A fully coupled online Weather Research and Forecasting with Chemistry model (WRF-Chem version 3.7.1) (Grell et al., 2005; Chapman et al., 2009) was employed to simulate the two severe haze events in Beijing from 7 to 20 December 2016, and the initial 4 d are spin-up. This model adopts Lambert projection and two nested domains with grid resolutions of 30 km (domain 01) and 10 km (domain 02). Figure 1 shows that the outer domain covers most of China with 100 (west–east) × 100 (south–north) grid cells, and the second domain covers the BTH region with 58 (west–east) × 76 (south–north) grid cells. The number of vertical layers is 29, with the first 15 layers below 2 km for finer resolution in the PBL. Meteorological initial and boundary conditions in this model were derived from National Centers for Environmental Prediction (NCEP) Final (FNL) Operational Model Global Tropospheric Analyses (ds083.2) with a spatial resolution of 1∘ × 1∘. MOZART-4 (Model for Ozone And Related chemical Tracers-4) simulation results provided the initial and lateral boundary conditions for the concentrations of chemical species in our model (Emmons et al., 2010).

Anthropogenic emission data in the year 2016 were obtained from the MEIC inventory with a spatial resolution of 0.25∘ × 0.25∘ (Zheng et al., 2018). This inventory includes sulfur dioxide (SO2), nitrogen oxides (NOx), carbon monoxide (CO), non-methane volatile organic compounds (NMVOCs), ammonia (NH3), BC, organic carbon (OC), PM2.5, PM10, and carbon dioxide (CO2), which were categorized into agriculture, industry, residence, transport, and power generation sectors (Li et al., 2017). The biogenic emissions were calculated online using MEGAN (Model of Emissions of Gases and Aerosol from Nature), including isoprene, terpene, and other substances emitted by plants (Guenther et al., 2006). Biomass burning emissions were taken from the Fire INventory from NCAR (FINNv1.5), which provides daily emissions at a horizontal resolution of ∼ 1 km2 (Wiedinmyer et al., 2011).

The parameterization schemes of physical and chemical processes of the WRF-Chem model adopted in the study are summarized in Table 1. The Carbon-Bond Mechanism version Z (CBMZ) is chosen to simulate the gas-phase chemistry. The aerosol scheme is the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC), which includes sulfate, nitrate, ammonium, chloride, sodium, BC, OC, and other inorganic aerosol, and the aerosol particles are divided into eight particle size segments. However, the formation of secondary organic aerosol is not considered in this scheme (Zhang et al., 2012; Gao et al., 2016a). In MOSAIC, the aerosol particles are assumed to be an internal mixture, and aerosol optical properties are calculated by the volume averaging mixing method (Barnard et al., 2010; Stelson, 1990). The choice for photolysis schemes is the Fast-J photolysis scheme.

The IPR analysis has been widely applied to illustrate the impacts of each physical and chemical process on the variations in O3 concentrations (Zhang and Rao, 1999; Jiang et al., 2012; Gao et al., 2017, 2018). The improved IPR analysis method developed by Chen et al. (2019) in the WRF-Chem model is used in this work to quantitatively analyse the contributions of physical and chemical processes to PM2.5 concentrations, including the contributions from the sub-grid convection (CONV), vertical mixing (VMIX), chemistry (CHEM), regional transport (TRA), wet scavenging (WET), emission source (EMI), and other processes (OTHER). CONV refers to the transport within the sub-grid wet convective updrafts, downdrafts, and precipitation (Chen et al., 2019), and VMIX is affected by atmospheric turbulence and vertical distribution of PM2.5 concentrations (Zhang and Rao, 1999; Gao et al., 2018). CHEM represents PM2.5 production and loss including gas-phase, cloud, and aerosol chemistry. TRA is caused by advection, which is highly related to wind and horizontal distribution of PM2.5 concentrations (Gao et al., 2018; Chen et al., 2019). WET represents the wet removal processes of aerosols by in-cloud scavenging and below-cloud washout. EMI is controlled by emission source. OTHER represents the processes other than the above six processes in the model. The NET is the sum of all physical and chemical processes, which matches the variations in PM2.5 concentrations. It is worth noting that each IPR variable is an accumulated value which is the sum of each time step.

To evaluate the model performance in simulating near-surface meteorological fields, the observed hourly temperature at 2 m (T2​​​​​​​), relative humidity at 2 m (RH2), wind speed at 10 m (WS10), and wind direction at 10 m (WD10) at Beijing Capital International Airport station (40.08∘ N, 116.58∘ E) are collected from NOAA's National Climatic Data Center (http://gis.ncdc.noaa.gov/maps/ncei/cdo/hourly, last access: 3 February 2022). Due to the limited observations of planetary boundary layer heights (PBLHs), shortwave downward radiation flux (SWDOWN), and total cloud cover in Beijing, the reanalysis data of 3-hourly PBLH, SWDOWN, and total cloud cover for Beijing from the Global Data Assimilation System (GDAS) with a spatial resolution of 1∘ × 1∘ (http://ready.arl.noaa.gov/READYamet.php, last access: 3 February 2022) were used for model evaluation. More details about the GDAS dataset can be found in Rolph (2013) and Kong et al. (2015). The radiosonde data (temperature and relative humidity profiles) in Beijing were obtained from the University of Wyoming, Department of Atmospheric Science (http://weather.uwyo.edu/upperair/sounding.html, last access: 3 February 2022). Hourly concentrations of PM2.5, CO, NO2, SO2, and O3 at Beijing station were obtained from the China National Environmental Monitoring Center (CNEMC, http://www.cnemc.cn/, last access: 3 February 2022), which were used to evaluate the model performance in simulating pollutants at the surface. Aerosol optical depth (AOD) at 550 nm over China retrieved from the MODIS (Moderate Resolution Imaging Spectroradiometer) satellite was used to evaluate the horizontal distribution of simulated optical properties of aerosols in this study (https://ladsweb.modaps.eosdis.nasa.gov/, last access: 3 February 2022). The MYD03 (Level-1A) product with 1 km spatial resolution from the Aqua platform and the MOD03 (Level-1A) product with 1 km spatial resolution from the Terra platform were used in this study. The values of daily aerosol optical depth (AOD) at 500 and 675 nm in Beijing were obtained from the AERONET dataset (https://aeronet.gsfc.nasa.gov/, last access: 3 February 2022).

The vertical profiles of BC mass concentrations in Beijing were collected by King Air 350 aircraft using SP2 from 11–12 and 16–19 December 2016. The aircraft departed from Shahe (∼ 20 km to central Beijing) (Fig. 1) at 12:00–13:00 local time (LT) and returned around 15:00–16:00 LT, which avoided the possible diurnal variation in the PBL among flights. Most flights could reach 2.5 km. Zhao et al. (2019) reported that these vertical profiles of BC could be expressed as an exponential decline function C(h)=C0e-hhs except 11 December 2016, where C(h) (µg m-3) is BC concentration at altitude h (km), C0 (µg m-3) is BC concentration at the surface, and each hs value is calculated for each flight of BC vertical profile using nonlinear regression (Table S1 in the Supplement). Tian et al. (2019) observed a regional transport of pollution in Beijing from 10 to 12 December 2016 using SP2, and they found a different vertical structure of BC from that of Zhao et al. (2019), with the BC concentration at the altitudes of 400–900 m being 1.5 times higher than the near-surface BC concentration on 11 December 2016. More detailed information about the King Air 350 aircraft dataset can be found in Zhao et al. (2019), S. Ding et al. (2019), and Tian et al. (2019).

To compare the DRE of BC with the original and corrected vertical profiles and quantify the role of BC vertical profiles in influencing meteorological conditions and air pollutants, we performed the following numerical experiments as summarized in Table 2.

CTRL. This is the control simulation with the direct and indirect radiative effects of all aerosols (BC, OC, sulfate, nitrate, ammonium, Na+, Cl-, and other inorganics – OIN) included for the time period of 11–20 December 2016. The vertical profiles of BC were the default ones simulated by the model.

In the case of NoBCrad, the BC DRE was turned off by setting the BC mass concentration equal to zero when calculating the optical properties of BC, following the studies of Qiu et al. (2017) and Chen et al. (2021). In the VerBC_obs experiment, we modified the simulated BC vertical profile online using the observed BC vertical profile on the corresponding day. Firstly, we interpolated the observed BC concentrations to the height of each layer in the model as Cobs_int(i). Each layer in the model has a top height and a bottom height, and we selected the middle height of this layer for interpolation. Secondly, we used Cobs_int(i) to calculate the BC mass column burden in each layer (Mobs_int(i)) in the model, and Pobs_int(i) is the percentage of BC mass column burden in each layer to the total BC mass column burden (Fig. S1) calculated by 1Mobs_int(i)=Cobs_int(i)⋅Hsim_top(i)-Hsim_bot(i), where Hsim_top(i) is the top height of layer i and Hsim_bot(i)is the bottom height of layer i. 2Pobs_int(i)=Mobs_int(i)∑i=116Mobs_int(i)⋅100% In the VerBC_obs simulation, the simulated BC mass column burden was redistributed to each layer below 2.5 km according to the calculated Pobs_int(i). These procedures ensure that the modification of the BC vertical profile for each day in the model by using the observed data does not change the total BC mass column burden. Since the aircraft measured only BC concentrations below 2.5 km, we modify the BC profile up to the 16th model layer (about 2.5 km in Beijing).

In the experiment of VerBC_hs1∼6, we also used the above method to modify the BC vertical profile by an exponential decline function, which is C(h)=C0×e-h/hs. However, in cases of VerBC_hs1∼6, we modified for the dates of 12 and 16–19 December. On 11 December, BC did not show an exponential decline with height due to the regional transport. In the simulation of VerBC_RT, the method and setting were the same as VerBC_hs1∼6, except that the BC vertical profile in the model was modified according to the observed one on 11 December 2016. In the VerBC_obs, VerBC_hs1∼6, and VerBC_RT cases, the modifications of BC vertical profiles were performed only when the direct radiative forcing of BC was calculated. All other physical and chemical processes in these experiments still used the original BC vertical profiles simulated by the model. The BC vertical profiles were only modified in the blue square shown in Fig. 1a.

Figure 2a–i show the horizontal distributions of simulated surface layer PM2.5 concentrations at 14:00 LT from 11 to 19 December 2016. In Beijing, high PM2.5 concentrations of 234.1 and 165.9 µg m-3 occurred on 11 and 12 December, respectively. The severe pollution in Beijing on 11 December was caused by regional transport from the heavily polluted southern area under a prevailing southerly air flow (Tian et al., 2019). From 16 December, PM2.5 started to accumulate in eastern China, and the concentrations of PM2.5 reached the highest value of 217.8 µg m-3 on 19 December in Beijing. The daily PM2.5 concentrations (Fig. 2j) in Beijing had low values from 13–15 December 2016. The model results for Beijing in this paper are the averages over the region of the blue square shown in Fig. 1a unless stated otherwise. The severe pollution from 16–19 December 2016 was mainly affected by local emissions. We are mainly focused on the two heavy pollution incidents (11–12 and 16–19 December 2016) in the following sections.

Results from the CTRL simulation were compared with the observed hourly surface concentrations of PM2.5, NO2, O3, CO, and SO2 from 11–19 December 2016 in Beijing in Fig. 3. The observed maximum PM2.5 concentration of 219.5 µg m-3 occurred on 18 December, far exceeding the national air quality standard for daily PM2.5 of 75 µg m-3 (Wang et al., 2017). The correlation coefficient (R), mean bias (MB), normalized mean bias (NMB), and mean fraction bias (MFB) are summarized in Table 3. The model can reasonably reproduce the temporal variations in PM2.5, NO2, O3, and CO; the correlation coefficients between simulated and observed hourly concentrations are 0.77, 0.78, 0.66, and 0.73, respectively. The correlation coefficient for SO2 is lower (0.38). Gao et al. (2016b) explained that the WRF-Chem model cannot represent the SO2 concentration and its change with time well due to the uncertainty in SO2 emissions and missing heterogeneous oxidation. Compared with observations, the model overestimates the concentrations of PM2.5 and NO2 in Beijing with the MBs and NMBs of 13.2 µg m-3 and 10.0 % and 8.5 ppbv and 21.6 %, respectively, and underestimates the concentrations of O3 (-0.1 ppbv, -1.2 %) and CO (-0.1 ppmv, -4.9 %). It should be noted that the model performance in simulating PM2.5, SO2, CO, and O3 is better during the two haze events than on clean days. For hourly PM2.5, for example, the MBs (NMBs) are 29.1 µg m-3 (82.5 %) on clean days and 6.3 µg m-3 (3.5 %) during the two haze events. The possible reasons for the overall overestimation of PM2.5 are as follows: (1) the model biases in underestimating WS10 and daytime PBLH and (2) the uncertainties in anthropogenic emission data (e.g. the overestimation in the BC emissions) (Qiu et al., 2017; Chen et al., 2021). Overall, the model can capture the two severe pollution events in Beijing from 11–19 December 2016 fairly well.

Because of the lack of measured BC vertical profiles from 13–15 December 2016 in Beijing, Fig. 4 compares only the simulated vertical profiles of BC with observations for the two polluted events (11–12 and 16–19 December 2016). Observed mass concentrations of BC decreased exponentially with altitude on all days except for 11 December when regional transport of pollution dominated. On 11 December, the observed maximum mass concentration of BC (7.0 µg m-3) occurred at 850 m altitude, which was much higher than the surface layer concentration of 4.7 µg m-3. Compared with the observed vertical profiles of BC, the model can represent the decreases in BC mass concentration with height on 12 and 16–19 December well but cannot reproduce the vertical profile on 11 December. Possible reasons for the model's failing to represent the BC vertical profile on 11 December are as follows: (1) the model cannot capture the wind at high altitudes and does not reproduce the high-altitude BC concentrations in the surrounding areas of Beijing, and (2) the model underestimates the daily maximum PBLH in Beijing, which inhibits the upward transport of surface layer BC. Averaged over the two pollution events, the simulated BC mass concentration was overestimated by 87.4 % on the ground and underestimated by 33.1 % at an altitude of 1000 m compared with the observations in Beijing. The inaccuracy of the vertical distribution of BC would lead to inaccurate representation of the interactions between BC and PBL, especially in heavily polluted events.

The first haze event started on 11 December when southeasterlies transported polluted air from southern BTH to Beijing (Fig. 2a). Although the southeasterlies turned into northeasterlies in Beijing on 12 December, PM2.5 concentrations were still high because of the high relative humidity (63.2 %) that was conductive to the formation of secondary aerosols. With the relatively high wind speed of 3.6 m s-1 and low relative humidity of 37.2 % in Beijing from 13–15 December, the haze pollution gradually disappeared (Fig. 2c–e). From 16 to 19 December, PM2.5 began to accumulate again with unfavourable diffusion conditions (WS10 of 1.4 m s-1) and enhanced formation of secondary aerosols under high relative humidity of 67.1 % (J. Li et al., 2019; Dai et al., 2021). Throughout the simulated period of 11–19 December 2016, Beijing had no precipitation and was partly cloudy (Fig. 5g–h). Figure 5 shows the hourly simulated and observed T2, RH2, WS10, WD10, PBLH, SWDOWN, precipitation, and total cloud cover in Beijing from 11 to 19 December 2016. The statistical metrics are summarized in Table 3. In the two severe haze events, the observed maximum RH2 on each day exceeded 70.0 %, which accelerated the formation of secondary aerosols (Sun et al., 2006; Wang et al., 2014). Compared with the observations, the model can represent the temporal variation in T2 and RH2 well with correlation coefficients of 0.77 and 0.75, respectively, but slightly overestimates T2 with a MB of 0.1∘ and underestimates RH2 with a MB of 3.4 %. For WS10, observations and simulated results both show low wind speed with the mean values of 1.5 and 1.4 m s-1 in Beijing during the two periods of haze events. Such a meteorological condition was very beneficial to the accumulation of near-surface pollution. The WRF-Chem model also captures the high values of WS10 from 14 to 15 December. For wind direction at 10 m, the NMB is -9.0 % and the R is 0.45, which indicates that the model can simulate the change of wind direction during the period of heavy pollution. For PBL, the reanalysis PBL was 118.7 m during the two severe haze events, compared to 287.5 m during the clean period. The model can represent the change of PBLH in Beijing from 11 to 19 December 2016 with R of 0.72. The model overestimates PBLH by 30.9 m (17.7 %) in Beijing as averaged over 11–19 December 2016. The overestimation is mainly in the hours of 00:00–08:00 and 17:00–23:00 LT. It is noted that the reanalysis PBLH values provided by GDAS of NOAA were mostly 50–60 m at 00:00–08:00 and 17:00–23:00 LT in Beijing, far below the simulated mean value of 154.5 m in these hours. There might be biases in the PBLH from GDAS. Several previous studies showed that the values of observed PBLH from lidar measurements were about 200 m at night during haze events (Wang et al., 2012; Luan et al., 2018; Chu et al., 2019). The simulated SWDOWN in CTRL experiment agrees well with the observations with R and MB of 0.76 and -14.9 W m-2. Due to the limitation of the model outputs, the model provides only information of whether there is cloud in the grid or not. The model can reproduce the presence of cloud from 11–19 December 2016 well. Both observations and model results show no precipitation in the studied time period.

The simulated and observed vertical profiles of temperature in Beijing from 11–19 December 2016 are shown in Fig. S2. The observed vertical temperature profiles are available only at 08:00 and 20:00 LT. During the two severe pollution events, strong temperature inversions below 1500 m were observed in Beijing, which inhibited vertical mixing and caused the accumulation of pollutants near the ground. The model captures these temperature inversions well but overestimates the inversion layer height on 11 December and underestimates the inversion layer height from 16 to 19 December. The inaccuracy of the simulated inversion layer height may be due to the fact that the model cannot correctly represent the vertical profiles of BC (Fig. 4).

AOD (AAOD) is the measure of aerosols (absorbing aerosols) distributed within a column of air from the surface to the top of the atmosphere (Khor et al., 2014). Figure S3 shows the horizontal spatial distributions of observed and simulated AOD at 550 nm over the NCP averaged over 11–19 December 2016. The model can generally reproduce the horizontal distribution of AOD, with a spatial correlation coefficient of 0.89. However, the model underestimates AOD over the NCP region. Many previous studies have shown that MODIS retrieval tends to overestimate AOD over NCP (Li et al., 2016; Qiu et al., 2017). We also compared the simulated hourly AAOD at 550 nm with AERONET AAOD at Beijing and Xianghe stations in Fig. 6. The correlation coefficient between simulations and observations is 0.85. Compared with AERONET AAOD, simulated AAOD values at Beijing and Xianghe are overestimated by 0.02 (33.3 %) and 0.02 (39.9 %), respectively.

Figure 7 shows the atmospheric temperature and PBLH simulated from the CTRL simulation and their changes caused by BC DRE with the original profiles (CTRL minus NoBCrad) and modified profiles (VerBC_obs minus NoBCrad), over Beijing from 11 to 19 December 2016. Light-absorbing BC heated the air at around 300 m on 11 and 16–19 December, regardless of the original or modified BC vertical profiles (Fig. 7b and c). With the original and modified BC profiles, the maximum warming effects in the PBL were 0.8 and 0.9∘, respectively, at 14:00 LT on 18 December. Although BC concentration was the highest at the surface, the largest increase in temperature occurred in the upper layers because of the stronger shortwave absorption efficiency of BC at higher altitude (Ding et al., 2016; Wang et al., 2018). The warming at around 300 m resulted in a more stable stratification, thereby weakening convective motions (Gao et al., 2018). The largest reductions in PBLH were 133.8 m (28.0 %) at 14:00 LT on 12 December and 141.2 m (59.0 %) at 14:00 LT on 18 December in Beijing with the original and modified BC vertical profiles, respectively. On 11 December when regional transport of pollution dominated, relative to the simulation with the original BC profile, simulated air temperature with the modified profile was lower by about 0.5∘ within the PBL (Fig. 7d), which was caused by the observed maximum mass concentration of BC around 850 m altitude (Fig. 4a). Correspondingly, the maximum reduction in PBLH of 74.2 m was also simulated on 11 December. On 16–19 December when local emissions dominated, compared to the effects of the original BC profiles, the air temperatures at around 300 m were all higher with modified BC. The largest difference of +0.1∘ was simulated in the PBL on 18 December (Fig. 7d).

Figure 8 shows the spatial distributions of changes in T2, sea-level pressure (SLP), and wind at 10 m caused by BC DRE with the original and modified vertical profiles. BC DRE with both the original and modified vertical profiles produced anomalous northeasterlies in eastern BTH during the two haze events. The mechanism of such changes is that BC DRE induced a strong warming over the Bohai Sea in the east of BTH with a maximum warming of about 1.8∘, resulting in an anomalous low pressure here and consequently anomalous northeasterlies in eastern BTH (Fig. 8c–d). The similar changes in winds caused by the heating effect of BC were also reported in previous studies (Gao et al., 2016b; Qiu et al., 2017; Chen et al., 2021).

By altering the meteorological conditions, BC exerts feedback onto PM2.5 concentrations. Figure 9 illustrates the impacts of BC DRE with the original and modified vertical profiles on surface layer PM2.5 as well as the differences in simulated surface layer PM2.5 between VerBC_obs and CTRL (VerBC_obs minus CTRL) in Beijing during the two haze events. Because of the differences in BC-induced changes in air temperature, wind field, and PBLH, changes in surface layer PM2.5 concentrations in northern and southern Beijing were different. In the first haze event of 11–12 December, although PBLH was reduced in northern Beijing due to BC DRE, enhanced northerlies brought in relatively clean air to northern Beijing, leading to decreases in surface layer PM2.5 concentrations with maximum values of 12.5 µg m-3 (9.4 %) and 10.6 µg m-3 (8.0 %) in this region with the original and modified BC vertical profiles, respectively. Nevertheless, PM2.5 concentrations increased by up to 17.8 µg m-3 (6.6 %) and 24.0 µg m-3 (9.3 %) in southern Beijing due to the BC effect with the original and modified vertical profiles, respectively. In the second haze event of 16–19 December, the surface layer PM2.5 concentrations increased in most areas of Beijing with both vertical profiles. Compared to the simulation with the original profiles, the modified profiles of BC led to larger increases in PM2.5 concentrations over Beijing, and the maximum differences in PM2.5 were simulated over central Beijing, which were 9.3 µg m-3 (3.6 %) and 5.5 µg m-3 (3.1 %) in the first and second haze events, respectively.

To explain the changes in surface layer PM2.5 concentrations in Beijing due to BC effects, we carried out process analysis for PM2.5 for 12:00–18:00 LT of each day when the DRE of BC is the largest (Fig. 9a3, b3, and c3). From 11 to 19 December 2016, VMIX had a dominant positive contribution to changes in PM2.5 concentration, which reached the maximum contributions of 32.4 and 33.9 µg m-3 on December 18 with the original and modified BC vertical profiles, respectively. The vertical mixing was strongly restrained by PBLH; therefore, the decreases in PBLH caused accumulation of PM2.5 in the lower layers. Meanwhile, CHEM contributed 4.8 and 6.1 µg m-3 to PM2.5 changes because more aerosol precursors restrained in the boundary layer led to the formation of secondary particles. TRA was the major process that had negative contribution to the changes in PM2.5, which can be explained by the enhanced northerlies in the central part of the NCP due to BC effects as shown in Fig. 8. Relative to the case with the original BC vertical profiles, VMIX and CHEM contributions increased largely with modified profiles, with increases of 8.6 µg m-3 (6.5 %) and 7.7 µg m-3 (26.8 %), respectively, as averaged over the two haze events, reflecting the further decreases in PBLH (Fig. 7d).

Figure 10 shows the vertical profiles of the contributions of physical–chemical processes to changes in PM2.5 over Beijing due to BC DRE with the original (CTRL minus NoBCrad; Fig. 10a1 and b1) and modified vertical profiles (VerBC_obs minus NoBCrad; Fig. 10a2 and b2) in the two haze events. In the first haze event of 11–12 December when regional transport of pollution dominated, the NET contribution to PM2.5 was positive below 256 m, because the positive contribution of VMIX was larger than the negative contribution of TRA. However, in the upper layers (from 256 to 1555 m), the contributions of VMIX and CHEM became negative with both the original and modified vertical profiles, which can be explained by the decreases in PBLH inhibiting the transport of low-layer pollutants to the upper layer. Compared to the original BC vertical profiles, the modified BC vertical profiles increased PM2.5 in all the vertical layers below 2080 m, in which the positive contribution between 256–757 m was caused by TRA. These results agree with the observed high concentrations of BC at altitudes of 600–1500 m on 11 December (Fig. 4a). In the second haze event, the NET contribution to PM2.5 was positive below 127 m and negative at 127–504 m. However, the effects of BC on PM2.5 were small above 504 m because BC concentrations decreased rapidly with altitude.

It is of interest to compare the performance of CTRL (with the original BC vertical profiles) with that of VerBC_obs (with modified BC vertical profiles) in simulating meteorological parameters and PM2.5 during the two haze events. Figure S4 shows the comparisons between observed T2, RH2, WS10, WD10, and PBLH and the simulated values from the CTRL and VerBC_obs simulations in Beijing in the two haze events (11–12 and 16–19 December 2016). Relative to the CTRL simulation with the original BC vertical profiles, the VerBC_obs simulation with modified BC vertical profiles has better performance in simulating T2, WS10, and PBLH except for WD10 and RH2 in the first pollution event. While the MBs of T2, RH2, WS10, WD10, and PBLH are 0.2∘, 0.0 %, -0.4 m s-1, 3.8∘, and 45.0 m in CTRL, they are 0.0∘, 2.2 %, -0.1 m s-1, 10.9∘, and 29.0 m in VerBC_obs, respectively (Table S3). In the second pollution event, the positive bias in PBLH (MB = 43.7 m, NMB = 42.9 %) in CTRL is reduced to 33.9 m and 33.3 % in VerBC_obs.

Table S4 shows the statistical comparison between observed hourly surface layer PM2.5 and the model results from CTRL and VerBC_obs in Beijing for each day during the two haze events. The model with modified BC vertical profiles can enhance the capability in simulating the temporal variation in PM2.5 for each day; the correlation coefficient between simulated hourly concentrations and hourly observations in each day of the studied period increased from 0.04–0.84 in CTRL to 0.24–0.93 in VerBC_obs.

Figure 12 shows the simulated changes in atmospheric temperature induced by BC DRE with exponential functions (VerBC_hs1-6 minus NoBCrad) and with the transport-dominated vertical profile (VerBC_RT minus NoBCrad). BC had a significant warming effect at altitudes of 256–421 m from 12:00 to 18:00 LT (Fig. 7). Generally, with the value of hs gradually increasing, the BC-induced warming in the afternoon around 300 m became smaller, which can be explained by the highest mass fraction of BC at the altitudes of 256–421 m to total BC column burden in VerBC_hs1 case (31.7 %) and the lowest percentage in the VerBC_hs6 case (21.7 %) among the six sensitivity experiments (Fig. S1). The maximum warming around 300 m was 0.42∘ in the VerBC_hs1 case and 0.19∘ in the VerBC_hs6 case. It should be noted that BC led to a significant cooling effect at the surface (below 80 m) when hs values were 0.79, 0.82, and 0.96, with changes in temperature by -0.08, -0.09, and -0.13∘, respectively. Because more BC mass was assigned to high altitudes (above 1000 m) with higher hs, less solar radiation could reach the ground (Fig. S5). These results are consistent with those found in previous modelling and observational studies (Cappa et al., 2012; Ferrero et al., 2014; Ding et al., 2016; Wang et al., 2018). Meanwhile, in the case of VerBC_RT, BC also had a cooling effect of -0.30∘ at the surface (Fig. 12g). In current regional air quality models, the uncertainties in BC profiles could influence the capability of a model to simulate a cooling effect of BC on surface air temperature (Wang et al., 2019).

We further use the difference in temperature between the upper PBL (TH; 256–421 m) and the ground (TL; 0–127 m) (ΔTBC=TH-TL) averaged over 12:00–18:00 LT of 12 and 16–19 December to quantify temperature inversion caused by BC DRE. BC aerosol leads to cooling at the surface and warming in the upper PBL, both of which weaken the convection in the boundary layer and consequently reduce the PBLH (Ding et al., 2016; Wang et al., 2018; Chen et al., 2021). In our study, with hs values increasing from 0.35 to 0.96, ΔTBC increased from 0.17 to 0.42∘, and the ΔTBC value was 0.51∘ in the VerBC_RT case (Fig. 13a). The larger ΔTBC indicates stronger cooling at the surface. Such temperature inversion at 12:00–18:00 LT resulted in more stable stratification and further inhibited the development of PBL. The cooling at the surface also reduced sensible heat flux from the surface (Fig. S5), suppressing vertical turbulence and hence reducing PBLH (Wilcox et al., 2016). As a result, the reductions in PBLH were larger with higher hs (Fig. 13b). The minimum decrease in PBLH was -31.9 m (-14.3 %) with a hs value of 0.35, and the maximum decrease was 48.9 m (22.0 %) with a hs value of 0.96, as averaged over the period of 12:00–18:00 LT on 12 and 16–19 December. In the case of VerBC_RT, the mean PBLH was reduced by 56.9 m (25.6 %) during the period of 12:00–18:00 LT.

Figure 14a shows the changes in surface layer PM2.5 concentration caused by BC DRE with six exponential functions (VerBC_hs1-6 minus NoBCrad) and the transport-dominated vertical profile (VerBC_RT minus NoBCrad) averaged over 12 and 16–19 December 2016. From 00:00 to 11:00 LT, the surface layer PM2.5 exhibited larger BC-induced decreases with a higher value of hs. This can be explained by the negative contribution of the TRA process that increased during the period of 00:00–05:00 LT (Fig. 14b and c) when the hs value changed from 0.35 to 0.96. The surface layer PM2.5 concentration was reduced by up to 9.1 µg m-3 (6.2 %) and 12.6 µg m-3 (8.6 %) at 05:00 LT with hs values of 0.35 and 0.96, respectively. Compared to the NoBCrad case, the surface layer PM2.5 concentrations were reduced by up to 13.8 µg m-3 (9.4 %) at 05:00 LT due to BC DRE in the VerBC_RT case. From 12:00 to 18:00 LT, the BC-induced increase in surface layer PM2.5 concentrations was larger as hs values were higher; relative to NoBCrad simulation, the mean PM2.5 concentrations were increased by 5.5 µg m-3 (3.4 %) and 7.9 µg m-3 (4.9 %) with the hs values of 0.35 and 0.96, respectively. Because the PBL was suppressed by BC DRE from 12:00 to 15:00 LT, the contributions of VMIX and CHEM to surface layer PM2.5 were positive and larger in magnitude than the negative contribution of TRA. The NET of all processes was negative from 16:00 to 18:00 LT due to the continuous growth of a negative contribution of TRA. The negative contribution of the TRA process from 12:00 to 18:00 LT can be explained by the enhanced northerlies in the central part of BTH caused by BC DRE, which transported cleaner air masses into Beijing (Fig. S6). From 19:00 to 23:00 LT, the surface layer PM2.5 concentrations were decreased by BC DRE, which can be explained by the dominant negative contribution of TRA from 19:00 to 21:00 LT. At 22:00 LT, the reduction in surface layer PM2.5 was 7.5 µg m-3 (4.0 %) when the hs value was 0.35 and 6.6 µg m-3 (3.5 %) when hs was 0.96.