Microphysical simulations of new particle formation in the upper troposphere and lower stratosphere

Using a three-dimensional general circulation model with sulfur chemistry and sectional aerosol microphysics (WACCM/CARMA), we studied aerosol formation and microphysics in the upper troposphere and lower stratosphere (UTLS) as well as the middle and upper stratosphere based on three nucleation schemes (two binary homogeneous schemes and an ion-mediated scheme related to one of the binary schemes). Simulations suggest that ion-mediated nucleation rates in the UTLS are 25 % higher than its related binary scheme, but that the rates predicted by the two binary schemes vary by two orders of magnitude. None of the nucleation schemes is superior at matching the limited observations available at the smallest sizes. However, it is found that coagulation, not nucleation, controls number concentration at sizes greater than approximately 10 nm. Therefore, based on this study, processes relevant to atmospheric chemistry and radiative forcing in the UTLS are not sensitive to the choice of nucleation schemes. The dominance of coagulation over other microphysical processes in the UTLS is consistent with other recent work using microphysical models. Simulations using all three nucleation schemes compare reasonably well to observations of size distributions, number concentration across latitude, and vertical profiles of particle mixing ratio in the UTLS. Interestingly, we find that we need to include Van der Waals forces in our coagulation scheme to match the UTLS aerosol concentrations. We conclude that this model can reasonably represent sulfate microphysical processes in the UTLS, and that the properties of particles at atmospherically relevant sizes appear to be insensitive to Correspondence to: J. English (englishj@colorado.edu) the details of the nucleation scheme. We also suggest that micrometeorites, which are not included in this model, dominate the aerosol properties in the upper stratosphere above about 30 km.


Introduction
The tropical upper troposphere is known to be a net source region of new particles (e.g. Brock et al., 1995;Clarke and Kapustin, 2002). These particles may descend into the marine boundary layer and act as cloud condensation nuclei (CCN)

WACCM with sulfur chemistry
We use WACCM3 version 3.1.9 tag 9 with 30-min time steps at 4 • latitude by 5 • longitude horizontal resolution with 66 vertical levels based on hybrid-sigma coordinates, providing 15 vertical levels in the UTLS between 50 and 500 hPa. We use the WACCM mass-conserving finite volume dynamical core based on a flux-form semi-Langrangian 5 transport scheme Rood, 1996, 1997). The vertical diffusion algorithm in WACCM handles eddy and molecular diffusion for gases. A 63-species chemistry module is implemented. We utilize WACCM's standard 56-species chemical package which includes Ox, NOx, HOx, ClOx, and BrOx chemical families along with CH 4 and its products and 7 ions (Kinnison et al., 2006), and add 7 sulfur-bearing gases: S, SO, SO 2 , 10 SO 3 , HOSO 2 , H 2 SO 4 , and OCS. Their reaction rates and photo-dissociation rates are given in Table 1.
The model includes emissions of carbonyl sulfide (OCS) and sulfur dioxide (SO 2 ), two primary sulfur emissions of importance to the UTLS region. OCS is specified with a constant surface concentration of 510 pptv. SO 2 is specified from a two-dimensional 15 monthly mean surface emissions dataset (Lamarque et al., 2010;Smith et al., 2010). Wet deposition for all constituents (including the aerosol bins from CARMA) is calculated using WACCM's existing techniques (Barth et al., 2000). WACCM treats dry deposition of gases (Barth et al., 2000), while dry deposition of aerosols is not treated in this model. Introduction to 1 micron radius, with mass doubling between bins. The particles are assumed to have spherical shape. Sulfate surface tension is calculated using the constants from Sabinina and Terpugow (1935). Since the bins only carry sulfate, the equivalent sulfate aerosol size (including sulfuric acid and water) is determined by the technique of Tabazadeh et al. (1997), which calculates weight percent sulfuric acid as a function of 5 temperature and water activity. Weight percent sulfuric acid is assumed to be independent of particle size. We did not include any other types of aerosols. Although other aerosols, such as organics, are known to compose a significant fraction of the aerosol mass in the UTLS, sulfates are believed to be the primary source of new particles in this region, and we wanted to clearly isolate the impact of sulfates. 10 Fall velocities are calculated by assuming a Stokes-Cunningham equation with Knudsen number corrections from Fuchs (1964), using the equivalent aerosol size (sulfuric acid plus water). Since WACCM handles advection by winds as well as eddy diffusion, no additional eddy diffusion of aerosol particles is added by CARMA. However, CARMA treats Brownian diffusion of aerosols, which is important above 100 km, and 15 not well treated by algorithms in WACCM. CARMA calculates the effect of coagulation of particles of equivalent aerosol size using the numerical approach described in Toon et al. (1988). Coagulation coefficients are calculated to include Brownian, convective and gravitational effects. A sticking coefficient of 1 is used, which assumes that all particles stick together upon colliding. A correction for the impact of inter-particle 20 Van der Waals forces on coagulation is included (Chan and Mozurkewich, 2001). Sulfate aerosol growth and evaporation is calculated via sulfuric acid equilibrium vapor pressure over binary solution using the method of Ayers et al. (1980) with a temperature correction by Kulmala (1990) and thermodynamic constants from Giauque (1959

Description of nucleation schemes
Three nucleation schemes are implemented in CARMA: two binary homogeneous nucleation (BHN) schemes and one ion-mediated nucleation (IMN) scheme.

Zhao BHN scheme
The "Zhao BHN" scheme predicts the binary homogeneous nucleation rate of sulfuric 5 acid and water using classical nucleation theory (e.g. Flood, 1934;Reiss, 1950;Hamill et al., 1977) with modifications for calculating the saddle point in Gibbs free energy by Zhao and Turco (1995). Instead of searching for the Gibbs free energy saddle point in two-dimensional space, the coordinate system is transformed to a function of cluster volume and sulfuric acid weight fraction of a solution droplet. This provides for a 10 unique solution in a 1-dimensional parameter space. Water equilibrium vapor pressure over a binary solution is calculated using the technique of Lin and Tabazadeh (2001). Sulfuric acid equilibrium vapor pressure over binary solution is calculated in the same manner as aerosol growth/evaporation: using the method of Ayers et al. (1980) with a temperature correction by Kulmala (1990)  nucleation can be reduced to unary nucleation of sulfuric acid except that the clusters containing different numbers of sulfuric acid molecules also contain a semi-fixed number of water molecules at a given temperature and relative humidity. The kinetically self-consistent "Yu BHN" model is constrained by the measured bonding energetics of H 2 SO 4 monomers with hydrated sulfuric acid dimers and trimers (Hanson and Love-5 joy, 2006;Kazil et al., 2007) and gives BHN nucleation rates in good agreement with available experimental data. While the laboratory data used to constrain the "Yu BHN" model substantially reduces the model uncertainty, they were measured under tropospheric conditions and can't be extrapolated to dry stratospheric conditions. As a result, the application of the present "Yu BHN" scheme should be limited to the tropo-10 sphere. The "Yu BHN" scheme is available as a set of two lookup tables, a low temperature

Yu IMN scheme
The "Yu IMN" scheme predicts ion-mediated nucleation rates of sulfuric acid and water. Ions of positive and negative charge stabilize the molecular cluster due to molecular attractions of opposite polarity. This scheme uses the same low temperature lookup table as the Yu BMN scheme, while a different high temperature table is used, as 5 described in Yu (2010). For the Yu IMN scheme, a globally constant input value of 10 ion-pairs per cm 3 is prescribed. Although the ionization rate varies spatially and temporally, it is relatively constant in the UTLS and is estimated to be between 5 and 20 ion-pairs per cm 3 (Usoskin et al., 2009

Model validation
We compare simulations using one nucleation scheme (Zhao BHN) with observations. Initial values for atmospheric state, gas properties and aerosol properties are read in 15 from a baseline run with a 5-yr spinup time. A three-year simulation was conducted, with the third year analyzed. Analysis of sulfate mass and number concentration indicate that the model achieved steady state in less than one year when using the common spin-up file. 20 Calculated OCS is uniformly mixed in the troposphere (Fig. 2a), due to its long photochemical lifetime there. In the stratosphere, its mixing ratio decreases with altitude due to photolytic conversion of OCS to SO 2 . Figure 2b shows OCS correlated with N 2 O, a long-lived tracer with well-understood chemistry, from our calculations as well as from balloon-borne observations (Geoff Toon, private communication agreement in the slope of this correlation indicates that the model correctly treats photochemical losses of OCS. Calculated surface SO 2 concentrations vary by five orders of magnitude across the earth's surface (Fig. 3a), with highest concentrations in the industrial mid-latitudes, particularly in eastern Asia, eastern United States, and Europe. SO 2 mixing ratio 5 decreases with altitude in the troposphere (Fig. 3b), with the highest concentrations near 30

Simulations of sulfur gas precursors
• N, correlating with the peak latitude of surface emissions. SO 2 mixing ratios decrease rapidly just above the tropopause due to slow vertical transport relative to chemical loss mainly by reaction with OH. A peak occurs in the tropics above 25 km where OCS is converted into SO 2 .
10 Figure 4a shows latitudinal variation in SO 2 mixing ratios in the Pacific upper troposphere between 8 and 12 km from model calculations and PEM-TA, PEM-TB, and ACE-2 aircraft observations (Thornton et al., 1999). Our calculations are slightly lower than the observations, but generally within or close to the observed variability. Figure 4b shows vertical profiles of SO 2 mixing ratios compared to 6 ACE-2 aircraft observations As shown in Fig. 5a, calculated H 2 SO 4 mixing ratios increase from 25 to 35 km due to sulfate aerosol evaporation. H 2 SO 4 also has a local maximum in the Northern Hemisphere sub-tropical upper troposphere due to availability of SO 2 and OH for chemical conversion. As Fig. 5b shows, calculated H 2 SO 4 mixing ratios are generally within the standard deviation of PEM-TA aircraft observations (Lucas and Prinn, 2003). H 2 SO 4 5 averages about 0.1 pptv throughout most of the tropical troposphere and lower stratosphere. As Fig. 5c shows, calculated H 2 SO 4 mixing ratios in the stratosphere at 43 • N closely match balloon-borne observations Reiner and Arnold, 1997;Schlager and Arnold, 1987;Viggiano and Arnold, 1981), with a peak near 35 km. 10 Calculated sulfate mass mixing ratios versus N 2 O are compared to a compilation of NASA aircraft observations (Wilson et al., 2008) in Fig. 6. Calculated sulfate mass mixing ratio generally is within the variability in the mid-latitude UTLS (220 to 300 ppbv N 2 O). Calculated sulfate mass mixing ratio is about 50% too high at low N 2 O values (polar mid-stratosphere). It is possible that simulated sedimentation rates are to slow 15 in the midlatitude stratosphere. Recent calculations with our WACCM/CARMA model including both sulfates and meteoric dust improves this correlation. However, as we will discuss below our model underpredicts aerosol volume (also measured by Wilson et al., 2008) versus CO. It is possible that these conflicting differences in aerosol volume and sulfate mass versus tracer abundance are related to transport or tracer chemistry 20 issues within WACCM. It is also possible there are errors in the observations, or errors with comparing aircraft flights on particular days with averaged model data.

Sulfate aerosol properties
Model calculations are compared to SAGE II extinction measurements at two wavelengths in Fig. 7. Here, the calculation is within about 50% of the observations at both wavelengths for all three latitude regions from the tropopause through the mid- 25 stratosphere. Below the tropopause, SAGE II has higher extinction than the calculations, with high variability. It is likely clouds are interfering with measurements below the tropopause, as has been noted in prior analyses of SAGE II extinction measurements 12451 Introduction  (Wang et al., 1995(Wang et al., , 1996. In the upper stratosphere, WACCM extinctions decline sharply with higher altitude, while SAGE II extinctions level off at about 10 −6 km −1 at 1024 nm near 35 km. Hervig et al. (2009) have observed from AIM solar occultation measurements that micrometeorites, sedimenting down from the mesopause, have an extinction near 10 −6 at a 1037 nm near 35 km. Recent calculations with our 5 WACCM/CARMA model including both sulfates and meteoric dust improves this correlation between the model and SAGE II data above 35 km, reinforcing this suggestion. Hunten et al. (1980) originally suggested the presence of these particles, and they have long been sought in rocket measurements with little quantitative success. It is ironic that SAGE II has seen them throughout its observational record, but their presence 10 was not recognized. While WACCM extinction is within 50% of SAGE II in the mid-latitudes, WACCM is higher than SAGE II at 1024 nm in the tropics, suggesting that the WACCM particles are slightly too large in the tropics. Indeed, calculated effective particle radius (Fig. 8) is about 25% higher than SAGE II in the UTLS. Model calculations of size distribu- 15 tions in the UTLS at 41 • N are compared to balloon-borne observations (Deshler et al., 2003) in Fig. 9. Vertical profiles of calculated particle concentration are within 50% of observations at the smallest size (>0.01 microns), while at larger sizes the model underpredicts number concentration below the tropopause and overpredicts number concentration in the mid-stratosphere. 20 Vertical profiles of calculated sulfate number concentration in the nm size range are compared to aircraft observations (Borrmann et al., 2010;Brock et al., 1995) in Fig. 10. Here, two Zhao BHN calculations are compared: a run with Brownian coagulation and no inter-particle forces (noVW), and our base case in which the Brownian coagulation kernels are adjusted to include the effect of a Van der Waals forces between the 25 particles. Van der Waals forces have been observed to be important for sulfuric acid aerosols in several laboratory studies (Schmid-Ott and Burtscher, 1982;Alam, 1987;Huang et al., 1990) and we include a size-dependent expression for the Hamaker constant based on laboratory measurements (Chan and Mozurkewich, 2001 10a) and extratropics (Fig. 10b), calculated and observed particle mixing ratios increase in the troposphere, peak near the tropopause where the highest nucleation rates are observed, and decrease in the stratosphere, as expected. Including the effect of Van der Waals forces on coagulation results in calculations that are within the error bars of the observations. Prior to including the effect of Van der Waals 5 forces on coagulation, the model had always overpredicted particle mixing ratio in the mid-stratosphere despite modifications to nucleation schemes, sulfur emissions, fall velocity schemes, and growth equations. The impact of including Van der Waals forces highlights how important coagulation rates are to stratospheric aerosol properties. Calculated aerosol number, area, and volume versus carbon monoxide (CO) are 10 compared to an average of 13 flights in the tropical UTLS between 2004 and 2006 in Fig. 11. Again, the Zhao BHN calculations with and without the Van der Waals coagulation correction are compared. Calculated number concentrations (Fig. 11b) for both simulations are within the error bars at lower CO, but increase to up to an order of magnitude too high above 55 ppbv CO. In the model, this CO region is present 15 near 200 hPa and 20 • N, where the model predicts peak nucleation. It is possible that the model and data do not have corresponding geographical areas with the same CO values. Model output were too limited in the range of longitudes covered by aircraft observations, so all longitudes were included. The Zhao no VW scheme predicts higher aerosol number where peak nucleation is observed, but lower number outside this 20 region. Calculated aerosol area (Fig. 11c) and volume (Fig. 11d) are about half the observations. It is odd that the model underestimates aerosol area and volume in the Northern Hemisphere between 3 • S and 23 • N, yet overestimates aerosol mass in the Northern Hemisphere between 60 and 90 • N (Fig. 6c). The comparisons are made with coordinates of CO and N 2 O, respectively, rather than geographic location, so this 25 discrepancy may be due to differences between modeled and observed geographic locations or errors in the observations. Introduction

Differences in nucleation rates
Contour plots of calculated nucleation rates are provided in Fig. 12, while peak and 10 average nucleation rates and critical radii sizes in the UTLS are provided in Table 2. All three schemes predict similar patterns of nucleation -the highest rates are predicted in the tropical upper troposphere, with lower nucleation rates predicted in other parts of the troposphere and polar stratosphere, but their magnitudes differ significantly. Near the surface, the Yu IMN scheme predicts several orders of magnitude higher nucle-15 ation rates than the Yu BHN, suggesting that ion nucleation from cosmic rays can have a large influence on new particle formation in this region, in agreement with many other studies (Yu and Turco, 2001;Lovejoy et al., 2004;Eisele et al., 2006;Kazil et al., 2010 that the uncertainty associated with BHN computations is much larger than the effects of ions on nucleation in the UTLS. The large differences between BHN schemes have been documented previously , and can be partially explained by differences in predicted critical radii -the Yu schemes predict critical radii that are 60% larger than the Zhao BHN scheme. The larger sizes of new particles predicted by 5 the Yu schemes partially offsets lower nucleation rates, resulting in a less substantial difference in sulfate mass and number concentration at larger sizes (e.g. Zhao BHN predicts a 100 times higher particle number creation rate from nucleation but only 17 times higher particle mass creation rate). Finally, note that the Yu BHN and Yu IMN lookup tables, designed for tropospheric conditions, were originally found to predict 10 unrealistic nucleation rates in the middle and upper stratosphere due to exceptionally low relative humidities being outside the table bounds. While setting nucleation to zero if relative humidity was less than the table minimum resolved much of this issue, it is possible that this approach may predict too little nucleation in certain regions. 15 Calculated size distributions are compared with data from 56 aircraft flights from a range of NASA field programs summarized by Lee et al. (2003). Size distributions are calculated for three regions: Tropical troposphere (7-17 km), mid-high latitude UTLS (7-13 km), and high-latitude stratosphere (17-21 km), and the data are separated into series with or without recent new particle formation (NPF). Recent NPF was defined as 20 meeting two conditions: (i) number concentrations with diameter 4-6 nm exceeds that of number concentration with diameter 6-9 nm, and (ii) number concentrations with diameter 4-9 nm exceed 1 cm −3 . Simulation size bin ranges are selected based on the closest bins available to the size specified in Lee et al. (2003). Calculated 1-day averages of the third year are checked for NPF conditions and segregated into two 25 sets of data (with and without recent NPF). Simulation "data" points include values for 360 days in the third simulation year. The model outputs daily averages, so these criteria will not provide instantaneous indicators of recent NPF. of simulation data points considered NPF days and no NPF days is provided in Table 3. All three schemes reported all days were NPF days in the tropical troposphere, most days were NPF days in the high-latitude UTLS, and very few NPF days occurred in the high-latitude stratosphere. Lee et al. reported 16% of size distributions to be considered NPF events. 5 Size distributions for each of the three regions are provided in Fig. 13. In the tropical troposphere (Fig. 13a), high numbers of particles are observed and predicted, as expected due to this region being conducive to NPF. Relative differences in number concentrations between the three schemes at the smallest sizes are explained by differences in nucleation rates. All three schemes predict approximately two times too 10 many of the smallest particles, and are missing the observed size mode at 30 nm. It is possible that this discrepancy is due to the lack of other aerosol types in the model. Advection of aged aerosol from other regions could contribute to growth rather than nucleation, reducing the number concentration at the smallest sizes and possibly creating a mode near 30 nm. A similar trend is observed in the mid-high latitude UTLS 15 region where NPF was observed (Fig. 13b); all three of the simulations predict two times too many particles at the smallest sizes. In the mid-high latitude UTLS where NPF was not observed (Fig. 13d), only the Yu BHN predicted days with no NPF. This simulation replicates both the 10 nm and 100 nm modes that are observed, albeit with a larger 10 nm mode and a smaller 100 nm mode. In the high-latitude stratosphere 20 (Fig. 13c), all three schemes reproduce the observed 100 nm mode, with particle number within a factor of two of that observed. All three schemes predict a broader mode than observed, with the Yu BHN scheme better reproducing the mode at the small end. However, only 14, 2, and 4 days, respectively for the Zhao BHN, Yu BHN, and Yu IMN schemes met the criteria for stratospheric NPF. When plotting all simulation 25 output regardless of whether the grid cells met the criteria for recent NPF (Fig. 14), all three simulations predict a similar size mode in the stratosphere. In most cases, the three nucleation schemes produce simulations that differ at the smallest sizes due to differing nucleation rates, but become nearly indistinguishable from one another at Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | sizes larger than 10 nm, suggesting that coagulation, not nucleation is the dominant process determining aerosol number at atmospherically relevant sizes.

Effects of nucleation rate on aerosol number concentrations
We illustrate vertical profiles of calculated sulfate number concentration (>8 nm) compared to aircraft observations (Borrmann et al., 2010;Brock et al., 1995) in Fig. 10. All 5 three simulations with varying nucleation rate correlate very well with observations in both the tropics (Fig. 10a) and extratropics (Fig. 10b). Although nucleation rates differ by up to two orders of magnitude, there is very little difference in number concentration of particles >8 nm. Likewise, comparisons of aerosol number (>4 nm) versus CO suggest differences due to nucleation schemes (Fig. 11b), but aerosol area (Fig. 11c) and 10 volume (Fig. 11d) are virtually unaffected by nucleation scheme. Again, this suggests that the choice of nucleation scheme is nearly irrelevant compared to the impacts of coagulation at atmospherically relevant sizes. Similar trends are seen when comparing calculated zonal-averaged number concentrations in the upper troposphere to aircraft observations from the CARIBIC campaign 15 (Heintzenberg et al., 2003). In the 4-12 nm size range (Fig. 15b), predicted number concentrations vary by a factor of 5 between nucleation simulations, with the highest nucleation rates (Zhao BHN) being associated with the highest number concentration. But at sizes above 12 nm ( Fig. 15c and d), the differences in number concentration between the nucleation schemes become muted as coagulation become dominant. When 20 comparing the model to the observations, however, in this comparison there are numerous discrepancies. Observed number concentrations peak near the equator while the simulations peak near industrial latitudes. In the 4-12 nm size range (Fig. 15b) is known to be important in this region (Kazil et al., 2010). Any of these discrepancies may be due to a mismatch between the spatial scale of the observations and simulations. The observations are taken across a flight path at a specific altitude, latitude, and longitude, while the model simply averages a region over the entire altitude and latitude range. A contour plot of calculated number concentration for the Zhao BHN 5 case as a function of latitude and longitude between 216-316 hPa (Fig. 15a) shows that number concentration can vary up to two orders of magnitude at the same altitude across the globe.

Effect of nucleation rate on effective radius and extinction
Vertical profiles of effective radii and extinctions for each of the three calculated nu-10 cleation schemes are compared to SAGE II satellite observations in Figs. 8 and 16. All three nucleation schemes yield essentially identical results. Effective radius is important for radiative forcing, while extinction is proportional to surface area, which is important to heterogeneous chemistry. Hence the choice of nucleation rate should not be important to radiative forcing or atmospheric chemistry. 15

Conclusions
We have implemented a three-dimensional general circulation model with sulfur chemistry and sectional aerosol microphysics (WACCM/CARMA). Three nucleation schemes are available in this model: two BHN schemes -one based on classical nucleation theory (Zhao BHN)  needed to extend the Yu schemes into dry stratospheric conditions (RH<0.1%). Calculations suggest that ion-mediated nucleation rates in the UTLS are 25% higher than binary only; however, the two binary schemes vary by two orders of magnitude. More importantly, it is found that coagulation, not nucleation, controls number concentration at sizes greater than approximately 10 nm. Lee et al. (2003) suggested that ion nucle-5 ation was important in the UTLS, on the basis of their ability to match observed size distributions with a model based on ion clusters. In contrast we find that identical size distributions are produced for each mode of nucleation. The dominance of coagulation over other microphysical processes is consistent with other recent work using microphysical models; Pierce and Adams (2007) found coagulation to be more important than nucleation in tropospheric studies, and Timmreck et al. (2010) found coagulation to drive stratospheric particle sizes from the eruption of Mount Toba to much larger values than previously assumed. We compared our calculations to observations from the tropopause to the midstratosphere. Above about 30 km, the model underpredicts SAGE extinctions, which 15 we suggest is due to the importance of micrometeorites, as observed by Hervig et al. (2009). We also found that including Van der Waals forces improved the model calculations for the numbers of particles in the UTLS. We conclude that this model contains the sulfate microphysical processes needed for simulations in the UTLS, and that the properties of particles with sizes relevant to climate, cloud physics and hetero-20 geneous chemistry are not sensitive to the details of the nucleation scheme or to the presence or absence of ion nucleation. ments of submicron particle abundance and volatility, Atmos. Chem. Phys., 10, 5573-5592, doi:10.5194/acp-10-5573-2010, 2010.      (Bates et al., 1998;Hoell et al., 1999) aircraft observations binned into averages plus/minus standard deviation at different altitudes (Lucas and Prinn, 2003) from flights in August and September 1996 between 24 • N and 24 • S. Simulation lines are an average of July and August between 24 • N and 24 • S. (c) Vertical profile of calculated H 2 SO 4 number concentration at 43 • N compared to various balloon-borne observations at the same latitude Reiner and Arnold, 1997;Schlager and Arnold, 1987;Viggiano and Arnold, 1981   • N) compared to aircraft observations (Brock et al., 1995). Observations are medians plus/minus 25th/75th percentiles. Brock et al. mixing ratios include particles greater than 8 nm diameter and are based on 5 worldwide aircraft campaigns between 1987 and 1994, with data points attributed to the eruption of Mt. Pinatubo removed. Scout (SCOUT-O3; Stratospheric-Climate Links with Emphasis on the Upper Troposphere and Lower Stratosphere) and Trocc (TROCCINOX; Tropical Convection, Cirrus, and Nitrogen Oxides Experiment) mixing ratios include particles greater than 6 nm diameter and are from 2005 aircraft campaigns. It is assumed that no water is present on the particles. Calculated mixing ratios in both regions include 8.0 nm dry diameter and larger. The "Zhao no VW" simulation uses Brownian coagulation kernels based on collision theory, while the other three simulations include the effect of Van der Waals forces on the collision cross section using the calculations of Chan and Mozurkewich (2001)  Comparison of zonal-average number concentrations to aircraft observations as a function of latitude over the altitude region 8.5-11.3 km for three particle diameter ranges: (b) 4-12 nm, (c) >12 nm, and (d) >18 nm. Observations are averages of 6 commercial flights between Germany, Namibia, and South Africa in May, July, and December 2000 (Heintzenberg et al., 2003). Simulations are annual and zonal averages at the bin ranges closest to the dry diameters specified (4.0 nm, 12.8 nm, and 16.2 nm diameters, respectively).