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Efficient control of atmospheric sulfate production based on three formation regimes


The formation of sulfate (SO42−) in the atmosphere is linked chemically to its direct precursor, sulfur dioxide (SO2), through several key oxidation paths for which nitrogen oxides or NOx (NO and NO2) play essential roles. Here we present a coherent description of the dependence of SO42– formation on SO2 and NOx under haze-fog conditions, in which fog events are accompanied by high aerosol loadings and fog-water pH in the range of 4.7–6.9. Three SO42– formation regimes emerge as defined by the role played by NOx. In the low-NOx regime, NOx act as catalyst for HOx, which is a major oxidant for SO2, whereas in the high-NOx regime, NO2 is a sink for HOx. Moreover, at highly elevated NOx levels, a so-called NO2-oxidant regime exists in which aqueous NO2 serves as the dominant oxidant of SO2. This regime also exists under clean fog conditions but is less prominent. Sensitivity calculations using an emission-driven box model show that the reduction of SO42– is comparably sensitive to the reduction of SO2 and NOx emissions in the NO2-oxidant regime, suggesting a co-reduction strategy. Formation of SO42− is relatively insensitive to NOx reduction in the low-NOx regime, whereas reduction of NOx actually leads to increased SO42– production in the intermediate high-NOx regime.

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Fig. 1: Pairs of ambient SO2 and NO2 concentrations observed worldwide.
Fig. 2: Simulated SO42− production rates as a function of NOx and SO2 emission rates under haze-fog conditions at an aqueous phase pH of 5.6.
Fig. 3: Simulated SO42− production as a function of NOx and SO2 emission rates under clean-fog conditions at an aqueous phase pH of 4.7.
Fig. 4: Predicted reduction of the SO42− production rate in response to 1% reduction of NOx or SO2 emissions.

Data availability

The datasets generated during and/or analysed during the current study are available at

Code availability

The computer code used to generate the results in this manuscript is available from the corresponding authors on request.


  1. 1.

    Stein, A. F. & Lamb, D. Chemical indicators of sulfate sensitivity to nitrogen oxides and volatile organic compounds. J. Geophys. Res. 107, 13–11 (2002).

    Article  Google Scholar 

  2. 2.

    Stein, A. F. & Lamb, D. Empirical evidence for the low- and high-NOx photochemical regimes of sulfate and nitrate formation. Atmos. Environ. 37, 3615–3625 (2003).

    Article  Google Scholar 

  3. 3.

    Tao, J., Zhang, L. M., Cao, J. J. & Zhang, R. J. A review of current knowledge concerning PM2.5 chemical composition, aerosol optical properties and their relationships across China. Atmos. Chem. Phys. 17, 9485–9518 (2017).

    Article  Google Scholar 

  4. 4.

    Wang, J. D. et al. Particulate matter pollution over China and the effects of control policies. Sci. Total Environ. 584, 426–447 (2017).

    Article  Google Scholar 

  5. 5.

    Yang, S. et al. Characteristics and formation of typical winter haze in Handan, one of the most polluted cities in China. Sci. Total Environ. 613, 1367–1375 (2018).

    Article  Google Scholar 

  6. 6.

    Lu, C. S. et al. Chemical composition of fog water in Nanjing area of China and its related fog microphysics. Atmos. Res. 97, 47–69 (2010).

    Article  Google Scholar 

  7. 7.

    Wang, G. H. et al. Persistent sulfate formation from London fog to chinese haze. Proc. Natl Acad. Sci. USA 113, 13630–13635 (2016).

    Article  Google Scholar 

  8. 8.

    Ronald, J. V. et al. Cleaning up the air: effectiveness of air quality policy for SO2 and NOx emissions in China. Atmos. Chem. Phys. 17, 1775–1789 (2017).

    Article  Google Scholar 

  9. 9.

    Shen, X. J. et al. Characterization of submicron aerosols and effect on visibility during a severe haze-fog episode in Yangtze River Delta, China. Atmos. Environ. 120, 307–316 (2015).

    Article  Google Scholar 

  10. 10.

    Cheng, Y. F. et al. Reactive nitrogen chemistry in aerosol water as a source of sulfate during haze events in China. Sci. Adv. 2, e1601530 (2016).

    Article  Google Scholar 

  11. 11.

    Xue, J., Yuan, Z. B., Yu, J. Z. & Lau, A. K. H. An observation-based model for secondary inorganic aerosols. Aerosol Air Qual. Res. 14, 862–882 (2014).

    Article  Google Scholar 

  12. 12.

    Xie, Y. N. et al. Enhanced sulfate formation by nitrogen dioxide: implications from in situ observations at the SORPES station. J. Geophys. Res. Atmos. 120, 12679–12694 (2015).

    Article  Google Scholar 

  13. 13.

    Xue, J. et al. Sulfate formation enhanced by a cocktail of high NOx, SO2, particulate matter, and droplet pH during haze-fog events in megacities in China: an observation-based modeling investigation. Environ. Sci. Technol. 50, 7325–7334 (2016).

    Article  Google Scholar 

  14. 14.

    Hagler, G. S. et al. Source areas and chemical composition of fine particulate matter in the Pearl River Delta region of China. Atmos. Environ. 40, 3802–3815 (2006).

    Article  Google Scholar 

  15. 15.

    Pathak, R. K., Wu, W. S. & Wang, T. Summertime PM2.5 ionic species in four major cities of China: nitrate formation in an ammonia-deficient atmosphere. Atmos. Chem. Phys. 9, 1711–1722 (2009).

    Article  Google Scholar 

  16. 16.

    Wang, Y. et al. The ion chemistry and the source of PM2.5 aerosol in Beijing. Atmos. Environ. 39, 3771–3784 (2005).

    Article  Google Scholar 

  17. 17.

    Tian, Y. Z. et al. Spatial, seasonal and diurnal patterns in physicochemical characteristics and sources of PM2.5 in both inland and coastal regions within a megacity in China. J. Hazard Mater. 342, 139–149 (2018).

    Article  Google Scholar 

  18. 18.

    Li, P. F. et al. Fog water chemistry in Shanghai. Atmos. Environ. 45, 4034–4041 (2011).

    Article  Google Scholar 

  19. 19.

    Wu, D. et al. Study on the chemical characteristics of polluting fog in Guangzhou area in spring. J. Trop. Meteorol. 15, 68–72 (2009).

    Google Scholar 

  20. 20.

    Benedict, K. B., Lee, T. & Collett, J. L. Cloud water composition over the southeastern Pacific Ocean during the VOCALS regional experiment. Atmos. Environ. 46, 104–114 (2012).

    Article  Google Scholar 

  21. 21.

    Sillman., S. The relation between ozone, NOx and hydrocarbons in urban and polluted rural environment. Atmos. Environ. 33, 1821–1845 (1999).

    Article  Google Scholar 

  22. 22.

    Wennberg, P. O. Let’s abandon the “high NOx” and “low NOx” terminology. IGACnews 50, 3–4 (2013).

    Google Scholar 

  23. 23.

    Straub, D. J., Hutchings, J. W. & Herckes, P. Measurements of fog composition at a rural site. Atmos. Environ. 47, 195–205 (2012).

    Article  Google Scholar 

  24. 24.

    Meng, Z. Y. et al. Vertical distributions of SO2 and NO2 in the lower atmosphere in Beijing urban areas, China. Sci. Total Environ. 390, 456–465 (2008).

    Article  Google Scholar 

  25. 25.

    Liu, M. X. et al. Fine particle pH during severe haze episodes in northern China. Geophys. Res. Lett. 44, 5213–5221 (2017).

    Article  Google Scholar 

  26. 26.

    Clifton, C. L., Altstein, N. & Huie, R. E. Rate-constant for the reaction of NO2 with sulfur(iv) over the pH range 5.3–13. Environ. Sci. Technol. 22, 586–589 (1988).

    Article  Google Scholar 

  27. 27.

    He, P. Z. et al. Isotopic constraints on heterogeneous sulfate production in Beijing haze. Atmos. Chem. Phys. 18, 5515–5528 (2018).

    Article  Google Scholar 

  28. 28.

    Gao, M. et al. Improving simulations of sulfate aerosols during winter haze over northern China: the impacts of heterogeneous oxidation by NO2. Front. Environ. Sci. Eng. 10, 16 (2016).

    Article  Google Scholar 

  29. 29.

    Li, M. M. et al. Formation and evolution mechanisms for two extreme haze episodes in the Yangtze River Delta region of China during winter 2016. J. Geophys. Res. Atmos. 124, 3607–3623 (2019).

    Article  Google Scholar 

  30. 30.

    Huang, L. et al. Enhanced sulfate formation through SO2 + NO2 heterogeneous reactions during heavy winter haze in the Yangtze River Delta region, China. Atmos. Chem. Phys. Diss. (2019).

  31. 31.

    Lee, Y. N. & Schwartz, S. E. Kinetics of oxidation of aqueous sulfur(iv) by nitrogen dioxide. In Proc. 4th International Conference, Santa Monica, California (eds Pruppacher, H. R. et al.) Vol. 1 (Elsevier, 1982).

  32. 32.

    Shen, C. H. & Rochelle, G. T. Nitrogen dioxide absorption and sulfite oxidation in aqueous sulfite. Environ. Sci. Technol. 32, 1994–2003 (1998).

    Article  Google Scholar 

  33. 33.

    Warneck, P. The relative importance of various pathways for the oxidation of sulfur dioxide and nitrogen dioxide in sunlit continental fair weather clouds. Phys. Chem. Chem. Phys. 1, 5471–5483 (1999).

    Article  Google Scholar 

  34. 34.

    Fairlie, T. D. et al. Impact of mineral dust on nitrate, sulfate, and ozone in transpacific asian pollution plumes. Atmos. Chem. Phys. 10, 3999–4012 (2010).

    Article  Google Scholar 

  35. 35.

    Trebs, I. et al. Relationship between the NO2 photolysis frequency and the solar global irradiance. Atmos. Meas. Tech. 2, 725–739 (2009).

    Article  Google Scholar 

  36. 36.

    Bott, A. & Carmichael, G. R. Multiphase chemistry in a microphysical radiation fog model—a numerical study. Atmos. Environ. 27, 503–522 (1993).

    Article  Google Scholar 

  37. 37.

    Herckes, P., Chang, H., Lee, T. & Collett, J. L. Air pollution processing by radiation fogs. Water Air Soil Poll. 181, 65–75 (2007).

    Article  Google Scholar 

  38. 38.

    Robert, M. A., Kleeman, M. J. & Jakober, C. A. Size and composition distributions of particulate matter emissions: part 2—heavy-duty diesel vehicles. J. Air Waste Manag. Assoc. 57, 1429–1438 (2012).

    Article  Google Scholar 

  39. 39.

    Wild, R. J. et al. On-road measurements of vehicle NO2/NOx emission ratios in Denver, Colorado, USA. Atmos. Environ. 148, 182–189 (2017).

    Article  Google Scholar 

  40. 40.

    Tan, Z. F. et al. Wintertime photochemistry in Beijing: observations of ROx radical concentrations in the north China plain during the BEST-ONE campaign. Atmos. Chem. Phys. 18, 12391–12411 (2018).

    Article  Google Scholar 

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This study was supported in part by the Research Grants Council of Hong Kong (grant nos. 615406 and 16122017). We acknowledge air quality data from the Atmospheric Research Center, Institute of Environment at HKUST.

Author information




J.X. and X.Y. contributed equally to this work. J.X., X.Y., and J.Z.Y. conceived the regime framework describing SO42– formation. X.Y. and J.X. performed model simulations. A.K.H.L and Z.B.Y. were instrumental in starting the project. J.X., X.Y., Z.B.Y, S.M.G., J.Z.Y. and J.H.S. wrote the manuscript.

Corresponding authors

Correspondence to John H. Seinfeld or Jian Zhen Yu.

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The authors declare no competing interests.

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Peer review information Primary Handling Editor(s): Xujia Jiang

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Supplementary Figs. 1–11 and Tables 1–11

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Xue, J., Yu, X., Yuan, Z. et al. Efficient control of atmospheric sulfate production based on three formation regimes. Nat. Geosci. 12, 977–982 (2019).

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