A study of uncertainties in the sulfate distribution and its radiative forcing associated with sulfur chemistry in a global aerosol model

Introduction Conclusions References


Introduction
Secondary aerosols are formed from their precursor gases in the atmosphere through condensation and nucleation processes after oxidation.They have various components such as sulfate (SO 2− 4 ), ammonium, nitrate, and a part of organic matter (secondary organic aerosol; SOA).Most secondary aerosols are considered to be major anthropogenic aerosols (e.g.Seinfeld and Pandis, 1998).Also, they can become cloud condensation nuclei (CCN) and may have a large impact on the earth's radiation budget through the aerosol indirect effect (e.g.McFiggans et al., 2006).Proper estimates of the radiative impact due to the anthropogenic aerosols, therefore, need accurate modeling studies to predict the secondary aerosols.Schulz et al. (2006) presented the AEROCOM model inter-comparison of anthropogenic aerosol direct radiative forcings calculated by nine global aerosol models.They showed that the magnitudes of the radiative forcing due to total anthropogenic aerosols range from +0.04 W m −2 to −0.41 W m −2 .Also they showed that the radiative forcing due to anthropogenic sulfate aerosol is estimated to be between from −0.16 W m −2 to −0.58 W m −2 ; this range is larger than those due to black carbon (BC) and organic carbon (OC) aerosols.This comparison suggests that a large portion of the differences in the radiative forcings of total anthropogenic aerosols among models still stem from modeling of the radiative forcing due to sulfate component.4 )m −2 and aerosol direct radiative forcing due to anthropogenic sulfate aerosols under the all-sky condition at the top of atmosphere (y-axis) in Wm −2 and (b) between fraction above 5 km to the sulfate column burden (x-axis) in percentage and aerosol direct radiative forcing due to anthropogenic sulfate aerosols under the all-sky condition at the top of atmosphere (y-axis) in Wm −2 .The all data in closed circles in black are given by Schulz et al. (2006) and Textor et al. (2006).
The closed and open circles in red represent the result in this study and the original SPRINTARS.
Figure 1 shows scatter plots to show relations of global annual mean values of sulfate column burden and sulfate fraction above 5 km to its column burden with the aerosol direct radiative forcing due to anthropogenic sulfate aerosols using the AeroCom data from Textor et al. (2006), Schulz et al. (2006) and the present study.The figure can help us to understand how the relations among these key quantities are scattered showing that models still have problems in realistic simulation of the radiative forcing due to problems in modeling of both the sulfate burden and stratification.Figure 1a shows an obvious tendency that the aerosol direct radiative forcing increases as the sulfate column burden increases, though the rate of increase differs among models.Most sulfate aerosols are scavenged below 5 km, so that there is a model tendency of increasing sulfate column burden with increasing sulfate fraction above 5 km.In Fig. 1b, however, we do not find any systematic tendency between the aerosol direct radiative forcing and the sulfate fraction above 5 km if we include all the data points, reflecting the fact that a change in the height of a non-absorbing aerosol layer does not cause a noticeable change in the radiative forcing at the top of atmosphere.The results given by Fig. 1 lead us to a conclusion that uncertainties in the radiative forcing due to anthropogenic aerosols among global aerosol models are largely derived from the differences in the sulfate column burden and to a lesser extent in its vertical distribution.
Moreover, a detailed investigation of the results suggests that the different sulfate distributions among global aerosol models possibly come from model differences in both formation and loss processes.The major formation process of sulfate is that sulfur dioxide (SO 2 ), as a precursor for sulfate, is oxidized in the atmosphere and turns to sulfuric acid and then to a particle through condensation or nucleation pro-cesses.The major loss process of sulfate has been considered to be wet deposition because of its typical size ranging from 0.1 to 1 µm with its high CCN efficiency (e.g.Rasch et al., 2000).Most global models adopt a similar method for the wet deposition, i.e. in-cloud and below-cloud scavenging, using the ratio of the aerosol in the cloud to that in the interstitial phase and use similar magnitudes of the ratio (Textor et al., 2006).This suggests the wet deposition modeling is likely not the major reason for the difference in the sulfate distribution, whereas a difference in the cloud and precipitation process modeling can be one of the major reasons.In addition, a difference of the transport is beyond this study.
The other problem is the difference in the sulfate formation process.Since Langner and Rodhe (1991) first published the global sulfur cycle model, sulfur chemistry modeling studies indicate that the major process of the sulfate formation is the SO 2 oxidation in the aqueous phase by hydrogen peroxide (H 2 O 2 ) and ozone (O 3 ) (e.g.Roelofs et al., 2001).Figure 2 shows ratios between wet deposition flux and sulfate production rate in the aqueous-phase oxidation in global annual averages using results obtained by various global aerosol models.We can expect that the removal amount of SO 2 from the atmosphere increases as the ratio decreases when the sulfate production remains the same.In Fig. 2, the GISS and SPRINTARS models, which also have lower sulfate column burden as shown in Schulz et al. (2006), show substantially low values of the ratio to the other models.As a result, the difference in the modeling of SO 2 production in the aqueous phase can cause the difference in the sulfate distribution.
The question now arises: What is the main reason causing the differences in the aqueous-phase sulfur chemistry?One of the possible reasons is that the method of simplification of the process, which is necessary with limited computer burden allocated in the global aerosol model computation, is different among global aerosol models.It is important to quantify the impact of this simplification by comparing against models with more physical, and/or complex, representation of the sulfur cycle.The algorithms adopted in a global aerosol model SPRINTARS (Takemura et al., 2000(Takemura et al., , 2002(Takemura et al., , 2005) ) are described in Sects. 2 and 3. Investigation of impacts of different methods for sulfate formation is shown in Sect. 4. Sulfate distributions are computed in Sect. 5 and 6 with a more physical-based method in order to compare with observations.A discussion of the impact on aerosol direct radiative forcing is given in Sect.7.

Sulfur process
In most three-dimensional global aerosol models, three pathways of sulfate formation are considered (e.g.Textor et al., 2006).The first path is aqueous-phase oxidation of SO 2 by H 2 O 2 and O 3 .The second one is gas-phase oxidation of SO 2 by hydroxyl radical (OH).The third one is oxidation of dimethylsulfide (DMS), which is emitted naturally from marine phytoplanktons.The products in the oxidation are SO 2 and methanesulfonate (MSA).MSA is also an aerosol but its burden is much smaller than that of sulfate (e.g.Heinzenberg et al., 2000;Prospero et al., 2003).The other sources of SO 2 are industrial and human activities through fossil fuel combustion and forest fire through biomass burning.The SO 2 in the atmosphere is removed typically within one to three days by oxidation and wet and dry deposition processes (e.g.Seinfeld and Pandis, 1998;Barrie et al., 2001).All formed sulfate is assumed to exist in the particle phase because sulfuric acid has a low vapor pressure (e.g.Seinfeld and Pandis, 1998).Due to the small size and the high hygroscopicity, the wet deposition for sulfate aerosol is a major removal process in the atmosphere compared to the dry deposition (e.g.Rasch et al., 2000).
As suggested in Sect. 1, a difference in the aqueous-phase sulfur chemistry among global aerosol models can be a key to understand a difference in the sulfate simulation.The aqueous-phase sulfur chemistry includes SO 2 aqueous-phase oxidations whose treatment is largely different depending on models.The treatment includes a numerical solution in the oxidations, an integrated time resolution in the aqueousphase process, and a value of pH in the aqueous-phase.To save the amount of CPU time, the most simplified way to treat these processes in the model is to use an approximation in a quasi first-order reaction of the SO 2 aqueous-phase oxidations, a same time resolution as that in the transport model, and a fixed pH value in the calculation (e.g.Takemura et al., 2000).Similar kinds of approximation in the aqueousphase sulfur chemistry and other sulfur processes are adopted by most of global aerosol models (e.g.Textor et al., 2006).Physically based methods (e.g.Feichter et al., 1996;Boucher et al., 2002) set the timestep in the aqueous-phase chemical reaction to be shorter than that in the transport model, while simplified methods (e.g.Chin et al., 2000;Takemura et al., 2002) set the same time resolution in both the aqueous-phase chemistry and the transport model.For oxidants, i.e.O 3 , H 2 O 2 , and OH radical, physically based methods (e.g.Easter et al., 2004;Tie et al., 2005) calculate them with onlinecoupling to chemistry, while simplified methods (e.g.Barth et al., 2000;Koch et al., 2006) use their offline distributions.For dry deposition, physically based methods (e.g.Liu and Penner 2002;Gong et al., 2003) treat all components of the resistance using Zhang et al. (2001), while simplified methods (e.g.Rasch et al., 2000;Pitari et al., 1993Pitari et al., , 2002) ) assume the constant rate of the dry deposition.As shown in Textor et al. (2006), global aerosol models also include an offline calculation of oxidants, i.e.O 3 , H 2 O 2 and OH radical and a simplified dry deposition of gases and aerosols.Therefore, we show both these simplified and physically-based methods in the following subsections.

Treatment of the sulfur aqueous-phase processes
Two numerical solutions for aqueous-phase sulfur chemistry of global aerosol models are described here.In the approximation in the quasi first-order reaction, a change in the sulfate concentration during time dt is expressed as follows: www.atmos-chem-phys.net/11/10889/2011/Atmos.Chem.Phys., 11, 10889-10910, 2011 where k is the reaction rate, which is set to the same value as Takemura et al. (2000), and terms [SO 2 (aq)] and [H 2 O 2 (aq)] are aqueous-phase concentrations of SO 2 and H 2 O 2 , respectively.In the simplified method, the sulfur system is assumed to be an open system, which means the H 2 O 2 concentration in the aqueous-phase is always assumed to be constant as where the term of [A](t) means the concentration of a matter A at time t.In the case of SO 2 oxidation by O 3 , the expression of the sulfate concentration at time t is also similar to that in the SO 2 oxidation by H 2 O 2 .
On the other hand, the sulfur system can be treated more realistically by a closed system, i.e.H 2 O 2 concentrations in the aqueous-phase are changed by supply from the gas-phase and by loss in the liquid phase.In this system, the sulfate concentration is expressed by an analytical expression of the second-order reaction of SO 2 with H 2 O 2 as follows: when concentrations of H 2 O 2 and SO 2 are equal to each other.Otherwise, it follows: In the present study we set two sulfur process models, i.e. a simplified model used in the original SPRINTARS model and a more physical-based model with use of Eqs.(3) and (4).We hereafter call these two models original model and improved model.A resolution for time integration is also critical for the aqueous-phase sulfur chemistry.Soluble gases such as SO 2 , H 2 O 2 and O 3 in the atmosphere can be partitioned into gas and aqueous phases according to Henry's law.Henry's law equilibrium between gas and aqueous phases occurs typically within one second (Hobbs, 2000).In addition the SO 2 in the aqueous phase reacts so rapidly with H 2 O 2 that the time resolution to integrate the aqueous-phase chemical reaction equations should be finer (e.g.Seinfeld and Pandis, 1998).The timestep, for example, is set to two minutes in Boucher et al. (2002), four minutes in Feichter et al. (1996), ten minutes in Liao et al. (2003), and twenty minutes in Takemura et al. (2000).We thus introduce a sub-cycle calculation by dividing the timestep of general circulation model (GCM), which is typically several tens of minutes, into two minute sub-intervals for solving Eqs. ( 3) and (4) (see Fig. 3).During the calculation in the sub-cycle, the gas-phase concentrations of SO 2 and oxidants are changed only through Henry's law equilibrium.Oxidation of SO 2 by O 3 is also considered and is calculated just after the oxidation of SO 2 by H 2 O 2 .It should be noted that the order of the calculations affects the resulting sulfate concentration and impact on the annually averaged sulfate concentration near the surface and sulfate column burden by 5 % and 10 %, respectively.
A pH value in the aqueous-phase sulfur chemistry is fixed in the most simplified methods.In the present study the pH value can be given as, where , and [HSO − 3 (aq)] are hydrogen, sulfate, and sulfurous acid concentrations in the aqueous phase, respectively.In the typical pH range (4.0-5.6), the sulfurous acid concentration in the aqueous phase is equal to dissolved SO 2 concentration in the aqueous phase (e.g.Seinfeld and Pandis, 1998).The term [H + 0 ] is the hydrogen concentration under the condition of no sulfur components and is estimated to be 10 −5.6 .The term f 1 is a tunable factor set to 0.1 in the present study and the result of global pH distribution is shown in Fig. S1 in the Supplement.The weak dependence of the pH on the sulfur components is a better expression than the globally fixed pH, so that our improved method assumes the variable formulation of pH by Eq. (5).

Treatment of oxidants used in the sulfur chemistry
In global aerosol models, oxidants related to the sulfur chemistry are often prescribed using results from chemical transport models (e.g.Textor et al., 2006).Simulating the aerosol distribution with offline oxidant distribution is very effective to decrease the amount of CPU time, but may increase an error in the sulfate simulation.In this respect, the most important oxidant to be accurately assumed is probably H 2 O 2 because the H 2 O 2 can strongly affect the aqueous-phase concentration of SO 2 (e.g.Koch et al., 1999).This offline use of H 2 O 2 produces an overestimation of supply H 2 O 2 to sulfur oxidations and then an overestimation of sulfate aerosol particularly in wintertime urban areas (e.g.Roelofs et al., 1998).In winter, wet deposition of H 2 O 2 is known to be the most dominant loss process of H 2 O 2 because both OH concentration and actinic radiation are low.Therefore, the wintertime H 2 O 2 concentration strongly depends on clouds and precipitation.On the other hand, the H 2 O 2 variability caused by clouds and precipitation is neglected in the simulation using the offline H 2 O 2 distribution.Furthermore, H 2 O 2 at low temperature prefers to be in the aqueous phase according to Henry's law.Therefore, using the offline H 2 O 2 distribution will cause overestimation of the wintertime H 2 O 2 .To eliminate this overestimation in winter, the H 2 O 2 in the present improved model is treated as a prognostic tracer like in other The SO 2 in yellow and aqua represent SO 2 in the gas-phase and in the aqueous-phase, respectively.The pink, aqua, blue, and red circles correspond to the process of gas-liquid phase equilibrium through Henry's law, wet deposition, sulfate production reaction, and loop for the calculation in a sub-cycle timestep, respectively.modeling studies (Roelofs et al., 1998;Koch et al., 1999;Barth et al., 2000;Boucher et al., 2002).In the atmosphere, the H 2 O 2 is produced via hydroperoxyl radical (HO 2 ): where M represents a third body, which mainly represents water vapor and nitrogen gas.The H 2 O 2 is depleted via photo-association: where hv represents a dissociation energy, which is provided by the results from a chemical transport model, CHASER by Sudo et al. (2002), which has been implemented in the MIROC AGCM, every three hour.The H 2 O 2 is also depleted via OH: The reaction rates in Reactions (R1) and (R3) are estimated by Pitts and Pitts (1999).The other loss pathways for the H 2 O 2 are dry and wet deposition processes and oxidation of SO 2 in the aqueous-phase.The contribution of the latter process to the total loss process is so small that it is not considered for H 2 O 2 cycle in this study.
Other oxidants (O 3 and OH) are still calculated offline in this study, because their concentrations are relatively less important than those of H 2 O 2 (e.g.Roelofs et al., 1998) and their predictions are beyond the scope of our study.

Dry deposition module for sulfur components
The dry deposition process is important as a loss process of aerosols and their precursors.Modeling of this process also varies widely among global aerosol models (Textor et al., 2006).Basically, the flux for dry deposition can be expressed as a product of a dry deposition rate and a mass mixing ratio.The dry deposition rate is determined by the following three resistances: (1) aerodynamic resistance, R a , (2) quasi-laminar layer resistance, R b , and (3) surface or canopy resistance, R c (Seinfeld and Pandis, 1998).For particles, it is written by Seinfeld and Pandis (1998) and Zhang et al. (2001) as follows: where V s is the gravitational settling velocity.For gases, it is written by Seinfeld and Pandis (1998) as follows: Generally speaking, the dry deposition process is very effective for gases and coarse particles, whereas it is relatively unimportant for fine particles (Seinfeld and Pandis, 1998).At the same time, the dry deposition for gases is mainly determined by both R a and R c and that for fine particles is mainly determined by R b (Seinfeld and Pandis, 1998).The R b depends on a surface condition as in Zhang et al. (2001) for sulfate particles and in Wesely (1989) for SO 2 .Especially the R c for SO 2 can be calculated in principle in the model using the surface condition and the plant variability.Some models, however, ignore the R c in Eq. ( 7) to decrease the  a Values are aerosol growth factors, defined as the size changes of the particles, as a function of relative humidity (RH).b The hygroscopicity is set the same in Takemura et al. (2005).
c OA represents organic aerosols including POA and BSOA.The POA and BSOA have the same hygroscopicity as given by Takemura et al. (2002Takemura et al. ( , 2005)).amount of CPU time as in the original model in the SPRINT-ARS model (Takemura et al., 2000).On the other hand, the present improved model use above described dependences using the monthly distributions of R c , which is given by offline calculation of the CHASER model.

Dry deposition module for sulfur components model description for SPRINTARS
In this study, we use a global three-dimensional aerosol transport-radiation model, Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS), which is described in Takemura et al. (2000Takemura et al. ( , 2002Takemura et al. ( , 2005)) On the other hand, for POA, BSOA and sulfate aerosols, the dry mode radii are set to 0.1, 0.08 and 0.0695 µm, respectively (Takemura et al., 2005;Goto et al., 2008).These parameters and others are listed in Tables 1 and 2.
The emission inventories for 2000 for aerosols, with their precursors and oxidants, except for a precursor of BSOA and SO 2 are those described by Takemura et al. (2005).The precursor gas of BSOA is assumed to be biogenic monoterpene (C 10 H 16 ), which is obtained from the Global Emissions Inventory Activity (GEIA) database (Guenther et al., 1995), and its diurnal emission variation is calculated using temperature dependences.The anthropogenic SO 2 emission flux in 2000 used in this study is interpolated from: the EMEP emission inventory (http://webdab.emep.int/)over Europe, Streets et al. (2003) over Asia, and Takemura et al. (2005) in other regions.For comparison with the AEROCOM results, we also use the SO 2 emission inventory by Dentener et al. (2006).The SO 2 emission from continuous volcanic eruptions is based on the GEIA database and the SO 2 emission from biomass burning is based on the GEIA database and Spiro et al. (1992).The DMS emission flux is calculated using an empirical relation reported by Bates et al. (1987) as in Takemura et al. (2002) and Sudo et al. (2002).To predict the H 2 O 2 mixing ratio in our improved method, offline data for three-hour averaged HO 2 and hv are calculated by a chemical transport model, CHASER (Sudo et al., 2002).Other oxidants (O 3 and OH) distributions are also derived from the CHASER model.
The aerosol transport processes include emission, advection, diffusion, sulfur chemistry, wet deposition and gravitational settling.The radiation scheme, MSTRN-8, in the MIROC AGCM can handle scattering, absorption, and emission by aerosol and cloud particles, as well as absorption by gaseous constituents and can calculate the aerosol direct effect (Nakajima et al., 2000).The aerosol direct radiative forcing due to anthropogenic aerosols is calculated as the difference in net fluxes with and without anthropogenic aerosols under the same meteorological conditions by the method of Takemura et al. (2005) and Goto et al. (2008).Although the model can calculate the radiative forcing under the clear-sky and the all-sky conditions at any vertical levels, in this paper we show only the results under the all-sky conditions at the top of atmosphere (TOA) to discuss the sensitivity of the radiative forcing among different methods.For calculation of the aerosol indirect effect, we diagnose cloud droplet number concentration, liquid water content (LWC), and cloud droplet effective radius as described elsewhere (Suzuki et al., 2004;Takemura et al., 2005;Goto et al., 2008).
All experiments use the monthly-averaged global distributions for sea surface temperature and sea ice are provided by the Hadley Centre, UK Met Office (Rayner et al., 2003).

Sulfate simulation with original and improved methods
In this section, we investigate differences in sulfate simulation between original and improved methods of treating sul-fur chemistry.The results are studied in order to evaluate the effect of following five elements: (1) method of the solution for the aqueous-phase sulfur chemistry, (2) timestep to solve the aqueous-phase sulfur chemistry, (3) pH calculation in the aqueous-phase, (4) treatment of H 2 O 2 as a prognostic variable, and (5) dry deposition process of sulfur components.The summaries of the experimental conditions and the results are described in Tables 3 and 4, respectively.Among the results of Q1ST, the largest value of the annually averaged RB of the sulfate concentrations near the surface is shown over the polluted areas with ranges of +100.7 % to +165.7 %, as shown in Table 4.These values are much larger than those in the results of C2ND, because of the assumption of excess supply of H 2 O 2 in the aqueous-phase as shown in Fig. 4.
For the sulfate column burden, on the other hand, the annually averaged RBs are estimated to be minus almost over the world with the global mean value of −26.3 % in Q1ST and −11.9 % in C2ND, respectively, because of underestimated sulfate concentrations at upper heights (above boundary layers) caused by a lack of H 2 O 2 in the aqueous-phase in Q1ST as shown in Fig. 4. As a conclusion, the method with Q1ST largely overestimates the predicted sulfate concentration near the surface and the differences in the sulfate concentration between Q1ST and C2ND are much larger than those between C2ND and CTL.At the same time, the substitution of the quasi first-order solution by the second-order reaction increases the sulfate column burden all over the world except China.As mentioned later, this difference in the simulated sulfate column burden is the largest among all modifications of the sulfur processes in this study.

Timestep to solve the aqueous-phase sulfur chemistry
The timestep to solve the SO 2 oxidation process in the aqueous-phase is also critical to determine the accurate sulfate production.Theoretically, the timestep dt in Eqs. ( 3) and ( 4) is required to be very short because both the oxidation rate of SO 2 by H 2 O 2 and the rate of Henry's law equilibrium are very fast (e.g.Seinfeld and Pandis, 1998).On the other hand, the timestep in the model is limited by resulting computer burdens of the GCM calculation.Therefore, the sensitivity tests for different timesteps are required to determine the optimized ones for fast yet accurate simulation.The smallest timestep among GCMs is two minutes, so that the standard experiment in this study sets to two minutes (dt = 120 s).For the sensitivity experiments, timesteps are set to dt = 600 s, 240 s, 60 s, and 30 s.These values in the sensitivity experiments are used in the sulfur chemistry in other global aerosol models (e.g.Feichter et al., 1996;Boucher et al., 2002).Firstly, we conduct sensitivity experiments using a box model to calculate the aqueous-phase sulfur chemistry.In polluted areas where concentrations exceed 1 ppbv for SO 2 , 3 ppbv for H 2 O 2 , and 30 ppbv for O 3 concentrations, the RB values are estimated to be −47 % (dt = 600 s), −14 % (240 s), +3 % (60 s), and +3 % (30 s), respectively.The results indicate that longer timesteps decrease predicted sulfate formations due to insufficient supply of gases, especially SO 2 , from the gas-phase through Henry's law equilibrium.And the results also show that the timestep is enough to be equal to or less than 120 s.Secondly, we calculate global sulfate concentrations with various timesteps as shown in Table 4 under the experimental condition described in Table 3. Difference in the column burdens of simulated sulfate between experiments with the different timesteps is caused by differences in sulfate production rates under lower SO 2 concentrations, as suggested in the previous subsection.In the simulation with dt = 240 s (DT240 in Tables 3 and 4), the annually and globally averaged RB value of the sulfate concentration near the surface is estimated to be less than 5 %.The magnitude of the RB is smaller than that obtained by the box model calculation, because the aqueous-phase reaction occurs only in a cloudy area in the global calculation.The additional computer burden caused by using 120 s instead of 240 s is es-timated to be less than 1 %.Therefore, the timestep of 120 s is applicable in the global aerosol model and hence it is used in our improved model.

pH calculation in the aqueous phase
The pH in the aqueous phase is also critical to determine not only the reaction rate in the SO 2 aqueous-phase oxidation but also Henry's law equilibrium of the gases.At the same time, dissolved ions into aqueous phase through Henry's law determine the pH value.Therefore, the pH is an important variable that should be monitored to properly solve the SO 2 aqueous-phase oxidation.In most global aerosol models including the original SPRINTARS, the pH values are fixed and set to be 4.5 (Koch et al., 1999;Adams et al., 1999;Park et al., 2004;Easter et al., 2004;Liu et al., 2005) or 5.6 (Takemura et al., 2000).In polluted areas, for example, an acidity in the aqueous-phase is determined by a balance between cations and anions; therefore the pH value over polluted areas is lower than that over remote oceans due to abundance of sulfate.In order to calculate the change in pH, the pH value in this study is calculated online depending on several ion concentrations as in other studies (Feichter et al., 1996;Boucher et al., 2002;Sudo et al., 2002;Liao et 2003).The ion components considered are different from each model, so that the expression for the pH is different.In the improved method of this study, we calculate the pH value using Eq. ( 5) as shown in Sect. 2. The annually averaged pH value in low-level clouds is lowest in polluted areas with a range of 4.2-5.0 and highest in remote oceans with a range of 5.4-5.6, as also shown in Fig. S1 in the Supplement.
Next, sensitivity tests are performed by giving two different pH prescriptions at 4.5 and 5.6.We calculate the RB using the result with Eq. ( 5) as CTL.The annually averaged RB values of global sulfate concentrations near the surface are estimated to be −6.4 % (pH 4.5) and +1.5 % (pH 5.6), respectively, as shown in Table 4.The signs of the RB values are reasonable because a decrease in the pH causes a decrease in the sulfate production (e.g.Seinfeld and Pandis, 1998).The magnitude of the RB on a global scale is almost the same as that in the polluted areas.In the north Pacific polluted by anthropogenic aerosols from East Asia, the annually averaged RB values of surface sulfate concentrations are estimated to be −5.2 % (pH 4.5) and −3.6 % (pH 5.6), respectively.These results indicate that a slight decrease in the pH from 5.6 to 4.5 causes a slight decrease in the sulfate concentration everywhere and use of the variable pH will cause a decrease in the sulfate concentration in polluted areas and an increase in the sulfate concentration in outflow areas.The changes in the simulated sulfate concentrations over polluted and outflow areas bring results slightly closer to the observed values compared to those with the fixed pH method in the original SPRINTARS, which overestimates the sulfate column burdens over polluted areas and underestimates them over outflow areas as reported by Takemura et al. (2000).Furthermore, another sensitivity experiment is carried out using the variable pH method of Feichter et al. (1996), which assumes the relation [ as shown in results of PHF96 in Table 4. Differences in the simulated sulfate concentrations both at the surface and in the column all over the world between PHF96 and CTL are less than 3 %.In summary, the results with the variable pH expression, Eq. ( 5) in this study, are slightly better than those with the fixed pH of 5.6 and the additional computer burdens for the pH calculation are negligible, so the variable pH method with Eq. ( 5) can be applicable in the global aerosol model.

Treatment of H 2 O 2 as a prognostic variable
H 2 O 2 is also a critical composition to oxidize SO 2 in the aqueous-phase to provide sulfate in the atmosphere.In GCM run with the SPRINTARS model, the H 2 O 2 distribution is provided offline from an independent GCM run with the CHASER model.This offline use of H 2 O 2 distribution causes unrealistic variability in the wintertime H 2 O 2 near urban areas due to abundant H 2 O 2 (e.g.Koch et al., 1999).To eliminate this problem, the improved method of this study treats H 2 O 2 as a prognostic tracer as in several other models (Roelofs et al., 1998;Koch et al., 1999;Barth et al., 2000;Boucher et al., 2002).
For evaluating the method of offline H 2 O 2 distribution, we calculate the RB between results with online and offline H 2 O 2 distributions.As suggested by the previous studies such as Barth et al. (2000), the RB values using the result with online H 2 O 2 distribution as CTL are generally positive as shown in Table 4, because of excess H 2 O 2 especially in winter.In Europe, for example, the RB of the sulfate concentration near the surface is estimated to be +17.1 %.As a result, the simulated sulfate concentrations using the online H 2 O 2 distribution are underestimated near the surface as compared to observations, as also reported by other model studies (e.g.Roelofs et al., 1998).The reason is probably that additional oxidants or additional oxidation processes are needed to be implemented or that precipitation and cloud distributions in the simulation are not well represented (Roelofs et al., 1998;Boucher et al., 2002).In summary, even though inclusion of the prognostic H 2 O 2 tracer method does not always give better results for sulfate distribution, its treatment in the present study is more realistic than that in the simplified method.

Dry deposition process of sulfur components
The dry deposition process in global aerosol models is important especially for accurate simulation of gas and coarse particle distributions.Basically, the dry deposition rate for gases is determined by three factors, i.e. aerodynamic resistance R a , quasi-laminar layer resistance R b , and canopy resistance R c defined in Sect.2.3, but the original SPRINTARS ignores the dependence of the dry deposition rate on term R c , which can be critical for atmospheric sulfur cycle, especially for SO 2 (e.g.Seinfeld and Pandis, 1998).To evaluate this approximation, we first introduce these three factors as Eqs.( 6) and ( 7) in the dry deposition process of the present improved method.
We study the impact of SO 2 dry deposition using the improved method (as CTL) and the original method of SPRINT-ARS on the sulfate simulation.Table 4 shows that annually globally averaged RB values of surface sulfate and SO 2 concentrations and sulfate column burden are calculated to be −12.0% and −11.9 %, respectively.In other areas, their values are estimated to be at most −20 %.For SO 2 , annually globally averaged RB values of surface concentrations and column burden are calculated as −28.3 % and −24.4 %, respectively.In other areas, their values are estimated to be ranging from −30 % to −10 %.For gases, R c has a great impact on the dry deposition rate.Therefore, ignoring the term R c for SO 2 mainly causes an overestimation of dry deposition rate for SO 2 , and thus we found decreases in the sul-fate and SO 2 concentrations.In conclusion, we find that differences in the dry deposition modeling also have relatively large impacts on the sulfur budget compared to differences in other parts of the sulfur process.

Comparison of simulated global sulfate distributions with observation
In this section, we compare simulated sulfate distributions calculated by simplified and improved methods with observed values.The simplified methods mentioned above are adapted into the original SPRINTARS model (Takemura et al., 2005), so that hereafter we call the model OS.We also adapted the improved methods into the SPRINTARS model, and hereafter called NS.That means all five elements to investigate impacts of the sulfate prediction in the previous Sect.are considered in the NS calculation.(Park et al., 2004;Stier et al., 2005;Koch et al., 2006;Chin et al., 2007).Over East Asia, it should be noted that the monitoring sites of sulfate in the EANET observation network here are not available in China where the simulated sulfate concentrations in OS are likely to be much higher than those in the regional model simulations as suggested by a model intercomparison project (Hollway et al., 2008;Fig. S2 in the Supplement).In conclusion, the results in NS are much better than those in OS.The improvement of the surface sulfate concentration in NS probably is attributed to the suppression in the sulfate production rate under higher SO 2 concentrations, which is supported by the previous sensitivity tests.Secondly,Fig. 6 shows comparisons between simulated and observed vertical profiles of sulfate mixing ratios.The   Singh et al. (2009).In OS, the simulated sulfate mixing ratios near the surface are overestimated, whereas those in the levels above 6 km are much underestimated as compared to observed values.Figure 6b, for example, shows the simulated sulfate mixing ratios in OS at altitude of 6 km are much less than 100 pptv, whereas those in NS are approximately 100 pptv.From these comparisons, we conclude that the vertical profiles of simulated sulfate mixing ratios in NS are much closer to the observations in comparison with the simulated results obtained from OS.The improvement of vertical profiles in NS probably stems from the increase in the sulfate production rate under lower SO 2 concentrations as shown in Sect.4.1.

Oceans
In this section, we compare the simulated sulfate field with observations over ocean areas.We use datasets including ship measurements conducted by a group of the Pacific Marine Environmental Laboratory, NOAA (e.g.Quinn and Bate, 2005) shown in Fig. 7.As shown over lands in the previous subsection, the simulated sulfate concentrations near the surface in NS are lower than those in OS and are comparable to the observation values.Over oceans near lands, i.e. outflow regions, this tendency is shown in Fig. 7d-g (Quinn and Bates, 2003;Bates et al., 2006Bates et al., , 2008)), respectively.Over remote oceans, on the other hand, the differences in the simulated sulfate concentration between NS and OS are very small as shown in Fig. 7a and c, whose observations are carried out under the first Aerosol Characterization Experiments (ACE-1) around the Central Pacific and south of Australia during October-December 1995 by Bates et al. (1998a, b) and the Indian Ocean Experiment (INDOEX) ship measurement in January-March 1999 by Ramanathan et al. (2001).In other remote sites such as Fanning Island located at the central Pacific ocean, the simulated sulfate concentrations in both NS and OS are significantly lower than observed values (not shown).This underestimation is also shown in the simulated vertical profiles of the sulfate mixing ratios compared to observed values on the flight during the TRACE-P and the INTEX-B (Fig. 6).A future study is needed to correct this underestimation especially for better estimation of the indirect radiative forcing of anthropogenic aerosols, because we usually assume that the background aerosols represent natural aerosols.

Sulfur budget estimation
In this section, global budgets of simulated sulfate and SO 2 are compared with other modeling studies.Fig. 1 shows that the results of NS are more consistent with those of other AEROCOM models with its larger both sulfate column burden and fraction above 5 km, whereas OS, i.e. the original SPRINTARS model, are the lowest among AERO-COM models, because NS generally suppresses the sulfate formation at the surface and increases the sulfate formation in the upper atmosphere above approximately 6 km as shown in Sect. 5.It should be noted that the fraction of the simulated sulfate column burden in the polar region above 80 • degree is estimated to be 1.6 % in NS which is larger than 0.3 % in OS, though the magnitude in NS is still smaller than those of other AEROCOM models by 2-6 % (Textor et al., 2007).In conclusion, these improvements of consistency of NS with other AEROCOM models in the vertical and horizontal distributions of sulfur compounds seem to be related with each other, even though the differences in the global sulfate distribution between NS and other AEROCOM models exist.For Fig. 8. Global annual mean SO 2 budget in this simulations: LR91 (Langner and Rodhe, 1991), P95 (Pham et al., 1995), C96 (Chin et al., 1996), F96 (Feichter et al., 1997), C97 (Chuang et al., 1997), K99 (Koch et al., 1999), R00 (Rasch et al., 2000), T00 (Takemura et al., 2002), C00 (Chin et al., 2000), AS02 (Adams and Seinfeld, 2002), T02 (Takemura et al., 2002), B02 (Boucher et al., 2002), L03 (Liao et al., 2003), E04 (Easter et al., 2004), B04 (Berglen et al., 2004), RD04 (Rodriguez andDaddub, 2004), S05 (Spracken et al. 2005), L05 (Liu et al., 2005), K06 (Koch et al., 2006), B07 (Bauer et al., 2007), and V07 (Verma et al., 2007), respectively.The NS and OS represent simulations in this study and the original SPRINTARS.The AVE represents averaged values.example, our simulation with MIROC-AGCM tends to have larger sulfate concentrations over low latitudes and smaller ones over high latitudes compared to other AGCM simulations presented by Liao et al. (2003).The sulfate distribution depends on sulfur chemistry, deposition (mainly wet deposition), and transport (e.g.Rasch et al., 2001).After the modification of the sulfur chemistry, differences in the sulfate distribution still remain, so that they are probably caused by differences in wet deposition and transport.The wet deposition depends not only on the radius and wet growth of the particles but also on precipitation flux, cloud fraction, and advection of aerosol.As we mentioned in Sect. 1, the difference in the radius and wet growth of sulfate aerosols among sulfur chemistry models is not so large.Therefore, the differences in the sulfate concentrations over low latitudes are caused by (1) cloud and precipitation, which are determined mainly by schemes of the boundary layer and/or the cloud and precipitation, and (2) transport pattern, which is determined by schemes of the boundary layer and advection; but a detailed study is our future work.
Table 5 shows global budgets of sulfur components (DMS, SO 2 , and sulfate) obtained in NS and OS.Even the differences in the processes of DMS oxidation and its dry deposition between NS and OS exist, the difference in the production amount of SO 2 by DMS oxidation is within 10 %.Therefore, total SO 2 emissions in NS are almost same as those in OS.The following four loss processes of SO 2 are considered in NS and OS: SO 2 oxidation by OH in the gas phase, SO 2 oxidation by H 2 O 2 and O 3 in the aqueous  phase, dry deposition, and wet deposition by precipitation.Among these processes, the gas-phase oxidation of SO 2 in NS is almost same as that in OS as estimated to be 17.4 [TgS yr −1 ] (19 % for the total SO 2 loss process) in NS and 16.5 [TgS yr −1 ] (18 % for the total SO 2 loss process) in OS, which are within the uncertainty among other model estimates 5.7-22.0[TgS yr −1 ] (references in Fig. 8).On the other hand, a large difference between NS and OS occurs in the SO 2 aqueous-phase oxidation, and wet deposition and dry deposition.In OS, SO 2 budgets for aqueous-phase reaction and wet deposition are estimated to be 19.9 [TgS yr −1 ] (22 % for the total SO 2 loss process) and 21.2 [TgS yr −1 ] (23 % for the total SO 2 loss process), respectively, whereas those are estimated in NS to be 43.7 [TgS yr −1 ] (48 % for the total SO 2 loss process) and 5.0 [TgS yr −1 ] (5 % for the total SO 2 loss process), respectively.The differences are mainly caused by a difference in the sulfate production efficiency.As a result, a correlation of the simulated SO 2 budgets in NS between wet deposition and aqueous-phase reaction is much closer to that by other modeling studies (see Fig. 2).
In the other modeling studies, the SO 2 budget is estimated to be 15.2-55.5 [TgS yr −1 ] for the aqueous-phase reaction and 0.2-19.9[TgS yr −1 ] for the wet deposition, respectively (references in Fig. 8).In the dry deposition, the SO 2 flux  8).The ratio of the sulfate wet deposition to the sulfate total loss processes is estimated to be 85 % in OS and 88 % in NS, so that the contribution is almost equal to each other even though more physical-based dry deposition model for the sulfate is used in NS.
Figure 9 shows ratios of simulated SO 2 flux in the aqueous-phase reaction in summer to that in winter in three industrial areas using NS, OS and models used in the COSAM comparison, which estimates averaged budget of simulated SO 2 using different ten model results (Roelofs et al., 2001).In OS, winter-time aqueous-phase reaction fluxes are generally so large that the ratio becomes smaller than those of NS and the COSAM comparison.This low value in OS is caused by the treatment of use for offline H 2 O 2 distribution as mentioned in Sect.4.4.The ratio reflects a seasonal variation of SO 2 aqueous-phase oxidation, so that we also find a big difference in the seasonality between the simplified and improved sulfur schemes.

Aerosol direct radiative forcing
In this Sect.we discuss an evaluation of the aerosol optical and radiative fields, i.e. aerosol optical thickness (AOT) and aerosol direct radiative forcing (ADRF).Figure 10 shows annually averaged global AOT distributions simulated by both NS and OS and observed by both Terra/MODIS and Terra/MISR.Large differences are found over oceans, where the satellite-observed AOT is more than at least 0.1, whereas the simulated AOT is generally less than 0.1.There are several problems for accurate evaluation of AOT over ocean with both simulation and satellite observation.With regard to satellite observation, the retrieval of the AOT over oceans often suffers from cloud and whitecap contaminations and an ill assumption of the aerosol optical properties and sphericity of the particle shape (e.g.Chin et al., 2002;Chu et al., 2005).Especially the former two reasons lead to an overestimation of the retrieved AOT over oceans, especially the North Pacific and South Pacific.Chu et al. (2005) suggests that the retrieved AOT from MODIS tends to be positively biased in the dusty conditions.Additionally Winker (2008) showed differences in the retrieved AOT from MODIS and CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellites Observations) and pointed out remarkable overestimations of the AOT from MODIS in the AOT ranging from 0 to 0.1.On the other hand, SPRINTARS and most GCMs also have problems to simulate AOT especially over oceans (e.g.Takemura et al., 2002;Kinne et al., 2006;Yu et al., 2006).It seems that most GCMs underestimate background aerosols or transported aerosols from continents.
Figure 11 shows a histogram of the simulated and observed annual mean AOT for each area.In both Figs. 10 and 11, we find improvements of the simulated AOT in NS around areas such as Northeastern America, the North Atlantic, Europe, Eurasia continent, the North Pacific, the  Central Pacific, the coast of Africa to the Atlantic, and the Arctic.The AOT in NS is higher than the AOT in OS by 0.01-0.05,because of the increase in the sulfate column burden.These differences are also discussed in terms of the column burden in Sect. 5.The magnitudes of this difference between NS and OS are smaller than those among different satellites.In other areas especially tropical and subtropical areas, i.e.India, Southeast Asia, South Asia, and Mexico, the AOT in NS rather than in OS tends to be larger than the satellite-observed AOT by at most 0.1.As discussed in Sect.6, comparisons with other model results also suggest that this overestimation of AOT in NS is caused both by the overestimation of the sulfate concentrations and by the tendency in our GCM of high gradients of the aerosol distribution from the equator to the Poles at high altitudes.The latter means that simulated aerosols in the MIROC AGCM tend to concentrate around the low latitudes.Over these areas, it is difficult for AGCM to accurately simulate fields of clouds and precipitation and then to accurately simulate sulfate formation in the aqueous-phase and relative humidity (RH), which can also determine AOT.At the same time, the observed AOT over such areas can relatively be uncertain due to the presence of large clouds.Around the clouds, satellite-observed AOT tends to be larger with suffering from difficulty of retrieval mainly due to 3-D radiation bias (Wen et al., 2007).That means that the satellite-observed AOT near the cloudy areas is still highly uncertain, and therefore it is concluded that the validation of the simulated AOT using satellite-observed AOT over the tropics and the subtropics is relatively difficult.
Global annual mean ADRFs due to anthropogenic sulfate in NS and OS are compared with other studies.The ADRFs due to anthropogenic sulfate are estimated to be −0.35W m −2 by the AEROCOM exercises (Schulz et al., 2006) and −0.4±0.2W m −2 by the IPCC-AR4 assessment (Forster et al., 2007), respectively.The ADRF for NS is estimated to be −0.26W m −2 , whereas that for OS is estimated to be −0.18W m −2 .Using the AEROCOM emission inventory provided by Dentener et al. (2006), the ADRFs for NS and OS are estimated to be −0.30W m −2 and −0.21 W m −2 , respectively.The difference in the ADRF for NS and OS is large enough for us to conclude that the improvement of the sulfur scheme is important for the estimation of the ADRF due to sulfate.The improvement brings increases in the simulated sulfate column burden and then causes increases in the ADRF due to sulfate.This is why the differences in the simulated ADRF for NS and the other models are reduced with respect to those between OS and the other models (see Fig. 1).Judging from the validation of the simulated sulfate in NS and OS in Sect.5, we can conclude that the sulfate simulations in NS are much better than those in OS; therefore the simulated ADRF for NS is more reliable than that for OS.In addition, we can also conclude that the nature of the sulfur scheme has a large contribution to the uncertainty for the ADRF estimation.The annual averaged ADRF due to anthropogenic sulfate for NS and the difference in the ADRFs between NS and OS are shown in Fig. 12.The improvement of the sulfur scheme causes decreases in the ADRF over China with a range of 0.2-1 W m −2 , whereas it causes increases in the ADRF near aerosol source areas such as North America and Southeast Asia with ranges of 0.5-1 W m −2 and usually over land with ranges of 0.2-0.5 W m −2 , respectively.The big change in the radiative forcing over East Asia is mainly caused by the difference in the solution in the sulfur aqueous-phase reaction as shown in Table 4.Over oceans, the ratios of the differences between NS and OS exceed 2, so that the impacts of the new module are large.
In summary, the improvement of the sulfur scheme has a large impact on the radiative forcings.This study suggests that these improvements of the basic components in sulfur simulations are important not only for their proper simulations but also for their radiative impacts through the aerosol direct effect.

Conclusions
One of the most important contributors of the anthropogenic aerosol radiative forcing is the sulfate aerosol, because both the results given by Schulz et al. (2006) and Fig. 1 suggest that the uncertainty of radiative forcings due to anthropogenic aerosols are largely derived from the differences in the sulfate column burden and its vertical distributions.One of the possible reasons of the differences among models is that models adopt different simplified methods or different approximations of the sulfur processes.In this study, therefore, we investigated impacts of different parts in the sulfur chemistry module of a global aerosol model, SPRINT-ARS, on the sulfate distribution and its radiative forcing.We used simplified and more physically based methods of representing sulfur chemistry processes especially SO 2 reactions in the aqueous-phase, H 2 O 2 chemistry, and dry deposition process of sulfur components.The results showed that the difference in the aqueous-phase sulfur chemistry calculation among these treatments had the largest impact on the sulfate distribution with a relative bias of 70-160 %.The impact of the difference in the pH calculation in the aqueous phase among this study was the smallest with a relative bias of less than 5 %.The other treatments had relative biases of at most 20 %.Introduction of all the improvements mentioned above gave lower sulfate concentrations near the surface and higher sulfate column burdens compared to the original method used in the SPRINTARS model.That means that the model results become more comparable to in-situ measurements than those in the original method.At the same time, these improvements also led the computed sulfate column burdens and its vertical distributions in good agreement with other AEROCOM model values.As a result, the global annual mean aerosol direct radiative forcings (ADRFs) due

Fig. 1 .
Fig. 1.Correlation (a) between sulfate column burden (x-axis) in mg(SO 2−4 )m −2 and aerosol direct radiative forcing due to anthropogenic sulfate aerosols under the all-sky condition at the top of atmosphere (y-axis) in Wm −2 and (b) between fraction above 5 km to the sulfate column burden (x-axis) in percentage and aerosol direct radiative forcing due to anthropogenic sulfate aerosols under the all-sky condition at the top of atmosphere (y-axis) in Wm −2 .The all data in closed circles in black are given bySchulz et al. (2006) andTextor et al. (2006).The closed and open circles in red represent the result in this study and the original SPRINTARS.

Fig. 2 .
Fig. 2. Correlation of global annual mean SO 2 budgets between wet deposition fluxes (x-axis) and aqueous-phase reaction fluxes (yaxis) using model results by various CTM and GCM aerosol models, in TgS yr −1 .For reference, the 1:1 and 1:2 lines are shown as the solid and dashed lines, respectively.The closed circle in red represents the result in this study using a more physical-based sulfur processes.The open circle in red near the 1:1 line represents the result in Takemura et al. (2000), SPRINTARS, which uses a simplified sulfur process.The open circle in black represents the result in Koch et al. (2006).

Fig. 3 .
Fig. 3.A flowchart for aqueous-phase reaction of SO 2 in (a) the original SPRINTARS and (b) this study.The SO 2 in yellow and aqua represent SO 2 in the gas-phase and in the aqueous-phase, respectively.The pink, aqua, blue, and red circles correspond to the process of gas-liquid phase equilibrium through Henry's law, wet deposition, sulfate production reaction, and loop for the calculation in a sub-cycle timestep, respectively.

Fig. 4 .
Fig. 4.An example of predicted sulfate concentrations through the SO 2 aqueous-phase oxidation during twenty minutes for the conditions of 300 K and 5 ppbv H 2 O 2 .The x-axis values are initial SO 2 concentrations and the y-axis values are sulfate concentration formed from SO 2 oxidation by H 2 O 2 .
For proper simulations of the aerosol distribution, all experiments are conducted with nudged meteorological fields (wind, water vapor, and temperature) every six-hour.The data are reanalysis data provided by the NCAR/NCEP.All experiments, except for experiments for comparison of simulated aerosol mass concentrations with aircraft and ship observations, are run for two years (1 January 2002-31 December 2003) after using the first year for spin up.
s (referred to as fine second-order solution or CTL).

Fig. 5 .
Fig. 5. Simulated and observed monthly mean surface mass concentrations of sulfate over (a) North America, (b) Europe and (c) East Asia.The black line represents 1:1 line between observations and the simulations.The blue and green lines represent linear regressions of the simulations in NS and OS, respectively.The B r and R 2 values in the figure represent a relative bias, defined as a ratio of simulation to observation, and a correlation coefficient, respectively.The x-axis values are month and the y-axis values are sulfate mass concentrations in µg m −3 .

Fig. 7 .
Fig. 7. Temporal sulfate mass concentrations by measurements in Quinn and Bates (2005) in black, simulations of NS in blue and simulations of OS in green, during different measurements periods (see text).The x-axis values are date and the y-axis are sulfate concentrations in µg m −3 .
, which are several ship measurements conducted by the Asian Aerosol Characterization Experiment (ACE Asia) around the Japan Sea during March-April 2001 by Huebert et al. (2003), by the New England Air Quality Study (NEAQS) during July-August 2002 and 2004, and by the Texas Air Quality Study/Gulf of Mexico Atmospheric Composition and Climate Study (TexAQS/GoMACCS) in August 2006

Fig. 9 .
Fig. 9. Ratios of SO 2 aqueous-phase oxidation flux in summer to that in winter over three industrial regions using the COSAM exercises, OS and NS, respectively.

Fig. 12 .
Fig. 12. Annual mean aerosol radiative forcings due to anthropogenic sulfate components in (a) OS, (b) NS, and (c) the difference between NS and OS.

Table 2 .
Hygroscopicity in this model a .
; we give only a brief description in this paper.The SPRINTARS model has been implemented in an atmospheric GCM developed by the Center for Climate System Research of the University of Tokyo, National Institute for Environmental Studies, and the Frontier Research Center for Global Change (K-1 Developers, 2004; hereafter referred to as MIROC AGCM).The horizontal resolution of the triangular truncation is set to T42 (approximately 2.8 aerosol), sulfate, soil dust, sea salt, and the precursor gases of sulfate, i.e.SO 2 and DMS.The particles are treated as external mixtures for soil dust and sea salt.For carbonaceous aerosols, the BSOA and 50 % BC mass from fossil fuel source are treated as externally mixed particles, but other carbonaceous particles are treated as internal mixtures of BC and POA.For soil dust and sea salt aerosols, mixing ratios are calculated for various size bins.
• by 2.8 • in latitude and longitude) and the vertical resolution is set to 20 layers.The time step dt is set to 20 min.The model calculates the mass mixing ratios of the main tropospheric aerosols, i.e. carbonaceous aerosol (BC, POA, i.e. primary organic aerosol and BSOA, i.e. bio-genic secondary organic

Table 3 .
Experimental designs of comparison using original and improved methods.

Table 4 .
Annual mean relative bias (RB), defined as RB = (S −C)/C where S and C represent results simulated by the simplified and improved methods: (a) sulfate surface concentrations and (b) sulfate column burdens.The simplified methods are different in each experiment whose abbreviations are described in Table3.The improved method corresponds to the experiment named as CTL in Table3.

Table 5 .
Global budgets (TgS yr −1 ) of sulfur components (DMS, SO 2 and sulfate) in the simulations using NS and OS.The figures in blankets represent contributions to the total budget.