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ATMOSPHERIC SCIENCE LETTERS
Atmos. Sci. Let. (2010)
Published online in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/asl.285
Modelling the size distribution of geoengineered
stratospheric aerosols
Ren´
e Hommel* and Hans-F. Graf
Centre for Atmospheric Science, University of Cambridge, Cambridge, UK
*Correspondence to:
Ren´
e Hommel, Centre for
Atmospheric Science, University
of Cambridge, Lensfield Road,
Cambridge, CB2 1EW UK.
E-mail:
rene.hommel@atm.ch.cam.ac.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 increas-
ing 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 addi-
tion, one must bear in mind that such kind of geo-
engineering 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 sys-
tem. Wanted as well as unintended effects of arti-
ficial stratospheric aerosols are determined by their
size and composition. The latter predominately inter-
acts with the atmosphere’s chemistry and thus is a
major driver for changes in atmospheric composi-
tion, including loss of stratospheric ozone. Physical
parameters like the size spectrum of the aerosols ulti-
mately determine whether the geoengineered strato-
spheric 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). How-
ever, 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 approx-
imately 20 Tg SO2into the stratosphere (SPARC,
2006), for a few months generating a reduction of solar
insolation of about the right magnitude (−2Wm
−2)
to counteract the current anthropogenic greenhouse
effect. In a more recent modelling study, Heckendorn
et al. (2009), hereafter referred to as H09, calcu-
lated the aerosol size distribution by an interactive
and size-resolved treatment of aerosol microphysical
processes originating from different methods of SO2
injection into the stratosphere. They showed that the
stratospheric aerosol layer resulting from a continuous
injection of 20 Tg SO2per 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 SO2per year are
continuously supplied at the 50-hPa pressure level.
We perform two sets of simulation, which differ in
the way how the oxidised SO2is 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
R. Hommel and H.-F. Graf
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(SO2)year
−1] 4 10 4 4 5 5 5, cumulative
Effective radius (µm) —a—a0.17b0.43b0.3–0.35b0.35 0.77c
SADd(µm2cm−3)20<50 30– 40 ∼12 —a20.7 ∼500c
Burden [Tg(S)] 2.1 3.7 5.5 5.9 —a2.50−3.42 —e
Forcing (W m−2)−0.78 ±0.38 −1.06 ±0.31 —a—a−1.8 —e—e
aNot shown.
bPrescribed.
cAt the end of simulation.
dValues are for the equatorial stratosphere at 50 hPa (∼21 km).
eNot calculated.
2. Methods
2.1. Model
The aerosol microphysics module SAM2, applied here
in a zero-dimensional framework, treats the forma-
tion 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 1 ×10−3to 20.7µmin
radius. Forty-four logarithmically spaced size bins are
determined by mass doubling. Aerosol microphysics
processes of new particle formation due to binary
homogeneous nucleation (Vehkam¨
aki et al., 2002),
H2SO4condensation and evaporation, and coagula-
tion are considered in the model. The sulphuric acid
droplets are assumed to be spherical and in thermo-
dynamic equilibrium with their environment. Water
vapour growth and the sulphuric acid weight percent-
age are determined from partial and vapour pressures
of H2SO4and H2O. The size distribution is affected by
gravitational sedimentation. Similar to the studies of
Kokkola et al. (2009), we assume that gaseous H2SO4
is exclusively formed from the oxidation of SO2by
the hydroxyl radical OH. An OH concentration of
1×106cm−3is 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 parame-
terisations implemented in SAM2 and its overall per-
formance 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 sedimen-
tation (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 sup-
ply of SO2. Our experiments are conducted under cli-
matologically 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 inte-
grated the model using a time step of 900 s, which
is equivalent to that of a global model of medium
resolution (T42).
2.2. 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 H2SO4vapour. 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 SO2per year are added
to the stratosphere. In scenario 1 (S1) in each time
step, the oxidised SO2forming sulphuric acid vapour
is subtracted from the total source. In contrast, in
scenario 2 (S2) the SO2source was held constant,
thereby substituting any oxidised SO2. This means
that the SO2concentration accumulates, forming a
stratospheric reservoir which cannot be depleted by
oxidation to gaseous H2SO4due 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 SO2. 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 0.234 µm and a
geometric standard deviation σis 1.59. The initial total
number concentration is set to three particles per cm3.
Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. (2010)
Size distribution of geoengineered stratospheric aerosols
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 vol-
cano injecting SO2directly into the stratosphere. The
authors compared several zero-dimensional frame-
works, including SAM2, with a benchmark model
under similar conditions (30 hPa, 214 K, 10% rela-
tive humidity). It showed that SAM2 has deficits in
capturing the growth of sulphates due to limiting the
condensation sink when the partial pressure of H2SO4
exceeds a certain threshold. Although an advice to cir-
cumvent 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 bench-
mark 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 sedimenta-
tion was not considered. To investigate how SAM2
acts in a notional geoengineering case, it is neces-
sary 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 SO2concentration 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 (20.7µm2cm−3) and of the
size distributions effective radius (Reff)of0.35 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 Reff
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 Reff 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) SO2concentration (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.
Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. (2010)
R. Hommel and H.-F. Graf
For the same altitude, the smaller particles pre-
scribed in scenario bg2co2 of Rasch et al. (2008)
result in surface areas 1.5 – 2 times larger than mod-
elled 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 SO2, evolve compared to
particles formed from a burst-like instantaneous SO2
injection, originating from a large tropical volcanic
eruption, was shown in H09. Number densities for
geoengineered particles smaller than 0.1µm 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 ∼0.5µm. When
enough OH is available for SO2oxidation, 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 geo-
engineering 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 dis-
tribution in S1 does not vary much after the first year
of integration. Consequently, integrated size parame-
ters (Figure 1(b)) remain approximately constant over
that period. In S2, the SAD rapidly increases with
time because within the first 100 days existing par-
ticles 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 SO2abundance con-
stantly increases, coarse particles with mode diameter
at ∼0.45 and ∼4µm are formed. In the more real-
istic scenario S1, the mode diameter of the coarse
mode is approximately 0.6µm, 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 SO2). Also in
S1, number densities for particles with Dp <0.1µm
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 H2SO4supersaturations. We
rerun the model with reserving 10% (80%) of H2SO4
vapour for new particle formation and compare the
resulting size distributions with those of the origi-
nal model. Green (blue) curves in Figure 2 denote
results from a model that reserves 10 (80) % of the
H2SO4vapour 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 dis-
tributions 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 differ-
ent 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 concen-
trations are generally larger than in the scenario with
the weaker sulphur source. This is a first indication
that the model reserving 10% of the H2SO4vapour
for nucleation of new particles yields a more robust
solution than the original model.
We further tested the model sensitivity to the inte-
gration 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 sce-
narios the results are independent on the time step
length when 10% of the H2SO4vapour is reserved
for nucleation (Figure 3). The highest sensitivity is
seen in the accumulation mode for particles with
0.1≤Dp <1µm. Even in S2, the integrated accu-
mulation mode number density is well represented in
the model when the global model time step 900 s is
applied and simultaneously 10% of the H2SO4vapour
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 illus-
trated that this model solution periodically fluctu-
ates with a frequency of 200 – 250 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 parti-
cles are growing due to H2SO4condensation, 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
0.2µm and the particle removal rate strongly increases
with altitude (Kasten, 1968). In our experiments, we
Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. (2010)
Size distribution of geoengineered stratospheric aerosols
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 3650.
have not investigated the model behaviour at other alti-
tudes than the 50-hPa pressure level. Therefore, we
cannot attest how sedimentation affects the balance
between aerosol microphysical processes in the geo-
engineered stratospheric aerosol layer, as, e.g. shown
in H09. In their studies, sedimentation alters in par-
ticular 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 coag-
ulation more effectively reduces fine mode particles
for larger S injections. In our simulations, the bal-
ance between competing growth processes, H2SO4
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
Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. (2010)
R. Hommel and H.-F. Graf
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 domi-
nated by very large particles, hence their sedimen-
tation rates strongly influence the particle lifetime at
50 hPa and hence affect the shape of the size distri-
bution.
Figure 4. Model predicted number density in the first year,
integrated for accumulation mode particles (0.1 ≤Dp <1µm).
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.
3.2. Aerosol burden
In the previous section, it was shown that geo-
engineered 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 homo-
geneously 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 rep-
resentative size distribution of aerosols in the strato-
sphere. We make also assumptions for the horizontal
and vertical distribution of aerosols in order to ver-
tically 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 H2O, 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 distribu-
tions (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 pre-
scribed from observations after volcanic eruptions.
It is known from a variety of observations, in par-
ticular from the space-borne global monitoring of
stratospheric aerosols, as well as from two- and three-
dimensional model studies that in the absence of injec-
tions of volcanic material the stratospheric aerosol
Copyright 2010 Royal Meteorological Society Atmos. Sci. Let. (2010)
Size distribution of geoengineered stratospheric aerosols
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 alti-
tudes where the particles evaporate at ∼27 km (Barnes
and Hofmann, 2001).
To vertically distribute the equilibrium aerosol mix-
ing 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 bur-
den 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(SO2)
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 SO2
were supplied to the 50-hPa level. We designed two
scenarios that differ in the handling of the oxidised
SO2. 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 tech-
nique, which is used in many models to solve
concurrent physical processes, may result in fluctu-
ating aerosol size distributions when the SO2source
strength achieves critical values. This solution is not
independent of the integration time step length. Non-
iterative modifications in the sequential processing of
H2SO4gas-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 geoengi-
neered 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 par-
ticles 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 SO2and, hence, sul-
phuric acid vapour, in our scenarios coagulation gener-
ally 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 geoengi-
neered stratospheric aerosols strongly depend on the
accurate description of the aerosol size. This can be
achieved in two ways: either climate models incor-
porate aerosol modules which, like our scheme, pre-
dict 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 configura-
tion. 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.
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