Quantifying the relationship between PM 2 . 5 concentration , visibility and planetary boundary layer height for long-lasting haze and fog – haze mixed events in Beijing

Air quality and visibility are strongly influenced by aerosol loading, which is driven by meteorological conditions. The quantification of their relationships is critical to understanding the physical and chemical processes and forecasting of the polluted events. We investigated and quantified the relationship between PM2.5 (particulate matter with aerodynamic diameter is 2.5 μm and less) mass concentration, visibility and planetary boundary layer (PBL) height in this study based on the data obtained from four long-lasting haze events and seven fog–haze mixed events from January 2014 to March 2015 in Beijing. The statistical results show that there was a negative exponential function between the visibility and the PM2.5 mass concentration for both haze and fog–haze mixed events (with the same R2 of 0.80). However, the fog–haze events caused a more obvious decrease of visibility than that for haze events due to the formation of fog droplets that could induce higher light extinction. The PM2.5 concentration had an inversely linear correlation with PBL height for haze events and a negative exponential correlation for fog–haze mixed events, indicating that the PM2.5 concentration is more sensitive to PBL height in fog–haze mixed events. The visibility had positively linear correlation with the PBL height with an R2 of 0.35 in haze events and positive exponential correlation with an R2 of 0.56 in fog– haze mixed events. We also investigated the physical mechanism responsible for these relationships between visibility, PM2.5 concentration and PBL height through typical haze and fog–haze mixed event and found that a double inversion layer formed in both typical events and played critical roles in maintaining and enhancing the long-lasting polluted events. The variations of the double inversion layers were closely associated with the processes of long-wave radiation cooling in the nighttime and short-wave solar radiation reduction in the daytime. The upper-level stable inversion layer was formed by the persistent warm and humid southwestern airflow, while the low-level inversion layer was initially produced by the surface long-wave radiation cooling in the nighttime and maintained by the reduction of surface solar radiation in the daytime. The obvious descending process of the upper-level inversion layer induced by the radiation process could be responsible for the enhancement of the lowlevel inversion layer and the lowering PBL height, as well as high aerosol loading for these polluted events. The reduction of surface solar radiation in the daytime could be around 35 % for the haze event and 94 % for the fog–haze mixed event. Therefore, the formation and subsequent descending processes of the upper-level inversion layer should be an important factor in maintaining and strengthening the longlasting severe polluted events, which has not been revealed in previous publications. The interactions and feedbacks between PM2.5 concentration and PBL height linked by radiation process caused a more significant and long-lasting dePublished by Copernicus Publications on behalf of the European Geosciences Union. 204 T. Luan et al.: Quantifying the relationship between PM2.5 concentration terioration of air quality and visibility in fog–haze mixed events. The interactions and feedbacks of all processes were particularly strong when the PM2.5 mass concentration was larger than 150–200 μg m−3.

PM 2.5 concentration and PBL height through typical haze and fog-haze mixed event and found that a double inversion layer formed in both typical events and played critical roles in maintaining and enhancing the long-lasting polluted events.The variations of the double inversion layers were closely associated with the processes of long-wave radiation cooling in the nighttime and short-wave solar radiation reduction in the daytime.The upper-level stable inversion layer was formed by the persistent warm and humid southwestern airflow, while the low-level inversion layer was initially produced by the surface long-wave radiation cooling in the nighttime and maintained by the reduction of surface solar radiation in the daytime.The obvious descending process of the upper-level inversion layer induced by the radiation process could be responsible for the enhancement of the lowlevel inversion layer and the lowering PBL height, as well as high aerosol loading for these polluted events.The reduction of surface solar radiation in the daytime could be around 35 % for the haze event and 94 % for the fog-haze mixed event.Therefore, the formation and subsequent descending processes of the upper-level inversion layer should be an important factor in maintaining and strengthening the longlasting severe polluted events, which has not been revealed in previous publications.The interactions and feedbacks between PM 2.5 concentration and PBL height linked by radiation process caused a more significant and long-lasting de-

Introduction
Due to rapid economic development, haze and fog events characterized by the high fine particulate matter (i.e.PM 2.5 , particulate matter with aerodynamic diameter is 2.5 µm and less) levels have occurred during the last few decades in China, especially in the most developed and highly populated cities (Chan and Yao, 2008;Zhang et al., 2013;Huang et al., 2014;Zhang and Cao, 2015).For instance, in January 2013, Beijing (and all of inland China) suffered under extremely severe and persistent haze and fog pollution, registering the highest PM 2.5 hourly concentration of 886 µg m −3 (Zhang et al., 2013(Zhang et al., , 2014;;H. Wang et al., 2014).The high frequency of extremely severe and persistent haze and fog events in China leads to great public concern over poor visibility, adverse health effects (Tie et al., 2009;Chen et al., 2013;Pope and Dockery, 2013;Di et al., 2017) and climate change impacts (Qian et al., 2006;Liao et al., 2015).
Aerosol particles and fog droplets are responsible for the reduction of visibility by scattering and absorbing light, according to their number and properties, such as size, shape and chemical composition.Atmospheric humidity is a major factor affecting the particle properties, as aerosols can grow by the uptake of water.When relative humidity (RH) is larger than 95 %, the atmospheric visibility can be critically reduced (Chen et al., 2012).When RH is larger than 100 %, some of the hygroscopic aerosols can be activated and form fog droplets (Pruppacher and Klett, 1978).The sudden increase in particle size causes a sharp drop in visibility, usually to distances below 1000 m (Elias et al., 2009).Baumer et al. (2008) found that the visibility decrease was associated with a continuous increase in the number size distribution of particles with diameters larger than 300 nm in southwest Germany.Particles have grown into a size interval in which their diameter is of the same order as the wavelength of the visible light, which leads to a more effective light scattering.Therefore, the visibility should decrease.
Large emission sources emit primary aerosols and the precursors of secondary aerosols, resulting in high loads of aerosols (i.e.sulfate, nitrate, ammonium, black carbon, organic carbon, dust) (Zhang et al., 2009(Zhang et al., , 2012(Zhang et al., , 2013)).This is the main reason for the deterioration of visibility and frequent haze events through light extinction (Cao et al., 2012;Han et al., 2016).During the haze periods, the concentration of particulate matter is much higher than that on normal days, and fine-mode aerosols are predominant (Quan et al., 2011;Zhang and Cao, 2015).Han et al. (2016) found that the 71 ± 17 % of PM 10 was PM 2.5 in Beijing and the increasing of PM 2.5 contributed significantly to visibility impairment.
In addition, the interactions between aerosol pollution and climate change have been substantially addressed in recent publications, for example anthropogenic climate change (Cai et al., 2017), reduced Arctic sea ice (Wang et al., 2015;Zou et al., 2017), the Tibetan Plateau warming (Xu et al., 2016), influences of ENSO events on haze frequency in eastern China (Gao and Li, 2015), weakened East Asian winter monsoon (Li et al., 2016), decadal weakening of winds (Yang et al., 2016) and enhanced thermal stability of the lower atmosphere (Zhang et al., 2014;Chen and Wang, 2015).Dustwind interaction (Yang et al., 2017a) and upwind transport (Yang et al., 2017b) could also intensify haze events in China.
Fog and haze events usually occur in the stable planetary boundary layer (PBL), which is located at the lowest atmospheric layer and strongly influenced by the exchange of momentum, heat and water vapour at the earth's surface.Many previous publications showed that fog and haze events were usually formed in a weak high-pressure system with low surface wind, which was unfavourable for air mixing and pollutants diffusion (Liu et al., 2007;Kang et al., 2013; X.J. Zhao et al., 2013; G. J. Zheng et al., 2015).The aerosols directly emitted from polluted source and those secondly formed might be concentrated in the PBL, resulting in high concentrations near the surface.Sun et al. (2013) suggested that the PM 2.5 distribution depicted a "higher-bottom and lower-top" pattern based on the observation of the 325 m tower in Beijing.Zhang and Cao (2015) showed that the PM 2.5 concentration at night was about 2 times higher than that in the afternoon.The lowest concentrations were observed in afternoon hours when the PBL height became larger and wind speed increased.Many studies also found that the diurnal variation of the pollutants was anticorrelated with the diurnal variation of PBL height (Chou et al., 2007;Boyouk et al., 2010).Yang et al. (2013) indicated that one of the possible factors leading to the deteriorated air quality in Hong Kong was the decreasing trend of the daily maximum mixing layer height based on 6.5 years measurements.
Interactions between aerosols, radiation and atmospheric boundary layer structure are very complex processes and still uncertain in many aspects.Aerosols such as black carbon can strongly absorb solar radiation and modify the vertical profile of temperature in the atmosphere and stabilise the PBL structure (Ding et al., 2016).The accumulation of aerosols in the PBL can lead to a more stable atmosphere.Analysis of a heavy pollution episode in fall 2004 over northern China showed that the instantaneous irradiance at the surface decreased by about 350 W m −2 and the atmospheric solar heating was about 300 W m −2 ; therefore, a more stable atmosphere was expected (Liu et al., 2007).Quan et al. (2013) found that the heat flux of surface and PBL height in haze condition were significantly lower than that under clear sky conditions and proposed that the feedback might exist between PBL height and aerosol loading.The enhancement of aerosols tends to depress the development of PBL by decreasing solar radiation, while the repressed structure of PBL will in turn weaken the diffusion of pollutants, leading to the heavy pollution.
The model results from Gao et al. (2015) showed that during the fog and haze mixed event over the North China Plain, aerosols led to a significant negative radiation forcing at the surface and a large positive radiation forcing in the atmosphere and induced significant changes in meteorological variables in daytime.As a result, the atmosphere was much more stable and thus the surface wind speed decreased and the PBL height decreased.The maximum increase of hourly surface PM 2.5 concentration was 50 µg m −3 over Beijing.J. Wang et al. (2014) implied that the interaction between aerosol and radiation played an important role in the haze episode in January 2013 from simulated results by WRF-CMAQ.Petäjä et al. (2016) showed that aerosolboundary layer feedback remained moderate at fine particular matter concentrations lower than 200 µg m −3 but that it became increasingly effective at higher particular matter loadings due to the combined effect of high surface particular emissions and massive secondary particular matter production within boundary layer.
The influence of convective mixing on the air quality has been recognised for decades, yet data showing this phenomenon remain rather limited for the lack of temporal resolution in the PBL height measurement.The development and application of lidar have made such an investigation possible.The lidar technique has provided a useful tool to investigate cloud and aerosol properties with high temporal resolution in the atmosphere (Welton et al., 2002;Y. W. Zhang et al., 2015).It is also known to be suitable for studying the PBL and its evolution (Yan et al., 2013;Zhang et al., 2016).Micro Pulse Lidar (MPL) systems were used to measure aerosol properties during the Indian Ocean Experiment (IN-DOEX) 1999 field phase (Welton et al., 2000(Welton et al., , 2002)).Chen et al. (2001) observed seasonal changes of the mixing layer height in Japan by using the MPL.He et al. (2008) analysed aerosol vertical distribution in the lower troposphere by examining the aerosol extinction profiles derived from MPL measurements in Hong Kong.Yang et al. (2013) analysed the diurnal, seasonal and interannual variation of PBL height from a 6.5-year lidar data set over Hong Kong.Y. W. Zhang et al. (2015) showed the evolution of aerosol vertical distribution and the PBL height during the haze events in Shanghai.
Although there have been many theoretical and observational studies on the characteristics of PM 2.5 concentration, visibility and PBL height as well as their correlations, quantitative investigations on their relationship for long-lasting haze and fog-haze mixed events are few.The feedback mechanism between PM 2.5 concentration and PBL height has not been well understood.Since 2013, a comprehensive field campaign on haze and fog-haze mixed events has been conducted in northern China.State-of-the-art instruments such as MPL, ceilometer (CL31), profiling microwave radiometer (PMWR) and particulate monitor as well as some conventional meteorological instruments have been used in this field campaign.The data were acquired during the longlasting pollutant events from January 2014 to March 2015.In this study, the relationship between PM 2.5 , visibility and PBL height for both haze and fog-haze mixed events was investigated and quantified.The physical mechanism responsible for their relationships and feedbacks were also investigated and discussed.

Observational site and instruments
The observational site is located at the campus of China Meteorological Administration (CMA) (39 • 57 N, 116 • 20 E) in Beijing, northern China.It was built on the roof of a 20 m tall building in the year 2013, located in the northwest part of urban Beijing, close to the West 3rd Ring Road, without any major sources nearby.Data used in this study include the mass concentration of PM 2.5 , visibility and the PBL height obtained from the ceilometer as well as the temperature, RH, water vapour and liquid profiles retrieved by PMWR.The vertical profiles of aerosol in the troposphere and the PBL height were also obtained from a ground-based MPL installed in a working container 10 m from the building at the campus of CMA.The meteorological parameters (surface wind, ambient temperature and RH) were obtained from Haidian automatic weather station.Radiosonde sounding data (twice a day at 08:00 and 20:00 BST, Beijing standard time) and daily radiation data were obtained from Beijing Meteorological Administration station (39 • 56 N, 116 • 17 E; station no.54 511).These measurement sites are located within 30 km each other, as shown in Fig. 1.NCEP FNL (Final) Operational Global Analysis data were used to analyse the meteorological factors and weather patterns.The data on 1 The peak value of the optical energy of laser beam is 10 µJ.The pulse duration was set to 100 ns, and the pulse interval was set to 200 ns, corresponding to a vertical resolution of 30 m.Before processing the lidar data, the raw signal needed correction including optical overlap, afterpulse, dead time and background noise correction (Campbell et al., 2002(Campbell et al., , 2008)).Then the aerosol optical properties can be retrieved by the lidar equations using Fernald's algorithm (Fernald, 1984).The lidar signal is not available in the first hundred metres because of the afterpulse effect.The lowest sounding height was set to 100 m.
The ceilometer used in this study is a Vaisala CL31 model, described in detail in Münkel and Räsänen (2004) and Münkel et al. (2007).In brief, CL31 is equipped with an indium gallium arsenide/metal-organic chemical vapour deposition (InGaAs/MOCVD) pulsed diode laser emitting at 905 ± 10 nm with energy per pulse of 1.2 µJ ± 20 %.The emission frequency is 10 kHz, while the pulse duration is 110 ns.According to the Vaisala ceilometer CL31 User's Guide (2009), the full overlap of the instrument is achieved for altitudes higher than 10 m, although in practice on the order of 70 m (Martucci et al., 2010).The attenuated backscatter coefficient is obtained from 10 to 7500 m height, with a selectable spatial resolution of 5 or 10 m and temporal resolution of 2 to 120 s.In this study, we used 10 m raw range resolution and 16 s raw temporal resolution.This temporal resolution was deemed sufficient for analysing the development of PBL structure.Apart from the very strong backscatter from clouds and fogs, the weaker gradients of the backscatter intensity were mainly determined by the number and the size spectrum of aerosol particles suspending in the air.
TEOM 1405-DF particulate monitor (Tapered Element Oscillating Microbalance, Thermo Fisher Scientific, USA) was used to continuously measure particulate matter mass concentration.According to the TEOM 1405-DF Operating Guide (2009), the monitor draws ambient air through two TEOM filters at a constant flow rate, continuously weighing the filters and calculating near-real-time mass concentrations of both PM 2.5 and PM coarse (2.5 µm < particulate matter with aerodynamic diameter < = 10 µm).By adding these two values, the PM 10 mass concentration is obtained.The FDMS unit dries the sample flow and automatically generates mass concentration measurement that account for both nonvolatile and volatile particulate matter components.The volatile faction of the collected sample is automatically compensated by using a switching valve to change the path of the fine and coarse sample flows every 6 min.The filters were replaced when the filter loading percentage nears 100 %.
The profiling microwave radiometer (PMWR-3069A, Radiometrics Co., USA) collects atmospheric radiation measurements in the 20 to 200 GHz region to retrieve temper-ature, RH, water vapour and liquid profiles.The temperature profiling subsystem utilises sky brightness temperature observations at selected frequencies between 51 and 59 GHz.The water vapour profiling subsystem utilises sky brightness temperature observations at selected frequencies between 22 and 30 GHz.The water vapour channels are calibrated by means of tipping curves; the temperature channels are calibrated by a liquid nitrogen cold target.The temperature, RH, vapour density and liquid water content (LWC) profiles in this study are retrieved from PMWR measurements at zenith direction.The temporal resolution is 2-3 min, and the vertical resolutions are 50 m from the surface to 500 m, 100 m from 500 to 2000 m and 250 m from 2000 to 10 000 m.The accuracy of PMWR profiles is compatible with most meteorology applications, especially in the lower troposphere (Cimini et al., 2011;Ware et al., 2013;Gultepe et al., 2015).
The visibility sensor (PWD20, Vaisala Co., Finland) with a range of 10-20 000 m was employed to monitor atmospheric visibility.

Determination of the PBL height
The PBL height is determined at the altitude where a sudden decrease in the scattering coefficient occurs.In this paper, we used the wavelet covariance transform method by Brooks (2003) to inverse the PBL height by MPL, which is based on scanning the backscatter profile with a localised impulse function and maximising the covariance between the backscatter profile and impulse function.A step function Haar wavelet is defined as Eq.(1): where z is altitude, b is the location at which the Harr function is centred and a is the spatial extent of the function.The covariance transformation of the Haar function (W f ) is calculated by Eq. ( 2): where f (z) is the signal of the MPL backscatter profile and z b and z t are the lower and upper limits of the profile.
Ceilometer is a robust, low-power, low-cost and lowmaintenance lidar designed to determine the cloud base height but also provide the backscatter profile, though with less sensitivity than a lidar.Several studies have proposed that ceilometer-measured backscatter profiles can be used to derive the PBL height (Eresmaa et al., 2006(Eresmaa et al., , 2012;;Münkel, 2007;Haeffelin et al., 2012;Schween et al., 2014).A "structure of the atmosphere" (STRAT-2D) algorithm was selected for estimating the PBL height, which has been proposed in the literature (Morille et al., 2007;Haeffelin et al., 2012;Wiegner et al., 2014).To eliminate the influence of inherent noise and aerosol layers on the data, spatial and temporal averaging must be carried out before the gradient method used to calculate the PBL height.In this paper, the settings use 80 m height averaging close to the ground.This interval is gradually increased to 360 m averaging used at heights above 1500 m.Time averaging is dependent on the current signal noise.It varies between 14 min during nighttime and 52 min on a bright, cloudy day (Tang et al., 2016).This method uses the vertical aerosol backscatter gradient, whereby strong negative gradients can indicate the PBL height.STRAT-2D determines three candidates for PBL height: the largest, the second largest gradient and the lowest height gradient.

Data processing
In previous studies, the fog-haze pollution was defined as a phenomenon in which visibility is less than 10 000 m due to the dense accumulation of fine aerosol particles (Fu and Chen, 2017;Liu et al., 2017;Li et al., 2016).Here, we fur-ther divided the studied cases into haze events and fog-haze mixed events.According to the Kohler curve (Köhler, 1936), the haze aerosols can be transformed to fog droplets under certain meteorological conditions.The classification is usually done based on values of the visibility range (Cho et al., 2000;Tardif and Rasmussen, 2007;Elias et al., 2009).The international definition of a fog event is an observed horizontal visibility below 1000 m in the presence of suspended water droplets and/or ice crystals (NOAA, 1995).However, the fog droplets and haze aerosols are usually mixed and co-exist in the polluted region.In this study, if the fog occurred in the pollutant episode, it was defined as a fog-haze mixed event, which is similar to the study of Sun et al. (2006).If the fog did not occur during the entire pollutant episode, it was defined as a haze event.Since our study focuses on long-lasting haze and fog-haze mixed events, the parameters of the PM 2.5 concentration (> = 50 µg m −3 ) and lasting time (> = 72 h) of these events were included as additional criteria.It should be noticed that situations such as heavy rain event or light fog events, which cause the horizontal visibility to be below or above 1000 m, are not considered here.From January 2014 to March 2015, the total number of persistent pollutant cases is 11, in which four haze cases and seven fog-haze mixed cases were obtained.Table 1 listed all cases investigated.The RH in each haze event was lower than 90 %.The maximum RH of each haze event was 68, 89, 77 and 72 %, respectively.The maximum RH of each fog-haze mixed event was larger than 90 %.The results were consistent with the studies of Xu et al. (2016) and Q. Zhang et al. (2015), in which the observed RH less than 90 % was used to separate haze events from fog events under the visibility < 10 000 m due to the difficulty of measuring RH correctly.
3 Results and discussion

Relationship between visibility and PM 2.5 mass concentration
Previous studies indicated that the increase in PM 2.5 mass concentration contributed to visibility impairment significantly in China (Cao et al., 2012;Han et al., 2013;H. J. Zhao et al., 2013;Li et al., 2015;Han et al., 2016).The relationships between visibility and PM 2.5 mass concentrations for both long-lasting haze and fog-haze mixed events are shown in Fig. 2, and the corresponding regression results are given in Table 2.It shows that there is a negative exponential function between the visibility and the PM 2.5 mass concentration for both haze and fog-haze mixed events with the same R 2 of 0.80.The relationship for haze events is consistent with the previous result of Han's study on the relationship between daily averaged PM 2.5 concentration and visibility under stable meteorological condition from October 2013 to September 2014 at Beijing.However, the fog-haze mixed events could cause greater visibility impairments; for example, in the haze events, the visibility reduced from 5800 to 2700 m as the PM 2.5 concentration increased from 100 to 200 µg m −3 , and in the fog-haze mixed events the visibility reduced from 4700 to 1500 m for the same amount of PM 2.5 concentration increase.The differences between the two conditions are mainly due to the increase of RH and the formation of fog droplets that could induce higher light extinction.The averaged RH observed by Haidian automatic weather station in haze and fog-haze mixed events is 46.7 and 74.6 %, respectively.Under high RH conditions, a large amount of water vapour coated on water-soluble particle surface enlarges the particle size, which significantly enhances the particulate light scattering efficiency and deteriorates visibility.When haze aerosols are water vapour saturated, they can be activated to form fog droplets, which leads to a further decrease of visibility (Elias et al., 2009;Klein and Dabas, 2014;Guo et al., 2015).Moreover, in the aqueous phase, the production rate of sulfate and nitrate aerosols was enhanced by aqueous-phase chemistry (i.e.in-fog oxidation by dissolved ozone (O 3 ) and hydrogen peroxide (H 2 O 2 )) (Andreae and Rosenfeld, 2008;Seinfeld and Pandis, 2012) and heterogeneous chemistry (Pandis et al., 1992;B. Zheng et al., 2015;G. J. Zheng et al., 2015).Sulfur oxidation ratios showed a rapid increase as a function of RH, which varied from ∼ 0.05 at RH < ∼ 40 % to 0.2 at RH = ∼ 80 % and greatly increased to 0.4 via aqueousphase processing (Sun et al., 2014).Han et al. (2013) showed that sulfate and nitrate were the two major inorganic aerosol components of PM 2.5 in Beijing that evidently decreased visibility by contributing 40-45 % to the total extinction coefficient value.Cao et al. (2012) indicated that high secondary inorganic aerosol (i.e.SO −2 4 and NO − 3 ) were the main contributors for visibility < 5000 m.Kang et al. (2013) indicated that aerosol concentration in the diameter from 0.6 to 1.4 µm increased dramatically and can mainly be attributed to the remarkable increase of scattering coefficient and decrease of visibility in a long-lasting haze in Nanjing.Shi et al. (2014) addressed the relationship of visibility with PM 1 and total water-soluble ions during the periods of December 2012.They found that hourly total mass concentration of watersoluble ions had a better correlation with visibility and that the formation/dissociation of NH 4 NO 3 and NH 4 Cl exerted great impacts on visibility.Strong NH 3 and HNO 3 reaction x respects the mass concentration of PM 2.5 (µg m −3 ); y respects visibility (m).resulted in the enhancement of NH 4 NO 3 mass fraction under high RH condition that contributed to visibility degradation.

Relationship between PM 2.5 mass concentration and PBL height
The PBL height can be derived from both MPL and CL31 instruments.Figure S1 in the Supplement shows the PBL height determined by MPL versus that by CL31, and the 1 : 1 line is given for reference.The figure reveals R 2 = 0.70 with differences between −408 and 692 m.The number of the difference of PBL height retrieved by MPL and CL31 within ±300 m accounts for 97 % of the total.Tsaknakis et al. (2011) showed that the differences of PBL height derived by Raymetrics lidar and CL31 were about 50-100 m based on two midday cases.This difference may be attributed mainly to the different wavelengths used by MPL and CL31.The PBL height derived by MPL is usually used as a reference to detect the aerosol vertical distribution by more advanced and powerful lidars.It shows in Fig. S1 that CL31 underestimates at low PBL height and overestimates at high PBL height.Thus, the PBL heights derived from the MPL are used in the following part of this paper.The PBL heights in pollution condition varies from 150 to 1000 m and the heights under 500 m accounts for 87 %.
The PBL heights retrieved by measuring the attenuated backscatter profile of MPL and CL31 still exist some uncertainties (Tang et al., 2016;Geiß et al., 2017).Tang et al. (2016) found that PBL height cannot be correctly obtained through sudden changes in the attenuated backscatter profiles.In certain situations, such as when strong northerly winds with dry and clear air masses prevailed in the observation site and the atmospheric aerosols spread rapidly and became uniform in the vertical direction, the PBL height was substantially underestimated.
The statistical relationship between PM 2.5 mass concentration and PBL height is investigated and shown in Fig. 3.It shows that the PM 2.5 concentration has an inversely linear correlation with the PBL height with an R 2 of 0.34 for haze events and a negative exponential correlation with an R 2 of 0.48 for fog-haze mixed events, indicating that the PM 2.5 concentration is more sensitive to the PBL height in fog-haze mixed events.The PM 2.5 concentrations of 50, 100, 200, 300 and 400 µg m −3 correspond to the PBL heights of 830, 510, 330, 300 and 290 m, respectively, in fog-haze mixed events.The PM 2.5 concentrations of 100, 200 and 300 µg m −3 cor-respond to the PBL heights of 460, 370 and 280 m, respectively, in the haze events.When using CL31 data, we find that the basic relationship is the same as when using data from MPL; however, the correlation coefficients decrease substantially.Figure S2 shows that the PM 2.5 concentration has an inversely linear correlation with the PBL height with an R 2 of 0.2 for haze events and a negative exponential correlation with an R 2 of 0.34 for fog-haze mixed events.R 2 are both lower than that determined by MPL.
The feedback between PBL height and PM 2.5 mass concentration is obviously different in the haze events and foghaze mixed events.In the haze events the PM 2.5 mass concentration increases almost linearly with the decrease of PBL height, while in the fog-haze mixed events the PM 2.5 mass concentration initially tends to show a relatively slow increase with the decrease of PBL height.As long as the PBL decreases to the height below 400-500 m, the slight decrease of PBL height could cause a rapid increase of PM 2.5 mass concentration.Petäjä et al. (2016) investigated the haze cases in Nanjing and pointed out that the aerosol-boundary layer feedback remained moderate at fine particulate matter concentrations lower than about 200 µg m −3 became increasingly effective at higher particulate matter loadings.Our investigation shows that this phenomenon becomes more obvious in fog-haze mixed events.

Relationship between visibility and PBL height
Theoretically, the relationship between PBL height and atmospheric visibility is not obvious under clean and clear conditions.However, under polluted conditions the variation of PBL height may directly cause the variation of aerosol concentration within the PBL and induce the change in visibility.The statistical results in Fig. 4 show that there are strong relationships between visibility and PBL height for both haze and fog-haze mixed events.A positive linear correlation with an R 2 of 0.35 exists in haze events and a positive exponential correlation with an R 2 of 0.56 exists in fog-haze mixed events between visibility and PBL height.
As shown above, there were strong relationships between PM 2.5 concentration, visibility and PBL height for both haze events and fog-haze mixed events in Beijing.It is relatively easy to understand the relationship between PM 2.5 and visibility since the high PM 2.5 concentration can generally cause low visibility.However, many factors can cause the increase of PM 2.5 concentration, such as increased source emission  or outside pollution transport, and the lowered PBL height as well as the formation of secondary aerosol particles as suggested by previous studies.This study shows that there was a strong negative relationship between PM 2.5 and PBL height, suggesting that the lowering PBL height might play a dominant role in the obvious increase of PM 2.5 , in particular for high PM 2.5 conditions.The critical points are how to cause the lowering process of PBL height and how to maintain these persistent polluted events, which have not been clarified well in previous studies.In the following section, we will give two typical cases to further investigate these issues.

Physical mechanism responsible for the relationship between PM 2.5 , visibility and PBL height
To clarify the physical mechanism responsible for the relationship between PM 2.5 , visibility and PBL height obtained above, two typical cases of long-lasting haze and fog-haze mixed events are presented and further investigated by considering their representativeness and data completeness of all cases (Table 1).In all haze events, the haze event observed from 11 to 14 April was highly polluted with a maximum PM 2.5 concentration of 304 µg m −3 and minimum visibility of 1113 m.For all fog-haze mixed events, the fog duration was considered first.Two cases are chosen in which the fog duration accounted for more than 40 % of the total.One was observed from 19 to 26 February 2014, and the other occurred from 6 to 11 October 2014.The maximum PM 2.5 concentration was higher and the maximum RH reached 100 % in the fog-haze event occurring from 6 to 11 October 2014, which was chosen as a typical fog-haze event for the following study.

Typical haze event
A typical haze event in April 2014 lasted for 74 h, starting at 22:00 BST on 11 April and ending at 23:00 on 14 April, during which visibility was less than 10 000 m.The synoptic situation during the haze event was characterized as a saddle field.Beijing was located in a saddle between two pairs of high-and low-pressure centre.This weather system would lead to calm surface wind and stably stratified atmospheric conditions, which was favourable for the accumulation of air pollutants.A cold front passed through Beijing on 14 April and ended the long-lasting haze event.
Figure 5 shows the temporal variations of surface meteorological and environmental factors during the entire pro- cess of the haze event.Both air temperature and RH presented a clear diurnal cycle, but they showed a gradually increasing tendency during the haze period due to the persistent warm and humid southwestern airflow.The temperature increased from 7.9 to 25 • , with an average of 16.6 ± 5.1 • , while the RH was in the range of 28 to 89 %, with an average of 55 ± 17 %.The variation of RH inversely corresponded to that of temperature.The temperature and RH derived from PMWR showed a consistent tendency with those observed by the surface automatic weather station.The wind speed varied from 0 to 3.9 m s −1 , with an average of 0.8 m s −1 , suggesting that the horizontal diffusion of aerosols was very weak.The PM 2.5 mass concentration was inversely correlated with visibility.PM 2.5 peaked at 12:00 on 14 April with a value of 304 µg m −3 , corresponding to the hourly mean visibility of 1317 m.PM 2.5 decreased dramatically after 21:00 on 14 April.The visibility continued to rise until the end of the event.The average PM 2.5 / PM 10 is as high as 0.82, implying that fine particles were dominant in the atmosphere.
The temporal variation of vertical distributions of temperature, RH, LWC and vapour density retrieved by PMWR during the entire haze event is shown in Fig. 6.Many studies demonstrated that PMWR is a useful tool to sense the thermodynamic structure of the lower troposphere continuously by providing profiles of temperature and humidity with reasonable accuracy and height resolution (Ware et al., 2003(Ware et al., , 2013;;Xu et al., 2015).The intercomparison with the radiosonde data demonstrated the good correlation of temperature and vapour density retrievals (Guo and Guo, 2015;Xu et al., 2015).The biases of temperature retrieved by PMWR against radiosondes increased with height, and the maximum bias is 4 • under 2000 m; the bias of water vapour profile was smaller than 1 g m −3 (Guo and Guo, 2015).Compared to the radiosonde temperature profiles in Fig. 9a and c, the PMWR could not capture the temperature inversions at the upper level due to the lower vertical resolution.However, the relatively high RH value could be captured well at a height between 700 and 1600 m, indicating the dominant warm and humid southwesterly airflow during the haze event.The LWC was less than 0.01 g m −3 .
Figure 7 shows the time-height distribution of the backscatter density detected by the CL31, the normalised relative backscatter (NRB) of MPL and time evolutions of the MPL-derived PBL height and PM 2.5 mass concentration during the entire haze event.Compared to the MPL, CL31 could not detect all backscatter of the haze aerosols in fine particles due to the longer lidar wavelength (910 nm). Figure 7b shows that the height indicated by the high value of NRB tended to decrease during the entire haze event, indicating that the PBL height tended to decrease with time evolution until the end of the haze event.Generally, a negative correlation or negative feedback can be found between PM 2.5 concentration and PBL height (Fig. 7c).However, the feedback between PM 2.5 concentration and PBL height was relatively weak when the PM 2.5 concentration was below 200 µg m −3 .When PM 2.5 concentration was above 200 µg m −3 , the negative feedback became strong.For example, before 14 April, the daily averaged PBL height was above 400 m and the PM 2.5 concentration was generally below 200 µg m −3 .After 14 April, the PBL height rapidly reduced to 300 m and then the PM 2.5 concentration increased its maximum value of 300 µg m −3 .The interesting phenomenon that the feedback between PM 2.5 concentration and PBL height became stronger for higher PM 2.5 concentrations is similar to that in Nanjing in southern China (Petäjä et al., 2016).We can see that the relationships between PM 2.5 , visibility and PBL height in the typical haze case were consistent with those obtained by statistical analyses shown in Sect.3.1-3.3.
The decreasing PBL height compressed the aerosol particles into a shallow vertical layer, and prevented the vertical dispersion of the aerosol particles, leading to an increase in the surface aerosol concentrations, which is consistent with a previous study in the region (Quan et al., 2014).To further reveal the decreasing process of the PBL height, the timepressure distribution of vertical velocities in Beijing from 11 to 14 April 2014 is presented in Fig. 8.It indicates that before 13 April, the atmospheric layer from the surface to the middle of troposphere was under a weak updraft condition that favoured the upward diffusion of aerosols.After 13 April, the downdraft zone started to develop at the upper levels of boundary layer.The formation of this downdraft zone strongly suppressed the upward diffusion of polluted aerosol particles.Therefore, the occurrence of the downdraft zone was one of the important factors in the decrease of PBL height during the haze event.
To clarify the mechanism that caused the formation of downdraft zone and the lowering of the PBL height, we conducted analyses of radiation for this typical haze event.The aerosol-boundary layer feedback by blocking solar radiation process was suggested as a plausible explanation for the most severe haze episodes in China (Ding et al., 2016;Petäjä et al., 2016).However, the mechanism that causes the formation of downdraft zone has not been fully understood due to a lack of the direct observational data.The formation of the downdraft zone can be caused by many mechanisms such as a cooling process induced by upper-level cold air intrusion or cloud process or an enhanced long-wave radiation emission at the top of boundary layer due to the high accumulation of aerosols at this level.In the daytime, the growth of the PBL height is strongly dependent on the surface solar radiation.On clear days, the PBL can be fully developed through the solar radiation heating.However, if solar radiation is absorbed or scattered by aerosol particles or clouds, the PBL cannot be fully developed, and the daytime PBL heights can be significantly reduced (Yu et al., 2002).Table 3 presents the parameters of radiation from Beijing Meteorological station during the haze event.It shows that the daily total horizontal plane direct radiation was significantly reduced by about 35 %, from 7.67 MJ m −2 d −1 on 13 April to 4.91 MJ m −2 d −1 on 14 April, and at the same time the amount of total scattering radiation increased from 11.07 to 12.65 MJ m −2 d −1 .These results suggest that the reduction of surface solar radiation due to the increased aerosol loading could be an important factor in maintaining the haze event in the daytime.Generally, the strong daytime solar radiation process may break up the low-level inversion layer formed by long-wave radiation cooling in the nighttime and dissipate the haze pollution event.However, under high pollution conditions as the case studies here, the surface solar radiation could be strongly blocked and reduced by high aerosol loading in the daytime; under this condition, the inversion layer could be lifted to a higher level by the reduced solar radiation heating, but it could not be completely broken up.Thus, the haze weather could be continuous in the daytime.Moreover, the lasting inversion layer in the daytime could accumulate more and more polluted aerosols, which could cause much less surface solar radiation heating and further suppress the development of PBL height and, in return, produce much higher aerosol loading.This strong feedback between aerosol loading and PBL height linked by radiation process could be the main mechanism responsible for their relationship obtained above.
To further reveal the lowering process of PBL height and its impact on atmospheric stratification within the PBL in the haze event, the temperature and RH profiles and their variations are displayed in Fig. 9.It shows that the apparent features of vertical temperature and RH profiles were the formation of double inversion layers and their subsequent variations during the entire haze event.The formation of the upper-level inversion layer at around 1200-1600 m should be closely associated with the warm and humid airflow from southwest.Temperature, RH and wind distributions in 925 and 850 hPa at 08:00 BST on 13 April 2014 are shown in Fig. S3, from which we could see the weak warm air advection from the southwest and west at 925 and 850 hPa, respectively.Relatively high RH values could be also observed at the height between 700 and 1600 m in Fig. 6b. Figure 9a also shows that the upper-level temperature inversion layer had a tendency to descend with time evolution and corresponded well to the downdraft zone displayed in Fig. 8, indicating that the PBL height tended to descend during the haze event, which is consistent with that retrieved by MPL shown in Fig. 7c.At the same time, the low-level inversion layer initially formed by surface long-wave radiation cooling process in the nighttime on 12 April was lifted and enhanced in the daytime on 13 and 14 April.We propose that the enhanced low-level inversion layer at around 150-600 m was primarily caused by the descending process of the upper-level inversion layer at around 1200-1600 m.This can be explained by the increased temperature and humidity in the entire PBL during the haze event (Figs. 9,5a,b).Figure 5a shows that the surface air temperature tended to be cooling in the nighttime and warming in the daytime, but the tendency of temperature increased during the entire haze event, suggesting that the downdraft zone and the descending process of upper-level inversion layer might be primarily caused by the long-wave radiation cooling process in the nighttime and maintained in the daytime by the substantially reduced surface solar radiation process.This can be verified by the vertical distribution of vertical velocities shown in Fig. 8.It shows that the downdraft zone was initially formed in the nighttime on 13 April and continued until the end of haze event.In addition, the downdraft zone only occurred within a relatively narrow belt, and there were weak updrafts below it and almost no vertical winds above it, so it is hard to attribute its formation to the dominant weather system.It should be noted that the outgoing long-wave radiation cooling produced by the aerosol accumulation in the top of PBL might also contribute to the descending of the downdraft zone in the nighttime.However, this contribution cannot be quantitatively estimated due to the lack of measurement.It is obvious that with the increased accumulation of polluted aerosols in the daytime the low-level stable layer height was increased and its stability was further strengthened.For example, the inversion layer from 150 to 550 m with the lapse rate of air temperature is −0.38 • (100 m) −1 at 08:00 on 13 April, while the lapse rate of the same layer is −0.75 • (100 m) −1 at the same time on 14 April.Some researchers suggested that the heating process due to the solar radiation absorption by aerosols such as black carbon might play an important role in forming the deep inversion layer (Ding et al., 2016;Petäjä et al., 2016).This might be true for forming the relatively weak temperature inversion, but it is hard to explain the obvious increase of temperature and humidity in the entire vertical boundary layer in Fig. 9 and the prominent downward movement of airflow shown in Fig. 8.The descending process of the upper-level inversion layer should be responsible for the increase of temperature and humidity in the entire boundary layer and the enhancement of the lowlevel inversion layer, as well as the lowering PBL height in the daytime.Although the low-level inversion layer was confined to the surface due to the lack of solar radiation heating in the nighttime compared with that in the daytime, the enhancement of the low-level inversion layer was still evident during the descending process of upper-level inversion layer (Fig. 9c).
In all, the haze case studied above shows that the persistent advection of warm and humid southwestern air provided a long-lasting favourable condition for the formation of a stable upper-level inversion layer of PBL that weakened the upward mixing and diffusing of surface polluted aerosols in the PBL.As long as the accumulation of aerosols reached more than 150-200 µg m −3 , the low-level inversion layer initially formed by surface long-wave radiation cooling in the nighttime could not be broken up in the daytime due to the substantially weakening solar radiation heating induced by the high aerosol loading, so that the haze event could maintain and last until the end of haze event.At the same time, the descending process of the upper-level inversion layer induced by surface cooling process in the nighttime could also be maintained in the daytime and enhanced the low-level inversion layer by transporting the warm and humid air to the lower levels of the PBL.The descended warm and humid air from the upper inversion layer could significantly strengthen the low-level stability and in return rapidly increased the aerosol loadings.Therefore, the formation of double inversion layers and their subsequent changes linked by radiation processes should have a critical role in lowering PBL height and rapidly increasing PM 2.5 concentration, as well as maintaining the long-lasting and severe haze weather event.

Typical fog-haze mixed event
The typical fog-haze mixed event started at 22:00 on 6 October and ended at 18:00 on 11 October 2014 with a duration of 117 h.During the entire period, the North China Plain was controlled by the westerly airflow in the mid-troposphere.At the surface, a weak pressure field maintained before the arrival of the cold front, with light winds and high humidity.Moreover, the drizzle rain occurred in Beijing in the mornwww.atmos-chem-phys.net/18/203/2018/Atmos.Chem.Phys., 18, 203-225, 2018 ing of 8 October, which further increased the atmospheric humidity in the PBL.The radiation fogs formed from 9 to 11 October.The fog lasted 48 h in total and accounted for 42 % of the duration of the fog-haze mixed event.
Figure 10 shows the temporal evolution of surface meteorological and environmental factors in the entire process of the fog-haze mixed event.During the fog-haze mixed events, wind speed varied from 0 to 2.7 m s −1 , with an average of 0.5 m s −1 .The wind direction was easterly from midnight to afternoon and then changed to calm wind until the next morning.The temperature was in the range of 9.1 to 21.7 • , with an average of 15.6 ± 3.1 • , while the RH was in the range of 46 to 100 %, with an average of 88 ± 14 %.The visibility exponentially decreased with the PM 2.5 mass concentration increasing with an R 2 of 0.87.The visibility decreased to the minimum 534 m in the morning of 11 October.PM 2.5 reached the highest at 19:00 on 9 October with the value of 392 µg m −3 , corresponding to the hourly mean visibility of 898 m.After that there was a slight invasion of cold air, and PM 2.5 concentration decreased but remained at a high level.The decreasing of the temperature was favourable to the formation of fog.PM 2.5 decreased dramatically after 17:00 on 11 October.The visibility continued to rise until the end of the event.The averaged PM 2.5 / PM 10 was as high as 0.94.
The temporal variation of vertical distributions of temperature, RH, LWC and vapour density retrieved by PMWR during the entire fog-haze mixed event is shown in Fig. 11.When the precipitation events happened in the morning of 8 October, the profiles became unreliable due to contamination of rainwater on the sensor covering.The LWC was larger than 0.02 g m −3 in the morning of 10 and 11 October, which also indicated the fog formation (Guo and Guo, 2015).Moreover, the RH was high near the surface in the morning from 8 to 11 October.Relatively high RH values were also observed at the height between 500 and 1600 m.Compared to the radiosonde temperature profiles in Fig. 14a and c, the PMWR could not capture the temperature inversions at the upper level.Compared with the haze event, the fog-haze mixed event had a higher RH and induced the fog and drizzle formation, so the surface cooling induced by blocking the incoming solar radiation and subsequent descending process of PBL height became more obvious.
Figure 12 shows the time-height distribution series of the backscatter density detected by CL31 and the NRB detected by MPL, and time evolution of the MPL-derived PBL height and PM 2.5 mass concentration during the entire fog-haze mixed event.As seen in the Fig. 12a and b, aerosols were mostly confined to a shallow layer of few hundred metres.Due to the longer lidar wavelength, the CL31 has better detection capability of the raindrop and fog droplets compared to the MPL.Compared with the haze event, the fog and rain drops had stronger attenuation to the signal of MPL.Periods 1 and 2 in the Fig. 12b were caused by drizzles, and in the periods 3, 4 and 5 the strong attenuation was caused by fog droplets occurred in the high RH conditions.The daily averaged PBL heights from 7 to 11 October were 660, 350, 270, 270 and 270 m, respectively, while the daily averaged PM 2.5 concentrations were 122.7, 249.7, 333.3, 310.8 and 235.4 µg m −3 , respectively, indicating that the PM 2.5 concentration increased with the decease of PBL height.It can be seen that the relationships between PM 2.5 , visibility and PBL height in the typical fog-haze mixed event are also consistent with those obtained by statistical analyses shown in Sect.3.1-3.3.However, the feedback between the PM 2.5 concentration and PBL height was much stronger in the foghaze mixed event than in the haze event (Fig. 12c).It is obvious that the negative feedback between the PM 2.5 concentration and PBL height was much weaker when the PM 2.5 concentration was less than 200 µg m −3 , and it became much stronger when the PM 2.5 concentration reached more than 200 µg m −3 .
To reveal the lowering process of PBL height in the foghaze mixed event, the time-pressure distribution of vertical velocities during the fog-haze event in Beijing from 6 to 11 October 2014 is presented in Fig. 13.Similar to the haze event in Sect.3.4.1, the downdraft zone started to form at the upper levels of boundary layer in the afternoon of 7 October and lasted until a cold frontal system passed the area.The downdraft zone decreased from 700 to 850 hPa in the afternoon of 7 October, which led to the sharply decrease of PBL height in Fig. 12c.On 9 October, the height of the downdraft zone was the lowest and the updraft speed in the PBL was the lowest, corresponding to the most polluted day during the entire fog-haze mixed event.
The radiation processes were also analysed and compared for this typical fog-haze mixed event.We see that the decrease of surface radiation parameters was more obvious in the fog-haze mixed event shown in Table 4. Daily total horizontal (vertical) plane direct radiation was significantly reduced from 14.11 (24.94) to 0.86 (1.40) MJ m −2 d −1 during 6-11 October 2014, the reduction of horizontal (vertical) direct radiation was about 94 % in fog-haze mixed event while the total scattering radiation increased from 3.40 to 7.21 MJ m −2 d −1 , indicating that the daytime surface solar radiation reduction in the fog-haze mixed event was much stronger than in the haze event.Moreover, the decrease of radiation corresponded well to the high PM 2.5 concentration recorded due to the lowering PBL height.
Similar to the haze event, the double inversion layers and variations of temperature and RH profiles could also be found and were much stronger in the fog-haze mixed event (Fig. 14).The obvious upper inversion layer was closely associated with strong advection of warm and humid airflow from the southwest (Fig. S4).The relatively high RH values could be observed at heights from 500 to 1700 m in Fig. 11b.The daily averaged PBL height reached the minimum of 270 m and lasted until the end of the fog-haze mixed event in the evening of 11 October.Therefore, the enhancement of the low-level inversion layer caused by the stronger descending process of upper-level inversion layer and the lowering process of PBL height as well as the rapid increase of aerosol loadings were obvious in the fog-haze mixed event, indicating that the interactions and feedbacks between PBL height and aerosol concentration linked by radiation process were much stronger.More stable PBL and stronger low-level inversion could be formed and induced higher aerosol loading during the fog-haze mixed event.Although the absorption of light-absorbing particles such as black carbon may increase the temperature above the surface and the black car-  bon could contribute a fraction of about 3-15 % to the total mass concentrations in urban air (Yang et al., 2011;Huang et al., 2014), it could not be a dominant factor in forming the low-level inversion layer based on this study.The low-level inversion layer in the nighttime was relatively weaker in the fog-haze mixed event than in the haze event.This is because the surface long-wave radiation cool-ing in the nighttime could rapidly cause the formation of fog droplets as long as the air saturation condition was reached.During the formation of fog droplets, the condensational latent heating release could heat the air and weaken the inversion structure in the nighttime.
We can see that the influence of the double inversion layer on the meteorology and PM 2.5 was relatively stronger in   the fog-haze mixed event, but the physical mechanisms responsible for these influences were similar to those in the haze events.Table 5 summarises the averaged PM 2.5 mass concentration, PBL height, RH and radiation parameters in the haze and fog-haze mixed event.The averaged PM 2.5 concentration was 164.5 µg m −3 in the haze event while it was 250.4 µg m −3 in the fog-haze mixed event, corresponding to the averaged PBL heights of 470 and 360 m, respectively.The interactions and feedbacks between PBL height and PM 2.5 concentration were much stronger due to the formation of many fog droplets in fog-haze mixed event than that in haze event.The fog droplets could substantially block the solar radiation and caused much less solar radiation heating in the daytime, so that the averaged reduction of surface solar total radiation caused by the fog-haze mixed event was almost double compared to that by the haze event.Since the solar radiation absorbed by the earth surface may heat the bottom of atmospheric column, producing convective eddies that transport heat and water vapour upward and driving the growth of the PBL (Lee and Ngan, 2011), the substantial reduction of surface solar radiation in both haze and fog-haze mixed events could induce much less surface heating and formed a much lower PBL height.

Conclusion and discussions
In this study, the relationship between PBL height, PM 2.5 mass concentration and visibility for long-lasting haze and fog-haze mixed events in Beijing was investigated and quantified.Comprehensive measurements of aerosol characteristics and meteorological conditions have been conducted in the Chinese Academy of Meteorological Sciences (CAMS), Beijing, since 2013, and a total of 11 long-lasting haze and fog-haze mixed events were observed from January 2014 to March 2015.PBL heights of haze and fog-haze mixed events were retrieved using MPL NRB signal and correlated well with the PBL height derived by CL31.
The statistical results show that there was a negative exponential function between the visibility and the PM 2.5 mass concentration for both haze and fog-haze mixed events with the same R 2 of 0.80.Aerosols could cause greater visibility impairments in fog-haze mixed events due to the increase of RH and formation of more fog drops.The PM 2.5 concentration had inversely linear correlation with PBL height for haze events with an R 2 of 0.34 and negative exponential correlation with an R 2 of 0.48 for fog-haze mixed events, indicating that the PM 2.5 concentration is more sensitive to PBL height in fog-haze mixed events.The feedback between PBL height and PM 2.5 mass concentration became stronger when PM 2.5 mass concentration was more than 150-200 µg m −3 , particularly in fog-haze mixed cases, which is similar to the findings for haze events in Nanjing (Petäjä et al., 2016).However, our investigation shows that this phenomenon became more obvious in the fog-haze mixed event.Similar to the relationship between PM 2.5 concentration and PBL height, a positive linear correlation with an R 2 of 0.35 existed in haze events and positive exponential correlation with an R 2 of 0.56 existed in fog-haze mixed events between visibility and PBL height.
The statistical results show that there were strong relationships between PM 2.5 concentration, visibility and PBL height for both haze events and fog-haze mixed events in Beijing.In order to clarify the physical mechanism responsible for these relationships, the courses and effects of these quantities as well as the role of PBL height were further investigated based on two typical cases representing for haze and fog-haze mixed events.We found that both cases had an obvious structure of double inversion layers located at the upper and lower levels of PBL, respectively.The variations of the double inversion layers were closely associated with the processes of long-wave radiation cooling in the nighttime and short-wave solar radiation reduction in the daytime.The formation of upper-level inversion layer was closely associated with the persistent advection of warm and humid southwestern airflow and that of the low-level inversion layer was initially produced by the surface long-wave radiation cooling in the nighttime and continued and maintained by the substantial reduction process of surface solar radiation in the daytime.The obvious descending process of the upper-level inversion layer could be responsible for the enhancement of the low-level inversion layer and the lowering PBL height, as well as high aerosol loading for these polluted events.The descending process of the upper-level inversion layer was initiated by long-wave radiation cooling in the nighttime and continued and maintained by the substantial reduction process of surface solar radiation in the daytime.Therefore, the variations of all these quantities were closely linked and driven by different radiation processes and the change of the double inversion layers was closely related to the lowering PBL height and high PM 2.5 concentration.The reduction of surface solar radiation in the daytime could be around 35 % for haze event and 94 % for fog-haze mixed event.
The descending process of upper-level inversion layer could cause the warm and humid airflow from the southwest to move downward, inducing an increase of temperature and humidity in the entire PBL and forming a deeper and more stable PBL.All these processes can be clearly shown in the typical cases of this study.The descent of the upper-level inversion and its subsequent interactions and feedback with quantities such as low-level inversion layer, PBL height and PM 2.5 concentration were particularly strong when PM 2.5 mass concentration was larger than 150-200 µg m −3 .
The main differences of the meteorological conditions of the two cases are humidity and duration.Although both cases occurred in a stable weak pressure field covering northern China, the haze event was drier and duration was shorter while the fog-haze mixed event was more humid and had a longer duration.Since the fog droplets were formed in the fog-haze mixed event, the radiation reduction at surface was more obvious and stronger and caused a stronger descending process of the upper inversion layer.In most cases, light precipitation (drizzle rain or light snow) occurred during the fog-haze mixed event, while in all haze events during the observation period there was no precipitation.The foghaze mixed event was more favourable to form extremely high mass concentration of PM 2.5 (> 300 µg m −3 ) than the haze event.The daily averaged PBL height was lower than 110 m in the fog-haze mixed event.The relationships between PM 2.5 , visibility and PBL height in both typical cases are found to be consistent with those obtained by statistical analyses.
The new finding in this paper has important implications for explaining the frequent long-lasting polluted events in the study region.Generally, a typical pollution event is usually formed under a stable and shallow temperature-inversion condition at low atmospheric layers and would disappear or obviously decrease when the daytime solar radiation increases.However, in the study region, we found that many severe haze and fog-haze mixed events lasted for several days even for several weeks.Most previous publications attributed the reason as the persistent abnormal weather system or high emissions.However, this study shows that except for the influence of meteorological condition and high emissions, the interactions and feedbacks between meteorological factors and aerosols were crucial.We found that the formation of double inversion layers in the PBL and their subsequent variations linked by different radiation processes were crucial in enhancing and maintaining these polluted events, which could cause an important variation of dynamical-thermal processes in lower troposphere.Due to the complex interactions and feedbacks, an atmospheric environment with much deeper and more stable PBL could be formed that is hard to break up by daytime solar radiation heating process until the strong wind occurs and removes the high aerosol loading.
Competing interests.The authors declare that they have no conflict of interest.

Figure 1 .
Figure 1.Geographical location of the observation sit in Beijing.CMA, HD and NJ represent China Meteorological Administration, Haidian automatic weather station and Beijing Meteorological station, respectively.

Figure 2 .
Figure 2. Relationship between the measured visibility and PM 2.5 mass concentration under different RH conditions for (a) haze and (b) foghaze mixed events from January 2014 to March 2015 in Beijing.The black exponential curves present the fits of the squares.The red exponential curve is the fit of daily averaged visibility and PM 2.5 concentration from October 2013 to September 2014 on stable meteorological days in Han et al. (2016).

Figure 3 .
Figure 3. Relationship between PBL height and PM 2.5 mass concentration for (a) haze and (b) fog-haze mixed events from January 2014 to March 2015 in Beijing.

Figure 4 .
Figure 4. Relationship between visibility and PBL height for (a) haze and (b) fog-haze mixed events from January 2014 to March 2015 in Beijing.

Figure 5 .
Figure 5. Temporal variations of surface meteorological and environmental parameters observed during the entire haze event in Beijing: (a) temperature, (b) RH, (c) wind direction and wind speed, (d) visibility and (e) mass concentration of particulate matter.The temperature and RH derived from PMWR are also presented in (a) and (b).

Figure 6 .
Figure 6.Time-height cross sections of (a) temperature, (b) RH, (c) LWC and (d) vapor density retrieved by PMWR during the entire haze event in Beijing.

Figure 7 .Figure 8 .
Figure 7. Time-height cross sections of (a) the backscatter density detected by the CL31 and (b) the NRB detected by the MPL; (c) the time evolution of PM 2.5 mass concentration and PBL height retrieved by the NRB of MPL during the entire haze event in Beijing.

Figure 9 .
Figure 9.The temperature and RH profiles during the entire haze event in Beijing.(a) Temperature and (b) RH at 08:00 BST.(c) Temperature and (d) RH at 20:00 BST.

Figure 10 .
Figure 10.Temporal variation of surface meteorological and environmental factors observed during the entire fog-haze mixed event in Beijing: (a) temperature, (b) RH, (c) wind direction and wind speed, (d) visibility and (e) mass concentration of particulate matter.The temperature and RH derived from PMWR are also presented in (a) and (b).

Figure 11 .
Figure 11.Time-height cross sections of (a) temperature, (b) RH, (c) LWC and (d) vapor density retrieved by PMWR during the entire fog-haze mixed event in Beijing.

Figure 12 .Figure 13 .
Figure 12.Time-height cross sections of (a) the backscatter density detected by CL31 and (b) the NRB detected by MPL; (c) the time evolution of PM 2.5 mass concentration and PBL height retrieved by the NRB of MPL during the fog-haze mixed event in Beijing.

Figure 14 .
Figure 14.The temperature and RH profiles during the entire fog-haze mixed event in Beijing.(a) Temperature and (b) RH at 08:00 BST.(c) Temperature and (d) RH at 20:00 BST.

Table 1 .
The long-lasting haze and fog-haze mixed events from January 2014 to March 2015 in Beijing.
a The maximum RH of all valid data except missing measurement.b Fog-haze mixed event duration/fog duration.

Table 2 .
The exponential curve of visibility and PM 2.5 mass concentration for haze and fog-haze mixed events.

Table 3 .
Parameters of radiation from Beijing Meteorological station during the haze event.Daily total radiation is the sum of daily total scattering and daily total horizontal plane direct radiation.

Table 4 .
Parameters of radiation from Beijing Meteorological station for the fog-haze mixed event.Daily total radiation is the sum of daily total scattering and daily total horizontal plane direct radiation.

Table 5 .
The average PM 2.5 concentration, PBL height, RH and daily radiation parameters during the haze and fog-haze mixed event.