General considerations

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Sulphate aerosols are an important component of the Earth system in the troposphere and stratosphere. Because sulphate aerosols play a critical role in the chemistry of the lower stratosphere and occasionally, following a volcanic eruption, in the radiative budget of the Earth by reducing the incoming solar energy reaching the Earth surface, they have been studied for many years. A comprehensive discussion of the processes that govern the stratospheric sulphur cycle can be found in the recent assessment of stratosphere aerosols (SPARC 2006). Figure 12.1, taken from that report, indicates some of the processes that are important in that region.

Sulphate aerosols play additional roles in the troposphere (IPCC 2007a and references therein). As in the stratosphere they act to reflect incoming solar energy (the 'aerosol direct effect'), but also act as cloud condensation nuclei, influencing the size of cloud droplets and the persistence or lifetime of clouds (the 'aerosol indirect effect') and thus the reflectivity of clouds.

Figure 12.2 A very rough budget (approx. 1 digit of accuracy) for most of the major atmospheric sulphur species during volcanically quiescent situations, following Rasch et al. (2000), SPARC (2006) and Montzka et al. (2007). Numbers inside boxes indicate species burden in units of Tg S, and approximate lifetime against the strongest source or sink. Numbers beside arrows indicate net source or sinks (transformation, transport, emissions, and deposition processes) in TgSyr"1.

Figure 12.2 A very rough budget (approx. 1 digit of accuracy) for most of the major atmospheric sulphur species during volcanically quiescent situations, following Rasch et al. (2000), SPARC (2006) and Montzka et al. (2007). Numbers inside boxes indicate species burden in units of Tg S, and approximate lifetime against the strongest source or sink. Numbers beside arrows indicate net source or sinks (transformation, transport, emissions, and deposition processes) in TgSyr"1.

Although our focus is on stratospheric aerosols, one cannot ignore the troposphere, and so we include a brief discussion of some aspects of the tropospheric sulphur cycle also. A very rough budget describing the sources, sinks and transformation pathways1 during volcanically quiescent times is displayed in Figure 12.2. Sources, sinks and burdens for sulphur species are much larger in the troposphere than in the stratosphere. The sources of the aerosol precursors are natural and anthropogenic sulphur-bearing reduced gases (DMS, dimethyl sulphide; SO2, sulphur dioxide; H2S, hydrogen sulphide; OCS, carbonyl sulphide). These precursor gases are gradually oxidized (through both gaseous and aqueous reactions) to end products involving the sulphate anion (SO2") in combination with various other

1 Sulphur emissions and burdens are frequently expressed in differing units. They are sometimes specified with respect to their molecular weight. Elsewhere they are specified according to the equivalent weight of sulphur. They may be readily converted by multiplying by the ratio of molecular weights of the species of interest. We use only units of S in this chapter, and have converted all references in other papers to these units. Also, in the stratosphere, we have assumed that the sulphate binds with water in a ratio of 75/25 H2SO4/water to form particles. Hence

3 Tg SO2" = 2Tg SO2 = 1TgS ^ 4 Tg aerosol particles.

cations. In the troposphere where there is sufficient ammonia, most of the aerosols exist in the form of mixtures of ammonium sulphate ((NH4)2SO4) and bisulphate ((NH4)HSO4).

The stratospheric sulphur-bearing gases oxidize (primarily via reactions with the OH radical) to SO2, which is then further oxidized to gaseous H2SO4. Stratospheric sulphate aerosols exist in the form of mixtures of condensed sulphuric acid (H2SO4), water and, under some circumstances, hydrates with nitric acid (HNO3).

Although the OCS source is relatively small compared with other species, owing to its relative stability, it is the dominant sulphur-bearing species in the atmosphere. Oxidation of OCS is a relatively small contributor to the radiatively active sulphate aerosol in the troposphere, but it plays a larger role in the stratosphere where it contributes perhaps half the sulphur during volcanically quiescent conditions. Some sulphur also enters the stratosphere as SO2 and as sulphate aerosol particles. The reduced sulphur species oxidize there and form sulphuric acid gas. The H2SO4 vapour partial pressure in the stratosphere - almost always determined by photochemical reactions - is generally supersaturated, and typically highly supersaturated, over its binary H2O-H2SO4 solution droplets. The particles form and grow through vapour deposition, depending on the ambient temperature and concentrations of H2O. These aerosol particles are then transported by winds (as are their precursors). Above the lower stratosphere, the particles can evaporate, and in the gaseous form the sulphuric acid can be photolysed to SO2, where it can be transported as a gas, and may again oxidize and condense in some other part of the stratosphere. Vapour deposition is the main growth mechanism in the ambient stratosphere, and in volcanic clouds, over time.

Because sources and sinks of aerosols are so much stronger in the troposphere, the lifetime of sulphate aerosol particles in the troposphere is a few days, while that of stratospheric aerosol is a year or so. This explains the relatively smooth spatial distribution of sulphate aerosol and resultant aerosol forcing in the stratosphere, and much smaller spatial scales associated with tropospheric aerosol.

The net source of sulphur to the stratosphere is believed to be of the order of 0.1TgSyr-1 during volcanically quiescent conditions. A volcanic eruption completely alters the balance of terms in the stratosphere. For example, the eruption of Mount Pinatubo is believed to have injected approximately 10 Tg S (in the form of SO2) over a few days. This injection amount provides a source approximately 100 times that of all other sources over the year. The partial pressure of sulphuric acid gas consequently reaches much higher levels than those during background conditions. After an eruption, new particles are nucleated only in the densest parts of eruption clouds. These rapidly coagulate and disperse to concentration levels that do not aggregate significantly. Particle aggregation is controlled by Brownian coagulation (except perhaps under very high sulphur loadings). Coagulation mainly limits the number of particles, rather than the overall size of the particles, which depends more on the sulphur source strength (although considering the overall sulphur mass balance, the two processes both contribute). The particles' growth is thus influenced by both vapour deposition and proximity to other particles.

The primary loss mechanism for sulphur species from the stratosphere is believed to be the sedimentation of the aerosol particles. Particle sedimentation is governed by Stokes' equation for drag corrected to compensate for the fact that in the stratosphere at higher altitudes the mean free path between air molecules can far exceed the particle size, and particles fall more rapidly than they would otherwise. The aerosol particles settle out (larger particles settle faster), gradually entering the troposphere, where they are lost via wet and dry deposition processes.

Examples of the non-linear relationships between SO2 mass injection, particle size and visible optical depth as a function of time assuming idealized dispersion can be found in Pinto et al. (1998). These are detailed microphysical simulations, although in a one-dimensional model with specified dispersion. The rate of dilution of injected SO2 is critical owing to the highly non-linear response of particle growth and sedimentation rates within expanding plumes; particles have to be only 10 |xm or less to fall rapidly, which greatly restricts the total suspended mass, optical depth and infrared effect. The mass limitation indicates that 10 times the mass injection (of say Pinatubo) might result in only a modestly larger visible optical depth after some months.

The life cycle of these particles is thus controlled by a complex interplay between meteorological fields (like wind, humidity and temperature), the local concentrations of the gaseous sulphur species, the concentration of the particles themselves and the size distribution of the particles.

In the volcanically quiescent conditions (often called background conditions), partial pressures of sulphur gases remain relatively low, and the particles are found to be quite small (Bauman et al. 2003), with a typical size distribution that can be described with a lognormal distribution with a dry mode radius, standard deviation and effective radius of 0.05/2.03/0.17 |xm, respectively. After volcanic eruptions when sulphur species concentrations get much higher, the particles grow much larger (Stenchikov et al. 1998). Rasch et al. (2008) used numbers for a size distribution 6-12 months after an eruption for the large volcanic-like distribution of 0.376/1.25/0.43 |xm following Stenchikov et al. (1998) and Collins et al. (2004). There is uncertainty in the estimates of these size distributions, and volcanic aerosol standard distribution aLN was estimated to range from 1.3 to greater than 2 in Steele & Turco (1997).

When the particles are small, they primarily scatter in the solar part of the energy spectrum, and play no role in influencing the infrared (long-wave) part of the energy spectrum. Larger particles seen after an eruption scatter and absorb in the solar wavelengths, but also absorb in the infrared (Stenchikov et al. 1998). Thus small particles tend to scatter solar energy back to space. Large particles scatter less efficiently, and also trap some of the outgoing energy in the infrared. The size of the aerosol thus has a strong influence on the climate.

12.2.2 Geo-engineering considerations

To increase the mass and number of sulphate aerosols in the stratosphere, a new source must be introduced. Using Pinatubo as an analogue, Crutzen (2006) estimated a source of 5 Tg S yr-1 would be sufficient to balance the warming associated with a doubling of CO2. Wigley (2006) used an energy balance model to conclude that approximately 5 Tg S yr-1 in combination with emission mitigation would suffice. These studies assumed that the long-term response of the climate system to a more gradual injection would be similar to the transient response to a Pinatubo-like transient injection. A more realistic exploration can be made in a climate system model (see Section 12.2.4).

Rasch et al. (2008) used a coupled climate system model to show that the amount of aerosol required to balance the warming is sensitive to particle size, and that non-linearities in the climate system mattered. Their model suggested that 1.5 Tg S yr-1 might suffice to balance the greenhouse gases' warming, if the particles looked like those during background conditions (unlikely, as will be seen in Section 12.2.3), and perhaps twice that would be required if the particles looked more like volcanic aerosols. Robock et al. (2008) used 1.5-5 Tg S yr-1 in a similar study, assuming larger particle sizes (which, as will be seen in Section 12.2.3, is probably more realistic). They explored the consequences of injections in polar regions (where the aerosol would be more rapidly flushed from the stratosphere) and tropical injections.

All of these studies suggest that a source 15-30 times that of the current non-volcanic sources of sulphur to the stratosphere would be needed to balance warming associated with a doubling of CO2. It is important to note that in spite of this very large perturbation to the stratospheric sulphur budget, it is a rather small perturbation to the total sulphur budget of the atmosphere. This suggests that the enhanced surface deposition (as for example 'acid rain') from a stratospheric geo-engineering aerosol would be small compared with that arising from tropospheric sources globally, although it could be important if it occurred in a region that normally experienced little deposition from other sources.

There are competing issues in identifying the optimal way to produce a geo-engineering aerosol. Since ambient aerosol can be a primary scavenger of new particles and vapours, their very presence limits new particle formation. When the stratosphere is relatively clean, the H2SO4 supersaturation can build up, and nucleation of new particles over time occurs more easily, with less scavenging of the new particles. Thus, the engineered layer itself becomes a limiting factor in the ongoing production of optically efficient aerosols.

Many of the earlier papers on geo-engineering with stratospheric aerosols have listed delivery systems that release sulphur in very concentrated regions, using artillery shells, high-flying jets, balloons, etc. These will release the sulphur in relatively small volumes of air. Partial pressures of sulphuric acid gas will get quite high, with consequences to particle growth and lifetime of the aerosols (see Section 12.2.3 for more detail).

An alternative would be to use a precursor gas that is quite long-lived in the troposphere but oxidizes in the stratosphere and then allow the Earth's natural transport mechanisms to deliver that gas to the stratosphere, and diffuse it prior to oxidation. OCS might serve as a natural analogue to such a gas (Turco et al. 1980), although it is carcinogenic and a greenhouse gas.

Current sources of OCS are <1-2 Tg S yr-1 (Montzka et al. 2007). Perhaps 15 per cent of that is estimated to be of anthropogenic origin. Only approximately 0.03-0.05 Tg S yr-1 is estimated to reach the tropopause and enter the stratosphere (Figure 12.2 and SPARC 2006). Residence times in the troposphere are estimated to be approximately 1-3 years, and much longer (3-10 years) in the stratosphere. Turco et al. (1980) speculated that if anthropogenic sources of OCS were to be increased by a factor of 10, then a substantial increase in sulphate aerosols would result. If we assume that lifetimes do not change (and this would require careful research in itself), then OCS concentrations would in fact need to be enhanced by a factor of 50 to produce a 1 Tg S yr-1 source.

It might also be possible to create a custom molecule that breaks down in the stratosphere that is not a carcinogen, but using less reactive species would produce a reservoir species that would require years to remove if society needs to stop production. Problems with this approach would be reminiscent of the climate impacts from the long-lived chlorofluorocarbons (CFCs), although lifetimes are shorter.

12.2.3 Aerosol injection scenarios

An issue that has been largely neglected in geo-engineering proposals to modify the stratospheric aerosol is the methodology for injecting aerosols or their precursors to create the desired reflective shield.

As exemplified in Section 12.2.4 below, climate simulations to date have employed specified aerosol parameters, including size, composition and distribution, often with these parameters static in space and time. In this section, we consider transient effects associated with possible injection schemes that use aircraft platforms, and estimate the microphysical and dynamical processes that are likely to occur close to the injection point in the highly concentrated injection stream. There are many interesting physical limitations to such injection schemes for vapours and aerosols, including a very high sensitivity to the induced nucleation rates (e.g. homogeneous nucleation) that would be very difficult to quantify within injection plumes.

Two rather conservative injection scenarios are evaluated, both assume baseline emission equivalent to approximately 2.5 Tg S yr-1 (which ultimately forms approx. 10 Tg of particles) as follows: (i) insertion of a primary aerosol, such as fine sulphate particles, using an injector mounted aboard an aircraft platform cruising in the lower stratosphere and (ii) sulphur-enhanced fuel additives employed to emit aerosol precursors in a jet engine exhaust stream. In each case injection is assumed to occur uniformly between 15 and 25 km, with the initial plumes distributed throughout this region to avoid hot spots. Attempts to concentrate the particles at lower altitudes, within thinner layers, or regionally - at high latitudes, for example - would tend to exacerbate problems in maintaining the engineered layer, by increasing the particle number density and thus increasing coagulation.

Our generic platform is a jet-fighter-sized aircraft carrying a payload of 10 metric tons of finely divided aerosol, or an equivalent precursor mass, to be distributed evenly over a 2500-km flight path during a 4-hour flight (while few aircraft are currently capable of sustained flight at stratospheric heights, platform design issues are neglected at this point). The initial plume cross section is taken to be 1 m2, which is consistent with the dimensions of the platform. Note that, with these specifications, a total aerosol mass injection of 10 Tg of particles per year would call for 1 million flights, and would require several thousand aircraft operating continuously in the foreseeable future. To evaluate other scenarios or specifications, the results described below may be scaled to a proposed fleet or system.

Particle properties

The most optically efficient aerosol for climate modification would have sizes, Rp, of the order of 0.1 |xm or somewhat less (here we use radius rather than diameter as the measure of particle size, and assume spherical, homogeneous particles at all times). Particles of this size have close to the maximum backscattering cross-section per unit mass; they are small enough to remain suspended in the rarefied stratospheric air for at least a year and yet are large enough and thus could be injected at low enough abundances to maintain the desired concentration of dispersed aerosol against coagulation for perhaps months (although long-term coagulation and growth ultimately degrade the optical efficiency at the concentrations required; see below). As the size of the particles increases, the aerosol mass needed to maintain a fixed optical depth increases roughly as ~Rp, the local mass sedimentation flux increases as and the particle infrared absorptivity increases as (e.g. Seinfeld & Pandis 1997). Accordingly, to achieve, and then stabilize, a specific net radiative forcing, similar to those discussed in Section 12.2.4 below, larger particle sizes imply increasingly greater mass injections, which in turn accelerate particle growth, further complicating the maintenance of the engineered layer.

This discussion assumes amonodispersed aerosol. However, an evolving aerosol, or one maintained in a steady state, exhibits significant size dispersion. Upper-tropospheric and stratospheric aerosols typically have a lognormal-like size distribution with dispersion aLN ~ 1.6-2.0 (lnaLN ~ 0.47-0.69). Such distributions require a greater total particle mass per target optical depth than a nearly monodis-persed aerosol of the same mean particle size and number concentration. Accordingly, the mass injections estimated here should be increased by a factor of approximately 2, other things remaining equal (i.e. for aLN ~ 1.6-2.0, the mass multiplier is in the range of 1.6-2.6).

Aerosol microphysics

A bottleneck in producing an optically efficient uniformly dispersed aerosol -assuming perfect disaggregation in the injector nozzles - results from coagulation during early plume evolution. For a delivery system with the specifications given above, for example, the initial concentration of plume particles of radius Rpo = 0.08 |xm would be approximately 1 x 109 cm-3, assuming sulphate-like particles with a density of 2 g cm-3. This initial concentration scales inversely with the plume cross-sectional area, flight distance, particle specific density and cube of the particle radius, and also scales directly with the mass payload. For example, if Rpo were 0.04 or 0.16 |xm, the initial concentration would be approximately 1 x 1010 or 1 x 108 cm-3, respectively, other conditions remaining constant.

For an injected aerosol plume, the initial coagulation time constant is

npo K co where npo is the initial particle concentration and Kco is the self-coagulation kernel (cm3s-1) corresponding to the initial aerosol size. For Rpo~0.1 |xm, K— 3 x 10-9 cm3 s-1 (e.g. Turco et al. 1979; Yu & Turco 2001). Hence, in the baseline injection scenario, tco — 0.07-7 s, for Rpo — 0.04-0.16 |xm, respectively. To assess the role of self-coagulation, these timescales must be compared with typical small-scale mixing rates in a stably stratified environment, as well as the forced mixing rates in a jet exhaust wake.

Turco & Yu (1997, 1998, 1999) derived analytical solutions of the aerosol continuity equation which describe the particle microphysics in an evolving plume.

The solutions account for simultaneous particle coagulation and condensational growth under the influence of turbulent mixing, and address the scavenging of plume vapours and particles by the entrained background aerosol. A key factor-in addition to the previous specifications-is the growth, or dilution, rate of a plume volume element (or, equivalently, the plume cross-sectional area). The analytical approach incorporates arbitrary mixing rates through a unique dimensionless parameter that represents the maximum total number of particles that can be maintained in an expanding, coagulating volume element at any time. Turco & Yu (1998, 1999) show that these solutions can be generalized to yield time-dependent particle size distributions, and accurately reproduce numerical simulations from a comprehensive microphysical code. Although aerosol properties (concentration, size) normally vary across the plume cross section (e.g. Brown et al. 1996; Diirbeck & Gerz 1996), uniform mixing is assumed, and only the mean behaviour is considered.

Quiescent injection plumes

An otherwise passive (non-exhaust) injection system generally has limited turbulent energy, and mixing is controlled more decisively by local environmental conditions. If the quiescent plume is embedded within an aircraft wake, however, the turbulence created by the exhaust, and wing vortices created at the wingtips, can have a major impact on near-field mixing rates (e.g. Schumann et al. 1998). For a quiescent plume, we adopt a linear cross-sectional growth model that represents a small-scale turbulent mixing perpendicular to the plume axis (e.g. Justus & Mani 1979). Observations and theory lead to the following empirical representation for the plume volume:

where V is the plume volume element of interest (equivalent to the cross-sectional area in the near-field), V0 is its initial volume and rmix is the mixing timescale. For the situations of interest, we estimate 0.1 < rmix < 10 s.

Following Turco & Yu (1999, eqn (73)), we find for a self-coagulating primary plume aerosol

1 + /mln(T+ fc//my where Np is the total number of particles in the evolving plume volume element at time t, and Npo is the initial number. We also define the scaled time, fc = t/rco and scaled mixing rate, fm = rmix/rco. The local particle concentration is np(t) = Np(t )/V (t).

In Figure 12.3, predicted changes in particle number and size are illustrated as a function of the scaled time for a range of scaled mixing rates. The ranges of

Figure 12.3 Evolution of the total concentration of particles Np and the mass-mean particle radius Rp in an expanding injection plume. Both variables are scaled against their initial values in the starting plume. The time axis ( fc = t/rco) is scaled in units of the coagulation time constant Tco. Each solid line, corresponding to a fixed value of fm, gives the changes in Np and Rp for a specific mixing timescale Tmix measured relative to the coagulation timescale Tco or fm = rmix/rco. The heavy dashed line shows the changes at the unit mixing time, for which fc = fm when the plume cross-sectional area has roughly doubled; the longer the mixing timescale, the greater the reduction in particle abundance and particle radius.

Figure 12.3 Evolution of the total concentration of particles Np and the mass-mean particle radius Rp in an expanding injection plume. Both variables are scaled against their initial values in the starting plume. The time axis ( fc = t/rco) is scaled in units of the coagulation time constant Tco. Each solid line, corresponding to a fixed value of fm, gives the changes in Np and Rp for a specific mixing timescale Tmix measured relative to the coagulation timescale Tco or fm = rmix/rco. The heavy dashed line shows the changes at the unit mixing time, for which fc = fm when the plume cross-sectional area has roughly doubled; the longer the mixing timescale, the greater the reduction in particle abundance and particle radius.

parameters introduced earlier result in an approximate range of 0.014 < fm < 140. At the lower end, prompt coagulation causes only a small reduction in the number of particles injected, while at the upper end reductions can exceed 90 per cent in the first few minutes. Particle self-coagulation in the plume extending over longer timescales further decreases the initial population - by a factor of a 1000 after 1 month in the most stable situation assumed here, but by only some tens of per cent for highly energetic and turbulent initial plumes.

The dashed line in Figure 12.3 shows the effect of coagulation at the 'unit mixing time', at which the plume volume has effectively doubled. Clearly, prompt coagulation significantly limits the number of particles that can be injected into the ambient stratosphere when stable stratification constrains early mixing. Initial particle concentrations in the range of approximately 1010-1011 cm-3 would be rapidly depleted, as seen by moving down the unit mixing time line in Figure 12.3 (further, 1011 cm-3 of0.08 |im sulphate particles exceed the density of stratospheric air). A consequence of prompt coagulation is that it is increasingly difficult to compensate for plume coagulation (at a fixed mass injection rate) by reducing the starting particle size. Initial particle concentrations could simultaneously be reduced to offset coagulation, but the necessary additional flight activity would affect payload and/or infrastructure. It is also apparent that rapid mass injections in the forms of liquids or powders for the purpose of reducing flight times would lead to mass concentrations greatly exceeding those assumed above (generally <1 x 10-4 g cm-3), causing large particle or droplet formation and rapid fallout.

Aerosol injection in aircraft jet exhaust The effects of high-altitude aircraft on the upper troposphere and lower stratosphere have been extensively studied, beginning with the supersonic transport programmes of the 1970s and extending to recent subsonic aircraft impact assessments (under various names) in the USA and Europe (e.g. NASA-AEAP 1997). These projects have characterized aircraft emissions and jet plume dynamics, and developed corresponding models to treat the various chemical, microphysical and dynamical processes.

Enhancing aircraft fuel with added sulphur compounds (H2S, Sn) could increase the particle mass in a jet wake. It is well established that ultrafine sulphate particles are generated copiously in jet exhaust streams during flight (e.g. Fahey et al. 1995). The particles appear to be nucleated by sulphuric acid on ions (hereafter chemiions, e.g. Yu & Turco (1997, 1998&)) formed in the combustion process of jet engines by radical reactions. Sulphuric acid is a by-product of sulphur residues in the fuel (typically less than 1 per cent sulphur by weight); most of this fuel sulphur is emitted as SO2. The fraction emitted as H2SO4 decreases as the fuel sulphur content increases, and accounts for roughly 2 per cent of the total sulphur as the fuel sulphur content approaches approximately 1 per cent.

The concentrations of chemiions in jet emissions are strongly limited by ion-ion recombination along the engine train to approximately 1 x 109 cm-3 at the exit plane (e.g. Arnold et al. 2000). Considering a variety of direct measurements of particles in jet wakes, Karcher et al. (2000) showed that chemiion nucleation is consistent with the observed relative constancy of the ultrafine volatile (non-soot) particle emission factor, Ep ~ 1-2 x 1017 kg-1 fuel (where it should be noted that the concentrations of soot particles are typically less than 1 per cent of the total number of particles emitted). Ep is quite insensitive to the fuel sulphur content, a fact that is also consistent with a chemiion nucleation source. While vapour trails formed in jet wakes can significantly modify the injected particle properties (e.g. Yu & Turco 1998a), condensation trails are extremely rare under normally dry stratospheric conditions.

If we imagine enhanced jet fuel sulphur contents of 5 per cent by weight (10-100 times current amounts) for geo-engineering purposes, then the annual consumption of approximately 50 Tg of such fuel during stratospheric flight (approx. half the amount used by current commercial aviation) could emit up to 2.5 Tg of sulphur that would eventually generate roughly 10 Tg of sulphate aerosol. The total number of particles emitted-for Ep ~ 1 x 1017 kg-1 fuel-would amountto approximately

5 x 1027. This number, uniformly dispersed over a 10-km thick layer from 15 to 25 km, yields an average concentration of approximately 1 x 103 cm-3 with a particle radius of roughly 0.06 |j.m; in other words, an ideal geo-engineered solar shield. These estimates (i) assume no unexpected chemistry or microphysics in the early wake that would alter the emission factor significantly, (ii) allow for an ideal distribution of sulphate mass among the particles, and (iii) ignore coagulation following emission.

The mixing rates in a jet wake are very rapid. Schumann et al. (1998) fit a wide range of exhaust plume observations in the upper troposphere and lower stratosphere with a 'universal' mixing curve. We use their result in the form

Equation (12.4) describes, roughly, plume dilution starting at the exhaust exit prior to mixing with turbine bypass air, through the jet zone, vortex region and into the ambient mixing regime. Schumann et al. (1998) state that the fit is best between 1 and 50 s. For the approximately 1 x 109 cm-3 incipient particles in the initial exhaust stream, the extent of self-coagulation can be projected using the more general analytical approach discussed earlier (Turco & Yu 1999). Thus, even at 10 s, approximately three-quarters of the initial particles remain (compared with an estimated 0.0007 per cent if mixing were completely suppressed). Clearly, prompt coagulation is not an issue in a jet exhaust plume.

Longer-term plume processing

The extended microphysical processing of an injection plume can be critical owing to the long induction time before the plume becomes widely dispersed as a part of the background aerosol. Yu & Turco (1999) studied the far-wake regime of jet exhaust for upper tropospheric conditions to estimate the yield of cloud condensation nuclei from volatile aircraft particulate emissions. In their simulations, the background aerosol surface area density (SAD) ranged from 12.7 to 18.5 |xm2 cm-3 for summer conditions. The resulting scavenging of fresh plume particles amounted to approximately 95 per cent after 10 days (that is, the effective emission index was decreased by a factor of 20). Moreover, only approximately 1 in 10000 of the original particles had grown to 0.08 |xm at that time, corresponding to a fuel sulphur content of 0.27 per cent by weight, with 2 per cent emitted as H2SO4. For a geo-engineering scheme with 5 per cent fuel sulphur, although the primary exhaust sulphuric acid fraction would probably be less than 1 per cent, the initial growth rate of the chemiions would probably be accelerated.

At typical mixing rates, background aerosol concentrations would be present in an injection plume within a minute or less. The natural stratosphere has an ambient aerosol concentration of 1-10cm-3, with an effective surface area of less than 1 |j.m2cm-3. However, in a geo-engineered stratosphere, at the desired baseline optical depth, a SAD greater than 10 |xm2cm-3 would prevail. Further, any attempt to concentrate the engineered layer regionally or vertically, or both, would greatly exacerbate both self-coagulation and local scavenging.

The coagulation kernel for collisions of the background engineered particles (assuming a minimum radius of approx. 0.1-0.2 |xm following ageing) with jet exhaust nanoparticles of approximately 10-80 nm is approximately 1 x 10-7 to 4 x 10-9cm3s-1, respectively (Turco et al. 1979). Using a mean scavenging kernel for growing jet particles of approximately 2 x 10-8 cm3 s-1, and a background concentration of 120 cm-3 (determined for a doubling of the mass injection rate to maintain the optical depth, see below), the estimated scavenging factor is exp(-2.5 x 10-6t). After 1 day, the reduction in number is a factor of approximately 0.80, and over 10 days, approximately 0.1, consistent with the result of Yu & Turco (1999). Keeping in mind that the optical requirements of the engineered layer are roughly based on total cross-section (ignoring infrared effects), while the scavenging collision kernel is also approximately proportional to the total background particle surface area (for the particle sizes relevant to this analysis), larger particles imply a lower concentration (and greater injection mass loading) but about the same overall scavenging efficiency.

The background aerosol will also affect the partitioning of any injected vapours between new and pre-existing particles. Considering the injection of SO2 in jet exhaust as an example, it should be noted that SO2 oxidation in the stabilized plume should occur over roughly 1 day, unless oxidants are purposely added to the plume. By this time the SO2 would be so dilute and relative humidity so low that additional nucleation would be unlikely.

At approximately 1 day, the residual plume exhaust particles may have achieved sizes approaching 0.05 |xm (Yu & Turco 1999). Then, considering the considerably larger surface area of the background aerosol, only a fraction of the available precursor vapours would migrate to new particles, with the rest absorbed on preexisting aerosol. Using an approach similar to that in Turco & Yu (1999), we infer that the jet-fuel sulphur injection scenario partitions roughly 20 per cent of the injected sulphur into new particles, with the rest adding to the background mass. Considering the higher fuel sulphur content, and reduced number of condensation sites, the residual injected plume particles could grow on average to approximately 0.08 |xm. While this is a desirable size, the effective emission index is an order of magnitude below that needed to maintain the desired layer under the conditions studied. Either the fuel sulphur content or fuel consumption could be doubled to regain the overall target reflectivity. Nevertheless, as the expanding injection plumes merge and intermix following the early phase of coagulation scavenging, the aerosol system undergoes continuing self-coagulation as the layer approaches, and then maintains, a steady state. The consequences of this latter phase are not included in these estimates.

Summary

A primary conclusion of the present analysis is that the properties of aerosols injected directly into the stratosphere from a moving (or stationary) platform, or in the exhaust stream of a jet aircraft, can be severely affected by prompt and extended microphysical processing as the injection plume disperses, especially owing to self-coagulation and coagulation scavenging by the background aerosol. Early coagulation can increase mass requirements by a factor of 2 or more primarily because increased particle size leads to reduced optical efficiency. In addition, the resulting dispersion in particle sizes implies even greater mass injections by up to a factor of approximately 2. Thus, consideration of particle aggregation and size dispersion increases, at least by several-fold, the estimated engineering and infrastructure development effort needed to produce a required net solar forcing. We wish to emphasize that these calculations are merely one exploration of an idealized set of delivery scenarios. Many others are possible, and would require similar sets of calculations, and, if deemed promising, far more elaborate studies.

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Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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