Atmospheric aerosol particles can exert various influences on the climate system. Aerosols change the Earth's radiation budget by directly interacting with solar and terrestrial radiation through absorption and scattering . Importantly, aerosol particles can also act as cloud condensation nuclei and ice-nucleating particles, consequently influencing the formation of cloud droplets and ice crystals and leading to additional indirect climate effects . However, these aerosol–cloud interactions still pose several remaining open questions and are the subject of ongoing research activities .

Especially the knowledge about the effect of ice-nucleating particles (INPs) on cirrus clouds and the resulting climate effects is highly uncertain . Cirrus clouds typically exert a warming effect on the global climate due to their strong absorption of outgoing terrestrial radiation that exceeds the reflection of solar radiation . INPs contribute to the climate impacts of cirrus by changing the microphysical properties of cirrus clouds. Compared to the homogeneous freezing of liquid aerosols, INPs can initiate heterogeneous nucleation of ice crystals at lower supersaturations with respect to ice . The resulting competition mechanism between heterogeneous and homogeneous nucleation for the available supersaturated water vapour critically depends on the abundance of INPs and their freezing properties and can induce substantial changes in the microphysical properties of clouds, e.g. via changes in ice crystal number concentration and ice crystal sizes, which in turn influence the cloud optical thickness . To characterize the global radiative impact of INPs the term “radiative forcing” (RF) is used, which is defined as the net change of the Earth’s energy balance , i.e. downward shortwave plus upward longwave radiative flux, due to some imposed perturbation (the impact of INPs on cirrus clouds, in this study).

In the past, several global modelling studies were performed to evaluate the radiative impact induced by INP effects on cirrus and mixed-phase clouds. While most studies agree on the sign of the global INP effect, i.e. a net negative radiative forcing leading to a cooling of the climate system, there are conflicting results concerning its magnitude. Estimates range from statistically insignificant effects to negative forcings ranging from a few -10 to several -100 mW m-2 or even positive forcings of the order of 100 mW m-2 . However, the comparison of different studies is complicated as (i) different model systems and techniques are used, (ii) different INP species with varying freezing properties are considered, and (iii) different sensitivities and effects are analysed. There are many reasons for this large range of possible climate effects, e.g. the complexity of the involved processes and the necessity for assumptions and parameterizations to represent sub-grid processes at the large-scale global model resolution. Part of the uncertainties in the INP–cirrus effect is related to the assumptions for the still poorly understood ice-nucleating properties of INPs. These are the critical saturation ratio (Sc) at which the INPs can initiate freezing and the active fraction (fact) of the aerosol particle population that can act as INPs. Typically, mineral dust and soot particles have been considered in global models for ice nucleation in the cirrus regime . However, our knowledge on the global INP population is still uncertain, as several recent studies reported a strong ice-nucleating potential of INP species that previously had not been considered for cirrus ice nucleation, e.g. glassy organic particles , and crystalline ammonium sulfate . Furthermore, it has been shown that the dynamic forcing, induced by the vertical velocities of the air parcels during the freezing process, is crucial for the competition between heterogeneous and homogeneous nucleation . Despite the importance of subgrid-scale variabilities of updraught speeds, global models are not able to resolve these due to their coarse resolution and need to adopt simplified representations, which can introduce additional uncertainties .

We analyse different aspects of INP-induced cirrus modifications in a global aerosol–climate model with the goal of exploring the large uncertainties in the understanding of the aerosol–cirrus effect. We employ the atmospheric chemistry general circulation model EMAC (ECHAM/MESSy Atmospheric Chemistry model; ) including the MESSy (Modular Earth Submodel System) aerosol microphysics submodel MADE3 (Modal Aerosol Dynamics model for Europe, adapted for global applications, third generation; ). The MADE3 aerosol is coupled to (cirrus) clouds via a two-moment cloud scheme as described by . In addition to mineral dust and soot, glassy organics and crystalline ammonium sulfate particles are represented as INPs in the model as described in detail by .

We investigate the impact of different subsets of the INP population, e.g. the effect of anthropogenic INPs. Also, the impact of ammonium sulfate INPs is evaluated, as recently reported a potentially large impact of this INP type. We further analyse the influences of different assumptions for the ice-nucleating properties of the INPs. In order to explore the sensitivity of INP–cirrus effects to the model dynamics, we perform mechanistic studies by varying the representation of vertical velocities in the model. We discuss possible sources of uncertainties in the simulated INP effects, e.g. due to the use of model nudging, dependencies on the applied model resolution, and model assumptions regarding the parameterization of INP–cirrus interactions. Additionally, we analyse the effect of highly efficient INPs, which have been proposed to engineer climate and reduce global warming by cirrus cloud seeding . By designing the simulation experiments for this analysis according to the study by , we improve the comparability and aim to explore the robustness of the resulting quantifications of the INP–cirrus effects presented here by comparing with a similar model study.

This paper is organized as follows. In Sect. 2 we provide an overview on the modelling framework EMAC, including the aerosol submodel MADE3 and its coupling to (cirrus) clouds. Results on the effect of INPs on cirrus clouds and radiation are presented in Sect. 3, regarding the impact of the assumed ice-nucleating properties of INPs, the effect of different INP species, the role of the representation of vertical velocities in the model, and the impact of highly efficient INPs proposed for cirrus cloud seeding. The work presented in this paper is in part based on the PhD thesis by Christof G. Beer , and some of the text therein is similar.

The EMAC model is a global numerical chemistry and climate simulation system and includes various submodels that describe tropospheric and middle-atmosphere processes. It uses the second version of MESSy to connect multi-institutional computer codes. The core atmospheric model is the ECHAM5 (fifth-generation European Centre Hamburg) general circulation model . In this work we apply EMAC (ECHAM5 version 5.3.02, MESSy version 2.54) in the T42L41 configuration with spherical truncation of T42 (corresponding to a horizontal resolution of about 2.8°×2.8° in latitude and longitude) and 41 non-equidistant vertical layers from the surface to 10 hPa. The simulated time period covers the years 2000 to 2010, while the year 2000 is used as a spin-up and excluded from the evaluation. Most simulations presented here are performed in nudged mode; i.e. model meteorology (temperature, winds and logarithm of the surface pressure) is relaxed towards ECMWF reanalyses (ERA-Interim; , ) for the simulated time period. The original reanalysis data with a spectral horizontal resolution of T255 (0.54°×0.54°) and a vertical resolution of 60 levels from the ground up to 0.1 hPa have been re-gridded to the model resolution used in this study. The nudging data have a temporal resolution of 6 h. Additional sensitivity experiments are performed in free-running mode to analyse the effect of nudging on the results also covering the time period 2001–2010, using prescribed long-term means (2001–2010) of sea surface temperature and sea ice concentration from the Met Office Hadley Centre dataset (HadISST; , ).

The aerosol microphysics submodel MADE3 simulates different aerosol species in nine log-normal modes that represent different particle sizes and mixing states. Each of the MADE3 Aitken-, accumulation-, and coarse-mode size ranges includes three modes for different particle-mixing states: particles fully composed of water-soluble components, particles mainly composed of insoluble material (i.e. insoluble particles with only very thin coatings of soluble material), and mixed particles (i.e. soluble material with inclusions of insoluble particles). A detailed description of MADE3 and its application and evaluation as part of EMAC is presented in . The optical properties of aerosols and clouds are calculated in the EMAC submodels AEROPT and CLOUDOPT , respectively, according to input from OPAC (optical properties for aerosols and clouds; , ). The OPAC package uses basic optical properties from .

The EMAC–MADE3 set-up applied here is in large part based on the set-up described in . We use the recent CMIP6 (Coupled Model Intercomparison Project, phase 6) emission inventory for anthropogenic and biomass burning emissions of aerosols and aerosol precursor species for the year 2014. Prescribed emission data are provided in a horizontal resolution of 0.5°×0.5°. The re-gridding to the actual model grid is performed during the model simulation using the algorithm NCREGRID . Since our study focuses on the radiative effects of aerosols on (cirrus) clouds, the concentrations of radiatively active gases other than water vapour (i.e. CO2, CH4, N2O, O3, and chlorofluorocarbons) are prescribed by means of global distributions. In order to simulate the effect of anthropogenic emissions on the INP–cirrus effects, a pre-industrial simulation is performed considering year 1750 emissions for anthropogenic and biomass-burning sources, instead of the 2014 (present-day) ones. Mineral dust emissions are calculated according to the online emission scheme of , as described and evaluated in . In order to isolate the effect of anthropogenic emissions, mineral dust emissions and all other natural emissions in the model (i.e. biogenic emissions, volcanic emissions, NOx emissions from lightning, emissions of secondary organic aerosol (SOA) precursors, dimethyl sulfide (DMS) emissions, and wind-driven sea spray emissions) are kept constant at their present-day value in all simulations performed here.

In this study, EMAC–MADE3 is employed in a coupled configuration, which includes a two-moment cloud microphysical scheme based on , employing a parameterization for aerosol-driven ice formation in cirrus clouds following . The scheme considers the competition between various ice formation mechanisms for the available supersaturated water vapour, i.e. homogeneous freezing of solution droplets, deposition and immersion nucleation induced by INPs, and the growth of pre-existing ice crystals. By way of simplification the scheme does not represent the whole freezing spectrum (from the freezing onset to the homogeneous freezing threshold) but considers one singular point in the spectrum, e.g. corresponding to the freezing onset. In each of the heterogeneous freezing modes the ice-nucleating properties of the INPs are represented by two parameters, namely the active fraction (fact) of ice-nucleating particles, which actually lead to the formation of ice crystals, and the critical supersaturation ratio with respect to ice (Sc), at which the freezing process is initiated. In addition to choosing fact representative of the freezing onset, we also consider a larger fact value representing the midpoint between the freezing onset and the homogeneous freezing threshold. With this sensitivity experiment we aim to explore the range of possible forcings due to uncertainties in the freezing properties of INPs also accounting for increasing activated fractions during the freezing process, which might be more representative for the total number of activated particles. We discuss possible sources of uncertainties influencing the simulated results due to the applied cirrus cloud parameterization in Sect. . The model set-up has been extensively tuned and evaluated with respect to various cloud and radiation variables by with further model improvements described in .

The aerosol-driven ice formation scheme includes additional model developments to represent crystalline ammonium sulfate (AmSu) and glassy organic particles (glPOM), in addition to mineral dust (DU) and soot (BC), as ice-nucleating particles. The model is able to distinguish between aviation soot and soot from other sources ; however, we choose the same freezing properties for these two soot classes in this study due to the uncertain freezing properties of aviation BC. The model improvements regarding glassy organics and crystalline ammonium sulfate were described in detail by and are briefly summarized here. Importantly, the particle phase state is tracked for glassy organics and crystalline ammonium sulfate, as only the respective glassy or crystalline phase facilitates ice nucleation. Natural SOA precursor emissions (e.g. isoprene, monoterpenes, and other volatile organic compounds) according to are considered for the glassy organics tracer in the model. We use a simplified representation for the glass-transition temperature Tg, depending on the relative humidity (RH). For temperatures T<Tg liquid SOA particles are transformed into a semi-solid, glassy state. Tg(RH) for the SOA proxy citric acid is calculated according to . For crystalline ammonium sulfate, a dedicated phase transition formulation via a hysteresis process depending on the relative humidity history is considered in the model. Efflorescence of aqueous ammonium sulfate particles occurs at a lower relative humidity than the deliquescence of ammonium sulfate crystals. The number concentrations of potential INPs are calculated for the different ice formation modes in the mixed-phase and the cirrus regime according to the procedure described in and adapted by considering the additional INP types ammonium sulfate and glassy organics. Different mixing states of particles are taken into account for the simulated ice-nucleation processes. For example, the model distinguishes between immersion freezing of mixed mineral dust particles and deposition freezing of insoluble mineral dust. The freezing properties, i.e. values for fact and Sc, for the different INP species are assumed according to and are summarized in Table .

In a set of sensitivity experiments we analyse the influence of variations in the updraught velocities on the INP–cirrus effects. In the reference case vertical velocities are parameterized in the model to account for the subgrid-scale variability of updraught velocities, which cannot be resolved with the coarse model resolution. As described in , the total updraught speed is represented as the sum of the large-scale vertical velocity, a turbulent component which is proportional to the square root of the turbulent kinetic energy (TKE; , ), and an additional term accounting for orographic gravity waves calculated by the orographic gravity wave submodel (OROGW) in EMAC, based on the parameterization by . The resulting global distribution of simulated vertical velocities (including also the single components) can be found in . To further investigate these dynamic influences on the INP–cirrus effects, we also consider an idealized representation of the vertical velocity. We prescribe constant values of the vertical velocity across the whole globe in the range from 1 to 50 cm s-1 to explore the full range of updraught speeds typically occurring in the atmosphere . This also enables the investigation of INP effects in regimes not covered by the updraught parameterization considering TKE and orographic gravity waves mentioned above. An overview of the different simulation experiments presented here is provided in Table .

As described in the previous section, the simulations presented in this study have been performed using the T42L41 model resolution, representing a horizontal resolution of about 2.8°×2.8° in latitude and longitude and 41 vertical layers. This model resolution is different from the one applied in previous studies by , i.e. T63L31 (corresponding to a horizontal resolution of 2.8°×2.8° and 31 vertical layers). For the present study focusing on the climate impact of INPs, we rely on the extensive model tuning of cloud and radiation properties by , applying the T42L41 resolution. Additionally, performing the large number of simulations presented here would not be feasible applying the T63L31 model set-up, which would require considerably more computational resources due to the increased horizontal model resolution. However, the lower horizontal resolution used in this study also has some drawbacks, which are discussed in the following. As described in , a lower horizontal model resolution can introduce a positive bias for aerosol number concentrations compared to observations, which are most pronounced in the upper troposphere. In Fig. S1 in the Supplement, we present a comparison of aerosol number concentrations for the different model resolutions, which complements Fig. 5 of with the results for the T42L41 resolution applied in the present study. Aerosol number concentrations above 400 hPa are about a factor of 2 to 3 larger in the T42L41 resolution compared to T63L31. As discussed in , this could be related to overestimated upward transport, possibly in convective plumes, or underestimation of aerosol scavenging through an efficiency of the wet deposition processes that is too low in the model.

Figure  shows the global distributions of the simulated INP number concentrations as shown in (; Fig. 5) but for the T42L41 model resolution. While the main findings and conclusions discussed in still hold for the decreased (increased) horizontal (vertical) model resolution, the simulated INP number concentrations are about a factor of 2 larger compared to the INP concentrations presented in for the T63L31 model resolution. The effect of a lower horizontal model resolution has to be considered for the interpretation of the resulting climate forcings due to INPs as presented here and would likely result in larger INP effects due to the increased concentration of INPs. Notably, the model resolution can also influence cloud formation in the model, e.g. via changes in the simulated vertical velocity, which acts as a driver for the supersaturation, and hence the ice-nucleation processes in the model can be influenced by the applied model resolution. In general, the differences in cloud frequency and vertical velocities between the T42L41 and T63L31 model resolutions are smaller compared to the differences in INP numbers, i.e. mostly below 50 % in the cirrus regime (data not shown). Nonetheless, the applied model resolution can influence the simulated INP–cirrus effects, and this impact should be the focus of future studies.

In this study we applied the EMAC–MADE3 global aerosol climate model coupled with a two-moment cloud microphysical scheme to quantify cirrus cloud and radiation modifications due to heterogeneous freezing induced by ice-nucleating particles. In addition to the widely investigated INP species, mineral dust and soot, we also analysed the effects of ammonium sulfate and glassy organic particles, which are only rarely considered as INPs in global modelling studies. Typical mechanisms for INP-induced cirrus effects, as simulated in this study, include the reduction in ice crystal number concentrations, increased sedimentation of larger ice crystals, resulting in a thinning of cirrus clouds, and also regional reductions in cirrus cloud occurrence. On the other hand, cirrus cloud coverage can increase, as INPs freeze at lower supersaturations compared to homogeneous freezing, resulting in earlier cirrus cloud formation during adiabatic cooling in updraughts and consequently increased occurrence frequencies.

The interplay of the above cirrus modifications results in a net negative global radiative forcing due to INP–cirrus interactions, i.e. a cooling effect, of -28±21 mW m-2. Assuming an enhanced ice-nucleating potential of INPs (by choosing a larger activated fraction) leads to about a factor of 2 larger INP–cirrus effects and results in an ERF of -55±31 mW m-2. The simulated forcings presented here are mostly on the lower end of the range of simulated cooling effects by previous global model studies e.g.. The radiative impact of glassy organic INPs simulated here is small and mostly not significant, suggesting that heterogeneous ice nucleation of glassy organic INPs has a negligible role on the global scale. This is in line with low glassy organic INP concentrations simulated by and low ice-nucleating abilities reported in recent laboratory studies e.g.. On the other hand, adding crystalline ammonium sulfate to an INP population consisting of mineral dust and soot results in an additional ERF of -22±17 mW m-2, which is nearly as large as the global effect of mineral dust and soot alone, i.e. -27±23 mW m-2. The strong impact of ammonium sulfate is related to its large simulated INP concentrations, especially in the Northern Hemisphere . We analysed the effect of anthropogenic INPs, i.e. black carbon and ammonium sulfate related to the combustion of fossil fuels and the use of ammoniacal fertilizers, by comparing the simulated INP–cirrus effects between present-day (2014) and pre-industrial (1750) conditions. Anthropogenic INP influences are largest in the Northern Hemisphere and amount globally to an ERF of -29±33 mW m-2. However, this anthropogenic INP–cirrus forcing is small compared with the current IPCC best estimate of the total effective radiative forcing due to aerosol–cloud interactions of -1.0±0.7 W m-2 .

We analyse and discuss the uncertainties regarding the INP–cirrus effects presented here. The use of model nudging can influence the simulated INP effects due to suppressing feedback mechanisms that would occur in the free-running mode. However, simulation results using the nudging technique are similar to those performed in the free-running mode. Additionally, the use of model nudging is important to achieve statistically significant results. We discuss possible model dependencies on the applied model resolution, which can influence the simulated INP concentrations, as well as cloud formation processes. For example, an increased horizontal grid resolution can lead to reduced INP number concentrations (about a factor of 2 in the cirrus regime). Therefore, the impact of the applied model resolution on the resulting climate forcing due to INPs should be the focus of future studies.

In additional sensitivity experiments we analyse the role of highly efficient INPs, e.g. proposed for cirrus cloud seeding as a means to reduce global warming by climate engineering. Our results show that this approach often results in the contrary effect, i.e. positive effective radiative forcings of up to 86 mW m-2, depending on the number concentration of INPs. Choosing INP concentrations that are too large often risks an overseeding of the clouds and results in strongly increased cirrus occurrence, as also stated by , , and , making the feasibility of this climate engineering approach highly uncertain.

The INP–cirrus effects shown here are strongly dependent on the representation of the vertical velocity in the model, which controls the adiabatic cooling rate during the uplifting of air parcels. By performing sensitivity experiments with a prescribed, geographically uniform, vertical velocity, we show that increasing the vertical velocity results in larger simulated INP–cirrus effects, e.g. global ERFs of -42 mW m-2 (at 1 cm s-1) to -340 mW m-2 (at 50 cm s-1). This strong sensitivity to the prescribed vertical velocity highlights the crucial role of the dynamic forcing for the simulated climate impact of INPs. The larger impact of changes in the vertical velocity with respect to the study by , where increased forcings of up to a factor of 2 were reported, is due to the differences in the investigated effects. While analysed the impact of aviation soot INPs under varying updraughts, this study investigates the effect of all INPs with respect to the case of purely homogeneous freezing. The present study corroborates the sign of the INP–cirrus effect, i.e. a cooling impact, as simulated in most previous global model studies . However, our results disagree with some previous studies in terms of the magnitude of the simulated climate forcings. This highlights the still large uncertainties in simulated INP-induced cirrus effects and the need for detailed analyses to investigate the causes of these large model diversities. Importantly, the present study suggests a strong contribution of ammonium sulfate to the simulated INP–cirrus effect, also regarding its influence on the anthropogenic INP–cirrus impact, and should be addressed in future studies.

In the future, more precise knowledge of the ice-nucleating properties of the different INPs from measurements, especially regarding ammonium sulfate and glassy organics, could help to further constrain their global impact in climate simulations. Additionally, research on the role of cloud-processing of INPs and its potential to enhance their ice-nucleating abilities needs to be continued. Considering the strong impact of ammonium sulfate INPs shown here, dedicated observations on atmospheric ammonium sulfate particles and further model studies could help to better constrain their climate impacts. With regard to the strong sensitivity of the simulated INP–cirrus effects on the vertical velocities in the model, dedicated field observations on atmospheric updraught speeds could help to improve the representation of vertical velocities in the model. A detailed combination of model–observation analyses on INP-induced cirrus modifications employing different measurement techniques like in situ aircraft observations, lidar measurements, and satellite remote sensing could help to constrain critical model parameters and in turn improve the simulated INP–cirrus effects. Additionally, recent advancements in the representation of INP-induced cirrus formation e.g., e.g. by explicitly following the freezing process along the whole activation spectrum instead of using sharp freezing thresholds, could help to improve the resulting simulated climate impacts. Regarding the wide range of simulated INP–cirrus effects from global model studies, performing commonly designed experiments in the context of intercomparison projects could increase the models inter-comparability and could help to better understand the diversity of simulated results. Notable examples of such inter-comparison exercises are the CMIP activities e.g. and the AeroCom community (e.g. , ; see also https://aerocom.met.no/, last access: 28 February 2024). Recently, and presented model analyses on the aviation soot–cirrus effect. The addition of ammonium sulfate and glassy organics as background INPs could lead to additional competitions between the different INP species and impact the simulated aviation soot effect, which should be re-evaluated in the future.