Field measurements were performed from 30 September to 17 November 2019 at a rural site in Heshan county, Guangdong Province, China. The site is located at the top of a small hill surrounded by small villages and residential towns, and it usually experiences air masses from cities of the highly industrialized PRD region. This site is authorized as a supersite operated by the provincial environmental monitoring authority, and therefore continuous qualified measurements of meteorological parameters such as air temperature, relative humidity (RH), wind speed and wind direction, as well as pollutant measurements such as of carbon monoxide, ozone and nitrogen oxides, are carried out. Physical and chemical properties of ambient aerosol were comprehensively measured during this field campaign, including multi-wavelength (450, 525, 635 nm) aerosol scattering coefficient (nephelometer, Aurora 3000) measurements under nearly dry (RH <30 %) and controlled but fixed RH conditions using humified nephelometer system (Kuang et al., 2020), multi-wavelength absorption measurements using an Aethalometer (Magee, AE33; Drinovec et al., 2015), aerosol size distribution measurements using a scanning mobility particle sizer (SMPS, TSI 3080) and an aerodynamic particle sizer (APS, TSI Inc., Model 3321), and aerosol chemical composition measurements using a soot particle aerosol mass spectrometer. The AE33 measurements were only valid from 30 September to 31 October. Continuous and stable measurements of aerosol chemical composition using the aerosol mass spectrometer measurements were valid from 10 October onwards. More details on the site and instrument set-up can be found in Kuang et al. (2021).

Accurate AAE and absorption measurements are crucial for the BrC quantification. Results of previous comparison studies of aerosol absorption measurements between the AE33 and photoacoustic soot spectrometer demonstrated that AAE will only be slightly influenced by the particle collection of AE33 on the filter (Saleh et al., 2013; Zhao et al., 2020). However, aerosol absorption values measured by AE33 bear uncertainties associated with loading and multiple scattering effects. Dual-spot mode was applied in AE33 measurements for dealing with the Aethalometer loading effect. A multiple-scattering correction factor (C) was used to convert the measured attenuation coefficient (bATN) by AE33 to the absorption coefficient of ambient aerosols (babs) at each wavelength through babs=bATN/C. C is considered to be dependent on filter tape (Drinovec et al., 2015), and aerosol chemical compositions (Wu et al., 2009; Collaud Coen et al., 2010). Results of Yus-Díez et al. (2021) showed that C values increased considerably when single scattering albedo (SSA) is higher than 0.95. However, as shown in Fig. S5, SSA is much lower than 0.95 during this field campaign with an average of 0.78. Moreover, the filter tape 8060 was used for AE33 during this field campaign. Zhao et al. (2020) evaluated C of filter tape 8060 through comparing AE33 measurements with a three-wavelength photoacoustic soot spectrometer, and their results demonstrated that C is almost independent of wavelength and differs little among measurements of different locations. Thus the wavelength-independent C of filter tape 8060 of 2.9 recommended by Zhao et al. (2020) was used, and this value is also almost the median value of C ranges used in Kasthuriarachchi et al. (2020).

The size-resolved aerosol chemical compositions of dried aerosol particles with aerodynamic diameter less than 1 µm were measured using a soot particle aerosol mass spectrometer (SP-AMS, Aerodyne Research, Inc., Billerica, MA, USA). As discussed in Kuang et al. (2021), the mass concentrations of aerosol chemical compositions from SP-AMS were validated by offline PM2.5 filter measurements, SMPS aerosol volume concentration measurements and online measurements for inorganic aerosol components. The source identification of organic aerosols was conducted using the PMF method based on the high-resolution organic aerosol (OA) data collected in V-mode (only tungsten vaporizer). As introduced in Sect. S1 of the Supplement, six OA factors were identified based on the best performance criteria of PMF quality parameters, and more details about the determination factor number and factor sources are presented in Sect. S1. Two primary OA factors include BBOA (O/C=0.48) and hydrocarbon-like organic aerosols (HOAs, containing cooking emissions, O/C=0.02). The other four factors were associated with secondary formations or ageing processes: (1) more oxygenated organic aerosols (MOOAs, O/C=1, associated with regional air mass (Kuang et al., 2021)), (2) less oxygenated organic aerosols (LOOAs, O/C=0.72, related to daytime photochemical formation), (3) nighttime-formed organic aerosols (Night-OAs, O/C=0.32, highly correlated with nitrate with r=0.67, and exhibiting sharp increases during the evening) and (4) aged BBOA (aBBOA, O/C=0.39, exhibiting similar diurnal behaviour to LOOA with strong daytime production). The mass spectral profile and time series of these organic aerosol factors are shown in Fig. S2, and details about the determination of these factors are introduced in Sect. S1. The BBOA factor will be the focus of this study. On the basis of the scheme proposed by Kuwata et al. (2012), the density of BBOA (ρBBOA) and HOA was estimated as 1.25 and 1.15 g cm-3 with O/C and H/C as inputs and is used in this study.

BrC absorbs significantly at near-UV and short-visible wavelengths but exhibits strong wavelength dependence (Saleh, 2020). The deconvolution of the spectral dependence of measured aerosol light absorption has been a common method to retrieve the BrC and BC absorption distribution: 1σBrCλ=σaλ-σBCλ, where σaλ represents measured total aerosol absorption at wavelength λ, σBCλ the absorption associated with BC (includes influences of BC size distributions and mixing states, etc.), and σBrCλ the light absorption contributed by BrC. The spectral dependence of BC absorption was usually accounted for using the Ångström exponent law (Laskin et al., 2015), which describes BC absorption as σBCλ=Kλ-AAE, where K is a constant factor associated with BC mass concentration. The traditional method usually assumes a constant AAEBC of 1 (de Sá et al., 2019) or a wavelength-independent AAEBC derived from near-infrared absorption measurements by assuming that the BrC absorption is negligible at near-infrared wavelengths. For example, σBC880nm and σBC950nm measured by AE33 can be used to formulate the spectral dependence of aerosol absorptions associated with BC as the following: 2σBCλ=σBC880nm×880λAAEBC,λ–880,3AAEBC,λ–880=AAEBC, 950–880. However, several recent modelling studies using Mie theory and BC measurements demonstrated that AAEBC varies as a function of wavelength, and the wavelength-independent assumption of AAEBC will bring large uncertainties into BrC calculation (Li et al., 2019; Wang et al., 2018). Wang et al. (2018) found AAEBC, 520–880 and AAEBC, 370–520 differed much from each other – however, the AAEBC, 370–520/AAEBC, 520–880 ratio varied little – and thus proposed an AAE ratio method to obtain real-time AAEBC, 370–520 and further deduced σBC370nm. This method assumes that BrC contributes negligibly at 520 nm, which might introduce uncertainties. In addition, this method is not applicable in retrieving the spectral dependence of BrC absorption because only the ratio AAEBC, 370–520/AAEBC, 520–880 was used. This modified wavelength-dependent AAE differentiation method was further partially adopted by Li et al. (2019), using AAEBC, 370–520 to account for spectral dependence of BC absorption for wavelengths <520 nm and AAEBC, 520–880 for wavelengths >520 nm; thus the wavelength-dependent AAEBC was partially but not thoroughly considered.

In this study, we introduce an AAE ratio RAAE(λ)=AAEBC,λ-880/AAEBC, 950–880 to take spectral dependence of AAEBC into account and use on-line measurements of AAE950–880 as AAEBC, 950–880 under the assumption of negligible absorption contributions of BrC at wavelengths of 880 and 950 nm. Thus, absorption measurements of 370, 470, 530, 590 and 660 nm can be used to retrieve the spectral dependence of BrC absorptions.

RAAE(λ) is influenced by many factors such as BC refractive index, coating shell refractive index, BC mixing state and BC mass size distributions (Li et al., 2019). A sensitivity experiment following the method of Li et al. (2019) is initiated to explore impacts of these optical and mixing state parameters on AAEBC,λ–880 and RAAE(λ); more details are available in Supplement Sect. S1. These parameters include the real part of the refractive index of BC coating materials and BC-free particles (Real_NBC), real and imaginary parts of refractive index of the BC core (Real_BC and Imag_BC), the mass fraction of externally mixed BC (r_ext), the number fraction of BC-free particles (R_NBC), geometric standard deviation (GSD), and geometric mean diameter (GM) of BC mass size distributions. Note that the imaginary parts of the refractive index of BC particle coating materials and BC-free particles were not perturbed in these simulations and were treated as zero under the assumption of materials other than BC being non-absorbing. In order to separate effects of BC and BrC on AAEλ–880 changes, this assumption must be made to obtain AAEBC,λ–880 variations associated only with BC absorption changes. Thus, the defect of this method is that the entangling effects of BrC coating on BC particles in AAEBC,λ–880 variations are not considered. Impacts of these parameters on AAEBC, 370–880 and RAAE (370) are investigated through perturbation parameters within atmospherically relevant ranges reported in previous studies (Bond et al., 2013; Tan et al., 2016; Zhao et al., 2019), and ranges of these parameters are listed in Fig. 1. The results of AAEBC, 370–880 are shown in Fig. 1a. It shows that variations of both refractive index of BC and coating materials and BC mixing states have non-negligible influences on AAEBC, 370–880; however, the BC mass size distributions represented by geometric standard deviation (GSD) and geometric mean diameter (GM) of BC mass size distribution play the most important roles. Nevertheless, for results of AAEBC,λ–880/AAEBC, 950–880 shown in Fig. 1b, when fixing the BC mass size distribution, AAEBC,λ–880/AAEBC, 950–880 exhibited much smaller variations, and even the refractive index of BC and shell or mixing state varied within atmospherically relevant ranges.

The result of sensitivity studies shown in Fig. 1b confirmed the applicability of the proposed new AAE ratio method under constrained BC mass size distributions. The elemental carbon fragments (Cx) retrieved from SP-AMS measurements cannot be used to quantify BC mass concentrations due to the lack of calibration parameters; however, its size distributions generally represent the relative contributions of BC mass within different diameter ranges. The real-time measured normalized Cx distributions are therefore used to distribute total BC mass to different diameter bins to calculate RAAE(λ), and the average normalized Cx distribution is shown in Fig. S6. The average and standard deviations of RAAE (370), RAAE (470), RAAE (520), RAAE (590) and RAAE (660) are 0.79 (±0.044), 0.85 (±0.038), 0.88 (±0.035), 0.9 (±0.035) and 0.93 (±0.031), respectively. Based on this method, the spectral dependence of BrC absorption can be derived as the following: 4σBrCλ=σaλ-σBC880nm×880λAAEBC, 950–880×RAAE(λ). Results of previous studies (Saleh, 2020; Yu et al., 2021) demonstrated that non-negligible BrC absorptions at the near-infrared range and results of Hoffer et al. (2017) demonstrated that the absorption coefficient of tar balls at 880 nm is more than 10 % of that at 470 nm. During this campaign, the average aerosol absorption at 880 nm is 26.7 Mm-1, derived average BrC absorption at 470 nm is 11.5 Mm-1, 10 % of BrC absorption at 470 nm accounts for on average 4.2 % of aerosol absorption at 880 nm, and the realistic BrC contribution at 880 nm is likely lower considering that tar balls represent the most efficient BrC. Thus, the assumption that negligible absorption contributions of BrC at wavelengths of 880 and 950 nm when deriving AAEBC, 950–880 from AE33 measurements holds in most cases when BC dominates. In addition, the key part of our newly proposed method is considering the spectral dependence of AAEBC through the ratio RAAE(λ) and AAEBC, 950–880; however, the accurate AAEBC, 950–880 derivations need the robust performance of AE33 at both 880 and 950 nm. Thus quality assurance of these measurements should be warranted before using the AAEBC, 950–880.

Biomass burning plumes around the observation site were frequently observed during this field campaign at dusk as shown in Fig. S7a and d and only sometimes during daytime periods (Fig. S7b, c). The average diurnal variations of resolved primary OA factors including both BBOA and HOA are presented in Fig. S8, in which average diurnal profiles of both BBOA and HOA exhibited sharp increases around 18:00 local time (LT), which should be associated with frequently observed biomass burning events and supper cooking in villages and towns near this site. However, diurnal behaviours of BBOA and HOA differ much from about 06:00 to 16:00 LT. HOA exhibited continuous decreases during this daytime period, which was associated with boundary layer processes and re-partitioning due to increasing temperature. The BBOA showed almost continuous but slow increases from morning to the afternoon, indicating strong daytime emissions of BBOA as shown in Fig. S7b and c, although not as prominent as the BBOA emission just before the fall of nighttime. The probability distribution of the ratio BBOA/HOA is also shown in Fig. S8b, which shows that the ratio BBOA/HOA reached beyond 2 in 57 % conditions with an average of 3.3, which demonstrates that biomass burning was a dominant primary aerosol emission source during this field campaign.

The observed AAEs between different wavelengths and 880 nm of total aerosol absorption are shown in Fig. 2a, and the average values of AAE370–880, AAE470–880, AAE520–880, AAE590-880, AAE660–880 and AAE950–880 are 1.17, 1.23, 1.18, 1.15, 1.08 and 1.04. The scatter plots of AAE370–880 and the ratio BBOA/BC shown in Fig. 2b show that AAE370–880 was highly correlated with BBOA/BC (r=0.8), indicating strong influences of BBOA on aerosol absorption wavelength dependence. The BrC absorption at multiple wavelengths are extracted using the improved AAE ratio method introduced in Sect. 2, and statistical ranges of BrC absorption, as well as their contributions to total aerosol absorption, are shown in Fig. 2d. Average values of derived σBrC at 370, 470, 520, 590 and 660 nm are 19.1, 11.5, 6.4, 3.45 and 1.13 Mm-1, and their contributions to total aerosol absorption are 23 %, 18 %, 12 %, 8 % and 3 %, respectively. Similar to some previous studies (Tao et al., 2020; Qin et al., 2018), these results shows that the contributions of BrC to aerosol absorption at wavelengths of less than 590 nm are not negligible. The derived time series of σBrC,370 are shown in Fig. S9d, depicting BBOA varying quite consistently with σBrC,370 and with high correlations (correlation coefficients between σBrC at 370, 470, 520, 590 and 660 nm and BBOA reaching 0.9, 0.83, 0.8, 0.76 and 0.69), suggesting that BBOA was the dominant contributor to BrC absorption.

During the observation period, BBOA contributed dominantly to BrC absorptions, and notable biomass burning events represented by BBOA mass concentration spikes as shown in Fig. S9 frequently occurred. Events with BBOA increasing suddenly, drastically and continuously within a half hour to several hours were identified as BBOA spikes. We do not have a criterion on this, and we choose spikes artificially. These identified spikes generally last about 0.5–1.5 h (from the beginning to the peak). The used BBOA spikes were shaded in Fig. S9, and some of identified spikes were not used because of the missing particle number size distribution measurements. These biomass burning spikes are related with biomass burning plumes that swept over the observation site; thus the difference between aerosol properties measured before and during these spikes can represent the properties of biomass burning aerosols. Theses spikes usually occurred during supper cooking time (∼ 18:00 LT), and typical biofuels used for cooking are mainly vegetation fuels such as local woods. SMPS directly measures the aerosol particle number size distribution (PNSD), thus also providing particle volume size distribution measurements (PVSD). Figure 3a shows the average differences of mass concentrations of different aerosol components of identified spikes with simultaneous valid SMPS data. Ammonium nitrate (AN) and ammonium sulfate (AS) were determined as the dominant form of ammonium, sulfate and nitrate ions during this field campaign and paired using the scheme proposed by Gysel et al. (2007). Note that the Δ shown in Fig. 3a and also hereafter means the difference between that variable before BBOA increases and when BBOA reaches its peak (the definition of the BBOA spike; these peaks are also marked in Fig. S9), corresponding to the start and end of BBOA increase. It shows that inorganic aerosol components increased a little bit, which is consistent with previous studies (Hecobian et al., 2011; Pratt et al., 2011) showing that biomass burning emits tiny amounts of inorganic aerosol. However, it is difficult to quantify how much of these inorganic aerosol increases was attributed to biomass burning emissions because the biomass burning spikes were usually observed during the periods with secondary nitrate formation (Kuang et al., 2021). Secondary organic aerosol components changed a little, with the slight increase in aBBOA suggesting plumes were aged a little bit. Obvious increases in HOA were observed, but the most prominent increase was BBOA. The average ΔBC/ΔBBOA ratio for cases when BC measurements were valid was 0.22, suggesting the observed biomass burning events are likely flaming and burning conditions with high combustion efficiency (Reid et al., 2005b; McClure et al., 2020). The cooking-related organic aerosol could not be separated from HOA in PMF analysis. The co-increase in HOA is due to the fact that these identified spikes occurred during periods of supper cooking as discussed before.

The average aerosol particle number and volume size distribution differences (ΔPNSD and ΔPVSD) calculated as the PNSD and PVSD differences between those at the BBOA peak concentration and those before the BBOA spikes are shown in Fig. 3b, and the example of calculating ΔPNSD and ΔPVSD is shown in Fig. S10. The average ΔPVSD can be well fitted using two log-normal modes (Mode 1 and Mode 2); the dominant one is BBOA, and the other is mostly associated with HOA according to the aerosol mass changes. Geometric mean (Dgv) and standard deviation (σg) values of the two PVSD log-normal modes are 180 and 390 and 1.46 and 1.5, respectively. In addition, the SP-AMS measurements provide organic aerosol size distributions with vacuum aerodynamic diameter (Dva), and their average distribution difference of organic aerosols during these spikes is also shown in Fig. S11 and could be generally fitted well using two log-normal modes of BBOA and HOA. The Dgv,Dva and σg values of the identified modes were 175 and 395 and 1.46 and 1.55, respectively. Dva and mobility diameter Dp of the SMPS were related through the effective density of particles as ρe=Dva/(Dp×CS), where ρe is the aerosol effective density and CS a factor related to aerosol shape, for which a value of 0.8 was adopted (Jayne et al., 2000). Based on densities of BBOA and HOA introduced in Sect. 2.2, identified Dgv of BBOA and HOA from SP-AMS measurements of 395 and 190 nm, which were quite close to the Dgv identified from SMPS measurements, further confirming the results from SMPS measurements. The average ΔPNSD is shown in Fig. 3b, displaying a number concentration peak near 90 nm; however, influences of HOA need to be excluded to identify biomass burning PNSD modes. As shown in Fig. 3b, converting the identified BBOA and HOA ΔPVSD modes to ΔPNSD modes cannot explain the observed PNSD difference, and the remaining mode is log-normal and peaks at 70 nm. These results indicate that two modes existed for biomass burning aerosols during this campaign, which is consistent with findings of previous studies (Okoshi et al., 2014; J. Liu et al., 2020).

For spikes where ΔBBOA dominated the mass changes, the Dgv and σg of BBOA PVSD was retrieved by fitting the larger mode of Δ PVSD, with retrieved results shown in Fig. 3d and e. The retrieved Dgv ranged from 245 to 505 nm with an average of 380 nm. Physicochemical properties of biomass burning emissions depended largely on combustion conditions. The BC/BBOA ratio is a proxy of biomass combustion efficiencies (McClure et al., 2020), and it was found that ΔCO/ΔBBOA was highly correlated with ΔBC/ΔBBOA (Fig. 3c, R=0.84). Thus, ΔCO/ΔBBOA was also used as a proxy for combustion efficiency in this study. Higher ΔCO/ΔBBOA corresponds to higher combustion efficiency. Retrieved Dgv values were moderately but negatively correlated with ΔCO/ΔBBOA (R=-0.69), and a linear relationship Dgv=551–13.3 × ΔCO/ΔBBOA was derived. This result is qualitatively consistent with previous studies that biomass burning aerosols were mainly in the accumulation mode, and their average sizes generally decreased as the combustion efficiency increased (Reid and Hobbs, 1998; Janhäll et al., 2010). Retrieved σg ranges from 1.2 to 2.0 with an average of 1.5 and is negatively and weakly correlated with Dgv (R=-0.32). Reid et al. (2005b) reported that Dgv is typically in the range of 250 to 300 nm with the σg on the order of 1.6 to 1.9 for freshly generated smoke and 30 to 80 nm larger for aged smoke with smaller σg (1.4 to 1.6). Levin et al. (2010) performed laboratory combustion of various wildland fuels and reported Dgv of 200 to 570 nm and σg of 1.68 to 2.97. The average Dgv and σg is near the reported Dgv range of Reid et al. (2005b) for aged smoke. The geometric mean of PNSD (Dgn) values is converted from retrieved Dgv and σg and also shown in Fig. 3e. Dgn ranges from 88 to 391 nm with an average of 235 nm. The average Dgn is similar to the reported average Dgn of aged smoke but the range is even beyond the range (100–300 nm) for both fresh and aged smoke reported by Janhäll et al. (2010), in which literature-published Dgn is reviewed, and also beyond the range (about 130–240 nm) reported in Laing et al. (2016) for aged biomass burning aerosol from wildfires in Siberia and the western USA. Similar with results of Janhäll et al. (2010), σg is highly but negatively correlated with Dgn (R=-0.97). The derived linear relationship σg=2.17–0.0027 × Dgn is close to that reported in Janhäll et al. (2010) (Fig. 3e). Janhäll et al. (2010) defined the fresh smoke as plumes younger than 1 h, but aged smoke is mostly plumes older than 1 d. The aged smoke in Laing et al. (2016) were also transported over 4–10 d. However, the smoke plumes reported in this study occurred during supper cooking time and swept over the observation site lasting about 1–3 h (from the beginning to BBOA concentration fall back the background levels), which is consistent with the time needed for cooking, which means that the age of plumes are on the order of hours and near-freshly emitted. This is indirectly confirmed by the observed changes in particle number concentrations in that the small Aitken mode dominates the particle number concentrations (Fig. 3b), because coagulation is quick and should cause a significant decrease in number concentrations of Aitken mode aerosols on timescales of hours (Sakamoto et al., 2015; Laing et al., 2016; Sakamoto et al., 2016). These results demonstrate that Dgn and Dgv vary over a wide range for near-freshly emitted BBOA from vegetation fire smoke. Laing et al. (2016) reported that Dgn was highly correlated with plume aerosol mass concentrations (PMs) but not with any normalized variable such as ΔPM/ΔCO. Similar results were obtained in this study (Fig. 3f). The derived Dgn was weakly correlated (R=-0.21) with ΔCO/ΔBBOA but highly correlated with ΔBBOA (R=0.82). The new finding here is that Dgv correlated obviously with ΔCO/ΔBBOA but weakly with ΔBBOA. As discussed in implications, BBOA volume size distributions determine BBOA bulk optical properties; thus accurate representations of BBOA volume size distributions in climate models might be more important than accurate representations of BBOA number size distributions.

The measured aerosol scattering coefficients at 525 nm (σsp,525) during BBOA spikes were used to calculate the MSEs using the differential method, thereby retrieving the real part of the BBOA refractive index (mR) on the basis of Mie theory. Truncation error, non-ideality of light source and RH conditions need to be corrected in the calculation of σsp,525 values under dry condition. The truncation error and non-ideality of light source were corrected using the empirical formula provided by Qiu et al. (2021). RH0 in the dry nephelometer was in the range of 20 % to 45 % with an average of 31 % and corrected by considering measured aerosol optical hygroscopicity through σsp,525=σsp,525,measured/(1+κsca×RH0100-RH0), where κsca is the optical hygroscopicity parameter derived from aerosol light scattering enhancement factor measurements (Kuang et al., 2017). To quantify MSEBBOA, MSEs of other aerosol components are needed. Using the paired campaign average size distributions of AS and AN (Fig. S3), MSEs of AS and AN were calculated as 4.6 and 4.8 m2 g-1, which were identical to those identified by Tao et al. (2019) during autumn at an urban area in this region but much higher than average values reported in Hand and Malm (2007). Through the analysis of the OA distribution measured by SP-AMS, it was found that the size distribution of secondary organic aerosol (SOA) can be represented by two log-normal modes (Fig. S4). One is aBBOA, and the other one includes MOOA, Night-OA, and MOOA. Thus, the MSE of MOOA, Night-OA and LOOA (MSESOA) was determined to be 6.3 m2 g-1, and MSEaBBOA was 4.5 m2 g-1. MSEHOA was calculated to be 3.2 m2 g-1 using the size distribution identified in Fig. 3b. MSEBC was calculated as 2.8 m2 g-1 using the average normalized Cx fragment distributions, which was also very close to the MSE of elemental carbon determined by Tao et al. (2019) (2.6 m2 g-1). The changes in aerosol scattering coefficients associated only with BBOA can be calculated as 5Δσsp,BBOA=Δσsp,measured-ΔAS×MSEAS-ΔAN×MSEAN-ΔHOA×MSEHOA-ΔBC×MSEBC-ΔaBBOA×MSEaBBOA-(ΔNight-OA+ΔMOOA+ΔLOOA)×MSESOA. More details about the MSE calculations of these components can be found in Sect. S1. In addition, to minimize the influences of uncertainties of used MSEs of other aerosol components on MSEBBOA derivations, only spikes with sum changes in ΔAS, ΔAN, ΔNight-OA, ΔMOOA, ΔLOOA and ΔaBBOA accounting for less than 25 % of ΔBBOA were used. Average changes in aerosol components for these spikes are shown in Fig. 4a, with changes in most individual aerosol components being almost negligible.

As shown in Fig. 4b, the derived Δσsp,525 associated with BBOA was highly correlated with ΔBBOA (R=0.91). MSEBBOA ranged from 3.1 to 7.5 m2 g-1 with an average of 5.3 m2 g-1. Reid et al. (2005a) reviewed the MSEs of biomass burning (MSEBB) aerosols and reported a range of 3.2–4.2 m2 g-1 for temperate and boreal fresh smoke and larger for corresponding aged smoke (4.3 m2 g-1). McMeeking et al. (2005) theoretically calculated the MSEs of smoke-influenced aerosols and reported a MSE range of 3–6 m2 g-1. Levin et al. (2010) conducted MSEBB measurements of fresh biomass burning smoke of various fuel types and reported a MSEBB range of 1.6 to 5.7 m2 g-1. Laing et al. (2016) reported a MSEBB range of 2.5 to 4.7 for aged biomass burning aerosols of wildfires, and a similar range was reported by Briggs et al. (2017). However, no study has specifically investigated MSEBBOA variations, which are very crucial for biomass burning aerosol climate effect simulations, since aerosol components in models are usually separately represented (Riemer et al., 2019). Although organic aerosols usually dominate mass concentration of biomass burning aerosols, the reported MSEBBOA range is generally higher than previously reported MSEBB ranges, which are likely associated with the fact that MSEBB includes influences of low scattering efficiency components such as BC. Another reason for this is that the identified geometric mean size of BBOA in this study was generally larger than those reported before. Many studies have shown that aerosol size distributions have crucial impacts on MSE variations (Hand and Malm, 2007). Both Levin et al. (2010) and Laing et al. (2016) have reported that MSEBB of biomass burning aerosols was highly correlated with Dgn. The relationship between MSEBBOA and Dgn and Dgv was investigated (Fig. 4c, only six points with both Dgv and σg retrieval are available). Unlike results of previous studies, MSEBBOA was positively but weakly correlated with Dgn (R=0.44). However, MSEBBOA was highly correlated with Dgv (R=0.86) and exhibited a non-linear response with the increase in Dgv. The non-linear increase phenomenon was reported first but confirmed by Mie theory simulations by assuming a fixed σg of 1.5 under varying conditions of Dgv and refractive index (Fig. 4c).

Aerosol refractive index was a fundamental parameter in simulating aerosol optical properties in models. However, aerosol refractive index investigations specific to BBOA are scarce because the direct retrieval of an aerosol refractive index at least needs accurate and simultaneous representations of MSEBBOA, BBOA density and BBOA size distribution shape. Only a few studies have indirectly retrieved mR of biomass-burning-related aerosols. For example, McMeeking et al. (2005) and Levin et al. (2010) have retrieved mR of biomass burning or smoke-influenced aerosols through using an iterative algorithm to match measured size distributions of different principles (mobility-related size versus optical size), and the reported mR ranges were 1.56 to 1.59 and 1.41 to 1.61, respectively. In this study, mR values of BBOA were retrieved using Mie theory with MSEBBOA, Dgn, σg and BBOA density as inputs as introduced in Sect. S1.4 of the Supplement. This method assumes the external mixing of BBOA with other aerosol components, which is due to characteristics and dominant contribution of freshly emitted BBOA to observed mass changes for identified biomass burning plumes. Note that the retrieval of mR would also be affected by the imaginary part of BBOA refractive index (mi,BBOA), and the mi,BBOA parameterization as a function of ΔCO/ΔBBOA introduced in the next section was used. Retrieved mR ranges from 1.47 to 1.64 with an average of 1.56. If mR changes from 1.47 to 1.64, it can result in a double MSEBBOA for given BBOA size distributions. Thus, the reported mR,BBOA range was wide with respect to MSE simulations and needs to be carefully parameterized in climate modes. The BBOA refractive index is determined by its chemical structure; thus its variation might be associated with fire combustion conditions. The relationship between mR,BBOA and ΔCO/ΔBBOA was further investigated and is shown in Fig. 4d. For ΔCO/ΔBBOA below 10 ppb (µg m-3)-1, mR was negatively correlated with ΔCO/ΔBBOA (R=-0.71) and thus like ΔBC/ΔBBOA, which, however, was not as significant (R=-0.27). These results demonstrate that fire combustion conditions might have significant impacts on mR,BBOA, which, however, needs further investigation.

Derived BrC absorptions of BBOA spikes were used to calculate MAEBBOA and retrieve mi,BBOA in combination with retrieved BBOA size distributions using Mie theory. Average changes in organic aerosol components for spikes with available σBrC values are shown in Fig. 5a. ΔBBOA dominated the mass changes; however, there were non-negligible changes for aBBOA, HOA and MOOA. The average MAEHOA, MAEaBBOA and MAEMOOA are estimated using multilinear regression for all data points as shown in Fig. S12 with values at 370 nm of 0.1, 0.96 and 0.9 m2 g-1, respectively. Thus the ΔσBrC,BBOA can be derived as 6ΔσBrC,BBOA(λ)=ΔσBrC,derived(λ)-ΔHOA×MAEHOA(λ)-ΔaBBOA×MAEaBBOA(λ)-ΔMOOA×MSEMOOA(λ). As shown in Fig. 5b, ΔσBrC,BBOA was moderately correlated with ΔBBOA (R=0.65), suggesting MAEBBOA=ΔσBrC,BBOA/ΔBBOA differs much among identified plumes. Derived MAEBBOA exhibited strong wavelength dependence, and average values at wavelengths of 370, 470, 520, 590 and 660 nm were 2.46, 0.99, 0.53, 0.28 and 0.11 m2 g-1, respectively. Figure 5c shows the spectral dependence of MAEBBOA and retrieved mi,BBOA(λ), and the formula form that parameterizes the spectral dependence was consistent with previous studies (Saleh et al., 2014). BBOA absorption properties depended largely on combustion conditions, consistent with results of previous studies (Saleh et al., 2014; Lu et al., 2015; Pokhrel et al., 2016; Xie et al., 2017; Cheng et al., 2019; McClure et al., 2020), and both MAEBBOA and retrieved mi,BBOA (520) were highly and linearly correlated with ΔBC/ΔBBOA (Fig. 5d and e). Results regarding mi,BBOA(λ) parameterizations as a function of ΔBC/ΔBBOA of previous studies are also shown in Fig. 5e. Results of Saleh et al. (2014) and Lu et al. (2015) at 550 nm were higher for ΔBC/ΔBBOA in the range of 0.05 to 0.4. The curve of McClure et al. (2020) described well the mi,BBOA variations for ΔBC/ΔBBOA less than 0.2. The mi,BBOA spectral dependence parameter wBBOA ranged from 2.5 to 5.5 with an average of 4.7 and was linearly and negatively correlated with ΔBC/ΔBBOA and much higher than those reported in Saleh et al. (2014) and Lu et al. (2015). Note that the parameterization schemes established in Saleh et al. (2014) and Lu et al. (2015) were based on datasets with most data points have BC/BBOA <0.1. The wBBOA was also higher than the fitted line of McClure et al. (2020) but was, however, actually consistent with the wBBOA range reported in Fig. 5c of McClure et al. (2020) for a BC/OA range of 0.1 to 0.55. This result implies that a single formula that parameterizes mi,BBOA over a wide BC/BBOA (combustion efficiency) range might lead to significant bias for specific BC/BBOA ranges. As shown in Fig. 1 of Lu et al. (2015), field-based mi,BBOA retrievals for BC/BBOA >0.1 are quite scarce, which hinders the accurate parameterization of mi,BBOA within the BC/BBOA range of this study. The combination of mi,BBOA(520) and wBBOA shown in Fig. 5e and f would bring a new parameterization scheme of mi,BBOA(λ) spectral dependence, which would fill the gap for field-based BBOA absorptivity parameterizations of BC/BBOA >0.1.