The model used in this study is UCLALES-SALSA, which is a large-eddy simulation model (UCLALES) fully coupled to the sectional aerosol model (SALSA). UCLALES-SALSA has been used to examine the impact of aerosols on stratocumulus clouds, radiation fog and cloud seeding and to examine the aerosol–PBL feedback in Beijing . LES models resolve the three-dimensional turbulent field of wind and scalar concentrations, directly resolve most of the energy and parameterise only the smallest scale eddies. UCLALES uses the Smagorinsky–Lilly subgrid model, with leapfrog time stepping used for advection of momentum variables and forward time stepping for advection of scalar variables, based on fourth-order differential equations. Boundary conditions are periodic in both horizontal directions and fixed in the vertical. The surface scheme for moisture and heat is based on a coupled soil moisture and surface temperature scheme by , which explicitly calculates surface temperature and sensible and latent heat fluxes. The surface scheme used in this case has been adapted and tested for the urban environment of Beijing and the setup which includes the addition of a diurnal anthropogenic heat flux (Qf) and alterations to the surface heat capacity value as detailed in .

SALSA is a sectional aerosol model which has been fully coupled to both UCLALES and the climate model ECHAM . SALSA bins aerosol particles according to size, with three bins for aerosol particles in the nucleation mode (diameter between 3 and 50 nm) and two sets of seven parallel size bins for aerosol particles in the Aitken, accumulation and course modes (diameters between 50 nm and 10 µm), which allow for aerosols to be both internally and externally mixed. In the results set out here, we assume all particles to be internally mixed. Processes including deposition of aerosols, semi-volatile condensation, nucleation and emissions are switched off, but aerosol coagulation and water condensation on aerosol particles are turned on. For these simulations, organic carbon (OC), SO42-, NO3-, BC and NH4+ are included. We use the same size distribution for all simulations (Table 1), and composition is varied slightly to examine the impact of fractional composition changes of BC (Table 2).

To calculate aerosol–radiation interactions, SALSA uses a four-stream radiative transfer scheme based on the work by . This scheme is fully coupled to UCLALES to allow for feedback on turbulent dynamics and is a four-stream method integrating over 6 SW bands and 12 LW bands. To account for the impact of aerosol size on aerosol–radiation interactions, we use pre-computed constant refractive indices and use lookup tables for the aerosol-extinction cross section, asymmetry parameter and single-scattering albedo, which are calculated as a function of the size parameter (α=Dpλ), where Dp is the particle diameter, and λ is the wavelength of light. In this work we set all imaginary parts of the refractive indices in the SW to zero apart from that of BC, which is set to values according to . This allows us to consider BC as the only absorbing aerosol. SALSA treats internal mixing for optical properties in a simple way, through volume averaging of the complex refractive index of each component in each particle. Optical properties of the entire particle are calculated from the average refractive index of the particle according to volume as detailed in . Therefore, the potential of scattering aerosols to enhance absorption of BC through the “lensing effect” is not considered here.

The work presented here is divided into three sections, and the specific setup for each sensitivity is detailed in the appropriate section. We perform simulations for 2 and 3 December 2016 in Beijing, varying the altitude of the aerosol layers and fractional composition. Initial meteorological conditions were taken from radiosonde profiles which are located at Beijing International Airport, with measurements being taken twice per day at 08:00 and 20:00 local time. Aerosol composition and size parameters were calculated based on ground-based measurements taken at 08:00 on 3 December 2016 during the Air Pollution and Human Health (APHH) winter field campaign (Shi et al., 2019). The initial aerosol vertical profiles were estimated based on the gradient of boundary layer profiles. The model was set up at 08:00 LST and run for 12 h including 1 h spin-up time. The horizontal domain size was 5.4×5.4 km2 with a resolution of 30 m, and the model top was set to 1800 m with a vertical resolution of 10 m. For all simulations, the initial size distribution is outlined in Table 1, while the fractional composition of the aerosol particles for BC and no BC simulations is detailed in Table 2. For all results, PBL top or maximum PBL height is taken as the height at which there is a maximum gradient in potential temperature (θ).

Individual case setups for the changing conditions examined in this paper are detailed in Sect. 2.2. Overall, three case study experiments with a total of 14 simulations were performed to examine the different impact of (1) aerosol loading at different altitudes both with and without the effect of BC (Case Aero_load), (2) different initial meteorological conditions (Case Met) and 3) changing concentrations of BC within the aerosol column (Case BC_load). Section 2.2.1 outlines the setup of simulations for the first case study (Case Aero_load), which examines the impact of varying the composition of aerosol layers at different altitudes to either include or not include BC. These six simulations are varied so that there are three different altitudes for an aerosol layer, and each layer either has a fractional composition of 10 % BC or no BC (Table 2). In these simulations, the aerosols are only present within the specified layer, with no aerosols present initially above or below the layer. Section 2.2.2 outlines the setup for the second case study (Case Met), which focuses on examining the effect of initial meteorological conditions on the impact of BC heating within the PBL on boundary layer. For these four simulations only, a surface aerosol layer is considered, and the initial meteorological conditions are either taken from the morning of 2 or 3 December 2016. Section 2.2.3 describes the setup for the third case study (Case BC_load) simulations, which examines the impact of varying the fraction of BC in different vertical layers for simulations where aerosols are present throughout the column.

Results from varying the height of aerosol layers in the column, with and without BC aerosols, show that at all altitudes, BC in the aerosol layer has more impact on PBL dynamics than the effect of scattering aerosols alone (no BC simulations) (Table ). Specifically, simulations without BC have a small effect on surface temperature, sensible heat flux and PBL height. At the surface (Aero_load_BCsurf), BC decreases downwelling surface SWR by 4 % compared to including only scattering aerosols (Aero_load_noBCsurf), due to the increased absorption caused by increasing the BC fraction. This decreases maximum surface sensible heat flux (SHF) by 11 % and slightly decreases surface temperature by 0.02 %. However, BC absorption of SWR at this altitude causes warming of the air layer above the surface (Aero_load_BCsurf), leading to a slight increase in air temperature at 10 m (0.07 %) and PBL height (0.4 %) compared to the Aero_load_noBCsurf simulation (Table ).

For further analysis, we calculated SW heating rate at time (t) by BC as the change in SW radiative flux (↓SW – ↑SW), divided by the specific heat capacity of air (Cp) and multiplied by the density of air (ρ) as in Eq. (1). Each time step (t+Δt) here is 2 min.

1SW heating rate(t)=(↓SW-↑SW)(t+Δt)-(↓SW-↑SW)(t)Cp⋅ρ

We calculate that the heating rate of BC varied between 0.1–0.2 K/h, which could lead to a maximum heating of the PBL throughout the day in wintertime Beijing of 1.6–2 K. If the temperature inversion during the day was small (1–3 K), this additional heating by BC within the PBL and at PBL top could break the temperature inversion at PBL top and increase PBL height. However, under a strong temperature inversion as on 3 December, this heating within the PBL was not strong enough to reduce the temperature inversion fully, and so there was a very small increase in PBL height. Consequently, BC heating within the PBL in this case only resulted in a very small (0.4 %) increase in PBL height (Table 6). The strength of the temperature inversion and the growth of the PBL throughout the day are impacted by the synoptic-scale meteorological conditions. Furthermore, the low albedo (0.2) and high heat capacity of the underlying surface, typical of an urban environment, mean that BC at the surface will have a lower impact than studies which have examined the effect of polluted environments over high albedo surfaces, for example, clouds or rural environments .

Figure 5 outlines the changes in SW downwelling and upwelling radiation as well as the SW heating rate due to the presence of BC in the aerosol layers for all three simulations which include BC (Aero_load_BC700, Aero_load_BC500 and Aero_load_BCsurf from left to right respectively). In the case of BC aloft (Aero_load_BC700) there is a reduction in downwelling SW radiation both within and under the aerosol layer (Fig. 5d) and a reduction in SW upwelling radiation (Fig. 5g) through the layer due to absorption. The reduction in downwelling radiation beneath the aerosol layer leads to a cooling effect due to less available radiation heating the air. Meanwhile the absorption of SW radiation in the aerosol layer causes heating. This results in a change in the thermal profile of the atmosphere; it enhances the temperature inversion and decreases maximum PBL height and atmospheric temperature (Table ).

Aerosol layers with identical mass mixing ratios are initialised between 500–950 and 700–1150 m to examine the impact of the altitude of the aerosol layer for aerosols above the PBL. The higher aerosol layer (700–1150 m) has less of an impact on PBL height than simulations with the lower aerosol layer (500–950 m). For example, Table 6 shows that case Aero_load_BC500 reduces maximum PBL height by 6.7 % compared to the base case, whereas case Aero_load_BC700 only reduces maximum PBL height by 2.96 %. When there are aerosols at 500 m, aerosols can become entrained into the upper PBL, as the PBL develops. This results in a strong heating at the top of and above the PBL, causing a larger decrease in PBL height compared to when the aerosol layer exists higher aloft. Figure  shows the potential temperature lapse rate throughout the day for each of the aerosol layers. This shows the inversion for including the aerosol layer at 500 m is much stronger than for the 700 m aerosol layer. This causes the larger suppression of PBL development observed under these conditions.

In these simulations we examined the sensitivity of BC surface heating on turbulent dynamics to different initial meteorological conditions. Specifically, we assessed whether BC at the surface can cause heating to a large enough extent to overcome the temperature inversion and enhance PBL development, under different initial conditions. On the 2 December, simulations with no aerosols (Met_0212_noaero) show a temperature inversion above PBL top (400–800 m) of ∼ 4 K at 14:00 LST, compared to ∼ 7 K on 3 December (500–900 m) (Fig. 7). Consequently, including BC at the surface shows a larger enhancement in turbulence for 2 December, when the initial temperature inversion is lower. In this case, BC at the surface causes a 5 % increase in PBL height, increasing turbulent kinetic energy (TKE) and minimising the decrease in sensible heat flux. This is despite the change in SW downwelling and upwelling radiation being similar for both days (Fig. ).

Due to the variation in initial meteorological conditions such as humidity, temperature and wind (Fig. ), it is difficult to ascertain whether the difference in PBL development caused by BC surface heating is a direct impact of the strength of the temperature inversion. However, it is clear that at least for the case of BC within the PBL, meteorological conditions affect the magnitude of surface heating on PBL development. These results highlight the susceptibility of the aerosol–PBL feedback to initial conditions as has been outlined in previous work by . In both cases, the BC concentrations cause a heating rate of 0.2 K/h at the surface, which leads to increases in the surface air temperature. Although there is increased turbulence caused by BC heating on 2 December, the level of heating within and at the top of the PBL is not enough to overcome the strong temperature inversion and the stagnation caused by aerosol–PBL feedback. Consequently, BC heating within the PBL under these conditions will be unlikely to promote haze dissipation due to the strength of the temperature inversion.

Figure  shows the potential temperature lapse rate at 12:00, 14:00 and 16:00 for simulations with no aerosols and with BC at the surface for 2 and 3 December. This shows BC at the surface reduces the temperature inversion at PBL top in both cases. Furthermore, at 14:00 the PBL top is higher on 2 December for simulations including BC at the surface (Met_0212_aero). Here, compared to 3 December (Met_0312_aero), the heating within the PBL and at PBL top appears to be almost strong enough to break the temperature inversion at PBL top and enhance PBL development. As can be seen in Fig. d, the aerosol layer becomes vertically mixed throughout the day as the PBL develops. These results show that under conditions with a weaker temperature inversion, BC heating at the surface enhances turbulent mixing to increase PBL development. If the heating caused by BC at the surface is strong enough, or under conditions where the temperature inversion is weaker, this may allow for BC to become vertically mixed to high levels. When the PBL collapses overnight, this leads to BC being present above the PBL, which may enhance atmospheric stagnation and enhance the intensity of pollution events.

Section 3.1 shows the aerosol radiative forcing and perturbations due to BC are higher than the scattering effect of other aerosols. However, the case Aero_load only identifies the effect of either aerosol concentrations within or above the PBL, where they can exist both within and above the PBL for several reasons. Here, we examine the idea of fully reducing BC at the surface as a proxy for decreasing BC emissions locally, where other species are still present, so, for example, targeting sources of BC, such as biomass burning without tackling other sources of inorganic aerosols or volatile gases. BC aloft is considered to be brought into Beijing through regional transport or entrainment from a polluted residual layer. A study by suggested that the impact of local BC emissions will heat the PBL and lead to pollutant dissipation through promoting atmospheric buoyant turbulence. Results from Sect. 3.1 and 3.2 show the reasonably low impact of BC at the surface in enhancing PBL development, compared to the suppression caused by the BC layer at PBL top. Furthermore, if BC from the surface gets mixed into the residual layer, it will negatively impact turbulent mixing the next day. This section looks at including BC and other aerosols both within and above the PBL and changing the relative BC concentration in the column.

In this section, we include aerosols throughout the column and varied the fractional aerosol composition to have BC (BC_load_full) and no BC (BC_load_noBC) throughout the profile and BC above 500 m (BC_load_500) and 1000 m (BC_load_1000) (Fig. 4). Our results show that including BC both within and above the PBL causes a large reduction in PBL height (17 %) compared to no BC (Table 7). In Sect. 3.1 and 3.2 simulations with BC have a slightly higher PBL height compared to those without (Table 3). Therefore, the decrease in PBL height for these simulations (BC within and above the PBL) indicates that the potential enhancement in turbulence by BC within the PBL (as seen in Sect. 3.1 and 3.2) is eclipsed by the effect of BC above the PBL, which acts strongly to prevent PBL development through the day. This is likely due to the low level of SWR available for BC heating at the surface in the full column BC simulations, due to absorption by BC at higher altitudes.

Table 7 shows that including BC has a significant impact on reducing SW downwelling and upwelling radiation, which consequently feeds back and reduces surface temperature and sensible heat flux. Simulations including BC across the entire column (BC_load_full) show the largest decrease in downwelling and upwelling SW radiation, due to the overall larger columnar concentration of BC. Including BC at the surface (BC_load_full)) leads to higher air temperature at 10 m compared to simulations with BC aloft (BC_load_500 and BC_load_1000) only but lower air temperature at 10 m than not including BC at the surface (BC_load_noBC). This is likely due to BC throughout the column absorbing radiation, which leads to heating but also reduces the amount of SW radiation reaching the air at the surface, consequently reducing surface air temperature. This work shows that any increase in PBL height due to BC at the surface is outweighed compared to the stronger impact of BC above and at PBL top (BC_load_500), which results in the largest decrease in PBL height for simulation with BC across the column (BC_load_full).

Figure 10 shows the BC heating rate per unit mass of BC, taken as the heating rate for BC_load_full – BC_load_noBC simulations. This shows the heating rate per unit mass of BC increases with height as suggested by . Firstly, we see a strong heating effect increasing up to the bottom of the PBL with a decrease in heating rate across the PBL and a further constant increase above the PBL. The larger heating rate of BC at higher altitudes is thought to be due to the higher incident radiation available for BC absorption. Consequently, the heating caused by BC in the atmosphere and the effect on PBL development will be dependent on the altitude of the BC layer as well as the total BC within the aerosol column. This may be important when examining the impact of BC within the PBL as if BC also exists aloft, as there will be less SW radiation reaching the surface due to BC at higher altitudes, and, consequently, as shown here, BC heating in the lower layers will be smaller.

Using a coupled aerosol–radiation LES model in this study allowed for direct investigation and quantification of the impact of absorbing aerosols on boundary layer dynamics. There is an array of benefits of using a high-resolution model which directly calculates rather than parameterises turbulent fluxes for the investigation of heavy pollution episodes. As previously highlighted in this paper, the importance of aerosol–boundary layer feedbacks on heavy pollution episodes, particularly in the megacity of Beijing, has been made clear in the literature over the last decade. Primarily, these studies have utilised measurements of aerosol properties alongside measurements of boundary layer dynamics and meteorology to infer the impact and relationship between aerosols and boundary layer dynamics. Modelling studies of the aerosol–boundary layer feedback mechanism have mostly utilised regional models such as WRF-CHEM, which do not directly resolve turbulent flows. Therefore, the work presented here showcases a novel methodology for investigation of the contrasting impact of absorbing aerosols on boundary layer dynamics and the usefulness of employing such high-resolution eddy-resolving coupled aerosol–dynamic models to examine physical processes and interactions which can severely influence pollution episodes.

However, applying the idealised model setup to a polluted megacity has limitations. Not being able to fully account for changes in synoptic conditions or understand the impact of regional transport of aerosols on the pollution episodes is a major limitation of the work presented here. Similarly, this work does not look at the impact of secondary aerosol formation which has been found to be a major factor in the rapid increase in PM2.5 concentrations during Beijing haze episodes. Specifically, with regards to the effect of black carbon on aerosol–boundary layer feedback, a current limitation of the work presented here is that it does not account for the absorption enhancement of black carbon by scattering aerosols through the lensing effect . Furthermore, in this work we consider the only absorbing aerosol to be black carbon, while brown carbon (BrC) has been found to be an important absorber of radiation in several polluted megacities. Although BrC is not as strong an absorber of radiation as black carbon, its presence in high concentrations in polluted urban environments means its impact on these feedbacks should not be discounted . There is scope within UCLALES-SALSA to change the refractive indices and mixing type to reflect some features related to changes in absorption. However, in this work, for simplicity and to allow for the ability to isolate different effects, these were not considered.

Combining all the results presented in this paper as well as other research by and , here we detail a potential mechanism for the influence of BC on air pollution episodes in Beijing (Fig. 11). Although this mechanism has not been fully tested in this work due to computational cost, we hypothesise that locally emitted BC which heats the PBL could promote PBL development (Sect. 3.2), resulting in the BC becoming well mixed through the PBL. When the nocturnal boundary layer forms, the BC will remain in the residual layer overnight and exist above the PBL the next day. This would then suppress PBL development as shown in Sect. 3.1 and 3.3 of this work and in the work by . However, if synoptic conditions on the next day changed to weaken the temperature inversion and the PBL developed, as observed during this haze episode by , the BC aloft could become entrained into the PBL to heat the surface layer and help promote buoyant turbulence and the dissipation of pollutants (Fig. 11). This mechanism could have strong influences for policy, and we would therefore recommend that further research be performed to directly investigate the mechanism and its potential to influence the severity and longevity of haze episodes.