Seasonal modeling analysis of nitrate formation pathways in Yangtze River Delta region, China

Nitrate (NO₃⁻) has been the dominant and the least reduced chemical component of fine particulate matter (PM_2.5) since the stringent emission controls implemented in China in 2013. The formation pathways of NO₃⁻ vary seasonally and differ substantially in daytime vs. nighttime. They are affected by precursor emissions, atmospheric oxidation capacity, and meteorological conditions. Understanding NO₃⁻ formation pathways provides insights for the design of effective emission control strategies to mitigate NO₃⁻ pollution. In this study, the Community Multiscale Air Quality (CMAQ) model was applied to investigate the impact of regional transport, predominant physical processes, and different formation pathways to NO₃⁻ and total nitrate (TNO₃, i.e., HNO₃+ NO₃⁻) production in the Yangtze River Delta (YRD) region during the four seasons of 2017. NO${}_{\mathrm{3}}{}^{-}/$PM_2.5 and NO${}_{\mathrm{3}}{}^{-}/$TNO₃ are the highest in the winter, reaching 21 % and 94 %, respectively. The adjusted gas ratio (adjGR = ([NH₃]+ [NO₃⁻]$)/$([HNO₃]+ [NO₃⁻])) in the YRD is generally greater than 2 in the four seasons across most areas in the YRD, indicating that YRD is mostly in the NH₃-rich regime and that NO₃⁻ is limited by HNO₃ formation. Local emissions and regional transportation contribute to NO₃⁻ concentrations throughout the YRD region by 50 %–62 % and 38 %–50 %, respectively. The majority of the regional transport of NO₃⁻ concentrations is contributed by indirect transport (i.e., NO₃⁻ formed by transported precursors reacting with local precursors). Aerosol (AERO, including condensation, coagulation, new particle formation, and aerosol growth) processes are the dominant source of NO₃⁻ formation. In summer, NO₃⁻ formation is dominated by AERO and total transport (TRAN, sum of horizontal and vertical transport) processes. The OH + NO₂ pathway contributes to 60 %–83 % of the TNO₃ production, and the N₂O₅ heterogeneous (HET N₂O₅) pathway contributes to 10 %–36 % in the YRD region. HET N₂O₅ contribution becomes more important in cold seasons than warm seasons. Within the planetary boundary layer in Shanghai, the TNO₃ production is dominated by the OH + NO₂ pathway during the day (98 %) in the summer and spring and by the HET N₂O₅ pathway during the night (61 %) in the winter. Local contributions dominate the OH + NO₂ pathway for TNO₃ production during the day, while indirect transport dominates the HET N₂O₅ pathway at night.

1 Introduction

The Yangtze River Delta (YRD) region, located in eastern China, is among the most populous and developed economic regions in China. Because of rapid population growth, economic advancement, urbanization, and industrialization during recent decades, the YRD region has frequently suffered from both fine particulate matter (PM_2.5) and ozone (O₃) pollution problems (Qin et al., 2021; Sun et al., 2019; Dai et al., 2021). Particulate nitrate (NO₃⁻) is a major PM_2.5 component, and high concentrations of NO₃⁻ are often observed during cold seasons in the YRD region, due to high precursors emissions and regional transport contributions. Huang et al. (2014) reported that the daily average PM_2.5 concentrations in Shanghai were 91 µg m⁻³ during haze pollution events of 5–25 January 2013, whereas NO₃⁻ accounted for 14 % total PM_2.5 mass. Huang et al. (2020a) observed that PM_2.5 concentrations in Nanjing were 271 µg m⁻³ on 30–31 December 2017 and that the fraction of NO₃⁻ was ∼27 %. Lin et al. (2020) found that the peak concentration of NO₃⁻ in Nanjing was 85 µg m⁻³ during haze pollution events in the spring of 2016.

Owing to the stringent emission control strategies since 2013, primary PM_2.5, the major precursors, i.e., sulfur dioxide (SO₂) and nitrogen oxides (NO_x, nitric oxide (NO) + nitrogen dioxide (NO₂)), emissions have decreased substantially in China, which led to significant decreases in total PM_2.5 and sulfate (SO₄²⁻) mass concentrations (Li et al., 2022; Chen et al., 2021). However, compared to SO₄²⁻ and other PM_2.5 components, the reduction rate of NO₃⁻ was much less slow (Wen et al., 2018; Zhai et al., 2021; Zhou et al., 2022; Wang et al., 2022). This led to a rise in the ratio of NO₃⁻ mass to total PM_2.5 in eastern China, rendering NO₃⁻ the dominant chemical component of PM_2.5 (accounting for 24 %–35 %, especially during the cold season and haze pollution events; Ding et al., 2019; Wen et al., 2018; Lin et al., 2020; Fu et al., 2020; Zhou et al., 2022; Xie et al., 2022). High concentrations of NO₃⁻ influence the hygroscopicity and optical properties of particles, contributing to the formation of haze and to visibility degradation (Hu et al., 2021; Xie et al., 2020). Mitigating NO₃⁻ pollution has become an urgent concern in the YRD.

NO₃⁻ is formed in the atmosphere by a series of chemical reactions leading to the production of nitric acid (HNO₃) and then following gas-to-particle partitioning (Griffith et al., 2015; Guo et al., 2018; Lin et al., 2020). The key NO₃⁻ formation pathways include the gas-phase oxidation (hydroxyl (OH) and NO₂) and the heterogeneous hydrolysis of dinitrogen a dinitrogen pentoxide (HET N₂O₅) on the wet particles' surface (Fan et al., 2021; Wang et al., 2018; Chen et al., 2020). The chemical transport models (CTMs), field observations, box model, and oxygen and nitrogen isotope techniques apply to quantify the contribution of different pathways to NO₃⁻ formation in various locations. For example, He et al. (2020) and Li et al. (2021b) reported that the OH + NO₂ pathway dominates daytime NO₃⁻ formation in the YRD, accounting for 60 %–92 % and 55 %–86 % in warm and cold seasons, respectively. The HET N₂O₅ pathway is the main nocturnal NO₃⁻ formation in winter, especially in severe haze episodes, with contributions of 44 %–97 % at night (Fu et al., 2020; He et al., 2018). Furthermore, Tan et al. (2021) and Wang et al. (2018) indicated that the chemical formation cannot explain the variation of TNO₃ at the surface (sum of NO₃⁻ and HNO₃), due to the concentrations of N₂O₅ being close to zero and controlled by high NO emissions at night. Fan et al. (2021) and Kim et al. (2014) further emphasized that the contributions of NO₃⁻ formation pathways differ significantly at vertical altitudes, owing to the vertical gradients of nocturnal NO₃ and total oxidant (NO₂+O₃) level within the planetary boundary layer (PBL). Prabhakar et al. (2017) revealed that the active nocturnal NO₃⁻ formation from the upper PBL contributed 80 % to daytime surface NO₃⁻ concentrations in the winter of 2013 in California.

The complex NO₃⁻ formation chemistry involves the anthropogenic emission of precursors (i.e., NO_x, and ammonia (NH₃)) and atmospheric oxidants (i.e., OH, O₃, and NO₃; Chan et al., 2021; Womack et al., 2019). Previous studies suggested that NO₃⁻ responds nonlinearly to precursor emission reductions in major Chinese regions (i.e., the North China Plain (NCP) and YRD), emphasizing that the uncoordinated control of precursors (i.e., SO₂, NH₃, and NO_x) increases the atmospheric oxidant capacity (AOC) and enhances NO₃⁻ formation in NO_x-rich regimes (Li et al., 2021b; Huang et al., 2020b; Lu et al., 2021a). Coupled with the chemical formation, regional transport also plays important roles in NO₃⁻ pollution formation. Previous modeling studies using the CTMs highlighted the important role of regional transport in NO₃⁻ concentrations in major regions of eastern China (Itahashi et al., 2017; Qu et al., 2021; Ying et al., 2014; Shen et al., 2020). For example, Huang et al. (2020a) reported that secondary pollutants are regionally transported between the NCP and YRD regions (a distance of 1000 km), and hence they simultaneously exacerbate the levels of secondary inorganic aerosols (SIAs) in two major Chinese regions. Ying et al. (2014) revealed that the regional air pollution transport from northern and central China contributed about 45 % to NO₃⁻ in Shanghai during the winter of 2009. Wu et al. (2017) suggested that the regional transport plays a key role in NO₃⁻ sources in Shanghai (accounting for about 90 %), while local emission only contributed 10 % for NO₃⁻ in January 2013. Shen et al. (2020) reported that the contribution of regional transport amounted to around 60 %–98 % for the high concentrations of NO₃⁻ under severe haze episodes in the two winters of 2015 and 2016 in the YRD. Qu et al. (2021) found that the indirect transport made a contribution of 43 % to NO₃⁻ in the Pearl River Delta (PRD) region in cold season of 2015, mainly due to chemical reactions between the locally emitted NO_x and transported O₃ at night. Du et al. (2020) also revealed that regional transport contributed about 56 % to NO₃⁻ in Beijing in winter 2017, mainly produced via indirect transport.

The NO₃⁻ chemical pathways and formation-controlling factors may be very different in different seasons in the same studying locations. Most previous studies have focused on only a few short periods of NO₃⁻ pollution episodes, and lacked seasonal analysis for the full year. This study aims to obtain a comprehensive understanding of the seasonal variations in the NO₃⁻ formation mechanisms, as well as to determine key precursors, dominant processes, and chemical pathways in the YRD. The Community Multiscale Air Quality (CMAQ) model was employed to investigate the contributions of various physical and chemical processes to NO₃⁻ and HNO₃ formation. Regional transport and chemical reaction pathways were quantified for the YRD region. The analyses were conducted in the four seasons of 2017 to compare and identify the key impact factors for NO₃⁻ in different seasons and to provide a scientific basis for designing effective emissions control strategies to mitigate the urgent NO₃⁻ pollution in the YRD region.

2 Methods

2.1 Model configuration

The CMAQ v5.2 model (Wyat Appel et al., 2018; Liu et al., 2020b; Sheng et al., 2022) was applied to investigate the major chemical pathways and physical processes that contribute to NO₃⁻ and TNO₃ formation in the YRD region. Two nested domains were used, as shown in Fig. 1. The outer domain (36 km horizontal resolution) spanned eastern and southeastern China, while the inner domain (12 km horizontal resolution) spanned the entire YRD region. The simulation periods were January, April, July, and October 2017, representing the winter, spring, summer, and autumn, respectively. The simulation began 3 d prior to each of the study periods, and the results were not included in the model analysis as they served as a spin-up of the model.

Figure 1 The entire YRD region as the target region (marked as red) in two nested simulation domains (36 and 12 km resolutions) and the location of five representative YRD cities used in modeling evaluations in the d02 modeling domain. Publisher's note: please note that the above figure contains disputed territories.

The CMAQ model was configured using the photochemical mechanism of the State-wide Air Pollution Research Center version 07 (SAPRC07tic) and the sixth-generation aerosol (AERO6i) module (Fu et al., 2020; Sulaymon et al., 2021). Further details about the CMAQ modeling system have been provided in previous studies (Hu et al., 2016; Liu et al., 2020b). The Weather Research and Forecasting model (WRF v4.2, https://www2.mmm.ucar.edu/wrf/users/, last access: 30 April 2021) was used to simulate the required meteorological field inputs, with initial and boundary meteorological conditions from the $\mathrm{1}{}^{\circ }\times \mathrm{1}{}^{\circ }$ National Centers for Environmental Prediction Final (NCEP/FNL) reanalysis data (https://rda.ucar.edu/datasets/ds083.2/, last access: 30 April 2021). The detailed configurations of the WRF model are shown in Table S1 in the Supplement and are consistent with Hu et al. (2016) and Wang et al. (2021). The anthropogenic emissions for the YRD region in 2017 were established by the Shanghai Academy of Environmental Sciences (SAES), a high-resolution (4 km ×4 km) anthropogenic emission inventory across the entire YRD region (An et al., 2021). The Multi-resolution Emission Inventory for China of the year 2017, with a resolution of $\mathrm{0.25}{}^{\circ }\times \mathrm{0.25}{}^{\circ }$ (MEIC v1.3, http://meicmodel.org, last access: 30 April 2021), provided the anthropogenic emissions for other Chinese regions outside the YRD (Zheng et al., 2018). Emissions from other regions outside China in the inner domain were calculated using the gridded Regional Emission inventory in ASia (REAS v3.2, $\mathrm{0.25}{}^{\circ }\times \mathrm{0.25}{}^{\circ }$ resolution) emissions of the year 2015. The Global Model of Emissions of Gases and Aerosols from Nature (MEGAN v2.1) was used to estimate biogenic emissions (Guenther et al., 2012). Biomass burning emissions were based on satellite observations including both gases and aerosols from the 2017 Fire Inventory from NCAR (FINN; Wiedinmyer et al., 2011). Further descriptions of the emission processing have been provided in previous studies by Hu et al. (2016) and Qiao et al. (2015) and are therefore not repeated here.

2.2 Contributions of transport

To quantify the contributions of local and regional transport to the surface concentrations of the nitrate-phase species (i.e., HNO₃ and NO₃⁻), four scenarios were simulated under the same meteorological fields. Briefly, in the first (base) scenario, the anthropogenic emissions in the YRD and outside regions for 2017 were included. In the second (YRD-zero) scenario, anthropogenic emissions in the YRD were set to zero, while anthropogenic emissions in regions outside the YRD were used. In the third (outside-zero) scenario, only anthropogenic emissions in the YRD were included, while the regions outside the YRD were set to zero. The fourth (all-zero) scenario represented the background case, where the anthropogenic emissions within the study domain were set to zero.

The predicted concentrations were denoted as C_base, C_YRD-zero, C_outside-zero, and C_all-zero, representing NO₃⁻ concentrations associated with the base, YRD-zero, outside-zero, and all-zero scenarios, respectively. The contributions of local YRD emissions, regional transport (the sum of direct and indirect transport from outside regions), direct transport (NO₃⁻ contributed by transported precursors from outside regions), indirect transport (NO₃⁻ contributed by transported and locally emitted precursors via the OH + NO₂ and HET N₂O₅ chemical pathway), and background were defined as F_Local, F_Region,F_Direct, F_Indirect, and F_Background, respectively, and they were calculated as follows:

$$\begin{array}{}\text{(1)}& {\displaystyle }{F}_{\mathrm{Local}}=\left(C_{\mathrm{outside}\text{-}\mathrm{zero}}-C_{\mathrm{all}\text{-}\mathrm{zero}}\right)/C_{\mathrm{base}},\text{(2)}& {\displaystyle }{F}_{\mathrm{Region}}=\left(C_{\mathrm{base}}-C_{\mathrm{outside}\text{-}\mathrm{zero}}\right)/C_{\mathrm{base}},\text{(3)}& {\displaystyle }{F}_{\mathrm{Direct}}=\left(C_{\mathrm{YRD}\text{-}\mathrm{zero}}-C_{\mathrm{all}\text{-}\mathrm{zero}}\right)/C_{\mathrm{base}},\text{(4)}& {\displaystyle }\begin{array}{rl}{F}_{\mathrm{Indirect}}& =\left[\left(C_{\mathrm{base}}-C_{\mathrm{outside}\text{-}\mathrm{zero}}\right)-\left(C_{\mathrm{YRD}\text{-}\mathrm{zero}}\right.\right.\\ & \left.\left.-C_{\mathrm{all}\text{-}\mathrm{zero}}\right)\right]/C_{\mathrm{base}},\end{array}\text{(5)}& {\displaystyle }{F}_{\mathrm{Background}}=C_{\mathrm{all}\text{-}\mathrm{zero}}/C_{\mathrm{base}}.\end{array}$$

Besides NO₃⁻, the major gases pollutants (i.e., NH₃, NO₂, and HNO₃), atmospheric oxidants (i.e., O₃ and OH,), and particulate pollutants (i.e., PM_2.5 and TNO₃) were also quantified. The values of the contributions of the local, direct, and indirect transport emissions can be greater or less than zero, which represents the generation or depletion of pollutants through chemical reactions between local and non-local precursors.

Figure 2 Time series of predicted (red) and observed (black) daily NO₃⁻ concentrations in four atmospheric environment supersites (a–d) in January, April, July, and October 2017.

Table 1 Model performance for meteorological parameters for January, April, July, October and the annual average of 2017 in the entire YRD region. The values that do not meet the criteria are denoted in bold. The equations for MB, RMSE, and IOA are defined in Table S4. The benchmarks are suggested by Emery and Tai (2001).

2.3 Process analysis

In the CMAQ model system, the process analysis (PA) tool has two components, the integrated process rate (IPR) and integrated reaction rate (IRR; Liu et al., 2011; Byun and Schere, 2006). The IPR analysis was applied to investigate the cumulative effect of chemical and physical processes to NO₃⁻ and HNO₃ formation and their daily variation within the PBL (Chen et al., 2019; Yang et al., 2020; Kim et al., 2014). These processes, as explained in Table S2, include aerosol processes (AERO), gas chemistry (CHEM), emission (EMIS), horizontal transport (HTRA), vertical transport (VTRA), dry deposition (DDEP), and cloud processes (CLDS). Furthermore, the IRR analysis was employed to quantify the rates of TNO₃ chemical reactions pathways (Qu et al., 2021; Fu et al., 2020; Shen et al., 2020). The complex chemical production of TNO₃ involves eight reaction pathways, detailed in Table S3 (Qu et al., 2021; Fu et al., 2020; Chuang et al., 2022). In the latter analyses, these pathways are grouped into three major TNO₃ production pathways, including the OH + NO₂, HET N₂O₅, and “others” pathways, according to their importance. Shanghai is selected as an example in the IPR and IRR analysis to explore the impacts of physical and chemical processes of NO₃⁻ and HNO₃ formation because it is the largest city in the YRD and has the most abundant measurement data.

2.4 Observation data

Hourly concentrations of six routine air pollutants (i.e., O₃, PM_2.5, NO₂, SO₂, and carbon monoxide (CO)) in five representative YRD cities (i.e., Shanghai, Nanjing, Hefei, Hangzhou, and Changzhou, shown in Fig. 1) during the four seasons were obtained from the China Ministry of Ecology and Environment (http://www.cnemc.cn/, last access: 27 September 2022). Furthermore, hourly NO₃⁻ concentrations were measured by the Monitors for AeRosols and Gases (MARGA 1S ADI 2080, Netherlands, Khezri et al., 2013) at four urban atmospheric environment supersites: Shanghai (31.23^∘ N, 121.54^∘ E), Hefei (31.78^∘ N, 117.20^∘ E), Hangzhou (30.29^∘ N, 120.16^∘ E), and Changzhou (31.76^∘ N, 119.96^∘ E). Observation data of meteorological parameters (temperature (T2, ^∘C), relative humidity (RH, %), wind speed (WS, m s⁻¹), and wind direction (WD, ^∘)) for 75 weather stations in the YRD were downloaded from the Chinese Meteorological Agency (http://data.cma.cn/en, last access: 30 November 2021).

The statistical metrics used for the WRF-CMAQ model evaluation include the mean bias (MB), normalized mean bias (NMB), normalized mean error (NME), correlation coefficient (R), root-mean-square error (RMSE), and index of agreement (IOA). Definitions and criteria of all statistical metrics are illustrated in Table S4. The benchmarks of major air pollutant (PM_2.5, NO₂, O₃, and NO₃⁻) concentrations are suggested by Emery et al. (2017) and Huang et al. (2021). The benchmarks of major meteorological parameters (T2, WS, and WD) are suggested by Emery and Tai (2001).

3 Results and discussion

3.1 Model evaluation

3.1.1 WRF model performance

Table 1 shows the modeling performance statistics of the meteorological parameters in the four seasons of 2017. Predicted T2 and WS values are slightly higher than the observations, and MB values of T2 and WS exceed the suggested benchmark (MB $\le \pm \mathrm{0.5}$) in all seasons. The seasonal and annual IOA values of T2 occur within the suggested benchmark (IOA ≥0.8). For WS, the seasonal and annual values of RMSE and IOA all meet the suggested criterion (RMSE ≤2.0 and IOA ≥0.6). The MB values of WD are slightly above the suggested benchmark (MB $\le \pm \mathrm{10}$) in the four seasons, except during spring. RH is generally underestimated compared to the observations with averaged MB values of −6.96, −10.7, −9.06, and −5.98 in winter, spring, summer, and autumn, respectively. There is no suggested criterion for the MB value of RH. In addition, high seasonal and annual values of R (0.85–0.95 for T, 0.87–0.91 for RH, 0.70–0.85 for WS, and 0.75–0.89 for WD) are found. The WRF performance in this study is comparable to WRF performance in our previous simulation studies (Wang et al., 2021; Hu et al., 2016; Sulaymon et al., 2021).

3.1.2 CMAQ model performance

Table 2 and Fig. S1 in the Supplement show the model performance and time series of major air pollutants in the four seasons. Overall, the CMAQ model has reasonably reproduced the observed PM_2.5, O₃, and NO₂ concentrations in the YRD region, especially in Shanghai. The daily concentrations of PM_2.5 are efficiently simulated in the five cities except Hefei, illustrated by the NMB, NME, and R values meeting the criteria established by Emery et al. (2017; NMB $\le \pm \mathrm{0.30}$, NME ≤0.50, and R>0.70). MDA8 O₃ values are slightly overestimated in Nanjing, Hefei, Hangzhou, and Changzhou. Predicted concentrations of NO₂ are generally lower than the observations in all five cities ($-\mathrm{0.15}<$ NMB $\le -\mathrm{0.05}$, $-\mathrm{10.37}<$ MB $\le -\mathrm{1.89}$). When compared to our previous studies (Hu et al., 2016; Wang et al., 2021; Ma et al., 2021; Sulaymon et al., 2021; Li et al., 2021a), the statistical results in this study show a better model performance.

Table 2 Model performance of major pollutants for the full year of 2017 in five representative YRD cities^a.

^a The year of 2017 includes the 4 typical months (January, April, July, and October). ^b MDA8 O₃, NO₂, SO₂, and PM_2.5 are given in units of µg m⁻³ and CO is given in units of mg m⁻³). ^c The equations of NMB, NME, MB, and R
are found in Table S4. The values that do not meet the criteria are highlighted in bold. The recommended benchmarks for MDA8 O₃, 24 h PM_2.5, and NO₃⁻ are suggested by Emery et al. (2017) and Huang et al. (2021).

Figure 2 illustrates the comparison of predicted and observed NO₃⁻ concentrations at the four supersites on daily timescales. The general temporal variations of observed NO₃⁻ concentrations are efficiently captured by the model. The daily concentrations of NO₃⁻ are efficiently predicted in four supersites, all within the benchmark (NMB $\le \pm \mathrm{0.60}$, NME ≤0.75, and R>0.6). However, in Hefei (Fig. 2b) the wintertime NO₃⁻ measurement data are not available, which is when NO₃⁻ shows the highest concentrations and is of most concern. Good agreement between predicted and observed values is demonstrated on daily timescales, especially in Shanghai (NMB $=-\mathrm{0.49}$; R=0.70), Hangzhou (NMB =0.11; MB =0.64), and Changzhou (NMB =0.36; R=0.56). Overall, the statistical performance metrics of predicted NO₃⁻ in this study are comparable to those of our previous works (Shi et al., 2017; Qu et al., 2021; Xie et al., 2022). Figure S2 shows the hourly predicted and observed NO₃⁻ concentrations in each season. NO₃⁻ concentrations are generally underestimated during the summer and autumn. One possible reason is that RH is slightly underestimated by the WRF model during these seasons (Table 1), which results in a lower buildup of NO₃⁻ concentrations. Other reasons could be associated with uncertainties in the NO₃⁻ formation mechanisms (missing or insufficient heterogeneous reactions) in the current CMAQ model and uncertainties in NO_x and NH₃ emissions (Zheng et al., 2020; Lu et al., 2021b; Zheng et al., 2015; Liu et al., 2019; Xie et al., 2022).

Figure 3 Contributions of background, local, indirect, and direct transport to nitrate-related species in 4 months of 2017 for the entire YRD region (a–d). Nitrate-related species represent NO₃⁻, HNO₃, PM_2.5, O₃, NO₂, NH₃, OH, and N₂O₅. The contributions of HNO₃ in January 2017 are shown in Fig. S6.

3.2 Regional transport contribution to nitrate in YRD

Figure S3 shows the spatial distribution of the seasonal (winter, spring, summer, and autumn) and annual (average of the four seasons) NO₃⁻, HNO₃, and TNO₃ concentrations under four emission scenarios in the d02 domain. Under C_base, the seasonal and annual NO₃⁻ concentrations for the entire YRD region were 16.0, 7.4, 1.0, 5.4, and 7.4 µg m⁻³, respectively (Table S5). Compared to C_base, the seasonal and annual NO₃⁻ concentrations in C_outside-zero decreased by 8.0, 2.8, 0.4, 2.2, and 3.3 µg m⁻³, respectively. Even more significant differences in NO₃⁻ are observed between C_base and C_YRD-zero. The NO₃⁻ decreased by 12.0, 6.9, 0.9, 4.8, and 6.1 µg m⁻³ in winter, spring, summer, autumn, and over the whole year, respectively, to become almost twice as high as those between C_base and C_outside-zero. The results suggest that the local anthropogenic emissions contribute more to the seasonal NO₃⁻ concentrations in the YRD.

Figure 3 shows the regional contributions of the background, local, direct, and indirect transport to nitrate-related species in the four seasons (results for Shanghai are shown in Fig. S4). The local emissions dominate NO₃⁻ concentrations throughout the YRD, accounting for 50.4 %–62.0 % in the four seasons (Fig. 3a). Figure 3c suggests that the precursors (NO₂ and NH₃) are dominated by the local emissions (more than 93.0 %). The contributions of the total regional transport are 49.5 %, 38.0 %, 41.6 %, and 42.0 % in winter, spring, summer, and autumn, respectively. The indirect transport contributes 24.2 %–37.0 % of NO₃⁻ concentrations and exceeds the contributions from direct transport in the spring, summer, and autumn. Similarly, Qu et al. (2021) reported that the reaction between the locally emitted NO₂ and transported O₃ dominates the production of indirect NO₃⁻ transport in the PRD region.

In Fig. 3b, the local emission and indirect transport have negative contributions to O₃ concentration, leading to the depletion of O₃ in the four seasons. For O₃, the local emissions have negative contribution in winter (−46 %) and autumn (−12 %). The negative contributions of the indirect transport are −6 %, −8 %, −8 %, and −4 % in winter, spring, summer, and autumn, respectively. In Fig. 3d, the indirect transport contributes from −42 % to −12 % of OH concentrations in the four seasons. The negative indirect transport contributions to O₃, N₂O₅, and OH suggest that the atmospheric oxidants are consumed in the YRD, which in turn enhances the chemical production of NO₃⁻.

3.3 Formation processes of nitrate

Figure 4 shows the modeled diurnal variations of three nitrate phases (NO₃⁻, HNO₃, and TNO₃), the major precursors (i.e., O₃, NO₂, and NH₃), and the major atmospheric oxidants (OH and N₂O₅) in the four seasons for the entire YRD region in the base scenario. Except for summer, higher predicted TNO₃ and NO₃⁻ concentrations are observed in early morning hours (06:00–08:00 BJT, Beijing time), while lower TNO₃ and NO₃⁻ concentrations are observed around 16:00–18:00 BJT. Predicted concentrations of TNO₃, HNO₃, and O₃ show the same diurnal variations in the summer, and peak around 12:00 BJT (the most active photochemical hours). The opposite results in the profiles of TNO₃'s diurnal variation between summer and non-summer periods are mainly attributed to the temperature effect on the gas-to-particle partitioning between NO₃⁻ and HNO₃. As shown in Fig. S3, NO₃⁻ dominates the TNO₃ concentrations and determines its diurnal variations in non-summer periods, while HNO₃ dominates the diurnal variation in summer. A two-peak mode diurnal variation of NO₂ and NH₃ is identified in the four seasons. High concentrations of NO₂ and NH₃ occur in the early morning (06:00–08:00 BJT) and early evening (18:00–19:00 BJT), due to the local transportation emissions during rush hours. OH and N₂O₅ have a one-peak-mode diurnal variation in the four seasons. OH peaks around 12:00 BJT, similar to HNO₃, while N₂O₅ peaks around 18:00–20:00 BJT.

Figure 4 Monthly diurnal variations of three nitrate phases (NO₃⁻, HNO₃, and TNO₃), the major nitrate precursors (NO₂, NH₃, and N₂O₅), and atmospheric oxidants (O₃ and OH) for the entire YRD region under the base scenario. The x axis marks each hour of the day (local time in Beijing).

Figure 5 Diel variations in physical and chemical processes rates of NO₃⁻ and HNO₃ production (a–h) within the PBL in Shanghai. The red line represents the net IPR value for each hour of the day; its value scale is on the right y axis.

Figure 6 (a) Mean diurnal variations of TNO₃ production rates in different pathways in 2017 in Shanghai. (b) Average potential contribution of OH + NO₂, HET N₂O₅, and others to TNO₃ chemical production in Shanghai within the PBL under the base case simulation. Daytime (07:00–18:00 BJT) and nighttime (19:00–06:00 BJT) are given separately. OH + NO₂ and HET N₂O₅ pathways are denoted as “OH NO₂” and “HET N₂O₅” in Figs. 6 and 7.

Table 3 Seasonal TNO₃ production rates (ppb h⁻¹) and contributions (%) of the major production pathways in five representative cities.

Table 4 Comparison of contributions of major nitrate formation pathways in China and other regions^a.

^a The 24 peer-reviewed publications are conducted in the major regions and megalopolises of China (the North China Plain (NCP), Yangtze River Delta (YRD), Pearl River Delta (PRD)), the United States, and the global region.
The comparison serves to quantify the relative contribution of two main nitrate formation pathways in different seasons. ^b Methods include the 3D CTMs, nitrogen and oxygen isotopes analysis, field determination, and box models.
^c Surface represents the surface layer.

Figure S6 shows seasonal variations in NO${}_{\mathrm{3}}{}^{-}/$PM_2.5, NO${}_{\mathrm{3}}{}^{-}/$TNO₃, nitrogen oxidation ratios (NOR = [NO₃⁻]$/$([NO${}_{\mathrm{3}}{}^{-}]+$ [NO₂])), and adjusted gas ratio (adjGR = ([NH₃]+ [NO${}_{\mathrm{3}}{}^{-}\left]\right)/$([HNO₃]+ [NO₃⁻])) in the YRD. NO${}_{\mathrm{3}}{}^{-}/$PM_2.5 and NO${}_{\mathrm{3}}{}^{-}/$TNO₃ are the highest in the winter, accounting for 21±5 % and 94±3 %, respectively. The averaged NOR values for the entire YRD region are 0.24, 0.16, 0.03, and 0.13 mol mol⁻¹ in winter, spring, summer, and autumn, respectively. The highest value of NOR in winter suggests a high conversion efficiency of NO₂ to NO₃⁻. AdjGR values are generally greater than 2 in the four seasons across most areas in the YRD, indicating that YRD is mostly in the NH₃-rich regime. Therefore, NH₃ is not a limiting factor of NO₃⁻ formation in YRD.

Figure 5 illustrates a two-peak-mode diurnal variation of the net IPR rates of NO₃⁻ production in the four seasons. Peak hours are around noon (10:00–11:00 BJT) and in the early evening (19:00–21:00 BJT), with peak rates of 1.2–1.5, 0.7–0.8, 0.4–0.6, and 0.1–0.2 µg m⁻³ h⁻¹ in the winter, spring, summer, and autumn, respectively. AERO processes (including condensation, coagulation, and aerosol growth) are the dominant contributors to NO₃⁻ formation, with peak rates of 2.1, 1.3, 1.5, and 0.4 µg m⁻³ h⁻¹ in the winter, spring, summer, and autumn, respectively. The sharp decline hours of the net IPRs (around 11:00–18:00 BJT) are mainly dominated by TRAN (sum of HTRA and VTRA) processes, with mean rates of −1.4, −0.8, −0.7, and −0.3 µg m⁻³ h⁻¹ in the winter, spring, summer, and autumn, respectively. However, in summer, TRAN processes constitute the dominant source after midnight (01:00–06:00 BJT), owing to the stable PBL weakening the contribution of vertical transport and accelerating the accumulation of NO₃⁻ concentrations at the surface (Huang et al., 2020c). In Fig. S7, VTRA processes act as the main positive contributor to NO₃⁻ buildup production from 00:00 to 23:00 BJT at layer 1 (surface layer), while AERO processes make the negative contribution to NO₃⁻ within layers 1–8 (from the surface to 800 m). Above layer 10, AERO processes for NO₃⁻ production are positive in the daytime, which is conducive to the accumulation of NO₃⁻ concentrations.

For HNO₃, a one-peak-mode diurnal variation of the net IPR rates is found, and peak times are at 20:00 BJT in the winter and around 09:00–12:00 BJT in other seasons (Fig. 5). Meanwhile, CHEM (gas chemical processes) processes are the major contributor to HNO₃ formation, with the peak rates being 0.6, 1.4, 2.3, and 0.7 ppb h⁻¹ in the winter, spring, summer, and autumn, respectively. In the spring, summer and autumn, the peak times of HNO₃ formation are consistent with the first peak times of NO₃⁻. The seasonal net IPR rates reached a maximum of 0.3, 1.0, and 0.1 ppb h⁻¹, respectively. CHEM and VTRA processes are the dominant contributors to HNO₃ production, especially from 07:00 to 13:00 BJT (net IPR rates >0), with seasonal peak rates of 1.5, 2.7, and 0.8 ppb h⁻¹, respectively. AERO, DDEP, and HTRA processes are the dominant contributors to the HNO₃ sharp decline (14:00–17:00 BJT), with the lowest net IPR rates of −0.8, −0.7, and −0.3 µg m⁻³ h⁻¹ in the spring, summer, and autumn, respectively. DDEP processes are the dominant sink of HNO₃ in summer ($-\mathrm{0.64}\pm \mathrm{0.20}$ ppb h⁻¹). However, in the winter, the peak times of HNO₃ production are the opposite regarding the first peak time of NO₃⁻ production but are consistent with the second peak time. HTRA makes a positive contribution to HNO₃, with peak rates of 0.18 ppb h⁻¹ at 20:00 BJT. In Fig. S12, the only large sink is the AERO process, consistent with efficient partitioning of HNO₃ into particle-phase NO₃⁻ in cold seasons.

Table 3 illustrates that in cold seasons (winter and autumn) within the PBL about 60 %–78 % of TNO₃ is produced through OH + NO₂, 21 %–36 % through HET N₂O₅, and 2 %–5 % through the others pathways in the five representative YRD cities. Meanwhile, 71 %–83 % of TNO₃ is produced through OH + NO₂, 10 %–23 % through HET N₂O₅, and 4 %–13 % through the others pathways (mainly contributed by NO₃+ Org and N₂O₅ H₂O) in warm seasons (summer and spring). Table 4 shows the comparison of the contribution of major TNO₃ production pathway studies in China and other regions using different methods. The results are in agreement with the contribution of NO₃⁻ pathways in previous modeling and observational studies. For example, Li et al. (2021b) modeled that OH + NO₂ and HET N₂O₅ pathways dominate NO₃⁻ production in the YRD region in the warm and cold seasons of 2016 using a CTM, accounting for 86 %–92 % and 8 %–14 % in the surface layer, respectively. He et al. (2020) reported that the OH + NO₂ pathway dominates NO₃⁻ production in Shanghai on the surface layer using nitrogen isotope analysis, accounting for 84 %–92 % and 55 %–77 % in the warm and cold seasons of 2016, respectively. Alexander et al. (2020) highlighted that the OH + NO₂ and HET N₂O₅ pathways contribute the same proportion (both 41 % in the four seasons) to NO₃⁻ production in the global region using the CTM and oxygen isotopes analysis.

Figure 6a shows the diurnal variations of TNO₃ formation reaction rates through three major pathways in Shanghai within the PBL. The average diurnal trends of TNO₃ production rates are consistent with the CHEM process rates of HNO₃ production (Figs. 5 and 6). The chemical production of HNO₃ quickly transforms to particulate NO₃⁻ through AERO processes in the presence of abundant NH₃. The averaged TNO₃ production rates are 0.31±0.14, 0.65±0.37, 1.09±0.68, and 0.28±0.22 ppb h⁻¹ in the winter, spring, summer, and autumn, respectively (Table S6). Moreover, the seasonal peak rates of TNO₃ production are 0.6, 1.4, 2.3, and 0.7 ppb h⁻¹ around 11:00–13:00 BJT, respectively. In accordance with the seasonal variation of HNO₃ net IPR rates, TNO₃ production rates are the fastest in summer.

In Shanghai, TNO₃ chemical production is dominated by the OH + NO₂ pathway on the daily timescale, accounting for 69.3 %–86.9 % of the total, while the HET N₂O₅ pathway is likewise a relatively important pathway (accounting for 11.1 %–28.4 %) in the four seasons (Fig. 6b). Notably, TNO₃ production rates are dominated by the OH + NO₂ pathway during the daytime (7:00–18:00 BJT, accounting for 88.4 %–97.9 % of the total) in all seasons, while the HET N₂O₅ pathway becomes more important for the TNO₃ production during the nighttime (19:00–06:00 BJT, accounting for 42.5 %–61.6 %). During winter, TNO₃ formation via the HET N₂O₅ pathway becomes dominant over the OH + NO₂ pathway, accounting for 62 %, 65 %, and 68 % in Shanghai, Hangzhou, and Nanjing at night, respectively. O₃ strongly coordinates TNO₃ production via the HET N₂O₅ pathway during the nighttime. Similarly, He et al. (2018) observed that the HET N₂O₅ pathway was the major contributor to NO₃⁻ production in the winter of Beijing at the surface layer using oxygen and nitrogen isotopes analysis, accounting for 56 %–97 % of the total during the nighttime. In another CTM study in the NCP, the HET N₂O₅ pathway was the dominant contributor to nocturnal NO₃⁻ production within the PBL in winter, with a contribution of 83 % at night (Liu et al., 2020a). In Fig. S8, the seasonal TNO₃ production rates (ppb h⁻¹) and contributions (%) of the major pathways have been compared between vertical layers and PBL. The OH + NO₂ pathway dominated TNO₃ production at all layers, accounting for more than 58 %, 78 %, 80 %, and 83 % in winter, spring, summer, and autumn, respectively. The OH + NO₂ pathway rate decreases with altitude at vertical layers, where its contribution decreases from 87 % to 58 %, from 91 % to 78 %, from 93 % to 80 %, and from 95 % to 83 % in the four seasons, respectively. The HET N₂O₅ pathway becomes more important for the TNO₃ production within layers 4–8 (250 to 580 m) in winter, accounting for 37 % (Fig. S8b).

Figure 7 Mean diurnal variations of TNO₃ production rates in major pathways from the local and transport (sum of indirect and direct transport) contributions.

Figure 8 The seasonal rates of TNO₃⁻ production and the major pathways in the base case and from the local and transport contributions within the PBL. The error bar indicates 1 standard deviation.

Figure 7 displays the contributions of TNO₃ formation pathways from the local and transport (sum of indirect and direct transport) contributions. For the local contribution, the averaged TNO₃ production rates are 0.27±0.14, 0.56±0.37, 1.05±0.69, and 0.26±0.21 ppb h⁻¹ in the winter, spring, summer, and autumn, respectively (Table S7). During the daytime, the OH + NO₂ pathway contributes almost all TNO₃ production rates from the local contribution, accounting for about 89 %–98 % of the total, with mean rates of 0.33±0.17, 0.83±0.34, 1.55±0.59, and 0.40±0.22 ppb h⁻¹ in the winter, spring, summer, and autumn, respectively. The results suggest that the locally emitted NO₂ reacts with OH-dominated TNO₃ production during the day in the YRD region.

For the transport contribution, the averaged TNO₃ production rates are 0.04±0.01, 0.08±0.02, 0.03±0.02, and 0.02±0.01 ppb h⁻¹ in the winter, spring, summer, and autumn, respectively (Table S8). The HET N₂O₅ pathway is noted as the dominant pathway for TNO₃ production of the transport contribution, accounting for around 72 %–86 % during the nighttime. Figure 8 compares the seasonal TNO₃ production pathways rates between local, indirect, and direct transport contributions within the PBL. The regional production is mainly contributed by indirect transport, especially in the winter and summer. The results suggest that the transported O₃ from outside the YRD region reacts with the locally emitted NO₂, supporting TNO₃ production via the HET N₂O₅ chemical pathway during the nighttime.

Overall, our findings illustrate that local emissions dominate NO₃⁻ formation in the YRD (50 %–62 %) and more specifically locally emitted NO_x reacting with OH and partitioning into particles with NH₃ (mostly from local sources, more than 93.0 %), indicating that the uncoordinated control of precursors (i.e., NO_x and NH₃) and reduction of the oxidative capacity of the atmosphere is crucial for NO₃⁻ reduction. Furthermore, regional transport contributes 38 %–50 % to NO₃⁻ formation in the YRD region. Indirect transport contributes 24 %–37 % through transported O₃ reacting with local NO_x at night, indicating that the simultaneous controlling of O₃ and NO₃⁻ in the larger-scale region is also important for NO₃⁻ reduction in the YRD.

This paper has investigated the seasonal variations in the NO₃⁻ formation mechanisms, including local emission and regional transport contributions, as well as dominant processes and major chemical pathways in the YRD region. However, there are still some limitations in this paper, such as the insufficient heterogeneous chemistry on the dust particles' surface and uncertainties in precursor emissions in the model, and these affect the model performance of NO₃⁻ during the spring and autumn (Xie et al., 2022). Furthermore, the integrated reaction rate (IRR) analysis was employed to quantify the rates of TNO₃ (sum of NO₃⁻ and HNO₃) chemical pathways, which potentially lead to differences in chemical pathway rates and contributions between NO₃⁻ and TNO₃. Figure 6b illustrates that TNO₃ chemical production is dominated by the OH + NO₂ pathway on the daily timescale, accounting for 69.3 %–86.9 % in Shanghai. Notably, due to the higher temperature during the daytime, the potential production for NO₃⁻ is not as high as that of the nocturnal chemical pathway (mainly the HET N₂O₅ pathway at night), which potentially led to underestimates in the nocturnal pathway contribution to NO₃⁻.

4 Conclusions

This study investigates the contributions of regional transport and major chemical pathways to NO₃⁻ and HNO₃ formation in the YRD in different seasons using the WRF-CMAQ model. The modeled results show that local emissions dominate NO₃⁻ concentrations in the YRD (50 %–62 %), while regional transport contributes 38 %–50 % to NO₃⁻ (indirect transport contributes 24 %–37 %). Except for during winter, HNO₃ was dominated by the contributions of local emissions (61 %–75 %), and indirect transport contributed negatively (−24 % to −41 %). In Shanghai, the IPR analysis reveals that AERO processes were the predominant contributors to NO₃⁻ formation within the PBL. TRAN processes were the largest sinks in NO₃⁻ formation in the winter, spring and autumn, while the positive contributors were at night in summer. For HNO₃, CHEM processes were the only positive contributor during the day. The OH + NO₂ pathway is the predominant contributor (60 %–83 %) among all chemical pathways, while the HET N₂O₅ pathway is also important (10 %–36 %) in the YRD region. The TNO₃ production is dominated by the OH + NO₂ pathway during the day (98 %) in summer, while the HET N₂O₅ pathway dominates during the night (61 %) in winter. The TNO₃ production rates from the local and transport contributions were further elucidated. The OH + NO₂ pathway from the local contribution strongly dominates the TNO₃ production during the day (89 %–98 %). At night, the HET N₂O₅ pathway is mainly dominated by indirect transport (via reaction with transported O₃ at night).