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Air quality and visibility are strongly influenced by aerosolloading, which is driven by meteorological conditions. The quantification oftheir relationships is critical to understanding the physical and chemicalprocesses and forecasting of the polluted events. We investigated andquantified the relationship between PM2.5 (particulate matter withaerodynamic diameter is 2.5 µm and less) mass concentration, visibilityand planetary boundary layer (PBL) height in this study based on the dataobtained from four long-lasting haze events and seven fog–haze mixed eventsfrom January 2014 to March 2015 in Beijing. The statistical results showthat there was a negative exponential function between the visibility and thePM2.5 mass concentration for both haze and fog–haze mixed events (withthe same R2 of 0.80). However, the fog–haze events caused a moreobvious decrease of visibility than that for haze events due to the formationof fog droplets that could induce higher light extinction. The PM2.5concentration had an inversely linear correlation with PBL height for hazeevents and a negative exponential correlation for fog–haze mixed events,indicating that the PM2.5 concentration is more sensitive to PBL heightin fog–haze mixed events. The visibility had positively linear correlationwith the PBL height with an R2 of 0.35 in haze events and positiveexponential correlation with an R2 of 0.56 in fog–haze mixed events.We also investigated the physical mechanism responsible for theserelationships between visibility, PM2.5 concentration and PBL heightthrough typical haze and fog–haze mixed event and found that a doubleinversion layer formed in both typical events and played critical roles inmaintaining and enhancing the long-lasting polluted events. The variationsof the double inversion layers were closely associated with the processes oflong-wave radiation cooling in the nighttime and short-wave solarradiation reduction in the daytime. The upper-level stable inversion layerwasformed by the persistent warm and humid southwestern airflow, while thelow-level inversion layer was initially produced by the surface long-waveradiation cooling in the nighttime and maintained by the reduction ofsurface solar radiation in the daytime. The obvious descending process of theupper-level inversion layer induced by the radiation process could beresponsible for the enhancement of the low-level inversion layer and thelowering PBL height, as well as high aerosol loading for these pollutedevents. The reduction of surface solar radiation in the daytime could bearound 35 % for the haze event and 94 % for the fog–haze mixed event.Therefore, the formation and subsequent descending processes of theupper-level inversion layer should be an important factor in maintaining andstrengthening the long-lasting severe polluted events, which has not beenrevealed in previous publications. The interactions and feedbacks betweenPM2.5 concentration and PBL height linked by radiation process caused amore significant and long-lasting deterioration of air quality andvisibility in fog–haze mixed events. The interactions and feedbacks of allprocesses were particularly strong when the PM2.5 mass concentration waslarger than 150–200 µg m−3

atmospheric chemistry and physics

Quantifying the relationship between PM&amp;lt;sub&amp;gt;2.5&amp;lt;/sub&amp;gt; concentration, visibility and planetary boundary layer height for long-lasting haze and fog–haze mixed events in Beijing