In the Arctic at Abisko, observed fbb ranges from the fall and wintertime low of 31 % to the summer high of 59 % (Fig. 2a) due to the large contribution from open fires in Europe in summer (Winiger et al., 2016). The model also shows a peak in fbb in summer, but the seasonal variation is relatively flat (from 23 % in winter to 27 % in summer). We attribute the discrepancy to two reasons. First, fbb values of emissions at the site lack seasonal variations, as shown in Fig. 2a. Second, the coarse resolution does not solve the vortex structure of the low-pressure and frontal systems, which is important for poleward transport of BC (Ma et al., 2014; Sato et al., 2016). At Barrow (Fig. 2b), observed fbb values show two peaks in summer (34 %) and winter (37 %), while modeled fbb shows a single strong peak in summer (78 %). In summer, the magnitude and variations of fbb in the atmosphere are similar to those of fbb in local emissions, suggesting that the atmospheric fbb is largely determined by local emissions. The 129 % overestimate of fbb is largely due to the overestimate of local open burning emissions. In spring, fall and winter, the modeled atmospheric fbb values are much larger than the fbb of local emissions, indicating a large contribution from long-range transport.

In contrast to the seasonal cycles of fbb at sites in the Arctic, at Bode (Fig. 2c) over the Himalayan–Tibetan Plateau, fbb values are the lowest in summer (observation: 17 %) and highest in winter (observation: 42 %; Li et al., 2016). The similar trend is observed at Lumbini (Fig. 2d), only with smaller amplitude (summer low: 42 %; spring high: 58 %; Li et al., 2016). The lower fbb in summer is because of several reasons. First, less biofuel is consumed for domestic heating in warmer seasons (Li et al., 2016). Second, the region is barely affected by open fires. Third, biomass-sourced BC is removed more efficiently by the frequent precipitation in summer both over the Himalayan–Tibetan Plateau and over the surrounding source regions, such as India and eastern Asia (Li et al., 2016). The GEOS-Chem-simulated atmospheric fbb values of BC at all sites over the Himalayan–Tibetan Plateau (results for Bode and Lumbini are shown in Fig. 2c and d, and the others are not shown) have weak or no seasonal variations. In addition, the model does not capture the observed increasing trend of fbb along the Mustang Valley and Langtang Valley. Possible reasons for the discrepancies are many. First, the fbb values of local emissions have no seasonal variations, as shown in Fig. 2c and d. Second, it is conceivable that the coarse model resolution of global models does not reproduce the complex topography and transport pathways of BC over the Himalayan–Tibetan Plateau (He et al., 2014). However, the mean modeled atmospheric fbb generally agrees with observations (within 60 %), and the modeled atmospheric fbb generally follows the fbb of local emissions across the whole plateau. These comparisons suggest that the atmospheric fbb over the Himalayan–Tibetan Plateau is largely determined by fbb in emissions in the region.

At the SLC (North America; Fig. 2e), Tokyo (eastern Asia; Fig. 2f), Maldives Climate Observatory in Hanimaadhoo (MCOH) and Indian Institute of Tropical Meteorology in Sinhagad, India (SINH; southern Asia, Fig. 2g and h), sites, no big differences of fbb among seasons were observed (SLC: 8 %–13 %; Tokyo: 33 %–41 %; MCOH: 52 %–53 %; SINH: 48 %–56 %). However, BC concentrations show strong seasonal variations at the four sites, with high loadings in winter and low loadings in summer (Mouteva et al., 2017; Yamamoto et al., 2007; Budhavant et al., 2015). At SLC, the most significant local sources of PM2.5 particles are mobile emissions, which are relatively stable through the whole year (Mouteva et al., 2017). The second most important source is non-mobile sources with solid burning, mostly wood burning, which is not allowed to be used when air quality forecasts predict an inversion period (Mouteva et al., 2017). This restriction limits the extra use of solid fuels in winter, and thus limits their effects on BC concentrations and fbb in the atmosphere. So the higher concentration of BC in winter in SLC is largely determined by the low boundary-layer height (Mouteva et al., 2017). The model overestimates fbb at SLC in all seasons by a factor of 2–4 (Fig. 2e). As described in Mouteva et al. (2017), the observations were in an urban environment with strong influence from local emissions. However, modeled fbb in the atmosphere is much higher than the fbb values of local emissions based on emission inventories in this study (Sect. 2), suggesting that the modeled atmospheric fbb at the site is largely affected by the surrounding regions. The misrepresentation of the source region (local versus regional) is probably one reason for the large bias of modeled fbb against observations. At the Tokyo site in eastern Asia, the model reproduces both the magnitude and the seasonal variations of observed fbb. The much lower fbb value in emissions than in the atmosphere also indicates a regional effect. In southern Asia, GEOS-Chem reproduces the similar observed high fbb values at MOCH (summer: 52 %; winter: 53 %) and SINH (summer: 48; winter: 56 %) within 30 %. However, reasons for the high fbb values at the two sites are different. Since there are no local emissions at MCOH, fbb at the site is largely affected by long-range transport. In contrast, fbb in the atmosphere follows fbb in local emissions at SINH, suggesting that the atmospheric fbb at the site is mostly affected by local emissions. At MCOH the high fbb is probably from the large fbb in the outflow of Africa, while at SINH local burning of agricultural crop residues is the major source (Budhavant et al., 2015).

GEOS-Chem suggests that the Southern Hemisphere has a higher contribution from biomass burning both for BC in surface air (50±11 %) and in deposition (53±10 %, Fig. 3a and b). The high fbb values in S America and Australia are largely from active open fires (accounting for 48 % and 81 % of the total biomass burning contributions, respectively), while in Africa biofuel consumption is the major biomass burning source (model: 64±20 %; Fig. 3c and d). Because of the strong seasonal variations of open fire emissions, the highest fbb values in Africa, S America, the S Pacific, Australia and the Antarctic usually occur during September to November (58 %–71 %), and the lowest values are in March–May (32 %–56 %; Fig. S4).

In the Northern Hemisphere, the largest fbb values of both BC in the atmosphere (93±5 %) and in deposition (92±6 %) are in northern Congo, where biomass burning contribution dominates over fossil fuel emissions. southern Asia also shows large fbb values (54 % for BC in air and in deposition) due to large biofuel consumption. In other regions, such as Europe, Canada, the US, Siberia and the Arctic, fossil fuel contribution (65 %–80 %) is much larger than biomass burning. fbb values of BC in air and in deposition in different regions have different seasonal variations (Figs. S4–S5). Atmospheric fbb values in Canada, Siberia, the Arctic and the Antarctic have the strongest seasonal variations, with a peak in summer (49 %–70 %) because of the large fraction of open fire emissions (Figs. S6–S7). In the US, southern Europe, eastern Asia and southern Asia, seasonal variation of fbb is relatively flat, which is also shown by observations at a few sites (Fig. 2).

Biofuel emission estimates are associated with large uncertainties (Fernandes et al., 2007). Source apportionment of BC in Europe based on multi-wavelength aethalometer measurements showed that fbb in winter (24 %–33 %) is much higher than that in summer (2 %–10 %), suggesting that wood burning for domestic heating increases the fbb value in the atmosphere in winter significantly (Herich et al., 2011). In addition, Winiger et al. (2017) analyzed fbb based on carbon isotope measurements at Tiksi in Russia and suggested that domestic use (∼60 % of which is from biomass burning) accounted for 35 % of BC at the site, following transport (38 %). We find that during the cold season, mean fbb values in Europe and the Arctic (most sites are north of 45∘ N; Table S1) are underestimated by 68 % and 50 % in the standard simulation, probably due to the underestimate of domestic heating in winter. However, in eastern Asia (all sites are south of 45∘ N), mean fbb in winter is overestimated by 22 %. Thus, we doubled biofuel emissions from domestic heating north of 45∘ N during cold seasons in Experiment A (Exp. A) to investigate the uncertainty associated with biofuel emissions. It is conceivable that the largest effects occur in the northern four regions, including Europe, Siberia, Canada and the Arctic. As a result, fbb values increase by ∼30 % in Europe, Siberia and the Arctic and by 15 % in Canada in winter, which is larger than those in spring and fall (4 %–13 %; Fig. 4). Consequently, the low bias of fbb in Europe is reduced from -63 % to -54 %. This improvement suggests that the biofuel emissions at high latitudes in the Northern Hemisphere are probably too low in current bottom-up BC emission inventories, supporting previous estimates (Herich et al., 2011).

Recent measurements find that in freshly emitted fossil fuel plumes, the fraction of thickly coated hydrophilic BC is ∼ 10 % (Moteki et al., 2007; Schwarz et al., 2008; Shiraiwa et al., 2007), while in biomass burning plumes the fraction reaches up to 70 % (Schwarz et al., 2008; Akagi et al., 2012). The higher hygroscopicity of BC in freshly emitted biomass burning plumes enhances the subsequent wet scavenging rate and thereby reduces fbb in the atmosphere. In the standard simulation, we assume that 20 % of freshly emitted BC particles are hydrophilic. We investigate the effects of the initial hygroscopicity of BC in fresh emissions on atmospheric fbb of BC in Exp. B by assuming that 70 % of freshly emitted BC particles from biomass burning are thickly coated and hydrophilic. The resulting fraction of hydrophilic BC in biomass burning plumes in the 12 regions increases by 0 %–20 % (varying with seasons and regions), lowering fbb in the atmosphere by up to 11 % in Canada in summer. The largest reduction of fbb shows in June–August (-7 % averaged for all regions; Fig. 4), when open fires are frequent and active globally (Giglio et al., 2013; van der Werf et al., 2010). During this time, the largest reductions are in Canada (-11 %) and Siberia (-10 %), where the fraction of hydrophilic BC in biomass burning plumes increases by a large fraction (11 %–13 %). In the S Pacific, the reduction of fbb is large (-10 %) as well because large precipitation (28 kg m-2 month-1) over this region removes more biomass burning BC particles in the outflow of S America. During September–November, the relative reduction of fbb in the Northern Hemisphere (-6 %) is much larger than that in the Southern Hemisphere (-1 %) because fbb values in the Southern Hemisphere are too large (Fig. S5). The changes of fbb values in other seasons in all regions are marginal.

Mixing organic and inorganic particles with larger hygroscopicity, BC particles become more hydrophilic during the aging process (Bond et al., 2013). It is assumed that BC particles are converted from hydrophobic to hydrophilic with an e-folding time of 1.15 d after emission in the standard simulation (Park et al., 2005). However, observations showed that the fraction of thickly coated hydrophilic BC in urban fossil fuel plumes increases linearly with plume age (0.5 % h-1–2.3 % h-1, Moteki et al., 2007; Shiraiwa et al., 2007; Subramanian et al., 2010; McMeeking et al., 2011), while BC aging follows a logarithmic trend with an e-folding time of 4 h in biomass burning plumes (Akagi et al., 2012). The aging rates differ among plumes because of different BC sizes, co-emitted hygroscopic materials and oxidation capacities of the plumes (Bond et al., 2013). Thus, in Exp. C, we assume that fossil fuel combustion generated BC ages linearly with a rate of 1 % h-1, while BC from biomass burning plumes ages with an e-folding time of 4 h. This means that the fossil fuel plumes age slower than the standard simulation and are scavenged slower, while the biomass burning plumes age much faster and are removed from the atmosphere faster in precipitation. This aging scheme leads to a 0 %–24 % increase in the fraction of hydrophilic BC in the atmosphere, which reduces fbb by up to -14 %. The largest reduction of fbb is in the S Pacific in fall (MAM) and summer (DJF) in the Southern Hemisphere, followed by the Antarctic (-12 %) during MAM and the Arctic (-11 %) during SON. The reduction of fbb is larger in remote regions and smaller in source regions because it takes time for the different aging rates in fossil fuel and biomass burning plumes to affect the hygroscopicities of BC in the two plumes and the subsequent aging rates.

BC particles emitted from biomass burning plumes are usually larger in size and thicker in coating thickness (Schwarz et al., 2008; Sahu et al., 2012), suggesting an easier removal from the atmosphere. For example, observations (Schwarz et al., 2008; Sahu et al., 2012) showed that the mass median diameter of BC particles in biomass burning plumes is 193 nm with a coating thickness of 65 nm, while in fossil fuel plumes, the mass median diameter and coating thickness are 175 and 20 nm. In addition, because of the different coating materials, hygroscopicities of BC-containing particles in the two kinds of plumes are different as well. The coating materials of BC in urban plumes are dominated by sulfate and followed by nitrate and primary and secondary organics (Shiraiwa et al., 2007), while in biomass burning plumes, the major coating materials are organics (Sahu et al., 2012). For ambient air, characteristic κ values of organics and inorganics are 0.1 (0.01–0.5) and 0.7 (0.5–1.4; Petters and Kreidenweis, 2007; Gunthe et al., 2011, and references therein). Higher hygroscopicity of BC in fossil fuel plumes suggests that they are easier to activate and serve as cloud condensation nuclei (CCNs) compared to BC particles in biomass burning plumes. The higher hygroscopicity and smaller size of BC particles in fossil fuel plumes have the opposite effect on their removal rate. Thus, we investigate the total effects of size-resolved scavenging in Exp. D; we use the TOMAS microphysics scheme to process the aging and wet scavenging of BC with different sizes from fossil fuel combustion and biomass burning. The mass median diameters of fossil fuel and biomass burning BC particles are assumed to be 160 and 200 nm, respectively. Size-resolved coagulation, condensation, nucleation and cloud processing are implemented. Coating materials included are sulfate, nitrate, sea-salt, organics and mineral dust. The size-resolved aging and scavenging scheme leads to a larger increase in the fraction of hydrophilic BC in fossil fuel plumes (by 16 %; 0 %–31 %, varying with regions) than in biomass burning plumes (by 12 %; 0 %–23 %). This increase in both fossil fuel and biomass burning plumes suggests that BC particles are removed faster in the size-resolved simulation than in the standard simulation with a bulk removal parameterization. The larger increase in the fraction of hydrophilic BC in fossil fuel plumes means that BC in fossil fuel plumes is removed faster than that in biomass burning plumes in the size-resolved simulation. This is probably because the total effect of higher hygroscopicity of coating materials and smaller size of BC in fossil fuel plumes enhances their removal. Thus atmospheric fbb increases in most regions during MAM (by 1 %–14 %), SON (by 0 %–7 %) and DJF (by 1 %–12 %). The most noticeable characteristic is that the increase in fbb in the Northern Hemisphere is larger than that in the Southern Hemisphere due to the large fraction of fossil fuel emissions in the Northern Hemisphere.

Finer model resolution is capable of reproducing small-scale meteorological conditions, which is critical to BC transport (Sato et al., 2016). We use horizontal resolution of 4∘ lat × 5∘ lon in the standard simulation and Exps. A–D because the size-resolved microphysical scheme TOMAS in Exp. D is computationally expensive. We investigate the uncertainty associated with model resolution in Exp. E by using a finer horizontal resolution of 2∘ lat × 2.5∘ lon (Fig. 4). We find that, relative to the standard simulation, fbb in Exp. E changes by -5 %–5 % in the 13 regions in all seasons. In most regions, the absolute change is smaller than or equal to the change in Exp. A–D, except in mid-latitude and tropical regions in Exp. A. Averaged over the whole globe, the relative change of fbb to the standard simulation is -1 %.

Carbon isotope measurements of BC sources are associated with large uncertainties. The thermal-optical protocol used for the carbon isotope measurements of BC produces ∼30 % difference of observed fbb values (Zhang et al., 2012), which is equal to or larger than the uncertainties of modeled fbb associated with biofuel emissions north of 45∘ N, the aging rate and wet scavenging discussed in Sect. 4.3.1–4.3.4. The comparison of the two sets of data in Sect. 4.1 and 4.2 is within a similar uncertainty range. In addition, we do not have carbon isotope measurements in the Southern Hemisphere to constrain the model results. Our analysis in this study is based only on model results.

In addition to the biofuel emissions discussed in Sect. 4.3.1, open fire emissions, particularly in the boreal regions, are associated with large uncertainties (Randerson et al., 2012). Konovalov et al. (2018) found that open burning emissions of Siberian fires during May to September from GFED4 is possibly underestimated by a factor of 2, constrained by satellite observations of the aerosol absorption optical depth and the aerosol extinction optical depth. However, we find that during the same season, mean atmospheric fbb at Tiksi in Russia is overestimated by 88 %, indicating that open burning emissions in this region from GFED4 are possibly overestimated. This contradiction suggests that further studies are needed to better constrain the open burning emissions in boreal regions. In addition, the global fossil fuel (Bond et al., 2007) and biofuel emission inventory (Fernandes et al., 2007) used in this study are for the year 2000, and the emissions in Asia (Li et al., 2017) are for the year 2010. We estimated the fbb from 2007 to 2013 using these constant inventories and varying open burning emissions from GFED4. The lack of inter-annual variations of BC fossil fuel and biofuel emissions also produces uncertainties, but it is difficult to quantify based on current knowledge.