2.1. Global Aerosol and Chemistry Transport Model
 A global aerosol and chemistry transport model, the University of Michigan (Umich) version of the Lawrence Livermore National Laboratory (LLNL) IMPACT model [Liu and Penner, 2002; Feng et al., 2004; Rotman et al., 2004; Liu et al., 2005], was used as the framework for this study. The spatial resolution of the IMPACT model is 2° latitude by 2.5° longitude in the horizontal, with 26 layers in the vertical from the surface to 0.1 hPa (the mean pressure levels are 994, 971, 930, 875, 813, 745, 675, 605, 537, 472, 410, 353, 302, 258, 220, 187, 158, 133, 112, 94.1, 79.3, 67.0, 56.7, 37.7, 14.3, and 2.64 hPa). For this study, the transport model was driven by assimilated meteorological fields for year 1997, which were available at a 6-hour time interval from the NASA Goddard Data Assimilation Office (DAO) general circulation model (GCM) and were interpolated to a 1-hour time interval, which was the model time step for tracer advection.
 The IMPACT model uses a flux-form semi-Lagrangian advection scheme [Lin and Rood, 1996]. Dry deposition rates for gases are calculated using a package developed at Harvard University on the basis of the work of Jacob and Wofsy , Wesely , and Walcek et al. . Dry deposition of aerosol particles uses a resistance-in-series parameterization following Zhang et al. . The wet deposition scavenging parameterization is based on the Harvard wet scavenging model [Mari et al., 2000; Liu et al., 2001] that is enhanced over previous models [Giorgi and Chameides, 1986; Balkanski et al., 1993]. In convective updrafts, the fraction of tracer scavenged is calculated on the basis of the rate constant for conversion of cloud condensate (including liquid and ice) to precipitation (assumed to be 0.005 s−1) and the fraction of tracer present in the cloud condensate fi (scavenging efficiency). The scavenging efficiency of gases depends on their Henry's law coefficients, except for highly soluble HNO3 which is assumed to be completely removed. The scavenging efficiencies of sulfate, nitrate, ammonium, and carbonaceous aerosol are 1.0, 1.0, 1.0, and 0.4 in the IMPACT model, respectively. In addition, a first-order rainout (in-cloud scavenging of aerosols or gases by cloud or precipitation) and washout (below-cloud scavenging of aerosols or gases by cloud or precipitation) parameterization is applied for both convective and large-scale precipitation. The fraction of a tracer lost because of rainout depends on the wet scavenging efficiency of the tracer, the horizontal area-fraction of the grid box experiencing precipitation, and conversion rate of cloud condensate to precipitation. Washout by large-scale precipitation is computed as a first-order loss process using a rate which is calculated by multiplying a constant scavenging efficiency, 0.1 mm−1, by the precipitation rate (in mm hr−1) in the precipitating fraction of the grid box [Balkanski et al., 1993]. Resuspension is calculated in any grid box where there is net evaporation of precipitation. A fraction (assumed to be half) of or the entire tracer precipitating from above is released in the grid box to reflect the partial or total evaporation of precipitation, respectively. Cumulus transport in the IMPACT model was derived from the relaxed Arakawa-Schubert scheme, as described in detail by Penner et al. . The cumulus mass flux and convective cloud detrainment used in the scheme are derived from the DAO meteorological fields. A full description of the transport and deposition schemes is given in Rotman et al.  for the original IMPACT model.
 An online sulfur model that predicts the concentrations of SO2, SO42− (represented in 3 aerosol size bins or sections:<0.05 μm, 0.05–0.63 μm, 0.63–1.25 μm in radius), H2O2 and DMS was developed for the Umich version of the IMPACT model [Liu and Penner, 2002; Liu et al., 2005]. This model includes the Global Emissions Inventory Activity (GEIA) emissions of SO2 and SO42− from fossil fuel combustion and industrial activities, SO2 emissions from biomass burning, aircraft, and noneruptive volcanoes, as well as an oceanic DMS source. SO2 is oxidized to SO42− in cloud by dissolved O3 and H2O2, and in the gas phase by the OH radical. Both OH and NO3 radicals oxidize DMS and generate SO42−. H2O2 is included as a prognostic species, formed from two HO2 molecules. Three-dimensional monthly average O3, OH, and HO2 concentration fields are taken from a 1-year simulation of the chemical transport model GRANTOUR using the climate model CCM1 meteorological fields [Penner et al., 1994]. The diurnal cycle of OH and HO2 is approximated using the cosine of the solar zenith angle. NO3 is calculated interactively by a nitrogen chemistry model to be described next.
 Feedbacks between the processes we include in the model and the fixed concentrations used to simulate the sulfur cycle (i.e., O3, OH, and HO2) are possible. For example, the aqueous reaction of H2O2 with SO2 could decrease OH and HO2 concentrations and the aqueous reaction of O3 with SO2 could decrease O3. As we show below, there is also a feedback between NOx concentrations and the amount of nitrate in aerosols. The feedbacks between the formation of sulfate aerosol and O3, OH and HO2 are relatively small, because the loss rates due to these aqueous phase processes are small compared to the formation rates from gas phase chemistry. As discussed below, the feedbacks between the formation of nitrate in aerosol and NOx can be large, depending on the method used to calculate nitrate in aerosol. This change in NOx would also ultimately affect O3 concentrations, but an evaluation of this feedback is beyond the scope of the present paper.
 The wet size used in the dry deposition scheme is calculated by the empirical expression of Gerber ,
where Rw and Rd are the wet and dry particle radius, S is the relative humidity expressed as a fraction, and C1, C2, C3, and C4 are constants whose values are 0.4809, 3.082, 3.110 × 10−11, and −1.428, respectively. The model yields an annual average sulfate burden of 0.80 Tg S. This value is intermediate in comparison with other sulfur models that give burdens ranging from 0.53 Tg S [Chin et al., 1996] to 1.05 Tg S [Lelieveld et al., 1997].
 Sea salt emissions in the IMPACT model were provided by Gong et al. . An interpolation was made on the basis of the algorithm of Monahan et al.  to derive the size-segregated mass fluxes. Following emission, the sea salt mass is carried in 4 aerosol size bins (0.05–0.63 μm, 0.63–1.25 μm, 1.25–2.5 μm, 2.5–10. μm in radius). The constants C1, C2, C3, and C4 in the equation (1) which account for the relative humidity dependence of sea salt are 0.7674, 3.079, 2.573 × 10−11, and −1.424, respectively. The model predicted sea salt burden is about 3.13 Tg.
 The dust emission fluxes calculated by Ginoux et al.  were interpolated and represented in the same 4 size bins as the sea salt aerosol [Liu et al., 2005]. Although dust particles may acquire a soluble coating and absorb water, their dry sizes are used in the calculation of the dry deposition velocity since the extent of their water uptake is not well established. For in-cloud scavenging of dust particles, we followed the assumption of Ginoux et al.  and completely scavenged dust particles within both convective and large-scale clouds. The model calculated dust burden is about 23.21 Tg. Model estimates of dust burden range from 13.8 Tg by Takemura et al.  to 18.7 Tg by Tegen et al. , and to 31–40 Tg by Ginoux et al. . The large differences between these studies result from large uncertainties in emissions and the different wet and dry deposition schemes used in the models.
 A longer description of the aerosol module in the Umich/IMPACT model and a comparison of the model predicted aerosol concentrations and optical depths with the available observations are given by Liu et al. .
2.2. Nitrogen Chemistry
 The gas-phase precursors of nitrate, HNO3 and N2O5, are calculated online in the model with a simple nitrogen chemistry mechanism. The scheme allows 5 tracers to be transported: NOx (NO + NO2), NO3, N2O5, and HNO3. Table 1 lists the tropospheric chemical reactions included in the model. The NO2 concentrations are derived by assuming that photochemical equilibrium is reached between NO and NO2. Since the reactivity of NO3 on aerosol surfaces is much smaller than that of N2O5 and HNO3, heterogeneous hydrolysis of NO3 is neglected in this study. The chemistry of gas phase nitrogen in the stratosphere is treated more simply. Its sole function is to provide the proper partitioning between NOx and NOy = HNO3 + NOx for the input of NOy at the tropopause. Following Kraus et al. , NOx is converted to HNO3 everywhere above the tropopause with an e-folding time constant of 13 days. HNO3 is converted back to NO2 by photolysis, at varying frequencies up to 3 × 10−7.
Table 1. Tropospheric Gas-Phase Reactions and Heterogeneous Reactions Included in the Model
| ||Chemical Reactions|
|Day-time Scheme [Kraus et al., 1996]|
|(R1)||NO2 + OH + M HNO3 + M|
|(R2)||HNO3 + hν NO2 + OH|
|(R3)||HNO3 + OH NO3 + H2O|
|(R4)||NO2 + O3 NO3 + O2|
|(R5)||NO2 + NO3 N2O5|
|(R6)||N2O5 + H2O (a) 2HNO3|
|(R7)||NH3 + H2SO4(a) = (NH4)2SO4 or NH4HSO4 or (NH4)3H(SO4)2|
|(R8)||HNO3 + NH3 = NH4NO3|
|(R9)||HNO3 + NaCl(a) = NaNO3 + HCl|
|(R10)||2HNO3(g) + CaCO3 = Ca(NO3)2 + H2O + CO2|
|(R11)||2HNO3(g) + MgCO3 = Mg(NO3)2 + H2O + CO2|
|(R12)||2HNO3(g) + Na2CO3 = 2NaNO3 + H2O + CO2|
|(R13)||2HNO3(g) + K2CO3 = 2KNO3 + H2O + CO2|
 The global fields of OH and O3 are prescribed as monthly averages as described above. Photolysis frequencies were computed interactively every hour from a look-up table [Feng et al., 2004] that accounts for absorption by O2 and O3, Rayleigh scattering, and Mie scattering by clouds and aerosols. Five NOx sources (emitted as NO2) were included in this study following Rotman et al. : 21.5 Tg N per year from industrial activities/fossil fuel combustion, 6.4 Tg N per year from biomass burning, 5.0 Tg N per year from lightning, 5.5 Tg N per year from soil processes, and 0.5 Tg N per year from aircraft emissions. Initial stratospheric HNO3 concentrations were specified, on the basis of model results from a full chemistry version of the Umich/IMPACT model [Ito et al., 2004].
 The main limitation of this simplified nitrogen chemistry is that it omits organic nitrates. Since organic nitrates form in source regions and transport NOx to the remote troposphere, this omission may result in overpredicted NOx and HNO3 concentrations in source regions and underpredicted NOx and HNO3 concentrations in the remote troposphere [e.g., Singh et al., 1998, 2000; Schultz et al., 1999].
 For nitric acid, the effective Henry's law constant used in the dry deposition scheme is 3.17 × 1011 M atm−1 at pH = 5. The size-dependent dry deposition of nitrate aerosol used the effective radius for the dominant aerosol type in each size section. Thus the dry deposition of nitrate in the size section, r: 0.01–0.63 μm (bin 1) was treated the same as sulfate, while that in the size range from 0.63 to 2.5 μm (bins 2 and 3) was treated the same as sea salt, and that in the range 2.5–10 μm (bin 4), was treated the same as dust aerosol. The wet scavenging efficiency for nitrate aerosol was set to 1.0, the same as that for sulfate aerosol.
2.3. Ammonia Cycle
 The ammonia cycle was simulated by adding two tracers: ammonium (NH4+) and its gas-phase precursor ammonia (NH3) to the IMPACT model. Ammonia emissions were taken from the global inventory of Bouwman et al. . The total ammonia source included in this inventory is estimated to be 54 Tg N per year, and Table 2 lists the contributions from individual sources. The fact that fertilizer related activities contribute most to the ammonia emissions implies that agricultural regions tend to have the highest ammonia emissions. The total emissions estimate of this inventory is higher than the 45 Tg N per year used by Dentener and Crutzen  in their model of the ammonia cycle, lower than the 75 Tg N per year estimate of Schlesinger and Hartley , and almost the same as the 54 Tg N per year estimate of Warneck . Although some sources, for example, those from crops, fertilizer, and animal waste, should vary seasonally depending on the crop production cycle and temperature, their monthly variations are not available in the current ammonia inventory. Thus, in the absence of more detailed information, only the annual average emission fluxes from all the sources were used in this study.
Table 2. Global Ammonia Emission by Source [Bouwman et al., 1997]
|Source||Emission, Tg N per year|
|Soils under natural vegetation||2.4|
 Ammonia (NH3) undergoes one reaction in the atmosphere with the OH radical [DeMore et al., 1997],
We did not include this reaction in this study, since it only plays an insignificant role in the global ammonia budget [Adams et al., 1999]. For wet deposition of NH3, we use an effective Henry's law coefficient of 1.05 × 106 M atm−1 at pH = 5. Aerosol ammonium was treated similarly to nitrate aerosol in the dry and wet deposition schemes.
2.4. Heterogeneous Interaction of Aerosols and Gas-Phase Chemistry
 Aerosol particles are frequently found as internal mixtures with multiple components including sulfate, sea salt, nitrate and dust compounds [Okada et al., 1990; Fan et al., 1996; Zhou et al., 1996; Niimura et al., 1998; Yamato and Tanaka, 1994; Zhang et al., 2003], probably as a result of condensation and coagulation processes. Therefore sulfate, sea salt and mineral dust aerosols were assumed to be internally mixed in aerosol thermodynamics. Organic aerosol compounds may contribute to a large fraction of total aerosol mass; however, little is known about their composition and hygroscopic properties. Although a range of water-soluble organic compounds have been identified in the atmosphere [Saxena and Hildemann, 1996], a better characterization of the organic components of the aerosol is needed in order to characterize their water uptake and interaction with other compounds. Therefore we did not consider the formation of nitrate and ammonium on organic aerosols. Similarly, the uptake of nitrate and ammonium on black carbon was not considered, since black carbon is unlikely to be hydrated except in association with organics and other compounds.
 The chemical composition of sea salt aerosol is assumed to be 100% of NaCl. Dust aerosols generally consist of insoluble metal oxides and a small fraction of alkaline components. The alkalinity of dust is to a great extent determined by the calcium carbonate (CaCO3) content. This varies with the source region of the dust aerosol and may be modified by other pollutants during long-distance transport. In this study, mineral dust aerosol is assumed to be: 7% CaCO3, 5.5% MgCO3, 3.3% K2CO3, 2.6% Na2CO3, 60% SiO2, 14.1% Al2O3 and 6.9% Fe2O3 [Gillette et al., 1993]. This gives an average of Ca2+ content of 4.2%, which is somewhat larger than the global average crustal Ca content of 3.6% given by Jaenicke , but smaller than the value of 5% used in most previous model studies [Dentener et al., 1996; Liao et al., 2003]. In addition, whereas most previous studies considered only Ca2+ for the alkaline material in dust aerosol, we have explicitly included the effects of Mg2+, K+, and Na+. The heterogeneous reactions included in the model are also shown in Table 1.
 The heterogeneous uptake of nitrate and ammonium by aerosol mixtures is simulated in the Umich/IMPACT model using a hybrid dynamical approach (HDYN). With this method, a thermodynamic equilibrium model [Jacobson, 1999] is applied to aerosols in size bin 1 (D < 1.25 μm, hereafter referred to as the fine mode), while the gas and aerosol concentrations are determined by dynamically solving the mass transfer equations for particles in the other 3 bins (D > 1.25 μm, hereafter referred to as the coarse mode). Capaldo et al.  applied a similar approach in an air pollution model, and they found that this method maintained most of the predictive capability of dynamically solving mass transfer equations over the entire aerosol size range, and was 50 times more computationally efficient in their test cases. Following Capaldo et al. , we selected the same critical size (below which equilibrium is assumed and above which the mass transport is calculated) at a diameter equal to 1.25 μm. Wexler and Seinfeld  and Dassios and Pandis  calculated the equilibrium time constants for ammonium nitrate aerosol and indicated that particles with diameter less than 1 μm generally have equilibrium timescales of the order of a few minutes under typical atmospheric conditions. Since our transport model time step is one hour and the equilibrium timescale depends mostly on particle size, the equilibrium assumption is well justified for aerosols in the fine mode. This assures that results are similar to fully dynamical calculations. While Capaldo et al.  performed equilibrium calculations every 1 min, we only do so at the beginning of each model step. We tested this assumption, and under most conditions, there was less than a 7% percent difference compared to a calculation that adjusted concentrations to equilibrium every minute. Even smaller errors occur when conditions are near equilibrium. This is because the diffusion of gases to the coarse particles is slow and usually has little impact on fine-mode equilibrium processes over a 1-hour time step. The operator-splitting method used in the global model eliminates any effects from other processes during the model time step. Aerosol chemical composition is usually uniform over the submicron size range: continental aerosols are mainly composed of sulfate, ammonium, and nitrate; marine aerosols are mainly composed of sea salt. Therefore the chemical driving force among particles in the fine mode is similar and there is no need to use a finer division of size bins for the equilibrium calculation. However, since only one bin out of 4 bins is assumed to be in equilibrium in our calculation compared to 6 bins out of 10 bins in the work by Capaldo et al. , we only obtain a factor of 3 or 4 speed up compared to a full dynamical calculation over all bins in this study.
 The partitioning of nitrate and ammonium in the coarse mode is described by the mass transfer equations,
where Dg is the diffusivity, ri is the radius of particles in size bin i, ni is the aerosol number concentration, C∞ is the ambient gas-phase concentration (moles per m3 of air) and Ci is the aqueous-phase concentration. Ci,eq is the equilibrium vapor concentration on the particle surface, which is calculated with the thermodynamic equilibrium model based on the aerosol composition of each size bin. The formulation of the mass transfer coefficient ki is based on the solution of Fuchs and Sutugin , where Kni is the Knudsen number, and the accommodation coefficient (α) represents the sticking probability of a vapor molecule at the surface of a particle. We used 0.193, 0.092, and 0.1 for the accommodation coefficients of HNO3, NH3, and N2O5 on aerosols, respectively, on the basis of measurements at 298 K by Van Doren et al. [1990, 1991]. These values for α are at the upper end of the corresponding uptake coefficients (γ) used in the literature, satisfying the general relationship γ ≤ α. Equations (3) were integrated over the model time step (1 hour) and were solved simultaneously for aerosol nitrate (NO3−) and aerosol ammonium (NH4+) concentrations in each of the 3 aerosol bins of the coarse mode as well as for HNO3(g) and NH3(g).
 This hybrid dynamical method should be more accurate than thermodynamic equilibrium models. HDYN considers the diffusion constraint in the mass transport from gas phase to particles, which frequently causes coarse aerosols to be in a nonequilibrium state. This method is also better than the first-order removal approximation in which the removal rate K is usually defined as [Schwartz, 1986],
where r is the aerosol radius, A is the aerosol surface area, Dg (cm2 s−1) is the gas phase diffusion coefficient, and υ is the mean molecular speed (cm s−1). γ is the uptake coefficient, which is the ratio of the number of gaseous molecules entering the particle over the number of molecules colliding with the surface. Compared to the mass transfer equation (equation (3)), equation (4) does not explicitly include the equilibrium vapor concentration of species on particle surfaces (Ci,eq), which depends on the ambient relative humidity, temperature, and the immediate aerosol chemical composition during gas-to-aerosol diffusion. Instead, the dependence of the mass transfer rate on Ci,eq is approximately represented by uptake coefficients measured under certain laboratory conditions. The use of different uptake coefficients can significantly affect the results of global model studies. For example, Bauer et al.  found that with the upper limit for γN2O5 (0.02), tropospheric ozone mass is decreased by 0.8%, while with the lower limit of γN2O5 (0.003), the reaction had almost no impact on ozone concentrations. They also found that lowering the uptake coefficient of HNO3 by two orders of magnitude from 0.1 to 0.001 resulted in a much smaller decrease of tropospheric ozone (from 4.5% to 2.2%).
 Figure 1 shows a schematic of the integration of the hybrid dynamical approach into the global aerosol and chemistry transport model, Umich/IMPACT. The integrated model was run for a period of four simulation months: January, April, July and October, to obtain a representation of the annual average of the global concentrations of nitrate and ammonium aerosol. Unless otherwise specified, global and annual aerosol budgets were estimated from these 4-month simulations. A 2-month spin-up time was used to generate background values as initial concentrations for production runs. The global model requires 3 days of the CPU time on 64 IBM SP3 processors (each processor has a peak performance of 1.5 GFlops) to complete a 1-month simulation.
Figure 1. Schematic diagram of the integration of the hybrid dynamical (HDYN) method in the global chemistry and aerosol transport model (Umich/IMPACT).
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