Development and validation of a black carbon mixing state resolved three-dimensional model: Aging processes and radiative impact

2.1 WRF-Chem Model

[7] We developed a size and BC mixing state resolved model (MS-resolved WRF-chem model) based on the WRF-chem model (version 3.1.1) [Grell et al., 2005; Fast et al., 2006] with the MOSAIC aerosol module [Zaveri et al., 2008], which have been used in our previous studies [Matsui et al., 2009a, 2010, 2011]. In the original MOSAIC aerosol module, the mass concentrations of the following aerosol species and number concentrations are explicitly calculated for the size range between 40 nm and 10 µm with eight size bins: sulfate, nitrate, ammonium, BC, primary organic aerosol (POA), other inorganics (nonreactive dust), sea salt (sodium and chloride), and aerosol water. Secondary organic aerosol (SOA) is not included in this version of the WRF-chem model. The chemical processes considered in the WRF-chem model are emissions, gas-phase chemistry [Zaveri and Peters, 1999], aqueous-phase chemistry [Fahey and Pandis, 2001], binary homogeneous nucleation [Wexler et al., 1994], dynamical gas-particle partitioning (condensation/evaporation) [Zaveri et al., 2008], Brownian coagulation [Jacobson et al., 1994], and dry and wet deposition [Binkowski and Shankar, 1995; Easter et al., 2004]. Gas-particle partitioning is calculated for sulfate, nitrate, ammonium, and chloride [Zaveri et al., 2008]. Since SOA is not included currently, gas-particle partitioning of organics is not considered in our model. Water uptake is calculated using the Zdanovskii-Stokes-Robinson method [Zaveri et al., 2008]. The shift of aerosol size bins is calculated by a two-moment advection method [Simmel and Wurzler, 2006].

[8] In this study, the aerosol representation of the WRF-chem model was extended to resolve both aerosol size and BC mixing state. We adopted a 2-D aerosol bin representation, as shown in Figure 1. One dimension is aerosol dry diameter and the other is the BC mass fraction of the total aerosol mass concentration under dry conditions. This 2-D treatment is basically the same as that of Oshima et al. [2009a]. In this study, the aerosol size range between 40 nm and 10 µm (same as the original WRF-chem model) was divided into 12 bins. The BC mass fraction (between 0 and 1) was divided into 10 bins: one for pure BC (BC mass fraction >0.99), one for BC-free particles (BC mass fraction = 0), and the other eight bins for internally mixed BC (BC mass fractions of 0–0.1, 0.1–0.2, 0.2–0.35, 0.35–0.5, 0.5–0.65, 0.65–0.8, 0.8–0.9, and 0.9–0.99). Therefore, the MS-resolved WRF-chem model uses 120 aerosol bins (12 × 10 bins) in total.

[9] To calculate aerosol microphysical processes with the 2-D representation, we mainly modified two schemes in the MOSAIC aerosol module: 1) the shift of size and mixing state bins resulting from condensation/evaporation and aqueous-phase chemistry and 2) coagulation. The modification for other processes, such as nucleation and dry and wet deposition, is relatively minor because of no interaction between aerosol bins in these processes. The particles formed by nucleation are added to the smallest size bin (40 nm in diameter) as BC-free particles. For wet removal processes, the volume-averaged hygroscopicity and critical supersaturation are calculated for each of 2-D aerosol bins. Using this information, aerosol activation to cloud droplets is calculated for each bin by applying a maximum supersaturation determined from a Gaussian spectrum of updraft velocities [Abdul-Razzak and Ghan, 2000; Ghan et al., 2001; Gustafson et al., 2007; Chapman et al., 2009]. Interstitial and cloud-phase aerosols are tracked separately. Cloud-phase aerosols are removed by precipitation through cloud to rainwater conversion rate, which is calculated in the cloud microphysical scheme (Lin et al. [1983] scheme in this study). Cloud-aerosol interactions for convection (sub-grid-scale wet removal processes) are not considered in this study. In the following subsections, we describe the 2-D treatment of condensation/evaporation and coagulation processes.

2.2 2-D Treatment of Condensation/Evaporation

[10] The shift of aerosol size and mixing state bins is calculated after condensation/evaporation and aqueous chemistry schemes in the WRF-chem model. In our model, we first calculate the aerosol number and mass concentrations to be moved to other size and/or mixing state bins for all 120 bins using the schemes described in the next paragraph. Then, we calculate the updated number and mass concentrations for each bin by integrating the amounts that remain in the original bin and those moved from other 2-D bins.

[11] The amount to be shifted along the aerosol size bin is calculated by a mass and number advection scheme [Simmel and Wurzler, 2006], which is used in the original WRF-chem model (2). The amount to be shifted along the BC mixing state bin is calculated using the moving center approach [Jacobson, 1997]: if average BC mass fraction in a bin is not within the range of the original mixing state bin, all the particles in the bin are moved to an appropriate mixing state bin without changing the size bin.

2.3 2-D Treatment of Coagulation

[12] The coagulation scheme developed in this study is an extension of the one-dimensional (1-D) semi-implicit method [Jacobson et al., 1994; Jacobson, 2005] to a 2-D aerosol representation. In the original semi-implicit method, the total volume concentration in size bin k, at time t (v_k,t) can be written by equation (1),

(1)

where h is the time step, β_i,j is the Brownian coagulation kernel, n_j,t-h is the number concentration in bin j at time t-h, and NB is the total number of size bins. The value of f_i,j,k is the volume fraction partitioned to bin k when a particle in bin i and bin j coagulate, as defined by equation (2),

(2)

where u_k is the volume of a particle in bin k and V_i,j is the sum of u_i and u_j. This equation means that the volume of a coagulated particle (V_i,j) is divided into bins k and k + 1 based on the volumes of V_i,j, u_k, and u_k+1.

[13] This semi-implicit method for a 1-D aerosol representation (size dependence only) was extended to a 2-D aerosol representation that resolves the BC mixing state. As described below, we use the 2-D coagulation algorithm only for the calculation of number concentrations, while we use the 1-D coagulation algorithm to calculate coagulated mass concentrations of 10 species (10 times in each time step) and repartition them into different mixing state bins using the 2-D information for coagulated number concentration. This method is adopted to reduce the computational cost while giving up some accuracy.

[14] The number concentrations in size bin k and mixing state bin s at time t (n_k,s,t) are calculated by equations (3-1)–(3-4),

(3-1)

(3-2)

(3-3)

(3-4)

where v_i,is,t is the total volume concentration in size bin i and mixing state bin is at time t, n_j,js,t-h is the number concentration in size bin j and mixing state bin js at time t-h, and NB and NS are the number of size bins (12 in this study) and mixing state bins (10 in this study), respectively. S_i,is,j,js,s is the volume fraction for the partitioning between different mixing states (similar to f_i,j,k for different sizes), and the definition is given later. P_k,s and L_k represent the production and loss terms, respectively, due to coagulation processes in each time step. The values of f_i,j,k (volume fraction of partition) and β_i,j (coagulation kernel) are calculated using diameters and densities averaged over mixing state bins. In other words, we assume that the particles in the same size bins (but different mixing state bins) have the same (or average) dry and wet diameters as well as coagulation kernel. This is not necessarily correct, especially at high relative humidities, because particles in the same size bin (but different mixing state bins) can have different wet diameters and densities due to different chemical compositions. Nevertheless, we apply this assumption to reduce the computational cost and to make the 2-D and 1-D coagulation calculations consistent.

[15] It is noted that the way to describe the production (P_k,s) and loss terms (L_k) in equations (3-3) and (3-4) is slightly different than those in equation (1). The loss term in equation (3-4) includes a contribution from f_k,j,k, which is the volume fraction remaining in size bin k after the coagulation of particles in size bins k and j, to consider that the coagulated particles could have different BC mass fraction even if the size bin is not changed. This representation is essentially consistent with the treatment of Jacobson [2002b]. A main difference between our and Jacobson's scheme is that our 2-D scheme considers both increase and decrease in BC mass fraction due to coagulation, while in Jacobson [2002b] coagulated particles are assigned to a predetermined mixing state group and they do not move to a less mixed group by coagulation. To compensate for this loss contribution, the second term was added to the right-hand side of equation (3-3). Strictly speaking, v_k,is,t (volume concentrations at time t) should be used in this equation instead of using v_k,is,t-h. We use v_k,is,t-h, because their values at time t (v_k,is,t) are unknown in calculating equation (3-3) and iterative calculations are required to estimate v_k,is,t. As shown in Appendix A1, the performance (e.g., total number and mass concentrations, and mixing state) was generally similar between the calculations using equations (3-1)–(3-4) and more accurate iterative calculations in our simulations, while the simulations without the iterations are a factor of 50 faster than those of more accurate calculations. Consequently, we adopted this approximation for computational efficiency.

[16] The value of S_i,is,j,js,s is the volume fraction partitioned to mixing state bin s when particles in bin i and is and bin j and js coagulate. This value is defined by equation (4), to be consistent with equation (3-3),

(4)

where B_L,s and B_U,s are the predetermined lower and upper boundaries of BC mass fraction in bin s, m_c,i,is,t is the total mass concentrations of species c in bin i and is at time t, and NC is the number of chemical compositions. The numerator and denominator in equation (4) are the BC mass and total aerosol mass, respectively, of coagulated particles produced from bin i, is and bin j, js, and therefore their ratio becomes the mass fraction of BC.

[17] Following the description of the algorithm to calculate 2-D coagulation for aerosol number concentrations, in the rest of this section we describe the algorithm for 1-D coagulation for aerosol mass calculations and the method to redistribute the mass into the 2-D aerosol bins. Using the production terms, P_k,s (equation (3-3), we can estimate the mass fraction of coagulated particles in bin k, s diagnostically within the total mass of coagulated particles in size bin k (sum of mixing state bins) produced in a time step (F_BC,k,s and F_OTH,k,s) as equation (5):

(5-1)

(5-2)

where F_BC,k,s and F_OTH,k,s are the fractions of coagulated particles in bin k, s for BC and other species, respectively, and B_s is the predetermined value of the center of the BC mass fraction in bin s. We note that P_k,s/ΣP_k,is corresponds to the number fraction of coagulated particles in bin k, s within the total coagulated particles in size bin k (sum of mixing state bins) produced in a time step.

[18] The mass concentrations of species c in size bin k and mixing state bin s at time t can be calculated by using 1-D coagulation calculations (equation (1)) and the fractions of coagulated particles defined by equation (5), as shown in equation (6):

(6)

where M_c,i,t is the mass concentration of species c in size bin i at time t summed over the mixing state bins and N_j,t-h is the number concentration in size bin j at time t-h summed over the mixing state bins. In this equation, F_c,k,s is either F_BC,k,s for BC or F_OTH,k,s for all other species, assuming that the fractions of coagulated particles (F_OTH,k,s in equation (5-2)) are the same for all the aerosol species other than BC. The calculations are conducted from the smallest size bins following to the original semi-implicit method. We finally check whether the BC mass fraction of the production term (second term in the numerator in equation (6)) is within the range of bin s. If the fraction is not within the range of bin s, the coagulated particles of the bin are assigned to the proper mixing state bins without changing size bins at the end of coagulation scheme.

[19] Our scheme uses some assumptions for computational efficiency: 2-D calculations are conducted only once without iteration (for number concentrations), and 1-D calculations are applied 10 times (for mass concentrations of 10 species) in a time step. The uncertainties in the assumptions of the noniterative treatment (equation (3)) and 1-D calculations for mass concentrations (equation (6)) are described in Appendix A1.

[20] Our scheme is positive-definite for any time step [Jacobson, 2002b]. Total volume concentrations (TV) of individual species are conserved within 0.001% (0.00001) for any time step in our case (5 and 10), even though v_k,is,t-h is used instead of v_k,is,t in equation (3-3) (shown above). In case that TV is not conserved within 0.001%, a TV adjustment equation can be applied in our scheme (volume concentrations in each bin are multiplied by the TV ratio at t-h (before coagulation) and t (after coagulation)), although this adjustment is not used in our simulations shown in 5 and 10 (TV was conserved within 0.001% for all species for any time step).

2.4 Box Model Calculation

[21] To confirm that our model simulations with the 2-D bin representation are reasonable, we conducted box model simulations of condensation/evaporation (3) and coagulation processes (4). Other processes (e.g., deposition, dilution, and gas- and aqueous-phase chemistry) were not considered in these box model simulations. The aerosol size range was divided into 100 bins between 20 nm and 2 µm (dry diameter), and the BC mass fraction (between 0 and 1) was divided into 21 bins (2100 aerosol bins in total) for the box model simulations (this section only). The following meteorological and chemical parameters were given as initial conditions of the box model simulations: temperature (283 K), pressure (1000 hPa), relative humidity (50%), sulfuric acid (10 pptv), ammonia (10 ppbv), nitric acid (0.1 ppbv), and ammonium sulfate (3.3 µg m^–3). The concentration of sulfuric acid was assumed to be constant during the simulations, while other species could change their concentrations with time while conserving the total mass (gas + aerosol). Two types of simulations were conducted for 24 hours with an integration time step of 5 minutes: (1) both condensation and coagulation processes were considered (Figures 2a, 2c, 2e, and 2g) (referred to as COAGon) and (2) only condensation processes were considered (referred to as COAGoff) (Figures 2b, 2d, 2f, and 2h). The emissions of POA and BC were given to the box model during 0–12 hours of the simulations: 0.58 µg m^–3 h^–1 for POA and 0.20 µg m^–3 h^–1 for BC. We assumed that all the emissions were externally mixed particles (POA was given as BC-free particles and BC was given as pure BC particles). The size distributions of emissions were assumed to have a count median diameter of 70 nm with a standard deviation of 1.53.

[22] Figures 2a and 2b show the temporal variations of total mass concentrations for sulfate, POA, and BC and total number concentrations. The levels (orders of magnitude) of simulated mass and number concentrations are generally similar to those of Riemer et al. [2010] and Zaveri et al. [2010] (an ideal urban plume), although our simulation setups were not exactly the same as their simulations (e.g., initial conditions, meteorological parameters, emissions, and dilution effect). The mass concentrations are almost identical between the COAGon and COAGoff simulations, while the number concentrations are different.

[23] Figures 2c–2h show the BC mass fraction and total aerosol diameter (dry conditions) of each aerosol bin at 5 minutes, 12 hours, and 24 hours from the initial time. The color scales show the number concentrations for each bin. There are both pure and internally mixed BC particles at 12 hours because the emissions of BC particles were given as pure BC (BC mass fractions of unity) by 12 hours. On the other hand, all the BC particles become internally mixed by 24 hours due to no additional emissions during 12–24 hours. The BC mass fraction of internally mixed particles also decreases with time (aging of BC). It is clear from the comparison between the COAGon and COAGoff simulations that BC aging processes can be classified into two regimes. The condensation process is dominant for the growth of particles having smaller amounts of coatings (BC mass fractions are high) and smaller diameter (upper and left parts of Figures 2c–2h). On the other hand, the coagulation process is necessary for producing particles having larger amounts of coatings (BC mass fractions are low) (lower parts of Figures 2c–2h). Within the condensation-dominant regime, the decreasing rate of BC mass fractions (BC aging rate) is highly dependent on particle diameter: slower BC aging rate with larger particle diameter. This dependency is generally consistent with the box model simulations in previous studies [Oshima et al., 2009a; Zaveri et al., 2010; Riemer et al., 2010]. Particles having larger amounts of coatings (probably produced by coagulation processes) were also simulated in the previous studies [Zaveri et al., 2010; Riemer et al., 2010]. Their number concentrations increase with time both in our simulations and in the previous studies. Consequently, our box model simulations can represent the main features of BC aging processes simulated in the previous box modeling studies. The results shown in this section suggest the overall validity of our 2-D calculations of condensation and coagulation processes.

3.1 Measurements

[24] The A-FORCE aircraft campaign was conducted over the Yellow Sea and East China Sea in March and April 2009. Figure 3a (blue) shows the flight tracks during the A-FORCE campaign (21 flights in total). Vertical profiles of aerosols from near the surface to 9 km in altitude were obtained at various locations. Details of the A-FORCE campaign were given by Oshima et al. [2012], but information on measurements relevant to the present study is briefly described next. During the A-FORCE campaign, the number and volume concentrations of light scattering particles (LSP) (particles with volume-equivalent dry diameter of 180–850 nm with a nondetectable amount of BC core smaller than 75 nm in diameter) were measured together with BC-containing particles (particles having BC cores with mass-equivalent diameter of 75–850 nm) by the SP2 with high accuracy and temporal resolution [Moteki and Kondo, 2007, 2010; Kondo et al., 2011a]. The overall accuracy of the BC mass is estimated to be about 10% [Kondo et al., 2011a]. The shell (total dry diameter)-to-BC core diameter ratio (SC ratio) of individual BC-containing particles was measured by the SP2. The major source of uncertainty in the SC ratio is the assumed value for the complex refractive index of BC cores. If we change the assumed value from 1.76 + 0.44i to 2.0 + 1.0i, SC ratios of 1.2 and 1.5 are changed to 1.25 and 1.65, respectively, at BC core diameters around 200 nm.

[25] For quantitative comparison of BC mixing state between measurements and model calculations, we defined the following parameters: BC-free-to-total (BC-free + BC-containing particles) number concentration ratio, thinly coated BC (SC ratio <1.1)-to-total BC (BC-containing particles) number concentration ratio, and the number mean SC ratio. The same definitions are used for the comparison of these parameters between measurements and model calculations in 11 and 12. For example, when we compare “BC-free” particles between measurements and model calculations, we use the LSP for measurements and the sum of BC-free particles and BC-containing particles with BC cores smaller than 75 nm for the model calculations.

[26] We also use surface measurements of BC mass concentrations at the Fukue site (32.75°N, 128.68°E) (Figure 3a). BC mass concentrations were measured by a filter-based absorption photometer, the continuous soot monitoring system (COSMOS) [Miyazaki et al., 2008; Kondo et al., 2011a; Kanaya et al., 2013].

3.2 Calculation Setup

[27] The MS-resolved WRF-chem model was applied to East Asia in March and April 2009 when the A-FORCE aircraft campaign was conducted over the Yellow Sea and East China Sea (Figure 3a). Figure 3b shows the model domain used in this study. The outer (orange) domain covers East and Southeast Asia, and the inner (red) domain covers most of China, Korea, and Japan. The horizontal grid spacing is 360 km (30 × 20 grids) for the outer domain and 120 km (39 × 24 grids) for the inner domain. The number of vertical levels is 13 layers from the surface to 100 hPa. The spatial resolution employed by our simulations was coarse because of the detailed (heavy) calculations of the MS-resolved WRF-chem model. The simulation period was from March 21 to April 26, 2009 (37 days). The first 3 days were used for spin-up. The National Centers for Environmental Prediction (NCEP) Final (FNL) Operational Global Analysis data were used for meteorological initial and boundary conditions and for nudging of the horizontal wind field, temperature, and water vapor mixing ratio. The results of the inner domain are shown in this study.

[28] The emission inventories used in this study are as follows: anthropogenic, biomass burning, and volcanic emissions [Streets et al., 2003] and biogenic emissions in spring from the Global Emissions Inventories Activity (GEIA) [Guenther et al., 1995]. The emission of coarse particles is not included in this study to focus on BC. Since the volcanic emissions of Streets et al. [2003] are for the periods when the Miyakejima volcano was erupting, volcanic SO₂ emissions from it were modified to 1500 tons/day based on measurements of the Japan Meteorological Agency in 2009 (1000–2000 tons/day) (http://www.seisvol.kishou.go.jp/tokyo/320_Miyakejima/320_So2emission.htm, in Japanese). BC in emissions was assumed to be externally mixed with other aerosol species. BC was assigned to the bins for pure BC (BC mass fraction >0.99), and the other species were assigned to the bins for BC-free particles (BC mass fraction = 0). The uncertainty of this assumption is discussed in 13. The size distribution of primary aerosol emissions (both BC and BC-free particles) was assumed to be lognormal, with a count median diameter of 50 nm and a standard deviation (σ) of 2.0, considering the results of measurements in Tokyo and Beijing [Kondo et al., 2011a; Matsui et al., 2011] and the treatment of emissions in global modeling studies [e.g., Dentener et al., 2006; Stier et al., 2005; Reddington et al., 2011]. BC emissions are assumed to be constant during the calculation periods.

4.1 Comparison With Surface Measurements

[29] Figure 4a shows temporal variations of BC mass concentrations at the Fukue site. Red and blue arrows denote the periods influenced by high-pressure systems and the timing of cold front passages at Fukue, respectively. Temporal variations of observed BC mass concentrations are generally controlled by synoptic-scale meteorological variations: high concentrations during high-pressure periods and rapid decreases in concentrations during cold front passages. As a result, model simulations reproduced these observed temporal variations of BC reasonably well (correlation coefficient (R²) of 0.64 and normalized mean bias of 23%) in spite of coarse grid spacing.

[30] Figures 4b and 4c show the frequency distribution of the SC ratio (fraction of BC number concentrations) and mean SC ratio in the model calculations for a BC core diameter of 200 nm at the Fukue site. Since model simulations do not explicitly calculate the diameter of the BC core, we calculated the mean diameter of BC cores diagnostically for each bin by assuming a BC density of 1.7 g cm^–3 (used in MOSAIC) and chose a bin that had the closest BC core diameter to 200 nm for each mixing state. As seen in Figure 4, the mean SC ratio tends to be high when BC mass concentrations are high. The higher SC ratio is likely due to the faster growth of coating thickness because gaseous precursors (condensation rate) and aerosol number concentrations (coagulation rate) would also be high when mass concentrations are high. We cannot validate this calculated tendency directly because there are no measurements of BC mixing state at Fukue during the simulation periods. However, our simulation results (high SC ratio in air with high BC mass concentrations) are qualitatively consistent with the measurements of BC mixing state conducted at Fukue in March and April 2007 [Shiraiwa et al., 2008]. Shiraiwa et al. [2008] reported time series plots for both BC mass concentrations and median SC ratio at a BC core diameter of 200 nm, and these two parameters seem to have a positive correlation during their measurements [Shiraiwa et al., 2008, Figures 3b and 8].

4.2 Comparison With Aircraft Measurements

[31] Figures 5a and 5b show time series plots of BC mass concentrations and LSP volume concentrations along the flight tracks during the A-FORCE campaign. All of the 1-minute averages from 21 flights are plotted in order of sampling. Variations in this figure, therefore, reflect both temporal and spatial (including vertical) variations. Both observed and calculated concentrations are given at standard temperature and pressure (STP; 273.15 K and 1013 hPa) in this study. Model simulations generally reproduced observed concentrations and their variations for both BC mass and LSP volume concentrations. Figures 6a–6d show mean vertical profiles of BC mass and number concentrations and LSP volume and number concentrations over all flights during the A-FORCE campaign. Model simulations reproduced observed vertical profiles reasonably well for all the parameters. On average, the normalized mean biases of calculated concentrations were 17% for BC mass, 79% for BC number, –7% for LSP volume, and 4% for LSP number, respectively. Although SOA is not considered (2), LSP volume was not significantly underestimated in our simulation.

[32] Figures 7a and 7b show the frequency distribution of the SC ratio at a BC core diameter of 200 nm for both measurements and model simulations along the flight tracks during the A-FORCE campaign. Model simulations captured the observed spectra of the SC ratios. Calculated BC particles have various SC ratios from 1.0 to more than 2.0, as also seen in observed BC particles. Model simulations also reproduced the temporal variations of the mean SC ratio at a BC core diameter of 200 nm (Figure 7c), while the absolute coating thickness (SC ratio – 1) was underestimated by 30% on average: the period-averaged mean SC ratio is 1.40 for the measurements and 1.28 for the model simulations. This underestimation is partly because pure BC (BC mass fraction = 1) was assumed for all the BC emissions in our simulations. The sensitivity of the initial BC mixing state upon emission to the SC ratio is discussed in 13 SOA, which is not considered in our model (2), may also be a potential cause of the underestimation of the SC ratio.

[33] In general, the mean SC ratios are high when aerosol mass concentrations are high (mostly less than 2 km in altitude) (Figures 5a, 5b, and 7c). This may be because polluted air masses could have faster BC aging processes during transport (10). As shown in Figure 8, observed mean SC ratios at a BC core diameter of 200 nm tend to increase with BC mass concentration (used here as an indicator of the accumulation of aerosols), although 1-minute data are considerably scattered. A similar tendency was obtained for the model simulations, while absolute values were underestimated (shown above). This result suggests that model simulations can capture some fundamentals of BC aging processes as a whole, namely, condensation and coagulation processes as well as production of coating materials.

[34] Figure 9a shows the dependence of the BC-free-to-total number concentration (BC-free/total) ratio on total dry diameter during the A-FORCE campaign, for both measurements (blue) and model simulations (red). Each data point and vertical bar shows the median and 25th–75th percentile range over all flights, respectively. In this figure, the definition of BC-free particles is consistent between measurements and model simulations (7). The observed BC-free/total ratio decreases with total dry diameter. Model simulations reproduced the decreasing tendency of BC-free/total ratio with particle diameter, although they slightly underestimated the number fraction of BC-free particles.

[35] Figures 9b and 9c show the ratio of thinly coated BC particles (SC ratio <1.1) and mean SC ratio during A-FORCE. Note that Figure 9a shows the dependence on total dry diameter, while Figures 9b and 9c show the dependence on BC core diameter. The observed ratio of thinly coated BC particles is almost constant or slightly increases with BC core diameter (Figure 9b). The observed mean SC ratio decreases with BC core diameter (Figure 9c). This is likely because larger amounts of coating materials are necessary to increase coating thickness by the same degree at larger BC core diameter. Model simulations generally reproduced the ratio of thinly coated BC particles. The dependence of the mean SC ratio on BC core diameter was also reproduced well, while the absolute values tended to be underestimated (shown above).

[36] We note that there are many uncertainties in our simulations and evaluations of BC mixing state. First, since coagulation is a highly nonlinear process with respect to number concentration and size distribution (other microphysical processes could also have nonlinearity), the results may change if model simulations were conducted with finer grid spacing. Second, the comparison of BC mixing state with measurements has some uncertainties. For example, in selecting the particles with a BC core diameter of 200 nm in the model simulations, we chose the bins that have the nearest mean BC core diameter for each mixing state bin. However, if there were two bins equally close to 200 nm (e.g., 150 and 250 nm), the BC mixing state at 200 nm could be largely different, depending on whether the smaller or larger bin was selected. In addition, the BC core diameter, which was calculated diagnostically, was assumed to have a single (mean) value in each bin in the model simulations (10). However, this assumption may not be necessarily correct in the real atmosphere. If we allowed some variability of BC core diameter in each bin, some particles in a bin could have smaller or larger BC core diameters than the mean value. This may lead to an increase/decrease in the number concentrations of internally mixed (BC core >75 nm, definition of the SP2) and BC-free particles (BC core <75 nm) when we compare with the SP2 (e.g., Figure 9a). Finally, there are some uncertainties in the SC ratio measurements, as shown in 7.

[37] Although these uncertainties cannot be eliminated from our simulations and evaluations, our model simulations generally reproduced the main features of BC mixing state in the measurements (e.g., BC-free ratio, diversity of SC ratio, mean SC ratio, and their temporal variations and diameter dependence). This result shows that the model can simulate realistic BC mixing states in the atmosphere if microphysical processes, such as condensation and coagulation, are calculated explicitly with the detailed treatment of BC mixing state.

4.3 Sensitivity of Microphysical Processes and Emissions to BC Mixing State

[38] We next evaluate the importance of the coagulation process and the initial mixing state of BC upon emission as a mechanism determining the BC mixing state of atmospheric particles. For this purpose, we have conducted two sensitivity simulations: 1) with the coagulation process switched off and 2) with some amount of BC emissions treated as internally mixed particles.

4.3.2 BC Mixing State Upon Emission

[42] All the BC emissions are assumed to be externally mixed particles in our base case simulation. However, there are some internally mixed BC particles even in the vicinity of emission sources in the real atmosphere. Figure 10 shows the mean frequency distribution of the SC ratio at a BC core diameter of 200 nm at an urban site in Tokyo (0300 UT–0700 UT). Measurements of ambient air using the SP2 were conducted at the Komaba campus of the University of Tokyo (35.65°N, 139.67°E) on 1 and 11 September 2009 (this campus is located near the center of the city and surrounded by heavy-traffic highways [Takegawa et al., 2006]; the details of this site can be found in previous articles [e.g., Takegawa et al., 2006; Kondo et al., 2010; Matsui et al., 2009b]). As shown in Figure 10, the fraction of thinly coated BC (SC ratio <1.1) is about 50% at this site. Strictly speaking, these results may not correspond to the SC ratio of emissions because ambient air masses are measured. However, it is clear that about 50% of BC particles are coated moderately (SC ratio >1.1), at least within the subgrid scale of our simulations.

[43] Based on these measurements, we conducted a sensitivity simulation in which some portions of BC emissions were assumed to be internally mixed particles. The fractions of externally mixed particles (SC ratio = 1.0) and internally mixed particles with SC ratios of 1.1, 1.2, 1.3, and 1.4 were assumed to be 50, 30, 10, 5, and 5% of the total BC emissions, respectively, for all size bins. The coating material was assumed to be POA. We also assumed that the amounts of BC-free emissions were the same as the base case simulation. This assumption is reasonable because the contribution of POA within the coatings (internally mixed BC) to total POA emissions is sufficiently small (<5% in general) in this simulation.

[44] Some measurements suggest that there are more internally mixed BC particles in biomass burning emissions [e.g., Kondo et al., 2011b]. The contribution of biomass burning emissions is estimated to be sufficiently small for air masses observed during the A-FORCE campaign (Matsui et al., submitted to Journal of Geophysical Research). However, the amounts of biomass burning emissions become large during spring over Southeast Asia and South China. In air influenced by biomass burning emissions, the portions of internally mixed BC particles may become larger than those in our sensitivity simulations.

[45] The green lines in Figure 9 show the results of BC mixing state during A-FORCE when internally mixed BC emissions were considered. The BC-free fraction (Figure 9a), thinly coated BC fraction (Figure 9b), and mean SC ratios (Figure 9c) have similar diameter dependencies between the sensitivity and base simulations. On the other hand, the absolute values increased/decreased by changing the treatment of BC mixing state of the emissions. The BC-free fraction (median) decreased by 15% (from 0.75 (base simulation) to 0.65 (sensitivity simulation)) at a particle diameter of 300 nm. The thinly coated BC fraction and coating thickness (SC ratio – 1) (median) decreased by 40% (0.17–0.10) and increased by 36% (0.26–0.35), respectively, at a BC core diameter of 200 nm. Compared with the base case simulation, the thinly coated BC fraction and mean SC ratio have better agreement with measurements in the sensitivity simulation, while the BC-free fraction is more underestimated. Although not all the discrepancies between measurements and the base case simulation can be explained by the BC mixing state of the emissions, the mixing state of the emissions is found to be an important factor to understand the BC mixing state of atmospheric particles more quantitatively. A sub-grid-scale treatment of BC aging processes will therefore be important for calculations with coarse spatial resolution, such as global modeling studies.

4.4 Spatial Variability of BC Mixing State

[46] Since model simulations generally reproduced the main features of BC mixing states during the A-FORCE campaign, we briefly describe the spatial distributions of the BC mixing state over East Asia during the simulation periods to examine aging processes around source regions and during transport to downwind areas. Figures 11a–11f show snapshots of total aerosol mass concentrations (PM_2.5) and mean SC ratios at a BC core diameter of 200 nm and sigma level of 0.91 (~1 km in altitude) at 0300 UT on 4, 6, and 8 April. A plume of high aerosol mass concentration was seen over North China on 4 April (Figure 11a). This plume was transported southeastward from behind a cold front with an increase in aerosol mass concentration. Then, the plume was transported to the Yellow Sea by 6 April (Figure 11c) and to Japan by 8 April (Figure 11e). The plume was a cause of high BC mass concentrations observed at the Fukue site on 8 April (10, Figure 4a). The spatial distributions of the mean SC ratio correlate with those of PM_2.5 concentrations: high SC ratios are seen over the regions where PM_2.5 concentrations are high. The mean SC ratio within the plume was 1.3–1.4 on 4 April and gradually increased up to 1.6–1.8 by 8 April. These results suggest that the spatial and temporal variations of BC mixing state (SC ratio), as well as those of aerosol mass concentrations, are controlled regionally by synoptic-scale meteorological variations over East Asia and the western Pacific.

[47] To examine aging processes of measured air masses at Fukue from a Lagrangian viewpoint, 5-day backward trajectories were calculated by using the National Institute of Polar Research (NIPR) trajectory model [Tomikawa and Sato, 2005] combined with NCEP FNL data. One hundred twenty-five trajectories were released at 0300 UT on 8 April from around the Fukue site (5 longitudes (128.48°E–128.88°E) × 5 latitudes (32.55°N–32.95°N) × 5 vertical levels (930–970 hPa)). Among these trajectories, Figure 12a shows the trajectories transported within the planetary boundary layer (>800 hPa) during the 5-day calculation periods. The transport pathways of trajectories are generally consistent with those of the plume shown in Figure 11. Figure 12b shows the temporal variations of mean SC ratio along the backward trajectories. The mean SC ratio within the air masses gradually increased from 1.3 to 1.7 during the transport from North China (3 April) to the Fukue site (8 April).

[48] Figure 13 shows the spatial distributions of PM_2.5 concentrations, thinly coated BC fraction, mean SC ratio, and frequency of high values of mean SC ratio (>1.2) at a sigma level of 0.91 (~1 km in altitude) at noon during the simulation periods. PM_2.5 concentrations are the highest over North and Central China (25°N–40°N) (Figure 13a), and aged BC particles (with low thinly coated BC fraction and high SC ratio) are seen at 30°N–40°N over China, the Yellow Sea, and the East China Sea (Figures 13b and 13c). These distributions are likely because 1) emissions are the highest over North China and 2) aged polluted air masses are frequently transported from North China to the Yellow Sea and the East China Sea by synoptic-scale meteorological variations, as shown above (Figure 11). Model simulations suggest that most BC particles at 30°N–40°N had already experienced aging processes sufficiently over the Asian continent (Figures 13b–13d).

5.1 Off-line Calculations of Optical and Radiative Parameters

[50] We conducted off-line sensitivity calculations of optical parameters and radiative transfer using the results of mass and number concentrations in the base case simulation (12 × 10 aerosol bins). Local aerosol optical properties were calculated using the Mie theory algorithm developed by Bohren and Huffman [1998]. The shell-core treatment (BHCOAT) was used for internally mixed BC particles, while the code for well-mixed particles (BHMIE) was applied to pure BC and BC-free particles. The calculations were made for four wavelengths (300, 400, 600, and 999 nm), which are the same as the on-line calculations of optical properties in the WRF-chem model [Fast et al., 2006; Barnard et al., 2010]. Using these local aerosol optical properties, off-line radiative transfer calculations were made using the Goddard shortwave scheme (two-stream adding method based on Chou [1992]), which is implemented in the WRF-chem model. All the calculations were performed for clear-sky conditions. The off-line optical and radiative calculations were conducted for the following three treatments of aerosols and mixing states (Table 1): (1) optical properties were calculated for each of the 12 × 10 aerosol bins (multiple BC mixing state for each size bin) as in the base case simulation (Detailed-MS), and therefore they are used as the benchmark, (2) optical properties were calculated with the size dependence only (12 × 1 aerosol bins), and the average mixing state of aerosols was estimated for each size bin using the mass and number concentrations summed over all mixing state bins (Simple-MS), and (3) radiative effects were calculated without aerosols (No-aero). The sensitivity of the BC mixing state can be estimated by the comparison between Detailed-MS and Simple-MS calculations. Since both the Detailed-MS and Simple-MS calculations are made using the mass and number concentrations calculated in the base case simulations (12 × 10 aerosol bins), total mass concentrations of each species and total number concentrations are identical between these two off-line calculations.

[51] Figures 14a and 14b show the spatial distributions of period-averaged SSA at a wavelength of 600 nm and sigma level of 0.91 (~1 km in altitude) at noon for both Detailed-MS and Simple-MS. Detailed-MS calculations have higher SSA values than Simple-MS calculations over the whole domain. This result is consistent with the results of Oshima et al. [2009b]. The period- and domain-averaged SSA at noon are 0.922 and 0.892 for Detailed-MS and Simple-MS calculations, respectively (Table 2). Since aerosol optical depth (AOD) is almost identical between the two calculations (not shown), these results show that the absorption coefficient was overestimated by 40% (0.108/0.078) over East Asia when a single BC mixing state was assumed for aerosol optical calculations for the case we examined here.

[52] Figures 14c and 14d show the spatial distributions of the period-averaged heating rate by aerosols at a sigma level of 0.91 (~1 km in altitude) at noon. Heating rates reached more than 1.0 K/day over China for both the Detailed-MS and Simple-MS calculations. The period- and domain-averaged heating rates by aerosols at noon are 0.323 and 0.423 K/day for the Detailed-MS and Simple-MS calculations, respectively (Table 2). Therefore, the heating rate by aerosols was overestimated by 30% (0.423/0.323) in our calculations when a single BC mixing state was assumed for the radiation calculations.

[53] Figures 14e and 14f show the spatial distributions of the period-averaged change in downward shortwave radiative flux by aerosols at the surface (the difference between radiative flux with and without aerosols, i.e., aerosol radiative forcing) at noon. The absolute values of aerosol radiative forcing at the surface were estimated to be 50–60 W m^–2 over China and 20–40 W m^–2 over the Yellow Sea and the East China Sea for both Detailed-MS and Simple-MS calculations. The higher values in the Simple-MS calculations were likely because a higher absorption coefficient may have led to a decrease in the multiple scattering of radiation. The period- and domain-averaged aerosol radiative forcing (absolute values) at noon are 24.8 and 27.7 W m^–2 for Detailed-MS and Simple-MS calculations, respectively (Table 2). These results suggest that the absolute values of aerosol radiative forcing were overestimated by 12% (27.7/24.8) when a single BC mixing state was assumed for the radiation calculations. The degree of overestimation of the aerosol radiative forcing is smaller than that of the SSA and heating rate by aerosols likely because the fraction of BC to total aerosol mass concentrations is small (about 10%) within the simulation domain.

[54] These results show that the treatment of BC mixing state has a large impact on the optical properties of aerosols and radiative effects by aerosols. In Appendix A2, we show the dependence of the absorption coefficient on the number of mixing state bins (types) used in the optical calculations. These results suggest that 4 or 5 bins (types) for the BC mixing state are necessary in each size bin to estimate the radiative impact of aerosols with reasonable accuracy.

5.2 Overall Impact of BC Mixing State

[55] In this section, we examine the overall impact of BC mixing states on both radiative and removal processes. We conducted a sensitivity simulation using the WRF-chem model with the simple mixing state treatment (12 × 1 aerosol bins), and the off-line optical and radiative calculations (17) were applied to these simulation results (“All-Simple-MS” state in Table 1).

[56] Figure 15 shows the vertical profiles of BC mass concentration for both the base case and the sensitivity simulations on period and domain average. The concentration ratio of two simulations (All-Simple-MS/Detailed-MS) is also shown. The base case (detailed treatment of mixing state) tends to have higher BC mass concentrations than the sensitivity simulation (simple treatment of mixing state). This is likely because some fraction of BC was pure or thinly coated BC particles (lower hygroscopicity and removal efficiency) in the base case (Detailed-MS), while all the BC particles were simulated as internally mixed in the sensitivity simulation (All-Simple-MS). Since the hygroscopicity of BC (κ = 1e-6) is significantly smaller than that of other species (κ = 0.5 for inorganic species) in the model, aerosols having higher BC mass fractions are not activated efficiently, leading to less BC wet removal in the Detailed-MS calculations (compared with the All-Simple-MS calculations). The BC concentrations were underestimated in the All-Simple-MS calculations by 15–20% in the planetary boundary layer and up to 35% in the upper troposphere. This result suggests that the detailed BC mixing state representation is necessary to calculate BC transport to the free troposphere accurately. In contrast to BC mass concentrations, the mass concentrations of other species generally agreed to within 10% between the two simulations (not shown).

[57] The period- and domain-averaged SSA (600 nm) and heating rates by aerosols at noon are 0.907 and 0.355 K for the All-Simple-MS calculations at a sigma level of 0.91 (~1 km in altitude). These values are higher than in the Detailed-MS calculations, but lower than the Simple-MS calculations (Table 2). Specifically, the overestimations were reduced to 20% for the absorption coefficient and 10% for the heating rate by aerosols (30–40% in the Simple-MS calculations, 17) when all the parameters (including mass and number concentrations) were calculated with the simple treatment of mixing state (All-Simple-MS). This is because the overestimation of radiative parameters due to higher absorption efficiency (assumption of internally mixed BC) was largely canceled by the underestimation of BC concentrations (efficient wet removal processes) in the All-Simple-MS calculations (compared with the Detailed-MS calculations). The aerosol radiative forcing at the surface (period- and domain-average) estimated in the All-Simple-MS calculations was almost identical to that in the Detailed-MS calculations (–24.8 W m^–2) because of this cancellation, but for the wrong reasons. The cancellation of these two opposite effects (absorption and removal effects) will work in other model calculations if a simple treatment of BC mixing state is adopted (size dependence only).

[58] Finally, our model does not consider cloud-aerosol interactions for convection (sub-grid-scale wet removal), as shown in 2. Since our simulations are made with coarse grid spacing, wet removal amounts of aerosols may have some biases. Finer model simulations are important for understanding the removal effects of BC mixing state more quantitatively.