Auxiliary Material for “Efficient formation of stratospheric aerosol for climate engineering by emission of condensible vapor from aircraft”
by Jeffrey R. Pierce, Debra K. Weisenstein, Patricia Heckendorn, Thomas Peter, David Keith
Figure s1. Schematic showing the rough timescales where various processes are important within the aircraft plume following H2SO4 emission. The timescales for the processes vary from the values shown here depending on the nucleation, condensation and dilution assumptions tested in the plume model.
Aircraft plume aerosol model
To model aerosol formation and growth within the aircraft plume, we use an expanding Lagrangian-box version of the TwO-Moment Aerosol Sectional (TOMAS) microphysics model [Adams and Seinfeld, 2002]. The box tracks a radial cross section of the plume with time, assuming that the plume is well mixed radially and dilutes with time [Yu and Turco, 1998]. This version of TOMAS [Pierce and Adams, 2009] simulates aerosol number and mass in 43 lognormally spaced size bins with diameters ranging from 0.6 nm to 10 μm. For all simulations of the initial plume, we assume that any emitted SO3 (see injection methods for discussion) has already reacted to form H2SO4 (as justified by the large rate coefficient of SO3 + H2O under the moist aircraft-plume conditions [JPL, 2006]).
Therefore, the model is initialized with only H2SO4 vapor and background aerosols at a temperature of 220 K and a relative humidity of 10% (the results were not sensitive to reasonable perturbations in these inputs). The concentration of the aqueous sulfuric acid solutions in the aerosol droplets is assumed to be in equilibrium with vapor-phase water.
We explore several uncertain assumptions within the plume (Table s1). The first is the plume dilution rate. There is limited information on the dilution rates in stratospheric jet plumes; therefore, these represent an uncertain aspect of this study. To test some potential variability in the plumes, we define slow and fast dilution rates that are similar to those of Yu and Turco  describing the plume dispersion during the first 16 minutes after injection. After this time, the fast plume then dilutes at the same rate as the slow plume. The equations defining the cross-sectional area of the plume as a function of time are given in Table s1. The second uncertain assumption is the nucleation mechanism and rate. To address this we scale the kinetic barrierless nucleation theory of Clement and Ford  (every pair of H2SO4 molecules that collide form a stable cluster, an upper limit of nucleation rate). We chose to use barrierless nucleation because (1) nucleation should approach the barrierless limit for very high H2SO4 vapor concentrations and low temperatures (initial H2SO4 concentrations in the aircraft plume are on the order of 1015 molec cm-3, about six orders of magnitude higher than the highest H2SO4 concentrations in the atmosphere, and the temperature is 220 K) and (2) there are no other available nucleation parameterizations that can handle these high concentrations of sulfuric acid. To address the fact that the nucleation may not actually be as fast as barrierless nucleation would predict, we scale the rates by four scaling factors ranging from 1 to 10-9. The third uncertain assumption is the H2SO4 condensation accommodation coefficient (sticking probability). Values in the literature have been shown to range [Seinfeld and Pandis, 2006] from 0.01 to 1 and we test three values within this range. The fourth assumption is the sulfur emission rate per length of aircraft flight path, and we test 3 and 30 kg S km-1 of flight. H2SO4 emission rates per unit length along the flight track were chosen to yield size distributions that roughly bracket the radii that have the most favorable optical properties (Figure 1). These rates correspond to an aircraft delivering between 3 and 30 tonnes of sulfur over a 1000 km flight in the stratosphere. The final uncertain assumption is the number concentration of background stratospheric particles. We assume either 1 or 50 cm-3 to cover pristine and geoengineered stratospheric conditions (see Figure s3), both in a single lognormal mode with a number-median radius of 0.2 μm and a width parameter of 2.0 (see Figure 3). The background aerosol makes little difference to the resultant size distributions in the plume because 1) it represents a trivial fraction of the condensation sink when H2SO4 is condensing and 2) it does not dominate the coagulation sink for plume particles until the point where the plume particles are passed to the global model. We do not test uncertainties in coagulation since uncertainties in Brownian coagulation are generally much smaller than the uncertainties explored above [Seinfeld and Pandis, 2006].
As discussed in the main article, the final size distribution reached by the plume model (at the time when the coagulation of the plume particles with pre-existing stratospheric particles dominates over self-coagulation of the plume particles, which happens after several days for the geoengineered atmosphere and longer in the pristine) depends almost entirely on the sulfur emission rate per unit aircraft flight path length and the plume dispersion rate. The results were highly insensitive to the nucleation scale factors and the accommodation coefficients due to nucleation and condensation only occurring during the initial seconds to minutes of the plume. Beyond these initial seconds to minutes, the aerosol microphysics is dominated by self-coagulation of particles formed in the plume. Coagulation is proportional to the square of the particle concentration, so any initial differences in the particle size distribution would be damped by coagulation. These results are consistent with Turco and Yu .
The smoothing of initial differences in the size distribution is illustrated in Figure s2. Each panel shows the results of 12 simulations of the various combinations of nucleation scaling factors and accommodation coefficients. Figure s2a shows the aerosol size distributions at 1 ms into the fastdiluting plume with an ambient stratospheric aerosol concentration of 50 cm-3 at the emission rate of 3 kg km-1. Here, very large differences between the simulations are apparent because of the large differences in nucleation and condensation rates. Figures s2b and s2c show the aerosol number size distribution 1 hour after injection for the slow- and fast-diluting plumes, respectively, with an ambient stratospheric aerosol concentration of 50 cm-3 at the emission rate of 3 kg km-1. After 1 hour in the slowly diluting plume, there is very little difference between the simulations with different nucleation scale factors and accommodation coefficients. In the fast-diluting plume, only the slowest nucleation cases tend to deviate slightly from the others. Thus, the aerosol size distributions show little sensitivity to the accommodation coefficient and nucleation rate, which allows us to ignore exact details of the nucleation mechanisms (e.g. the role of ions [Yu and Turco, 1998]) and the accommodation coefficient.
There are several other uncertain factors that we do not explicitly address in this analysis. (1) The amount of primary soot produced by the aircraft is uncertain; however Yu and Turco  found that it made little difference on the nucleation and growth of particles in conventional jet plumes in the stratosphere. For our cases with additional H2SO4 emissions, the role of soot particles will be even smaller. (2) We assume that SO3 combines with H2O to form H2SO4 instantly upon cooling [Yu and Turco, 1998; JPL, 2006] . We discuss this issue further in the section on injection methods later in this supplementary material. (3) We assume that coagulation rates are accurate. Although charged particles can alter the coagulation rates of the smallest particles [Yu and Turco, 1998], Brownian coagulation rates are generally much more certain than nucleation and condensation rates [Seinfeld and Pandis, 2006]. (4) We assume that the plume is well mixed radially. In reality, this is not the case, and the rates of microphysical processes will vary radially (and temporally in the turbulent areas of plume near the aircraft). Spatial and teof emitted particles. This must be explored in future work. (5) We assume that the emissions always occur in areas away from other recently emitted plumes (within past ~2 days) such that the interaction between plumes is insignificant. The validity of this assumption will depend on aircraft flight strategies that are out of the scope of this paper.mporal inhomogeneities in the plume would likely broaden the size distribution
Figure s2. Particle number size distributions a) after 0.001 second in the fast-diluting plume, b) after 1 hour in the slow-diluting plume, and c) after 1 hour in the fast-diluting plume. Twelve simulations represent all combinations of the four nucleation scale factor assumptions (represented by colors) and three accommodation coefficient assumptions (represented by line type).
Stratospheric aerosol model
To determine how the aerosol burden and radiative forcing differ between SO2- and H2SO4- injection schemes, we use the AER 2-D aerosol model [Heckendorn et al., 2009; Weisenstein et al., 1997; Weisenstein et al., 2007]. This model resolves latitude and altitude (resolution approximately 9.5° and 1.2 km, respectively), and it assumes that the atmosphere is homogeneous longitudinally. The model domain is global from the surface to 60 km altitude. The assumption of zonally homogeneous conditions is an acceptable approximation in the stratosphere a few kilometers away from the tropopause [Weisenstein et al., 2007]. The configuration of the model is the same as in Heckendorn et al.  with 40 size bins spanning the range 0.4 nm to 3.2 μm by volume doubling. Only pure H2SO4/H2O aerosols (often called “sulfate aerosols”) are included, with surface emissions of OCS and SO2 providing the stratospheric sulfur input during volcanically quiescent periods; DMS, CS2, and H2S emissions are also included but primarily influence the model's troposphere. Microphysical processes include homogeneous nucleation, condensation, coagulation, evaporation, and gravitational sedimentation. Above about 35 km aerosols evaporate and photolysis of H2SO4 produces SO2 gas which later descends in the polar regions, reacts with OH, and nucleates and condenses to form new particles.
Geoengineering emissions are input to the 2-D model as particles, using the final size distributions from the plume model (number-median dry radius of 65, 95, or 180 nm, sigma of 1.5) after adjusting dry radius to wet radius. The input particle number density is scaled to match the desired total sulfur input and spread over the 30°N-30°S, 20-25 km region (in Heckendorn et al. , the emissions were all at the equator and 20 km). We assume here that individual plumes do not cross within two days. The model is integrated with continuous emissions until the aerosol concentrations in the stratosphere reach an annually-repeating steady state.
The calculated annual-average aerosol mass density, effective radius, and number density from the 2-D model for geoengineering cases with 5 MT S yr-1 of emission of H2SO4-derived 95 nm particles and SO2 with emissions spread between 30°S and 30°N and 20 and 25 km are shown in Figure s3. This figure shows that for a constant sulfur emissions rate, there is a higher mass density of sulfate and a smaller effective radius for the H2SO4-injection cases throughout the stratosphere. The fractional reduction in the effective radius is larger than the fractional increase in mass density. Since the scattering efficiency (Figure 1) is very sensitive to the effective radius at these sizes, a lower mass sulfate burden would be required to achieve a given radiative cooling using the H2SO4-injection scenarios. Number densities shown in Figure s3 are for particles with radius greater than 0.01 μm, which represents all particles outside nucleation regions. The SO2 emission cases lead to nucleation and a very broad size distribution (see Figure 3) which includes also more large particles and thus a larger effective radius, but a smaller number of particles greater than 0.01 μm. The H2SO4-emission calculation shown here is used as the ambient background for the plume simulations, with number concentration of 50 cm-3 in the injection region, as seen in Figure s3e.
Figure s3. Calculated annual-average aerosol mass density [μg m-3] (a and b), effective radius [μm] (c
and d), and number density of particles with radius greater than 0.01 μm [cm-3] (e and f) calculated by
the 2-D model for geoengineering cases with 5 MT S yr-1 emitted as particles with mean radius of 95 nm (a, c, and e) and 5 MT S yr-1emitted as SO2 (b, d and f) with emissions spread between 30°S and 30°N and 20 and 25 km.
In the article we focus on sulfur injection evenly distributed between 30°N and 30°S and between 20 and 25 km; however, in Figures 3 and 4 we also include cases where SO2 is injected only at the equator and 20 km (for comparison to Heckendorn et al. ). Broadening the injection location latitudinally and vertically increases both the burden and the radiative cooling for a given injection rate of SO2. This effect is largely due to a reduction in the coagulation of particles because of the more dilute injection scenario. It is clear from Figure 4 that the injection location is very important and must be explored systematically in future work.
Radiative forcing calculation
Because our goal is to compare the flux changes in top-of-atmosphere (TOA) shortwave (SW) radiation caused by various aerosol distributions, we calculate the radiative flux change directly from the aerosol scattering properties that are, in turn, computed using Mie theory. The solar-band radiative flux change is computed using a standard approximation [Seinfeld and Pandis, 2006]:
where ΔF is the change in the top-of-atmosphere shortwave flux, s is the index of 40 size bins and l is the index of the 19 latitudes in the AER model, Fl is the latitudinally dependent, annually and diurnally averaged shortwave flux at top-of-atmosphere, Ta is the fractional transmission of shortwave radiation to the scattering layer, A is the fraction of area covered by clouds, R is the surface albedo, s , l is the aerosol-size dependent and latitudinally dependent, annually and diurnally averaged aerosol upscatter fraction, τs,l is the aerosol-size dependent and latitudinally dependent optical depth of the stratospheric aerosols, and fl is the fraction of the Earth's area covered by latitude section, l.
For simplicity we assume that the aerosol is purely scattering (i.e. neglect absorption) and exists as a single layer entirely above clouds. We ignore multiple scattering. We assume Ta is exactly 1 at the stratospheric scattering layer. For A and R, we use globally averaged values of 0.6 and 0.15, respectively [Seinfeld and Pandis, 2006]. The instantaneous β values (prior to diurnal and annual averaging) are calculated from Mie theory assuming a refractive index of 1.4 and averaging over the solar spectrum.
The changes in TOA SW fluxes shown in our paper differ from those in Heckendorn et al.  in that they do not include feedbacks in temperature, dynamics, or trace gases induced by geoengineering. However, we have compared the TOA SW flux changes predicted by this simple scheme to online radiative transfer calculations of the global Chemistry Climate Model (CCM) SOlar Climate Ozone Links Version 2.0 (SOCOLv2.0), the same model used for SW flux calculations in Heckendorn et al. . As in Heckendorn et al. , SOCOL is run for 20 years to allow the atmosphere to adjust to a new steady state. Table s2 shows a comparison of TOA SW radiative flux changes predicted by the simple model and SOCOL. In all cases, the differences are less than 20%. Table s2. Comparison of TOA SW radiative forcing using the simple and SOCOL models.
Carrying payloads for deployment between 20 and 25 km altitude via aircraft is non-trivial. An aircraft engineering study of geoengineering by Aurora Flight Sciences is currently investigating the details of this task, thus we will not address it in this work. There are two plausible routes to generate vapor-phase H2SO4 on an aircraft. The most direct method is to transport liquid H2SO4 to the stratosphere directly and vaporize it onboard the aircraft. The power required for vaporization is not trivial, but is small compared to the aircraft engines thermal power rating. Assuming an aircraft velocity of 240 m sec-1 (0.8 Mach) and an injection rate of 100 kg H2SO4 km-1, the power is 12 MW.
The potential alternative method is to transport elemental sulfur and convert it to H2SO4 in situ. The advantage of this method, if feasible, is that the mass of S is only 32.6% the mass of H2SO4, so potentially much less mass must be lifted to the stratosphere compared to lifting H2SO4 directly. This conversion process is one of the largest (by mass) processes in industrial chemistry [Kirk-Othmer, 2004]. The standard process involves combustion of S in air producing SO2 that is converted to SO3 in the presence of a vanadium catalyst [Kirk-Othmer, 2004]. SO3 must then combine with water vapor to form H2SO4. Air for the process would be supplied by turbine bleed air; preliminary estimates from an ongoing aircraft engineering study of geoengineering by Aurora Flight Sciences suggest that sufficient air could be available. The H2O flux from fuel combustion will be larger than that required to form H2SO4 under most plausible injection scenarios. The timescale for recombination will likely not affect the results because the size distribution of particles generated in the aircraft plumes was found not to be strongly dependent on nucleation and condensation rates. However, a significant amount of engineering would be required to determine if the necessary amounts of sulfur could be burned using this method on an aircraft. Lightweight systems would need to be developed to make sulfuric acid, Preliminary discussions with NORAM engineering, a firm that specializes in design of sulfuric acid plants, suggests that existing designs would not work for this purpose, but that designs using specialty catalysts might be feasible, however we have not explored this approach in any detail.
Adams, P.J. and Seinfeld, J.S. (2001), Predicting global aerosol size distributions in general circulation models, J. Geophys. Res. 107 D001010.
Clement, C.F. and Ford, I.J. (1999), Gas-to-particle conversion in the atmosphere: II. Analytical models of nucleation bursts, Atmos. Env. 33 489-499.
Kirk-Othmer Encyclopedia of Chemical Technology, 5th ed. (2004) (John Wiley & Sons, Inc., Hoboken, NJ, USA).
Heckendorn, P., et al. (2009) , The impact of geoengineering aerosols on stratospheric temperature and
ozone. Env. Res. Let. 4 045108.
“JPL Publication 06-2, Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies”, (2006) (Evaluation Number 15, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California)
Pierce, J.R. and Adams P.J. (2009), A computationally efficient aerosol nucleation/condensation method: Pseudo-steady-state sulfuric acid, Aerosol Sci. Technol. 43 216-226.
Seinfeld, J.S., and Pandis, S.N. (2006), Atmospheric Chemistry and Physics: From Air Pollution to Climate Change 2nd ed., (John Wiley & Sons, Inc., Hoboken, NJ, USA).
Turco, R.P., and Yu, F. (1999), Particle size distributions in an expanding plume undergoing simultaneous coagulation and condensation, J. Geophys. Res., 104, 19,227-19,241.
Weisenstein D. K., et al. (1997), A two-dimensional model of sulfur species and aerosols, J. Geophys.
Res., 102 13,019-13,035.
Weisenstein D. K., J. E. Penner, M. Herzog, and X. Liu (2007), Global 2-D intercomparison of sectional and modal aerosol modules, Atmos. Chem. Phys. 9 2339-2355.
Yu, F. and Turco, R.P. (1998), The formation and evolution of aerosols in stratospheric aircraft plumes: 13
Numerical simulations and comparisons with observations, J. Geophys. Res. 103 25,915-25,934.
experiment; solar geoengineering; solar radiation management