Effects of Wegener-Bergeron-Findeisen Process on Global Black Carbon Distribution

. We systematically investigate the effects of Wegener-Bergeron-Findeisen (WBF) on BC scavenging efficiency, surface BC air , deposition flux, concentration in snow (BC snow , ng g -1 ), and washout ratio using a global 3D chemical transport 10 model (GEOS-Chem). We differentiate riming- versus WBF-dominated in-cloud scavenging based on liquid water content (LWC) and temperature. Specifically, we relate WBF to either temperature or ice mass fraction (IMF) in mixed-phase clouds. We find that at Jungfraujoch, Switzerland and Abisko, Sweden, where WBF dominates, the discrepancies of simulated BC scavenging efficiency and washout ratio are significantly reduced (from a factor of 3 to 10% and from a factor of 4–5 to a factor of two). However, at Zeppelin, Norway, where riming dominates, simulation of BC scavenging efficiency, BC air , and washout 15 ratio become worse (relative to observations) when WBF is included. There is thus an urgent need for extensive observations to distinguish and characterize riming- versus WBF-dominated aerosol scavenging in mixed-phase clouds and the associated BC scavenging efficiency. We find the reduction resulting from WBF to global BC scavenging efficiency varies substantially, from 8% in the tropics to 76% in the Arctic. The resulting annual mean BC air increases by up to 156% at high altitudes and at northern high latitudes because of lower temperature and higher IMF. Overall, WBF halves the model-observation discrepancy (from - 20 65% to -30%) of BC air across North America, Europe, China and the Arctic. Globally WBF increases BC burden from 0.22 to 0.29 − 0.35 mg m -2 yr -1 , which partially explains the gap between observed and previous model simulated BC burdens over land. In addition, WBF significantly increases BC lifetime from 5.7 days to ~8 days. Additionally, WBF results in a significant redistribution of BC deposition in source and remote regions. Specifically, it lowers BC wet deposition (by 37 − 63% at northern mid-latitudes and by 21 − 29% in the Arctic) while increases dry deposition (by 3 − 16% at mid-latitudes and by 81 − 159% in the 25 Arctic). The resulting total BC deposition is lower at mid-latitudes (by 12 − 34%) but higher in the Arctic (by 2 − 29%). We find that WBF decreases BC snow at mid-latitudes (by ~15%) but increases it in the Arctic (by 26%) while improving model comparisons with observations. In addition, WBF dramatically reduces the model-observation discrepancy of washout ratios in winter (from a factor of 16 to 4). The remaining discrepancies in BC air , BC snow and BC washout ratios suggest that in-cloud removal in mixed-phased clouds is likely still excessive over land. interstitial efficiency Wang et al., 2013, 2014; et al., 2013), (Doherty et al., 2010) Concurrent measurements of BC in fresh snow and rain (BC snow/rain ) and BC air (Cerqueira et al., 2010; Mori et al., 2014) provide better constraints on BC wet pylyethylene jars and transport back to the laboratory. The snow was transferred to a filtration apparatus where it was melted and filtered. The amount of BC on the filters was determined by optical analysis. The air samples were measured using the integrating sandwich technique. At Zeppelin, BC snow and BC air was measured concurrently in April and May 2007. BC snow was concentrated by nuclepore filters and then determined using a multiwavelength underestimates the frequency of BC snow at 8–80 ng g -1 , while overestimates the frequency outside the range. More importantly, the observations have a single 35 maximum but the model shows a bimodal structure. WBF significantly improves the agreement between observed and simulated distribution by increasing the frequency of BC snow at 8–80 ng g -1 , resulting in a single maximum. WBF decreases median BC snow by ~15% (from 25.7 ng g -1 to 22.4 − 22.7 ng g -1 ) and improves the comparison with observations (median: 19.1 ng g -1 ). 4). The improvements are because WBF reduces BC rain/snow (discrepancy reduced from a factor of seven to a factor of four) and increases BC air (discrepancy

Abstract.We systematically investigate the effects of Wegener-Bergeron-Findeisen process (hereafter WBF) on black carbon (BC) scavenging efficiency, surface BC air , deposition flux, concentration in snow (BC snow , ng g −1 ), and washout ratio using a global 3-D chemical transport model (GEOS-Chem).We differentiate riming-versus WBFdominated in-cloud scavenging based on liquid water content (LWC) and temperature.Specifically, we implement an implied WBF parameterization using either temperature or ice mass fraction (IMF) in mixed-phase clouds based on field measurements.We find that at Jungfraujoch, Switzerland, and Abisko, Sweden, where WBF dominates in-cloud scavenging, including the WBF effect strongly reduces the discrepancies of simulated BC scavenging efficiency and washout ratio against observations (from a factor of 3 to 10 % and from a factor of 4-5 to a factor of 2).However, at Zeppelin, Norway, where riming dominates, simulation of BC scavenging efficiency, BC air , and washout ratio become worse (relative to observations) when WBF is included.There is thus an urgent need for extensive observations to distinguish and characterize riming-versus WBFdominated aerosol scavenging in mixed-phase clouds and the associated BC scavenging efficiency.Our model results show that including the WBF effect lowers global BC scavenging efficiency, with a higher reduction at higher latitudes (8 % in the tropics and up to 76 % in the Arctic).The resulting annual mean BC air increases by up to 156 % at high altitudes and at northern high latitudes because of lower temperature and higher IMF.Overall, WBF halves the model-observation discrepancy (from −65 to −30 %) of BC air across North Amer-ica, Europe, China and the Arctic.Globally WBF increases BC burden from 0.22 to 0.29-0.35mg m −2 yr −1 , which partially explains the gap between observed and previous modelsimulated BC burdens over land.In addition, WBF significantly increases BC lifetime from 5.7 to ∼ 8 days.Additionally, WBF results in a significant redistribution of BC deposition in source and remote regions.Specifically, it lowers BC wet deposition (by 37-63 % at northern mid-latitudes and by 21-29 % in the Arctic), while it increases dry deposition (by 3-16 % at mid-latitudes and by 81-159 % in the Arctic).The resulting total BC deposition is lower at mid-latitudes (by 12-34 %) but higher in the Arctic (by 2-29 %).We find that WBF decreases BC snow at mid-latitudes (by ∼ 15 %) but increases it in the Arctic (by 26 %) while improving model comparisons with observations.In addition, WBF dramatically reduces the model-observation discrepancy of washout ratios in winter (from a factor of 16 to 4).The remaining discrepancies in BC air , BC snow and BC washout ratios suggest that in-cloud removal in mixed-phased clouds is likely still excessive over land.

Introduction
Black carbon (BC) effectively heats the atmosphere by absorbing solar radiation and has been regarded as the second largest warming agent after CO 2 (Ramanathan and Carmichael, 2008;Bond et al., 2013;IPCC 2014).Moreover, BC deposited on snow and ice reduces surface albedo and accelerates melting (Flanner et al., 2007;He et al., 2014b; Published by Copernicus Publications on behalf of the European Geosciences Union.IPCC, 2014;Liou et al., 2014).However, there are large uncertainties in estimating direct radiative forcing of BC, mainly arising from the uncertainties in predicting BC distribution (Bond et al., 2013).Current models in the project Aerosol Comparisons between Observations and Models (AeroCom) underestimate aerosol absorption optical depth (AAOD) of BC observed by the AErosol RObotic NETwork (AERONET) and satellite by a factor of 1.6-4 (Bond et al., 2013) but overestimates BC air observed in remote Pacific by a factor of 2-5 (Schwarz et al., 2010;Q. Wang et al., 2014;X. Wang et al., 2014).Moreover, inter-model disagreement of BC loadings simulated by AeroCom models is up to 2 to 3 orders of magnitude (Koch et al., 2009;Bond et al., 2013).The large discrepancy with observations and large disagreement among models are primarily attributed to wet deposition, which is the dominant mechanism to remove BC from the atmosphere (Textor et al., 2006;Koch et al., 2009;Bond et al., 2013) and consequently determines its lifetime and atmospheric burden.The major process of wet scavenging is in-cloud scavenging (Taylor et al., 2014), which occurs in two stages: aerosol activation to form cloud droplets, and removal of droplets by precipitation.The ability of a particle to be activated as a cloud condensation nucleus (CCN) and thereby be scavenged by in-cloud scavenging depends on its hygroscopicity, size, and super-saturation in the cloud (Ghan et al., 2011).The partition of BC particles between condensed phase and interstitial air in clouds is quantified by scavenging efficiency, which is defined as the ratio of aerosol mass mixing ratio in cloud drops and ice crystals to total aerosol mass mixing ratio in clouds (including aerosols in interstitial air and in cloud drops).
The determining factors controlling BC scavenging efficiency in clouds are the properties of BC particles, including their hygroscopicity, size, and chemical composition (Sellegri et al., 2003;Hallberg et al., 1992Hallberg et al., , 1994)).Local changes of updraft velocity and critical super-saturation significantly affect local BC scavenging efficiency.Such effects are also observed at long-time averages.In mixed-phase clouds, the effect of cloud microphysics on BC scavenging is considerably more complex.One complicating factor is the so-called Wegener-Bergeron-Findeisen process (hereafter WBF; Wegener, 1911;Bergeron, 1935;Findeisen, 1938), where water vapor transfers from liquid to ice phases when vapor pressure is between the saturation vapor pressure over ice and water droplets.Liquid cloud droplets evaporate and release the aerosol materials in the droplets back into interstitial air, resulting in a slower scavenging of aerosols in mixed-phase clouds.The water vapor evaporated from water drops deposit onto ice surface and snow particles form.Accordingly, WBF leads to slower BC scavenging and faster snow growth.Theoretical estimates show that snow growth rate from WBF is a function of temperature (Pruppacher and Klett, 2010).As temperature lowers from 0 to −14 • C, snow growth rate is estimated to increase drastically from 0 to 5.2 × 10 −8 (g s −1 ) at 500 hPa (Pruppacher and Klett, 2010), and BC scaveng-ing efficiency at Jungfraujoch is observed to decrease from 0.6 to 0.2 (Cozic et al., 2007).From −14 to −25 • C, the estimated snow growth rate from WBF varies in a relatively smaller range (4.8-5.5 × 10 −8 g s −1 , Pruppacher and Klett, 2010), and BC scavenging efficiency varies in 0.1-0.2(Cozic et al., 2007).The two anti-correlated trends indicate that WBF is a very important factor that explains the observed temperature dependence of BC scavenging efficiency at Jungfraujoch.Another process that affects BC scavenging in mixed-phase clouds is riming (Hegg et al., 2011).Riming occurs when LWC is high and gravitationally settling of snowflakes and ice crystals collect the water drops along their pathways, thereby scavenging BC particles in the water drops.At Zeppelin, where snow particles show predominantly rimed structures, BC scavenging efficiency changes marginally (within 5 %) from summer (0.77) to winter (0.81) as the average temperature lowers from −2 • C in summer to −14 • C in winter (Heintzenberg and Leck, 1994).The different trends of the scavenging efficiency with temperature observed at Jungfraujoch and Zeppelin indicate that WBF and riming are the major processes that determine BC scavenging efficiency in mixed-phase clouds.Therefore, the decreasing of BC scavenging efficiency with decreasing temperature at Jungfraujoch is mainly attributed to WBF (Cozic et al., 2007).Recent studies have found that this reduction of BC scavenging efficiency from WBF not only affects wet scavenging of aerosols but also strongly affects cloud feedbacks and climate sensitivities (Tan et al., 2016).Thus, it is critical to differentiate WBF and riming process in model simulations.
BC scavenging efficiency is typically prescribed as a constant (between 0 and 1) in global chemical transport models (CTMs) for computational efficiency consideration and the limited understanding of the processes controlling the partition of BC between interstitial air and condensed phases in mixed-phase clouds (Textor et al., 2006).Textor et al. (2006) and Wang et al. (2011) treated BC scavenging in mixedphase the same as in warm liquid clouds.Stier et al. (2005) used a scavenging efficiency of 0.40 for soluble Aitkenmode aerosols and 0.75 for accumulation-mode aerosols in mixed-phase clouds, lower (by 0.10) than their corresponding values in liquid-only clouds.Using the same model, Bourgeois and Bey (2011) applied a substantially lower scavenging efficiency (0.06) for both Aitken-and accumulationmode aerosols in mixed-phase clouds based on measurements from Henning et al. (2004).The lower scavenging efficiency results in 5-fold higher BC burden in the Arctic (from 0.75 to 3.7 Gg) and 3-fold longer BC lifetime (from 1.8 to 5.8 days).Liu et al. (2011) and Browse et al. (2012) also showed that BC loading and lifetime are both very sensitive to scavenging efficiency.It is clear that a systematic examination of BC scavenging efficiency and wet deposition is warranted.To that end, recent comprehensive largescale measurements of BC snow in North America (Doherty et al., 2014), China (Huang et al., 2011;Ye et al., 2012;X. Wang et al., 2013X. Wang et al., , 2014;;Zhang et al., 2013), and the Arctic (Doherty et al., 2010) provide a unique opportunity.Concurrent measurements of BC in fresh snow and rain (BC snow/rain ) and BC air (Cerqueira et al., 2010;Mori et al., 2014) provide better constraints on BC wet deposition.
BC scavenging efficiency varies as a function of BC aging in GEOS-Chem (Park et al., 2005;Wang et al., 2011).Specifically, in warm and mixed-phase clouds, hydrophilic BC particles are completely (100 %) incorporated in cloud drops and serve as CCN, while hydrophobic BC particles remain in interstitial air.In ice clouds, hydrophobic BC particles serve as ice condensation nuclei, while hydrophilic BC particles are not scavenged.In this study we investigate the effect of WBF on BC scavenging, its distribution in air and snow, and the budget using GEOS-Chem.Specifically, we distinguish riming-versus WBF-dominated in-cloud scavenging in mixed-phase clouds and parameterize BC scavenging efficiency accordingly.We evaluate model results of BC scavenging efficiency (Sect.4.1), BC air (Sect.4.2), BC wet deposition fluxes (Sect.4.3), BC snow (Sect.4.4), and BC washout ratio (Sect.4.5).We further discuss the WBF effects on global BC budget (Sect.5), followed by conclusions and implications (Sect.6).

Observations
Figure 1 shows sites with measurements of BC scavenging efficiency, BC air , BC snow , and BC washout ratio in the Northern Hemisphere.

Scavenging efficiency measurements
BC scavenging efficiencies in mixed-phase clouds are not well understood.In mixed-phase clouds, BC is partitioned between condensed phase (water drops and ice crystals) and interstitial air, which is crucial for accurate estimates of the in-cloud scavenging of BC.Following Hallberg et al. (1992) and references thereafter, the scavenging efficiency is defined as where r scav. is BC scavenging efficiency, [BC] condensed the mass mixing ratio of BC in condensed phase, and [BC] interstitial the mass mixing ratio of BC in the interstitial air.
There are eight surface sites that reported measurements of BC scavenging efficiencies (Table 1 and Fig. 1).Cloud droplets and interstitial air were collected through different inlets.Cloud droplets were collected by a counterflow virtual impactor (CVI) (Ogren et al., 1985).Interstitial air was sampled by impactor-type collectors such as annular-slit impactor, round jet impactor, and mini-cascade impactor.Field calibration of the two inlets as well as theoretical consideration and laboratory calibration showed that the overall un- certainty of mass concentration of particles of the two phases in clouds was close to 15 % (Sellegri et al., 2003).The scavenged fraction was then computed from the comparison between cloud impactor samples and interstitial aerosols (e.g., Hallberg et al., 1992Hallberg et al., , 1994;;Heintzenberg and Leck, 1994;Gieray et al., 1997;Hitzenberger et al., 2000Hitzenberger et al., , 2001)).Longterm measurements of BC mass mixing ratios in clouds require that the in situ sites are located at high altitudes with frequent clouds.Only a few sites meet these requirements.Thus, available measurements of BC scavenging efficiencies are very limited.
The observed BC scavenging efficiencies increase with increasing distance from source regions, from 0.06 in heavily polluted fog in Po Valley, Italy (44.6 • N, 11.6 • E; sea level), (Hallberg et al., 1992) to 0.81 at Zepplin (79 • N, 12 • E; 0.47 km) in the Arctic (Heintzenberg and Leck, 1994) (Table 1).The observed scavenging efficiencies were vastly different at the Po Valley: 0.06 from Hallberg et al. (1992) and 0.39 from Gilardoni et al. (2014).Reasons for the difference are unclear.Freshly emitted BC particles are mostly hydrophobic and cannot serve as CCN (Weingartner et al., 1997).Hydrophobic BC particles mix with hydrophilic materials (e.g., sulfate, nitrate or soluble organics) during transit and become hydrophilic and larger in size (Sellegri et al., 2003).The incorporation of BC particles into cloud droplets via nucleation scavenging is thus enhanced (Moteki et al., 2012;Taylor et al., 2014).Both cloud dynamics (e.g., updraft velocity) and microphysics (nucleation, condensation and coagulation) complicate and determine the partition of BC particles between condensed phase and interstitial air in mixed-phase clouds (Cozic et al., 2007).When riming occurs, large snow crystals collect cloud water drops along their pathways and BC particles in these cloud water drops are likewise removed (Heintzenberg and Leck, 1994;Hegg et al., 2011).BC scavenging efficiency due to riming is thus similar to that in warm clouds.For example, at Zeppelin, where the riming process was typically dominant, L. Qi et al.: Effects of the WBF process on global BC distribution BC scavenging efficiencies in winter (0.77) (mostly mixedphase clouds and ice clouds) and in summer (0.81) (mostly warm liquid clouds) were within 5 % (Heintzenberg and Leck, 1994).In contrast, when the WBF process occurs, ice crystals grow at the expense of water droplets and hence BC particles inside the water droplets are released back into the interstitial air, thereby lowering in-cloud BC scavenging efficiency.The scavenging efficiency at Jungfraujoch (46.5 • N, 8 • E; 3.85 km), where the WBF process dominates in mixedphase clouds, was higher in warm clouds (0.6) in summer and substantially lower in mixed-phase clouds (0.05-0.10) in spring (Cozic et al., 2007).Cozic et al. (2007) reported comprehensive observations of BC scavenging efficiency at Jungfraujoch, a site regularly engulfed by clouds (30 % of the time) and far away from pollution sources.The site is well suited for investigating continental background aerosols and clouds from a ground-based platform.Cozic et al. (2007) examined the partitioning of BC in mixed-phase clouds by sampling through two inlets, with one heated inlet collecting aerosols in cloud drops, ice crystals and the interstitial air and the other collecting only aerosols in the interstitial air.They found that the scavenging efficiency of BC was influenced by LWC, BC content, temperature and IMF.We use their results to parameterize the effect of WBF on BC scavenging efficiency in this study (See Sect.3).

BC in surface air
Surface BC air has been widely measured across the Arctic, North America, Europe and Asia (Fig. 1).Observations in the Arctic are available at Denali, Alaska; Barrow, Alaska; Alert, Canada; Zeppelin, Norway; and Summit, Greenland (see details in Qi et al., 2017).We also use here measurements of BC air at 178 sites as part of the Interagency Monitoring of PROtected Visual Environment (IMPROVE; Malm et al., 1994;http://vista.cira.colostate.edu/improve/)network in North America.IMPROVE measurements were made every 3 days and 24 h averages were reported.Additionally, we use BC air observations from East Asia in 2006 (X.Y. Zhang et al., 2008).Observations of BC air in Europe are from the European Monitoring and Evaluation Programme (EMEP) network (EMEP/MSC-W et al., 2014; http://ebas.nilu.no).We use here daily EMEP measurements.
The thermal optical reflectance (TOR) combustion method is used to measure BC concentrations by IMPROVE and EMEP network based on the preferential oxidation of organic carbon (OC) and elemental carbon (EC) at different temperatures (Chow et al., 1993(Chow et al., , 2004)).Heating protocols used by IMPROVE network are as follows: the sample filter is heated stepwise at temperatures of 120 • C (OC1), 250 • C (OC2), 450 • C (OC3), and 550 • C (OC4) in a non-oxidizing (He) atmosphere, and at 550 • C (EC1), 700 • C (EC2), and 800 • C (EC3) in an oxidizing atmosphere of 2 % oxygen and 98 % He.Evolved carbon is oxidized to CO 2 and then reduced to CH 4 for detection.The pyrolyzed or charred OC is monitored by reflectance at wavelength λ = 633 nm.The portion of EC1 until the laser signal returns to its initial value is assigned to pyrolyzed organic carbon (OP).EC is defined by EC1 + EC2 + EC3 − OP.We use EC here to approximate the concentration of BC.EMEP use different protocols.Samples were heated up to either 850 • C (NIOSH) (and hence a fraction of EC may be combusted) or 650 • C (EUSAAR_2; EUROPA, 2008).BC-like products of OC pyrolysis can lead to uncertainty in measuring BC mass.The uncertainty is estimated to be ∼ 20 % based on the repeatability and reproducibility of the measurements (EMEP/MSC-W et al., 2014).

BC in snow
We use BC snow (ng g −1 ) to constrain BC deposition on snow-covered surfaces.There is now a comprehensive set of BC snow measurements, from sampling the full snowpack depth, in the Northern Hemisphere (Fig. 1): the Arctic (Doherty et al., 2010), North America (Doherty et al., 2014), northern China (Wang et al., 2013), and Xinjiang, China (Ye et al., 2012).For direct comparison with model results, we merge the observations in the same model grid cell.We exclude samples with obvious contamination from dust, soil, or local emissions as indicated in the observations.This leaves out a sample number of 334 from the Arctic, 158 from North America, 97 from northern China, and 47 from Xinjiang, China.Doherty et al. (2014) grouped samples in North America into four geographic regions based on land surface type and seasonal average snow water equivalent: Canada, the Great Plains, the Pacific Northwest, and the Intra-Mountain Northwest.Here we follow the same definitions.Wang et al. (2013) defined three subregions of northern China: Inner Mongolia, Northeast Border, and Northeast Industrial.We use the same definitions in this study.The largest uncertainties of these measurements are uncertainties of BC mass absorption cross section (−25 %), BC and non-BC absorption Ångström exponent used to estimate BC snow (∼ 50 %, Doherty et al., 2010).Other uncertainties include instrumental uncertainty (≤ 11 %) and under-catch correction (±15 %) (see details in Doherty et al., 2010).The resulting overall uncertainty of the observed BC snow is < 60 %.

Washout ratio measurements
Washout ratio is a more easily measured parameter (compared to scavenging efficiency) that characterizes wet scavenging of BC.It is defined as the ratio of BC mass mixing ratio in fresh rain and snow to that in surface air following Hegg et al. (2011), where r washout is the washout ratio, [BC] rain/snow the BC mass mixing ratio in fresh rain or snow, and [BC] air the BC mass mixing ratio in surface air.Washout ratio is an ambiguous metric for scavenging because it is rare that surface BC air is representative of that at the altitude where BC aerosols are scavenged.On the other hand, washout ratio does subsume a number of individual processes such as in-cloud scavenging and below-cloud scavenging to give an estimate of an overall assignment (Hegg et al., 2011).Thus, unlike BC scavenging efficiency, which quantitatively describes the partition of BC in condensed phase and interstitial air in clouds, BC washout ratio is only a qualitative index for scavenging, which might partly explain why we have such limited observations of washout ratios so far.During snow season, washout ratio characterizes the riming-versus WBF-dominated snow formation process and BC scavenging in mixed-phase clouds.
The washout ratio at Zeppelin, where snow particles show rimed structures, shows that BC particles are scavenged efficiently and the scavenging efficiency was ∼ 770 (Hegg et al., 2011).However, at Abisko and Changbai, where pristine crystal snow particles formed mainly from the WBF effect, BC was scavenged much less efficiently than that in rimingdominated condition, resulting in a much smaller washout ratio (∼ 150; Noone and Clark, 1988;Z. W. Wang et al., 2014).This is because BC particles in cloud drops were released back to the interstitial air and not subject to scavenging.
Figure 1 shows nine remote sites with concurrent measurements of BC rain/snow and BC air to estimate washout ratio (black triangles in Fig. 1).BC air and BC rain/snow were measured at Cape Hedo (26.9 • N, 128.3 • E,;0.06 m) in the East China Sea during 2011-2013.BC air was measured with an integration time of 1 min using a filter-based absorption photometer.The accuracy of this measurement has been estimated to be about 10 % based on the consistency of the measured BC concentration by three methods, including a filter-based absorption photometer, thermal-optical transmittance method and single-particle soot photometer (Mori et al., 2014;Kondo et al., 2011).BC rain/snow was measured with a system based on an ultrasonic nebulizer, with an overall accuracy of about 25 % (Mori et al., 2014).BC air and BC rain/snow were measured concurrently in Europe at two rural background sites -Aveiro (40.5 • N, 8.6 • W, 0.05 km) and K-puszta, Hungary (47 • N, 19.5 • E, 0.2 km) -and two mountain sites, Schauinsland, German (47.9 • N, 7.9 • E, 1.2 km) and Sonnblick, Austria (47 • N, 13.4 • E, 3.1 km) in 2002-2004(Cerqueira et al., 2010)).Sampling of rain and snow mainly focused on major precipitation events in order to collect large volumes over short-time periods.Samples were collected on an event basis with a stainless steel funnel connected to a pre-cleaned glass bottle.In order to minimize dry deposition of particles, the collector was deployed when rain started to fall and was removed immediately after filling or at the end of the event.BC rain/snow was measured using the thermal-optical method described by Castro et al. (1999).Weekly air samples corresponding to the precipitation period were taken and BC air was determined by thermal-optical method with the NIOSH protocol (Pio et al., 2007).2).At Changbai, snow samples were collected once per week during three winters in 2009-2012 (Z.W. Wang et al., 2014).BC snow was measured using the thermal-optical method with IMPROVE protocol and BC air was determined using a particle soot absorption photometer (PSAP).At LAVO, seven precipitation samples were collected in March 2006 using an automated rain sampler EcoTech with up to 95 % capture efficiency (Hadley et al., 2010).BC rain was measured by a modified version of thermo-optical analysis described in detail in Hadley et al. (2008).BC air was measured by seven-wavelength Aethalometer with an overall uncertainty of about ±30 %.
At Abisko, snow samples were taken in March and April in 1984 (Noone and Clark, 1988).Snow samples were taken using a plastic spatula to scrape fresh snow into polyethylene jars and then transported back to the laboratory.The snow was transferred to a filtration apparatus, where it was melted and filtered.The amount of BC on the filters was determined by optical analysis.The air samples were measured using the integrating sandwich technique.At Zeppelin, BC snow and BC air were measured concurrently in April and May 2007.BC snow was concentrated by Nuclepore filters and then determined using a multiwavelength spectrophotometer.
Aerosol absorption is measured by PSAP and BC air is computed using a mass absorption cross section of 11 m 2 g −1 at 550 nm (Hegg et al., 2011).
3 Model description and simulations

Model description
GEOS-Chem is a 3-D global chemical transport model driven with assimilated meteorology from the Goddard Earth Observing System (GEOS) of the NASA Global Modeling and Assimilation Office (GMAO).The GEOS-5 reanalysis meteorological dataset is used to drive model simulations at 2 • latitude × 2.5 • longitude horizontal resolution with 47 vertical layers.BC aerosols are emitted by incomplete combustion of fossil fuel, biofuel and biomass.Global anthropogenic emissions from Bond et al. (2007) are used with Asian emissions from Zhang et al. (2009).Previously missed gas flaring emissions are also included in this study (Stohl et al., 2013; the flaring emission inventory is available at http://eclipse.nilu.no/).Biomass burning emissions are from GFED3 emission inventory, with a small fire contribution included (Randerson et al., 2012).About 80 % of the freshly emitted BC aerosols are assumed to be hydrophobic (Park et al., 2003) and are converted to hydrophilic with an e-folding time of 1.15 days, which yields a good simulation of BC export efficiency in continental outflow (Park et al., 2005).Dry deposition of BC is computed using a resistance-inseries method over all surface types (Wesely, 1989;Zhang et al., 2001).Due to the lack of land surface module in GEOS-Chem, we approximate BC snow using BC deposition flux and snow precipitation rate, following He et al. (2014a).More details are provided in Qi et al. (2017).

Wet scavenging
Aerosol wet deposition in GEOS-Chem was first described by Liu et al. (2001).It includes in-cloud and below-cloud scavenging in large-scale and convective precipitation.Incloud scavenging rate is parameterized following Giorgi and Chameides (1986), where φ is in-cloud scavenging rate, λ the removal frequency determined by precipitation forming rate, and [BC] condensed BC mass mixing ratio in condensed phase, including cloud water drops and ice crystals.
[BC] condensed is estimated as where [BC] total is BC mass mixing ratio in clouds, including BC in interstitial air and in condensed phase, and r scav.the BC scavenging efficiency.In GEOS-Chem, it is assumed that hydrophilic BC particles are 100 % incorporated in condensed phases, while hydrophobic BC particles remain in interstitial air in warm liquid clouds (Wang et al., 2011).r scav. is thus the fraction of hydrophilic to total BC, which is determined by the initial fraction when aerosols are emitted and the following aging process during transport.In ice clouds, hydrophobic BC can serve as ice nuclei (Andreae and Rosenfeld, 2008), and the resulting r scav. is the fraction of hydrophobic BC to total BC.In convective mixed-phase clouds, rapid updrafts bring water vapor to the middle and upper parts of the clouds and the resulting environmental vapor pressure is usually above the saturation vapor pressure of water.In this condition, both water and ice grow and the WBF process is suppressed (Liu et al., 2011).We assume no WBF effect in convective mixed-phase clouds.In large-scale mixed-phase clouds, cloud microphysics, which determines the rates of riming versus WBF, play a very important role in determining BC scavenging efficiency.If the riming rate is much larger than WBF rate (riming-dominated), most snow particles are formed from riming and show rimed structures.BC particles in water drops are removed efficiently from the atmosphere.In contrast, if the rate of WBF is much larger than riming rate (WBF-dominated), most snow particles are formed from WBF and show pure crystal structure.BC particles in cold water drops are released back into the interstitial air and their removal is strongly slowed down.In the control experiment, riming-only (default configuration of GEOS-Chem), it is assumed that all snow particles are formed by riming process in mixed-phase clouds, and r scav. is treated the same as that in warm liquid clouds, which is determined solely by the hygroscopicity of BC (Table 4).In experiments WBF T and WBF IMF , we distinguish riming-versus WBF-dominated conditions and parameterize r scav.under these two conditions.Following Fukuta and Takahashi (1999), we assume riming dominates the in-cloud scavenging in large-scale mixed-phase clouds when temperature is between 261 and 265 K and LWC > 1.0 g m −3 because the terminal velocity of snow particles was largest at 263 K and large LWC provided more water drops for the falling snow particles to collect along their pathways based on lab experiments.In this condition, hydrophilic BC particles in water drops are brought to the surface by the rimed snow particles and removed from the atmosphere, so the scavenging efficiency is simply the fraction of hydrophilic to total BC.We assume that WBF dominates under other conditions (258-261 and 265-273 K) in large-scale mixed-phase clouds and r scav.follows observations from Cozic et al. (2007).In experiment WBF T , r scav. is exponentially related to temperature (Table 4, Cozic et al. 2007).
Although the above two parameterizations of the WBF effect include the determining factors of WBF rate, other variables that strongly affect the local WBF rate are missing, such as local updraft velocity, local vapor pressure, and distribution of cold water drops and ice crystals in mixed-phase clouds.
In a follow-up study, we couple a cloud-resolving model with detailed cloud microphysics to GEOS-Chem to estimate the rate of WBF and riming and to further investigate their roles in determining global BC distribution.

Results and discussions
The primary goal of this study is to assess the impact of WBF on global BC distribution.In this section, we compare BC distribution from GEOS-Chem with and without WBF (Sect.3.2).The differences can then be attributed to the WBF effect.We present the comparison of BC scavenging efficiency in Sect.4.1.In Sect.4.2, we show how WBF affects BC air .Following this, we present the comparison of BC wet deposition fluxes (Sect.4.3) and BC snow (Sect. 4.4).Finally, we show the effect of WBF on the BC washout ratio.1).At Jungfraujoch, WBF reduces BC scavenging efficiency both in summer (July-August, from 0.90 to 0.48-0.59)and in late winter and early spring (February-March, from 0.29 to 0.10-0.11)and significantly reduces model-observation discrepancies (50 to −20-0 % in summer and from a factor of 3 to 10 % in late winter and early spring).At Puy de Dôme, WBF brings the simulated BC scavenging efficiency (0.48 for WBF IMF and 0.63 for WBF T ) within the uncertainty range of observations (0.43 ± 0.17).However, at sites where riming dominates in-cloud scavenging in mixed-phase clouds, for instance Zeppelin (Hegg et al., 2011), accounting for WBF leads to scavenging efficiencies considerably lower than observations (Table 1).Rimingonly reproduces the observed high scavenging efficiencies (0.81 in summer and 0.77 in winter) at Zeppelin to within 50 %.Similarly, at Mt. Sonnblick, an elevated site (3.10 km), the simulated scavenging efficiency with riming-only (0.67) agrees with the observed values (0.74 ± 0.19) within 10 % in April and May.WBF strongly reduces BC scavenging efficiency (0.09-0.26) at the site.
At lower altitudes, where temperature is higher and mixedphase clouds are less frequent, WBF has a relatively weak effect, for example, at the Po Valley and Great Dun Fell (Table 1).At the Po Valley, the measurements were in fog.We use BC scavenging efficiency of the lowest clouds in GEOS-Chem for comparison.All three model results -riming-only, WBF T , and WBF IMF -agree with the observations (0.39) to within 20-60 %.At Great Dun Fell, WBF reduces BC scavenging efficiency by less than 25 %.
To sum up, differentiating riming-versus WBF-dominated in-cloud scavenging in mixed-phase clouds improves the comparison at sites where WBF dominates but degrades the comparison at sites where riming dominates.We attribute the discrepancy to several reasons.First, WBF is parameterized based on observations at a single site (Sect.3.2); extrapolating it to global scale may introduce large uncertainties.Second, LWC, a key parameter that separates the two conditions (Sect.3.2), is biased high and associated with large spatial discrepancies in GEOS-5 reanalysis (Li et al., 2012;Barahona et al., 2014).Third, this separation is based on a lab experiment (Fukuta nd Takahashi, 1999), while conditions in the real atmosphere are certainly more complex.This calls for more extensive measurements of BC scavenging efficiency in mixed-phase clouds to better understand the scavenging processes.
In addition to the uncertainties in differentiating rimingversus WBF-dominated in-cloud scavenging in mixed-phase clouds, uncertainties associated with other processes that determine the hygroscopicity, size and composition of BC particles also affect scavenging efficiency.Aged BC particles (e.g., coated by hydrophilic species) with higher hygroscopicity and larger size are more likely to be activated and serve as CCN (Wyslouzil et al., 1994;Weingartner et al., 1997;R. Zhang et al., 2008), and the scavenging efficiency is considerably higher than freshly emitted BC particles.Sellegri et al. (2003) reported scavenging efficiencies of 0.39 ± 0.16 for BC aerosols with diameters less than 0.3 µm and hydrophilic material fractions less than 38 %.The scavenging efficiency increased to 0.97 ± 0.02 for particles with a diameter larger than 0.3 µm and the fraction of hydrophilic material at 57 % or higher.In this study, we assume 80 % of freshly emitted BC particles are hydrophobic and externally mixed with co-emitted hydrophilic particles (Cooke et al., 1999).However, field observations show that the fraction systematically differs among urban plumes (∼ 10 %) and biomass burning plumes (∼ 70 %) (Schwarz et al., 2008).The simple assumption of 80 % hydrophobic BC for all sources thus carries uncertainties for BC scavenging efficiency.Moreover, we assume hydrophobic BC particles are converted to hydrophilic with an e-folding time of 1.15 days (Park et al., 2005).However, the conversion is much faster (a few hours) in source regions where the concentration of hydrophilic materials is high, while the conversion is much slower in remote regions (a few days) (He et al., 2016).Therefore, the uniform conversion rate used in this study might underestimate the scavenging efficiency near source regions.In addition, faster conversion from hydrophobic to hydrophilic near sources might cause more hydrophilic BC particles to be scavenged near sources and thus alter the scavenging efficiency at remote regions.In addition, we assume all hydrophobic particles serve as ice nuclei.This simplification might also involve uncertainties in BC scavenging efficiency.First, current field observations and lab experiments show contradictory result for the ice nucleation ability of BC particles (Murray et al., 2012).Kamphus et al. (2010) found that soot particles were not enhanced in the ice phase compared to the background aerosol, while Cozic et al. (2008) found that the black carbon mass fraction was enhanced from 5 % in the background to 27 % in ice residues.Gorbunov et al. (2001) found that hydrophilic soot was 3-4 orders of magnitude more efficient at producing ice, while other studies (e.g., Andreae and Rosenfeld, 2008, and references therein) found that the ability of heterogeneous ice formation of pure hydrophobic soot particles is reduced by the presence of organic materials or sulfuric acid.Second, ice nucleation on soot particles is complex because soot particles from different combustion sources have different ice nucleating abilities (Murray et al., 2012, and references therein).

Seasonal variations of BC scavenging efficiency
Figure 2 shows model-simulated monthly mean BC scavenging efficiencies in the Arctic, the northern mid-latitudes, and the tropics at 0-2, 2-5, and 5−10 km altitudes.The values are averaged for 2007-2009.BC scavenging efficiencies in the Arctic show strong seasonal cycle below 5 km.If only the riming process in mixed-phase clouds is considered (experiment riming-only), BC scavenging efficiency is determined exclusively by its hygroscopicity (Wang et al., 2011).We find that more than 90 % of BC particles in the Arctic are hydrophilic.In warm and mixed-phase clouds, hydrophilic BC particles serve as CCN and are incorporated in cloud water drops, while hydrophobic BC particles remain in the atmosphere (Wang et al., 2011).Figure 2 shows that in the middle and lower troposphere (< 5 km), where most clouds are warm and mixed-phase in summer, BC scavenging efficiency is approximately the ratio of hydrophilic to total BC (0.80-0.90).In ice clouds, hydrophobic BC particles serve as ice nuclei and are removed with the falling snowflakes, while scavenging of hydrophilic BC particles is suppressed completely (Wang et al., 2011).Consequently, when ice clouds dominate in most of the wintertime, BC scavenging efficiency is around the ratio of hydrophobic to total BC (∼ 0.10).WBF reduces BC scavenging efficiency by 22-69 % in summer and by 63-85 % in winter.In the upper troposphere (>5 km), where ice clouds dominate year-round, BC scavenging efficiency likewise is around the ratio of hydrophobic to total BC (∼ 0.1) and shows little to no seasonal variation.
In the northern mid-latitudes, the seasonal cycle of BC scavenging efficiency is weaker than that in the Arctic -the value in winter is much higher (0.4-0.6) in the mid-latitudes as a result of higher temperature and lower frequency of pure ice clouds (Zhang et al., 2010).WBF reduces BC scavenging efficiency by 17-44 % in winter in the troposphere.The effect is relatively weaker than that in the Arctic (63-85 % reduction).In addition, the WBF effect increases with increasing altitude (from 0 at the surface to 39-50 % in the upper troposphere), different from that in the Arctic.
In the tropics, the seasonal cycle of BC scavenging efficiency disappears in the lower troposphere in all three model experiments, for two reasons.First, temperature is high throughout the year and clouds are mostly warm clouds.Second, most of the tropical clouds are convective where strong updrafts suppress WBF by bringing abundant water vapor to the clouds (Liu et al., 2011).However, in the tropical upper troposphere, WBF reduces BC scavenging efficiency by 33-47 % because the frequency of mixed-phase clouds is higher than that in the middle and lower troposphere.

BC concentration in air
GEOS-Chem captures the probability density function (PDF) of annual BC air at sites from IMPROVE and EMEP and in China and the Arctic (Sect.2.2) but overestimates the frequency of low BC air (experiment riming-only) (Fig. 3a).WBF releases BC in cloud water droplets back to the interstitial air and thus reduces BC scavenging efficiency and leaves more BC particles in the atmosphere (Sect.4.1).As Observations Riming-only WBFT WBFIMF such, including the WBF effect increases BC air and improves the agreement with observations compared with the control experiment, riming-only, particularly for the low values (Fig. 3a).WBF reduces the fraction of simulated BC air that is underestimated by more than a factor of 2 (from 47 to 28-35 %) (Fig. 3b).We use a ratio r to quantify the effect of WBF on BC air , where r is a fraction that describes the simulated changes in BC air with WBF parameterizations relative to that with riming-only, and [BC] WBF and [BC] riming-only are simulated BC air with and without WBF at the measurement stations (Sect.2.2).The fraction r is much larger in the Arctic (62-140 %) than in the northern mid-latitudes (0-40 %) (Fig. 4a) for several reasons.First, the frequency of mixed-phase clouds is higher in the Arctic (41-90 % from spring to fall) than in the mid-latitudes (∼ 20 %) (Pinto 1998;Shupe et al., 2006;Zhang et al., 2010;Morrison et al., 2012).Second, lower temperature and higher IMF in the Arctic result in a stronger WBF effect.Third, WBF increases BC air in the mid-latitudes and consequently the poleward transport of BC.In addition, WBF increases BC air substantially in winter and spring and hence delays the transition of high BC air in winter to low BC air in summer (Qi et al., 2017).We find that r increases with increasing altitude from surface (6-12 %) to ∼ 4 km (45-95 %) (Fig. 4b).This is because as altitude increases, temperature decreases and IMF increases, resulting in a stronger WBF effect and thus larger reductions of BC scavenging efficiency in the mid-latitudes (Fig. 2).As a result, less BC is scavenged and more BC particles remain in the atmosphere.Figure 5 shows IMPROVE and GEOS-Chem-simulated monthly mean BC air .In summer, the model underestimates BC air by 46-72 %.WBF increases BC air and reduces the discrepancy to 35-58 % (by 5-55 %) from the surface to ∼ 4 km.The relative change in BC air increases from surface (6-22 %) to above 3 km (21-78 %).The largest discrepancy (54-58 %) is at 1.5-3 km, where the influence of fire emissions is significantly underestimated (Mao et al., 2011(Mao et al., , 2014)).BC air is strongly underestimated in winter as well and the discrepancy increases monotonically with increasing altitude from ∼ 10 % at the surface to ∼ 70 % above 2.5 km in winter.WBF increases BC air monotonically from 5 % at the surface to 80-156 % above 2.5 km, reducing the discrepancy to within 30 %, particularly at higher altitudes.Above 2.5 km, the discrepancy of BC air decreases from 67-70 to 15-20 %.Cloud observations show not much riming or graupel snow particles and simulations over Montana and Nebraska in October-November suggest that rate of WBF is significantly larger than that of riming (Smith et al., 2009;Niu et al., 2008).WBF has little effect on BC air at sites in the lower troposphere in East Asia and Europe, where temperature is high and mixed-phase clouds rarely occur.

BC wet deposition fluxes
Table 3 shows observed and GEOS-Chem-simulated annual BC wet deposition fluxes.GEOS-Chem captures the high deposition flux at Cape Hedo in the East China Sea (52.5 mg m −2 yr −1 ) and the low deposition flux (5.0 mg m −2 yr −1 ) at the Azores (within 40 %).Cape Hedo receives outflow of East Asia (Mori et al., 2014), while the Azores is mainly affected by clean marine air (Cerqueira et al., 2010).Wet deposition fluxes at Schauinsland and Sonnblick are underestimated by ∼ 50 %.One possible reason is the underestimated precipitation at the two sites.In contrast, at K-puszta and Sakaerat, BC wet deposition fluxes are overestimated by a factor of 2-5.At K-puszta, BC in precipitation is overestimated, while BC air is underestimated (Sect.4.4), indicating that wet scavenging is too strong during transit to the site.At Sakaerat, wet deposition is overestimated by a factor of 5. WBF has opposite effects on BC wet deposition fluxes near source regions over land and in remote regions over ocean.Over land, WBF reduces annual wet deposition fluxes by ∼ 15 % at Schauinsland, Sonnblick and K-puszta.This is because of reduced BC scavenging efficiency (5-45 %).The largest effect of WBF is at Changbai, where WBF reduces BC wet deposition flux (November-April) by 45-66 % (from 53.8 to 18.1-29.7 mg m −2 ), reducing the discrepancy from +84 to −40-0 %.In contrast, WBF increases wet deposition fluxes at oceanic sites Cape Hedo and the Azores and costal site Aveiro by 8-50 %, even with a lower local scavenging efficiency (7-20 % reduction at the oceanic sites).We find that the increase in wet deposition fluxes is mainly from enhanced outflow from polluted land regions as a result of WBF.In the tropics, WBF has a minimal effect on wet deposition flux (< 1 %), for example at Sakaerat, because temperature at the site is above freezing throughout the year and mixed-phase clouds are very rare.

BC concentration in snow
Figure 6a presents the PDF of observed and GEOS-Chemsimulated BC snow in the Northern Hemisphere (Sect.2.3).Observed BC snow shows a lognormal distribution and varies by 3 orders of magnitude from a minimum of 1.8 ng g −1 in the Arctic to a maximum of 4758 ng g −1 in northern China.The model (experiment riming-only) underestimates the frequency of BC snow at 8-80 ng g −1 , while it overestimates the frequency outside the range.More importantly, the observations have a single maximum but the model shows a bimodal structure.WBF significantly improves the agreement between observed and simulated distribution by increasing the frequency of BC snow at 8-80 ng g −1 , resulting in a single maximum.WBF decreases median BC snow by ∼ 15 % (from 25.7 to 22.4-22.7 ng g −1 ) and improves the comparison with observations (median: 19.1 ng g −1 ).
Figure 6b shows observed and simulated medians of BC snow in the nine subregions as defined in Sect.2.3.Overall, GEOS-Chem captures the spatial distribution of BC snow from lowest in the Arctic to highest in the Northeast Industrial region in northern China but overestimates BC snow in the mid-latitudes (by up to a factor of 3) and underestimates   a The minimum and maximum deposition fluxes.b The deposition flux difference (WBF -riming-only) relative to that from the riming-only simulation.
BC snow in the Arctic (by 27 %).WBF reduces BC snow by 16-33 % in the mid-latitudes (discrepancy reduced to within a factor of 2), while it increases BC snow by ∼ 30 % in the Arctic (discrepancy reduced to within 15 %).The improvements are due to the redistribution of BC deposition as a result of WBF.WBF reduces BC deposition fluxes (by 12-34 %) in North America, northern China, and Xinjiang, China, while it increases the flux in remote Arctic by (7-21 %) (Table 5).
In the mid-latitudes, WBF reduces BC wet deposition fluxes (by 37-63 %), while it increases dry deposition fluxes (by %).This is because BC air in the boundary layer is increased with the WBF effect (Sect.4.2).The higher dry deposition flux partly offsets the lower wet deposition, resulting in a reduction of 12-34 % in the total BC deposition flux.In the Arctic, BC wet deposition flux decreases by 21-29 %, while dry deposition flux increases substantially by 81-159 %, much larger than that in the mid-latitude regions.As a result, the total deposition flux in the Arctic increases by ∼ 20 %.
Even with the WBF effect, BC snow is still overestimated across much of the mid-latitudes.This indicates that BC scavenging over East Asia and North America is likely overestimated in the model during snow season.The exception is in Inner Mongolia and the Northern Industrial region in China.In Inner Mongolia, snow samples were mixed with local soil and the measurements of BC snow were associated with very large uncertainties (Wang et al., 2013).In addition, most of the snow samples in this region were taken from thick drifted snow layers; therefore, BC snow does not correspond to BC deposition.In the Northern Industrial region (median: 856 ng g −1 , significantly larger than the global median of 19 ng g −1 ), BC deposition is strongly affected by emissions from local sources and dry deposition flux.At Changbai, for instance, WBF significantly improves the simulation of wet deposition flux (discrepancy lowered from +80 to −40-0 %, Table 3).However, dry deposition flux at the site is underestimated by a factor of 5. Thus, the underestimate of BC snow (by 34 %) in the region is likely because of the excessively low BC dry deposition.Hegg et al. (2011) reported that now particles mostly showed rimed structures at Zeppelin, resulting in high washout ratios (∼ 770, Table 2).Model-simulated washout ratio with riming-only (experiment riming-only) is in agreement with observations to within a factor of 2 at Zeppelin.When snow particles are pristine crystal formed mainly from WBF, for example, at Abisko (Noone and Clark, 1988), the observed washout ratios tend to be significantly lower (94 at Abisko and 145 at Changbai, Table 2).Modeled WBF reduces the washout ratio by a factor of 5 (from 482 to 96) and significantly lowers the discrepancy (from a factor of 4 to 2 %) at Abisko.WBF also drastically reduces the discrepancies at LAVO (from factors of 3-5 to 2). Figure 7 shows observed and GEOS-Chem-simulated monthly mean BC washout ratios, BC rain/snow and BC air at four mountainous sites in Europe and at Cape Hedo.We use only simulations when daily mean precipitation is above the monthly median to compute monthly means, because samples of BC in rain/snow were collected during major rain/snow events (Cerqueira et al., 2010).At Sonnblick (3.1 km), a site that is constantly in the free troposphere, washout ratios are overestimated by orders of magnitude.This is because BC rain/snow is overestimated, while BC air is underestimated.WBF significantly reduces the discrepancy of washout ratios, particularly in winter (discrepancy lowered from factors of 4-16 to less that 4).The improve-ments are because WBF reduces BC rain/snow (discrepancy reduced from a factor of 7 to a factor of 4) and increases BC air (discrepancy decreases from −77 to −51 %).Remarkable improvement of washout ratio simulation is also seen at Schauinsland (1.2 km).WBF lowers the discrepancy of washout ratio in winter and spring from a factor of 2 to ∼ 20 %.However, this improvement is because of decreased BC in snow, which degrades the comparison with observations.WBF does not affect washout ratios at the three sealevel sites Aveiro (0.47 km), K-puszta (0.19 km), and Cape Hedo (0.06 km).That is because cloud processes have a rather limited effect on BC at the surface (Sect.4.2).Even with the WBF effect, BC washout ratios are still largely overestimated, because BC air is underestimated and BC rain/snow is overestimated, particularly in summer.These overestimates suggest that wet deposition is likely too strong over Europe.5 Global BC budget

Washout ratio of BC
Compared to AERONET observations of BC AAOD mainly over land, AeroCom models (I and II) underestimate BC loading by 60-160 % (in South and Southeast Asia it is a factor of 3 and 4) (Bond et al., 2013).Bond et al. (2013) attributed the low bias to insufficient BC emissions.They then scaled BC emissions up according to the discrepancy of modeled versus observed BC AAOD and obtained a total global BC emission of 17 Tg yr −1 , twice the median value used in the AeroCom models.They reported BC loading of ∼ 0.50 mg m −2 after scaling (Table 6).Our results suggest that the discrepancy can be partially explained by WBF not being accounted for in the AeroCom models.WBF increases global BC loading by 0.07-0.13mg m −2 (by 32-60 %), depending on the WBF parameterizations used (based upon either temperature or IMF) (Table 6).Such increases are comparable to the median global BC loading from the Ae-roCom II models (Myhre et al., 2013).With WBF, our results show global BC loadings of 0.29-0.35mg m −2 , which is in remarkable agreement with the AERONET-based estimates (with scaled-up BC AAOD) as reported by Bond et al. (2013).However, we find that, even with WBF, model results still have large biases over land, with BC air biased low (Figs. 3  and 5), BC snow biased high (Fig. 6), and washout ratios too large (Fig. 7).These remaining discrepancies likely point toward excessive wet scavenging over land in the model.In North America, for instance, model-simulated BC snow is too high by ∼ 50 % (Fig. 6) and BC air in winter (IM-PROVE, Fig. 5) is low by up to ∼ 30 %.Additionally, model-simulated washout ratio at LAVO, California, is twice the observed value.In Europe, model-simulated washout ratios, particularly in summer, are excessively high, a result of overly high BC rain/snow and too low BC air predicted by the model (Fig. 7).
In contrast, compared to HIPPO over the remote Pacific, AeroCom models overestimate BC air by a factor of 2 to 5 (Schwarz et al., 2010).To narrow the gap between model results and HIPPO observations, previous studies resorted to either enhancing wet scavenging or accelerating BC aging near source regions.For example, Q. Wang et al. (2014) included scavenging of hydrophobic BC in convective updrafts and hydrophilic BC in cold clouds (< 258 K) by homogeneous freezing of solution droplets, neither of which was accounted for previously (Q.Wang et al., 2014).X. Wang et al. (2014) and He et al. (2016) used faster BC aging schemes, which led to stronger wet scavenging close to source regions and consequently weaker outflow from these regions.The BC loadings were estimated to be 0.08 mg m −2 (Q.Wang et al., 2014), 0.16 mg m −2 (X.Wang et al., 2014) and 0.25 mg m −2 (He et al., 2016), much lower than those constrained from AERONET measurements (∼ 0.50 mg m −2 ; Bond et al., 2013).
However, even with a faster aging scheme and stronger wet deposition, simulated BC air is still biased high by a factor of 2-3 relative to HIPPO observations over the remote Pacific.The remaining high bias is likely a result of either excessive Asian outflow of BC or insufficient scavenging of BC over the Pacific.At Cape Hedo in the East China Sea (directly downwind of major sources in eastern China), modelsimulated BC rain is an order of magnitude too high, while BC air is 50 % too large in October-January (Fig. 7).This overestimate of wintertime outflow of BC from the region is likely the reason for the overestimate of BC air over the Pacific in winter.Outside of winter, simulated BC air and BC rain at the site both agree with observations (within 50 %, Fig. 7).This suggests that the overestimate of BC air over the Pacific is likely the result of insufficient removal over the Pacific.
WBF results in more BC particles in the upper troposphere (Table 6).As a result, there is a significantly higher fraction of BC loading above 5 km altitude (from 21 to 25-29 %).This larger fraction, as expected, enhances the top-ofthe-atmosphere absorption forcing efficiencies (forcing per aerosol absorption optical depth; Bond et al., 2013) because of larger solar fluxes at higher altitudes (Bond et al., 2013;Samset and Myhre, 2011).The aforementioned fraction (25-29 %) falls in the range of AeroCom I model results (Schulz et al., 2006) but is 3 times higher than those constrained by HIPPO observations (9-12 %) (Q.Wang et al., 2014;X. Wang et al., 2014).Moreover, WBF increases BC lifetime from 5.7 to 6.9-8.0 days, an increase of up to 40 %.These longer lifetimes fall within the range of the AeroCom I model results (4.9-11.4days) but at the higher end (Schulz et al., 2006).However, these lifetimes are nearly twice as long as those constrained by HIPPO observations (Q.Wang et al., 2014;X. Wang et al., 2014).
The temperature threshold for mixed-phase clouds and ice clouds is very uncertain and controlled by processes such as the shattering of isolated drops during freezing and the production of ice splinters during riming (Gayet et al., 2009;Browse et al., 2012), which are not explicitly accounted for in GEOS-Chem.To examine the sensitivity of BC distribution to various threshold temperatures, we conduct additional simulations.In the standard simulation, clouds are assumed to be mixed-phase at 258-273 K.In the sensitivity studies, we vary the threshold between 268 and 248 K.The results are summarized in Table 6.The resulting BC deposition, loading, and lifetime are within 15 % of the standard simulation.This suggests that our results are rather insensitive to the threshold temperature.depend on local variables, such as local updraft velocity, local vapor pressure, distribution of cold water drops and ice crystals in mixed-phase clouds and so on.Coupling a cloudresolving model with detailed cloud microphysics is necessary to better estimate the rate of WBF and riming and to better identify their roles in global BC distribution.

Figure 6 .
Figure6.(a) Probability density function of observed (solid red line) and GEOS-Chem-simulated (dotted: riming-only; dashed: WBF T ; solid black: WBF IMF ) BC in snow (ng g −1 ) and (b) medians of observed and simulated BC in snow (ng g −1 ) in the Arctic, North America (Canada, the Great Plains, the Pacific Northwest, and the Rockies, as defined byDoherty et al., 2014)), northern China (Inner Mongolia, Northeast Border and Northeast Industrial, as defined byWang et al., 2013), and Xinjiang, China.The regions are symbol-coded and the simulations are color-coded (see text for details).Solid line -1 : 1 ratio line; dashed lines -1 : 2 (or 2 : 1) ratio lines.

Figure 7 .
Figure 7. Observed and simulated BC washout ratio, BC concentration in surface air and in snow at Cape Hedo in the East China Sea, Aveiro and K-puszta (rural sites), and Schauinsland and Sonnblick (elevated sites).

Table 1 .
Observed and GEOS-Chem-simulated scavenging efficiency of BC (fraction of BC incorporated into cloud droplets and ice crystals).Simulation with riming only in-cloud scavenging of BC in mixed-phase clouds.See text for details.b Simulation with in-cloud scavenging of BC by WBF, parameterized by temperature, in mixed-phase clouds.See text for details.c Simulation with in-cloud scavenging of BC by WBF, parameterized by ice mass fraction, in mixed-phase clouds.See text for details.
a d Observations in urban fog.

Table 2 .
Observed and GEOS-Chem-simulated BC concentration in snow and rain (µg L −1 ), BC concentration in surface air (µg m −3 ) and the corresponding washout ratio.
a Simulation with riming only in-cloud scavenging of BC in mixed-phase clouds.See text for details.b Simulation with in-cloud scavenging of BC by WBF, parameterized by temperature, in mixed-phase clouds.See text for details.c Simulation with in-cloud scavenging of BC by WBF, parameterized by ice mass fraction, in mixed-phase clouds.See text for details.

Table 4 .
GEOS-Chem simulations of global BC distribution.ExperimentsBC scavenging efficiency in large-scale mixed-phase clouds Riming-only (control) Same as that in warm clouds, r scav.=

Table 6 .
Global annual budget of BC.Ranges are given in parentheses.