In the absence of tangible progress in reducing greenhouse gas emissions, the implementation of solar radiation management has been suggested as measure to stop global warming. Here we investigate the impacts on northern midlatitude cirrus from continuous SO2emissions of 2–10 Mt/a in the tropical stratosphere. Transport of geoengineering aerosols into the troposphere was calculated along trajectories based on ERA Interim reanalyses using ozone concentrations to quantify the degree of mixing of stratospheric and tropospheric air termed “troposphericity”. Modeled size distributions of the geoengineered H2SO4-H2O droplets have been fed into a cirrus box model with spectral microphysics. The geoengineering is predicted to cause changes in ice number density by up to 50%, depending on troposphericity and cooling rate. We estimate the resulting cloud radiative effects from a radiation transfer model. Complex interplay between the few large stratospheric and many small tropospheric H2SO4-H2O droplets gives rise to partly counteracting radiative effects: local increases in cloud radiative forcing up to +2 W/m2for low troposphericities and slow cooling rates, and decreases up to −7.5 W/m2for high troposphericities and fast cooling rates. The resulting mean impact on the northern midlatitudes by changes in cirrus is predicted to be low, namely <1% of the intended radiative forcing by the stratospheric aerosols. This suggests that stratospheric sulphate geoengineering is unlikely to have large microphysical effects on the mean cirrus radiative forcing. However, this study disregards feedbacks, such as temperature and humidity changes in the upper troposphere, which must be examined separately.
 The basic concept of solar radiation management (SRM) is to reduce the amount of incoming solar radiation absorbed by the Earth to counteract global warming. Recently, this geoengineering technique has received enhanced attention in both scientific and mass media. The idea to increase the Earth's albedo by injecting SO2 into the lower stratosphere was first proposed by Budyko in the early 1970s [Budyko, 1977]. Because it mimics the action of large volcanoes on the climate [Robock and Mao, 1995], it was reconsidered by Crutzen  and Wigley . Crutzen suggested that a constant stratospheric aerosol burden corresponding to 5–6 Mt of sulphur might suffice to compensate for a doubling of CO2. Although many model studies [Matthews and Caldeira, 2007; Rasch and Crutzen, 2008; Robock and Oman, 2008; Tilmes and Garcia, 2009; Heckendorn and Weisenstein, 2009] quantified undesirable effects of this geoengineering technique (e.g., ozone-layer depletion, tropospheric chemistry effects, regional climate effects, too rapid sedimentation of coagulating particles, etc.), it is still considered to be one of the more efficient geoengineering approaches to compensate climate change. However, previous investigations have concentrated on the impact on chemistry and stratospheric circulation, whereas the impact on cirrus clouds in the upper troposphere has not yet been taken into account until very recently [Kuebbeler and Lohmann, 2012].
 Changes in cirrus cloud formation and evolution have been listed by Robock  as potential “side effects” of geoengineering, which may have repercussions for global climate. Cirrus clouds have a large impact on the Earth's radiation budget; they partly scatter incoming solar radiation back to space and trap outgoing longwave radiation (OLR). In contrast to liquid clouds, both effects are of comparable absolute size but different sign [Zhang and Macke, 1999]. The net effect of cirrus clouds on Earth's radiation budget is not well known. Fu and Baker  and Corti and Peter  showed that forcing due to cirrus clouds depends in a nonlinear way on the cloud optical depth and cloud top height. Recent GCM studies [Sanderson and Piani, 2008; Mitchell and Rasch, 2008] showed that upper tropospheric cloud cover and humidity significantly affect climate sensitivity. Injection of sulphur into the lower stratosphere might affect cirrus clouds when the largest geoengineered aerosol particles sediment or are mixed into the upper troposphere via stratospheric intrusions. As will be shown in this study, the resulting increase in the number density of the largest H2SO4-H2O droplets in the upper troposphere will impact the ice crystal number densities (Nice) in cirrus clouds formed via homogeneous nucleation, which in turn affects the radiative properties of the cirrus clouds. Furthermore, this may lead to changes in cloud lifetime and thickness, again influencing their radiative properties.
 Several studies have addressed the potential effects of volcanic aerosols on cirrus cloud properties. Some of them, based on aircraft observations [Sassen and Horel, 1990; Pueschel and Russell, 1994], satellite data analysis [Sassen et al., 1990; Weare, 1992, Wylie et al., 1994, Kent et al., 1995] or model simulations [Jensen and Toon, 1992; Minnis et al., 1993] suggested an increase in condensation nuclei (CN) and albedo of upper tropospheric clouds. Nevertheless, other studies [Jensen and Toon, 1994; Wylie and Menzel, 1999; Luo and Rossow, 2002] showed no significant climate feedback by aerosol-cirrus-radiative interactions, or supposed that it was not related to microphysical but rather to large scale climate variations (e.g., El Niño) [Song and Starr, 1996] or earlier smaller volcanic events [McCormick and Veiga, 1992]. Luo and Rossow , however, point to the potential importance of temporary local effects. Sensitivity studies on the global scale were performed by Lohmann and Kärcher , obtaining an ice crystal number increase of up to 50% in the tropics in the year after the Pinatubo event for a more realistic scenario, but no trend in cloud optical properties or radiative forcing. The net global impact remained hard to quantify due to the lack of precise parameterizations.
 It is important to note that cirrus properties depend much more on factors such as temperature and local dynamics than on the number of CN present [Jensen and Toon, 1994; Hoyle and Luo, 2005; Barahona and Nenes, 2008]. Kärcher and Lohmann  state that the number of homogeneously formed ice crystals (IC) is insensitive to the original aerosol size distribution, except when a sufficient number of larger aerosol particles are present in an air parcel. The presence of a few larger aerosol particles could dry the air more efficiently, since they nucleate first in a cooling event, suppressing further nucleation in smaller particles and leading to the formation of large ice particles with high sedimentation speeds. Spichtinger and Cziczo  demonstrate this mechanism for simultaneous occurrence of heterogeneous and homogeneous ice nucleation, where the presence of a few solid ice nuclei leads to a reduction in the final ice crystal number concentration. With respect to geoengineering, Heckendorn and Weisenstein  highlight the importance of aerosol particles larger than 1 μm, which would result from the coagulation of freshly nucleated particles with particles from the stratospheric aerosol background mode after geoengineering the lower stratosphere using SO2emissions.
 Very recently, Kuebbeler and Lohmann  published a study investigating impacts of stratospheric geoengineering on cirrus clouds using a general circulation model with a coupled aerosol-cloud model (ECHAM5-HAM). Their simulations suggest that the enhanced temperature and reduced vertical velocity reduce the rate of homogeneous ice nucleation, so that continuous injection during 5 years of 5 Mt-SO2/a leads to a reduction of 5–50% in Nice. An overall negative forcing of 0.93 W/m2is obtained, neutralizing about 40% of the negative radiative forcing from the geoengineering. Microphysical impacts on cirrus caused by the change in aerosol size due to geoengineering were included in this study, but not separated from impacts caused by changing temperatures or cooling rates. Moreover, Kuebbeler and Lohmann  applied a simplified scheme with monodisperse solution droplets. The present work is complementary to their work, as it applies a comprehensive microphysical scheme and investigates the microphysical impacts while keeping other quantities fixed.
 What would be the possible direct microphysical impact of geoengineered stratospheric aerosols on cirrus clouds over the northern hemisphere (NH) midlatitudes? Will the resulting cloud changes contribute to the general aim of geoengineering, i.e., global cooling, or will they reduce its efficiency or add to the detrimental side effects [Robock, 2008]? These questions have been investigated for the northern hemisphere (NH) midlatitudes, where air from the stratosphere is particularly efficiently mixed into the troposphere within tropopause folds. However, in contrast to Kuebbeler and Lohmann , this study assumes that except for changes in cirrus clouds directly resulting from the homogeneous ice crystal nucleation, all other conditions remain unchanged. In particular, feedbacks on ice crystal nucleation via the intended cooling effect and resulting changes in upper tropospheric humidity or vertical velocities are neglected in this study. In order to quantify the implications for upper tropospheric cirrus clouds, we apply a combination of independent tools and models: (1) an aerosol model to estimate the aerosol size distribution in the upper troposphere/lower stratosphere region resulting from the injection of sulphur into the stratosphere; (2) a box model for detailed microphysical analysis of the impact of geoengineered H2SO4-H2O aerosols on ice number density and size; (3) trajectory calculations based upon reanalysis data to determine the percentage of trajectories influenced by stratospheric aerosols that reach cirrus-like conditions; and (4) a radiative transfer model to estimate changes in optical depth and cloud radiative forcing due to geoengineering influence. In the next section we will explain the model setup and the main impact of artificially produced aerosols on cirrus clouds through the change in the ice crystal number density. In section 3, different amounts of stratosphere-to-troposphere transport and air-mass mixing is considered by means of trajectory calculations and using ozone as a stratospheric tracer. The changes in the cloud visible optical depth and radiative forcing due to geoengineering are presented and discussed in section 4, and a summary is provided in section 5.
2 Microphysics of Cirrus: Natural and Geoengineered Cases
 Cirrus are ice clouds that can have a large spread in particle size, ice water content, and optical depth properties, ranging from subvisible, via semi-transparent, all the way to thick nontransparent cirrus decks from thunderstorms [Mace and Benson, 2006]. In the present study we focus on cirrus which form in situ homogeneous freezing of aqueous solution droplets (in short: homogeneous nucleation) during the convectively inactive wintertime in the northern midlatitude upper troposphere. As described by Spichtinger and Gierens , these clouds form in ice-supersaturated regions, moister and colder than surrounding air masses, with saturation ratios over ice (Sice) exceeding 1. Supercooled aqueous solution particles containing sulphuric acid are important precursors to form ice crystals. Significant amounts of sulphur injected into the lower stratosphere would enhance the loading of aqueous sulphuric acid aerosols in the upper troposphere, in particular with respect to the largest H2SO4-H2O droplets, with repercussions for the microphysical properties of cirrus clouds.
2.1 Aerosol Size Distribution
 Following Heckendorn and Weisenstein , we used the size distribution for different continuous sulphur injection rates (1 and 5 Mt-S/a) at 20 km altitude (≈ 50 hPa pressure level) at the equator computed by means of the AER (Atmospheric and Environmental Research, Inc.) 2-D microphysical aerosol model. This model has been intensely tested and compared with satellite measurements and with other models in the SPARC Assessment of Stratospheric Aerosol Properties (ASAP) report [Thomason and Peter, 2006]. For a detailed model description, see Weisenstein et al. [1997, 1998, 2007]. The two-dimensional model is forced by dynamical fields (winds, eddy-diffusion coefficients) derived for 1992, the year after the Mt. Pinatubo eruption. The model takes account of the comprehensive sulphur chemistry for the following sulphur species: carbon disulphide (CS2), dimethyl sulphide (DMS), hydrogen sulphide (H2S), methyl sulphonic acid (MSA), carbonyl sulphide (OCS), sulphur dioxide (SO2), sulphur trioxide (SO3) and sulphuric acid (H2SO4). Concentrations of the oxidants OH, O, NO3, and of H2O and O3 are taken from the AER 2-D chemistry model [Weisenstein and Ko, 1996] with updated rate constants. OH fields yield an average e-folding time for SO2chemical loss of about 30 days. The AER 2-D aerosol model takes all relevant microphysical processes into account (bimolecular nucleation, coagulation, condensation/evaporation, sedimentation), uses 40 size bins (in a range from 0.4 nm–3.2 μm by volume doubling). The geoengineering cases are compared to natural non-volcanic (“background”) aerosol concentrations in the lower stratosphere, indicated as “60 kt-S/a case”: the natural flux of sulphur from the troposphere into the stratosphere is about 60 kt-S/a, mostly as OCS and SO2[Thomason and Peter, 2006], which is fully taken into account by the model. In a geoengineering scenario with continuous sulphur injection, very different size distributions are generated than after a volcanic eruption. This is due to the fact that the continuous SO2 injection enhances the coagulation of nucleation mode particles with the largest preexisting particles as well as the condensation of additional gas phase H2SO4on pre-existing particles, both leading to the formation of an extra-large size mode. Particles with radii larger than 1 μm in the tails of the geoengineered size distributions [Heckendorn and Weisenstein, 2009] are particularly suited to subsequently alter the ice nucleation processes for upper tropospheric cirrus.
 Cirrus simulations are performed by applying aerosol size distributions, which reflect a mixture of a tropospheric aerosol size distribution (described below) and stratospheric aerosol size distribution from the 2-D AER model at 55°N latitude and 75 hPa pressure altitude in January 1992 (Figure 1a). This latitude was chosen to avoid centers of the jet streams at lower latitudes. The pressure level of 75 hPa was chosen to ensure that the stratospheric fraction of the aerosol size distribution is indeed purely stratospheric (as the 2-D AER aerosol model has itself only a simplified treatment of tropospheric aerosols without treatment of aerosol components other than H2SO4-H2O). An example of the resulting aerosol distribution for 10% of stratospheric plus 90% of tropospheric air is shown in Figure 1b.
 In the end, we will be interested in estimating the impact of geoengineering on cloud radiative forcing (CRF) averaged over an entire region. Therefore, we have chosen the northern winter time hemisphere, where we expect most cirrus to be formed in situ slow ascent. These regions might be most easily affected by geoengineered aerosols which get mixed into the troposphere, e.g., in tropopause folds. In this way, we intend to avoid confusion with anvil cirrus arising from deep convective outflows, which are unlikely to be affected by geoengineered aerosols.
 This study investigates the impact of geoengineering by assuming that ice particles nucleate homogeneously in preexisting aqueous solution droplets, which upon an increase in relative humidity take up water and dilute. This uptake may be kinetically limited, which affects nucleation and cloud formation. We describe the ice nucleation process by means of the water-activity-based freezing theory of Koop and Luo  and neglect potential complications resulting from heterogeneous nucleation on solid ice nuclei (IN) [DeMott et al., 2011], which might lead to a modification of homogeneous nucleation events [e.g., Spichtinger and Cziczo, 2010]. We also neglect the possibility of the formation of glassy particles, whose water activity (aw) does not readily equilibrate with gas phase relative humidity [Murray et al., 2010; Wilson et al., 2012] (rendering the application of Koop and Luo  impossible). This approach allows the major category of aerosols to be accurately described with respect to their ice nucleation ability, namely aqueous sulphuric acid particles (H2SO4-H2O droplets, natural or geoengineered) or other low viscosity aqueous aerosols containing dissolved salts, inorganic acids, or low volatility organics.
 For the tropospheric particles, we use the in situ measurements of Minikin and Petzold , which describe an extra-tropical background of aerosol particles in the Aitken mode with number density 300 cm−3STP, which is in agreement with the initialization of model studies [e.g., Kärcher and Lohmann, 2002]. The tropospheric mode is approximated by a lognormal size distribution with a geometric standard deviation of 1.4 and mode radius of 25 nm for the dry mass. These values are within the range as measured in the upper troposphere [e.g., Ström et al., 1994; Schröder and Ström, 1997] and within the range assumed in former model studies [Jensen and Toon, 1994; Gierens and Ström, 1998; Lin and Starr, 2002; Kärcher and Lohmann, 2002b; Spichtinger and Gierens, 2009]. However, this tropospheric size distribution is narrower than distributions often used for upper tropospheric background air, see for instance, Jensen and Toon  and Jensen and Toon , and much narrower compared to stratospheric distributions. This renders the contrast between tropospheric and stratospheric aerosols larger, so that the conclusions on the importance of the geoengineering aerosols during cirrus formation will provide the largest possible effect.
 Figure 1b shows this typical upper tropospheric aerosol size distribution (pink curve) in combination with aerosol distributions caused by intrusion of 10% of stratospheric air, with and without geoengineering influence. Continuous sulphate injection provides more material for continuous growth of particles by condensation as well as for nucleation. This is the reason why geoengineering effect is also seen for very small particles. As mentioned above, the coagulation of freshly nucleated particles with the accumulation mode enhances the formation of large aerosols, forming a tail in the geoengineering size distribution.
 A couple of geoengineering studies suggested the importance of the spatial and temporal distribution of sulphate injections [e.g., Heckendorn et al., 2009; Niemeier et al., 2011; English et al., 2012], concluding that a larger spread in the emissions (in latitude and altitude) could increase the equilibrium aerosol burden for a given injection rate. Pulse emissions (once per month or twice/a) could reduce the mode radius of the aerosol distribution, getting closer to the size of particles observed following recent volcanic eruptions. Pierce and Weisenstein  considered direct injection of H2SO4vapor from aircraft as a better method to increase sulphate burden and have control of the particle size. However, we again focus on maximizing the effects on cirrus clouds, and hence apply the scenario with large particles by Heckendorn and Weisenstein  in the present work.
2.2 Zurich Optical and Microphysical Box Model (ZOMM)
 The Zurich Optical and Microphysical box Model (ZOMM) used here for Lagrangian microphysical calculations has been designed for assessing properties of polar stratospheric clouds and cirrus clouds [e.g., Luo et al., 2003; Hoyle et al., 2005]. ZOMM is a spectral microphysical model comprising detailed descriptions of the most important processes such as nucleation, diffusional growth/evaporation and sedimentation of the ice particles, and a kinetic treatment of the uptake/release of water by the solution droplets. Particle coagulation is negligible on the time scales of interest here and hence not treated. Especially, ice aggregation is of less importance for the low temperature regime (T<−40°C) and for low vertical velocities [e.g., Kajikawa and Heymsfield, 1989].
 In the present study, we initialized the model with the size distributions from the AER aerosol model diluted into a tropospheric air mass with a prescribed lognormal distribution as described above (rm=25 nm, σm=1.4, Nm=300 cm−3). Two initial temperatures were considered Tinit=210/230K for idealized trajectory calculations with constant cooling rates, typical for cirrus cloud formation (with corresponding initial pressures according to the US standard atmosphere). For each trajectory calculation, initial H2O mixing ratios were assumed to be at ice saturation (Sice=1). Sedimentation of the ice crystals was explored using the box model in a column mode (with stacked boxes), but is not shown subsequently. Vertical velocities w=0.01/0.05/0.1/0.2/0.3/0.5/0.8/1.0/2.0 m/s were assumed reflecting constant adiabatic cooling induced by the large-scale motion or mesoscale fluctuations. The cooling stopped when the temperature was 4 K below the frost point (initial temperature). This cooling of 4 K was needed to make sure that the homogeneous nucleation is completed. Then we increased the temperature by 2 K and kept it constant for 1 hour. This ensures that the clouds grow to the same ice water content (IWC) in both geoengineered and natural cases, so that differences in the results are only determined by the changes in the ice crystal number density. We checked that the final IWC reached in this way is furthermore largely consistent with the climatology of Schiller and Krämer , which was derived from airborne observations of total and gas phase water for the different latitudes, analyzed as a function of temperature.
2.3 Ice Crystal Number Densities
 Supersaturations with respect to ice occur in rising air parcels, and are subject to the competition between the adiabatic cooling rate and depositional growth of the ice crystals. Both factors in combination determine the degree of supersaturation during cirrus formation and, thus, the number of aerosol particles that nucleate ice. This interplay between microphysics and small-scale meteorology, which determines the microphysical properties of the resulting clouds, has been highlighted by Kärcher and Lohmann , Hoyle and Luo , and Spichtinger and Cziczo . The size distribution of the preexisting aerosols also plays an important role. Although the small particles outnumber the larger ones by far (see Figure 1b), homogeneous ice nucleation will preferably occur in the larger particles. This is because the rate of homogeneous nucleation events in an aerosol particle is proportional to its volume, and also because the Kelvin effect keeps the smaller particles at slightly higher H2SO4-concentrations and, thus, lower water activities [Meilinger and Koop, 1995]. At the other end, the uptake of water by extremely large aerosol particles (r>1 μm) is gas phase diffusion-limited, so that these particles during a cooling event need more time to increase their water activity and therefore do not nucleate ice before the somewhat smaller particles do so (see Figure A1). The latter is a kinetic effect that is often ignored in modeling cirrus formation, e.g., when the aerosol particles are assumed to be in equilibrium with the gas phase (as is usually the case in models with bulk microphysics or in global circulation models). The time constant for equilibration of solution concentrations in droplets is proportional to the square of the particle radius [e.g., Meilinger et al., 1995]. This explains the non-monotonous nucleation behavior with very small particles being limited by size and Kelvin effect, intermediate particles being preferred, and very large particles being limited by uptake kinetics which leaves them undiluted in a cooling event. As we show below, such kinetic limitations play a major role under geoengineered conditions with very large aerosol particles. Moreover, when the geoengineered aerosol contains a large condensed phase volume, this may take up significant amounts of the total water before ice nucleation, which lowers the relative humidity and, thus, lowers the ice nucleation rate.
2.4 Pure Stratospheric Aerosol Distributions
 In order to understand the basic processes that determine the Nice in the presence of larger aerosols originating from the stratosphere, we first show a case study calculating the Niceobtained from a single large particle mode with a lognormal size distribution (before using the mixed tropospheric/stratospheric size distribution of Figure 1b). This single mode has fixed number density (Nm=10 cm−3) and distribution width (σm=1.8), typical stratospheric values, but we vary the mode radius (rm), see Figure 2. All runs were performed with the same initial conditions (T=210 K, p=255 hPa) and constant cooling rate of 10 K/h, which corresponds to 0.3 m/s vertical updraught, the most common small-scale cooling rate for midlatitude cirrus clouds [Hoyle and Luo, 2005]. Maximum ice densities are obtained for the aerosols with mode radius between 0.6 and 0.8 μm. The decrease in Nicetowards very small mode radii is caused by the Kelvin effect, while a decrease towards the largest radii is due to the kinetically limited uptake and loss of H2O to and from the liquid aerosols.
 Three kinetic regimes, which determine the impact of geoengineered aerosols, are depicted in Figure 2:
rm<0.1 μm: The Kelvin effect constricts nucleation for very small particles, i.e., the smaller rmthe more difficult it is to have continued nucleation beyond the freezing of the very first ice particles.
 0.1 μm<rm<0.7 μm: Two effects are at work. First, the Kelvin effect, although small, continues to play an important role: small enhancements in the H2O vapor pressure yield slightly lower (by 1% or less) water activities in the droplets, but given the strong dependence of the nucleation rate on water activity, this leads to significantly less freezing. Second, large interstitial droplets are kinetically limited in releasing excess water to the gas phase, allowing them some extra time for freezing. Both effects together lead to the slowly progressing nucleation shown in Figure 2.
rm>0.7 μm: In this regime the very large droplets can take up substantial amounts of water without themselves reaching a water activity (aw) sufficient for freezing due to kinetic limitations. However, they deplete the gas phase, lowering the supersaturation also for the smaller droplets, and both effects quench nucleation.
 The dashed line in Figure 2 shows the same calculation, but with a gas phase diffusivity (Dg) of the water molecules between the gas phase and the droplets increased by a factor of 100, which illustrates the importance of a proper description of the droplet kinetics. When the gas-to-liquid transfer time is shortened (Dg×100), the large liquid particles lose their water too fast, once the very first ones have frozen (due to a hastened Bergeron-Findeisen process), and this increased diffusional growth of the already formed ice crystals effectively suppresses further nucleation.
 Figure 3 shows scenarios corresponding to three cases of stratospheric distributions, i.e., 60 kt-S/a natural, volcanically quiescent sulphur flux into the stratosphere, and the 1 and 5 Mt-S/a geoengineered scenarios. The evolution of Nice and gas phase saturation ratio for geoengineered and natural cases are presented for the cooling rate of 10 K/h, showing higher Nice in the geoengineered cases due to the presence of larger particles, which are not quenched by the Kelvin effect. The geoengineered scenarios in Figure 3 fall into the second regime in Figure 2, i.e., kinetic limitations of H2O loss from the large droplets increase their nucleation probability. Spectrally resolved information providing detailed account for these findings can be found in Appendix A.
 In Figure 4, we investigate Nicefor natural and geoengineered scenarios plotted as a function of tropospheric/stratospheric air mixing ratio for the same forcing conditions as in previous plots (dT/dt=−10 K/h, T=210 K, p=255 hPa). We term the degree of tropospheric/stratospheric mixing “troposphericity” (=0 for pure stratospheric air, =1 for pure tropospheric air). Figure 4shows three scenarios for natural (red curve: natural 60 kt-S/a) and geoengineered conditions (green and blue curves: 1 and 5 Mt-S/a, respectively).
 All three curves in Figure 4 show a similar, at first sight surprising behavior, namely Nicecontinuously decreasing as a function of troposphericity as long as this parameter is smaller than 0.5, and then a sharp increase when the mixture approaches purely tropospheric conditions. When passing from zero to higher troposphericities in Figure 4, Nice first drops continuously because the number density of large (i.e., not subject to Kelvin effect) droplets decreases, and therefore Nicedecreases. This happens irrespective of geoengineering, because there are about 10 cm−3stratospheric particles, and of those a significant fraction nucleates (i.e., reducing their number shows immediate effect irrespective of their size). However, when troposphericity approaches unity and too little of these large solution droplets are around to nucleate and deplete the gas phase, the tropospheric droplets will be activated. Due to their small mode radius (rdry=25 nm) relative humidity needs to ramp up to a very high value before nucleation kicks in. Owing to the similarity of their sizes (σ=1.4), many of them reach very high water activities at almost the same time, and this enables them to freeze almost simultaneously. And owing to their large number density (N=300 cm−3), a relatively large number of ice particles is generated. This explains the sharp maximum in each of these curves.
 Differences between the three scenarios are detailed in Appendix A, and can be summarized as follows:
Low troposphericity regime. The more large geoengineered particles exist, the less particles have to struggle against the Kelvin effect, and the more interstitial droplets keep high water activities and make themselves available to further nucleation due to kinetically slowed H2O loss. In essence this means that geoengineering under these conditions leads to an increase in Nice(see also Figures 2 and 3).
High troposphericity regime. Here the stratospheric particles are readily used up during ice nucleation due to their small number density. However, the resulting growing ice does not suffice to reduce the relative humidity in the rapidly cooling air. Therefore, some of the much smaller tropospheric particles need to be activated as well. This additional activation is less efficient; the more the already growing ice particles have depleted the gas phase, i.e., the larger the stratospheric particles were at the beginning. In essence this means that geoengineering under these conditions leads to a decrease in Nice. This scenario is quasi-identical to the case of heterogeneous (few particles, nucleating at low supersaturations) versus homogeneous (many particles, nucleating at high supersaturations) nucleation [Spichtinger and Cziczo, 2010].
 It is also clear that the stronger the geoengineering, the higher the troposphericity at which the transition between both regimes occurs. Interestingly, even the natural case shows a pronounced dependence on troposphericity, suggesting a generally strong influence of the stratospheric background aerosol on the cirrus cloud formation. To the best of our knowledge, we are not aware that this effect has been investigated in the literature.
 Beside the size effects discussed so far, temperature, pressure, and updraught velocity also affect the nucleation process. Faster vertical upwelling causes higher cooling rates, which allows more ice particles to nucleate because higher supersaturations can be reached as a consequence of finite ice particle growth and vapor depletion rates. This systematic behavior is reflected in all cases shown in Figure 5. Reductions in temperature lead to generally higher Nice, because diffusional growth of ice particles is slower, allowing more particles to freeze. However, lower temperatures in the atmosphere occur at lower pressures, which largely compensates the effect on nucleation rates and hence on Nice [Hoyle and Luo, 2005]. Two (p,T)-pairs are shown in Figure 5.
 The changes in Nicecaused by the presence of geoengineered aerosols are the following:
Very high cooling rates. Under these conditions the stratospheric aerosols, whether geoengineered or not, play no role. The 1 cm−3stratospheric particles are readily nucleating, but have insufficient time to deplete the gas phase, before the more numerous tropospheric particles can start nucleating (−dT/dt>30 K/h ↔w>1 m/s).
Very low cooling rates. Under these conditions, nucleation occurs only in a fraction of the stratospheric aerosols (1 cm−3), but not at all in the tropospheric particles. This works better for larger particles as the Kelvin effect is less important. Therefore, Niceincreases with geoengineering intensity. However, this effect is weak, because cooling is so slow that already the first few particles suffice to deplete the supersaturation and details of their generation are less important (−dT/dt<2 K/h ↔w<6 cm/s).
Intermediate cooling rates. In this regime, geoengineering may lower the Nice by up to a factor 3. Suppressing the supersaturation at the beginning of the nucleation event, due to the growth of ice crystals formed by the few larger stratospheric droplets, interferes with the nucleation of the smaller tropospheric particles, and this reduces Nice(3 K/h <−dT/dt<30 K/h ↔ 10 cm/s <w<1 m/s). This effect is comparable with the competition of different nucleation processes (homogeneous versus heterogeneous nucleation), known as “negative Twomey effect” [Kärcher and Lohmann, 2002; Spichtinger and Cziczo, 2010].
 In summary, geoengineering (and equivalently volcanic) H2SO4/H2O aerosols may have highly significant effects on the morphology of cirrus clouds, e.g., by changing ice crystal number densities by up to factors of 4, with corresponding repercussions for cloud optical depths. Subsequently, we will use these microphysical results and combine them with trajectory calculations to estimate the effect of geoengineered aerosols on cirrus clouds in the northern midlatitudes.
3 Mixing of Different Air Masses: Stratosphere-Troposphere Exchange
 In the midlatitudes, stratosphere-troposphere exchange is dominated by intrusions of stratospheric air being mixed into the troposphere [Browell and Danielsen, 1987]. Several studies [Post, 1986; Kent and McCormick, 1991], using lidar or satellite (SAGE II) aerosol extinction, showed enhanced aerosol layers in the upper troposphere after major volcanic eruptions which originated from the stratosphere. As concluded by Post , the downward transport was affected by tropopause folds, and was much more rapid than the aerosol sedimentation rate. Furthermore, Sassen and Starr  found that high ice crystal concentrations in cirrus formation regions, measured during the FIRE Intensive Field Observation II in 1991, directly after the Mt. Pinatubo eruption, might have resulted from the volcanic aerosols in layers with intense stratosphere-to-troposphere transport and mixing.
 During the last decade, trajectory-based investigations of stratosphere-troposphere exchange provided novel insight into the amplitude and seasonality of this phenomenon and the associated physical processes [e.g., Wernli and Bourqui, 2002; Stohl et al., 2003; Bourqui, 2006; Hoor et al., 2010]. In order to obtain a quantitative insight into the amount of mixing of stratospheric and tropospheric air with direct impact on cirrus formation, trajectory studies using ERA Interim reanalysis from the European Centre for Medium Range Weather Forecast (ECMWF) were carried out by means of the Lagrangian analysis tool (LAGRANTO, by Wernli and Davies).
3.1 Quantification of Troposphericity
 A set of 20 day backward trajectories arriving in NH midlatitudes at points close to ice saturation (hereafter called “endpoints”) is analyzed. Trajectories with an ice saturation ratio Sice>0.9 at their endpoints are chosen from equally spaced points (horizontally every 200 km, vertically every 30 hPa, therefore every trajectory represents the same mass of air) for January 1992, starting daily at 00 UTC. This year is chosen since the atmospheric dynamics under geoengineering scenarios might be similar to those in 1992, after the Mt. Pinatubo eruption. A winter month was chosen because then the Brewer-Dobson circulation is most efficient in transporting the stratospheric aerosols into the extratropical troposphere, and because the winter season is less affected by cirrus from convective outflow, which is not of interest in the present context. The total number of trajectories was 91,958 (about 3000 trajectories per day) fulfilling the main criteria of having Sice>0.9 and T<233 K at their endpoint, in order to constrain the analysis to cold cirrus-like conditions.
 We are most interested in the subset of these trajectories that originated from the stratosphere. We determine this subset by first selecting only those trajectories which have at least one trajectory point above the dynamical tropopause, i.e., potential vorticity ȣPVȣ> 2 PVU in the extra-tropics and potential temperature Θ > 380 K in the tropics (the latter for trajectories originating in the tropics and arriving in the midlatitudes after their 20 days travel time) [e.g., Holton et al., 1995]. However, processes such as latent heat release, radiation and frictional mixing, can also generate high PV values in the troposphere, in particular in the boundary layer. In order to avoid confusion in the trajectory identification algorithm with these processes, we demand that also an ozone threshold criterion must be satisfied to identify the stratosphere, namely that the ozone mixing ratio (from ERA Interim) must reach a threshold [O3] > 40 ppbv. This value is in accordance with the lower boundary of ozone standard deviation for tropopause-referenced ozone climatology (1994–2003) from the MOZAIC (Measurements of OZone, water vapor, carbon monoxide and nitrogen oxides by in-service Airbus airCraft) programme [Thouret and Cammas, 2006] for the month of January. In the latitude band 30°N–60°N, we find 16,253 trajectories satisfying the PV and ozone criteria.
 As the ozone mixing ratio is a good stratospheric tracer, we quantify the troposphericity of an air parcel by
where O3max is the maximum ozone value for each trajectory, O3(t) is the ozone value at a given time step, while O3tropois the averaged minimum value of ozone determined from each trajectory during the whole month:
This reflects the tropospheric background ozone value in the upper troposphere in midlatitudes. A value of m=0 indicates that an air parcel contains only stratospheric air, while m=1 is fully tropospheric.
3.2 Statistics of Troposphericity
 The trajectories originating from the stratosphere mix gradually with tropospheric air, shifting towards higher values of troposphericity along their 20 days travel time until they reach conditions suitable for cirrus cloud formation. The bar chart in Figure 6 indicates the percentage of trajectories satisfying cirrus-like conditions that have been in the stratosphere at some point in their 20 day history (i.e., ∣PV∣> 2 PVU, m<0.95), showing a strongly positive correlation with troposphericity m. Each bar comprises trajectories ending in the interval [ m−0.05, m+0.05]. A relatively large percentage of trajectories (≈ 0.8%) is stratospheric at their endpoint (i.e., m<0.05). For example, such trajectories may have originated in the stratosphere, then entered the troposphere and picked up moisture, and finally reentered the stratosphere. We take also these trajectories into account since they fulfil the above-mentioned criteria (in particular Sice>0.9), indicating the formation of cirrus clouds above the local tropopause. Conversely, we exclude trajectories with m>0.95 and interpret these trajectories as fully tropospheric, i.e., not affected by stratospheric aerosols. According to Figure 6, 11.2% of the trajectories that reach cirrus-cloud conditions in NH midlatitudes are influenced by stratospheric aerosols with troposphericities m≤0.95. (We checked that the subsequent results do not change significantly when a finer binning with Δm=0.01 is chosen.)
English and Toon  found significant perturbations to tropospheric aerosol (up to 100 times) in the upper troposphere and near the poles in their geoengineering simulations with the WACCM/CARMA model simulating sulphate as the only aerosol type. The geoengineering cases we employ here should provide an upper limit to the impact on cirrus cloud properties, and our approach of combining tropospheric and stratospheric aerosol distribution should be more realistic than previous simulations.
 In order to constrain the temperature of the trajectories when they meet cirrus conditions, Figure 7 shows the temperature distribution as a function of troposphericity m. The mean temperature values will be used in the next section as the value in the cloud center for each mixing case, when specifying the location of a cirrus cloud in a radiative transfer model. The corresponding pressure is obtained from the US standard atmosphere.
4 Radiative Transfer Calculations
 We will now combine the box model-based microphysics and the trajectory statistics to estimate the effects of geoengineering on the radiative properties of midlatitude cirrus clouds. Cirrus clouds have a large influence on the energy budget of the Earth-atmosphere system owing to their microphysical and radiative properties [Wang and Minnis, 1996; Reichardt and Reichardt, 2002; Hoyle and Luo, 2005; Schiller and Krämer, 2008]. They significantly affect the water budget of the upper troposphere altering top-of-atmosphere (TOA) radiative fluxes, thus having a large impact on global annual mean net radiation. This high cirrus, as they are of interest here, trap more OLR in the Earth-atmosphere system than they reflect solar radiation, thus causing a net warming effect [Chen and Rossow, 2000; Mitchell and Finnegan, 2009].
4.1 Radiative Transfer Model
 Changes in the microphysical properties of cirrus clouds may affect their optical properties and lifetime, i.e., changing their albedo and net radiation effect. In order to quantify the change in the cloud radiative forcing (CRF) caused by the application of a geoengineering scheme, a standalone, off-line version of the radiation transfer model, based on the radiation parameterization by Fu and Liou, is used in this study. In this model the single scattering properties of monodisperse hexagonal ice crystals are defined as a function of IWC and mean effective size. Particle size and Nice, which are the input for the radiation transfer model, are obtained from the microphysical box model described in section 2.
 The radiation transfer model is a two stream radiative transfer code, containing six bands in the solar and 12 bands in the thermal infrared regime. It calculates fluxes and heating rates for every level and TOA fluxes of the OLR and net shortwave radiation. The optical properties (optical depth, asymmetry factor, single scattering albedo) are parameterized as a function of IWC and effective size of ice crystals. It requires pressure, temperature and humidity profiles as input, and further an altitude-dependent ozone mixing ratio and constant mixing ratios of other radiatively active gases. It determines the solar zenith angle as a function of Julian day and time, calculating daily mean radiation fluxes and heating rates with 1 h temporal resolution, which we averaged over the diurnal cycle. Infrared surface emissivity is set to 1. For more details about the underlying radiative transfer model we refer to Fu and Liou.
4.2 Calculation of Cloud Radiative Forcing
 In order to apply the results on cirrus microphysics and trajectory-based stratosphere-troposphere exchange and mixing in sections 2 and 3 to cloud radiative properties in the NH midlatitudes, we introduce the concept of cloud radiative forcing (CRF) and then discuss typical conditions in terms of cooling rates, cirrus level temperatures, and cirrus geometric thicknesses. CRF determines the change in the radiation fluxes at TOA due to a presence of clouds as compared to a clear sky case e.g., [Chen and Rossow, 2000; Corti and Peter, 2009]. Net CRF for each troposphericity m is calculated for natural and geoengineered cases as
where and are the shortwave and longwave broadband radiative fluxes under “all-sky” conditions at the TOA for each tropospheric/stratospheric mixing m, while and are the shortwave and longwave radiative fluxes for clear sky conditions. The difference between natural and geoengineered values of is then calculated as
Here indicates an overall warming effect for the Earth-atmosphere system due to geoengineering, while is an overall cooling effect. A mid-latitudinal mean change in CRFnetis obtained by appropriate weighting with m:
where the weighting factors are calculated as
with representing the number of trajectories ending in [ m−0.05, m+0.05] and the number of all 91,958 trajectories in NH midlatitudes. The weighting factors are shown in Figure 6, and the temperature dependencies in Fall,m and Fcs are in accordance with the white line in Figure 7. In order to obtain regionally averaged CRF, the weighted difference in the net CRF for each troposphericity was then multiplied with the average cloud amount from the AIRS-LMD cloud climatology [Stubenrauch and Cros, 2010] for thin or moderate cirrus.
 We assume our clouds to have geometrical thicknesses of 0.7, 1.4, 2.1, and 3 km, which are typical for thin and moderately thick midlatitude cirrus [Noël and Haeffelin, 2007; Nazaryan and McCormick, 2008; Lamquin and Stubenrauch, 2008; Stubenrauch and Cros, 2010]. During their nucleation, these clouds have been exposed to a wide range of mesoscale cooling rates (as shown by Hoyle and Luo ), with a most likely value of dT/dt≈−10 K/h (corresponding to a vertical velocity of w≈30 cm/s), which is characteristic for the midlatitude upper troposphere. Synoptic scale values are w≤8 cm/s, with typical values around 5 cm/s [Spichtinger and Gierens, 2005a]. Stronger upwelling is the result of mesoscale activity such as gravity waves [Fritts and Alexander, 2003; Spichtinger and Gierens, 2005b; Joos and Spichtinger, 2009], or turbulence as a product of breaking waves and instabilities (dynamical and/or convective) [Bretherton and Smolarkiewicz, 1989; Dobbie and Jonas, 2001; Marsham and Dobbie, 2005; Fusina and Spichtinger, 2010]. We capture this wide spread by investigating three different vertical velocity regimes, namely 5, 30, and 60 cm/s.
4.3 Geoengineering-Induced CRF Changes
 Figure 8shows the changes in the visible optical thickness and net CRF due to geoengineering influence as a function of troposphericity m for the case of 1.4 km thick clouds generated by a constant cooling rate dT/dt=−10 K/h (w≈30 cm/s). According to the optical depth nomenclature of Stubenrauch and Cros , this is a case of a typical “thin cirrus”, whose optical thickness rises with increasing troposphericity due to increased IWC at lower cloud altitudes and higher temperatures (Figure 7). Optical depths and CRF of natural and geoengineered cases display a similar dependence on troposphericity as Nicein Figure 4, as can be expected from the correlation between Nice and optical depth τvis. For m<0.6 geoengineering causes a slight (< 10%) increase in optical thickness (Δτvis≈+0.04 for 5 Mt-S/a) due to geoengineering, whereas m>0.6 show a stronger (≈ 20%) decrease of up to Δτvis≈−0.2. Net CRF displays a similar response to geoengineering, with up to +2 W/m2at low and −6 W/m2at high troposphericities. The largest changes in net CRF from the other considered cases with slower (dT/dt=−1.5 K/h) or faster (dT/dt=−20 K/h) cooling rates are +1.4 W/m2and −5.8 W/m2for the 1 Mt-S/a injection and +2.0 W/m2and −7.5 W/m2for the 5 Mt-S/a injection, respectively.
 The non-monotonic response in Δτvisand can be understood in terms of the microphysical behavior of Nice in Figure 4. This complex behavior suggests that, although the effect of geoengineering on individual cirrus clouds can result in a change in radiative forcing by several Watts per square meter locally, the averaged effect on a whole latitude band will be much smaller due to a large degree of compensation. Indeed, the changes in the mean net CRF averaged over the whole NH midlatitudes are surprisingly small, in the ±0.04 W/m2range. These values are summarized in Table 1, comparing the changes in the mean net cloud radiative forcing under natural and geoengineered conditions and for the pure tropospheric case. Interestingly, radiative forcing estimates are not much different from the effect of natural background aerosols. Clouds being affected by geoengineering aerosols yield an overall warming effect when generated in very slow vertical updraughts (either synoptic scale ascent or when a small-scale warming event partly compensates a stronger cooling during nucleation; compare the −1.5 K/h columns in Table 1). Conversely, an overall cooling effect is induced when the cloud is generated by higher vertical velocities. These changes are two orders of magnitude lower than the intended cooling effect by the geoengineered stratospheric particles (e.g., −3.7 W/m2needed to offset the radiative forcing of a CO2doubling). We do not expect large changes in this general behavior in other latitude bands or other seasons. If different at all, then the induced effects should be even smaller in magnitude, as the midlatitudinal tropopause folds during the convectively calm winter seasons should maximize the effects of stratospheric aerosols on cirrus formation. Thus, we do not expect large global effects on cirrus clouds stemming directly from the microphysical changes caused by artificially produced stratospheric aerosols. However, this result holds for the microphysical effects only and assumes everything else to stay constant. In particular, the cooling of the ground and the expected changes in the global water cycle have been neglected in this study. Resulting feedbacks, such as cloud lifetime changes and changes in upper tropospheric relative humidity need to be considered in future work.
Table 1. Changes in the Mean Net Cloud Radiative Forcing for NH Midlatitudes Under the Natural (60 kt-S/a) and Geoengineered Conditions (1 and 5 Mt-S/a) Compared to the Pure Tropospheric Casea
Δ z (m)
aaValues for ΔCRFnet(in mW/m2) have been obtained by folding Nice(Figure 4) with troposphericities (Figure 6) and evaluating at the appropriate temperatures (Figure 7). Values are shown for three different cooling rates, −dT/dt−1.5, −10, and −20 K/h, corresponding to small- or mesoscale vertical upwelling velocities of roughly 5, 30 and 60 cm/s, respectively. Results are shown for geometric thicknesses, Δz, of the cirrus clouds between 700 and 3000 m.
5 Summary and Conclusions
 This model study investigates effects of geoengineered stratospheric H2SO4-H2O aerosol particles on the microphysical and optical properties of cirrus clouds. These particles, generated by continuous SO2injections and meant to reflect a part of the sunlight from the stratosphere back to space and thereby cool the ground, eventually return to the troposphere via stratosphere-troposphere exchange. Mixing of the stratospheric dry air laden with large aerosol particles with the moist tropospheric air may lead to conditions prone to cirrus cloud formation. Due to their very large particle sizes, the geoengineered particles affect the nucleation of cloud ice in hitherto unexplored manners.
 The impact on northern hemisphere midlatitude cirrus clouds has been studied for two cases of continuous equatorial SO2 injections with 1 and 5 Mt-S/a, respectively. The study is constrained to wintertime conditions in order to focus on high altitude in situ cirrus cloud formation, in order to avoid confusion with anvil cirrus arising from deep convective outflows. The size distribution originating from the stratosphere was taken from the AER 2-D microphysical aerosol model [Weisenstein and Penner, 2007] and used as input for the Zurich optical and microphysical cirrus cloud model (ZOMM) with spectral microphysics [Luo and Voigt, 2003] to investigate changes in the ice crystal number density (Nice) and size distribution caused by the implemented geoengineering scenarios. The resulting impact on the optical thickness and net cloud radiative forcing (CRF) due to the geoengineering was then investigated using a column radiation transfer model [Fu and Liou, 1993]. Upscaling to NH midlatitudes is achieved by means of comprehensive trajectory modeling using ozone as a tracer for “troposphericity”, defined as the degree of mixing of the size distribution of large stratospheric aerosols and the size distribution of smaller, yet much more numerous tropospheric aerosol particles.
 The microphysical simulations highlight two parameters as particularly important: troposphericity and the cooling rate of the moist air during cirrus formation. The results lead to the interesting conclusion that, under geoengineered conditions, a full treatment of the kinetically impeded H2O uptake by the large droplets before ice formation and the impeded H2O release by large interstitial droplets after ice formation are essential in determining the final ice crystal number density. These kinetic limitations for large particles, together with the Kelvin effect for small particles, lead to opposing effects that geoengineering has on Nice: an increase in Niceat low troposphericities and a reduction at high troposphericities.
 A comprehensive 20 day backward trajectory study based on ERA Interim reanalysis data was performed to identify air masses that underwent stratosphere-to-troposphere transport and soon thereafter became sufficiently moist for cirrus cloud formation. To this end troposphericity was quantified by using the ERA Interim ozone fields. According to the analysis, 11.2% of all cirrus-forming air parcels had stratospheric influence (quantified by a potential vorticity of at least 2 PVU and a troposphericity of at most 95%), while the other 88.8% were purely tropospheric.
 The complex interplay between the few large stratospheric droplets and the many small tropospheric droplets gives rise to a similarly complex optical response of the cirrus clouds as evidenced by the radiative transfer modeling: for synoptically slow upwelling without small-scale temperature perturbations, geoengineering is predicted to induce a small enhancement in CRF, i.e., a warming effect of maximum +2 W/m2locally in the presence of thin cirrus clouds, while faster vertical velocities upwelling, as they are typical for small-scale temperature fluctuations lead to a decrease in CRF with maximum change of −7.5 W/m2. Despite these large local changes related to cloudy conditions in the presence of thin or moderate cirrus, the changes in CRF averaged over the whole midlatitudes are smaller by two orders, because of three reasons: (1) averaging over troposphericities leads to a partial compensation, at least for faster upwelling; (2) according to the trajectory analysis, only 11.2% of all cirrus are affected by stratospheric aerosols; and (3) on average, only 10.4% or 13.6% of the northern midlatitudes are covered by thin or moderate cirrus, respectively (following the AIRS-LMD climatology from Stubenrauch and Cros ). Therefore, the resulting midlatitudinal averages are in the range of +0.02 W/m2to −0.04 W/m2depending on upwelling velocities and geoengineering scenario. These values are two orders of magnitude smaller than the intended radiative forcing by the geoengineered aerosols in the stratosphere, as required to compensate for CO2doubling (several Watts per square meter). Another interesting point is that the radiative forcing estimate of the natural background aerosols compared to the pure tropospheric case is already significant and not much different with an applied geoengineering scheme. Accordingly, we conclude that the microphysical impact on cirrus clouds from geoengineered stratospheric sulphate aerosols is not an important side effect. Other feedbacks, such as cooling-induced changes in the hydrological cycle, resulting changes in upper tropospheric humidity and thus in nucleation probability, ice particle sedimentation, and cloud lifetime need to be taken into account in future studies.
Appendix A:: Spectral Evolution of Freezing in Distributions of Large Aerosol Particles
 Details in water partitioning in large aqueous solution droplets (e.g., H2SO4/H2O droplets) determine the ice crystal number density (Nice) during a freezing event. Niceis determined by the Kelvin effect affecting the small droplets, by slow H2O uptake of large droplets during the initial cooling, and by the slow H2O release by interstitial aerosols during initial freezing. These processes determine the water activity, aw, of the aqueous particles, and thus directly affect the nucleation rate. Figure A1 displays the spectral evolution as determined from the Zurich Optical and Microphysical box Model (ZOMM) for the case of a cooling rate of 10 K/h. The droplets are allowed to freeze homogeneously using nucleation rates by Koop and Luo . The left column in Figure A1 shows the freezing of undiluted stratospheric air, the right column diluting the stratospheric air with tropospheric air in a ratio 1:9 (i.e., troposphericity 0 and 0.9, respectively). As is most evident in the undiluted case with 5 Mt-S/a geoengineering, freezing starts at droplet radii around r0≈1.5 μm (dotted red curve in lowermost left panel). This position coincides with the highest value of the blue curve, the maximum ice saturation ratio Sice(or water activity) as a function of particle size. Starting from r0 more droplets with smaller and larger sizes nucleate, until so many particles are frozen, grown and have depleted the gas phase water, that further nucleation becomes impossible. The spreading of nucleation towards particles with r<r0 is limited by the Kelvin effect, leading to a reduction in Sice(blue curve). Conversely, the spreading of nucleation towards particles with r>r0 is limited by them lagging behind in taking up H2O during the cooling process, because gas phase diffusion is very slow for a droplet of this size. But also after the first ice particles are nucleated, large interstitial droplets remain amenable to ongoing nucleation in the cooling air parcel because the Bergeron-Findeisen process (which makes H2O molecules diffuse through the gas phase from the liquid to the solid particles) is also slowed kinetically for these large droplets. It is interesting to see that in the 5 Mt-S/a case, not all large particles are activated, since they remain too concentrated.
Pure stratospheric regime. In the unmixed stratospheric case (left column in Figure A1), the more large geoengineered particles exist, the fewer particles have to struggle against the Kelvin effect, and the more interstitial droplets keep high water activities and make themselves available to further nucleation due to kinetically slowed H2O loss. In essence this means that geoengineering under these conditions leads to an increase in Nice (see also Figures 3 and 4 at small troposphericities) albeit the smaller frozen fraction due to the larger aerosol number concentration.
Highly tropospheric regime. In the diluted case (troposphericity 0.9, right hand side of Figure A1), the situation changes considerably. Here the stratospheric particles are readily used up in the ice nucleation due to their small number density, irrespective of the geoengineering scenario (see dotted red curves). However, the resulting growing ice does not suffice to reduce the relative humidity in the rapidly cooling air parcel. Therefore, some of the much smaller tropospheric particles need to be activated as well. This additional activation is less efficient, the more the already growing ice particles have depleted the gas phase, i.e., the larger the stratospheric particles were at the beginning. In essence this means that geoengineering under these conditions leads to a decrease in Nice (see also Figure 4 at troposphericity 0.9).
Appendix B:: Changes in Nice Depending on the Cooling Rates for Different Stratospheric/Tropospheric Mixing Ratios
 Figure B1 shows ice crystal number density as a function of vertical velocity, depending on the stratosphere/troposphere mixing and temperature regime. Larger percentage of stratospheric air (upper panel) leads to an increase in Nice, since the nucleation process is governed by these particles, while the small percentage of tropospheric aerosols is not even affected. Increasing the updraught speed will result in activating a larger number of stratospheric particles, which yields a higher ice number density in geoengineering cases due to the larger amount of “good” nuclei compared to the background case. A decrease in the geo- Nice takes place at 210 K temperature between 0.5 and 1 m/s vertical updraught, because higher cooling rates can also activate the smaller particles from the stratospheric distribution due to reduced ice particle growth and vapor depletion rates. Fewer larger aerosols nucleate and more smaller particles would activate. If more large particles would activate, the supersaturation would be strongly depleted, not giving a chance to smaller particles to freeze, as is the case in geoengineering scenarios. With increased contribution of tropospheric air (middle and lower panel), the turnover to fewer ice crystals occurs at lower vertical velocities, where the influence of the smaller particles (either stratospheric or tropospheric ones) becomes already important at low updraughts (0.1 to 0.5 m/s), decreasing the total Nice. Their activation is less efficient if there is a larger number of initially formed ice crystals, meaning that eventually fewer crystals will be nucleated in the geoengineering case. For larger vertical velocities and a larger amount of tropospheric air, the importance of preliminary nucleated large particles becomes less significant for the final ice number concentration, due to the ability of much larger number density of small particles to be activated simultaneously in a high updraughts. In the lower panel, for 210 K, the number of nucleated ice particles reaches the tropospheric mode ice density for updraughts larger than 1 m/s, meaning that the large aerosols from geoengineering case are completely negligible for the final ice number concentration.
Appendix C:: Details of the Radiative CodeInput Parameters
 The pressure profiles are interpolated using the US standard atmosphere; temperature profiles are calculated using a constant lapse rate reaching the surface temperature of T=266.9 K; surface albedo is α=0.25 (mean values for Jan 2000/2001 from ERA40 reanalysis for 50° NH); tropopause is located at 10 km altitude; TOA altitude is at 20 km; the profiles are divided into 50 m thick layers; layers below the cloud are assumed to have a constant value of relative humidity with respect to ice RHi of 60% and above the cloud a linearly decreasing RHi from 40% to 5% and then to 1% in the stratosphere; cloudy model layers are provided with the information of ice water content and ice crystal number density from the microphysics box model with RHi = 100% inside the cloud.
 We are grateful for funding within COST Action ES0604 “Atmospheric Water Vapour in the Climate System (WaVaCS)” by the Swiss State Secretariat for Education and Research (SER-No. C08.0037, Lagrangian Measurements and Modeling of Cirrus Clouds (LAMMOC)). Partial funding is further acknowledged from the Swiss National Centre of Competence in Research on Climate (NCCR Climate). We thank Dr. Fabian Fusina for providing us with the stand-alone, off-line version of the Fu and Liou radiation transport model, and Dr. Thierry Corti for providing ERA40 mean surface properties. We also thank Dr. Andrew Gettelman for valuable comments and interesting suggestions that improved the quality of the paper.