2.1 Model configuration

The simulations were conducted with the WRF-Chem version 3.6.1 (Grell et al., 2005) single-column model (SCM). Except for advection, the physical and chemical processes are exactly the same as in the three-dimensional version, which is a fully coupled online meteorology–chemistry model including emission and deposition of pollutants, gaseous and aqueous chemical transformation, aerosol chemistry, and dynamics. The WRF-Chem SCM runs on a 3×3 grid with periodic lateral boundary conditions in both zonal and meridional directions. We used a spatial resolution of 4 km and a vertically stretched sigma coordinate with the model top set at a constant pressure, corresponding to about 6000 km. One hundred vertical levels were placed equidistantly with a height of 60 m from the ground surface to model top to better resolve the vertical structure of the atmosphere and ensure identical BC mass loadings.

The parameterization schemes were selected following the work by Ding et al. (2016), in which the model configuration showed good performance on boundary layer meteorology. The RRTMG short- and longwave radiation schemes (Iacono et al., 2008) were used to couple with aerosol scheme in order to reproduce aerosol–radiation interactions. The YSU non-local-K boundary layer scheme (Hong et al., 2006) and the Noah land surface scheme (Tewari et al., 2016) were applied for boundary layer evolution and land–atmosphere interactions, respectively. For representation of cloud and precipitation processes the Lin microphysics scheme (Lin, 1983) together with the Grell–Deveny cumulus parameterization (Grell and Devenyi, 2002) were employed. The CBMZ (Carbon Bond Mechanism version Z) photochemical mechanism combined with MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) aerosol model (Fast et al., 2006; Zaveri and Peters, 1999) was applied to represent atmospheric chemistry. Aerosols were assumed to be spherical particles. The size distribution was divided into four discrete size bins defined by their lower and upper dry particle diameters (0.039–0.156, 0.156–0.625, 0.625–2.5 and 2.5–10.0 µm). Aerosol water content is calculated using the Zdanovskii–Stokes-Robinson method according to relative humidity (Zaveri et al., 2008). In each bin, aerosols are presumed to be spherical and internally mixed. The volume-averaged mixing rule is adopted to calculate the bulk refractive index by considering both aerosol water content and chemical compositions, including BC, sulfate, nitrate, and ammonium. Mie theory is then used to calculate the extinction coefficient, single-scattering albedo (SSA) along with asymmetry factor for each bin. Model domains and configuration selections are summarized in Table 1.

Table 1WRF-Chem SCM model settings and configuration options.

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The WRF-Chem SCM was initialized with monthly averaged radio-sounding measurements at 12:00 UTC taken in Beijing (116.28^∘ E, 39.93^∘ N) to represent the typical atmospheric stratification in wintertime. Daily sounding data are archived at http://weather.uwyo.edu/upperair/sounding.html. The soil temperature profile was taken from the monthly averaged WRF regional simulation results for December 2013. The initial condition of atmospheric pollutants, which is mainly concerned with BC will be given in details in the following section. Vertical mixing of aerosol is switched off to ensure that the concentration and altitude of aerosol layer do not vary with PBL evolution. Each numerical experiment was conducted for a time period of 72 h with the first 48 h as model spin-up time.

2.2 Design and analysis of numerical experiments

We conducted a set of multidimensional experiments. Each individual experiment contains hundreds of simulations and can be divided into two groups. These two experiment groups shared exactly the same model settings and configurations except that one was with aerosol radiation interaction (ARI) and the other without (noARI). Each group consists of several parallel experiments with various initial conditions of airborne pollutants or surface parameters. To investigate the impact of heterogeneity in vertical distribution of BC on the dome effect, BC plumes with a width of 300 m were settled at different altitudes, ranging from the ground surface to about 2000 m. BC concentration was assumed to be 0–30 µg m⁻³ according to existing field measurements across China (Zhang et al., 2013; Sun et al., 2004; Zhao et al., 2013a). BC concentrations in the plume were presumed to be a Gaussian distribution vertically, with a maximum value ranging from 0 to 30 µg m⁻³ in the central axis, the altitude of which also ranges from 150 to 2250 m with an interval of 300 m.

Furthermore, to better understand the difference of the dome effect over different underlying ground surfaces (i.e., urban and rural areas) and its roles in regional air pollution, we conducted similar parallel numerical experiments over both urban and rural land surfaces. The distinct differences in important surface parameters between them are listed in Table 2. It is well known that BC emission is mainly related to fossil fuel combustion in China; hence, it is usually co-emitted with other gaseous pollutants like SO₂ and NO_x and then mixed with their oxidation products, i.e., sulfate and nitrate, during transportation and aging processes (Wang et al., 2014b; Huang et al., 2013; Cheng et al., 2006). To quantify the impact of mixing with these scattering aerosols, we also performed another two parallel simulations with different SNA (sulfate, nitrate and ammonium) aerosol concentration levels in the BC plume. The mass ratio of BC to SNA was derived from year-round measurement in Beijing (Zhang et al., 2013).

Table 2Distinctive differences of surface parameters between urban and rural land cover.

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3.1 One-dimensional modeling of the dome effect of BC

The dome effect of black carbon was first revealed by Ding et al. (2016) based on integrating online coupled regional simulation and corresponding observations during the winter haze event in December 2013, when severe PM_2.5 pollution covered East China with hourly concentrations up to ∼900 µg m⁻³ and visibility less than 100 m (Zheng et al., 2015). In this study, it was proven that BC plays an important role in aggravating haze pollution via aerosol–PBL interaction. To clearly demonstrate BC-induced aerosol–PBL interaction, we selected one typical episode during 23–24 December 2013 in Beijing and initialized the WRF-Chem SCM with an averaged BC profile taken from three-dimensional simulation results for the same case by Ding et al. (2016). The regional WRF-Chem simulation of winter haze in December 2013 in Ding et al. (2016) had been verified to perform well in capturing the temporal variations of BC. The inputted BC vertical profile in Fig. 1 indicated that, during the abovementioned case, BC concentration reached up to approximately 30 µg m⁻³ near the ground surface and decreased rapidly with altitude to a relatively constant value of less than 5 µg m⁻³ above 800 m. However, although the BC profile featured its maximum concentration near the surface, the heating efficiency of BC due to shortwave radiation absorption peaked around 600–800 m, indicating that BC in the upper PBL is more efficient in terms of absorbing shortwave radiation and heating surrounding air masses. Such a heating profile is partly caused by the fact that incident solar radiation is attenuated by aerosols, trace gases and cloud when transferring within the atmosphere. Therefore, BC at higher altitudes tended to be subjected to higher incident radiation flux and absorb more solar energy. At the same time, lower air density caused the upper air to be more readily heated compared with that near the surface. Due to light absorption caused by BC together with additional extinction caused by scattering aerosols, solar radiation reaching the surface was diminished to a relatively large extent, resulting in less sensible heat flux and thus lower temperature in the near-surface atmosphere.

Figure 1Vertical profiles of BC and shortwave heating rate included by unit BC mass in the afternoon (12:00–16:00 LT) during a heavily polluted episode on 23–24 December 2013 in Beijing. The black dashed line denotes the average PBL height during the same daytime period. The BC profile was extracted from regional WRF-Chem modeling by Ding et al. (2016).

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Overall, upper-level warming and surface cooling substantially modified the temperature stratification. As illustrated in Fig. 2, the afternoon upper-level heating and morning surface cooling could be clearly identified. The strongest upper-air warming had remained at over 1.0 ^∘C between 1000 and 1200 m since midday (12:00 LT) because the incident shortwave radiation was most intense and the heating effect had already been accumulated before midday. The strongest cooling effect appeared in the morning (09:00–11:00 LT) and decreased very sharply after noon. The reason is that, with increasingly intense turbulence during morning boundary evolution, part of the surface cooling was gradually compensated for by the entrainment of more warmed air into the turbulent PBL from above when the PBL was developed in the late morning. The warming and cooling of different atmospheric levels remarkably altered the stratification, thereby weakening convective motions. Stable stratification combined with decreased sensible heat flux at the ground surface greatly suppressed vertical turbulence in the boundary layer (Wilcox et al., 2016), contributing to a delay of PBL development and an earlier drop as well as a substantial decrease in PBL height, which hindered the air pollutants from being further dispersed vertically. These modifications in temperature stratification were relatively extensive in East China during winter according to the simulation conducted in Ding et al. (2016). For the whole month of December in 2013, the occurrence probability of enhanced atmospheric stability (PBL height decreasing over 10 %) due to the dome effect could reach up to 66, 73, 69 and 66 % in Zhengzhou, Shijiazhuang, Shanghai and Nanjing, respectively (Ding et al., 2016).

Figure 2Diurnal variations of the air temperature change caused by aerosols during haze episodes in Beijing and of PBL height for simulation scenarios with (solid line) and without (dashed line) ARI.

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3.2 Impacts of altitude and concentration of BC aerosol layer

As previously mentioned, specific synoptic conditions, chimney plumes and regional transport of air pollution could result in non-uniformly distributed pollutant profiles (Xu et al., 2014; Guinot et al., 2006; Ding et al., 2009). Vertically inhomogeneous distribution of BC aerosol has been frequently observed by in situ aircraft and tethered balloon measurements (Zhao et al., 2015; Li et al., 2015). Given that BC was measured to rise around 800–1000 m during daytime in a haze episode (Li et al., 2015) and the upper-PBL BC has higher light-absorbing efficiency where solar heating usually maximizes, a BC plume with a maximum concentration of 10 µg m⁻³ at the central axis is taken as a typical example to illustrate the perturbations on detailed physical processes related to PBL evolution due to a vertically non-uniform BC profile. As displayed in Fig. 3, with the existence of absorptive BC, incident solar radiation at the surface is diminished by about 5.9 W m⁻² at 12:00 LT, leading to a decline of 0.2 ^∘C in surface temperature and a decline of 3.6 W m⁻² in surface sensible heat flux, which would otherwise heat the lower atmosphere, promote turbulent motions and enhance the PBL development. At the same time, absorbed radiation energy is converted to thermal energy and leads to substantial heating near the top of the PBL, as reflected by a rise in air temperature around 1.0 ^∘C. Accordingly, modified temperature profile results in a more stable stratification with its exchange coefficient falling by 15 % (Fig. 3b), i.e., less turbulence mixing. Similarly, a substantial decrease in PBL height is attributed to less surface heat flux accompanied by stable stratification, which is showed in Fig. 3c.

Figure 3(a) Vertical distribution of BC aerosols (contour) and shortwave heating rate at 14:00 LT for runs with (solid line) and without (dashed line) ARI. (b) Vertical potential temperature profile (red) and exchange coefficient profile (blue) for runs with (solid line) and without (dashed line) ARI. The black dashed line represents the averaged PBL height during 12:00–16:00 LT. (c) Diurnal variations of PBL height for runs with (solid line) and without (dashed line) ARI and shortwave radiation attenuation at the surface induced by BC absorption.

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To shed more light on the impacts of various BC vertical distributions on the dome effect, we conducted hundreds of parallel numerical experiments by changing the altitude and concentration magnitude of BC from the simulation shown in Fig. 3 to a larger extent in order to figure out how the PBL evolution responds to varying BC profiles and mass loading. Specifically, we manually increase BC concentrations from 0 to 30 µg m⁻³ with an increment of 2 µg m⁻³, all of which are placed at altitudes from 150 to 2250 m with an increment of 300 m. Thus, the multidimensional experiment consists of 105 parallel numerical simulations. All the individual simulations (marked by black dots in Fig. 4) and resultant perturbations on PBL height and the turbulence coefficient under different altitude and concentration loadings of BC are shown in Fig. 4. As several studies have pointed out, BC near the ground surface warms the Earth–atmosphere system and favors the development of the PBL by trapping more solar radiation that should be reflected by land and then promoting convective motions (Huang et al., 2015; Barbaro et al., 2014). The increased air temperature near the surface weakens the capping inversion, acting to cancel the effect of reduced buoyancy flux at the ground surface and raising the top of the PBL (Yu et al., 2002). However, this enhancement in PBL development is not that noticeable in magnitude while compared with PBL suppression due to BC at higher altitude. Consistent with several existing observational and numerical studies, absorbing smoke aloft is capable of remarkably changing the energy balance between the surface and the atmosphere in a way that stabilizes the boundary layer and suppresses convection (Koren et al., 2004; Ackerman et al., 2000). As demonstrated in Fig. 4, the PBL top could be decreased by about 15 % and the turbulent exchange coefficient dropped by over 20 % due to high-altitude BC plume. The substantial suppression effect induced by the BC plume maximizes around the top of the PBL and can be attributed to two main reasons. Firstly, incident solar radiation flux at the top of the PBL is usually most intense. After being absorbed by BC, it can effectively heat the surrounding air and change the strength of the capping inversion. Secondly, the turbulent exchange coefficient falls to a relatively small value when close to the top of the PBL (Fig. 3b), indicating that vertical turbulence exchange for heat at this height is rather weak. Therefore, the warming layer is prone to being kept at that level rather than diffusing vertically, further strengthening the capping inversion and consequently lowering the PBL height.

Figure 4PBL height (contour map) and turbulence exchange coefficient (grey dashed isoline) variations in percentage as a function of the altitude and mass concentration of BC aerosol layers. Note: each dot on the figure represents an experiment with different BC input. The x axis gives concentrations in the center of the inputted BC plume, while the y axis gives the altitude of the residing plume. The yellow dashed line represents the original PBL height without any BC plume.

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Another interesting fact is that, while BC layer is located above the original top of the PBL (i.e., above the 1300 m in Fig. 4), the boundary layer also becomes shallower but relatively less notable compared with upper-PBL BC layer (i.e., 600–1000 m). In this case, BC also blocks part of the incoming solar radiation and diminishes surface fluxes proportionally; nevertheless, it no longer alters the temperature stratification of the PBL below. It is well known that changes in the height of the PBL are determined by the surface buoyancy flux and the capping inversion, and both of them are affected by BC plumes (Ding et al., 2017, 2016). Since the impact of column loading of BC to surface buoyancy flux will not change substantially in the lower troposphere, here the different impact of BC on PBL height around the capping inversion (i.e., 600–1200 m) with the above altitudes indicates that the upper-air warming due to BC layer plays a more dominant role in depressing the PBL height and hence enhancing the near-surface air pollution.

3.3 Amplified dome effect by mixing with scattering aerosols

During wintertime heavily polluted episodes, when both primary and secondary pollutants increase dramatically, BC will be coated by scattering aerosols through condensation of low-volatility gases and coagulation with secondary aerosols and thus becomes hydrophilic and more internally mixed (Shiraiwa et al., 2007; Chen et al., 2016). Theoretically, its absorption properties can be significantly enhanced by internal mixing with other compounds because the coatings act as a lens and enlarge its mass absorption cross section effectively (Bond et al., 2013; B. Chen et al., 2017). Here, although organic matter also grows rapidly during hazy days, we do not include it in this work due to the uncertainties in its optical properties as well as less notable hygroscopicity. We analyzed this absorption amplification effect based on consistent in situ measurements during the development of severe haze pollution in Beijing in January 2013 (Sun et al., 2014). Compared with the clean period, the secondary aerosol increased significantly during haze episodes. Take sulfate aerosol for instance, its concentrations during hazy days were approximately 55 times higher than those under clean condition. Based on the ratio of BC to SNA during different periods and assuming BC concentration is 5 µg m⁻³ (Zhang et al., 2013), absorption at the simulated wavelength (i.e., 300, 400, 600 and 1000 nm) was amplified by factors of 1.8, 1.7, 1.6 and 1.4, respectively (Fig. 5). These absorption coefficient amplification factors are comparable with in situ observations during clean period and haze event in the North China Plain (B. Chen et al., 2017). To investigate the relative importance of amplified absorption for each band, the solar spectral irradiance at sea level is also given for reference. The absorptive magnification for radiation at the wavelength of 400–600 nm tends to have a dominant effect since the solar irradiance peaks in this band. Accordingly, shortwave heating rate also increased from about 0.15 to over 0.22 K h⁻¹, which considerably accelerates the warming effect induced by BC (Fig. 5).

Figure 5Aerosol absorption coefficient at different wavelengths (300, 400, 600, and 1000 nm) and shortwave heating rate at 12:00 LT for runs during a clean period and haze episode when the ratio of BC and SNA is 1:3 and 1:8, respectively. The yellow shaded area schematically shows solar spectral irradiance at sea level.

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In addition to directly increasing the absorption cross section, SNA could undergo deliquescence and lead to an increase in aerosol diameter to a large extent, especially under humid conditions, indirectly enhancing the light-absorbing capacity (Tsai and Kuo, 2005; Zheng et al., 2015; Liu et al., 2011). To comprehensively understand this enhancement effect induced by SNA, we conducted tens of sensitivity experiments under different levels of SNA concentration and relative humidity (RH). As presented in Fig. 6, aerosol absorption extinction coefficient increases with SNA concentration. This dependence on SNA is much notable under lower RH (50 %) before aerosol starts to deliquesce. By contrast, when the air becomes more humid, aerosol water uptake becomes increasingly more important. According to year-round observational data (Zhang et al., 2012), SNA concentrations and humidity condition vary a lot across China. For typical cities in China, the annual-averaged SNA level ranges from 40–60 µg m⁻³ in Nanjing (118.95^∘ E, 32.12^∘ N) and Shanghai (121.45^∘ E, 31.22^∘ N) to almost 140 µg m⁻³ in Beijing (116.30^∘ E, 39.99^∘ N), but the annual mean BC concentrations are approximately 5 µg m⁻³ (Ye et al., 2003; Zhang et al., 2013). In Nanjing, with a lower SNA level but higher RH, SNA-induced hygroscopic growth may play the dominant role in the enhancement of aerosol light-absorbing efficiency. Instead, relatively higher SNA concentration in Beijing makes the main contribution according to Fig. 6. Specifically, the absorption could be elevated by 63 % when RH rises from 50 to 90 % in Nanjing, while for Beijing the corresponding enhancement is only 18 %. Such disparities indicate that aerosol absorption and further impact on boundary layer evolution have a closer link to humidity and will be more important in coastal region at lower latitudes in China.

Figure 6Variation of absorption extinction coefficient at 400 nm as a function of different mass concentrations of scattering aerosols mixing with BC. The BC concentration is fixed at 5 µg m⁻³ under various moisture conditions of relative humidity, i.e., 50, 70 and 90 %. Three main cities (BJ, SH and NJ) are marked in the figure with their annual mean PM_2.5 concentrations.

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Enhanced light absorption and heating efficiency by mixing with SNA certainly perturb aerosol–PBL interactions (Fig. 7). Overall, the PBL responses tend to be magnified in terms of both increased PBL top by near-surface BC and suppressed convections by upper-level BC. For typical wintertime meteorological conditions in Beijing, aging processes could lead to a decline of 5 W m⁻² in surface heat flux and an additional 15 % decrease in the PBL top at a maximum when compared with those caused by freshly emitted BC. What is more, when BC concentration is fixed at 5 µg m⁻³ and SNA concentration exceeds 80 µg m⁻³, this absorption enhancement leads to the phenomenon that even BC at lower altitudes may increase the stratification and exert a negative effect on PBL development, as shown in Fig. 7. However, this abrupt change is not observed in simulations with only SNA aerosols included. In other words, there probably exists a critical point of the BC∕SNA ratio for its associated dome effect, from which the impact of lower-level BC on PBL suppression would be oppositely attributed to a large decrease in surface sensible heat flux.

Figure 7Enhanced decreasing/increasing of PBL height (contour map) and enhanced reduction of sensible heat flux at surface (dashed isoline) caused by amplified absorption of BC internally mixed with scattering aerosols. BC concentration is fixed at 5 µg m⁻³, and the ratio of scattering aerosol components is ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}:{\mathrm{NO}}_{\mathrm{3}}^{-}:{\mathrm{NH}}_{\mathrm{4}}^{+}=\mathrm{3}:\mathrm{2}:\mathrm{1}$, which is based on year-round observations in Beijing (Zhang et al., 2012). The x and y axes are the same as Fig. 4.

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Figure 8Net downward shortwave radiation at surface (SWnet_Surf), surface temperature (Temp_Surf), upwelling shortwave radiation at model top (SWupward_Top) and shortwave heating rate, PBL height for urban and rural underlying surfaces without aerosol effect (a–e), and their corresponding perturbations due to aerosol–boundary layer interaction (f–j).

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Figure 9Different PBL height variations due to specific BC distribution over (a) urban surface and (b) rural land surface. The x and y axes are the same as Fig. 4.

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3.4 A comparison of the dome effect over urban and rural areas

In the past, BC-induced aerosol–PBL interaction has mostly been investigated for cities. However, urban areas only take up approximately 5 % of the area in China, while cropland is the dominant surface type and also features dense population and high PM_2.5 exposure (Liu, 2005; Xu et al., 2011). Frequent regional-scale haze pollution and cropland-dominant land cover in China make it necessary to understand this interaction over rural areas (Yang et al., 2015; Zhao et al., 2013b). The differences in surface parameters between cities and rural area are listed in Table 2. Comparatively, rural surfaces, including cropland and pasture, are characterized by larger surface albedo, higher soil moisture and greater heat capacity.

The radiation energy balance without any influence from aerosol already shows great disparities for the two kinds of land surface. Under the same level of incident solar radiation intensity, net shortwave radiation at the ground surface is mainly determined by land surface albedo. In comparison with urban areas, less net downward solar radiation on rural surfaces is ascribed to larger albedo reflecting more solar radiation, accompanied by higher upwards shortwave radiation flux at the top of the atmosphere, as shown in Fig. 8. Correspondingly, the surface temperature in rural areas at noon is almost 1.5 ^∘C colder than that in urban areas, indicating a strong urban heat island effect (Oke, 1982). As for the atmospheric heating, there is little difference over both surface types when excluding the radiative perturbation of aerosols. The resultant height of the PBL is expected to be 250 m lower in rural areas.

If taking the aerosol radiative effect into account when BC is 10 µg m⁻³ around an altitude of 1000 m, over both urban and rural areas, net downward shortwave radiation flux, surface temperature and upwelling shortwave radiation show a notable decrease. At the same time, atmospheric heating rate in the upper air increases in response. The most distinctive difference between these two kinds of land surface is that upwelling shortwave radiation flux at the top of the atmosphere over rural surfaces shows a reduction twice high as over urban surfaces, indicating that a larger portion of solar energy is blocked in the atmosphere, which corresponds to a much stronger atmospheric heating rate due to radiation absorption. At the same time, it suggests a slightly larger decrease in surface temperature over rural surfaces, followed by a lower sensible heat transfer into the atmosphere. The greater surface cooling together with more intense upper warming jointly enhances stable stratification. Therefore, the decrease in the PBL top in rural areas is double that in cities, as shown in Fig. 8.

A comprehensive analysis of responses of the PBL to various magnitudes and altitudes of BC aerosol over urban and rural land surfaces is illustrated in Fig. 9. As mentioned before, since the PBL is less well developed in rural area, the altitude of the BC plume with maximum suppression effect on the PBL was slightly lower than that over cities. Additionally, BC-induced heating is more intensive over rural surfaces due to the fact that larger albedo results in more shortwave radiation reflected by the ground surface, part of which is absorbed by BC aerosol when transferring upwards. Consequently, the promotion and suppression effect on the PBL attributed to BC aerosol over rural surfaces is about 15 % larger than that over urban surfaces. That is, BC would exert a more intense dome effect over rural surfaces. It should be noted that residential combustion of raw coal and biofuel in a small domestic stove in rural area is responsible for the majority of BC emission in China (Zhi et al., 2008; Li et al., 2017a). A more stable PBL and more significant dome effect over rural surfaces would further favor the formation and accumulation of regional air pollution.