Influence of photochemical aging on light absorption of atmospheric black carbon and aerosol single scattering albedo

Coating enhancement of black carbon (BC) light absorption (Eabs) is a large uncertainty in modelling direct radiative forcing (DRF) by BC. Reported Eabs values after atmospheric aging vary 20 widely and the mechanisms responsible for enhancing BC absorption remain elusive. Here, we report on the direct field measurement of size-resolved mixing state, Eabs and aerosol single scattering albedo (SSA) at λ = 532 nm at a rural site in East China from June to July 2016. Strong diurnal variability of Eabs, SSA, and Ox (Ox = NO2 + O3, a proxy for atmospheric photochemical aging) was observed. A method that combined Eabs and SSA was developed to retrieve the fraction contribution of BC 25 absorption (fBC), lensing driven enhancement (fLens), as well as the fractional contribution of coating absorption (fraction absorption contribution (fShell), the coated shell diameter (DShell) and the imaginary part of the complex refractive index (CRI) of the shell (kShell)). Parameterization of Eabs and SSA captures much of the influence of BC coating and the particle absorption. In our measurements at this site, the absorption amplification depended mainly on the coating thickness and the absorption of 30 coating materials. The lensing driven enhancement was reduced by light absorption of the shell. Our 2 observations highlight the crucial role of photochemical processes in modifying the absorption of BCcontaining particles. One implication of these findings is that the contribution of light-absorbing organic compounds (Brown carbon, BrC) at longer aging time should be included in climate models.

Abstract. Coating enhancement of black carbon (BC) light absorption (E abs ) is a large uncertainty in modelling direct radiative forcing (DRF) by BC. Reported E abs values after atmospheric aging vary widely and the mechanisms responsible for enhancing BC absorption remain elusive. Here, we report on the direct field measurement of size-resolved mixing state, E abs , and aerosol single-scattering albedo (SSA) at λ = 532 nm at a rural site in east China from June to July 2016. Strong diurnal variability of E abs , SSA, and O x (O x = NO 2 + O 3 , a proxy for atmospheric photochemical aging) was observed. A method that combined E abs and SSA was developed to retrieve the fraction contribution of BC absorption (f BC ), lensing-driven enhancement (f Lens ), as well as the fractional contribution of coating absorption (fraction absorption contribution (f Shell ), the coated shell diameter (D Shell ) and the imaginary part of the complex refractive index (CRI) of the shell (k Shell )). Parameterization of E abs and SSA captures much of the influence of BC coating and the particle absorption. In our measurements at this site, the results showed that the absorption amplification depended on the coating thickness and the absorption of coating materials, and photochemistry plays a role in modifying the absorption of BC-containing particles. The lensing-driven enhancement was reduced by light absorption of the shell. One implication of these findings is that the contribution of light-absorbing organic compounds (brown carbon, BrC) at a longer aging time should be included in climate models.

Introduction
Black carbon (BC) is the most efficient light-absorbing component of atmospheric aerosols (Jacobson, 2001;Moffet and Prather, 2009;Cappa et al., 2012) and plays an important role in the global climate system (Ramanathan and Carmichael, 2008;Bond et al., 2013). However, accurately constraining the direct radiative forcing (DRF) of BC is a challenge owing to the discrepancy between observed and modelled estimates of BC light absorption (Gustafsson and Ramanathan, 2016). For example, a recent study has shown that the improved model-estimated DRF of BC (+0.21 Wm −1 ) by including BC absorption enhancement and separately treating the aging and physical properties of fossil fuel and biomass burning BC was about 3 times lower than the values reported in the Intergovernmental Panel on Climate Change (IPCC) 5th assessment report (+0.6 Wm −2 ), which suggested an overestimation of BC lifetime and an incorrect absorption attribution of light-absorbing organic compounds (brown carbon, BrC) (X. . BC particles are produced from incomplete combustion of fossil fuels, biofuels, and residual biomass (Novakov et al., 2003;Bond et al., 2004Bond et al., , 2007. Freshly emitted BC is mainly externally mixed and occurs in fractal-like agglomerates. Atmospheric BC particles undergo several aging processes, including coagulation with other particles, condensation of vapours onto surfaces, and chemical oxidation (Slowik et al., 2004;Zhang et al., 2008;Petzold et al., 2013). Individual BC particles become coated (i.e., internally mixed) with sulfate, ammonium, organics, nitrate, and water (Bond and Bergstrom, 2006;Cheng et al., 2006;Schwarz et al., 2008;Ervens et al., 2010;Zaveri et al., 2010). Aging processes dramatically change the morphology, hygroscopicity, and mixing state of BC-containing particles, thereby altering their optical properties and the magnitude of their contribution to climate forcing (Jacobson, 2001;Bond and Bergstrom, 2006;Schwarz et al., 2008;Zhang et al., 2008).
The light absorption enhancement of BC particles caused by coating is quantified by E abs , the ratio of the absorption coefficients of coated and bare BC. E abs introduces a large uncertainty in the DRF of BC, which is the second most important contributor to global warming (Jacobson, 2001;. Current models simply adopt a constant enhancement value (∼ 1.5 or 2) for the calculation of DRF of BC Bond et al., 2013;. In contrast, reported E abs values vary widely (Peng et al., 2016;Liu et al., 2017). Field measurements along the California coast and ground site in Sacramento (California) , Shenzhen (South China) (Lan et al., 2013), the Nagoya urban area (Japan) (Nakayama et al., 2014), and urban Los Angeles (USA) (Krasowsky et al., 2016) found negligible absorption enhancement (E abs < 1.1) and weak dependence on the extent of photochemical aging (estimated from the value of −log([NO x ] / [NO y ]), where NO x = NO + NO 2 and NO y includes the sum of NO x and its oxidation products; Deolal et al., 2012). Biomass burning measurements showed an absorption enhancement of 1.7 at λ = 532 nm . Recent observations in Chinese cities (Peng et al., 2016;X. Cui et al., 2016;Xu et al., 2016;Chen et al., 2017;Cheng et al., 2017; provide evidence for a higher E abs in polluted conditions, with values ranging from 2 to 3. The mechanisms responsible for enhancing BC absorption remain elusive due to the complexity of the aging process and its varied sources. More studies in receptor locations with a longer BC aging time are required to better constrain E abs (Gustafsson and Ramanathan, 2016;Boucher et al., 2016).
In this work, the influence of photochemical aging on BC mixing state, E abs , and aerosol single-scattering albedo (SSA, ω, defined as the ratio of scattering to extinction co-efficient) at a rural site in east China during the summer was studied by using a volatility tandem differential mobility analyser (VTDMA) and a thermal denuder (TD) approach combined with a cavity-enhanced albedometer operating at λ = 532 nm. In summer, O x (O x = O 3 + NO 2 ) exhibits good correlation with secondary pollutants Cevik et al., 2016;Ji et al., 2016). The concentration of O x was used as a proxy for atmospheric photochemical aging (Hallquist et al., 2016;. We find that photochemical aging results in the growth of particle coating and higher fractions of internally mixed BC particles. The modelling and parameterization of E abs and SSA capture the variability of BC coating amount and the particle absorption and provide a plausible new method to better constrain the contribution of BC to the DRF.  (Fan et al., 2010;Li et al., 2011;Deng et al., 2012); it is a rural background site surrounded by basic farmland protection areas and has no significant industrial pollution sources or tall buildings nearby.
Instruments were installed in a temperature-controlled room with two sample inlets about 1 m above the roof ( Fig. S1 in the Supplement). Each inlet consisted of one PM 2.5 cyclone (BGISCC2.654) with a 50 % cut point at 2.5 µm, and was first dried below 40 % relative humidity (RH) using a diffusion drier. The sampling rates at both inlets were controlled with mass flow controllers (MFCs) and set at 10 L min −1 . One of the inlets was used for the volatility measurements; the other inlet stream was used for the optical measurements. Trace gas pollutants such as CO, NO x , SO 2 , and O 3 were, respectively, measured by Thermo 48i, 42i, 43i, and 49i analyser.

Volatility measurement
Size-resolved mixing state of BC was measured with a VT-DMA developed in-house. The VTDMA was structurally similar to other systems described in the literature Wehner et al., 2009;Cheung et al., 2016) and comprised the following: 1. an electrostatic classifier (DMA, differential mobility analyser, TSI 3080) for the initial selection of monodisperse particles; 2. a custom-built stainless steel heating tube (inner diameter of 0.77 cm, 80 cm long, and heated to 300 ± 5 • C) for removing nonrefractory particulate matter; and 3. a scanning mobility particle sizer (SMPS, TSI 3936) comprising a DMA (TSI 3080) and a condensation particle counter (CPC, TSI 3776) for measuring the size distribution of the heated sample in the range of 15 to 661 nm.
Diffusion losses and the effect of multicharged particles were corrected by the instrument software. The residence time of the sample in the heating tube was about 1.2 s and is comparable with other VTDMA systems (0.3-1 s) (Brooks et al., 2002;Philippin et al., 2004;Villani et al., 2007).

Optical measurement
The optical properties of dry PM 2.5 particles were measured with a cavity-enhanced albedometer operating at λ = 532 nm (Zhao et al., 2014;Xu et al., 2016). The albedometer combined broadband cavity-enhanced spectroscopy (BBCES) with an integrating sphere (IS) for direct, in situ, and simultaneous measurement of extinction (b ext ) and scattering (b scat ) coefficients, thus allowing the calculation of the absorption (b abs ) coefficient and SSA. Compared with our previously reported 470 nm system (Zhao et al., 2014;Xu et al., 2016), the new 532 nm albedometer was modified by inserting a quartz tube within the IS to prevent the degradation of the IS reflectivity and to reduce the sample's residence time (Dial et al., 2010;. The sample volume of the albedometer was about 0.3 L and the flow rate was 1.5 L min −1 at atmospheric pressure. The details of the evaluation of the instrument have been described in our previously published paper (Zhao et al., 2014;Xu et al., 2016;. Detection limits of each parameter were determined by using an Allan variance analysis. With a 30 s integration time (an average of 300 individual spectra, each with 100 ms exposure time), the detection limits under ambient aerosol loading condition for the scattering and extinction measurements were better than 0.15 and 0.12 Mm −1 , respectively. The accuracy of the instrument was evaluated with laboratory-generated, NIST traceable monodispersed polystyrene latex (PSL) spheres. During field observations, the optical system was calibrated with N 2 , CO 2 , and PSL every 2 weeks.
The total uncertainties (summed in quadrature of each error source) in extinction, scattering, absorption coefficients, and SSA measurements were estimated to be less than 4 %, 3 %, 5 %, and 4 %, respectively. Uncertainty in extinction mainly arose from the uncertainties in mirror reflectivity (1 -R, ∼ 1 %), the ratio of cavity length to the cell length containing the air sample when the cavity mirrors were purged (R L , ∼ 3 %), and particle losses in the cavity (∼ 2 %). Uncertainty in the scattering measurement was mainly caused by uncertainties in the experimentally determined scattering cal-ibration coefficient (K', ∼ 2 %), particle losses in the cavity (∼ 2 %), and the truncated fraction of total scattering. (Since most particles in the observation were smaller than 1 µm, the uncertainty associated with truncation angle was < 1 %, as discussed in Sect. S2 in the Supplement.) Since measurements of the extinction and scattering coefficients were of the identical sample, particle losses do not affect the SSA measurement (Zhao et al., 2014;Xu et al., 2016).
The sampled ambient air was divided into two channels: the first channel was directly pumped into the albedometer to measure the ambient absorption coefficient (b abs,ambient ); another channel was installed with a TD (Dekati Ltd., Finland) operating at 300 • C to evaporate semi-volatile particulate components for measuring the absorption coefficient of refractory BC (rBC; b abs,TD ) (Olson et al., 2015). These two channels were switched automatically every 5 min with an electric ball valve. The flow rate of the TD was 10 L min −1 . Particle losses inside the TD are discussed in detail in Sect. S3 in the Supplement and are generally caused by diffusional and thermophoretic processes (Wehner et al., 2002;Fierz et al., 2007). The optical loss of the TD of ambient aerosol was estimated to be ∼ 32 %. The measured b abs,TD was corrected with the particle losses for further calculation of the absorption enhancement (E abs = b abs,ambient / b abs,TD ). The total uncertainty in E abs measurement was about 9 % (mainly contributed by uncertainties in the measurement of b abs,ambient (5 %), b abs,TD (5 %), and particle losses inside TD (6 %)).

Results and discussion
The concentrations of PM 1.0 , PM 2.5 , and trace pollutants (CO, NO 2 and O 3 ) measured at the station over the measurement period are shown in Fig. 1. For assessing the effect of photochemical oxidation on the aerosol optical properties, the time series of the O x concentration is also shown in the figure. Both O x , PM 1 and PM 2.5 concentrations have clear diurnal cycles. The corresponding meteorological conditions are shown in the Supplement Fig. S8. The average ambient temperature (T ), relative humidity (RH), and wind direction (WD) were 26.0 ± 3.3 • C, 90 ± 11 %, and 2.0 ± 1.1 m s −1 , respectively. The prevailing winds were southerly. Generally, the low wind speed favoured the accumulation of pollutants, and the RH was also quite high. The average concentrations of PM 2.5 and PM 1.0 were 28 ± 14 and 25 ± 13 µg m −3 , respectively. The 48 h backward trajectories ending at 500 m above ground level at the Shouxian site are shown in Fig. S9 in the Supplement. The trajectories were aggregated into five groups after taking into account the wind direction, speed, and the geometric distance between individual trajectories (S. . The air masses in clusters 1, 3, 4, and 5 originated from long-range transport with high speeds for over 40 h. Air masses in cluster 2 originated from the vicinity of Anhui province and moved slowly. The long aging time and residence time of the air masses led to well-aged particles before arriving at the observation site. All air masses were at relatively low altitudes (< 1500 m) and remained within the boundary layer over this 2-day period.

Size-resolved mixing state of BC
Following the approach of Philippin et al. (2004), Cheng et al. (2009), andWehner et al. (2009), most compounds were assumed to be volatilized at 300 • C and the residual non-volatile particles were regarded as rBC. An example of the measured size distribution is shown in Fig. 2. The heated size distribution was divided into three size ranges -"high-volatility" (HV), "medium-volatility" (MV), and "low-volatility" (LV) -to calculate the number fraction of internally mixed BC particles: where N MV is the number concentration of MV particles and is considered to be internally mixed BC. N LV is the number concentration of LV and is considered to be externally mixed BC Wehner et al., 2009;Cheung et al., 2016).
To assess the influence of atmospheric photochemical aging on the mixing state of BC, scatter plots of F in at different diameters and O x concentrations are shown in Fig. 3. Data points are colour-coded with respect to the concentrations of CO, which is related to primary BC emission. The value of F in reflects the competition between fresh emission and atmospheric aging . The freshly emitted particles have lower F in values, while the aging process converts externally mixed particles into internally mixed and then increases the value of F in . In this work, low F in values tended to appear at high CO concentrations, consistent with freshly emitted BC. The observed decreasing trends in F in with O x for particle diameters of 50 and 100 nm were probably due to the increment of the relative contribution of fresh emissions in the small particle size range.
A positive correlation between F in and O x was observed for particle diameters of 150, 200, 250, and 300 nm, respectively. The corresponding oxidation rates of F in were 0.07 and 0.12 % ppb −1 and 0.16 %, and 0.17 % ppb −1 . Particles of these sizes have greater internal mixing and may be more susceptible to photochemical oxidation processes. Very recently, Q.  reported a similar correlation between the number fraction of thickly coated rBC (F rBC , the mixing state of individual rBC was measured with single particle soot photometer, SP2) and O x concentration in highly polluted megacities. The reported oxidation rates of F rBC were 0.58 % ppb −1 for Beijing and 0.84 % ppb −1 for Xi'an, respectively. Photochemical aging resulted in higher amounts of internally mixed BC and a larger fraction of thickly coated BC under more oxidizing conditions.

Temporal and diurnal variations in optical properties
Time series of the measured optical properties are shown in Fig. 4 and include the extinction (b ext ), scattering (b scat ), and absorption (b abs ) coefficients, the SSA for ambient particles (b ambient ) and for particles passed through TD (b TD ), and the corresponding E abs . The mean (and standard deviation) of b ext,ambient , b scat,ambient , and b ext,TD , b scat,TD were 92 ± 64, 81 ± 55, 12 ± 7, and 6.5 ± 4.1 Mm −1 , respectively. The scattering fraction remaining (b scat,TD / b scat,ambient ) was about 0.09 ± 0.05 and indicated that most of the coating species evaporated in the TD at 300 • C. Our value is comparable to the value of 0.08 ± 0.02 reported by Nakayama et al. (2014). The change in the morphology during heating was negligible. The observed diurnal variation in optical parameters (b ext,ambient , b scat,ambient , ω ambient , b abs,ambient ,b ext,TD ,b scat,TD , b abs,TD , ω TD , E abs ), mass concentrations of PM 2.5 , as well as the mixing ratio of CO and the photochemical oxidant (O x ) are shown in Fig. 5. Broadly similar diurnal patterns were observed for the extensive optical properties (b ext,ambient , b scat,ambient , b abs,ambient , b ext,TD , b scat,TD , b abs,TD ) of ambient particles and particles passed through the thermodenuder, and the mass concentrations of PM 2.5 . A strong diurnal variation and similar diurnal patterns in ω ambient , ω TD , E abs , and O x were observed. Patterns of the extensive optical properties and PM 2.5 indicate some local particle emissions from early morning anthropogenic activities. While these changes Figure 2. Examples of the particle number size distributions of ambient aerosol (black points), as well as the VTDMA measured room temperature bypass sample (∼ 25 • C, blue open circles), and the sample passed through a custom-built heating tube at 300 • C (D p,300 • C , red points) for the initial selected diameter of 150 nm (D p ). The corresponding Gaussian fit of the size distributions are shown as black, blue, and red lines. The size distribution obtained after heating was divided into three size ranges according to previously reported empirical cutting diameters. (1) Particles with diameters D p,300 • C / D p < 45 % were denoted as "high-volatility" (HV) and were not considered to be BC. (2) Particles with diameters 45 % < D p,300 • C / D p < 82 % were considered to be internally mixed BC particles (a non-volatile core coated with a volatile shell) and were denoted as "medium-volatility" (MV). (3) Particles with diameters 82 % < D p,300 • C / D p < 120 % were denoted as "low-volatility" (LV) and were considered to be externally mixed BC.  are radiatively significant, changes in PM 2.5 during the early daylight period are weak, suggesting that emitted particles are small and contribute little to the overall particle mass concentration. The SSA shows that particles tend to be more strongly absorbing in early morning than later in the day; however, measured SSA values are not especially low (mean ω ambient ≥ 0.85), consistent with the background nature of the Shouxian site. Thus, freshly emitted particles are therefore relatively unimportant at this site. CO concentrations show minor diurnal variation, consistent with the regional nature of air masses at this site.
Daytime increases in the boundary layer into the midafternoon are especially evident in the PM 2.5 concentration profile. In contrast, ambient scattering and extinction profiles are broadly flat over the same period, indicating more intense photochemical processing and extensive secondary aerosol generation. The same effect is responsible for the mid-afternoon maximum in the intensive optical property ω ambient .

Influence of photochemical aging on E abs and SSA
SSA is one of the most relevant intensive optical properties (Jo et al., 2017) because it describes the relative strength of the aerosol scattering and absorption capacity and is a key input parameter in climate models. Changes in particle size, morphology, chemical composition, and mixing state caused by atmospheric chemical aging processes will alter SSA. The relationships between hourly-averaged ω, ω TD , and E abs with hourly-averaged O x , as well as the scattering plot of hourly averaged ω, ω TD , and E abs that binned in O x (with the same data points in each bin) and the frequency distributions of the hourly averaged data are shown in Fig. 6. Approximately 90 % of the values of ω, ω TD , and E abs during the measurement were within the range of 0.80-0.91, 0.43-0.65, and 1.0-3.5, respectively.
During the summer, O 3 has a central role in the generation of secondary aerosol. Positive correlations between ω, ω TD , and O x concentrations were observed in our measurements ( Fig. 6a and b), which suggests that higher O x actually increases the mass fraction of secondary aerosol particles and the overall ensemble of particle material and SSA. Our result is consistent with Beijing summer observations, where SSA was linearly correlated with the mass fractions of secondary aerosols . The increase in ω TD resulted from incomplete vaporization of non-volatile constituents in the heating tube (Cheung et al., 2016), the generation of low-volatility oxygenated organic aerosol during photochemical aging (Paciga et al., 2016), and the changes in BC morphology (Radney et al., 2014). Summertime volatility measurement of organic aerosol in the megacity Paris shown that about 10 % mass fraction remained with a TD operating at 180 • C (Paciga et al., 2016). However, recent re- Figure 5. The observed diurnal variation in aerosol optical parameters (extinction (b ext ), scattering (b scatt ), absorption (b abs ) coefficients, and SSA (ω)) of ambient particles (b ambient , a-c, g) and particles passed through the thermodenuder at 300 • C after correcting for particle losses (b TD , d-f, h). The absorption enhancement (E abs , i) was calculated as the ratio between b abs,ambient / b abs,TD . The mass concentrations of PM 2.5 (j) and the mixing ratios of CO (k) and O x (l) are also shown for assessing the effect of photochemical oxidation. The optical measurement at λ = 532 nm covered the period 16 June to 23 July 2016. The box and whisker plots show the mean (dots), median (centre solid line), lower and upper quartile (boxes), and 5th and 95th percentile (whiskers). search demonstrated that the remaining non-and low-volatile coating has a minor impact on the absorption measurement of heated particles using TD operating at 250 • C (S. . Theoretical and experiment results show that aging causes the dramatic changes in BC particle morphology He et al., 2015He et al., , 2016Scarnato et al., 2013; and leads to more compact black carbon with higher scattering cross sections (Peng et al., 2016;Y. Wu et al., 2018), which in turn results in an increase in ω TD (Radney et al., 2014;Forestieri et al., 2018). In this regard, the rise in ω TD with increasing O x concentration can be used as an indicator of the changes in BC morphology. The values of ω TD remained stable for O x mixing ratios larger than 45 ppbv, which possibly indicate that the change in the proportion of non-volatile constituents or BC morphology was negligible.
E abs also rose with higher O x mixing ratios ( Fig. 6c and Fig. S10 in the Supplement), but with a different pattern compared to ω and ω TD . From the scattering plot of the hourly averaged E abs that was binned in O x , a monotonic growth of E abs with increasing O x can be observed below 45 ppbv O x (from 2.1 to 2.6). For O x mixing ratios between 45 and 57 ppbv, E abs values remained constant (∼ 2.4). The small drop in E abs value for the O x bin larger than 57 ppbv was probably caused by the limited data numbers for O x larger than 75 ppbv and was statistically insignificance. The most frequently occurring value of E abs for the whole measurement was ∼ 1.7.
Since the emission sources, weather conditions, and aging degrees of BC particles varied from day to day, the relationship between E abs and atmospheric chemistry is rather complex. Four selected cases with different wind directions were used to demonstrate this complexity (as shown in Fig. 7, the day-and nighttime data were separated). The corresponding wind directions and speeds, RH values, and CO concentrations are shown in Fig. S10 in the Supplement. The patterns of E abs with O x were different for air masses from different directions. For cases 1 and 2, the mean values of E abs were comparable (1.9 ± 0.2 for case 1 and 1.8 ± 0.6 for case 2), and the hourly-averaged ω and ω TD grew with increasing O x in both cases. In case 1, E abs ranged from 1.5 to 2.3, with a growth rate of ∼ 0.01 ppbv −1 in the daytime. During this period, winds were typically from the north, which corresponding to a short transported pathway of air masses (Fig. S9 in the Supplement). The low degree of aging led to a small E abs value. In case 2, E abs ranged from 1.1 to 3.7, and the corresponding growth rates was ∼ 0.05 ppbv −1 in the daytime. It is worth noting that the low E abs values in this period corresponded to low ω values (Fig. 7c), which indicated the influence on the local emissions on E abs . For cases 3 and 4, ω and ω TD increased slowly with O x in comparison with cases 1 and 2. Monotonic relationships were found here, with growth rates of ∼ 0.01 and 0.05 ppbv −1 . The large E abs values in the daytime than nighttime suggested that photochemistry plays a positive effect on the increment of absorption enhancement. These results demonstrated the complex influence of emission and aging degree of BC particles in modifying the light absorption of BC-containing particles. For air masses from different directions, the relationship between E abs and O x may be different.
A list of recently reported E abs values is shown in Table 1. The averaged and standard deviation of E abs value at λ = 532 nm for this work was 2.3 ± 0.9, which agreed well with values from Boulder using the same TD method combined with a photoacoustic spectrometer (PAS)  from Yuncheng (X.  and Jinan  using an aerosol filtration-dissolution (AFD) method and from Beijing (Peng et al., 2016;Xu et al., 2016;Cheng et al., 2017) based on the mass absorption efficiency (MAE) method. Our result is also comparable to that reported in laboratory studies of thickly coated BC particles where E abs ranged from 1.8 to 2.4 (Bond et al., 2013). Shenzhen, China (urban) 1.07 (532 nm) Lan et al. (2013) August-September 2011; absorption coefficients at 405, 532, 781 nm measured were measured with PAS; rBC mass concentration was with SP2; MAE 532 nm = 6.5 ± 0.5 m 2 g −1 (with lowest value of 6.08 m 2 g −1 and highest value of 8.5 m 2 g −1 , respectively, treated as totally, externally mixed, and internally mixed); SP2 measured BC, core diameter ∼ 180 nm.
Xi'an, China (  A chamber study by Peng et al. (2016) suggested that the primary BC was in a chain-like structure with low particle density and then collapsed to a semi-spherical particle. During this stage, there is no significant absorption enhancement (E abs ranged from 1.0 to 1.4). With continued coating growth with several hours' aging in the chamber, the semi-spherical particle was further collapsed and finally transformed to fully compact spherical, internally mixed BC particles (E abs increased to ∼ 2.3-2.4) (Gustafsson and Ramanathan, 2016). Recent morphologically constrained modelling developed by Y.  demonstrated that after full aging, the BC particles became a more compact aggregation, which leads to a stable range of E abs (averaged value ∼ 2.5, with a minimum value of ∼ 2 and a maximum value of ∼ 3.5). Photochemical aging processes lead to internal mixing and a larger coating fraction that enhances the light-absorbing capacity of BC particles (Lack and Cappa, 2010). Our finding of the growth of E abs associated with the increasing O x concentration suggests that secondary organic aerosol (SOA) includes lightabsorbing organic compounds (BrC) , and that BrC's overall contribution to particle absorption grows under more oxidizing conditions. As discussed in the next section, we find an increase in the imaginary part of the complex refractive index (CRI) of the coated shell.

Coating absorption and light absorption enhancement
Mie theory, which was treated as the basis of the IPCC 5th assessment report due to its computational efficiency and applicability to radiative transfer models (Jo et al., 2017), is a powerful tool for optical data interpretation  and the reliability of the core-shell model has been verified in many optical closure studies Ma et al., 2012;C. Wu et al., 2018). According to Peng et al.'s (2016) chamber study results, BC particles change to a fully compact spherical morphology in less than 1 day. Volatility measurements and analysis of the air masses indicated that the atmospheric aerosol observed in summer at the rural site was well aged. In this work, the particle size distribution information was not available. A method based on single-particle core-shell Mie theory (Bohren and Huffman, 1983;Saleh et al., 2015) was developed to interpret the observed changes in E abs associated with O x in this work. The sensitivity of this assumption is discussed in Sect. S7 in the Supplement. The modelling was based on simultaneous constraining of E abs and SSA to retrieve the fraction contribution of BC absorption (f BC ), lensing-driven enhancement (f Lens ), coating absorption (f Shell ), as well as the coated shell diameter (D Shell ) and the imaginary part of the CRI of the shell (k Shell ). A scatter plot of measured diurnally averaged E abs and SSA for different photochemical oxidant concentrations is shown in Fig. 8. The solid points are the observed results and colour-coded with respect to the concentrations of O x . The open circles are the single-particle Mie core-shell modelled results with an optimized BC core size of 160 nm and colourand size-coded with respect to the imaginary part of the CRI of coating material (k shell ) and the diameter of coating material (D shell ), respectively. The colour-coded plot shows the connection between E abs , SSA, and atmospheric photochemistry. The modelled results are consistent with the observed results. Both SSA and E abs values rise with increasing D shell and k shell , indicating that the coating thickness and absorption play key roles in determining SSA and E abs . Both E abs and SSA increased under more oxidizing conditions. This can be explained by the photochemical production of coating species: with more intense photochemical aging, the fraction of internally mixed BC particles and coating thickness increased. Thickly coated BC was also observed by Q.  under higher O x mixing ratios.
The corresponding Mie theory calculation results are shown as open circles in Fig. 8 (with further details in Sect. S7 in the Supplement). Comparisons of modelling and observation E abs and SSA are shown as a scatter plot in Supplement Fig. S12. By fixing the BC core diameter, we can retrieve information on the coating shell (D Shell , k Shell ) and each contribution to light absorption (f BC , f Lens , f Shell ) under different oxidant conditions (Lack and Cappa, 2010), as shown in Fig. 9. The retrieved D shell ranged from 386 to 440 nm. The corresponding D shell / D core ratio ranged from 2.41 to 2.75, within the range of values (2-4) reported by C. . The plot of measured and modelled E abs with different D shell / D core is shown in the Supplement Fig. S13. The values of k shell ranged from 0.004 to 0.008 with a diurnal average value of 0.006 (±0.001). A comparison of the retrieved k shell with previously reported k values of fresh and aged organic materials is shown in Supplement Fig. S14, which includes BC, BrC aerosol production from biomass burning (BB), atmospheric humic-like substances (HULISs), Suwannee River fulvic acid aerosol (SRFA), and secondary organic material (SOM) produced by photo-oxidation of anthropogenic and biogenic organic precursors. The value of k shell reported here is comparable with those of BB aerosols (Chakrabarty et al., 2010) and SRFA (Bluvshtein et al., 2016), and is larger than those of SOM (Liu et al., 2013;, HULIS (P.  and urban BrC . The retrieved diurnal variations in coating shell (D Shell , k Shell ) and the fractional contribution to light absorption (f BC , f Lens , f Shell ) are shown in Fig. 9. Broadly similar patterns were observed for D Shell , k Shell , and f Shell with O x . D Shell and E abs tended to be lower in early morning and evening, which was in accordance with anthropogenic activity (with a high CO concentration, as shown in Fig. 5). Peak values of D Shell , k Shell , and f Shell appeared in the midafternoon, which corresponded to a more intense photochemical processing and extensive secondary aerosol generation and resulted in a thicker and more absorbing coating shell. The fractional contribution of f BC , f Lens , and f Shell ranged from 35 % to 49 %, 35 % to 42 %, and 11 % to 30 %, respectively, with a mean value of 43 % ± 4 %, 39 % ± 2 %, and 18 % ± 5 %. A ternary plot is shown in the Supplement Fig. S15. Our results suggest that the contribution of the lensing effect to absorption enhancement is limited (Bond and Bergstrom, 2006). The lensing effect is reduced due to the greater absorption of the shell (Lack and Cappa, 2010). The change in optical properties at higher oxidant conditions implies a non-negligible contribution of absorbing secondary aerosol material to photochemistry and should receive more attention in climate modelling (Jo et al., 2016).

Conclusions
In this work, the size-resolved mixing state of atmospheric BC particles, light absorption enhancement, and SSA at λ = 532 nm was measured at a rural site in east China in the summer of 2016. The volatility measurement shows that atmospheric BC particles were well-aged. A single-particle core-shell Mie theory that connected E abs and SSA was developed to interpret the observation. Although further improvements of the calculation with size-distributed BC core and coated shell may give a more complete model, the model used currently with a fixed BC core diameter was found to be useful in illustrating the aging process. In our summertime observations, the increase in f Shell suggests that photochemistry plays a role in modifying BC absorption and indicates that light-absorbing organic compounds require more attention in climate modelling.
Author contributions. XX, WZ, and WZ designed the research and organized the field measurements. XQ conducted VTDMA measurements. XX, SW, QZ, and BF conducted optical measurements. YH, XD, BW, XL, SZ, and YT conducted the measurement of trace pollutants. XX, WZ, XQ, SW, DSV, and WC analysed data. XX, WZ, SW, DSV, and WC wrote the paper. All authors discussed the results and commented on the paper.
Competing interests. The authors declare that they have no conflict of interest.