Introduction

Fine particulate matter, or PM2.5, particles with diameter equal or smaller than 2.5 µm, is one of the major air pollutants contributing to poor air quality. Exposure to elevated levels of PM2.5 in the atmosphere poses significant threats to human health, adversely affecting the respiratory, cardiovascular and other human systems1. Recent epidemiological studies estimate that global excess premature deaths attributable to PM2.5 pollution range from 0.8 to 10.2 million per year2, underscoring the urgent need for PM2.5 pollution control. Given the complex chemical composition of PM2.53, a thorough understanding over the processes and influencing factors of its major components is essential for developing effective mitigation strategies.

Sulfate (pSO4) is one of the main inorganic components in PM2.5, accounting for 10-40% of its mass according to global observations4,5. A high proportion of pSO4 in PM2.5 is associated with high acidity and toxicity, posing significant threat on human health6,7. Beyond its health effect, pSO4 also contributes to ecosystem acidification and influences visibility and climate8,9,10. While pSO4 can be directly emitted from sources such as power plants, industrial facilities, residential combustion, shipping and volcanoes11,12,13,14, the majority of pSO4 is often chemically formed through the oxidation of its precursor, sulfur dioxide (SO2). In the gas phase, SO2 is oxidized by hydroxyl radical (OH) to form sulfuric acid (H2SO4), which can partition into the particle phase to produce pSO4. In the aqueous phase, multiple reaction pathways contribute to pSO4 formation, including oxidation by hydrogen peroxide (H2O2), ozone (O3), organic peroxides (e.g., methyl hydroperoxide (MHP) and peracetic acid (PAA)) and catalyzed by transition metal ions (TMIs; e.g., Fe3+ and Mn2+). Under heavily polluted conditions, additional new aqueous-phase or heterogeneous chemical mechanisms have been reported to explain the rapid growth of pSO4 concentrations, such as oxidation by NO215, photosensitizing compounds16 and catalysis by manganese17. The relative contributions of these reaction pathways to local pSO4 production depend on the chemical and meteorological conditions and remain an active area of relevant research18.

In addition to local emission and chemical production, cross-regional transport is often another critical process contributing to pSO4 pollution. The atmospheric lifetime of pSO4 in the troposphere spans 2 to 5 days19,20,21, enabling its transport over distances ranging from tens to thousands of kilometers and its vertical mixing within the atmospheric boundary layer (ABL). Source apportionment studies have reported substantial contributions of cross-regional transport to pSO4, particularly in regions with relatively low emissions22,23. The underlying dynamic and chemical processes associated with cross-regional pSO4 transport are often complex. In many regions, elevated pSO4 concentrations were observed from the ground up to the altitudes of 1–3 km21,24,25,26, covering both the ABL and the lower free troposphere. This distribution suggests that pSO4 may be efficiently transported into or out of a region via both horizontal advection and vertical exchange across the ABL top. Moreover, pSO4 can be produced from SO2 oxidation during transport27,28, and in some cases, pSO4 production within transported plumes contributed more to downwind pSO4 levels than formation within the receptor or source regions29,30. While many studies focus on local formation mechanisms of pSO4, its chemical evolution within transported air masses is insufficiently explored. A comprehensive knowledge of these dynamic and chemical processes governing cross-regional pSO4 transport is essential for supporting effective air quality improvement, particularly in regions strongly affected by such transport.

This study focuses on cross-regional pSO4 transport to the Pearl River Delta (PRD), a densely populated metropolitan region in South China with a population exceeding 85 million. Here, pSO4 accounts for 15-35% of PM2.5, making it the most abundant water-soluble component31,32,33,34. In the PRD, cross-regional transport plays a significant role in pSO4 pollution, contributing to over 60% of pSO4 levels during polluted seasons35,36,37. This is due to the import of anthropogenic pollution air masses from North and Central China, or the “Gigacity cluster” with intensive emissions38, driven by the winter East Asian monsoon (characterized by northerly winds). Despite their importance, studies on the detailed processes associated with cross-regional pSO4 transport to the PRD are still limited. Using the well-validated WRF/CMAQ models, we investigated the dynamic and chemical processes associated with cross-regional pSO4 transport from Oct. 11 to Nov.10, 2015, a period featuring three distinct PM2.5 pollution episodes under different weather systems. Specifically, this study examines: (1) the relative importance of horizontal transport and vertical exchange in pSO4 transport; and (2) the evolving pSO4 chemistry within the transported plumes, including the contributions of different reaction pathways to pSO4 and their influencing factors. The findings are expected to enhance our understanding of pSO4 pollution in the PRD and also provide valuable insights for other regions strongly influenced by cross-regional pollutant transport.

Results

Overviews of PM2.5 and pSO4 pollution

Based on the definition of polluted days in our previous study39 (daily PM2.5 > 35 μg/m3), 16 polluted days were identified during the study period, clustering into three episodes (Fig. 1a): E1 (Oct. 13-24), E2 (Oct. 28) and E3 (Nov. 3-5). They were driven by different weather systems, including subtropical high and typhoon periphery during E1 (Supplementary Fig. S1a-b), subtropical high during E2 (Supplementary Fig. S1c), and transformed high pressure during E3 (Supplementary Fig. S1d). Within E1, two sub-periods were distinguished: E1-1 (Oct. 13-15), influenced jointly by subtropical high and typhoon periphery, and E1-2 (Oct. 16-24), primarily driven by the peripheries of typhoons Koppu and Champi. Previous statistics40 suggest that ~70% of PM2.5 pollution episodes in the PRD were driven by these weather systems, but the underlying causes differ. Specifically, in E1-2, strong northerly winds under typhoon influence facilitated cross-regional PM2.5 transport from more polluted North and/or Central China, whereas in E2, moist southeasterly flows increased humidity (Supplementary Table S1), likely favoring local PM2.5 production and accumulation. A more detailed analysis of these episodes is provided in Supplementary Text S1.

Fig. 1: Series of PM2.5, pSO4 and its regional sources during the study period.
Fig. 1: Series of PM2.5, pSO4 and its regional sources during the study period.
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a Observed and simulated PM2.5 concentrations in the PRD, averaged over 18 sites from the Guangdong-Hong Kong-Macao PRD Regional Air Quality Monitoring Network. NMB, normalized mean bias; R, correlation coefficient. “(*)” denotes statistical significance at p < 0.05. b Simulated daily pSO4 concentrations in the PRD and their regional source contributions. In the (a) and (b), background shading in various colors marks different pollution episodes. c Mean proportions of background, local and regional contributions to pSO4 in the PRD during each episode.

During the study period, the mean simulated pSO4 concentration in the PRD was 8.1 µg m−3, accounting for 23.7% of PM2.5. Similar to PM2.5, pSO4 levels were higher on polluted days compared to clean days (Fig. 1b). The highest regional-mean concentration occurred in E2, reaching 11.4 µg m−3 and comprising 32.2% of PM2.5. Source apportionment results (Fig. 1b, c) underscore the dominant role of cross-regional transport (non-local sources) in pSO4 pollution: On a monthly average, it contributed to 76–88% of pSO4, with regional and background contributions accounting for 56–73% and 14–29%, respectively, while local emissions contributed only 12–24%. These contributions varied across episodes (Fig. 1c). The highest transport contribution was observed in E1-2, with regional and background contributions of 59% and 29%, respectively, consistent with favorable transport conditions. In E2, the local contribution peaked at 24%, reflecting the impact of moist southeasterly winds. The regional contributions of pSO4 in E1-1 and E3 fell between those of E1-2 and E2, indicating an intermediate influence of transport and local processes. Building on these results, the following analysis compares pSO4-related processes, particularly cross-regional transport, between the strong-transport E1-2 and the high-local-influence E2, aiming to elucidate the similarities and differences in the pSO4 pollution mechanisms under distinct conditions.

Budget analysis

The pollutant budget provides a process-based view of how different atmospheric processes (e.g., transport and chemical production) contribute to pollutant variations. Here, we quantified pSO4 mass budget within the ABL of the PRD, with its mean diurnal variations for both polluted and clean days displayed in Fig. 2a. Similar to O3 and PM2.5 mass budgets41,42, the variations in pSO4 mass reflects the impact of ABL diurnal cycle: Total pSO4 mass increased in the morning (6:00-14:00 local time (LT)) as the ABL developed, declined rapidly in the afternoon until ~19:00 LT when the ABL collapsed, and exhibited minimal changes at night during the ABL’s stabilization phase. Daytime pSO4 mass changes were more pronounced on polluted days compared to clean days.

Fig. 2: pSO4 mass budgets in the PRD.
Fig. 2: pSO4 mass budgets in the PRD.
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a Mean diurnal variations in pSO4 mass budget on polluted and clean days. Background shading in yellow, orange and dark blue indicates the morning, afternoon and nighttime periods, respectively. b Comparison of morning (6:00-14:00 local time (LT)) and afternoon (14:00-19:00 LT) budgets across different episodes. For each episode, the budget in the morning or afternoon is displayed in two rows: the first row presents mean horizontal transport fluxes across the PRD boundaries in four directions and mean hourly contributions from the aerosol process (labeled "AERO"); the second row shows mean vertical exchange fluxes, including those from ABLex-H (labeled “H”) and ABLex-A (labeled “A”). All budget terms are expressed in the unit of t h−1.

The contributions of individual processes (see Methods for definitions) to pSO4 mass variations highlight the major role of transport in shaping its budget in the PRD. Vertical exchange across the ABL top, especially that driven by diurnal variations in ABL height (ABLex-H), dominated the rapid morning increase as well as afternoon decrease in pSO4 mass, contributing ~66% and ~86%, respectively. This underscores the notable influence of ABL dynamics on pSO4 pollution. Horizontal transport was also important: Its positive fluxes occurred across the northern and eastern boundaries, while negative fluxes were found across the southern and western boundaries, consistent with prevailing northeast winds. Aerosol process and emission led to pSO4 increases, whereas dry deposition acted as a sink process. However, the effects of these local processes on pSO4 mass variations were much smaller than those of transport. Both transport and aerosol process contributed more on polluted days than on clean days, indicating that pSO4 pollution in the PRD was driven not only by enhanced local production but, more importantly, by intensified cross-regional transport.

We further compared pSO4 mass budgets across different pollution episodes. Figure 2b shows the mean contributions of horizontal transport, aerosol process (top row) and vertical exchange (bottom row) during the morning and afternoon for each episode. In the following text, we present the comparisons of contributions from ABLex-H and aerosol process, which reveal some unexpected features. Analyses of the other processes, including horizontal transport and vertical exchange driven by advections perpendicular to the ABL top and slopes (ABLex-A), are provided in Supplementary Text S2.

Higher ABLex-H fluxes of pSO4 were found in both the strong-transport and high-local-influence episodes (E1-2 and E2)

As shown in Fig. 2b, the morning influx and afternoon outflux of pSO4 via ABLex-H were both higher in E1-2 and E2 than in other episodes. This finding suggests that, unexpectedly, strong vertical exchange of pSO4 can occur under both strong-transport and stagnant conditions. Because the morning influx describes pSO4 entrainment from residual layers into the ABL, we examined the causes of its high values in the two contrasting episodes using cross sections of simulated wind fields and pSO4 concentrations on representative days (Oct. 18 for E1-2 and Oct. 28 for E2; Fig. 3). These cross sections were generated along a north-south transect across the PRD (Supplementary Fig. S2).

Fig. 3: Cross sections of simulated wind fields and pSO4 concentrations on representative days.
Fig. 3: Cross sections of simulated wind fields and pSO4 concentrations on representative days.
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a–c Oct. 18 (E1-2) and d–f Oct. 28 (E2), at 2:00 (a, d), 8:00 (b, e) and 14:00 LT (c, f). White solid lines denote the top of atmospheric boundary layers.

During E1-2, strong northerly winds induced by typhoon peripheries enhanced cross-regional pSO4 transport. Elevated pSO4 levels ( > 5 µg m−3) persisted below 1–1.5 km (Fig. 3a-c); As the ABL developed in the morning, large amounts of pSO4 were exchanged into the PRD. In contrast, during E2, weaker winds favored pollutant accumulation, with a polluted air parcel with pSO4 concentrations exceeding 12 µg m−3 residing to the north of the PRD (Fig. 3d). Under weak near-surface northerly flows, this parcel slowly moved southward and settled over the region (Fig. 3e). After sunrise, ABL growth entrained high levels of pSO4 from this parcel into the region (Fig. 3f). Therefore, stagnant polluted parcels can also lead to high ABLex-H influxes. Regional source attribution of these influxes (Supplementary Fig. S3; see Supplementary Text S3 for detailed calculation method) shows higher local contributions in E2 (27%) compared to much lower values in E1-2 (4%), further underscoring the distinct characteristics of pSO4 pollution in the two episodes. To summarize, these results demonstrate that both strong transport and high local influence (through accumulation) can result in similarly strong vertical exchange of pSO4, but through distinct mechanisms.

Despite favorable meteorological conditions for pSO4 formation, its contributions were lower in E2

Although local contributions to pSO4 were higher, comparisons of pSO4 mass budgets (Fig. 2b) indicate that the contributions of aerosol process in E2 were the lowest among all episodes, suggesting suppressed local production. This contradiction can be explained by reduced SO2 levels caused by clean southerly winds (Supplementary Table S1). While conditions favored pSO4 formation, as evidenced by a higher sulfur oxidation ratio (SOR, pSO4/(SO2 + pSO4); Supplementary Table S1), reduced SO2 availability ultimately limited the production. Therefore, on a regional scale, pSO4 pollution in E2 was primarily driven by local accumulation rather than by production.

pSO4 chemistry in the transported plumes

Analysis in the last section suggests high morning influxes of pSO4 via ABLex-H during both strong-transport and high-local-influence episodes (E1-2 and E2), though driven by contrasting transport processes. Since pSO4 can be substantially produced within transported plumes, it is essential to further investigate the different characteristics of pSO4 chemistry in these transport processes. To this end, we integrated backwards trajectories with model results to characterize pSO4 formation pathways during transport (see ‘Methods’).

Oct. 18 and Oct. 28 were selected as representative days for E1-2 and E2, respectively. To characterize the transport processes, 48-hour backward trajectories arriving at the PRD at 8:00 LT were calculated. This arrival time was chosen as it marks the onset of rapid ABL development, when pSO4 at various heights (100, 500, 1000 m) is likely mixed within the ABL and influences near-surface pollution. As illustrated in Fig. 4, the trajectories reveal distinct transport patterns under different weather conditions: On Oct. 18, typhoon peripheries induced rapid transport from the northeast, with long trajectories at all three heights (Fig. 4a). In contrast, on Oct. 28 under subtropical high, northerly transport occurred near the surface, while short, twisted, low-altitude trajectories at 500 and 1000 m reflected stagnation and even recirculation of local air masses around the PRD (Fig. 4b).

Fig. 4: 48-hour backward trajectories arriving at the PRD at 8:00 LT on representative days and variables along the trajectories.
Fig. 4: 48-hour backward trajectories arriving at the PRD at 8:00 LT on representative days and variables along the trajectories.
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a Oct. 18 and b Oct. 28. Results for trajectories arriving at the heights of 100, 500 and 1000 m are shown. Variables include (from top to bottom): (1) trajectory height (m); (2) temperature (°C); (3) relative humidity (RH, %); (4) total oxidants (Ox = O3 + NO2, ppb); and (5) sulfur oxidation ratio (SOR), pSO4/(SO2 + pSO4). Shaded areas denote nighttime periods.

Different transport processes created contrasting conditions for pSO4 production within transported plumes (Fig. 4). During E1-2, plumes were colder and dryer, whereas during E2, they were overall warmer and more humid. Under typhoon peripheries in E1-2, favorable conditions for O3 formation and enhanced downward O3 transport led to elevated Ox levels43, exceeding 80 ppb for most of the time along the trajectories. It indicates high potential for gas-phase oxidations to produce pSO4. In contrast, higher humidity during E2 likely facilitated aqueous-phase oxidations to produce pSO4.

Using the Sulfate Tracking Model (STM) module in CMAQ, we further identified the contributions of initial/boundary conditions, emission, gas-phase reaction and various aqueous-phase reaction pathways in cloud/fog water (details in Table 1) to pSO4 along the trajectories in the two episodes (Fig. 5). During E1-2, gas-phase OH oxidation was the main contributor to pSO4 in plumes arriving at 100 and 500 m, contributing nearly half of pSO4. This is consistent with elevated Ox levels along the trajectories. Background sources also played a considerable role, particularly at 1000 m, where they contributed ~53% of pSO4. pSO4 produced by aqueous-phase reactions accounted for only ~10% in plumes, mainly via H2O2 oxidation. In contrast, during E2, aqueous-phase reactions became the major source of pSO4 in plumes, contributing 40-60% at various heights, while the contribution of gas-phase oxidation was nearly negligible ( <15%). H2O2 oxidation remained the primary aqueous-phase pathway, but O3 and Fe3+/Mn2+-catalyzed oxidation also notably contributed when plumes were close to the ground. The evolution of SOR along the trajectories (Fig. 4) further supports contrasting pSO4 chemistry during two episodes: In E1-2, SOR remained moderate (0.4-0.6) on the day prior to the plumes’ arrival in the PRD, reflecting slower gas-phase production44, whereas in E2, SOR increased continuously to over 0.8, suggesting the significant role of aqueous-phase reactions. These findings reveal distinct chemical pathways dominated in-plume pSO4 formation in these episodes, underscoring how weather systems modulate meteorological conditions and oxidant availability, and thereby determine the mechanisms of pSO4 pollution.

Fig. 5: Results of pSO4 tracking along the 48-hour backward trajectories arriving in the PRD at 8:00 LT on representative days.
Fig. 5: Results of pSO4 tracking along the 48-hour backward trajectories arriving in the PRD at 8:00 LT on representative days.
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a, c Oct. 18 and b, d Oct. 28. Results for trajectories arriving at the heights of 100, 500 and 1000 m are shown. a, b display the contributions from gas-phase reaction (SGAS), aqueous-phase reactions (SAQ), direct emission (SEMIS) and background sources (SBG). c, d present the contributions of various aqueous-phase reaction pathways, including oxidations by H2O2 (SAQH2O2), O3 (SAQO3), O2 catalyzed by transition metal ions (SAQFEMN), methyl hydroperoxide (SAQMHP) and peracetic acid (SAQPAA). Definitions of these sources are given in Table 1. Shaded areas denote nighttime periods.

Table 1 pSO4 contributors tracked by CMAQ-STM
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To enhance the robustness of these conclusions, a sensitivity simulation was conducted by increasing SO2 emissions by 30%. The results, discussed in detail in Supplementary Text S4, indicate that the dominant pathways of sulfate production remain unchanged under higher SO2 availability, further highlighting the major role of weather systems and meteorological conditions in modulating sulfate production.

Discussion

Particulate sulfate (pSO4) is a major secondary inorganic component in PM2.5, yet its cross-regional transport processes and contributions to regional pollution remain insufficiently understood. Based on well-validated WRF/CMAQ simulations, we examined the dynamics and chemistry related to cross-regional pSO4 transport to the Pearl River Delta (PRD), South China. pSO4 in this region was significantly contributed by cross-regional transport, accounting for 76-88% during pollution episodes. Vertical exchange across the ABL top was identified as the main process for pSO4 import and export. Notably, strong exchange occurred in two contrasting episodes—one dominated by intense northerly transport and the other under stagnation—though through distinct mechanisms. Additionally, in-plume pSO4 chemistry differed markedly in these episodes, with the primary pSO4 formation pathway shifting from gas-phase OH oxidation in cold, dry, oxidant-rich plumes to aqueous-phase H2O2 oxidation in warm, humid plumes. These findings offer an integrated view of the dynamics and chemistry influencing cross-regional pSO4 transport to the PRD, advance our understanding of pSO4 pollution mechanisms, and support strategies for regional air quality improvement.

Building on these results, we highlight the prominent role of ABL dynamics in modulating cross-regional pSO4 transport. Our analysis shows that stagnation does not necessarily weaken pSO4 transport; instead, strong vertical exchange can still occur and aggravate regional pSO4 pollution. In this study, such exchange was linked to the residence or even recirculation of polluted air parcels, mostly in the nighttime residual layer. Since pSO4 in these parcels was not effectively removed by transport or deposition, it accumulated and contributed significantly to next-day pollution through entrainment during morning ABL development. Simultaneously, in-situ pSO4 formation was suppressed due to reduced SO2 availability. This indicates that local chemical production does not necessarily dominate pSO4 growth during stagnation; rather, accumulation and subsequent vertical exchange can also be critical drivers. The role of transport, particularly vertical exchange, should therefore not be overlooked in regional pSO4 pollution.

Considering the major contributions of cross-regional transport, chemical formation along the transport is likely critical for pSO4 pollution within the region. We found in-plume pSO4 chemistry responded strongly to weather conditions: gas-phase OH oxidation dominated during fast transport induced by typhoon peripheries, whereas aqueous-phase H2O2 oxidation served as the major pathway during slow transport under stagnation. These differences reflect the dependence of in-plume chemistry on plume environment—relatively cold, dry, oxidant-rich conditions in the former versus warmer and more humid conditions in the latter. As most existing studies focus on in-situ pSO4 chemistry, more modeling and observational efforts are required to better capture the complexities of in-plume pSO4 chemistry under varying weather systems.

Uncertainties in this study mainly arise from incomplete representation of pSO4 chemistry, as well as potential biases in SO2/pSO4 emissions and boundary-layer simulations. While further improvements in pSO4 simulations and additional vertical measurements of pSO4, ABL dynamics and key oxidants (particularly OH and aqueous-phase H2O2)23 would strengthen model evaluation, these uncertainties do not alter the main conclusions. In particular, the dominance of vertical exchange over horizontal transport is robust against plausible biases in ABL simulations, as the temporal variations of ABL height (\(\frac{\partial H}{\partial t}\) in Eq. (4)) would need to be unrealistically reduced to reverse this finding. Because sulfate production involves non-linear chemistry, future studies are needed to assess the potential influence of source apportionment method selection on quantified sulfate contributions. In addition, the lack of cloud/fog water pH in the CMAQ outputs limits an explicit assessment of its role in aqueous-phase chemistry. Addressing this limitation in future would provide a more complete understanding of in-plume pSO4 chemistry. Finally, although this study focused on a typical polluted month, investigations over longer time periods are necessary to comprehensively characterize cross-regional pSO4 transport and its impact on regional PM2.5 pollution.

From a policy perspective, we suggest that mitigating regional pSO4 pollution cannot rely solely on local emission control. Coordinated emission reductions across neighboring regions, together with continued exploration of the interactions among weather systems, meteorology, ABL dynamics and chemistry in cross-regional pSO4 transport, will be essential for the PRD and other regions strongly influenced by cross-regional transport. Given ongoing changes in pollutant emissions and potential climate-driven shifts in transport patterns, continuous evaluation of their coupled effects on sulfate pollution and its transport contributions would be critical for achieving long-term sustainable air quality improvement.

Methods

Model setup

The WRF meteorological model (version 3.2) and the CMAQ chemical transport model (version 5.0.2) were employed in this study with the same setups as in our previous studies41,42,43. Two-nested domains were designed with resolutions of 36 and 12 km (hereafter denoted as d01 and d02, respectively; Supplementary Fig. S4a), and simulations within d02 were used to investigate pSO4 pollution and processes in the PRD. The simulation period spanned Oct. 1 to Nov. 10, 2015, with the initial ten days (Oct. 1-10) used as the spin-up period and excluded from analysis. The WRF simulation setups, including physics options and data inputs, are provided in Supplementary Table S2. Specifically, the Asymmetric Convective Model version 2 (ACM2) boundary-layer scheme45 was selected to ensure consistency with vertical mixing scheme implemented in CMAQ. Chemical initial and boundary conditions for d01 were derived from MOZART-4 outputs46 for the same period. Multiple anthropogenic emission inventories were used for this study, including the localized PRD inventory from the Guangdong Environmental Monitoring Centre, the Multi-resolution Emission Inventory for China (MEIC) for mainland China47,48, the MIX inventory for other Asian regions49 and East Asian shipping emission inventory50. Biogenic emissions were estimated using the Model of Emissions of Gases and Aerosols from Nature51 (MEGAN, version 2.10). For chemical mechanisms, we selected SAPRC0752 for gas-phase chemistry and AERO6 for aerosol processes. Further details on the model setup are available in our previous publication43.

We also thoroughly evaluated the model’s performance in simulating PM2.5 pollution in the PRD, with complete evaluations available in Supplementary Text S5. Overall, the model showed an acceptable performance, and particularly, PM2.5 and pSO4 concentrations in the PRD were slightly underestimated by 22% and 17%, respectively, with high correlations ( > 0.6) with observations (Fig. 1a, Supplementary Fig. S5). The overall satisfactory performance in simulating pSO4 indicates that the current chemistry implemented in the model is adequate for investigating pSO4 pollution and related processes, which has also been supported by previous studies in this region53,54.

pSO4 source apportionment

This study identified three source contributions to pSO4: local, regional and background (Supplementary Fig. S4b). Local and regional sources separately refer to d02 emissions within and outside of the PRD, and background sources represent sources outside of d02 (i.e., boundary conditions in the d02 simulations). The contribution of cross-regional transport, or “transport contribution”, is equivalent to the sum of regional and background contributions.

We applied the Brute Force method55 (top-down) to quantify these contributions to pSO4 in the PRD, which estimates a source’s influence as the difference in the simulation results with and without emissions from that source. Three simulation cases were performed for source apportionment:

  • Base case, with all emissions included in the simulation;

  • No_PRD case, with emissions within the PRD zeroed out;

  • No_emis case, with all emissions within d02 zeroed out.

Let \({F}_{{base}}\), \({F}_{{no\_PRD}}\) and \({F}_{0}\) denote the simulated pSO4 concentrations in these three cases, respectively. Then, the contributions of local (\({f}_{{local}}\)), regional (\({f}_{{regional}}\)) and background (\({f}_{{bg}}\)) sources are calculated as follows:

$${f}_{{local}}={F}_{{base}}-{F}_{{no\_PRD}}$$
(1)
$${f}_{{regional}}={F}_{{no\_PRD}}-{F}_{0}$$
(2)
$${f}_{{bg}}={F}_{0}$$
(3)

Budget analysis

Here, we quantified the hourly pSO4 mass budget within the atmospheric boundary layer (ABL) of the PRD using WRF/CMAQ outputs (including simulated gridded meteorological variables, pSO4 concentrations and integrated process rates (IPRs) for pSO4) and following the method in our previous study41. The pSO4-related processes concerned in this study include:

  • Horizontal transport, classified by the segment of the PRD border (north, south, west and east; Supplementary Fig. S6), crossed by the air parcels.

  • Vertical exchange across the ABL top, driven by diurnal variations in ABL height (denoted as ABLex-H) and by advections perpendicular to the ABL top and slopes (denoted as ABLex-A). For a given model grid, the total vertical exchange fluxes of pSO4 (\({F}_{{ABLex}}\)) can be generally quantified by:

    $${F}_{{ABLex}}={F}_{{ABLex}-H}+{F}_{{ABLex}-A}={c}_{h}\frac{\partial H}{\partial t}{Sdt}+{c}_{h}\left({u}_{h}\frac{\partial H}{\partial x}+{v}_{h}\frac{\partial H}{\partial y}-{w}_{h}\right){Sdt}$$
    (4)

    Here, \({c}_{h}\) indicates pSO4 concentrations near the ABL top; H is the ABL height; S is the area of the grid; \({u}_{h}\), \({v}_{h}\) and \({w}_{h}\) separately indicate ABL-top wind speeds in the x, y and z direction.

  • Other processes, including aerosol process, cloud process, emission and dry deposition. Particularly, aerosol process includes gas-particle partitioning, particle formation and growth56, and generally represents an important process for the evolution of aerosol species. Cloud process encompasses aqueous reactions, wet deposition, and mixing within and below clouds56.

Additional details on these processes and the method of budget calculations are available in our previous publications41,42. Quantified hourly net contributions from various processes to pSO4 mass align well with simulated pSO4 mass variations (Supplementary Fig. S7), suggesting budget closure and thereby enabling further analysis based on the calculated pSO4 mass budget.

Sulfate tracking

The Sulfate Tracking Model57,58 (STM), integrated into CMAQ, was utilized to quantify the contributions of various sources to pSO4 concentrations. Further details on the pSO4 contributors tracked by STM are listed in Table 1.

Investigating pSO4 processes in the transported plumes

To investigate pSO4-related processes within transported plumes, we applied the method outlined in a previous study29, with the workflow illustrated in Supplementary Fig. S8. Backward trajectories of plume arriving at the Modiesha site in the central PRD were derived based on the WRF outputs, the “arw2arl” conversion tool and the Hysplit trajectory model59. To examine variations in plumes arriving at different altitudes of the ABL, trajectories were generated at three arrival heights: 100 m, 500 m and 1000 m. Along these trajectories, we extracted meteorological variables, pollutant concentrations, STM results and other relevant parameters from the model outputs for detailed analysis.