Dynamics of the sulphate aerosol size distribution on a global scale



[1] Parameterizations for size-dependent aerosols have been implemented in the Canadian Centre for Climate Modelling and Analysis (CCCma) atmospheric general circulation model (AGCM). This new model version considers comprehensive physical and chemical processes that are associated with the sulphate aerosol size distribution, including nucleation, condensation, hygroscopic growth, aqueous-phase chemistry, and dry and wet deposition. Results from in situ surface and airborne observations and remote sensing were used to validate the model. The comparisons give evidence for realistic sulphate size distributions over the regions where sulphate is the dominant aerosol type. In agreement with earlier published studies, it is found in sensitivity tests that the global sulphate burden is predominantly affected by wet deposition. However, the mass size distribution is mainly affected by coagulation, condensation, and below-cloud scavenging on the global scale. There is only weak sensitivity of the simulated mass size distribution to changes in in-cloud oxidation and the efficiency of nucleation. It is shown that the low sensitivities are caused by a compensating effect of coagulation in the former and low sensitivity of the mass size distribution to changes in nucleation rate and condensation efficiency for the latter case.

1. Introduction

[2] Aerosols play an important role in climate change since they have the potential to offset part of the global warming induced by increasing of greenhouse gases. In contrast to greenhouse gases, modeling the impact of aerosols on climate is still associated with considerable uncertainty, which is especially the case for the effect of aerosols on clouds. Twomey [1974] first found that cloud reflectance increases with aerosol particle concentration for constant cloud water content since aerosols can act as cloud condensation nuclei (CCN). This is called the cloud albedo effect, i.e., first indirect effect. On the other hand, higher aerosol concentrations lead to smaller cloud droplets at a given supersaturation, thus less efficient formation of precipitation. This is the cloud lifetime effect, i.e., second indirect effect [Albrecht, 1989]. Interactions of aerosols with clouds depend strongly on their size distributions [e.g., Feingold, 2003].

[3] It is evident that an explicit treatment of aerosol size distribution in GCMs is important to better represent the effects of aerosols on radiation and aerosol-cloud feedbacks, and to simulate current, past and future climate change more accurately.

[4] There are generally two approaches that are used to represent aerosol size distributions: The modal approach and the sectional (or bin) approach. According to the first approach, the size distribution is approximated by analytical functions [Giorgi and Chameides, 1986; Whitby and McMury, 1997]. For the sectional approach, the particle size distribution is approximated by a number of discrete bins [Jacobson, 1997; Lurmann et al., 1997; Russel and Seinfeld, 1998; von Salzen and Schlünzen, 1999; Gong et al., 2003]. Most global models do not yet account for variable size distributions, with a few exceptions [e.g., Adams et al., 2001; Jacobson, 2001].

[5] Similar to other global climate models, the fourth generation of the Canadian Centre for Climatic Modelling and Analysis (CCCma) atmospheric general circulation model (AGCM4) [von Salzen et al., 2005] includes parameterizations of bulk aerosol processes that produce realistic results for three-dimensional and prognostic sulphate and sea salt aerosol concentrations. All relevant chemical and microphysical processes included in the model are based on the assumption of bulk aerosol [Lohmann et al., 1999]. As part of this study, a size-dependent bin aerosol module including chemical and microphysical processes has been incorporated into AGCM4. Observational data sets are used to validate the results of the new model for size distribution. The approach and results are described in sections 2 and 3.

[6] In the second part of this paper, the new model is used to systematically investigate the roles of different aerosol dynamical processes for the sulphate aerosol size distribution on a global scale. Atmospheric aerosol size distributions are usually characterized by three different modes: the nuclei mode (particle diameter Dp < 0.1 μm), accumulation mode (0.1 < Dp < 1 μm), and coarse mode (Dp > 1 μm) [Whitby and Sverdrup, 1980; Seinfeld and Pandis, 1998]. Nuclei and accumulation mode particles are generated by combustion processes and processes that are associated with a transfer of chemicals from the gas to the particle phase, i.e., by homogeneous nucleation and condensation. On the other hand, coarse mode particles are generated by mechanical processes (e.g., mineral dust, sea salt). Coagulation among accumulation mode particles is very inefficient. Additionally, sedimentation and deposition processes limit the growth and lifetime of atmospheric particles. Hence the transfer of particles from the accumulation mode to the coarse mode is negligible in the atmosphere. Although the broad features of aerosol size distributions are well understood, the appropriate number of size modes and their statistical properties is poorly understood. There is evidence for considerable variability of size distributions for a wide range of spatial and temporal scales [e.g., Gilliani et al., 1995; von Salzen et al., 2000; Birmili et al., 2001]. For example, Jaenicke [1993] reported that the statistical properties of nuclei, accumulation, and coarse modes vary substantially between different locations. The statistical properties of size distributions have been related to various aerosol dynamical processes. Kerminen and Wexler [1995] found that in-cloud production of sulphate explains the bimodality of the accumulation mode for observed marine aerosol size distributions. Capaldo et al. [1999] concluded that the combined action of aerosol nucleation and wet deposition explain size distributions of secondary aerosol in the marine planetary boundary layer.

[7] For continental aerosols, Wexler et al. [1994] argued in contrast to other studies [e.g., Whitby, 1978] that coagulation may not be important for the evolution of accumulation mode aerosol size distributions on regional scales under typical continental conditions compared to other more efficient processes such as nucleation and condensation.

[8] Jacobson [2003] found in a single column model study that washout may be a more important in-plus-below-cloud removal mechanism of aerosol number than rainout but that the opposite is true for the aerosol mass concentration.

[9] The strong nonlinear dependency of most aerosol dynamic processes on particle size implies that studies of aerosol size distributions and processes for a particular region may not be useful in explaining results in other regions. In the current study it is therefore attempted to systematically investigate the roles of different aerosol dynamical processes for the sulphate aerosol size distribution on a global scale. The approach and results are described in section 4.

2. Model Description

[10] A developmental version of the fourth generation CCCma atmospheric general circulation model (AGCM4) is used here. AGCM4 uses a spectral representation with a triangular truncation of 47 waves (T47) corresponding to a horizontal resolution of 3.75° × 3.75°. Thirty-five levels are used in the vertical. This version of the model is based on the third generation CCCma atmospheric GCM, AGCM3 (N. McFarlane et al., internal report, Canadian Centre for Climate Modelling and Analysis, Environment Canada, Victoria, British Columbia, Canada, 2006). A description of AGCM4 is given by von Salzen et al. [2005].

[11] The parameterization of the bulk sulphur cycle in AGCM4 includes emissions, transport, gas-phase and aqueous-phase chemistry, and dry and wet deposition. For both cumulus clouds and stratiform clouds, in-cloud oxidation occurs with respect to hydrogen peroxide (H2O2) and ozone (O3) as oxidants [von Salzen et al., 2000]. Monthly mean emissions of gas-phase sulphur dioxide (SO2) are prescribed in the model on the basis of the global emission (GEIA) inventory. Three-dimension daily averaged concentrations of OH, O3, H2O2 and NO3 from the MOZART model [Brasseur et al., 1998; Hauglustaine et al., 1998] are used for aqueous and gas-phase chemical processes. Additionally, concentrations of NH3 and NH4+ from Dentener and Crutzen [1994] are used for the calculation of pH-dependent reaction rates in clouds.

[12] The new sulphur cycle parameterizations for prognostic size distributions are based on the original bulk sulphur cycle in AGCM4 and the Canadian Aerosol Module (CAM) [Gong et al., 2003]. Twenty-four lognormally spaced bins are used in the particle radius ranging from 0.005 to 20.38 μm. The treatment of gas-phase chemistry is the same as that used in the bulk sulphur cycle which accounts for the gas-phase production of SO2 for oxidation of DMS by OH and NO3 and oxidation of SO2 by OH to H2SO4 [Lohmann et al., 1999].

[13] Some processes, such as in-cloud chemistry and scavenging, and dry deposition, are modified to account for size-dependent aerosol. The parameterizations of size-dependent processes are described in the following section.

2.1. Nucleation and Condensation

[14] In this work the chemical production and loss of gaseous H2SO4 is represented by

equation image

Here the first term represents the production of gaseous H2SO4 from oxidation by OH and SO2, image is the corresponding rate coefficient. COH and image are the concentrations of OH and SO2. The last two terms represent the loss of gaseous H2SO4 due to condensation and nucleation. The nucleation term knucl and the exponent S for binary homogeneous nucleation of sulphuric acid and water vapor are parameterized according to the approach of Kulmala et al. [1998]. New particles generated from binary homogeneous nucleation of gaseous H2SO4 and water vapor are attributed to the smallest bin. Parameters kcond is given by the approach described by von Salzen et al. [2000] and von Salzen [2005]. In order to solve this equation, the steady state solution is calculated using the Newton-Rhapson iterative method. The result then used to calculate the time evolution of H2SO4 due to nucleation and condensation according to the equation (1) [von Salzen et al., 2000].

2.2. Coagulation

[15] The parameterization of Jacobson [1994] is used to account for the effect of collision between particles:

equation image

where i and k are size bin indices. The change of the particle number in bin k are determined by production when particles in bin k-i coagulate with particles in bin i, and loss when particles in bin k coagulate with all particles. The parameter β is the coagulation kernel which accounts for processes such as Brownian motions, turbulence and gravitational settling. A semi-implicit scheme proposed by Jacobson [1994] is used to solve equation (2), which is volume conserving [Gong et al., 2003].

2.3. In-Cloud Chemistry

[16] In-cloud chemical production is an important source of sulphate aerosol [e.g., Barth et al., 2000]. In AGCM4, the in-cloud sulphate production depends on the availability of SO2, and the oxidants hydrogen peroxide (H2O2) and ozone (O3) for the oxidation rate formulations given in Table 1.

Table 1. Chemical Reactions Included in the Model Indices
ReactionRate Coefficient or Equilibrium ConstantaUnitsReferenceb
Gas-Phase Reactions
DMS + OH → SO29.6 × 10−12 exp(−234/T)cm3molec−1s−11
DMS + NO3 → SO21.9 × 10−13 exp(500/T)cm3molec−1s−12
SO2 + OH → H2SO4a0 × m/(1+ a0 × m/a) × 0.6[1./(1.+log(a0m)/a)2] with a0 = 3 × 10−31 × (300/T)3.3 and a = 1.5 × 10−12cm3molec−1s−13
Equilibrium Reactions
SO2(g) + H2O(aq) ↔ SO2(aq)1.23 × 3120(1/T-1/298)M/atm4
SO2(aq) ↔ H+ + HSO335.53(1/T-1/298)M4
HSO3 ↔ H+ + SO32–6.72 × 10–5M/atm4
O3(g) + H2O(aq) ↔ O3(aq)29.44(1/T-1/298)M/atm4
H2O2(g) + H2O(aq) ↔ H2O2(aq)6.4 × 108M/atm4
Aqueous-Phase Reactions
S(IV) + H2O2 → S(VI) + H2O8 × 104 exp[−3650(1/T-1/298)] (0.1+ [H+])−1M s−15
S(IV) + O3 → S(VI) + O24.4 × 1011 exp(−4131/T) + 2.6 × 103 exp(−966/T)[H+]−1M s−16

[17] The parameterization of in-cloud oxidation in AGCM4 accounts for the dependency of the in-cloud oxidation rates on the pH of the cloud water. The H+ concentration is calculated from an ion balance equation that accounts for the dissolution of the chemical species SO2, NH3, HNO3, and CO2 in cloud droplets [von Salzen et al., 2000].

[18] In this study, a bulk approach has been used instead of size-dependent in-cloud chemistry in order to obtain a model approach with reasonable efficiency. A simple approach has been used to distribute additional sulphate by in-cloud oxidation over the bins of the activated particles. The production of SO42− within individual cloud droplets of different size is approximated as a purely volume-controlled process. It is assumed that the cloud droplet have identical chemical composition and transport limitation effects can be neglected for the gas and aqueous chemical species. This approach is similar to that in NARCM [von Salzen et al., 2000].

2.4. Dry Deposition

[19] A size-dependent dry deposition approach is used, which includes the deposition processes of Brownian diffusion, impaction, interception, gravitational settling and particle rebound [Zhang et al., 2001]. The dry deposition velocity can be expressed as

equation image

where Vg is the gravitational settling velocity which is determined by the particle size. Ra is the aerodynamic resistance above the canopy, which can be calculated according to the height, roughness, stability and friction. The surface resistance (Rs) depends on the size of particles, atmospheric conditions and surface properties. High-resolution (1 km × 1 km) global land cover data are used here that include 15 land use categories, and five seasonal categories for calculating the dry deposition velocity [Gong et al., 2003].

2.5. Wet Deposition

[20] Wet removal includes rainout (in-cloud scavenging) and washout (below-cloud scavenging). The in-cloud removal of soluble gas (SO2) is parameterized by using

equation image

Here a is cloud fraction, H is Henry's law constant, C is gas-phase SO2 concentration, τ = LWC/(Qaut + Qacc), LWC is cloud liquid water content, Qaut is the rate of autoconversion of cloud liquid water, and Qacc is the rate of accretion of cloud liquid water by rain [Croft et al., 2005]. The in-cloud removal of and particles are parameterized by using

equation image

Here C is in-cloud aerosol concentration.

[21] In order to calculate the scavenging rate of aerosols or clouds by rain and snow, the collection efficiency of aerosol particles by hydrometeors (E) is required. E is the efficiency of reduction of particles below cloud by precipitation, and is a result of the combined action of Brownian diffusion, inertial impaction, and interception. A size-dependent scheme for below-cloud scavenging [Slinn, 1984] has been applied to calculate the collection efficiency E for particles. Figure 1 shows that small and large particles have high collection efficiency while removal of accumulation mode is least efficient.

Figure 1.

Global and annual average collection efficiency as a function of particle size for the levels 995 and 780 hPa (solid curve and dashed curve).

[22] The scavenging rate for rain and snow below cloud base is approximated according to Slinn [1984]. For rain,

equation image

where f is a numerical factor of order unity (0.5), ri is the radius of aerosol particles. The precipitation rate P is also used to obtain the mean drop radius Rm. C is the below-cloud aerosol concentration. For snow,

equation image

where λ and Dm are characteristic length scales, and γ is a constant of order unity (0.6). Depending on temperature, λ and Dm have different values for different types of snows.

2.6. Water Uptake

[23] As soluble species, sulphate aerosol particles will grow with increasing relative humidity. The particle density is also changed as the particle size increases. The aerosol dynamical processes associated with size distribution such as condensation, gravitational settling and activation strongly depend on the size and density of particles, so it is necessary to include water uptake in the model in order to simulate the aerosol size distribution. The equilibrium condition for a solution droplet in moist air is given by the Köhler equation,

equation image

where fr = r/rd is the ratio of the particle radius over the dry particle radius rd (assuming a sphere). The exponential in this equation accounts for particle curvature on the relative humidity with A′ given by

equation image

where σ is the surface tension between the droplet and air, ρw is the density of water, Rw is the gas constant for water vapor, T is the temperature. The exponential form for the water activity is

equation image

where equation image is the practical osmotic coefficient for an aqueous solution of (NH4)2SO4, equation image is the volume of the droplet, Mw is the molecular weight of water, equation images is the molecular weight of (NH4)2SO4, ms and mw denote the masses of (NH4)2SO4 and water, respectively. Using equations (7) and (9), the Köhler equation can be written:

equation image

where B = equation imageequation image(Mw/equation images)(ρdw), ρd is the dry density of the aerosol. equation image has been obtained as a function of aw on the basis of a fit to laboratory results. An iterative procedure is used to obtain fr from equation (10) [Gong et al., 2003].

3. Simulation of Present-Day Sulphate Aerosol

[24] A simulation including all physical and chemical process described in section 2 has been performed with the model. The sea surface temperature (SST) and sea ice in the simulation are from the second phase of the Atmospheric Model Intercomparision Project (AMIP) for the period January 1956 through December 2000. The meteorological situation is the same as in the standard AGCM4 because feedbacks between sulphate size distribution and meteorological results are not considered in the version of the model used in this study. Instead, the feedbacks between the integrated sulphate from all size bins and meteorological situation are considered. The simulation is performed for a 3-year period.

3.1. Sulphate Aerosol Burdens and Size Distributions

[25] Figures 2a and 2b show the simulated sulphate concentration at the lowest model level. During the period 1 June to 31 August (JJA), the model captures the three major industrial SOX emission regions such as North America, Europe, and east Asia in the Northern Hemisphere. Maxima in South America and South Africa are mainly caused by biomass burning. In contrast to JJA, sulphate concentrations are considerably lower over the Northern Hemisphere during the period 1 December to 28 February (DJF) owing to low oxidation concentrations and oxidation rates in winter. Over the Arctic, transport of SOx from Eurasia contributes to a relatively high sulphate burden in this region.

Figure 2.

Simulated sulphate concentration (in μg S/m3) and mass mean diameter for the dry particles (in μm) at the model level 995 hPa for JJA (Figures 2a and 2c) and DJF (Figures 2b and 2d).

[26] The mass mean diameter (MMD) is a useful measure of the size of the aerosol particles and is considered in the following:

equation image

Here Ci is the sulphate concentration and Di is the mean diameter for bin number i. Figures 2c and 2d display the MMD spatial distribution for JJA and DJF. It shows that the spatial distribution of MMD is generally similar to the distributions of the sulphate concentration in both JJA and DJF near the surface (Figures 2a and 2b). The higher values over ocean in the Southern Hemisphere in winter is probably attributed to oceanic DMS emissions. It also can be found that the values of MMD can be small in regions with large concentrations and vice versa, e.g., for east Asia in DJF.

3.2. Comparison With Observations

[27] Figure 3 shows the geographical locations for various observations that are used in this study. Observations used to validate surface sulphate concentrations come from three different sources. The first one provides non-sea-salt sulphate concentrations over industrial regions, the Arctic and sub-Arctic, ocean and Antarctic [Chin et al., 1996]. The second one includes results for North America from the Canadian Air and Precipitation Monitoring Network (CAPMoN) and the Clean Air Status and Trends Network (CAST) [Ro et al., 1997]. Additional data (J. M. Prospero and D. L. Savoie, personal communication, 2000) give sulphate concentrations over the ocean and downwind of emission sources.

Figure 3.

Locations of sites with observational data used for comparisons. Squares [Chin et al., 1996], crosses (CAPMoN/CASTNet), and triangles (J. M. Prospero and D. L. Savoie, personal communication, 2000) refer to surface observations. Other data sets shown in rectangles are from New York City Urban Plume Experiment (NYC), Southern Oxidant Study (SOS), and ACE-Asia (PF1 and PF2).

[28] A comparison of simulated and observed surface concentrations is shown in Figure 4. This scatter plot shows the simulated surface sulphate concentration versus observations for JJA and DJF. Overall, the simulated sulphate concentrations agree well with the observations. For JJA, 82% of the simulated sulphate concentrations agree within a factor of 2 with the observations. The correlation coefficient for simulated and observed results is 0.93. The model overpredicts the mean surface concentration for JJA by 5%. However, the model underpredicts the surface concentrations by 20% for DJF with a correlation coefficient of 0.77. Seventy-six percent of the modeled results agree with the observations within a factor of 2 for DJF.

Figure 4.

Comparison between simulated and observed surface mass concentration. From top to bottom, comparisons are shown for JJA and DJF. Three lines indicate 2:1, 1:1, and 1:2 ratios. Modeled versus observed ratios and correlation coefficients are indicated in each plot.

[29] The radiative forcing depends not only on surface sulphate concentration, but also on the vertical distribution of the aerosol, composition, and size distribution. Only a limited number of observational data sets are available for in situ comparisons for vertical and size distributions. Two different data sets from aircraft observations are used in the current study. The data sets were taken during the New York City (NYC) Urban Plume Experiment from 1 to 28 July 1996 over New York [Kleinman et al., 2000] and during the Southern Oxidant Study (SOS) from 24 June to 20 July 1995, over Tennessee [Hübler, 1998] (Figure 3). The experiments involved 15 and 17 flights, respectively, and cover a wide range of conditions with varying amounts of aerosol for different regions and time periods. A Passive Cavity Aerosol Spectrometer Probe (PCASP) was used to sample the aerosol number size distribution between 0.1 and 3.5 μm particle diameter in 15 size bins. Another data set (PF1 and PF2) was taken during the Asian Pacific Regional Aerosol Characterization Experiment (ACE-Asia) from 30 March to 4 May 2001 over the regions shown in Figure 3. The data were collected using the NCAR/NSF C-130 during the ACE-Asia program to determine the number size distribution between 0.5 and 12 μm particle diameter in 224 size classes [National Center for Atmospheric Research, 2001].

[30] Figure 5 compares the simulated and observed aerosol mass size distributions for NYC, SOS and PF1 and PF2 at two height levels. For these results, the mass size distributions for the observations were calculated from the observed number size distributions on the basis of the assumption of ammonium sulphate aerosol. The size distributions were spatially averaged over the volumes of the corresponding AGCM grid cells according to the spatial coordinates of each single measurement on the flights. Furthermore, results for each experiment were averaged over the entire time period of the experiment and compared to monthly mean AGCM results for corresponding months.

Figure 5.

Comparison between modeled (curves with the asterisks) and observed sulphate mass concentration for (left) NYC and SOS in July and (right) PF1 and PF2 in April. From top to bottom, comparisons at level 800 ∼ 700 hPa and level 1000 ∼ 800 hPa are shown.

[31] The comparison indicates that the model successfully reproduces the size distribution in the accumulation mode size range (0.1 < Dp < 1.0 μm) for both locations over the eastern United States. The results for NYC are in very good agreement with observations in the free troposphere (800 ∼ 700 hPa) and near the surface (1000 ∼ 800 hPa), which is consistent with the fact that sulphate is the dominant aerosol component over the eastern United States [Malm et al., 2004]. Compared to NYC, the simulated mass concentrations over SOS are much lower than the observational results. Other aerosol components, such as organic carbon, whose particle size is similar to sulphate, probably contribute to this difference. However, differences between the simulated and observed in Figure 5 are probably mainly attributed to different meteorological and chemical situations owing to the fact that the observations are for a limited time period and space scale.

[32] In contrast to North America, the size distributions from ACE-Asia during spring are strongly influenced by the prevalence of Asian mineral dust since the dust storm activity from the Taklimakan desert and arid regions in Southeast Asia peaks during this time of the year [Zhang et al., 2003]. Consequently, considerably large mass concentrations are observed for particles with diameters larger than 0.6 μm. Concentration of coarse mode aerosol particles are much higher for a profile near Shanghai (PF1) compared to a location further offshore in the northeast of PF1 (PF2). However, the simulation does not account for the contribution of mineral dust to the size distribution. Simulated sizes of accumulation mode particles agree well with the observations at both sites. Similar to the other experiments, the absence of black and organic carbon aerosol likely contributes to the underestimate in accumulation mode aerosol concentrations in the simulation for PF1 and PF2.

[33] Modeled size distributions are slightly broader than the observed size distributions in Figure 5. It is expected that the agreement can be improved by increasing the number of size bins in the model. Tests indicate (not shown) that simulations for 12 size bins lead to much broader size distributions. This study uses 24 bins instead of a higher number of size bins in order to avoid unreasonably high computational costs. It should be pointed out that this aspect will be improved in the future by introducing a new numerical treatment for aerosol size distributions [von Salzen, 2005], which uses a more accurate and efficient method to represent particle size distributions.

[34] An additional observational data set from Aerosol Robotic Network (AERONET), is used to further test the model performance. AERONET is an international federation of sun photometer networks [Holben, 1998] with about 180 ground-monitoring sites. AERONET results have been used to determine mean column aerosol size distributions in various geographical locations (Figure 6; G. Lesins, personal communication, 2003). As the aerosol information is retrieved from solar radiation directly measured by sun photometer, only the simulation results that are for clear-sky conditions and during daytime can be used for the comparisons. A threshold of 0.15 for total cloud fraction is used for the diagnostic of simulated size distributions in order to reduce the contamination of simulation results by cloudy conditions. The simulated sulphate size distribution has been used to determine the vertically integrated aerosol volume size distribution for 22 bins between 0.05 and 15.0 μm particle diameter online during the simulation, corresponding to the size distribution used for observations.

Figure 6.

Locations of sites from AERONET. The different sites are grouped to represent sites over the eastern United States, Europe, ocean, South America, and the western United States.

[35] Figure 7 shows the simulated (purple curves) and observed (black curves) annually averaged aerosol volume size distributions for the AERONET sites. Although the omission of aerosol compounds other than sulphate in the simulation is a substantial approximation, the approach seems useful for regions that are strongly affected by sulphate aerosol, such as the eastern United States [Malm et al., 2004]. This figure shows that the model can reasonably well reproduce the observed size distributions for the accumulation mode for most locations. The coarse aerosol mode in the observations is expected to be associated with other aerosol types, specifically, mineral dust and sea salt which are not included in the simulation. As shown in Table 2, the ratios of the simulated to the observed total column volume of the accumulation mode (25% < rv < 85%) vary depending on the region. As expected, high-aerosol-precursor-emission regions such as North America and Europe generally have relatively high ratios compared to some regions where sulphate is an minor aerosol type, for example, for South America. Observations [Malm et al., 2004] give evidence that between 50 and 60% of the mass of the accumulation mode can be attributed to sulphate aerosol for the eastern United States, which appears to be consistent with an underprediction of aerosol volume by 45% (Table 2). For the eastern United States, organics contribute about 20% to the mass of the accumulation mode [Malm et al., 2004]. This ratio should be much higher for South America because of the important role of biomass burning in this region.

Figure 7.

Comparison between the observed from AERONET (black curves) and the modeled (purple curves) vertically integrated volume size distribution.

Table 2. Simulated (rs) and Observed (ro) Local Maximum of the Volume Size Distribution, Their Difference Δr, and Ratio of Total Simulated to Observed Accumulation Mode Volume Vs/Vo
 rs, μmro, μmΔr, μmVs/Vo, %
Eastern United States0.170.150.0255
South America0.150.110.0425
Western United States0.150.140.0165

[36] Table 2 shows that modeled location maximum of the volume size distribution occurs at slightly too large particle sizes in comparison to the AERONET data set for all locations. It should be noted that the relatively few observations that are available in this study, only allow qualitative comparisons. More observational data sets are needed for quantitatively more meaningful comparisons in the future.

[37] Figure 8 shows the seasonal variation of the size distribution for different locations. The model captures the observed seasonal variation; that is, the particle sizes are generally smaller in DJF compared to in JJA for the eastern United States, Europe, and the western United States. However, the model does not reproduce the basic feature of seasonal change in South America which again gives evidence for an important role of nonsulphate accumulation mode aerosol in this region. In addition, the simulated particle volumes are generally too low in DJF, which is consistent with the underestimation of sulphate concentrations (see Figure 2).

Figure 8.

Seasonal mean of vertically integrated size distribution from simulation (curves with asterisks) and AERONET.

4. Sensitivity of Size Distribution to Dynamical Processes

[38] The production and removal of aerosol involves strongly nonlinear physical and chemical processes. In order to better understand how these processes affect sulphate burden and size distribution, a number of sensitivity experiments, summarized in Table 3, have been performed with the model. The simulations were performed for a 3-year period for given sea surface temperatures (section 3).

Table 3. Summary of Experiments With Different Versions of the Sulphur Cycle
NameExperiment Description
REFEreference experiment, includes all processes
DRYDas REFE but no dry deposition
COAGas REFE but no coagulation
NUCLas REFE but with a nucleation efficiency reduced by 2 orders of magnitude
CONDas REFE but no condensation
COIPas REFE but no in-cloud production in cumulus clouds
COWDas REFE but no wet deposition due to cumulus clouds
STIPas REFE but no in-cloud production in stratiform clouds
STWDas REFE but no wet deposition due to stratiform clouds
NUCL/COAGas COAG but with reduced nucleation efficiency as in NUCL
STIP/COAGas COAG but no in-cloud production in stratiform clouds

[39] In the reference experiment (REFE), all dynamical processes described in section 2 are included. The sensitivity experiments DRYD, COAG, NUCL, COND, COIP, COWD, STIP and STWD are conducted to test the effects of dry deposition, coagulation, nucleation, condensation, cloud production and scavenging in convection and stratiform, on sulphate burden and size distribution, respectively. For all tests, except one, the parameterization that corresponds to each individual process was removed from the model code. For experiment NUCL, the nucleation efficiency was reduced by multiplying the last term in equation (1) by 0.01.

4.1. Sulphate Budgets

[40] An overview of the global mean sources and sinks of sulphate aerosols is given in Table 4 from the reference and sensitivity simulations. For the reference simulation, in-cloud oxidation of SO2 for stratiform cloud is the most important source of sulphate, which contributes 61% of the total sulphate production. Condensation accounts for 30% of the sulphate source, convective production only contributes 9%. For the sinks of sulphate, scavenging by large-scale layer cloud dominates the sulphate loss (66%), followed by dry deposition (22%). The scavenging by convective clouds contribute about 12%.

Table 4. Annually and Globally Averaged Sulphate Sources and Sinks in the Reference and Sensitivity Experimentsa
NucleationCondensationLayer ProductionConvection ProductionDry DepositionLayer Wet DepositionConvection Wet Deposition
  • a

    Units are Tg S yr−1.


[41] Theses results are consistent with the model studies of Langner and Rodhe [1991] and Pham et al. [1995]. These studies found in a global chemistry transport model that wet deposition is the most effective process with respect to removal of aerosol mass.

[42] Experiments DRYD, COWD and STWD produce only small changes in the source terms. The removal of a sink process in these experiments leads to compensating increases in the strengths of the other sink processes in these simulations.

[43] The removal of stratiform in-cloud production in STIP leads to marked increases in clear-sky and convective sulphate production rates. The reductions in sulphate production from the removal of in-cloud production in STIP are largely compensated by increased condensation and reduced wet deposition from stratiform clouds compared to REFE. The compensating effect from reduced wet deposition is considerable because stratiform clouds represent a net sink for sulphate aerosol in REFE on the global scale. Hence in-cloud produced aerosol is efficiently removed by wet deposition (Table 4). Although the timescale for sulphate production from condensation is about twice as large as the timescale for the production from in-cloud oxidation in stratiform clouds in REFE, the timescale for condensation decreases considerably without in-cloud oxidation in STIP. The reason for this is that a large amount of SO2 remains in the atmosphere if in-cloud oxidation is removed from the model. The in-cloud oxidation pathway represents a rather important sink for SO2 on the global scale [e.g., Lohmann et al., 1999].

[44] Similarly, the removal of condensation in COND leads to large increases in the nucleation rate but small changes otherwise. As expected, the removal or reduction of relatively weak processes, such as convective in-cloud production (COIP) and nucleation (NUCL) lead to only small changes for the other source and sink processes. Similarly, sources and sinks of sulphate are not sensitive to the removal of coagulation (COAG). However, it should be pointed out that COAG produces large changes for the sources and sinks of aerosol number concentration (not shown).

4.2. Sulphate Concentrations

[45] Table 5 summarizes the global annual mean sulphate burdens in the simulations. Compared to REFE, the total burden in the experiment NUCL is lower, while the burden is higher for the other experiments. The removal of stratiform sulphate wet deposition (STWD) leads to an increase of the sulphate burden by 224%. The removal of convective wet deposition (COWD) increases the sulphate burden by 78%. The increases of sulphate burden caused by the removal of dry deposition (DRYD), in-cloud production for stratiform clouds (STIP) and convection clouds (COIP) are 34%, 47% and 10%, respectively. The change of sulphate burden in COAG and COND is relatively small.

Table 5. Globally Averaged Annual Mean Sulphate Burden and Mass Mean Diameter From Reference and Sensitivity Experiments
 Total Burden, mg S/m2Mass Mean Diameter, μm

[46] Figure 9 shows the spatial distributions of annual mean sulphate burden and annually averaged zonal mean distributions of sulphate for the experiments. The basic distributions are similar in the sensitivity simulations and REFE.

Figure 9.

Simulated (left) annual mean sulphate column burden (in mg S/m2) and (right) zonal mass sulphate mass mixing ratios as function of latitude and pressure level (in ppb).

Figure 9.


Figure 9.


[47] The removal of wet deposition in stratiform (STWD) leads to a higher sulphate burden because of an increase in transport to high latitudes and to the upper troposphere. The increase in sulphate burden in STIP is attributed to an increase in SO2 concentration since a major sink of SO2; that is, in-cloud oxidation in stratiform clouds was removed. Thus the production of sulphate via condensation increases. On the other hand, in-cloud scavenging decreases owing to the removal of in-cloud production. Hence the sulphate burden increases.

[48] Compared to the production and scavenging in stratiform cloud (STWD and STIP), the removal of wet deposition in convection (COWD) does not change the source and sink terms a lot (Table 4), but nevertheless leads to a large increase in sulphate burden. The reason is that removal of convective scavenging increases the transport of aerosol to the upper troposphere. The lifetime of aerosol in the upper troposphere is much longer than in the lower troposphere owing to inefficient removal processes in this region. Hence the burden is increased. Increases in DRYD are mainly located in the low troposphere since dry deposition primarily affects concentrations near the surface.

[49] The experiments also show that COAG, COIP, NUCL and COND produce relatively minor changes in the global burdens which is somewhat consistent with the relatively small changes in sources and sinks in these experiments compared to REFE. COAG and COND produce very similar distributions and vertical profiles compared to REFE. A weaker increase in COIP is attributable to an increase in SO2 lifetime owing to an increase in convective transport of SO2 into the upper troposphere.

4.3. Sulphate Size Distributions

[50] Figure 10 compares the simulated global and annual means of the size distributions from all experiments. The peak of the size distribution is at around 0.3 μm in REFE. DRYD, COIP, COWD, STIP produce changes in mass but these changes affect all particles in a similar way so that the shape of the size distribution is not strongly affected. In particular, mode radius and width are similar (Figure 10). The reduction of nucleation efficiency in NUCL leads to particularly small change in the size distribution.

Figure 10.

Global and annual mean of the vertically integrated sulphate size distribution in the reference and sensitivity experiments.

[51] However, COAG, COND, and STWD produce significant changes in size distributions (Figure 10). In COAG, more mass is associated with small particles compared to REFE because fewer large particles are produced owing to the removal of particle growth by coagulation. Similar, the removal of particle growth by condensation in COND leads to smaller particle sizes compared to REFE.

[52] Global and annual means of mass mean diameter in the first model layer for all experiments are given in Table 5. The values of MMD in DRYD, COIP, COWD and STIP are similar to the value in REFE. However, the mass mean diameter increases for STWD while COAG and COND produce smaller mass mean diameter. These results give evidence that the sulphate size distribution is not significantly affected by dry deposition, in-cloud production and wet deposition in convective cloud, but affected by condensation, coagulation, and scavenging from stratiform clouds.

[53] Figure 11 illustrates how the size distribution vary as a function of latitude. The removal of condensation in COND leads to smaller particle sizes at mid latitudes. This is consistent with an important role of condensation for the growth of particles over the NH source regions. COAG produces reductions in particles size at all latitudes. Small particles are less efficiently scavenged than large particles, so that the transport from emission regions to more remote regions increases and concentrations of small particles increase at all latitudes. It is also found that coagulation is important especially for small particles with a diameter less than 0.1 μm, which is consistent with the model results of Jacobson [1997] and Jacobson [2001]; that is, coagulation reduces the number and volume concentration of particles less than 0.2 μm in diameter.

Figure 11.

Zonally and vertically averaged size distribution as a function of latitude from the reference and sensitivity experiments. Isolines are shown at 0.1, 0.5, 1, 2, 3, 4, 5, and 10 mg S/m2.

4.4. Further Analysis of the Sensitivity of the Size Distribution to Nucleation and In-Cloud Production

[54] Interestingly, the removal of in-cloud production (STIP) and substantial reduction in the nucleation efficiency (NUCL) does not lead to any marked changes in the particle size. This appears counterintuitive given that in-cloud production is the dominant source of sulphate in the atmosphere (Table 4) and that nucleation is the only source for the aerosol number in the simulations.

[55] To further explore the reason for the unexpected small changes in STIP and NUCL, these simulations were repeated but without the parameterization for coagulation (experiments STIP/COAG and NUCL/COAG).

[56] Similar to experiments STIP and REFE, the removal of in-cloud production in stratiform clouds produces an increase in the sulphate burden (Table 5). However, as shown in Figure 12, there is a considerable reduction in particle size in STIP/COAG compared to COAG, which leads to a smaller mass mean diameter (0.12 μm in STIP/COAG, compared to 0.19 μm in COAG).

Figure 12.

Same as Figure 10, for experiments REFE, COAG, STIP, STIP/COAG, NUCL, and NUCL/COAG.

[57] Results for STIP/COAG give evidence for a strong compensating effect of coagulation if in-cloud production in stratiform clouds is removed from the model. According to these results, the removal of in-cloud production leads to much smaller sizes and therefore an increase in the number concentration for smaller particles. If coagulation is considered, the increase in the number concentration for small particles leads to very efficient coagulation. Similarly, the large difference in particle sizes between STIP and STIP/COAG is due to a relatively strong effect of coagulation. In comparison, smaller differences in particle size between REFE and COAG are due to a weaker effect of coagulation for these simulations. Consequently, the net effect of removing in-cloud production and increased efficiency of coagulation is a relatively small change in particle size, as seen for simulations STIP and REFE.

[58] Another possible reason for the low sensitivity of the results in REFE to in-cloud sulphate production appears to be that a large fraction of the in-cloud produced aerosol is efficiently removed by wet deposition (see sections 4.1 and 4.2). Additionally, the removal of the in-cloud oxidation of SO2 leads to an increased condensational growth of aerosol particles under clear-sky conditions. However, although changes in the efficiencies of these processes indeed cause changes in the size distribution, these appear to be less important compared to the effect of coagulation as will be demonstrated near the end of this section.

[59] In order to interpret results of simulations STIP and STIP/COAG, it is also useful to reconsider the treatment of particle growth from in-cloud oxidation. As mentioned in section 2.3, it is currently not possible to account for the effects of size-dependent in-cloud chemistry in AGCMs owing to the large computational burdens that are associated with size-resolving chemical calculations. Instead, we assume that in-cloud production rates are proportional to the volume of the activated aerosol particles and that all cloud droplets have an identical chemical composition [von Salzen et al., 2000]. There is experimental evidence that aerosol growth rates are indeed volume controlled, at least for in-cloud production via H2O2 [Caffrey et al., 2001]. However, some modeling studies [e.g., Kreidenweis et al., 2003] give evidence that small particles grow more efficiently relative to large particles than would be predicted by a purely volume-controlled approach for the same total oxidation rate. Although the study by Kreidenweis et al. [2003] is for high oxidation rates that are not representative of global mean atmospheric conditions, it nevertheless appears that the assumption of volume-controlled growth likely leads to an overestimate of the growth of large particles relative to small particles for a given oxidation rate. This would imply that the production of large particles from in-cloud oxidation may be less efficient than simulated in this study. This is not contrary to the previous conclusion that in-cloud oxidation does not appear to be a very efficient mechanism for the production of large particles in the atmosphere on global scales.

[60] Although simulation NUCL/COAG produces slightly larger particle sizes than COAG, results in Figure 12 give evidence for still relative small changes, i.e., similar to simulations NUCL and REFE. Furthermore, differences between NUCL/COAG and NUCL and between COAG and REFE are similar, giving evidence for rather small differences in the effects of coagulation between simulations with reduced and original nucleation efficiency.

[61] In the following, a simple analytical model is used to further analyze the results of simulations NUCL/COAG and STIP/COAG. As described in Appendix A, the model is based on the assumption of steady state conditions. Furthermore, the model does not account for the effects of coagulation on the aerosol size distribution. The approach is to use the model as an additional diagnostic tool for the interpretation of the AGCM results. The model is applied to experiments COAG, STIP/COAG, and NUCL/COAG by using a least squares fitting procedure for the aerosol burden (Table 5) and production and loss rates (Table 4) as fitting parameters (see Appendix A for details). This approach provides diagnosed size distributions and information about the efficiencies of aerosol processes in the analytical model for the AGCM experiments. Although considerable approximations were made for the development of the analytical model, the simplicity of the model helps to identify and characterize fundamental relationships between particle size and aerosol processes, as will be shown in the following.

[62] The application of the analytical model to results of COAG yields an analytical mass size distribution that has the same total sulphate burden (difference less than 0.01%) and a slightly larger mass mean diameter (i.e., MMD = 0.23 μm, compared to MMD = 0.19 μm for COAG). For COAG/NUCL, the analytical model produces a mass mean diameter of MMD = 0.33 μm (compared to MMD = 0.22 μm for COAG/NUCL) for the same sulphate burden as from COAG/NUCL (difference less than 0.1%). Similar to the AGCM results for COAG/NUCL and COAG, the increases in particle size for reduced nucleation rates are larger for small particles compared to large particles according to the analytical model (not shown). Overall, compared to COAG/NUCL and COAG, the analytical model produces slightly larger, but qualitative similar changes for the mass size distribution.

[63] According to the results of the analytical calculations, the relatively weak response of the mass mean diameter to the substantially reduced efficiency of nucleation between COAG and NUCL/COAG is a consequence of an inherently weak sensitivity of the mass size distribution to changes in nucleation rate under global mean steady state conditions. According to these calculations, the reduction in the nucleation rate by a factor of 4.5 between COAG and NUCL/COAG leads to a similar reduction in the total aerosol number concentration (factor 4.7 difference) because the lifetimes of the aerosol particles are very similar for both cases (i.e., τr = 5.2 days for NUCL/COAG, compared to τr = 5.1 days for COAG, equation (A1)). Similarly, there is only a small difference between the in-cloud oxidation timescales (i.e., τp = 7.3 days for NUCL/COAG, compared to τr = 7.0 days for COAG, equation (A2)). The main difference between both cases is a 2.9-fold increase in the efficiency of condensation (i.e., g = 9.94 × 10−22 m2/s for NUCL/COAG, compared to g = 3.38 × 10−22 m2/s for COAG, equation (A3)). This increase in the condensation efficiency is mainly related to the reduction in particle number concentration. In equilibrium, the reduction in particle number leads to an increase in H2SO4 concentration owing to the fact that the gas-phase production of H2SO4 is nearly completely balanced by the removal of H2SO4 by condensation (see equation (1) and Table 4). However, this apparently large change in the condensation efficiency is not sufficient to cause a marked change in the mass mean diameter from the analytical model owing to a relatively low sensitivity of the analytical mass size distribution to changes in condensation efficiency for the conditions of the simulation.

[64] The analytical model has also been applied to results of experiment STIP/COAG. Similar to the AGCM results, the analytical model produces a marked reduction in the particle size if in-cloud production in stratiform clouds is removed (i.e., ΔMMD = −0.17 μm, compared to ΔMMD = −0.09 μm for the AGCM results). Additionally, there is very good agreement between the models regarding a substantial increase in aerosol mass for particle diameters smaller than about 0.1 μm and a decrease for particles larger than that (not shown).

[65] Owing to the strong coupling of in-cloud production and wet aerosol removal in layer clouds, the analytical model produces large changes in the timescales for these processes (i.e., τr = 9.3 days and τp = 40.3 days for STIP/COAG, compared to τr = 5.1 days and τp = 7.0 days for COAG). The model also produces large changes for the aerosol number concentration (i.e., a 4.6-fold increase) and condensation efficiency (g = 1.80 × 10−22 m2/s for STIP/COAG, compared to g = 3.38 × 10−22 m2/s for COAG).

[66] Additional calculations with the analytical model for different combinations of the changes in timescales and condensation efficiency for STIP/COAG and COAG give evidence that the large reduction in particle size for STIP/COAG is indeed mainly caused by the increase in the timescale for in-cloud production (τp). However, the increase in the removal timescale (τr) tends to cause an increase in particle size so that the net decrease in particle size from removal of stratiform in-cloud production is reduced by this change. The changes in nucleation rate and condensation efficiency, without any other changes, would cause a slight reduction in the mass mean diameter to MMD = 0.18 μm (compared to MMD = 0.23 μm for COAG) and very little change in aerosol mass (5% increase).

5. Summary

[67] In this paper, a physically based bin approach for simulations of sulphate aerosol size distributions has been implemented in the latest version of the CCCma AGCM. Compared to the bulk aerosol model, which is currently being used in the AGCM, the new model version includes processes such as hygroscopic growth of dry particles, nucleation/condensation, coagulation, in-cloud chemistry, and wet and dry deposition based on a bin representation of the sulphate size distribution.

[68] The simulated mass mean diameter (MMD) at the surface level is in the range from 0.2 to 0.4 μm, with typically higher values over the major emission regions.

[69] A comparison of sulphate surface concentrations indicates that the model results generally agree well with the available long-term observations. The spatial distribution and seasonal variability of sulphate are successfully captured as well. Airborne observations of size-dependent concentrations with vertical profiles from three experiments indicate that the model successfully reproduces the accumulation mode size distribution over Eastern North America and East China Sea. Although the particle size agree well for these experiments, the comparison gives evidence for an important role of nonsulphate aerosol species, such as mineral dust, whose size distribution are currently not included in the model. However, observations for longer time periods are necessary for more reliable comparisons. The comparisons with AERONET data indicate that the model underestimates the total vertically integrated aerosol volume. The underestimates are 45, 15, 45, 75, and 35%, for the eastern United States, ocean, Europe, South America and the western United States, respectively. Over the regions where sulphate is the governing aerosol, e.g., the eastern United States, there is strong evidence from surface observations that the differences in aerosol volume are caused by the omission of the contributions of non-(NH4)2SO4-aerosol species, such as organics. For South America, where biomass burning aerosol is more important, the underestimate is more substantial.

[70] Several sensitivity experiments were conducted to study the effects of aerosol dynamical processes on the size distributions. The model results indicate that the dominant sources and sinks of sulphate are in-cloud production and wet removal in stratiform clouds. Therefore removal of modal parameterizations for in-cloud chemistry and scavenging for stratiform clouds cause considerable changes in simulated sulphate burdens.

[71] In contrast, wet deposition in convective clouds is a relatively weak sink, but the removal of this process from the model leads to increased transport of aerosol to the upper troposphere where the lifetime of aerosol is long owing to inefficient removal by precipitation. This leads to a large increase in sulphate burden. Similarly, a weaker increase in sulphate burden from the removal of in-cloud production in the convection is attributed to increased transport of SO2 to the upper troposphere and subsequent formation of aerosol there.

[72] Experiments with the model without parameterizations of dry deposition, in-cloud production and wet deposition in convective clouds, and in-cloud production in stratiform clouds produce only small changes in the simulated size distribution. The removal of coagulation shifts the size distribution toward smaller particles without any marked effects on total sulphate concentrations.

[73] The removal of wet deposition in stratiform clouds increases the particle sizes. The treatment of below-cloud scavenging probably contributes to this shift since that the collection efficiency (Figure 1) has a minimum for particle diameters of about 0.4 μm so that the removal of this process increases mass more efficiently at this particle size compared to smaller or larger particles.

[74] The removal of sulphate acid condensation leads to increased concentrations of small particles and decreased concentrations of large particles.

[75] Simulations for a considerably reduced efficiency of nucleation (i.e., multiplication of the nucleation rate by 0.01) produce rather small changes in the size distribution in simulations with and without coagulation. A simple analytical model for aerosol size distributions that matches mean AGCM results was used to confirm that the response of the global mean aerosol size distribution is indeed very small to relatively large changes in nucleation rates.

[76] Results of an additional simulation without coagulation and in-cloud production in stratiform clouds gives evidence that the low sensitivity of the size distribution to the treatment of in-cloud production in layer clouds is due to a compensating effect of coagulation. Without coagulation, the model produces much smaller particle sizes if in-cloud oxidation is removed from the simulation compared to the simulation that includes coagulation.

[77] The results of the sensitivity tests give evidence for different roles of aerosol dynamical processes for the concentration and sizes of sulphate aerosol particles in the global atmosphere. There is evidence for strong and nontrivial interactions between different aerosol dynamical processes. These interactions clearly play important roles in the responses of the aerosol size distributions to changes in atmospheric processes in the global atmosphere.

[78] On the basis of these findings, it can be expected that future changes in sulphate emissions, chemistry, and climate may lead to changes in the efficiencies of these processes and may therefore lead to yet unknown feedbacks between climate and aerosols. In addition, information about the role of individual processes for aerosol concentrations and size are an important basis for the development of improved aerosol/climate models. In the future, results of the current study will be used to develop an accurate and more efficient model that will also include parameterizations of nonsulphate aerosols and parameterizations for the effects of aerosols on radiation and climates.

Appendix A:: Simple Mathematical Model of Size Distributions

[79] Features of aerosol size distribution, such as shape and mass mean diameter, are the consequence of highly nonlinear processes in the atmosphere. Owing to the substantial variety and complexity of the relevant chemical, macrophysical and microphysical processes that are involved, it is necessary to perform and analyze fully interactive numerical simulations of these processes for accurate estimates of the statistical properties of the aerosol size distribution.

[80] In the following, a relatively simple analytical model is described that can be used as a additional tool to highlight fundamental features of atmospheric aerosol size distributions and their relationships to atmospheric processes under idealized conditions. In particular, the model does not account for the effects of coagulation on aerosols. Furthermore, it is based on the assumption of steady state conditions.

[81] In order to obtain a simple analytical approximation of the number size distribution of the atmospheric aerosol, it is necessary to consider the effects of nucleation, condensation, dry and wet removal, and oxidation.

[82] Let τr = τr(R) be the characteristic timescale for the removal by dry and wet deposition of a particle with radius R from the atmosphere. With this assumption, the temporal evolution of the aerosol number concentration δN for particles within a radius range δR around R is given by

equation image

[83] Furthermore, a simple approximation of the growth of aerosol particles with mass m by oxidation of S(IV) is given by

equation image

where τp = τp(R) is the relevant timescale. As in reality, τp may also depend on the chemical composition of the cloud droplets or particles and the surrounding air. It should be noted that although it is convenient to assume that the oxidation rate is proportional to the aerosol mass (see also discussion in section 2.3), this is not an essential assumption at this stage.

[84] Finally, the growth of aerosol particles by condensation of H2SO4 and NH3 is approximated by

equation image

where g = g(R) is given by [e.g., von Salzen, 2005; Seinfeld and Pandis, 1998]

equation image

D represents the diffusivity of H2SO4 in air. ρp denotes the density of the dry aerosol (ρp = 1769 kg/m3). Here, f is the aerosol growth factor, i.e., the ratio of wet over dry particle radius. F and A are dimensionless and size-dependent factors that account for noncontinuum effects and imperfect surface accommodation. image and image denote the molecular weights of (NH4)2SO4 and H2SO4, respectively. image is the concentration of H2SO4 in the air.

[85] On the basis of equations (A2) and (A3), an expression for the growth of the particle radius by oxidation and condensation is given by

equation image

Integration of equation (A1) and substitution of equation (A5) yields

equation image

where R0 is the radius and δN0 the number concentration of the initial particles. In the following it assumed that R0 and δN0 refer to the smallest particles in the size spectrum, i.e., those that are produced by nucleation.

[86] In order to obtain an expression for the aerosol number distribution, it is necessary to consider that particles that are initially within a certain size range δR0 will occupy a different size range δR at a later time as a consequence of aerosol growth. The combined effect of growth and removal on the number concentration is given by the following continuity equation for particle number:

equation image

[87] The role of nucleation on the number size distribution in (A7) becomes apparent from a continuity equation for the smallest particles (i.e., with radius R0) in the size spectrum. For those particles, a balance between the production by nucleation and removal by particle growth under steady state conditions at radius R0 implies that

equation image

where dN0/dt is the nucleation rate and dR0/dt is given according to equation (A5).

[88] Combination of equations (A6) to (A8) finally yields

equation image

for RR0.

[89] Although it is clear that τr, τp, and g in equation (A9) generally depend on the size, it is convenient to assume that these are constant for the sake of simplicity. Although this assumption can be expected to affect the calculated size distribution, applications of the model to AGCM results give evidence for relatively small impacts on the response of the calculated size distributions to changes in the efficiencies of aerosol processes.

[90] The assumption of constant τr, τp, and g in equation (A9) gives

equation image

with k = 3τp/(2τr).

[91] For appropriate choices of the parameters, the size distribution according to equation (A10) depicts a single size mode. According to this result, nucleation does not directly affect the shape of the size distribution; that is, statistical quantities such as the mass mean diameter or mode radius are unaffected by changes in dN0/dt. However, it is clear from equations (1) and (A4) that, under steady state conditions, changes in nucleation rate will be accompanied by changes in the concentration of H2SO4, and therefore g, for a constant production rate for H2SO4.

[92] For applications of the analytical model in this paper, τr, τp, and g are obtained by fitting results of the analytical model to global mean results from the AGCM. This procedure provides analytical size distributions that can be compared to the AGCM results.

[93] A least squares fitting procedure is applied. The fitting parameters are the global integrated aerosol mass (Table 5) and the production (or loss) rates due to condensation, in-cloud production, and removal (Table 4). For in-cloud production, the sum of stratiform and convective production is used. For removal, the sum of stratiform and convective wet deposition and dry deposition is used.

[94] The aerosol mass concentration M according to the analytical model is given by

equation image

for dN/dR from equation (A10). For this equation, dN0/dt is directly available as the global mean nucleation rate (e.g., Table 4 shows results for the mass nucleation rate) for given R0 = 0.005 μm.

[95] The removal and oxidation rates according to the analytical model are given by

equation image
equation image

respectively. According to equation (A3), the condensation rate is given by

equation image

[96] Equations (A11) to (A14) are used in the least squares fitting to procedure to obtain τr, τp, and g for given aerosol production and loss rates and mass concentration.


[97] We thank Glen Lesins for generating data from AERONET results. We also thank two anonymous external and two internal reviewers (John Scinocca and Jiangnan Li) for their helpful comments and suggestions. Funding for this study has been provided by the Climate Change Action Fund (CCAF), NSERC, and Environment Canada.