₃ and submicron NH₄NO₃ is unlikely to be achieved at temperatures below -10 °C, given the relatively long equilibration timescales. Based on the results of characteristic timescales analysed by Wexler and Seinfeld (1990, 1992) and dynamically simulated by Meng and Seinfeld (1996), particles with diameters of approximately 0.5–0.7 µm generally require hours to approach equilibrium – typically on the order of ∼ 1–6 h with a more conservative upper bound of ∼ 6–20 h. Under such low-temperature conditions, the assumption of instantaneous thermodynamic equilibrium becomes questionable; therefore, equilibrium thermodynamic modelling was not applied here. At even lower temperatures, the equilibration timescale would extend to tens of hours for highly viscous or glassy particles, as suggested by Li and Shiraiwa (2019).

Correlation analysis between simultaneously measured f-NO3- and HNO3gas∗ showed that f-NO3- concentrations higher than 4 µg m⁻³ occurred when HNO3gas∗ concentrations were lower than 0.4 µg m⁻³ in both years (Fig. 3d and h). Thus, the high f-NO₃ concentrations were not likely caused from the secondary formation of f-NO3- from HNO3gas∗ in ambient air, as further discussed in Sect. 3.5 below. Considering that the concentrations of NH_3gas (data not shown here) were generally more than one order of magnitude higher than those of HNO3gas∗, NH_3gas should not be the limiting factor for f-NO3- formation, and was therefore excluded from further analysis below.

Climate anomaly can have significant impacts on air pollution (Andersson et al., 2007; Wetherbee and Mast, 2016; Yao and Zhang, 2020). One of the factors related to climate anomaly in winter Canadian urban atmospheres is AO (Burakowski et al., 2008; Higgins et al., 2002; Yao and Zhang, 2020). Other climate drivers, such as ENSO, Arctic sea-ice variability, and long-term warming, may influence f-NO3- during the warming season. However, their impact on the annual trend is likely negligible, as it is dominated by wintertime f-NO3-. As shown in Figs. S1 and S2, the mean wind speed from January to March across Alberta decreased significantly in 2010 compared to the other years. The AO index during the winter period in 2010 was in the most negative phase observed in the last four decades (Fig. S1d). Typically, the belt of strong winds circulating around 55° N latitude weakens during such a phase, which allows colder Arctic air masses to penetrate further south into the mid-latitudes (Higgins et al., 2002). The substantial decrease in WS during the winter period of 2010 likely contributed to the higher annual average f-NO3- in this year. It is noticed that the recorded ambient T in Edmonton in this winter was similar to the climatic mean value (https://www.ncei.noaa.gov/products/land-based-station/integrated-surface-database, last access: 13 November 2025), further supporting the hypothesis that it is the weaken WS caused by AO anomaly, rather than changes in T, that enhanced the accumulation of f-NO3-.

To further examine the effects of the AO anomaly on f-NO3- accumulation in 2010 relative to that in 2015, we conducted the identical-percentile regression analysis between the two years (Fig. 4c–e). With the intercept being forced to zero, similar to the approach commonly used in chemical experiments for establishing the standard curve (Yao et al., 2011), the slope of the regression equation was 2.74 if using all the data (0th to 100th percentiles), 1.56 if using the central 50 % data (25th to 75th percentiles), and 1.41 if only using the lower 50 % data (0th to 50th percentiles). The differences in f-NO3- concentration between the two years were clearly enlarged when higher concentrations were included, due to the AO anomaly effect in the winter of 2010. Assuming a log-normal distribution of the data, the lower percentiles and higher percentiles data, i.e., 0th to 2.5th percentiles and 97.5th to 100th percentiles, are normally excluded from 95 % confidence level. This is because these data points have lower probability densities and their corresponding values are more vulnerable to climate anomaly impact such as AO with negative and positive phases. The highest probability density should always occur at the 50th percentile, where the corresponding value should be least affected by AO. To minimize potential error from using a single value, we used the average values of the 47.5th–52.5th percentiles, which were 0.63 µg m⁻³ in 2010 and 0.45 µg m⁻³ in 2015. The ratio of these two values (= 1.4) was nearly identical to the slope of the regression equation using data from the 0th to 50th percentiles presented above. Thus, the annual average f-NO3- in 2010 was recalculated by the corresponding value in 2015 being multiplying by a factor of 1.4 in order to deduct the AO anomaly effect. The recalculated annual average f-NO3- in 2010 would decrease from the original value of 2.1 to 1.2 µg m⁻³. Interestingly, removing the AO effect in 2010 would only have a minor impact on the decadal trends from 2007 to 2019, e.g., the Sen's Slope only showed small changes: which was 0.063 µg m⁻³ yr⁻¹ using the original annual average values including the year 2010, 0.060 µg m⁻³ yr⁻¹ if excluding the year 2010, and 0.057 µg m⁻³ yr⁻¹ if replacing the year 2010 value with 1.2 µg m⁻³.

Overall, the AO largely affected the annual average f-NO3- in 2010. Nevertheless, such an impact only has marginal effects on the decadal trends of f-NO3-, as the AO typically oscillates between negative and positive phases within 2–3 years (Fig. S1d). The enhanced or weakened effects of AO in 2–3 years can be largely canceled out in extracting the decadal trend of f-NO3-. The overall effect appeared to be too small to explain the above-mentioned disproportionate responses of the annual average f-NO3- to the reduced NO_x emissions, and more exploration on this issue is presented in Sect. 3.5 and 3.6 below.

From the analysis presented in the previous section we concluded that the high concentrations of f-NO3- in the winter were mainly due to local accumulation under stagnant meteorological conditions, rather than long-range transport driven by north-westerly winds. This raised the fundamental question: what is the role of primary emissions in combustion plumes or secondary formation of NH₄NO₃ in ambient air in contributing to f-NO3- in Canadian urban atmospheres during the cold season? To answer this question, we proposed a hypothesis, i.e., whether HNO3gas∗ concentrations significantly increased under conditions with low f-NO3- concentrations compared to cases with high f-NO3- concentrations, and then examined the hypothesis below. Theoretical analysis and implications of the hypothesis were provided in Supplement (Sect. S4).

To examine the weaker hypothesis outlined above, we first divided the 2010 observations into two temperature regimes: T < 0 °C and 0 °C < T ≤ 4 °C. Observations with T < 0 °C were further divided into two subsets based on f-NO3- concentrations, using the thresholds of > 4 and ≤ 4 µg m⁻³. These three groups were then compared, i.e., Group 1: T < 0 °C and f-NO3- > 4 µg m⁻³, in which case there were 19 samples with average HNO3gas∗ and f-NO3- concentrations being 0.15 ± 0.09 and 8.8 ± 4.4 µg m⁻³, respectively; Group 2: T < 0 °C and f-NO3- < 4 µg m⁻³, in which case there were 26 samples with average HNO3gas∗ and f-NO3- concentrations being 0.15 ± 0.12 and 1.3 ± 0.7 µg m⁻³, respectively; and Group 3: 0 °C < T ≤ 4 °C, in which case there were 13 samples with average HNO3gas∗ and f-NO3- concentrations being 0.15 ± 0.11 and 1.3 ± 1.7 µg m⁻³, respectively. Apparently, the average HNO3gas∗ concentrations did not differ between the three Groups (P < 0.01); thus, the initial hypothesis has to be rejected. This suggests that the process of secondary formation of NH₄NO₃ from HNO3gas∗ was not the main contributor to the observed high concentrations of f-NO3-, leaving the process of primary emissions as the only major contributor. In addition, the markedly reduced f-NO3- concentrations at T > 0 °C were likely due to volatilization of a portion of primarily emitted f-NO3-.

To further test the robustness of the above analysis, we expanded the dataset to include measurements at T ≤ 4 °C from both 2010 and 2015, yielding a total of 108 f-NO3- samples (Group 1: n = 23; Group 2: n = 54; Group 3: n = 31). The mean (± SD) concentrations of f-NO3- and HNO3gas∗ were 8.7 ± 4.1 and 0.16 ± 0.11 µg m⁻³ for Group 1, 1.4 ± 0.95 and 0.17 ± 0.16 µg m⁻³ for Group 2, and 0.9 ± 1.1 and 0.15 ± 0.10 µg m⁻³ for Group 3, respectively. Even with the expanded dataset, mean HNO3gas∗ did not differ significantly among the three groups (Welch one-way ANOVA, P=0.74), despite the intentionally large contrast in f-NO3- imposed by the group definitions.

The above analysis results suggest that the trend of f-NO3- in Edmonton was likely governed by the primary emissions of f-NO3- aerosols, as well as the extents of their volatilization and dispersion during the cold season. The dependence of volatilization of f-NO3- on ambient T and dispersion on WS has been recently confirmed in observational and modeling studies (Huo et al., 2025; Peng et al., 2024; Shen et al., 2022). As mentioned in the Introduction, the primary emissions of f-NO3- likely have two major sources (or processes). The first source is also conventionally defined as condensable particulate emission and associated with the combustion of (N₂ + O₂), which produces various oxidized nitrogen species, including HNO3gas∗, NO_x, etc. (Environmental Protection Agency, 2017). The amount of primary NH₄NO₃ formed from HNO3gas∗ in cooling plumes theoretically depends on the combustion technology, the use of catalytic reduction systems employing NH₃, and the ambient T (Palash et al., 2013; Javed et al., 2007; Zhang et al., 2021), which may not be controlled by NO_x emission levels. In some reported cases, mitigation measures reduced NO_x emissions, but simultaneously increased primary emissions of f-NO3- (Feng et al., 2020; Palash et al., 2013; Javed et al., 2007; Yang et al., 2024; Zhao et al., 2020). As evidences presented in Sections 3.3, this phenomenon likely occurred across various Canadian urban atmospheres. In contrast, the second source in fresh cooling plumes is directly linked to NO_x emissions through the chemical conversion of NO₂ in cooling plume droplets, although it is highly sensitive to the lifetime of these droplets (Shen et al., 2022; Wang et al., 2016; Wang et al., 2020). In addition, primary nitrate aerosols from traffic emissions were reportedly unimportant in urban atmospheres across Canada and U.S. (Chalbot et al., 2013; Jeong et al., 2020), leaving only one possibility that primary nitrate aerosols were mainly derived from stationary combustion sources.

Although secondary f-NO3- formation should always occur to some extent in ambient air, the relative contribution from this process to the total f-NO3- is very small during the periods with high f-NO3- concentrations. As shown in Sect. S3 in the Supplement, the modeled maximum potential contribution from secondary formation can only account for a small fraction of the observed f-NO3- (< 15 % in the baseline runs, and < 45 % even in the empirical-estimate runs known to have overpredictions in general). These results support the hypothesis presented above that primary f-NO3- was the dominant contributor to the high f-NO3- concentration in winter. Moreover, higher f-NO3- concentrations were generally observed under low wind speeds (WS < 1–2 m s⁻¹). Given that the sampling site is about 17 km from the farthest urban edge, the transport time for both primary and secondary f-NO3- to reach the site was therefore estimated to be approximately 2–4 h. This timescale is far too short for substantial secondary formation of f-NO3- in such cold ambient air (T < -10 °C), unless in-source processes dominated (Environmental Protection Agency, 2017; Shen et al., 2022; Zhang et al., 2023). Within this 2–4 h transport window, the amount of HNO3gas∗ dry deposition should also be minimum, especially under low-temperature conditions.

Three categories of uncertainties that may affect the observed trends of f-NO3- in Edmonton were analyzed: (i) differences in observational results between the speciation sampler and the Dichotomous sampler, (ii) spatial inhomogeneity due to highly localized factors, and (iii) artifacts introduced by the sampling frequency (e.g., every third or sixth day), which may influence the calculation of annual averages. For category (i) uncertainty, PM_2.5 mass concentrations measured by the two different instruments at site S-90132 in 2010 showed strong agreement for most samples, with occasional discrepancies at lower concentration levels (Fig. S6). Specifically, when the regression intercept was forced to zero, the resulting equation was y=1.02×x (R2 = 0.94), and the difference in annual average concentrations was less than 10 % (10.3 µg m⁻³ from the Dichotomous sampler vs. 11.1 µg m⁻³ from the speciation sampler).

For category (ii) uncertainty, Fig. S7 compares real-time PM_2.5 mass concentrations measured simultaneously at two sites 7 km apart (S-90132 and S-90130) from 2011 to 2014. Other years were excluded due to significant data loss at one or both sites. Regression slopes between the two sites (with intercepts forced to zero) are 0.86, 0.82, 0.58, and 0.67, with corresponding differences in annual average concentrations of 21 %, 15 %, 40 %, and 39 % in 2011, 2012, 2013, and 2014, respectively. The significant year-to-year differences between the two sites are unlikely caused by mitigation policies, climate variability, or changes in the atmospheric formation pathways of PM_2.5, but rather by spatial inhomogeneity driven by highly localized factors that varied from year to year (Yeganeh et al., 2025). The influence of such localized effects appears to be substantial and may represent an important, yet often overlooked, contributor to the disproportionately large decreases in the annual average f-NO3- relative to reductions in provincial total NO_x emissions over decadal timescales. More broadly, pronounced intra-urban spatial heterogeneity has been documented for many ionic aerosol components (with sulfate generally exhibiting a more regional character), underscoring the importance of high-resolution urban monitoring for interpreting long-term trends. At the same time, compared with routine PM mass measurements, sustained long-term, high-resolution chemical speciation monitoring requires substantially greater investment in instrumentation, maintenance, and operational resources, making such measurements more challenging to maintain over multi-year periods. This practical limitation highlights the need to carefully consider site representativeness and spatial heterogeneity when interpreting long-term nitrate trends derived from fixed-site observations.

It is noted that while the annual average PM_2.5 mass concentrations were significantly higher at S-90130 than S-90132 (P < 0.01) during 2010–2014, the opposite trend was observed for the annual average f-NO3-, e.g., higher at S-90132 during 2007–2019 compared to those at S-90130 during 1990–2005. The highest annual average f-NO3- concentration at S-90130 appeared in 2000 and that at S-90132 appeared in 2010 (Fig. 1a). The mass fractions of f-NO3- in PM_2.5 were 0.050 ± 0.065 in 2000 and 0.13 ± 0.13 in 2010 (Fig. S4), indicating that PM_2.5 at S-90132 contained more f-NO3- aerosols during 2007–2019 than at S-90130 during 1990–2005, strongly supporting the hypothesis that mitigation measures reduced NO_x emissions in Edmonton, while simultaneously increased primary f-NO3- emissions from the first source (see Sect. 3.3) after 2005.

Concerning category (iii) uncertainty, no continuous measurements of f-NO3- were available to assess its magnitude. We thus used continuous measurements of PM_2.5 data at S-90130 as a proxy for this evaluation. Given that the annual average PM_2.5 mass concentration in 2010 was approximately 50 % larger than in 2011, the analysis was conducted using data from 2011 to 2020 instead of 2010 to 2020. Daily average PM_2.5 mass concentrations were first calculated for every day of the year. Then for each year, annual average PM_2.5 mass concentrations were calculated from daily average concentrations using (i) full dataset, (ii) one in every 3 d data (three subsets), and (iii) one in every 6 d data (six subsets). Thus, a total of 10 sets of annual average PM_2.5 data series was created for the period of 2011–2020, which was then used for decadal trend analysis. The trend derived from the full dataset showed a decreasing trend with a Sen's Slope of 0.43 µg m⁻³ yr⁻¹. Consistent decreasing trends were also obtained from using the one in every 3 d subset data series, with Sen's Slope values of 0.46, 0.46, and 0.42 µg m⁻³ yr⁻¹, respectively, indicating an error of less than 8 %. When using the one in every 6 d subset data series, five out of six data subsets also showed a decreasing trend, with Sen's Slope values of 0.47, 0.50, 0.45, 0.45, and 0.44 µg m⁻³ yr⁻¹, respectively, indicating an error of less than 10 % in most cases. However, one subset data series showed a probable decreasing trend, with a Sen's Slope of 0.38 µg m⁻³ yr⁻¹.

Using the same approach described above, we also compared the decadal trends obtained from using one in every 3 d data, which are readily available, with those from using one in every 6 d data, which are arbitrarily split from the former data set into two subsets. One of the two subsets for f-NO3- showed a decreasing trend with a Sen's Slope of 0.055 µg m⁻³ yr⁻¹, which is close to the original value of 0.063 µg m⁻³ yr⁻¹; however, the other subset exhibited a stable trend. For f-SO42-, both subsets showed decreasing trends, with Sen's Slope values of 0.033 and 0.018 µg m⁻³ yr⁻¹, respectively, although deviating to some extent from the original estimate of 0.022 µg m⁻³ yr⁻¹. For f-NH4+, both subsets showed stable trends, consistent with the results derived from the original dataset. Overall, using one in every three or 6 d data can generate decadal trends with reasonable accuracy, although the obtained trends need to be interpreted carefully when the trends are not significant or the changing rates are very small.

In the literature (Sect. S1 in the Supplement), changes in atmospheric NH₃ and f-SO42- have been reported to influence long-term trends in f-NO₃ to some extent. However, evidence of increasing atmospheric NH₃ in Canada, together with reduced NH₃ consumption for neutralizing the two major inorganic acids, suggests that NH₃ is generally abundant and unlikely to be the limiting factor for f-NO3- formation (Yao and Zhang, 2019). Consistent with this interpretation, large f-NO3- / f-SO42- mass ratios are frequently observed in high-f-NO3- samples during the cold season across Canada. For example, in Edmonton in 2010, samples with f-NO3- > 4 µg m⁻³ exhibited f-NO3- / f-SO42- mass ratios ranging from 1.5 to 12, with a median of 5.5. These results indicate that the elevated f-NO3- concentrations overwhelmingly dominated its long-term trend. In such cases, the slight decrease in f-SO42- may exert only a minor influence on the trend in f-NO3-. Nevertheless, these complex interactions warrant further investigation using three-dimensional (3-D) air quality modelling; however, such efforts remain challenging, as illustrated below.

Existing studies using 3-D chemical transport models (CTMs) simulating particulate NO3- over North America are summarized in Sect. S5 in the Supplement. Several key points can be generated from these studies. (1) CTMs are widely applied and can often reproduce broad spatial patterns and major controlling processes of particulate NO3- over the United States and Canada; however, they frequently exhibit systematic biases in magnitude, long-term trends, and sensitivities to emission controls, with a substantial risk of error compensation (ECCC, 2016; Kim et al., 2014, 2023; Luo et al., 2019; Pappin et al., 2024; Pun et al., 2009; Russell et al., 2019; Semeniuk et al., 2025; Shah et al., 2018; Smyth et al., 2009; Walker et al., 2012). (2) The standard GEOS-Chem v12.0.0 simulation substantially overestimated surface PM_2.5 NO3- over the U.S. (1.89 µg m⁻³ vs. 0.70 µg m⁻³), with pronounced spatial heterogeneity: outside California, the normalized mean bias reached +176 %, whereas California exhibited an opposite bias of -62 %, implying region-dependent dominant error sources (e.g., meteorology, emissions, and/or thermodynamics) (Luo et al., 2019; Walker et al., 2012). (3) Simulated particulate NO3- often responds to NO_x controls in a strongly non-linear, and sometimes counterintuitive manner, posing a persistent “acidity–partitioning” challenge for trend attribution. For instance, in the northeastern United States, observations show that PM₁₀ nitrate increased by 95 % (urban) and 57 % (rural) from 2005 to 2015 despite declining NO_x emissions, and this behavior was attributed to changes in aerosol acidity and gas–particle partitioning feedbacks that can offset the expected effect of precursor reductions (Kim et al., 2023). Finally, condensable particulate nitrate, as defined in US EPA Method 202 (Environmental Protection Agency, 2017), as well as its enhanced fraction under sub-freezing conditions, is generally not represented in current emission inventories. Given its potential importance, as suggested by our analysis presented above, incorporating temperature-dependent condensable nitrate into emission inventories is likely necessary to improve the representation and prediction of f-NO3- in 3-D air quality modelling.