Selection of aerosol precursor
Some of the anticipated risks of SAI, including ozone loss, stratospheric heating, increased diffuse radiation and acid deposition might be reduced by using aerosols based on engineered solid particles. Calcite, alumina and diamond particles, for example, have a high refractive index and might reduce forward scattering (Pope et al. 2012; Weisenstein et al. 2015; Dykema et al. 2016) and the use of alkaline metal salts such as CaCO3 might counteract ozone depletion due to acid neutralisation on their outer surface (Keith et al. 2016). However, significant unknowns remain in the use of engineered aerosols. These pertain to their implementation, e.g. the technology and injection strategy for successful aerosol formation, and to their impacts, e.g. possible chemical interactions with stratospheric compounds and their influence on ecosystems once deposited (Pope et al. 2012; Weisenstein et al. 2015).
An alternative is to use sulphate aerosols. The physical properties and costs of sulphur are well known, and their background presence in the atmosphere due to volcanic and industrial emissions allows rough estimations of their side effects and radiative forcing (Crutzen 2006; Pope et al. 2012). These estimates are still imprecise, as the altitudes and particle sizes considered in current SAI scenarios differ from those associated with volcanic and industrial sources. The resulting uncertainties, however, are generally considered to be far less than those associated with engineered aerosols.
Sunlight-scattering sulphate aerosols in the stratosphere consist of particles mostly comprised of aqueous H2SO4. These can be introduced into the atmosphere either by injection of precursor compounds or by direct injection of H2SO4. The injection of precursor compounds, such as SO2, is potentially advantageous from the storage point of view, due to their mild corrosion characteristics and lower net weight. However, in the atmosphere SO2 oxidises to form H2SO4 only after a relatively long time of ≈ 40–50 days (Tilmes et al. 2017; Vattioni et al. 2019), meaning that the conditions of sulphate aerosol formation cannot be controlled. Injection of SO2 typically leads to particles that are larger than optimal and therefore are less effective scatterers and have shorter stratospheric residence times (e.g., Pierce et al. 2010). The slow conversion of SO2 into H2SO4 also means that a substantial part of the injected sulphur in the stratosphere is not in sulphate aerosol form. With SO2 as the injection species, on average more than one-eighth of the annually injected sulphur mass is present in form of SO2 and is thus ineffective. Furthermore, not all injected SO2 oxidises to H2SO4; a part of the precursor mass is removed from the stratosphere by diffusion and mixing without having undergone oxidation and aerosol formation at all (Vattioni et al. 2019).
In contrast, the direct injection of H2SO4 in gas phase facilitates directing the initial particle formation process (Pierce et al. 2010; Benduhn et al. 2016). In conditions where particle growth is self-limited and independent of nucleation rate, particle sizes are determined by the initial H2SO4 concentration and the diffusivity of the background flow in which it is injected (Benduhn et al. 2016; Turco and Yu 1997). Direct H2SO4 injection targeting an initial particle radius of approximately 0.1 μ m is expected to lead to a favourable aerosol size distribution throughout the aerosol’s stratospheric residence time (Pierce et al. 2010; Benduhn et al. 2016), which allows irradiation reduction to be increased by 17–70%, depending on injection details, relative to that obtained by injection of SO2 (Vattioni et al. 2019). The aerosol distribution of directly injected H2SO4 derives its stronger irradiation reduction from containing larger numbers of smaller particles. Yet, this also leads to a larger total particle surface area. This has the disadvantage of increasing adverse effects associated with stratospheric sulphate aerosol presence, such as ozone depletion and stratospheric warming (Pope et al. 2012; Heckendorn et al. 2009). However, the increased scattering efficiency due to particle diameter decrease outweighs the increased adverse effects, as shown by (Vattioni et al. 2019). This implies that direct H2SO4 injection under ideal circumstances can achieve a given negative radiative forcing target with lower annual sulphur delivery rate and less adverse effects than SO2 injection.
In all, direct H2SO4 injection appears promising with respect to SO2 injection, though direct comparisons are relatively sparse and significant uncertainties remain. Still, the apparent benefits of direct H2SO4 injection lead us to mainly focus on this scenario for our aircraft-based delivery system. We will assume that the H2SO4 is transported in liquid phase, due to a lack of proven technology for in-flight H2SO4 production from precursors (Smith et al. 2018). This necessitates the use of an evaporation system to ensure that the H2SO4 is injected as a condensable gas. The temperature of the engine exhaust flow in which the H2SO4 gas is injected may be high enough to enable simultaneous evaporation and injection, eliminating the need for a separate evaporation system. However, because the injection specifics are very important for aerosol particle formation, as outlined below, we assume a conservative configuration including an evaporation system.
As mentioned, direct H2SO4 vapour injection only allows indirect control of particle formation via nucleation, condensation and coagulation. To obtain more direct control of particle size, these formation processes would have to be eliminated or completed in a controlled environment inside the aircraft. To our knowledge, however, no spray technology to reliably produce ideally sized droplets at high enough rates exists (Technical and Business Development Director Micron Sprayers Ltd., personal communication, Nov 4, 2019) and it is unlikely that the circumstances needed to allow automated and controlled nucleation, condensation and coagulation to take place can readily be created inside an aircraft. Therefore, we base our injection strategy on the existing literature on aerosol formation by condensation of gas phase H2SO4 injection into an expanding plume.
Delivery rates and location
Specifying the goal of potential SAI is not trivial, and different focus parameters can be chosen, such as e.g. global average temperature reduction, warming rate reduction, regional temperature reductions or average radiative forcing. In the latter case, the target negative radiative forcing could be based on the current positive radiative forcing with respect to pre-industrial times, or roughly 2.5 to 3 Wm− 2 (IPCC 2018). To provide conservative measures of the costs and emissions of an SAI delivery system, such a mission objective will be considered in the present study. This corresponds to an annual delivery rate of 15 Mt H2SO4 year− 1 (5 Mt S year− 1) (Pierce et al. 2010).
This study assumes that the delivery takes place at altitudes near 20 km. This is sufficiently far above the tropopause to prevent mixing of aerosols into the troposphere and fast sedimentation (Rasch et al. 2008; Pierce et al. 2010). Even though an increased coagulation rate reduces the efficiency of individual particles if injected above 20 km, higher injection altitudes will still yield a more effective irradiation reduction, given the resulting longer residence time of the aerosols (Tilmes et al. 2017; Vattioni et al. 2019). However, as will be discussed in Sections 3 and 5, delivery at altitudes higher than 20 km is likely to be unfeasible.
Injection latitudes near 15∘ North and South will be assumed, as these have been shown to be favourable for global aerosol coverage and stratospheric residence times (Tilmes et al. 2017; Vattioni et al. 2019). It may be assumed that a steady state of aerosol coverage and optical depth is reached after approximately two years (Tilmes et al. 2017; Reed 1966; Uppala et al. 2005).
As described in the next section, the rate at which H2SO4 can be delivered within a single flight is dependent on the technology employed. Consequently, three H2SO4 injection scenarios will be examined. For comparison, we will also examine a scenario in which only SO2 is delivered, at annual delivery rates sufficient to produce equivalent negative short-wave radiative forcing.
H2SO4 dispersion rate (DR)
Two parameters driving the production of optimally sized particles from direct H2SO4 vapour injection are the initial H2SO4 concentration and background flow diffusivity. According to Benduhn et al. (2016), initial concentrations suitable for expanding aircraft engine plumes vary between 3 ⋅ 1015 and 1018 molecules H2SO4 cm− 3 (Benduhn et al. 2016) (or Cinit = 0.0005 - 0.2 kgm− 3). Maintaining initial concentrations near the lower limit of this interval requires low injection rates and correspondingly long flight times, which substantially increases the costs associated with delivery. On the other hand, the use of high initial concentrations requires high engine plume diffusivities. Currently the maximum achievable levels of diffusivity in stratospheric engine plumes can only be estimated. To deal with this uncertainty, we examine three direct H2SO4 injection scenarios. These differ most crucially in terms of their implied dispersion rates (DR).
The dispersion rate DR in kg H2SO4m− 1, for the injection of H2SO4 at a rate \(\dot {m}\) kg s− 1, into an engine plume with a volume flow \(\dot {V}\) m3s− 1 emitted from an aircraft travelling at speed vac ms− 1 is given by:
$$ DR = \frac{\dot{m}}{v_{ac}} = \frac{C_{init}\dot{V}}{v_{ac}} $$
(1)
This assumes that the H2SO4 concentration, Cinit, is uniform within the plume. The total aircraft payload delivered is given by the value of DR integrated over the range of the flight.
Previous studies have assumed that constant, uniform diffusivities between 102 and 103 m2s− 1 can be maintained in an aircraft engine plume throughout the aerosol’s early growth phase (a period on the order of seconds to minutes) (Pierce et al. 2010; Benduhn et al. 2016; Smith et al. 2018). However, aircraft engine plumes typically do not display constant, uniform background diffusivities. Normally the diffusivity declines in the initial minutes of particle growth, as energetic engine-driven mixing is gradually replaced by mixing at the much larger scales associated with wing tip vortices (Yu and Turco 1998; Schumann et al. 1998). The magnitude and distribution of diffusivity will thus depend on the specific details of the engine and aircraft configuration. To capture the effects of such variations, the three direct H2SO4 injection scenarios considered below have been developed using different options for engine plume injection.
Core injection (CI) scenario
As will be discussed in Section 3, the scale of the intended mission justifies the development of a specialised turbofan engine. Turbofan engines have two different volume flows, the first associated with the warm, high-velocity engine core and the second associated with the cool, low-velocity outer bypass. For the first scenario, we assume that H2SO4 is injected into the core flow only. This is chosen mainly because it is most consistent with plume models applied in literature (Pierce et al. 2010; Benduhn et al. 2016). We thus assume it achieves a diffusivity value of 102 m2s− 1, similar to the value used by Yu and Turco (1998) and measured by Schumann et al. (1998). This is the most conservative of the scenarios considered, as it ignores the potential gains obtainable by also injecting into the bypass flow.
Targeting an initial particle radius of ≈ 0.1 μ m at the assumed diffusivity requires an initial H2SO4 concentration of approximately 1016 cm− 3 (Benduhn et al. 2016). For the specific aircraft design considered later in this paper, the core volume flow is 260 m3s− 1 at the high thrust settings necessary for stratospheric cruise. At the corresponding aircraft cruise speed of vac = 210 ms− 1, the resulting dispersion rate is relatively low: DR = 0.002 kgm− 1. This is more conservative than the value for the equal diffusivity and initial concentration used by Pierce et al. (2010), who assumed uniformly high diffusivities throughout the aircraft wake and a relatively large effective aerosol outlet area of 6 m2, leading to a large volume flow for injection.
Full injection (FI) scenario
The outer bypass flow of the proposed turbofan engine can be expected to have relatively low values of diffusivity, owing to its relatively low velocities. However, as its volume flow is 7.5 times greater in magnitude than that of the core flow, it can help increase the DR to reduce required flight time. Thus, in the second scenario, injection into the full engine flow is considered. It is assumed that exhaust mixers are used to achieve a well-mixed and uniformly seeded initial plume. These are commonly employed in low-bypass turbofans (Larkin and Blatt 1984; Holzman et al. 1996) and some high-bypass turbofan engines (Mundt and Lieser 2001). The use of such mixers is a relatively conservative assumption, as lighter, but less proven alternatives exist, such as the use of overexpanded bypass flows. These show the potential for providing uniform mixing in the early plume at virtually no thrust penalty (Debiasi et al. 2007). Both conventional mixers and overexpanded bypass flows can be expected to have the additional advantage of reducing jet noise (Mundt and Lieser 2001).
Well-mixed early plumes have been found to display slightly higher diffusivities than core-only flows (Debiasi et al. 2007). Hence, it will be conservatively assumed that the mixed core and bypass flow approximately maintains the diffusivity value of 102 m2s− 1. As for the first scenario, this requires an initial H2SO4 concentration of approximately 1016 cm− 3. Owing to the higher total volume flow, however, the resulting dispersion in this scenario is DR = 0.02 kgm− 1.
Optimised full injection (OFI) scenario
The first two scenarios assume relatively conservative values of diffusivity. However, improved engine flow mixing technology or more accurate measurements and simulations of plume growth might show that higher values can be attained. Thus, the third scenario will consider the case where a relatively high value of diffusivity, 3 ⋅ 102 m2s− 1, is achieved in combination with both core and bypass injection. This corresponds to a much higher initial H2SO4 concentration of 3 ⋅ 1017 cm− 3, which is still well within the desired aerosol regime described in Benduhn et al. (2016). The resulting dispersion rate, DR = 0.5 kgm− 1, is substantially larger than those of the first two scenarios.
Precursor gas (SO2) injection scenario
When precursors such as SO2 are injected, aerosol formation does not occur until long after delivery and is thus virtually independent of injection specifics. In this case, the dispersion rate in flight is not constrained. This means cost-efficient, short, high-payload flights can be employed. Furthermore, recent studies have demonstrated that negative radiative forcing from point source injection of SO2 at 20 km peaks for injection locations around 15∘ N and could achieve radiative forcing reductions of 2.5 to 3 Wm− 2 as well (Tilmes et al. 2017; MacMartin et al. 2017). However, due to the slow conversion to H2SO4, average particle sizes increase and scattering efficiency decreases. As a conservative estimate, we assume that approximately twice the amount of sulphur is required to achieve the same radiative forcing with SO2 with respect to H2SO4 injection, based on radiative forcing estimates from (Pierce et al. 2010; Tilmes et al. 2017). To assess the combined effects of the constrained DR but lower annual delivery requirement in H2SO4 injection scenarios, a fourth, SO2 precursor injection scenario will be examined (SO2). It assumes the delivery of 20 Mt SO2 y− 1 (10 Mt S) at the same altitudes and latitudes as the H2SO4 scenarios, delivered in short-range flights from four airports approximating point sources. The top half of Table 2 summarises the most important differences between the four scenarios.