Optical properties of clouds containing black carbon (BC) particles in their water droplets are calculated by using the Maxwell Garnett mixing rule and Mie theory. The obtained cloud optical properties were then applied to an interactive system by coupling an aerosol model with a General Circulation Model. This system is used to investigate the radiative forcing and the equilibrium climate response due to BC in cloud droplets. The simulated global annual mean radiative forcing at the top of the atmosphere due to the BC in cloud droplets is found to be 0.086 W m−2. Positive radiative forcing can be seen in Africa, South America, East and South Asia, and West Europe, with a maximum value of 1.5 W m−2 being observed in these regions. The enhanced cloud absorption is shown to increase the global annual mean values of solar heating rate, water vapor, and temperature, but to decrease the global annual mean cloud fraction. Finally, the global annual mean surface temperature is shown to increase by +0.08 K. The local maximum changes are found to be as low as −1.5 K and as high as +0.6 K. We show there has been a significant difference in surface temperature change in the Southern and Northern Hemisphere (+0.19 K and −0.04 K, respectively). Our results show that this interhemispheric asymmetry in surface temperature change could cause a corresponding change in atmospheric dynamics and precipitation. It is also found that the northern trade winds are enhanced in the Intertropical Convergence Zone (ITCZ). This results in northerly surface wind anomalies which cross the equator to converge with the enhanced southern trade winds in the tropics of Southern Hemisphere. This is shown to lead to an increase (a decrease) of vertical ascending motion and precipitation on the south (north) side of the equator, which could induce a southward shift in the tropical rainfall maximum related to the ITCZ.
 Clouds, which cover about 60% of the Earth's surface, play a significant role in the radiation budget of the earth-atmosphere system. Clouds reflect solar radiation back into space and reduce the radiative flux to the surface. They also absorb the infrared radiation emitted from surface of the Earth and reduce the loss of energy in the earth-atmosphere system [Forster et al., 2007]. Therefore, any change of cloud optical properties can disturb the energy balance of the earth-atmosphere system.
 Black carbon (BC) is an important anthropogenic aerosol produced from the incomplete combustion of hydrocarbon-containing materials. Since pre-industrial time, the BC loading in the atmosphere has grown considerably. This reflects the increasing usage of fossil fuels and biofuels, coupled with the increasing world population [Bond et al., 2007; Lu et al., 2010]. BC aerosol comprises a small portion of atmospheric aerosols (typically less than 15% of the total aerosol mass). However, the impact of BC aerosol on the climate is substantial. BC is a strong absorber of solar radiation. This can enhance the absorption of solar energy in the earth-atmosphere system and increase the atmospheric temperature directly. This effect has been considered as a potential source of global warming [Jacobson, 2002; Menon et al., 2002; Chung and Seinfeld, 2005; Ramanathan and Carmichael, 2008; Shindell et al., 2012]. When BC is mixed with sulfate and other water-soluble aerosols, it can act as the condensation nuclei for a water cloud. BC can even act as ice nuclei. Thus, BC can change cloud albedo and lifetime and so indirectly affect the climate system [Hansen et al., 2005; Lohmann and Feichter, 2005; Zhang and Wang, 2011]. BC aerosol affects clouds in two major ways. First, the embedding of BC in cloud droplets can affect the cloud optical properties. In particular, BC can reduce the cloud droplet single scattering albedo (SSA) due to its strong absorbing ability. This can increase the absorption of solar radiation, and this extra heating in clouds can exacerbate cloud evaporation. Thus, the atmospheric heating rate profile is affected [Chuang et al., 2002; Jacobson, 2006; Zhuang et al., 2010; Ghan et al., 2012; Li et al., 2013]. Second, BC particles interstitially existing between cloud droplets can also enhance the absorption compared to BC existing in clear sky. This is due to the fact that relative humidity is higher inside a cloud [Jacobson, 2012]. Both effects increase the cloud absorption and so have impact on cloud burn-off and climate.
 BC aerosols are mostly hydrophobic when emitted, but they gradually become hygroscopic over time due to chemical and physical processes in the atmosphere. The hydrophilic BC particles can act as effective cloud condensation nuclei [Cooke et al., 2002; Roberts and Jones, 2004], which results in the mixing of BC in cloud droplets. As far back as 1984, Chýlek et al.  investigated the effect of BC on the absorption of solar radiation by clouds by assuming the water droplet containing the arbitrarily distributed spherical BC particles. BC aerosol has drawn more attention in recent years, but there has been little research on the climate impact of BC in cloud droplets. Chuang et al.  developed a scheme to calculate the cloud droplet SSA of BC in cloud droplets. They were the first to take into account the impact of the extra BC absorption in the climate model of CCM1/NCAR. Their results showed that the effect of BC in cloud droplets could reduce the reflection of solar radiation and causes an increase of radiative forcing at the top of the atmosphere (TOA). Zhuang et al.  investigated the impact on regional cloud radiative forcing and climate by BC in cloud droplets, using a regional climate model based on the method of Chuang et al. . Their results also indicated that BC in cloud droplets could cause a positive radiative forcing at TOA. They also found that the extra heating from BC in cloud droplets could affect atmospheric circulation and hydrologic cycle. The above two works, however, used only an empirical formula to calculate the cloud droplet SSA for BC in cloud droplets.
Li et al.  pointed out that the method to calculate SSA by Chuang et al.  was deficient in several aspects. Specifically, it was suggested the cloud effective radius should be used instead of cloud droplet size since the cloud effective radius is used in cloud optical property parameterizations to represent cloud drop size distribution. Second, the cloud optical properties should be calculated exactly by Mie theory instead of an empirical formula. Third, all cloud optical properties rather than just the SSA should be taken into account to avoid the inconsistency with the cloud optical property variables used in climate models.
 Thus, further investigation is needed, based on using an accurate method for calculation of cloud optical properties, to evaluate the impact on radiative forcing and climate response, due to BC in cloud droplets. This paper mainly addresses these issues.
 In this study, we first calculate the cloud droplet refractive index by the Maxwell-Garnett (MG) mixing rule [Chýlek et al., 1988, 1996]. Then the cloud optical properties are obtained based on the Mie theory and cloud droplet size distribution. The refractive index obtained by the MG mixing rule is derived from an effective-medium approximation that gives an average complex refractive index based on the volume fractions and complex refractive indices of both the medium and the absorbing substance within it.
 The refractive index of cloud droplets can be calculated in a more sophisticated way by using the dynamic effective medium approximation (DEMA) [Stroud and Pan, 1978; Chýlek et al., 1988; Jacobson, 2006]. This method takes into account the polydispersion of spherical absorbing inclusions within the medium. DEMA gives different efficiencies for the same volume fraction but different size distributions of absorbing material. For a fixed water droplet size, Jacobson  showed that the absorption efficiency could be slightly higher by DEMA compared to that of MG. However, the relationship between aerosol size distribution and cloud droplet size distribution is difficult to determine, as both are assumed to have long tails in their size distributions. A question arises as to how to treat the aerosol size distribution inside a very small cloud droplet. Is the aerosol size distribution in different sizes of cloud droplets the same? The method of DEMA could be more accurate when we have better observational evidence to understand the size distributions of aerosols inside cloud droplets.
 This model, like most of other GCMs, does not explicitly calculate the activation of cloud condensation nuclei (acted by aerosols including BC) to cloud droplets. Instead the concentration of BC in cloud droplets is determined by the mass concentrations of hydrophilic BC and cloud liquid water. This could be a source of uncertainty. Recently, the physical evolution of cloud droplets from aerosol particles (including the hygroscopic BC) has been applied to some climate models [Jacobson, 2006; Gustafson et al., 2007; Ghan et al., 2012].
 After obtaining the cloud optical properties, we apply them to an interactive system by coupling a climate model with an aerosol model. The purpose is to investigate the radiative forcing and the equilibrium climate response due to BC in cloud droplets. In section 2, the climate and aerosol models used in the study are introduced and the method for calculating the optical properties of mixing droplets is discussed. Also, the experimental design is presented. In section 3, the corresponding results in radiative forcing and climate response are analyzed. Finally, we conclude with a brief summary.
2 Model and Scheme
2.1 Aerosol-Climate Online Coupled Model
 A General Circulation Model (GCM) of BCC_AGCM2.0.1 (Beijing Climate Center atmospheric general circulation model) coupled with a Canadian Aerosol Module (CAM) [Zhang et al., 2012] is used in this study. BCC_AGCM2.0.1 was developed by the National Climate Center of the China Meteorological Administration based on the Community Atmosphere Model Version 3 (CAM3) developed by the National Center for Atmospheric Research in the United States. This model employs a spectral resolution of T42 (approximately 2.8° latitude × 2.8° longitude grid) and a terrain-following hybrid vertical coordinate with 26 levels with a rigid lid at 2.9 hPa. The main features of BCC_AGCM2.0.1 are described by Wu et al. . However, the primary radiative parameterization and the cloud overlap scheme in BCC_AGCM2.0.1 are replaced with a correlated k-distribution radiation scheme and a Monte Carlo independent column approximation developed by Zhang et al. [2003, 2006a, 2006b] and Jing and Zhang . These two modifications have improved the accuracy in gaseous absorption and radiative transfer process through subgrid-scale clouds. The new radiation scheme contains 17 bands (eight for longwave radiation and nine for shortwave radiation), and the spectral ranges of each band are listed in Zhang et al. . The model includes the main greenhouse gasses of H2O, CO2, O3, N2O, CH4, and CFC (CFC11, CFC12, CCL4, and CFC22). In this study, BCC_AGCM2.0.1 is coupled with a slab ocean model, which is from Hansen et al. .
 The CAM, a size-segregated multi-component aerosol model, was developed by Gong et al. [2002, 2003]. The following five aerosol types were included: sulfate, BC, organic carbon (OC), soil dust, and sea salt. Each aerosol type is divided into 12 bins as a geometric series for radius between 0.005–20.48 µm. The total number of advected aerosol quantities is 60 in the model. The model includes the processes of emission, transport, chemical transformation, cloud interaction, and deposition for atmospheric aerosols. BC particles are mostly hydrophobic when emitted. However, BC aerosols become hydrophilic as they age in the atmosphere. The detailed aerosol aging process is shown in Gong et al. . The wet removal of aerosols follows two processes: below-cloud scavenging and in-cloud rainout [Gong et al., 2003]. The removal rate of aerosols due to below-cloud scavenging by precipitation is calculated according to Slinn , and the rainout removal tendency inside the clouds is expressed according to Giorgi and Chameides . The emissions of sulfate, BC, and OC are derived from AeroCom data [Dentener et al., 2006]. The emission of soil dust and emission of sea salt are calculated online using the schemes developed by Marticorena and Bergametti  and Gong et al. , respectively. BCC_AGCM2.0.1 and CAM have been coupled online and can simulate the mass concentration, optical properties, and direct radiative forcing of typical aerosols with a high level of accuracy [Zhang et al., 2012].
2.2 Parameterization of Optical Properties of Cloud Droplets Including BC
 BC particles can be assumed to be randomly embedded in cloud droplets since the mean radius of BC is much smaller than that of cloud droplets. The refractive index of cloud droplets containing various particles can be calculated by the MG mixing rule [Chýlek et al., 1988, 1996]:
where m = n + i · k is the refractive index for the mixture droplet with n and k being the real and imaginary parts, mw and mBC are the refractive indices of water and BC, respectively, and η is the volume fraction of BC in clouds. The volume fraction of BC in clouds, η, in climate models is defined as [Li et al., 2011]
where f is the cloud fraction in a model grid cell, MBC and Mw are the mass concentrations of hydrophilic BC and cloud liquid water, respectively, and ρBC and ρw are the densities of hydrophilic BC and cloud liquid water, respectively. According to Hansen et al. , the soluble proportion of BC particles should be set as 0.6 for industrial (fossil fuel) BC and 0.8 for biomass burning BC. All the hydrophilic BC is assumed to be embedded in the cloud droplets due to the lack of physical parameterization of cloud microphysics in this model. In reality, some hydrophilic BC particles could exist interstitially between cloud droplets. The proportions of soluble BC to total BC and the amount of hydrophilic BC entering into cloud droplets are depend strongly on many local physical and chemical conditions. Also the results should be expected to vary greatly by regions. In this work, the assumption that all hydrophilic BC is embedded in cloud droplets could generate uncertainties in results.
 The cloud droplet size distribution, n(r), in the atmosphere is represented by gamma functions [Pruppacher and Klett, 1997]:
where A, α, and β are constants and r is the radius of the cloud droplet. α and β can be obtained from the effective radius, re, and effective variance, ve. Li et al.  showed that cloud radiative forcing is very sensitive to re but not to ve, so a constant value of ve = 0.172 has been adopted in the parameterization of cloud optical properties [Dobbie et al., 1999]. Based on these, we can calculate the cloud droplet optical properties using Mie theory. The refractive indices of water and BC are from D'Almeida et al. , with a value of 1.75 + 0.44 i at 550 nm for BC.
 The cloud droplet effective radius is divided into six bins with size of 1.5, 3.0, 5.0, 10.0, 20.0, and 40.0 µm, which matches the radiation scheme used in BCC_AGCM2.0.1. We divide the values of η into eight bins as 0, 10−9, 10−8, 10−7, 10−6, 10−5, 10−4, and 10−2. Accordingly, the cloud droplet optical properties defined as an (6 × 8) array for effective radius and η are calculated and incorporated into the model. At each model time step, the cloud optical properties at any values of droplet effective radius and η can be obtained through bilinear interpolation. This table look-up method is different from the perturbation method shown in Li et al. . Both methods can effectively handle the cloud optical properties.
2.3 Experimental Design
 Two experiments were performed. In the first experiment (EXP1), clouds are assumed to consist of pure water and so their optical properties are not affected by BC. In the second experiment (EXP2), the extra absorption due to the presence of BC in cloud droplets is taken into account. The microphysical role of BC is assumed to be the same in both experiments. The instantaneous radiative forcing is calculated by calling the radiation scheme twice at each radiative time step in EXP1. In the first, the radiative effect due to BC in cloud droplets is included; in the second, BC particles in cloud droplets are not activated in radiation. The difference of net solar radiation flux at TOA or the surface between the two calls is defined as the corresponding radiative forcing. Each experiment is run for 80 years. The first 30 years is the spin-up period and the last 50-year simulation is averaged and analyzed to determine the radiative forcing and climate response. We also performed an additional experiment to simulate the direct radiative forcing based on the assumption that all the BC particles are in the atmosphere.
 The model's results have been subjected to a t-test to estimate their statistical significance by assuming each model year to be an independent sample. We also divide the data into N-year segments (N = 2, 3, 4, 5) instead of 1-year segments to test the temporal correlation of the samples. The results show that the areal fraction of significant differences is roughly the same with increasing N, especially for the main features. It is therefore suitable to use each model year as an independent sample for evaluating statistical significance.
3 Results and Discussions
3.1 Change of Cloud Optical Properties Due to Presence of BC in Cloud Droplets
 The imaginary part of cloud droplet refractive index is very sensitive to the presence of BC in cloud droplets, while the real part shows very little sensitivity. The change in the imaginary part of the refractive index mainly occurs in the solar spectral range, especially for the wavelengths λ ≤ 1 µm as shown in Chýlek et al.  and Li et al. . The imaginary part of the cloud droplet refractive index increases substantially with the increase of η. This suggests that the presence of BC in cloud droplets can strongly increase the cloud solar energy absorption.
Reddy and Boucher  pointed out that in the atmosphere, η = 10−7 is a common value of the BC volume fraction in clouds based on a GCM simulation. In Figure 1, the changes of cloud optical properties for different cloud droplet effective radius are shown for η = 10−7. It is found that the change of the extinction coefficient is very small. However, the changes of the absorption coefficient, SSA, and asymmetry factor are clearly seen in Figure 1. With increases of effective radius, the changes in SSA and asymmetry factor become larger, but the change in absorption coefficient becomes smaller. This is attributed to the decrease of extinction coefficient with the increase of effective radius, since the absorption coefficient is defined as the extinction coefficient times the co-single scattering albedo. In Figure 2, the band-mean absolute differences of cloud optical properties due to BC in cloud droplets are shown for the 17 bands used in BCC_AGCM2.0.1. Generally, the differences of cloud optical properties appear in the solar wavebands of 10–17. The results are consistent with those in Figure 1.
 Considering the difference between the absorption cross-section of cloud droplets with and without BC, the enhancement ratio is defined as this difference divided by the absorption cross-section of an equal mass of BC residing within the air [Flanner et al., 2012]. Figure 3 shows the enhancement ratio versus wavelength for two BC volume fractions. For the smaller volume fraction, η = 10−7, the enhancement ratios drop to close to zero for a wavelength larger than 1.8 µm; for the larger volume fraction, η = 10−5, the enhancement ratio can exceed 3 even when the wavelength is close to 4 µm. Additionally, the enhancement ratio is sensitive to the cloud droplet size, in particular for η = 10−5. The enhancement ratios are in the range of 2–4 at 0.55 µm except for the case of large cloud droplets (e.g., Re = 20.0 µm) at η = 10−5. Chýlek et al.  found that the absorption of BC in a cloud droplet was increased by a factor of 2–2.5 at 550 nm. Also, the enhancement in absorption for a soot-water drop mixture was a factor of 2.5–4.5 at 635 nm measured by Mikhailov et al. . These are consistent with the results of Figure 3.
3.2 Distributions of the Simulated BC Concentration and η
 Figure 4(a) shows the annual mean distribution of the simulated BC burden. The maximum BC burdens appear over central Africa, South America, and East Asia. In particular, in eastern and northern China and India-Bengal, the maximum value is about 1.6 mg m−2. There are also relatively large BC concentrations in eastern North America, West Europe, and Australia. The simulated global annual mean burden of BC is found to be 0.14 mg m−2. The distribution and magnitude of the simulated BC concentration in this study are consistent with the results of other models in AeroCom (http://aerocom.met.no/cgi-bin/aerocom/surfobs_annualrs.pl). The BC aerosol is mainly located in the mid and low troposphere, and the highest concentrations appear over the surface layer close to the BC sources in tropical and subtropical regions of the Northern Hemisphere (NH). BC concentrations drop rapidly with height (Figure 4b). A similar vertical distribution of BC concentrations was provided by Reddy and Boucher . Figure 4(c) shows the annual mean distribution of the simulated column burden of BC within cloud droplets. Generally, the large in-cloud BC column burdens occur over the strong source regions. The global annual mean burden of BC within cloud droplets is about 0.006 mg m−2, which is larger than the corresponding value of 0.0041 mg m−2 estimated by Jacobson .
 In Figure 5, the comparison of the simulated BC mass concentrations with the measured results is shown. The IMPROVE (Interagency Monitoring of Protected Visual Environments) monitoring network consists of aerosol, light scattering, light extinction, and scene samplers in a number of National Parks and Wilderness areas in the United States. The measured data in rural, remote, and marine sites are obtained from Chung and Seinfeld . All of them are surface measurements. It is seen that the magnitudes of the simulated BC concentration by our model agree reasonably with those of the measurements at most of these sites. However, the simulated values are less than the measured results at some rural and remote sites. This could be caused by various factors including the uncertainty in source emissions, the error of the observational instruments, the limitations in model resolution, and the implementation of physical processes in the model. The underestimation of BC concentrations could cause an underestimation of the related radiative effect.
 Equation ((2)) indicates that the magnitude of η is determined by the BC mass concentrations, cloud water content, and cloud fraction. Figure 6a presents the annual mean global distribution of the simulated η at the lowest model layer in logarithmic scale. η is found in magnitude of 10−7 in most regions, especially over ocean. This is consistent with the results given by Reddy and Boucher . η reaches a magnitude of 10−5 in East Asia, West Europe, and the west coast of Africa with the maximum value approximating 4 × 10−5. This is due to the high BC loading and large cloud fraction. It is seen from the vertical distribution of η in Figure 6b that the large values of η appear in the mid and low troposphere and the values drop rapidly with height. This is similar to the vertical distribution of BC concentrations.
3.3 Changes of the Simulated Cloud Optical Properties
 Figure 7 shows the annual mean changes of the simulated cloud optical properties at 550 nm, due to the presence of BC in cloud droplets. It is found in Figure 7a that the cloud absorption optical depth increases substantially in areas such as East Asia and South Asia, where the BC emission is large. The largest change of cloud column absorption optical depth can exceed 0.06 (Figure 7a). The decrease of cloud SSA primarily occurs in East Asia, South Asia, West Europe, eastern USA, central Africa, and South America, with the maximum change of −3.0 × 10−3 in North China (Figure 7b). The cloud asymmetry factor generally increases in the above areas with the maximum change up to 1.5 × 10−3. The increase of asymmetry factor is caused by the weaker back scattering due to the enhancement of absorption by including BC (Figure 7c). It can be seen from Figure 7 that relatively small changes in cloud optical properties also occur over large ocean areas. We conclude that this is because of the long-distance transport of BC.
3.4 Radiative Forcing Due to Mixing of BC in Cloud Droplets
 The presence of BC in cloud droplets leads to an increase of solar absorption, thereby causing a positive radiative forcing at TOA. The simulated global annual mean radiative forcing at TOA is 0.086 W m−2, which is larger than the results of 0.07 W m−2 obtained by Chuang et al.  and 0.069 W m−2 obtained by Zhuang et al. . Though the global mean forcing is very small, the regional forcings can be much larger. They can even be comparable to the global annual mean direct radiative forcing (DRF) of BC at TOA, as shown by this model (Figure 8c). DRF is defined as the instantaneous change of net radiative flux at TOA for all sky from two calculations at each model time step. The first calculation accounts for BC radiative effect. In the second calculation, the concentration of BC is set to zero in model radiation algorithm. A positive forcing exceeding 0.2 W m−2 occurs in most regions of East Asia, South Asia, West Europe, and eastern North America. This is particularly true in South America and Africa with a maximum forcing up to 1.5 W m−2, as shown in Figure 8a. It is seen from Figure 8c that large BC DRF at TOA appears in East Asia, central Africa, Western Europe, eastern U.S., and South America, where the maximum value reaches approximately 1.0 W m−2. The simulated global annual mean DRF of BC at TOA is 0.09 W m−2. The downward solar radiation flux at the surface is decreased due to the increase in cloud absorption, thereby leading to a negative forcing at the surface (Figure 8b). The simulated global annual mean radiative forcing at the surface is −0.04 W m−2. The negative forcing at the surface mainly appears in East Asia, South Asia, West Europe, eastern North America, and equatorial South America and Africa.
3.5 Climate Response
 Figure 9 shows the differences between EXP2 and EXP1 in global annual mean vertical profiles of several physical quantities. The presence of BC in cloud droplets evidently decreases the cloud SSA in the low and mid troposphere, where BC is mainly located. This results in an increase in cloud absorption optical depth, with a maximum value exceeding 0.00014 at 550 nm (Figure 9a). The enhanced solar absorption by cloud droplets causes an obvious increase in solar heating rate and temperature in the troposphere (Figures 9b and 9d). The largest increase in global annual mean atmospheric temperature appears in the mid troposphere, with a maximum value close to 0.1 K. Also, the change in global annual mean temperature near the surface is 0.08 K. The increase in temperature causes more surface evaporation and enhances the water-holding capacity of the air. This leads to an increase in atmospheric water vapor amount (Figure 9e and Table 1). In turn, the water vapor in the atmosphere, which acts as greenhouse gas and solar energy absorber, can further warm the surface. This produces a positive feedback mechanism [Jacobson, 2006].
Table 1. Global Annual Mean Difference for Several Physical Quantities Between EXP2 and EXP1
* Represents significance at ≥95% confidence level from the t-test. The column cloud optical depth and absorption optical depth, column cloud water path, total cloud fraction, and total water vapor are defined as the sum of the global mean results from each individual model layer, respectively.
 The increase in absorption of solar radiation by cloud can change the atmospheric thermodynamics, which leads to changes in relative humidity and cloud fraction. These changes of temperature and water vapor lead to an increase in relative humidity and cloud fraction in the lower troposphere (Figures 9f and 9g). In the mid and higher troposphere, the increase in temperature causes a decrease in relative humidity and cloud fraction. From Figures 9f and 9g, it is seen that the cloud fraction is decreased corresponding to the reduction of relative humidity in the mid troposphere, though the cloud water path is increased in some altitudes. The changes of cloud fraction and cloud water path result in changes of longwave heating rate as well (Figures 9c and 9h).
 Table 1 shows the differences between EXP2 and EXP1 for several global annual mean physical quantities. BC in cloud droplets causes an increase in the cloud optical depth and absorption optical depth at 550 nm by 0.045 and 0.0017, respectively. Additionally, BC in cloud droplets causes a 0.4% decrease of cloud fraction, and an increase of 0.08 K in surface temperature. The local maximum changes in the annual mean surface temperature exceed −1.5 K and +0.6 K in NH and Southern Hemispheres (SH), respectively (Figure 10a). The changes in surface temperature mainly occur in the mid and high latitudes of both the NH and SH. It is seen from Figure 10b that the net radiative flux at the surface is lower in most of the mid and high latitudes of NH, especially in the northern Pacific and Atlantic, central Eurasia, Western Europe and western North America. This can lead to the decrease of surface temperature. The surface cooling in the NH causes less surface water evaporation and weakens the water-holding capacity of the air (Figure 10c). This kind of positive feedback effect further cools the atmosphere. Over most ocean areas in the mid latitudes of SH, the increase of surface net radiative flux is also consistent with the increase of surface temperature. This enhances the surface evaporation and the water-holding capacity of air in these areas (Figure 10c).
 The changes in surface temperature can also be interpreted from the vertical changes in cloud fraction shown in Figure 11a. In the NH, the effect of BC in cloud droplets results in an increase in low cloud fraction and a decrease in mid and high cloud fractions. The increase of low cloud fraction can cause more solar reflection, and the decrease of mid and high cloud fractions can cause more outgoing longwave radiation. Both effects can cool the surface temperature. In the SH, the change of cloud fraction is generally opposite to that of the NH, especially for the mid and high clouds. This could cause an increase in surface temperature. Jacobson  also indicated that the increases of surface temperature in the SH are possibly due to the long-distance transport of BC and local feedback of clouds to large-scale meteorology. A response to changed atmospheric circulation may be the primary cause that leads to these changes in mid-to-high latitudes of SH.
 Figure 11 also shows the simulated annual mean differences in zonally averaged temperature and relative humidity between EXP2 and EXP1. In the NH, the decrease of the net radiation flux at the surface (Figure 11a) results in the decrease of surface temperature, which leads to less water vapor in the atmosphere due to weaker surface evaporation. This causes a decrease of tropospheric temperature since water vapor has strong greenhouse effect. It is shown in Figure 11b that the local zonally averaged near-surface temperature is reduced by 0.2 K near 60°N. However, the temperature is increased in other latitudes of the troposphere. The changes of tropospheric relative humidity are not always consistent with changes of temperature, but they are largely consistent with changes of cloud fraction (Figures 11a and 11c). The relative humidity is mainly decreased in the middle troposphere between 0°–60°N. This is probably due to a significant decrease of water vapor. It is increased in the most other regions.
 The local temperature changes cannot necessarily be explained by the local processes, but can be strongly influenced by the changes in heat transport. In Figure 10d, it is shown that BC in cloud droplets causes a decrease in surface pressure in northern USA, Western Europe and eastern Russia, but an increase in the North Pacific, Northwest Atlantic, and western Russia. This leads to the cold advections in northwestern USA, North Atlantic, and central Russia (Figure 12b), and pronounced cold anomalies in surface temperature in those regions (Figure 10a). There are also regions of positive temperature anomalies caused by warm advection due to changes in surface pressure at the high latitudes of NH (Figures 10a and 12b). Likewise, the change in the pressure gradient suggests a southward shift of the southern storm track in the SH. The warm anomalies at the high latitudes of SH (~60°S) are more likely the result of heat transport by baroclinic eddies penetrating further south. The changes of meridional circulation also show the southward moving of cold or warm air (Figure 12). The clockwise circulations appearing in the mid and high latitudes of NH can cause the ascending motion developed between 40°N and 60°N and the descending motion in Arctic, which leads to an increase of southward transport of cold air in the lower troposphere. A similar circulation occurs in the mid and high latitudes of SH, which leads to an increase of southward transport of warm anomalies. Figure 13 shows the zonally averaged change in total atmospheric heat transport due to BC inclusions in cloud droplets. It is seen that BC in cloud droplets induces an increase of total heat transport significantly from the tropics to the high latitudes of SH and a decrease of total heat transport to the extratropics of NH. The changes of heat transport result in a warming effect in the SH and a cooling effect in the NH. Furthermore, the warming/cooling effect can have feedback on surface temperature.
 In summary, the presence of BC in cloud droplets leads to more absorption of solar radiation by cloud, which directly affects the vertical distributions of cloud and water vapor. Thus, the net radiation flux arriving at surface is influenced, as the net radiation at surface is decreased significantly in the northern Pacific and Atlantic, central Eurasia, and western North America. This leads to a change in surface temperature in those regions. The changes in thermodynamics can have an influence on atmospheric circulation and heat transport. The result of heat transport helps to understand the warming/cooling effect in the SH/NH.
 Figure 14 shows the simulated annual mean differences of precipitation between EXP2 and EXP1. The precipitation decreases in most tropical regions of NH, while it mainly increases in the tropical areas of SH. The largest change of precipitation appears in the tropical Pacific and Indian Oceans, with a maximum increase (decrease) up to ±0.4 mm day−1 (Figure 14a). It is noted that the change of the annual mean surface temperature is +0.19 K in the SH and −0.04 K in the NH. This interhemispheric asymmetry in surface temperature change can significantly affect the atmospheric dynamics. Thus, the northern trade winds are enhanced in the Intertropical Convergence Zone (ITCZ), and the northerly surface wind anomalies cross the equator to converge with the enhanced southern trade winds in the tropics of SH (Figure 12b). Therefore, the enhancing (weakening) of the vertical ascending motion and precipitation appears on the south (north) side of equator (Figure 12a). This possibly induces a southward shift in the tropical rainfall maximum related to the ITCZ. This is consistent with the hypothesis that the ITCZ should move toward the relatively warmer hemisphere in response to surface temperature changes [Broccoli et al., 2006]. It is worth noting that the enhanced SH warming and southward shift of the ITCZ in these simulations are opposite of what has actually occurred during recent decades.
 The purpose of this work is to study the radiative forcing and climate impact due to the changes of cloud optical properties by BC in cloud droplets. In contrast to previous works on this topic, our study is based on the accurate calculation of cloud optical properties from the MG mixing rule and Mie theory. The obtained cloud optical properties are then applied to an interactive system coupling, a GCM with an aerosol model. We are then able to investigate the radiative forcing and the equilibrium climate response due to BC in cloud droplets.
 The presence of BC in cloud droplets leads to a positive radiative forcing at TOA. The simulated global annual mean forcing at TOA is 0.086 W m−2. The local radiative forcing can be much larger. The forcing exceeds 0.2 W m−2 in most regions of East Asia, South Asia, West Europe, and eastern North America, especially in South America and Africa where the maximum forcing reaches 1.5 W m−2. The downward solar radiation flux at the surface inevitably decreases due to the increase of cloud absorption, thereby leading to the negative forcing at the surface.
 The increase in solar absorption when BC is present in cloud droplets causes an increase in solar heating rate and temperature in troposphere. The largest increase in global annual mean atmospheric temperature of approximate 0.1 K appears in the mid troposphere. The global mean surface temperature is increased by 0.08 K. The increase in temperature causes a higher surface evaporation, a larger water-holding capacity of the air, and a lower cloud fraction. All of these cause the further warming of the atmosphere. This process produces a positive feedback mechanism.
 The changes in annual mean surface temperature, due to BC in cloud droplets, mainly occur in the mid and high latitudes of both Hemispheres. In the NH, this effect results in an increase of low cloud fraction and a decrease of mid and high cloud fractions. The increase in low cloud causes more solar reflection, and the decrease in mid and high cloud fractions causes more outgoing longwave radiation. Both can cool the surface temperature. The surface cooling in the NH causes less surface water evaporation and weakens the water-holding capacity of the air in these areas. This kind of positive feedback further cools the atmosphere. In the SH, the change of cloud fraction is generally opposite to that of the NH, especially for the mid and high clouds, which could cause the increase of surface temperature.
 From the perspective of heat transport, it is found that BC in cloud droplets induces an increase of heat transport from the tropics to the high latitudes of SH and a decrease from the equator to the extratropics of NH. This leads a warming effect in the SH and a cooling effect in the NH.
 There are significant changes of surface temperature in the SH and NH (+0.19 K and −0.04 K, respectively). The interhemispheric asymmetry in surface temperature changes causes significant changes in atmospheric dynamics and precipitation. In the ITCZ, the northern trade winds are strengthened, and the northerly surface wind anomalies cross the equator and converge with the enhanced southern trade winds in the tropics of SH. This results in an increase (a decrease) of vertical ascending motion and precipitation on the south (north) side of equator. This can possibly induce a southward shift in the tropical rainfall maximum related to the ITCZ.
 The authors would like to thank three anonymous reviewers and Editor Dr. Steven Ghan for their constructive comments. This work was financially supported by National Basic Research Program of China (2011CB403405), National Natural Science Foundation of China (41205116), and CAMS Basis Research Project (2012Y003).