Modelling the size distribution of geoengineered stratospheric aerosols

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1 ATMOSPHERIC SCIENCE LETTERS Atmos. Sci. Let. 12: (2011) Published online 20 August 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI: /asl.285 Modelling the size distribution of geoengineered stratospheric aerosols René Hommel* and Hans-F. Graf Centre for Atmospheric Science, University of Cambridge, Cambridge, UK *Correspondence to: René Hommel, Centre for Atmospheric Science, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW UK. Received: 22 February 2010 Revised: 7 June 2010 Accepted: 9 June 2010 Abstract A modelling study on the growth of geoengineered stratospheric aerosols reveals that in steady state a large fraction of aerosols grow to micrometre sizes so that the sedimentation of aerosols might limit the geoengineered aerosol layer s ability to achieve its target cooling effect. Copyright 2010 Royal Meteorological Society Keywords: aerosol; stratosphere; geoengineering 1. Introduction Solar radiation management by artificially increasing the albedo of the stratospheric aerosol layer has been suggested as a potentially accomplishable method to counteract anthropogenic future greenhouse gas warming (The Royal Society, 2009; Robock et al., 2009). However, this would require interference with the global energy budget, and potential impacts on ecosystems and societies are very uncertain. In addition, one must bear in mind that such kind of geoengineering would at best treat symptoms of the enhanced greenhouse effect but not causes. Hence, it is crucial to extremely carefully investigate the effects of such interference with the natural system. Wanted as well as unintended effects of artificial stratospheric aerosols are determined by their size and composition. The latter predominately interacts with the atmosphere s chemistry and thus is a major driver for changes in atmospheric composition, including loss of stratospheric ozone. Physical parameters like the size spectrum of the aerosols ultimately determine whether the geoengineered stratospheric aerosol layer is able to compensate part of the anticipated future greenhouse gas warming or not. So far, only a few modelling studies addressed the global impact of geoengineered stratospheric aerosols by interactively treating the aerosol size (Rasch et al., 2008; Robock et al., 2008; Tilmes et al., 2009). However, in these studies, the aerosol size spectrum was not determined by aerosol microphysical processes. The aerosol size distributions were instead prescribed based on observational findings after the Mt Pinatubo eruption, which in summer 1991 injected approximately 20 Tg SO 2 into the stratosphere (SPARC, 2006), for a few months generating a reduction of solar insolation of about the right magnitude ( 2 Wm 2 ) to counteract the current anthropogenic greenhouse effect. In a more recent modelling study, Heckendorn et al. (2009), hereafter referred to as H09, calculated the aerosol size distribution by an interactive and size-resolved treatment of aerosol microphysical processes originating from different methods of SO 2 injection into the stratosphere. They showed that the stratospheric aerosol layer resulting from a continuous injection of 20 Tg SO 2 per year would not be able to compensate a warming resulting from 2 W m 2 due to the anthropogenic greenhouse effect. Hence, there is some uncertainty of the effects of sulphate aerosols in the stratosphere, possibly closely related to the size of geoengineered aerosols, in particular to the ratio of fine to large particles. An overview of key quantities derived in those studies is given in Table I. In the present study, we investigate how aerosols grow in the stratosphere when 5 Tg SO 2 per year are continuously supplied at the 50-hPa pressure level. We perform two sets of simulation, which differ in the way how the oxidised SO 2 is subtracted from its source. The scenario 1 (S1) is constructed to be more realistic whereas scenario 2 (S2) has to be seen as an upper limit case for the response of the model. We utilise the aerosol microphysics module SAM2 (Hommel et al., 2008), which resolves the main processes determining the size distribution of aerosols. From our more realistic scenario, we estimate the stratospheric aerosol burden in a very idealised manner. Results of our box model study are compared with those of previous studies (overview in Table I) based on more complex models regarding, e.g. transport of the aerosols. Copyright 2010 Royal Meteorological Society

2 Size distribution of geoengineered stratospheric aerosols 169 Table I. Results from scenarios of geoengineering from studies which applied moderate continuous supplies of sulphur in the stratosphere. Study Heckendorn et al. (2009) Rasch et al. (2008) Robock et al. (2008) This study Scenario GEO2 GEO5 bg2co2 volc2 5 Mt/a tropical S1 S2 Injection [Tg(SO 2 )year 1 ] , cumulative Effective radius (µm) a a 0.17 b 0.43 b b c SAD d (µm 2 cm 3 ) 20 < a c Burden [Tg(S)] a e Forcing (W m 2 ) 0.78 ± ± 0.31 a a 1.8 e e a Not shown. b Prescribed. c At the end of simulation. d Values are for the equatorial stratosphere at 50 hpa ( 21 km). e Not calculated. 2. Methods 2.1. Model The aerosol microphysics module SAM2, applied here in a zero-dimensional framework, treats the formation and evolution of stratospheric sulphuric acid aerosol (Timmreck & Graf, 2000; Hommel, 2008). The scheme utilises the fixed sectional approach to resolve an aerosol distribution from to 20.7 µm in radius. Forty-four logarithmically spaced size bins are determined by mass doubling. Aerosol microphysics processes of new particle formation due to binary homogeneous nucleation (Vehkamäki et al., 2002), H 2 SO 4 condensation and evaporation, and coagulation are considered in the model. The sulphuric acid droplets are assumed to be spherical and in thermodynamic equilibrium with their environment. Water vapour growth and the sulphuric acid weight percentage are determined from partial and vapour pressures of H 2 SO 4 and H 2 O. The size distribution is affected by gravitational sedimentation. Similar to the studies of Kokkola et al. (2009), we assume that gaseous H 2 SO 4 is exclusively formed from the oxidation of SO 2 by the hydroxyl radical OH. An OH concentration of cm 3 is prescribed in a diurnal cycle between 06 : 00 and 18 : 00 and held to zero during night time. Reaction rate constants of the three-body reaction are based upon the 2003 JPL recommendations (Sander et al. 2003). A complete description of the parameterisations implemented in SAM2 and its overall performance in the context of a global aerosol-climate model, resolving the troposphere and the stratosphere up to 80 km, can be found in a companion paper (Hommel et al., 2010, unpublished). The altitude where sulphur (S) is injected into the stratosphere determines the particle residence time that is controlled by size-dependent gravitational sedimentation (Kasten, 1968). In the (sub)tropics, the steady state of natural aerosols is maintained between 20 and 25 km (Barnes and Hofmann, 2001; SPARC 2006), hence this region is appropriate for the proposed supply of SO 2. Our experiments are conducted under climatologically mean conditions for an idealised model level at the equator, centred at 50 hpa ( 21 km). Ambient conditions (temperature 200 K and relative humidity 0.2%) were taken from Hommel (2008) and kept constant for the 10 years of integration. We integrated the model using a time step of 900 s, which is equivalent to that of a global model of medium resolution (T42) Experiments The growth of aerosol particles is evaluated in two scenarios of geoengineering. In each scenario, we investigate three different treatments of the processes nucleation and condensation. Both scenarios compete for the formed H 2 SO 4 vapour. Furthermore, in each case, we examine how the model solution depends on the integration time step length, so that aerosol growth is investigated in a total of 12 ensembles members. In both scenarios, 5 Tg SO 2 per year are added to the stratosphere. In scenario 1 (S1) in each time step, the oxidised SO 2 forming sulphuric acid vapour is subtracted from the total source. In contrast, in scenario 2 (S2) the SO 2 source was held constant, thereby substituting any oxidised SO 2. This means that the SO 2 concentration accumulates, forming a stratospheric reservoir which cannot be depleted by oxidation to gaseous H 2 SO 4 due to OH limitation (Pinto et al., 1989). Within the limitation of a box model, S1 is a realistic scenario with prognostic aerosol microphysics, similar to the experiments of H09 with continuous S-supply in the equatorial stratosphere. S2, however, should be regarded as an upper limit estimate of particle growth under an inexhaustible supply of SO 2. Hence, it is a severe test case for the model stability and dependency on the integration time step length. In each ensemble, aerosols are initialised as in Kokkola et al. (2009) with a unimodal distribution whose geometric mean diameter is µm and a geometric standard deviation σ is The initial total number concentration is set to three particles per cm 3.

3 170 R. Hommel and H.-F. Graf 3. Results and discussion 3.1. Aerosol growth Kokkola et al. (2009) investigated the growth of stratospheric aerosols when sulphur is supplied with a rate similar to a large eruption of a tropical volcano injecting SO 2 directly into the stratosphere. The authors compared several zero-dimensional frameworks, including SAM2, with a benchmark model under similar conditions (30 hpa, 214 K, 10% relative humidity). It showed that SAM2 has deficits in capturing the growth of sulphates due to limiting the condensation sink when the partial pressure of H 2 SO 4 exceeds a certain threshold. Although an advice to circumvent the problem was not given, the study also showed that SAM2 accurately follows the predictions of aerosol size distributions when the stratospheric S load is only moderately enhanced. Furthermore, the model was able to track size distributions of the benchmark model in the heavily polluted case when the integration time step length was strongly reduced. The experiments were performed for a simulation period of only 10 days and particle removal due to sedimentation was not considered. To investigate how SAM2 acts in a notional geoengineering case, it is necessary to perform longer integrations (so that in principle the desired cooling effect can be reached), requiring sedimentation as an important sink for stratospheric aerosols. We investigate how the initialised stratospheric background aerosol population evolves when sulphur is added continuously to the system. The integration period is set to 10 years in all ensembles. In these studies, we identified that the problem with SAM2 in Kokkola et al. (2009) is related to the operator-splitting technique used to solve competing microphysical processes. To avoid the rather large effort of the implementation of an implicit or adaptive time stepping method, we suggest another, much easier solution by reserving a certain amount of sulphuric acid vapour for nucleation. The performance of the new method is tested in this section. We tested the model with a certain fraction (10 and 80%) of the available sulphuric acid vapour reserved in each time step for the new particle formation and evaluated the scheme s sensitivity to the modified gas-to-particle partitioning. The evolution of modelled key quantities is shown in Figure 1. In S1, both the SO 2 concentration and the aerosol mixing ratio achieve a steady state after a few months of integration (Figure 1(a)). In S2, both parameters increase continuously. In Figure 1, it is demonstrated that in S2 the solution of the original unmodified model as applied in Kokkola et al. (2009) oscillates, whereas the model in which we introduced changes reaches a stable steady state. The results of scenario 1 are identical in both model versions. In S1, equilibrium values of the aerosol surface area density (SAD) of (20.7 µm 2 cm 3 ) and of the size distributions effective radius (R eff ) of 0.35 µm (Figure 1(b)) are in the order of values observed in the northern hemisphere mid-latitudes in the stratosphere during the first year after the Mt Pinatubo eruption (Grainger et al., 1995; Bauman et al., 2003) but are approximately only half the size of observed values in the tropical stratosphere (SPARC, 2006). Clear but rather weak oscillations in the evolution of R eff in scenario 1 provide an indication that the aerosol population is balanced not until year 3 of integration. In S2, after 3 years, the SAD clearly exceeds S1 values by an order of magnitude. Values of R eff are larger by a factor of two. Thus, in scenario 2, which acts as an upper limit test case for the model, larger sulphate droplets are predicted than observed after a volcanic perturbation of the stratosphere. Needless to say, those values are substantially larger than those predicted from different S-injection scenarios in the study of H09. Figure 1. Predicted evolution of model key quantities. (a) SO 2 concentration (black) and total sulphate aerosol mixing ratio (green). (b) Aerosol surface area density (black) and effective radius (blue). Continuous lines correspond to scenario one experiments, dotted lines to scenario two. Both parameters in (b) are adapted to the detection range of optical sensors (D 100 µm); see Kokkola et al. (2009). Bright colours and thick lines denote results made by the unmodified model as also applied in Kokkola et al. (2009); thin lines and darker colours denote results from the modified model as described in section 3.1.

4 Size distribution of geoengineered stratospheric aerosols 171 For the same altitude, the smaller particles prescribed in scenario bg2co2 of Rasch et al. (2008) result in surface areas times larger than modelled in S1. The prediction of surface areas from prescribed size distributions approach may yield overestimated interferences with the catalytic cycles destroying ozone in the stratosphere when integrated in a chemistry climate model, as, e.g. in Tilmes et al. (2009). How engineered stratospheric aerosols, built from a quasi-permanent injection of SO 2, evolve compared to particles formed from a burst-like instantaneous SO 2 injection, originating from a large tropical volcanic eruption, was shown in H09. Number densities for geoengineered particles smaller than 0.1 µm in radius are significantly larger than in the volcanic case. In contrast, volcanic aerosol is concentrated in the coarse mode with a mode radius of 0.5 µm. When enough OH is available for SO 2 oxidation, new particles are formed quickly when the precursor gas reaches the stratosphere. Those ultra-fine particles are rapidly scavenged by larger particles, so that the number density in the Aitken mode is strongly reduced (Kokkola et al., 2009). In the volcanic case, when most of the injected sulphur is partitioned into the particle phase a few months after the eruption, the number density of particles in the nucleation and Aitken modes tends to be close to zero (H09). In the geoengineering case, however, fine mode particles are always present when sulphur is supplied from below in a more or less continuous way. In the following, we investigate how in our geoengineering scenarios aerosol size distributions evolve in the unmodified model, where we do not interfere the gas-to-particle partitioning. This is shown by the red curves in Figure 2. At the end of the simulation, a size spectrum is formed, which can be described by a monotonically decreasing curve in S1 and a spectrum that is clearly bimodal in S2. The shape of the size distribution in S1 does not vary much after the first year of integration. Consequently, integrated size parameters (Figure 1(b)) remain approximately constant over that period. In S2, the SAD rapidly increases with time because within the first 100 days existing particles completely consume all the available sulphuric acid vapour so that further nucleation is prevented (later we show that this is an oscillating process). In S2, where the stratospheric SO 2 abundance constantly increases, coarse particles with mode diameter at 0.45 and 4 µm are formed. In the more realistic scenario S1, the mode diameter of the coarse mode is approximately 0.6 µm, which is in-between the solutions found in H09 for the 55-hPa pressure level when sulphur is continuously injected with 2 and 5 Tg (equivalent to 4 and 10 Tg SO 2 ). Also in S1, number densities for particles with Dp <0.1 µm are similar to those predicted in H09 at 55 hpa. Now we investigate whether the model solution is affected as it became obvious in Kokkola et al. (2009) by limitations for large H 2 SO 4 supersaturations. We rerun the model with reserving 10% (80%) of H 2 SO 4 vapour for new particle formation and compare the resulting size distributions with those of the original model. Green (blue) curves in Figure 2 denote results from a model that reserves 10 (80) % of the H 2 SO 4 vapour for nucleation in each time step. In the first few days of integration, the aerosol spectra in both scenarios evolve quite similar and independent of modifications made in the sequential processing of aerosol microphysics. Although in S1, size distributions evolve differently within the first months of integration (clearly seen at day 100), after 1 year the steady state of the three solutions is very similar. Only in the model which reserves most of the vapour for nucleation, approximately one order of magnitude larger number densities of particle nuclei as well as Aitken mode particles are found. In the severe test case S2, the steady state of the modified models is different from that of the original model. But the shapes of the size distributions predicted by the modified models are equal to S1, except that particle number concentrations are generally larger than in the scenario with the weaker sulphur source. This is a first indication that the model reserving 10% of the H 2 SO 4 vapour for nucleation of new particles yields a more robust solution than the original model. We further tested the model sensitivity to the integration time step length (dt). We applied time steps of 1 and 900 s. For technical reasons, we were not able to run the model with dt = 1 s for longer than 1 year. We found that at day 365 in both scenarios the results are independent on the time step length when 10% of the H 2 SO 4 vapour is reserved for nucleation (Figure 3). The highest sensitivity is seen in the accumulation mode for particles with 0.1 Dp < 1 µm. Even in S2, the integrated accumulation mode number density is well represented in the model when the global model time step 900 s is applied and simultaneously 10% of the H 2 SO 4 vapour is reserved for nucleation (Figure 4). The solution of the unmodified original operator-splitting scheme at dt = 900 s is completely different from the other cases. In the bottom panel of Figure 4, it is illustrated that this model solution periodically fluctuates with a frequency of days. When in S2 the SAD exceeds a critical value (around day 50), nucleation is prevented and a unimodal size distribution forms quickly. The larger those particles are growing due to H 2 SO 4 condensation, the weaker is the accumulation mode number density and the larger is the amount of particles removed from the box due to gravitational sedimentation. This reduces the particle surface area so that particles may form from the gas phase again and the cycle repeats (Figure 1). One of the major pathways removing particles from the stratosphere is gravitational sedimentation. The process is important for particles with diameters above 0.2 µm and the particle removal rate strongly increases with altitude (Kasten, 1968). In our experiments, we

5 172 R. Hommel and H.-F. Graf Figure 2. Model predicted aerosol size distributions for scenario 1, left column, and scenario 2, right column, dependent on adjustments in the gas-to-particle partitioning. Diagnosed, from top to the bottom, at initial time step, and at noon of days 1, 10, 100, 365 and have not investigated the model behaviour at other altitudes than the 50-hPa pressure level. Therefore, we cannot attest how sedimentation affects the balance between aerosol microphysical processes in the geoengineered stratospheric aerosol layer, as, e.g. shown in H09. In their studies, sedimentation alters in particular the role of coagulation in the particle growth process as a function of the strength of the S source. In higher altitudes, coagulation is more effective for weaker S sources, whereas in lower altitudes coagulation more effectively reduces fine mode particles for larger S injections. In our simulations, the balance between competing growth processes, H 2 SO 4 vapour condensation and coagulation, is unaffected by the strength of the S source in the stratosphere. Sedimentation might play a role in the severe test

6 Size distribution of geoengineered stratospheric aerosols 173 Figure 3. Dependency of model predicted aerosol size distributions on the integration time step length with (lines) and without (symbols) adjustments made in the gas-to-particle partitioning after 1 year of integration. case S2 where the particle size spectrum is dominated by very large particles, hence their sedimentation rates strongly influence the particle lifetime at 50 hpa and hence affect the shape of the size distribution. Figure 4. Model predicted number density in the first year, integrated for accumulation mode particles (0.1 Dp <1 µm). The upper panel shows scenario 1 experiments, the middle panel scenario 2 experiments. In both panels, black (red) lines denote experiments conducted with an integration time step length of 900 s (1 s). Cross symbols denote experiments conducted with conservative operator splitting, open diamonds denote experiments where, at each time step, 10% of the available sulphuric acid vapour is reserved for new particle formation via binary homogeneous nucleation. In the bottom panel it is shown how the management of competing gas-to-particle partitioning processes affect the evolution of scenario 2 size distributions when the global model time step length of 900 s is used Aerosol burden In the previous section, it was shown that geoengineered stratospheric aerosols as predicted by the aerosol microphysics module SAM2 are similar in size as predicted by the two-dimensional aerosol module AER, which was utilised in the geoengineering studies of H09. To compare our results against the results of other studies (Table I), in a very idealised manner, we estimate the burden of the geoengineered aerosol layer under the assumption that anywhere in the stratosphere aerosol particles would grow to sizes as predicted in scenario 1. We do not quantify the burden from scenario 2. We assume that geoengineering is performed homogeneously over the globe, and we assume further that the terminal size distribution of S1, reached in the 10th year of integration, may be thought of as a representative size distribution of aerosols in the stratosphere. We make also assumptions for the horizontal and vertical distribution of aerosols in order to vertically distribute the equilibrium aerosol mixing ratio of 9.83 ppbm, which we calculated in S1 for the 50- hpa idealised model level. We distribute those profiles over the globe and finally derive the burden from this idealised aerosol layer. This, of course, ignores that other factors like concentrations of OH and H 2 O, and the stratospheric temperature also control the aerosol formation, their growth, and dispersion. From making such assumptions, it is clear that we can only roughly approximate the burden. However, from the similarity between the size distributions shown in Section 3.1 and in the H09 study, we expect that the estimated sulphur burden may not be too far from the burden calculated in H09 (scenario GEO2 ).Thelatterisless than half the burden predicted in Rasch et al. (2008) by utilising prescribed background aerosol distributions (case bg2co2 ). Hence, our study would imply that the radiative forcing and thus the target cooling effect of geoengineered stratospheric aerosols, which is proportional to the stratospheric burden, may be overestimated when aerosol size distributions are prescribed from observations after volcanic eruptions. It is known from a variety of observations, in particular from the space-borne global monitoring of stratospheric aerosols, as well as from two- and threedimensional model studies that in the absence of injections of volcanic material the stratospheric aerosol

7 174 R. Hommel and H.-F. Graf Figure 5. Estimated annual mean global total aerosol burden in comparison with the works of Rasch et al. (2008) and Heckendorn et al. (2009). layer is well mixed (SPARC, 2006). Furthermore, observations as well as models show that the vertical distribution of stratospheric aerosols does not exhibit strong gradients in central regions of the layer, i.e. from a few kilometres above the tropopause to altitudes where the particles evaporate at 27 km (Barnes and Hofmann, 2001). To vertically distribute the equilibrium aerosol mixing ratio, we applied a Gaussian profile for altitudes between 100 and 10 hpa. For standard widths of the Gaussian profile of 1.5 and 2 mimicking the mixing ratio gradients above the tropopause and within the evaporation regime at higher altitudes, we obtain that the global annually averaged stratospheric aerosol burden lies between 2.50 and 3.42 Tg(S). In Figure 5 and Table I, this burden is compared to the results of H09 and Rasch et al. (2008). It is seen that our rough estimate is 20 60% larger than the 2.1 Tg(S) shown in H09 for the 4 Tg(SO 2 ) injection scenario, whereby both SAD and size spectra of aerosols are very similar in both studies. The burden derived in Rasch et al. (2008), scenario bg2co2, is approximately twice as large as our estimate. Also, their burden derived from applying a volcanic aerosol distribution (case volc2 ) is only marginally larger than in their background case bg2co2, whereby the SAD of the latter is three times larger than in the former case. In other words, their burden is almost independent on the size of aerosols under similar injection conditions. That means, if the removal of large particles due to sedimentation is not largely underestimated in the Rasch et al. model, their stratospheric aerosol abundance is overestimated and so is the radiative forcing of prescribed aerosol size distributions. 4. Conclusions We tested the aerosol microphysics module SAM2, which was designed for large scale climate models, in a zero-dimensional framework under conditions which are thought to be representative as a solar radiation management method with human-induced stratospheric sulphate aerosols. Five teragram of SO 2 were supplied to the 50-hPa level. We designed two scenarios that differ in the handling of the oxidised SO 2. Scenario 1 is a realistic approach, while scenario 2 represents an upper limit case for the model s ability to capture the growth of aerosols. Results are compared with previous studies based on more complex models. We found that the classic operator-splitting technique, which is used in many models to solve concurrent physical processes, may result in fluctuating aerosol size distributions when the SO 2 source strength achieves critical values. This solution is not independent of the integration time step length. Noniterative modifications in the sequential processing of H 2 SO 4 gas-to-particle partitioning improved the model behaviour significantly and made the solution robust with respect to the integration time step length. It turns out that a prescribed rate of 10% of sulphuric acid being reserved for nucleation leads to robust results that do no longer depend on the time step. In previous studies, it was assumed that geoengineered stratospheric aerosols would be smaller in size than their volcanic analogue (Crutzen, 2006, Robock et al., 2008; Rasch et al., 2008). Our studies confirm findings of H09 that geoengineered stratospheric particles are likely to be larger than those observed in the stratosphere after large volcanic eruptions. In SAM2, aerosol size distributions are primarily shaped by condensation. Coagulation might effectively remove aerosol nuclei when large particles grow beyond a certain threshold size. However, due to modifications made in the sequential processing of microphysics and due to the continuous supply of SO 2 and, hence, sulphuric acid vapour, in our scenarios coagulation generally plays a minor role in the growth of geoengineered stratospheric aerosols. From estimates of the stratospheric burden, an aerosol layer formed from particles as predicted in our realistic scenario S1, it is likely that climate model predictions of the cooling effect of geoengineered stratospheric aerosols strongly depend on the accurate description of the aerosol size. This can be achieved in two ways: either climate models incorporate aerosol modules which, like our scheme, predict the size distribution of the particles interactively or climate models apply consistent climatologies of aerosol surface area and mixing ratio for atmospheric chemistry and radiation derived from realistic offline models. The hazards inherent in any geoengineering approach require the best possible model configuration. We would argue that the most reliable results will be obtained with well-tested stratospheric aerosol microphysics and chemistry models implemented in the global model. References Barnes JE, Hofmann DJ Variability in the stratospheric background aerosol over Mauna Loa Observatory. Geophysical Research Letters 28:

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