Regional impacts of black carbon morphologies on aerosol-radiation interactions: A comparative study between the US and China

. Black carbon (BC) is one of the dominant absorbing aerosol species in the atmosphere. It normally has complex fractal-like structures due to the aggregation process during combustion. A wide range of aerosol-radiation interactions (ARI) of BC has been reported throughout experimental and modeling studies. One reason for the large discrepancies among multiple studies is the application of the over-simplified spherical morphology for BC in ARI estimates. Here, we employ a regional chemical transport model coupled with a radiative transfer code which utilizes the non-spherical BC optical simulations to re- 5 evaluate the effects of particles’ morphologies on BC ARI. Anthropogenic activities and wildfires are two major sources of BC emissions. Therefore, we choose four typical polluted cities in East China which are dominated by urban emissions, and three locations in the northwest US that are dominated by fire emissions in this study. Our modeling results show that spherical BC models overestimate the aerosol optical depth (AOD) at 550 nm wavelength up to 0.03 (EAE),


Introduction
Black carbon (BC), as the main absorbing aerosol in the atmosphere, exerts a positive radiative forcing, and lofts smoke plumes (Buseck and Buseck, 2000;Streets et al., 2006;Moosmüller et al., 2009). However, there are still large uncertainties in evaluating the BC radiative effects. An important cause of the discrepancy is BC's complex morphology. BC morphologies 25 are commonly simplified as homogeneous spheres in climate modeling. However, many studies have shown that BC particles, especially those nascent ones, have fractal-like structures. The spherical assumption for BC can lead to a large deviation from the field measurement data and non-spherical simulated results (Chakrabarty et al., 2007;Luo et al., 2018c;He et al., 2015;Liu and Mishchenko, 2005;Luo et al., 2018d;Mishchenko et al., 2016a;Luo et al., 2021b). Based on the sampled BC images, researchers found that the shape of uncoated BC aggregates can be fitted well by a fractal law with monomer number (N s ), 30 mean monomer radius (R), fractal prefactor (k 0 ), fractal dimension (D f ) and the radius of gyration (R g ) (Mishchenko et al., 2002;Sorensen, 2011;Luo et al., 2021a): Previous studies have shown that aggregated particle models are more realistic to reproduce the optical measurement results (Bi et al., 2018;Luo et al., 2019Luo et al., , 2018b. Some studies have used the non-spherical BC models to investigate the radiative properties of BC (Wu et al., 2015;Liu et al., 2015a;Liu and Mishchenko, 2005;Yin and Liu, 2010;Teng et al., 2019;Luo 35 et al., 2018a;Kahnert, 2010a). However, extremely limited number of studies have evaluated the ARI of non-spherical BC in regional or global climate models. Kahnert (2010b) has made efforts to simulate the radiative properties of freshly emitted BC using the Multiple-scale Atmospheric Transport and CHemistry (MATCH) model. That study assumed a fixed solar zenith angle (SZA) and restricted the modeling region in Western Europe. However, expanding the modeling range to regions with different emission characteristics is important to understand the effects of BC sources on aerosol-radiation interactions (ARI).

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The direct radiative effect (DRE) was widely used to evaluate the climate effects of aerosol (Bond et al., 2013;Saleh et al., 2015). IPCC (2014) suggested using the new terminology of ARI instead of DRE. Thus, in this work, we use the terminology of ARI to replace DRE. A global mean BC ARI of +1.1 W m −2 has been reported by Bond et al. (2013). However, the BC ARI values estimated based on in-situ optical measurements in some regions are much larger than the rest. BC emissions in China roughly account for one-fourth of its global anthropogenic emission budget (Streets et al., 2001). East China, a typical polluted these regions is important to understand the detailed plume dynamics and the warming effects of BC. The northwest US, as one of the most frequent wildfire regions in the world, has also been investigated in addition to East China.
In this work, we employed Weather Research and Forecasting coupled to Chemistry (WRF-Chem) to simulate the aerosol mass concentrations. Note here that WRF-Chem assumes aerosols to be spherical. Therefore, the radiative parameters of aggregated models were calculated offline using an optical module, Flexible Aerosol Optical Depth (FlexAOD). We calculated 55 the ARI at the top of the atmosphere (TOA) using the radiative transfer model (libRadtran) after the particles' optical properties were calculated. Among all the radiative parameters, we investigated aerosol optical depth (AOD), aerosol absorption optical depth (AAOD), extinction Ångström exponent (EAE), absorption Ångström exponent (AAE), single-scattering albedo (SSA), and ARI at the TOA, which were widely used in remote sensing and climate effect evaluation.
2 Aerosol distribution simulation 60 In this work, WRF-Chem version 4.1.3 was used to simulate the transport of atmospheric species. Two areas were selected to represent the BC sources with different emission characteristics. East China, a main polluted region in the world, represented the typical polluted urban region. It consists of 115 east-west grids and 105 south-north grids centered at 112.00 • E, 35.00 • N with a grid resolution of 18 km. North America, one of the most frequent forest fire regions in the world, was also investigated in this work. The fire region consists of 120 east-west grids and 120 south-north grids centered at 121.48 • W, 39.89 • N with a 65 grid resolution of 4 km. The schematics of the two studied regions are shown in Figure S1. Both regions have 33 vertical layers above the ground, with a top pressure of 50 hPa.
We used the Model of Emissions of Gases and Aerosols from Nature (MEGAN) to compute the biogenic emissions over two regions (Guenther et al., 1994(Guenther et al., , 2006. The anthropogenic emission inventory is vital to estimate the aerosol distributions. The anthropogenic inventory in the mainland of China was compiled by the multi-resolution emission inventory for China (MEIC) 70 (Li et al., 2014;Liu et al., 2015b) for East China in the year 2016. We used MIX anthropogenic inventory for the region outside China (Li et al., 2017b). The Regional Acid Deposition Model version 2 (RADM2) atmospheric chemical mechanism (Stockwell et al.) and the Model Aerosol Dynamics for Europe with the Secondary Organic Aerosol Model (MADE/SORGAM) were applied in this study (Seinfeld et al., 2001;Ackermann et al., 1998). Fast-J photolysis scheme (Wild et al., 2000) was used to simulate the photolysis rates. The physical scheme options in WRF-Chem are shown in Table S1.

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The EDGAR-HTAP anthropogenic inventory for 2010 was used in the North American region. MOSAIC aerosol scheme (Zaveri and Peters, 1999;Zaveri et al., 2008) and CBM-Z (carbon bond mechanism) photochemical mechanism (Zaveri and Peters, 1999) was used in forest fire region simulation. The Fire emission was provided by the Fire INventory from NCAR (FINN) (Wiedinmyer et al., 2011). Note here EDGAR-HTAP anthropogenic inventory and FINN were provided for the MOZART chemical mechanism, so we manually mapped the emission for the MOZART chemical mechanism to the CBM-Z chemical 80 mechanism based on the study of Emmons et al. (2010). The National Center for Environmental Prediction (NCEP) Global Forecast System's final gridded analysis data set was used to provide the meteorological initial and boundary conditions. The chemical initial and boundary conditions were obtained from the Model for Ozone and Related Tracer, version 4 (MOZART-4).
3 Calculating the ARI of BC

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In this work, we only consider externally mixed BC aerosols, which is commonly represented by fractal structures. D f is a key parameter to describe the compactness of fractal BC (Wang et al., 2017;Yuan et al., 2019), and the BC morphology can vary from a chain-like structure to a spherical structure if D f increase from approxiamtely 1.8 to 3. The freshly emitted BC generally exhibits a fluffy structure with a D f of approximately 1.8 (Heinson et al., 2010(Heinson et al., , 2017. The laboratory measurements also showed that the freshly emitted BC generally presents a small D f . Chakrabarty et al. (2006) have shown that D f of BC 90 emitted from wildland fuels generally exhibits a range of 1.67 -1.83. A D f range of 1.6 -1.9 was observed for BC produced from diesel combustion (Wentzel et al., 2003). China et al. (2013) indicated that the BC freshly emitted from wildfire generally exhibits a D f range of 1.74 -1.92. However, a more compact structure was commonly observed for BC in the atmosphere with the particle aging (Li et al., 2003;Adachi et al., 2014;Chen et al., 2016;Adachi et al., 2007). A D f range of 2.2 -2.4 was observed in the study of Adachi et al. (2007). The fractal structures with a larger are widely used to describe the BC with 95 more compact structures (Adachi et al., 2007). Chakrabarty et al. (2006) further showed that the D f of aged BC can reach up to 2.6. To represent both fluffy and compact BC, D f s of 1.8, 2.2, and 2.6 were considered. Even though k 0 was also measured in a wide range in the atmosphere, its impact was relatively small, so we assumed a fixed k 0 of 1.2 in this work. The typical morphologies of fractal BC are shown in Figure 1.
The volume-mean particle radius was commonly used to describe the size of non-spherical BC. N s and R are two important 100 parameters to describe the volume-mean particle radius of BC. Previous studies have observed a range of approximately 8 -57 nm for BC monomer radius (Eggersdorfer and Pratsinis, 2012;Mikhailov et al., 2006;KOylU and Faeth, 1992;Lee et al., 2002), while Kahnert and Kanngießer (2020) further showed that the typical range is approximately 10 -25 nm. In this work, we assumed a fixed monomer radius of 20 nm. We considered an N s range 1 -1000 to represent BC with different sizes. The volume-mean particle radius (r p ) can be calculated using: We must clarify that BC can internally mix with other compositions, and the morphology can become more complex (Wang et al., 2021(Wang et al., , 2017. However, we mainly focus on the freshly emitted BC, and only consider externally mixed BC. Further investigations would be performed for more complex internally mixed BC in the future.

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BC refractive index shows a little spectral dependence (Chang and Charalampopoulos, 1990), while it doesn't vary largely with wavelengths in the short wavelength range, and the absorption Ångström exponent is approximately 1 Lack and Cappa, 2010). Therefore, BC refractive index is commonly assumed to be spectrally invariant (Bond and Bergstrom, 2006). The suggested BC refractive index values by Bond and Bergstrom (2006) were commonly used. In this work, the median value of 1.85 +0.71i was used, as it was widely used in many regional and global climate models (e.g. WRF-Chem). The size distribution of BC and OC also suffers large uncertainties from different fuels and conditions. The size distribution of BC is commonly fitted by a lognormal size distribution with a geometric mean radius (r g ), and a geometric standard deviation (σ g ) (Schwarz et al., 2008;Mishchenko et al., 2016b): where r p is the aerosol radius, N 0 is the total number concentration calculated by the mass concentration obtained from WRF-120 Chem by assuming BC mass density, r g , and σ g . The details about the calculation of N 0 are shown in Curci (2012). Firstly, by assuming N 0 = 1, we created a look-up table for different r g and σ g , and then the optical properties were obtained by plugging in the tested BC's r g and σ g .
BC geometric mean radius of 0.05 -0.06 µm is frequently observed by instruments and widely assumed in numerical studies (Alexander et al., 2008;Coz and Leck, 2011;Reddington et al., 2013;Liu et al., 2018). In this work, BC geometric mean radius 125 was assumed to be 0.05 µm. σ g was assumed to be a fixed value of 1.6. We used the volume-equivalent radius of non-spherical BC to characterize the BC size. The density of BC was assumed to be 1.8 gm −3 based on the suggested values by Bond and Bergstrom (2006).

BC radiative properties
In this work, BC radiative properties were calculated using the multiple sphere T-matrix method (MSTM) (Mackowski and130 Mishchenko, 2011, 1996). Using MSTM, the extinction efficiency (Q ext ), scattering efficiency (Q sca ), and phase function (P ) can be directly calculated. Then, extinction cross-section (C ext ) and scattering cross-section (C sca ) were obtained using: where r p represents the volume-equivalent radius of non-spherical BC. In this work, we have calculated the optical properties of BC with a N s range of 1 -1000. Bulk extinction cross-section (< C ext >), scattering cross-section (< C sca >) and phase function <P> were calculated using the following equations: 5 https://doi.org/10.5194/acp-2021-1090 Preprint. Discussion started: 19 January 2022 c Author(s) 2022. CC BY 4.0 License.
In climate modeling, instead of using the phase function, the Legendre expansion coefficients were commonly used: where θ is the scattering angle, P S are generalized spherical functions, α S are the expansion coefficients, and S mas is the order of truncation of the expansion. In this work, we used the pmom code in the Libradtran software to calculate the Legendre expansion coefficients. The asymmetry parameter (g) was calculated using: The radiative properties of fractal BC and BC spheres were calculated at 300 nm -4000 nm wavelengths. The step size of ∆λ = 50 nm was chosen when λ is less than 1000 nm, while ∆λ= 200 nm was selected for 1000 nm ≤λ ≤ 2000 nm, and ∆λ= 400 nm when λ ≥ 2000 nm. We created look-up tables for < C abs >, < C sca >, and the Legendre expansion coefficients of phase functions for each σ g and r g . Thus, the optical properties of BC can be obtained by interpolating the look-up tables.  Tables S2 -S3. After the WRF-Chem species were mapped, the size distribution, refractive indices, and hygroscopic growth factors were then assigned.

Flexible
The FleAOD firstly reads the aerosol mass concentrations from WRF-Chem, then transforms to aerosol volume concentrations based on the assigned mass densities. Based on the assigned normalized size distributions, we can calculate the number concentration (N 0 ) of each aerosol. FlexAOD pre-calculates the optical properties of each aerosol by assuming N 0 = 1 with 160 the assumed size distributions. The total scattering/extinction coefficients can be obtained by multiplying the pre-calculated scattering/extinction cross-sections with the number concentrations. The total phase function is identical to the pre-calculated phase function by assuming N 0 = 1. In FlexAOD, aerosol shapes were assumed to be spherical and the corresponding optical properties of each aerosol species were calculated using the Mie code provided by Mishchenko et al. (1999), and the bulk optical properties were then calculated by combining an assembly of aerosols.

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FlexAOD assumed that the BC shape was spherical. To consider the non-spherical structures, BC optical properties were overwritten using the look-up tables created in Section 3.3. As described in Section 3.3, we have created look-up tables for  Nakao et al. (2013) reported that the density of OC with lower oxidation was approximately 1 -1.2 g cm −3 . For freshly formed OC, 0.9 -1.1 g cm −3 was used by Liu et al. (2017). In this work, the density of OC was assumed to be 1.2 g m −3 . OC size is also commonly fitted by a lognormal size 175 distribution. In the study of He et al. (2016) and Dentener et al. (2006), r g = 0.03 µm and r g = 0.075 µm were assumed for hydrophobic and hydrophilic OC, respectively. In this study, all OC was assumed to be hydrophilic, and we assumed a r g of 0.075 µm and a σ g of 1.6. The refractive indices of dust were identical to those used in the GOCART Model (Chin et al., 2002), and the refractive indices of other chemical species were adapted from the OPAC package (Hess et al., 1998). The physical properties are displayed in Table S4. Similar to the study of Curci et al. (2019), the hygroscopic growth factors of different 180 aerosols were taken from the OPAC package (Hess et al., 1998). For dust, the gamma distribution was assumed: (Martin et al., 2003;Curci, 2012): where a and b are two parameters for the distribution, and b is in the range of 0 -0.5.
We must clarify that many internally mixed particles exist in the atmosphere, while in this study we mainly aim to study 185 the morphological effects of freshly emitted particles, and more complex particles may be investigated in the future. Effective refractive indices were calculated using the volume mixing method for hydrophilic particles.
The total column SSA and AOD were calculated by FlexAOD, and AAOD was calculated by: AAE and EAE were calculated by: here λ 1 and λ 2 represent two reference wavelengths; AAOD 1 and AAOD 2 represent the AAOD at corresponding wavelengths; AOD 1 and AOD 2 represent the AOD at corresponding wavelengths.

ARI modeling
The optical properties (Extinction coefficient, SSA, Asymmetric factor (ASY)) calculated using FlexAOD at each WRF-Chem grid were inputted into a radiative transfer model, libRadtran (Mayer and Kylling, 2005), to calculate the radiative fluxes at the top-of-the-atmosphere (TOA). The radiative transfer equation was solved by DISORT radiative transfer equation solver (Stamnes et al., 1988;Buras et al., 2011). Based on the longitude, latitude, and UTC time, libRadtran can select a standard at-200 mosphere background and determine the solar zenith angle (SZA).. The albedo information was obtained from NASA EARTH OBSERVATIONS (NEO). Besides, we filled the missing values with the albedo provided by WRF-Chem. In this work, we just considered the ARI for clear-sky. The radiative transfer calculations were performed for each hour and then were averaged over one day. In this work, the direct radiative effects (ARI) of BC aerosol were calculated using following equations: where F ↓ represents downward radiative flux and F ↑ represents upward radiative flux. In this work, we just considered the ARI at the TOA.

Impacts of BC morphology on AOD and AAOD
To verify the modeling performance for the aerosol concentrations, we compared the simulated PM2.5 concentrations with observations at some monitoring sites, and the results are shown in Figure 2. In the figures, the left column represents the typical cities in China, and the right column represents the sites in North America. As shown in Figure 2, the calculated PM2.5 concentrations in China are generally consistent with the observations. Even though the simulated PM2.5 concentrations in 215 the fire region are a little higher than the observations, the deviations are not large, and the general trends are consistent.
Therefore, it is reasonable to represent the atmospheric aerosol concentrations using WRF-Chem modeling. We just compare the calculated AOD and AAOD in Beijing with observations from AErosol RObotic NETwork (AERONET), as the optical observations are limited in our simulation region. As shown in Figure 3, the calculated AAOD and AOD can generally represent the observations.

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For the fire region, even though the surrounding BC concentrations are small, BC concentrations at fire sites are extremely high. In this study, we selected three fire sites to evaluate the morphological effects on the BC ARI. The positions of the selected sites are shown in Table S5, and they represent the fire sites with high aerosol concentrations. As shown in Figure 4, BC concentrations at fire sites can even exceed approximately 400 µg/m 3 , which should have a strong impact on the aerosol radiative effects. In East China, we select Beijing, Shanghai, Tianjin, and Nanjing as the typical sites to represent the polluted 225 urban cities. As shown in Figure 4, even though maximum BC concentrations in the polluted urban cities are much smaller than the fire site, the mean BC concentrations are also high, which can reach approximately 12 µg/m 3 . The simulated BC concentrations generally agree with the measurements of Zhang et al. (2012) for the urban region, where BC concentrations were observed to be approximately 4 -12.7 µg/m 3 . Figure 5 shows the mean BC AOD and AAOD as a percentage of the total AOD and AAOD. In typical China polluted cities, BC AOD accounts for approximately 4.6% -7% of the total AOD, while BC AOD in fire sites can account for larger than 10% of the total AOD. At 450 nm, in both polluted urban and fire sites, the fractions of BC AAOD are close, which is approximately 30%. This means that the relative proportions of BC and OC in polluted urban sites are close to those of fire sites.
BC morphologies can have significant impacts on the BC AOD and AAOD fractions. As BC morphologies change from from a fractal dimension of 1.8 to a spherical structure, BC AOD fraction can vary in the range of approximately 4.6% -5.8%, 5.0% 235 -6.2%, 5.5% -6.9%, 4.8% -6.0%, 9.0% -11.1%, 10.3% -12.7%, 9.1% -11.2% in Beijing, Shanghai, Tianjin, Nanjing, Fire  Shanghai and Nanjing, the maximum BC AOD is approximately 0.07 and 0.1, respectively. In fire sites, BC AOD is much larger, BC AOD can reach approximately 0.5, 0.9, and 0.6 in Loc1, Loc2, and Loc3, respectively. From Figure 6, we can also see that BC AOD calculated using the sphere model is relatively higher than those using fractal aggregate models. Besides, with the given size distribution, the more compact structure can lead to larger AOD, which is consistent with the findings of Liu and Mishchenko (2005). As shown in Figure 7, in the polluted urban area, a spherical assumption for BC lead to an underestimation 250 of less than 0.03 for AOD, while the underestimation can reach approximately 0.15 in fire sites. The underestimation accounts for a large proportion of BC AOD, which can exceed 20% of the total BC AOD. Therefore, BC AOD and AAOD suffer a non-neligible uncertainty from BC morphologies. At fire sites, BC AAOD at 450 nm wavelength can reach approximately 0.7. Our results also show that the sphere model can underestimate BC AAOD. As shown in Figure 9, at typical polluted cities, the sphere model can underestimate AAOD by 260 approximately 0.016, while at fire sites, the AAOD underestimation using the sphere model can reach approximately 0.04. In general, the AAOD underestimation using the sphere model is approximately 8% of the total BC AAOD.

Impacts of BC morphology on AAE and EAE
The absorption Ångström exponent (AAE) calculated using different models is shown in Figure 10. Obvious deviations between fractal aggregate models and the sphere model are found for AAE estimation. With more compact structures, smaller 265 AAE can be observed, which agrees with the findings of Li et al. (2016) and Liu et al. (2018). At typical polluted cities, AAE at 450 -850 nm wavelength pair varies from approximately 1.5 to approximately 2.5, while AAE at fire site can reach as large as approximately 3.0. The observed large AAE is caused by large portions of brown carbon, which significantly absorbs radiation in ultra-violet (UV) and short visible wavelengths. However, as this study mainly focuses on the effects of BC morphologies, the AAE uncertainties caused by OC absorption are not considered in this work. Figure 11 shows that the sphere 270 model can underestimate the AAE by approximately 0.17, which is approximately 17% of BC AAE. As AAE is commonly used to determine the aerosol type, BC morphologies may affect the threshold values for distinguishing the aerosol types.
EAE, as the spectral-dependence of extinction, is widely used to determine the size information of aerosols. Smaller aerosols normally have larger EAE. Figure 12 shows the EAE calculated using different BC models. By using AERONET observation data, in Beijing, Shaheen et al. (2019) showed that the mean EAE at 440 -870 nm in winter was approximately 1.06 ± 0.36.

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The Sun-sky radiometer Observation NETwork (SONET) data conducted by Xie et al. (2015) demonstrated that EAE in the winter of Beijing was commonly within the range of approximately 0.5 -1.5. Our calculated results generally agree with the observation from previous studies. In most cases, the calculated EAE is commonly within the range of 0.5 -1.5, even though some smaller EAE is also observed. In the four typical urban cities, EAE values at 450 -850 nm are similar, and they commonly vary from approximately 0.3 to approximately 1.5. However, EAE at fire sites is commonly within the range of 280 approximately 1.5 -1.85, which is much larger than the values in the polluted urban area. The reason may be that dominating aerosols in the fire region is commonly occupied by carbonaceous aerosols, which are commonly in fine mode. Compared to AAE, the effects of BC morphologies on the total EAE is relatively small. As shown in Figure 13, the EAE differences between fractal BC and spherical BC are within 0.05.

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SSA, as the ratio of scattering to extinction, is widely used to infer aerosol types. Figure 14 shows the comparison of SSA using different BC models. By using AERONET data, Shin et al. (2019b)

Impacts of BC morphology on ARI
BC ARI at the TOA using different BC models is presented in Figure 16. Generally, with a more compact structure, BC presents smaller ARI at the TOA. Figure 17 shows the difference of BC ARI at the TOA between fractal aggregate models and the sphere model. In the polluted urban area, the spherical assumption can underestimate BC ARI by approximately 1.0 Wm −2 , and the underestimation at fire sites can reach approximately 0.6 Wm −2 . As shown in Beijing, Shanghai, Tianjin, and Nanjing, respectively. In fire sites, the BC ARI differences using different models are relatively smaller. When modifying BC structure from a sphere to a fractal aggregate with a D f of 1.8, mean BC ARI increases from +5.52 to +5.90 Wm −2 , +6.64 to +7.05 Wm −2 , +4.91 to +5.23 Wm −2 at Loc1, Loc2, and Loc3, respectively, and the relative uncertainties are approximately 6.9%, 6.2%, 6.5%, respectively. By using different measured BC profiles, Lu et al. (2020) showed BC shape can introduce approximately 5% relative uncertainties in East China. However, our results show that much larger uncertainties can be introduced from BC morphologies. The reason is that in the study of Lu et al. (2020), D f = 2.8 was assumed for BC aggregates, which is close to spherical shape. This D f value is maybe a little larger than the observed D f .
Besides, due to different mean solar angles, our results show the ARI uncertainties caused by BC morphologies may vary in 325 different regions. Therefore, the BC morphological effects on the BC ARI should be carefully considered in different regions.

Summary and Conclusions
In this study, we numerically investigated the effects of BC morphologies on ARI at four cities in East tively. At fire sites, the uncertainties are smaller but still non-negligible. When modifying BC from spheres to fractal aggregates with a D f of 1.8, the mean BC ARI increases from +5.52 to +5.90 Wm −2 , +6.64 to +7.05 Wm −2 , +4.91 to +5.23 Wm −2 at Loc1, Loc2, and Loc3, respectively, and the relative variations are approximately 6.9%, 6.2%, 6.5%, respectively. Therefore, the effects of BC morphologies on the regional radiative effects should be carefully evaluated.
Sphere Observation  Data availability. The data can be requested from the corresponding athour.
Author contributions. JL and QXZ conceived the presented idea. JL developed the models, performed the computations, and wrote the paper.
ZQL, CZ, YMZ, RKC, YZ verified the simulation methods and results. QXZ revised the paper and supervised the findings of this work. GC developed the FlexAOD model. All authors discussed the results and contributed to the final paper.