Exploring the uncertainties in the aviation soot-cirrus effect

. A global aerosol-climate model, including a two-moment cloud microphysical scheme and a parametrization for aerosol-induced ice formation in cirrus clouds, is applied in order to quantify the impact of aviation soot on natural cirrus clouds. Several sensitivity experiments are performed to assess the uncertainties in this effect related to (i) the assumptions on the ice nucleation abilities of aviation soot; (ii) the representation of vertical updrafts in the model; and (iii) the use of reanalysis data to relax the model dynamics (the so-called nudging technique). Based on the results of the model simulations, 5 a radiative forcing from the aviation soot-cirrus effect in the range of − 35 mW m − 2 to 13 mW m − 2 is quantiﬁed, depending on the assumed critical saturation ratio for ice nucleation and active fraction of aviation soot, but with a conﬁdence level below 95% in several cases. Simple idealized experiments with prescribed vertical velocities further show that the uncertainties on this aspect of the model dynamics are critical for the investigated effect and could potentially add a factor of about two of further uncertainty to the model estimates of the resulting radiative forcing. The use of the nudging technique to relax model dynamics 10 is proved essential in order to identify a statistically signiﬁcant signal from the model internal variability, while simulations performed in free-running mode and with prescribed sea-surface temperatures and sea-ice concentrations are shown to be unable to provide robust estimates of the investigated effect. A comparison with analogous model studies on the aviation-soot cirrus effect show a very large model diversity, with a conspicuous lack of consensus across the various estimates, which points to the need for more in-depth analyses on the roots of such discrepancies. conﬁguration which includes a detailed parametrization for aerosol-induced ice formation in cirrus clouds Rather than attempting to provide a single estimate of the aviation soot-cirrus effect, the goal of this study is to explore the uncertainties related to the microphysical 90 and dynamic aspects of this effect, in order to provide a realistic, albeit broad, range of possible values for the resulting climate impact. The microphysical analysis focuses on the ice nucleating properties of aviation soot, based on the results of the laboratory measurements reported in the literature. We show that the variation in both the critical saturation ratio S crit for ice nucleation and the active fraction f act of aviation soot can have a signiﬁcant impact not only on the magnitude but also on the sign of the resulting RF. We attempt to relate this changes to the underlying physical processes as represented in the model. This work helps to disentangle and quantify the main uncertainties in the aviation-soot cirrus effect, but its actual magnitude (and to a lesser extent also its sign) remain uncertain. Our model simulations show that a more precise characterization of the ice nucleating properties of aviation soot could help to constrain at least the sign of the resulting RF. Further laboratory measurements are therefore needed, in particular concerning the role of cloud processing. In situ measurements are also essen- 550 tial, in order to characterize the microphysical properties of the population of aviation soot, like number and size. On the Recent advancements in the

reported by Gettelman and Chen (2013), who applied the CAM5 model with the assumption that soot has similar ice nucleating properties as mineral dust (i.e., S crit = 1.2 − 1.3), but with lower (and presumably more realistic) active fractions. Zhou and Penner (2014) again used the CAM5 model with the Liu and Penner (2005) ice nucleation parametrization, but provided an explicit calculation of the soot active fraction by considering its pre-processing in contrail cirrus. This resulted in 0.6% of aviation soot being an efficient INP, leading to a RF quantified in the range of −350 mW m −2 to 90 mW m −2 , depending on Furthermore, we analyse the role of the model's representation of vertical updraft by means of mechanistic studies in which a very simple representation of such updraft is implemented in order to explore the sensitivity of the relevant microphysics to the model dynamics. This parametric approach has proven useful in a previous climate impact study (Righi et al., 2013), where we analysed the uncertainties related to the assumptions on the size distribution of aerosol particles from different transport emission sources, including aviation. On a more general level, such methods :::::::: parametric :::::::::: approaches : were successfully used, 100 for instance, to constrain the uncertainties on the microphysical properties of warm clouds  and on the aerosol indirect effect Regayre et al., 2020).
This paper is organized as follows: in Sect. 2 the processes controlling the aviation-soot cirrus effect and its large uncertainties are discussed and the results of available laboratory studies are summarized. The model setup, which is largely based on Righi et al. (2020) but has been further improved here, and the performed numerical experiments are described in Sect. 3. The 105 results are presented and discussed in Sect. 4 and we summarize the main outcomes of this study in Sect. 5.

Uncertainties in the soot-cirrus effect
As mentioned in the introduction, aerosol-induced ice formation in the cirrus regime (T −37 • C) can occur either via homogeneous freezing or by heterogeneous freezing on the surface of an INP. The latter process usually requires a lower critical supersaturation over ice and can therefore occur prior to the onset of homogeneous freezing, attenuating or even inhibiting the 110 direct freezing of supercooled liquid solution aerosol. This has of course important consequences on the microphysical properties of cirrus, since it affects the number concentrations and size of IC and, in turn, the lifetime and the radiative properties of the clouds. Cirrus clouds generally exert large RFs, both in the shortwave and in the longwave spectrum, with the latter being slightly larger, which results in an overall warming effect (Hartmann et al., 1992;Hong et al., 2016;Chen et al., 2000;Gasparini and Lohmann, 2016). If a cirrus cloud is dominated by homogeneous freezing, adding more INPs typically results 115 in a decrease of IC number concentration (ICNC) and a corresponding increase in their size (the so-called negative Twomey effect; Kärcher and Lohmann, 2003). Adding INPs to a cirrus cloud where heterogeneous freezing already dominates, on the other hand, could result in a further increase of ICNC and a decrease in crystal sizes. As shown by previous studies (e.g. Zhang et al., 1999), an increasing IC size reduces the longwave cloud forcing (i.e., less warming) but also the shortwave cloud forcing in absolute terms (i.e., less cooling), and their combination can be either a net warming or a net cooling depending on the cloud 120 ice water content. Other effects, such as a more efficient sedimentation of less abundant, larger IC or an increased deposition of water vapour in the presence of more efficient INPs (dehydration; Jensen et al., 2001Jensen et al., , 2013 add even more complexity to this picture and to the interpretation of the model results. For a reliable quantification of the effect of aviation soot on cirrus clouds and its climate impact, it is therefore essential not only to have a reliable estimate of the ice nucleating properties of aviation soot, but also of the dynamic processes that control the background state of natural cirrus clouds in the model. Cirrus 125 formed in slow (fast) updraft :::::: updrafts : are usually dominated by heterogeneous (homogeneous) nucleation, resulting in lower (higher) concentrations of IC and larger (smaller) IC sizes Krämer et al., 2016;Krämer et al., 2020). Hence, the way aviation-soot INPs can impact on these clouds depends not only on their ice nucleation ability but also  [%] 210 K 220 K 230 K Figure 1. Summary of ice nucleating properties of soot measured in different laboratory studies (Möhler et al., 2005;Koehler et al., 2009;Crawford et al., 2011;Kanji et al., 2011;Chou et al., 2013;Kulkarni et al., 2016;Mahrt et al., 2018;Nichman et al., 2019;Mahrt et al., 2020) compared with the values assumed in model studies on the impact of aviation soot on cirrus (Hendricks et al., 2005;Penner et al., 2009;Liu et al., 2009;Hendricks et al., 2011;Gettelman and Chen, 2013;Zhou and Penner, 2014;Penner et al., 2018;Zhu and Penner, 2020). The parameters explored in this study are symbolized with stars. The vertical dashed lines show the homogeneous ice nucleation threshold at 210 K, 220 K and 230 K. on the dynamical background conditions. In the present study we therefore focus on both the microphysical and the dynamic aspects, by analysing the uncertainties related to the assumptions on aviation soot INP characteristics and exploring the impact 130 of different (simplified) representations of the dynamic forcing in the model. We stress again that the main goal of this study is not to provide an updated estimate on the aviation soot-cirrus effect, but to explore its sensitivity to aviation soot microphysics and, to some extent, to the underlying model dynamics. Figure 1 summarizes the ice nucleating properties of different soot types retrieved from the literature, including cloudprocessed soot. These properties are given in terms of ice saturation ratio S ice and active fraction f act and are compared with soot as a better INP, especially in terms of critical supersaturation ratio. Recent laboratories studies (Marcolli, 2017;Mahrt et al., 2020) support indeed higher ice nucleation efficiency for soot particles which experienced cloud processing, for example in contrails, but this applies only to particles with diameters of about 400 nm, which implies that only a very low fraction of aviation soot can effectively be active as INPs in the upper troposphere. Further note that the experimental results show a clear 145 temperature dependence on the soot ice nucleating properties, which is mostly ignored by the model parametrizations ::: This :::: was ::: also ::: the ::::::::: conclusion ::: by ::::::::::::::::: Kärcher et al. (2021): ::: In : a ::::: recent :::::::::::::: process-oriented ::::::: analysis ::::: using : a ::::::::::::: high-resolution :::::: column :::::: model ::::: based :: on ::: the ::::::::::::: parametrization ::: by :::::::::::::::::: Marcolli et al. (2021), :::: they ::::::::: suggested :::: that ::: less ::::: than ::: 1% :: of ::::::: aviation :::: soot :::::::: particles ::: can :::: lead ::: to ::: the :::::::: formation :: of ::: ice ::::::: crystals :: in :::::::::: competition :::: with :::::::::::: homogeneous ::::::: freezing. To explore this parameter space in sufficient detail, also reproducing the assumptions of previous model studies, we therefore perform nine sensitivity simulations in this study, varying 150 S crit from 1.2 to 1.4, and f act from 0.1% to 10%. These assumptions are marked with the black star symbols in Fig. 1 and result in nine combinations of these two parameters. Note that values :::::: Values :: of : S crit > 1.4 would mostly exceed the homogeneous freezing threshold at relevant cirrus temperatures and are therefore not worthy to be explored for the scope of the present study.
All previous model-based investigations on the aviation soot-cirrus effect considered approximated representations of the vertical updraft and its subscale variability: a common approach uses the square-root of the turbulent kinetic energy (TKE) as 155 a proxy for such variability . Later studies (Kuebbeler et al., 2014) also included the contribution of orographic gravity waves generated on the lee of mountain ranges (Joos et al., 2008), while recent models (Penner et al., 2018) used methodologies based on measurements (Podglajen et al., 2016) to consider the contribution of gravity waves to the vertical velocity. In this study, the aviation soot-cirrus effect is quantified with the EMAC-MADE3 model (see Sect. 3), which follows the TKE approach for the subscale vertical velocity, also considering the impact of orographic waves in relevant 160 regions. To further investigate how different cirrus regimes may react to the perturbation represented by aviation-soot INPs, we also consider an idealized representation of the vertical velocity. We prescribe constant values of the vertical velocity in the range from 2 cm s −1 to 50 cm s −1 , to explore the full range of possible updraft regimes, including both slow and fast updrafts (Kärcher et al., 2006;Krämer et al., 2020). While this approach is of course idealized, it offers the possibility to separate the microphysical from the dynamic effect by artificially introducing a spatially uniform dynamic regime, thus allowing to 165 interpret the competition among the different INPs considered by the model purely in terms of their microphysical properties.
Furthermore, it enables the investigation of INP effects under possible regimes, not covered by the TKE and orographic gravity wave approaches mentioned above.
Another relevant improvement to the model configuration applied here is the introduction of an additional tracer BCtag to which the soot emissions from the aviation sector are assigned. The BCtag tracer is distributed into the same 6 modes as the standard BC tracer of MADE3, namely Aitken, accumulation and coarse mode, each with insoluble and mixed states. The BC and BCtag tracers have the same physical properties and undergo exactly the same processes in the model, but allow 205 for different ice nucleating properties between background and aviation soot in the cirrus parametrization. The ice nucleating properties of mineral dust and background soot are the same as in R20, namely S crit = 1.1 − 1.2 with a temperature-dependent active fraction for mineral dust in the deposition mode, S crit = 1.3 and f act = 5% for mineral dust in the immersion mode (Kuebbeler et al., 2014), and S crit = 1.4 and f act = 0.25% for background soot (Hendricks et al., 2011). The S crit and f act parameters for aviation (and in part also background) soot are explored in more detail in the dedicated sensitivity studies, as discussed in Sect. 2. To avoid confusion, we note here that the MADE3 BC and BCtag tracers :: of ::::::: MADE3 : actually refer to black carbon, i.e. an aerosol type composed only of carbon, but we are using the term soot in this paper for consistency with most of the literature on aviation effects, although these definitions are not fully consistent (see Petzold et al., 2013, for a more detailed discussion on this terminology).
To calculate the number concentration of INPs for the different types we use the same approach as R20, while for the 215 newly introduced BCtag tracer we derive the number concentration from the tracer mass, by assuming aviation soot to follow the bimodal size distribution measured by Petzold et al. (1999) in the plume of a B737-300 aircraft. This distribution is characterized by median diameters of 25 and 150 nm, and geometric standard deviations of 1.55 and 1.65, for the Aitken and accumulation modes, respectively. The same size distribution parameters were used in Righi et al. (2013) to characterize particle number emissions from aviation. Introducing the BCtag tracer has the advantage that a lower number of simulations needs to 220 be performed to isolate the impact of aviation soot on cirrus clouds, since only two experiments are required for that, i.e. with and without the effect of the BCtag INPs in the cirrus parametrization. The difference between these two experiments hence provides an estimate of the resulting climate impact . :::::: climate :::::: impact :: of ::::::: aviation :::: soot :: on :::::: natural ::::: cirrus :::::: clouds, ::::: while ::::::::: excluding :: the :::::: effects :: of ::: the :::::::::: interactions :::: with :::::: clouds :: at ::::: lower ::::: levels ::::: (e.g., :::::: sulfate :::::: impact :: on :::::: liquid ::::::: clouds). The statistical significance of this estimate is also improved with respect to an approach where no tagging of aviation soot is included, since in that case 225 four experiments would be required (with and without aviation, with and without soot impact on cirrus) to isolate the effect.
Another advantage of this tagging approach is that different ice nucleation abilities can be assumed for aviation soot and background soot, i.e. soot from background sources. The aviation soot-cirrus effect is estimated by calculating the difference between a given simulation and a baseline experiment (BASE), where aviation soot (i.e., the BCtag tracer) is not considered as INP in the cirrus parametrization. A paired sample t-test is applied to verify the null hypothesis that the annual mean values of 230 a given quantity (e.g., RF) are identical in the two simulations (with and without aviation-soot impact on cirrus). We express the response of the test in terms of confidence level, i.e., 100(1 − p), where p is the p-value. Unless otherwise specified, we regard the results as statistically significant when the null hypothesis can be rejected at a : confidence level larger than 95% (p < 0.05).
4 Results and discussion

Geographical distribution of aviation soot and INPs
Before analysing the aviation-soot radiative effects, we present in Fig. 4  patterns is that particles in the Aitken mode, which dominate total particle number, are characterized by a shorter lifetime due

The aviation soot-cirrus effect
The RFs from the aviation soot-cirrus effect under the nine different assumptions for the ice nucleating properties of aviation soot are presented in form of a matrix in Fig. 5. The EMAC-MADE3 simulations estimate this effect to be in the range 320 of −35 mW m −2 to 13 mW m −2 , but lacking sufficient statistical significance for S crit = 1.3 and S crit = 1.4. The effect is negative (cooling) for low critical saturation ratios (higher nucleation efficiencies) and tends to increase towards a positive (warming) effect for medium to high critical saturation ratios (medium to low nucleation efficiencies). The statistical insignificance of the RF for some combinations of the parameters, however, makes it difficult to draw general conclusions from these overall numbers alone.

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To facilitate the interpretation, we separate in Fig. 6a-d the different components of the RF, namely shortwave and longwave, all-sky and clear-sky. As expected, these graphs demonstrate how the aviation-soot cirrus effect actually results from the opposite changes in the shortwave (Fig. 6a) and longwave (Fig. 6b) all-sky RFs, which also have a much higher statistical significance than the total RF. The effect in the shortwave corresponds to a warming (i.e., a reduced cooling), meaning that aviation soot reduces the (background) cooling impact of natural cirrus clouds in the shortwave. This could be a manifestation of the 330 negative Twomey effect (Kärcher and Lohmann, 2003): the additional INPs from aviation compete with homogeneous freezing for the available supersaturation and lead to the formation of fewer and larger IC in these clouds, thereby decreasing their reflectivity and their shortwave cooling. This interpretation is consistent with the very small changes in the clear-sky part of the shortwave spectrum (Fig. 6c) . Furthermore, the ::: and :: it : is :::::: further ::::::::: supported :: by ::: the : general decrease in the number concentration of homogeneously formed IC ::::::::::: homogeneous ::::::: freezing ::::::: fraction : (Fig. 6e)seems to support this hypothesis, although the changes 335 in overall ICNC are very small and not statistically significant (Fig. 6f). The decrease in cloud frequency (Fig. 6h), could also contribute to these changes in the shortwave RF, especially at higher S crit , where the competition bewteen homogeneous and hetereogenous ::::::: between :::::::::::: homogeneous ::: and :::::::::::: heterogeneous : freezing which drives the negative Twomey effect can be expected to be less important . ::: (see ::::: again :::: Fig. :::: 6e). The warming effect in the shortwave spectrum is counteracted by a cooling (i.e., a reduced warming) in the longwave (Fig. 6b), due to the fact that larger IC usually sediment more efficiently and reduce the 340 lifetime of the cirrus clouds, resulting therefore in a decrease of their (background) warming effect and hence in a cooling. This is supported by the overall decrease in cloud frequency shown in Fig. 6h. The cooling (reduced warming) effect in the longwave is further enhanced when the nucleation efficiency of aviation soot is high (S crit = 1.2): in this case also the clearsky RF (Fig. 6d) significantly contributes to the cooling. A possible aviation-induced (or aviation-enhanced) dehydration of the affected air masses is suggested here, resulting from the increased deposition of supersaturated water vapor on the very 345 efficient INPs from aviation, which are then rapidly removed via sedimentation (Jensen et al., 2001. This reasoning is supported by the marked decrease in total water (sum of water vapour and ice water, Fig. 6g) and in cloud frequency (Fig. 6h): here small ( 1%) but statistically significant decreases in the simulations with S crit = 1.2 are evident. For lower ice nucleation efficiencies (S crit ≥ 1.3), the changes are about one order of magnitude smaller and mostly not statistically significant. We can therefore conclude that the aviation-soot INPs can effectively enhance the dehydration of the upper troposphere and induce 350 a statistically significant cooling effect when high nucleation efficiencies are assumed. For lower efficiencies (higher critical saturation ratios), the warming (reduced cooling) in the shortwave , :::::: appears :: to ::: be ::::: more :::::::: important : (possibly due to enhanced cloud lifetime ( : a :::::::: reduction :: in ::::: cloud ::::::::: frequency, Fig. 6h) , appears to be more important and leads to a moderate :::::: slightly ::::::: positive overall RF effect.
The above analysis is based on globally averaged values, but large regional variations can be expected. This is because of the 355 uneven geographical distribution of aviation-soot and other INPs (Figs. 1 : 4 : and S1) and of cirrus clouds, but also because of the large spatial variations in the vertical velocity simulated by the model as shown in Fig. 2. As discussed above, the latter effect is particularly important, as it controls the prevalence of homogeneous over heterogenous :::::::::::: heterogeneous ice formation regimes    1.2, Fig. 7a,d,g), the net cooling effect is common to all regions and particularly strong in the Northern Hemisphere, where the aviation traffic is most intense and aviation soot shows the largest values of mass and number concentrations ( Fig. 1 : 4). This cooling effect in the Northern Extratropics :::::::::: Extra-tropics : decreases gradually with decreasing ice nucleation efficiency S crit . For low efficiencies (S crit = 1.4, Fig. 7c,f,i) 365 the warming effect from the Southern Extratropics :::::::::: Extra-tropics : and Tropics dominates and results in a global warming effect.
A reason for this pattern could be the smaller mean vertical velocities and the relatively clean background compared to the Northern Hemisphere. The additional aviation-emitted soot in this region could lead to enhanced heterogeneous nucleation and, due to the smaller cooling rates, to less homogeneous freezing, thus strengthening the negative Twomey effect.
As above, decomposing the RF effect in its different parts helps to disentangle the physical reasons for these aviation-370 induced effects on the RF. This is shown in Figs. S2-S5 ::::: S2-S6 : in the Supplement. The warming effect in the shortwave ( Fig. S2) is characterized by a very noisy pattern, with a prevalence of strong local warming effects especially in the Northern Extratropics :::::::::: Extra-tropics, although the generally low confidence level (< 90%) of the results hampers the identification of coherent patterns. The low values of the clear-sky RF (Fig. S4) confirm the dominance of cloud effects in the shortwave. The longwave effect (Fig. S3) shows a distinct and strong cooling over the continental regions of the Northern Extratropics :::::::::: Extra-tropics, 375 especially at high f act , with a slight dependency on S crit . This pattern very closely matches the ones of the orographic vertical velocity ::: one :: of ::: the :::::::::::: homogeneous ::::::: freezing ::::::: fraction (Fig. 2c). In ::: 3f): :: in : these regions, homogeneous ice formation is therefore expected to dominate the total ICNC, while aviation-soot can effectively compete against this process for the available water vapour. Its impact appears to be very effective regardless of the critical supersaturation, as long as the latter remains below the homogenous ::::::::::: homogeneous freezing threshold and a sufficient fraction (i.e. 10%) of aviation soot particles can be active as 380 INPs. The consequence of this is a marked decrease in the cloud frequency (Fig. S6), which then results in the reduced longwave warming. Of course, the shortwave radiation component (Fig. S2) is also affected, and indeed shows a warming over the continents, but the signal is very noisy and not as evident as in the longwave. A possible explanation for this could be that other shortwave forcers like low-level clouds are contributing to the model variability, hence enhancing the noise, while in the longwave the cloud radiative effects are mostly due to cirrus clouds only. At high nucleation efficiencies (S crit = 1.2), a significant 385 cooling is evident also in the clear-sky longwave RF (Fig S5), with a pretty uniform distribution in the extratropics :::::::::: extra-tropics, possibly due to a dehydration effect leading to a reduction in water vapour concentration and a resulting decrease in watervapour-induced warming. The clear-sky longwave effect rapidly disappears at higher S crit , and in the Northern-Extratropics ::::::: Northern ::::::::::: Extra-tropics : it turns to a warming, thus contributing to the decrease of the RF with S crit in this region.
The results of our simulations show therefore that the largest (in absolute terms) and most statistically significant effect is 390 simulated for large efficiencies of aviation soot, i.e. S crit = 1.2 and f act = 10%, resulting in a cooling effect of −35 mW m −2 .
Good nucleation abilities for aircraft soot (S crit 1.2) could be considered realistic for soot particles undergoing cloud preprocessing, e.g. in contrails. Laboratory measurements (Mahrt et al., 2020) show, however, that only large soot particles with a diameter above ∼ 400 nm may gain improved ice nucleation abilities resulting from such a pre-processing effect, but particles of this size are rare in the upper troposphere. Considering the measured size distribution by Petzold et al. (1999) as in Sect. 3, 395 one can estimate the fraction of particles with diameter larger than 400 nm to be of the order of 0.001%, i.e. two orders of magnitude below the lowest f act considered in this study (0.1%). The parameters measured by Petzold et al. (1999) refer to a young plume, so aging processes and soot aggregation within contrails might contribute to increase the fraction of larger particles in the population, but it is unlikely that a significant fraction of aviation soot will end up in the size range where RF (all-sky) pre-processing is effective, as also confirmed by aircraft measurements of ice residuals in cirrus and contrail cirrus (Voigt et al., Our results generally point towards a relatively small aviation-soot cirrus effect, of the order of ten ::: tens ::: of mW m −2 (in absolute terms), with statistically non-significant figures in several cases. This is in contrast with the estimates by Zhou and Penner (2014), Penner et al. (2018) and Zhu and Penner (2020), who reported larger effects, of the order of hundred mW m −2 (in absolute terms), also testing various assumptions on the ice nucleation abilities of aviation soot and experimenting with dif-405 ferent parametrizations for ice nucleation. Due to the high complexity of the involved models and the coupling between their different components (aerosol, clouds, radiation and dynamics), it is challenging to track down the reasons for this disagreement, which could be due not only to different models' schemes and parametrizations, but also to the diverse configurations and tuning approaches. For example, Gettelman and Chen (2013) used a similar model (CAM5) as the aforementioned studies, but found no statistically significant effect of aviation soot on natural cirrus clouds, thus being more consistent with the results presented here. McGraw et al. (2020) used a model version from the same family (CESM2, which is based on CAM6 for the atmospheric component), also concluding that the impact of aviation soot is not statistically significant. This was also the case in Hendricks et al. (2011), who used an ECHAM-based GCM as the present one and the same cirrus clouds parametrization, albeit with different aerosol and cloud microphysical schemes. :::::::::::::::::::: Kärcher et al. (2021) also :::::: argued :::::: against ::::: large ::: RF ::::: effects ::::: from :::::: aviation ::::::::: soot-cirrus ::::::::::: interactions, ::::::: pointing :: to ::: the ::::::::: limitations :: of ::::: global ::::::: models :: in :::::::::: representing ::: key ::::::::: processes :: as : a ::::::: possible :::::: reason 415 :: for :::::::::::: overestimated :::::: effects. : In conclusion, a consensus among modelling groups on the aviation-soot cirrus effect is still lacking and future research should consider working towards a concept for a model intercomparison study with common assumptions and detailed analyses of the differences among model configurations and tuning approaches.
We finally recall that the sensitivity experiments conducted in this section are focusing on the ice nucleation abilities of aviation soot, while the properties of background soot (i.e., soot originating from other anthropogenic and biomass burning 420 sources) are not varied and are assumed to be S crit = 1.4 and f act = 0.25% as in Hendricks et al. (2011, see also Sect. 3). As a further sensitivity study, we perform two simulations assuming S crit = 1.2 for background soot (simulations BASE-BG12 and S12F10-BG12, see Table 1). This experiment pair results in an aviation soot-cirrus effect of −25.7 mW m −2 (99.2% confidence level), which is lower (in absolute term) than the corresponding case calculated above with S crit = 1.4 for background soot (and S crit = 1.2 for aviation soot in both cases). This was to be expected, since increasing the ice nucleation abilities of background 425 soot enhances the competition with aviation soot and the other INPs for available water vapour, thus reducing the impact of aviation soot on natural cirrus clouds. The properties of background INPs could therefore be a further source of uncertainties for the aviation-soot cirrus effect and will be the subject of a companion study.

Dependency of the aviation soot-cirrus effect on the model representation of the vertical velocity
Besides the ice nucleating properties of soot, another major source of uncertainties in model studies attempting to quantify the 430 climate impact of aviation on cirrus clouds is the representation of vertical velocities. In the cirrus parametrization adopted here (Kärcher et al., 2006), the vertical velocity is a key parameter, as it controls the critical supersaturation, the competition between homogeneous and heterogeneous freezing , ::: (Fig. ::::: 3e,f), : as well as the nucleation rate in cirrus clouds. Ice formation in cirrus clouds is strongly influenced by small scale updrafts, of the order of 1-10 cm s −1 (Barahona et al., 2017), but due to their coarse spatial resolution, global models are not able to represent such phenomena in sufficient detail, and rough approximations are 435 usually introduced to account for them. As explained in Sect. 3, in the EMAC-MADE3 configuration adopted here, the subscale vertical velocity is accounted for by adding an extra-term proportional to the square root of the turbulent kinetic energy to the large-scale, grid-box mean, vertical velocity. In the vicinity of mountain ranges, this term is replaced by the contribution of orographic waves to small-scale fluctuations in the vertical velocity, based on the parametrization by Joos et al. (2008), which could lead to stronger updraft of the order of several tens of centimeters per second.

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To further explore the limitations behind this approach and their possible impact on the estimated aviation-cirrus effects presented in Sect. 4.2, we perform an additional set of sensitivity experiments, prescribing a geographically uniform constant (i) -Cloud frequency above 400 hPa (f-i) depict the aviation-soot-induced relative changes in ICNC from homogeneous freezing, ICNC, total water (as the sum of water vapour and ice water), and cloud frequency, respectively, all spatially averaged above 400 hPa and over cloudy and cloud-free model grid-boxes.
The values above or below each bar indicate the confidence level. Significant and non-significant results are further marked using filled and hatched bars, respectively.
vertical velocity in the range from 2 ::::::: cm s −1 to 50 cm s −1 . Such an assumption is of course not realistic, but the goal here is not to provide a refined estimate on the aviation soot-cirrus effect, but rather to understand the role of dynamic forcing on the results and hence to estimate the uncertainties associated with the RF effects quantified in the previous section. A prescribed 445 constant uniform field allows, for example, to explore regions of the world which could be important for the cirrus effect, but where the model does not simulate a sufficiently strong updraft for ice formation to occur. Due to the large amount of computational resources required, we restrict this sensitivity analysis to a single pair of assumption :::::::::: assumptions for the ice (i) -Cloud frequency above 400 hPa 2 cm s 1 5 cm s 1 10 cm s 1 20 cm s 1 50 cm s 1 Figure 9. :: As :::: Fig. : 8, ::: but ::::::: showing :::: zonal ::::::: averages. ::::: Values :::: with : a :::::::: statistical ::::::::: significance :::: below :::: 95% ::: are ::::: drawn :: in :::: gray.
nucleation abilities of aviation soot. To facilitate the analysis, we select the case S crit = 1.2 and f act = 10%, which is more likely to return statistically significant results, as demonstrated in Fig. 5.

Impact of nudging
All the results discussed so far refer to model simulations performed in nudged mode, i.e. relaxing meterological :::::::::::: meteorological variables (temperature, divergence, vorticity and surface pressure) towards reanalysis data. This approach has been chosen in order to maximize the chances to obtain statistically significant results for the small climate effects and radiative forcings investigated here ::: RFs :::::::::: investigated ::::: here, and it is a common practice in this kind of studies. This technique ensures that the as the one represented by the impact of aviation soot on cirrus clouds. However, nudging is known to have an impact on simulated temperature profiles (Schultz et al., 2018), in turn affecting the heating rates and all kinds of radiative adjustments 495 in the atmosphere, which implies a : potential influence on the effective radiative forcing ::: RF of the climate perturbation under consideration (e.g., Forster et al., 2016;Johnson et al., 2019). In an attempt to characterize the impact of nudging on our results, we repeat the BASE, S12F10 and S14F10 simulations in free running mode (BASE-FREE, S12F10-FREE and S14F10-FREE, respectively) and in nudged mode but without relaxing temperature (BASE-FREE-T, 12F10-FREE-T :::::::::::::: S12F10-FREE-T : and S14F10-FREE-T, respectively, see Table 1). In these simulations, short term feedbacks on temperature (and in the FREE The resulting all-sky RFs from the aviation soot-cirrus effect are compared in Fig. 10 for the three configurations (nudged, nudged without temperature and free) and the two values of the S crit parameter. As expected, the free running simulations are characterized by a much larger statistical noise, which prevents to draw any robust and statistically significant conclusion on the investigated effect and supports our choice for a nudged configuration. The results of the nudged experiments are, however, 510 consistent with the free running ones, since they lie within the uncertainty ranges. The two nudging methods (with and without temperature) are highly consistent for S crit = 1.2, which further support the robustness of the results dicussed ::::::: discussed : in this work, although a feedback of temperature nudging on the dynamics cannot be excluded. For S crit = 1.4, the two nudging methods show RFs with opposite sign, although both are statistically non-significant at the 95% confidence level, therefore no conclusions can be drawn in this case. Nevertheless, this sensitivity study confirms the main conclusions of this work, that 515 large aviation soot-cirrus effects can be simulated only under the assumptions of good ice nucleation ability of aviation soot particles (S crit = 1.2).

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Our results partly support the findings of Liu et al. (2009), who also reported a change of sign in the aviation-soot cirrus effect from negative to positive when increasing the critical saturation ratio from 1.2-1.3 to 1.4, although our RF values are considerably smaller, possibly due to the much lower active fraction assumed in this study: 0.1-10% compared to 100%.
Systematically larger negative RFs are found also by the studies of Penner et al. (2009), Zhou and Penner (2014), Penner et al. (2018 and Zhu and Penner (2020), all assuming generally good ice nucleation abilities for aviation soot. Our study 535 therefore agrees with these in terms of the sign of aviation-soot effect, but there is a clear disagreement in the magnitude. This could be due to the details of the cloud microphysical parametrizations, to differences in the model setups (e.g., in the use of nudging) or in the representation of the vertical velocity, which can have a large impact on the resulting effects, as shown by our idealized sensitivity experiments. The model setup adopted here is very close to the one used in Hendricks et al. (2011), who used a similar base model (ECHAM4) and the same cirrus parametrization (Kärcher et al., 2006). They nevertheless found 540 a non-significant impact of aviation soot on natural cirrus clouds, which can possibly be ascribed to the use of a free-running model setup in that study, while the nudging mode used here likely helped to extract a statistically significant information from the model. Non-significant results were also found by Gettelman and Chen (2013) and, more recently, by McGraw et al. result of this paper is archived at the German Climate Computing Center (DKRZ) and can be made available to members of the MESSy community upon request. The output of the model simulations discussed in this work is available at https://doi.org/10.5281/zenodo.5146195 (Righi, 2021).
Author contributions. MR conceived the study, designed and performed the simulations, analysed the data and wrote the paper. JH conceived 580 the study and contributed to the model configuration, to the interpretation and to the text. CB contributed parts of the model code and configuration, to the interpretation and to the text. Financial support. This study was supported by the DLR aviation research program (Eco2Fly project), by the DLR transport research program (TraK project), by the DLR space research program (MABAK project) and by the European Commission via their Horizon 2020 E., and Takahashi, K.: Global emissions pathways under different socioeconomic scenarios for use in CMIP6: a dataset of harmonized