The cloud particle measurements were obtained using the Cloud Combination Probe (CCP) and the Precipitation Imaging Probe (PIP), mounted on the HALO aircraft. Together, these instruments provide nominal cloud particle size distributions from 2 to 6400 µm. A detailed description and characterization of the instrumentation and data set are available in and . Further instrumentation of the mission is described in .

The Cloud Droplet Probe (CDP), part of the CCP, is a forward scattering probe that sizes and counts particles in the 2–50 µm range based on Mie theory . Based on inter arrival time analysis , no evidence of shattering artifacts was identified in the data, attributed to the aerodynamic tip design of the instrument arms and the typically low particle concentration in cirrus .

The Cloud Imaging Probe (CIPgs) and PIP are optical array probes that record two-dimensional images of particles by capturing their shadow projections on a laser-illuminated 64-diode array, as the particle passes the sample area of the instrument . The CIPgs records grayscale images with four intensity levels, improving the shape analysis, while the PIP operates in monoscale. To ensure consistency, a 50 % grayscale threshold was applied to the CIPgs image data . The CIPgs covers nominal particle size ranges from 15 to 960 µm with a pixel resolution of 15 µm, while the PIP detects particles from 100 to 6400 µm with 100 µm pixel resolution. Particle diameters were determined using the minimum enclosing circle method , and the data were evaluated applying the all-in method . One-pixel images and other artifacts from electronic noise were identified and excluded from the analysis.

To obtain a complete particle size distribution, data from the three instruments were combined (CDP: 2–37.5 µm; CIPgs: 37.5–247.5 µm; average CIPgs-PIP: 247.5–637.5 µm; PIP: 637.5–6400 µm; further details can be found in and Sect. 4.3 of ). Particle number concentrations from each three instruments were measured at a 1 s time resolution. The key microphysical cirrus parameters analysed in this study include ice crystal number concentration (Nice) and ice water content (IWC), both derived from the combined data set. We calculate the IWC via the mass-dimension relationship m=a⋅Db (in cgs units) with coefficients a=0.00528 and b=2.1, as proposed by , and where D represent the particle diameters measured by the cloud probes. Nice was calculated directly from the binned particle concentrations obtained from the combined distribution. Additionally, we derive mean volume diameters (Dice) from Eq. 25 in . Note that we use here this approach to better match the model methods, previous publications showed effective diameters as size representation (e.g., ). We estimate an overall counting and sizing uncertainty of 20 % and 50 %, respectively . Only measurements taken at ambient temperatures below - 38 °C were considered to ensure fully glaciated clouds.

The aerosol measurement system utilized by the German Aerospace Center (DLR) aboard the HALO aircraft is known as the AMETYST (Aerosol MEasuremenT sYSTem) and measures aerosol particles up to approximately 3 µm. Particles with diameters larger than 12 nm are measured using a Condensation Particle Counter (CPC; model Grimm SkyCPC 5.410), while an Optical Particle Counter (OPC; model SkyOPC 1.129) is employed for larger particle sizes (250 < D [nm] < 3000) . Both instruments were adapted by DLR for aircraft applications . The operation principle is based on the detection of forward scattered light from a laser beam, similar to the principle of forward scattering cloud probes.

The OPC not only provides information on the total number of sampled particles, but also allows for the derivation of particle sizes, with particle counts sorted into various size channels . However, particles falling within the CPC size range are not directly detectable. Instead, the instrument creates a highly supersaturated environment using the vapor of a working substance, typically butanol, to activate all particles and grow them to sizes detectable by the instrument's optical block . A sigmoid function representing the counting efficiency dependent on size enables the determination of the cut-off diameter, which represents the size of particles counted with an efficiency of at least 50 %. It mainly depends on the temperature difference between the saturator and condenser, adjustable through laboratory calibrations accordingly . However, when using an aircraft as measurement platform, the cut-off diameter is further influenced by losses in the sampling lines from the inlet to the instrument.

The AMETYST system comprises three CPCs. CPC0 and CPC3 for total aerosol concentrations, with nominal cut-off diameters of ≈ 7 and ≈ 18 nm, respectively. However, the real cut-off diameter of CPC0 increases with decreasing pressure due to inlet losses. reported cut-off diameters of 11.2 nm at 500 hPa and 18.5 nm at 150 hPa for the AMETYST system. The inlet system was improved for the CIRRUS-HL campaign, and a smaller cut-off diameter of ≈ 12 nm is assumed for these measurements . Additionally, CPC2 is dedicated to measuring non-volatile particles larger than approximately 14 nm. Non-volatile particles can be measured by positioning a thermodenuder upstream of the CPC . By adjusting the set temperature to the evaporation temperature of the volatile material, only non-volatile particles are retained. The upper diameter limit of the CPC is governed by the inlet characteristics (specifically, the HASI isokinetic inlet), estimated to fall between 1.5 and 3 µm. However, this upper limit is not particularly relevant for integrated number concentration measurements as the lower particle size mode dominates, offsetting the contribution of larger particles to the total number concentration.

The simulations for this study have been performed with the global climate model EMAC. EMAC 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 study we apply EMAC (ECHAM5 version 5.3.02, MESSy version 2.54) in the T42L41DLR 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 analysed in this study covers the duration of the CIRRUS-HL campaign taking place in June and July 2021. The model time step of the simulation has a length of 15 min and we use a time interval of 1 h for the output of model data along backward trajectories. The simulations have been performed in nudged mode, i.e. the model meteorology (temperature, winds and logarithm of the surface pressure) is relaxed towards ECMWF reanalysis data (ERA-Interim; , ) for the simulated time period.

The aerosol microphysics are simulated using the submodel MADE3 that considers different aerosol species in nine log-normal modes representing 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 are presented in .

In this study, EMAC is employed in a coupled configuration featuring a two-moment cloud microphysical scheme based on , which parametrizes aerosol-driven ice formation in cirrus clouds following . The scheme considers different ice formation mechanisms that compete for the available supersaturated water vapour, i.e. homogeneous freezing of solution droplets, deposition and immersion nucleation induced by INPs, and the growth of preexisting ice crystals. For simplicity the scheme does not represent the entire freezing spectrum (from the freezing onset to the homogeneous freezing threshold) but instead considers one single point in the spectrum, e.g. corresponding to the freezing onset. We note that the model simulate secondary ice production (SIP), i.e. the Hallet–Mossop mechanism (rime splintering) is parametrized according to . However, uncertainties remain as other types of ice multiplication processes are missing in the model parametrization, e.g. droplet shattering and ice-ice collisional breakup, which should be explored in future studies.

The ice-nucleating properties of INPs in each of the heterogeneous freezing modes are represented by two parameters, i.e. the active fraction (fact) of INPs representing the portion of aerosol particles that 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 the model simulation performed in this study we consider heterogeneous ice nucleation on mineral dust (DU) via both deposition and immersion freezing, and on aviation black carbon (BCav) and black carbon from surface sources (BC) via deposition freezing. The ice-nucleating properties of the different INPs are summarized in Table . The vertical velocities driving the freezing processes are parameterized to account for subgrid-scale variabilities of updraft velocities, which cannot be resolved with the coarse model resolution. As described in , the total updraft 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 . Further details on the aerosol–cloud coupling are described in and .

The EMAC setup applied here is in large parts based on the setup described in . The model simulation is driven by the anthropogenic and open-burning emission data sets developed in support of the CMIP6 project . Emissions for the year 2021 follow the SSP3-7.0 scenario, projecting a radiative forcing of 7.0 Wm-2 in the year 2100 .

Note that in this study, BCav particles are assumed to act as efficient INPs with Sc=1.2 (see Table ). However, a recent laboratory study by analysed black carbon emitted from commercial aircraft engines and determined that BCav has potentially a low ice nucleation efficiency. This suggests that the assumed Sc value is likely an overestimation. Variations in the ice nucleation ability of BCav not only affect the number concentration of newly formed ice crystals and the frequency of BCav-induced nucleation events, but also influence heterogeneous freezing on DU and BC, as well as homogeneous nucleation, due to the competition for available water vapor. The decision to assign a high Sc value to BCav was made to simplify the interpretation of the results, making their effect more prominent, and to assess an upper limit for identifying and discussing its potential impact on cirrus formation. For more details about the uncertainty related to this assumption see .

In order to ensure the comparability with the aircraft measurements, we use the diagnostic submodel S4D (Sampling in 4 Dimensions; , ) of EMAC to extract model output along the aircraft trajectories of the flights conducted during the CIRRUS-HL campaign at every model time step (i.e., every 15 min). To match the model time step, we also average the observed aerosol and ice cloud properties over 15 min (an overview of the data before averaging is provided in Sect. ). This averaging interval also provides a spatial scale comparable to the model grid resolution of 2.8° × 2.8°, as an average cruise speed of 250 km results in a flight distance of 225 km in 15 min. To improve statistical robustness and account for flight path variations not captured by the model time resolution (e.g., short-term climbs or descents followed by further altitude changes, see Fig. 1 in , ), we include model output from ± 1 pressure level around the flight path pressure level. In addition, the same ice crystal size range is applied to both observations and model simulations, defined between 3 and 200 µm. The results obtained using this methodology are presented in Sect. .

Using the new high-volume flow aerosol particle filter sampler (HERA), integrated into the HALO aircraft to sample INPs , we gained insights into INP number and type in the mixed-phase temperature regime. However, these in situ measurements were not suitable for the cirrus regime. Similar to other state-of-the-art INP samplers, HERA faces limitations in providing reliable measurements below -30 °C and does not reach the colder temperatures typically observed in cirrus (< -38 °C). Moreover, for this specific investigation, sampling at low temperatures alone is insufficient, as the focus is on characterizing the influence of INPs along the backward trajectories of the air masses. Therefore, Lagrangian sampling of INPs and clouds would be required to track cloud evolution over time with in situ measurements which represents a technical and operational challenge.

Due to these limitations, we use model data to analyse aerosol effects on cirrus formation and microphysical properties observed during CIRRUS-HL. By using global simulations of INP concentrations and newly formed ice crystals, we can obtain data across different latitudes, longitudes, pressure levels, and times (considering the respective resolution in the model) and combine this information with backward trajectories of the sampled air masses (the results are shown in Sect. ). For this analysis, we use the same model configuration as in the S4D simulations described above, but without applying the S4D submodel and with an output interval of 1 h to align with the time resolution of the backward trajectory data. 10 d backward trajectories were calculated from the flight tracks using the Lagrangian analysis tool LAGRANTO and European Centre for Medium-Range Weather Forecasts (ECMWF) analyses. Cirrus trajectories were considered from their formation point onward, which was determined as the last time step before IWC=0 when tracing the trajectory backward. They were classified as “liquid origin” if liquid water was present along the trajectory (LWC>0) and as “in situ origin” otherwise, based on the ECMWF reanalysis data .

In this section, we present 1 Hz aerosol and cirrus particle measurements performed during the CIRRUS-HL campaign to analyse their properties at high and mid-latitudes. This overview also serves as a detailed reference for the subsequent analysis and evaluation with the model data described in Sect. . Figure  displays vertical profiles of three integrated aerosol particle size modes, while Fig.  presents cirrus microphysical properties as a function of the ambient pressure. The aerosol measurements for particles with D> 12 nm obtained from the CPCs consist of 375 352 1 Hz samples, and measurements from the OPC total 431 907 samples. Cirrus measurements, constrained by the temperature threshold of - 38 °C, include 77 087 samples. Both aerosol and cirrus particle data are grouped into mid-latitudes (ML) and high latitudes (HL), using the threshold of 60° N, as previously applied in . High-latitude measurements were less frequent, accounting for 28 % of all aerosol samples and 36 % of cirrus particle data, respectively.

Given that the primary objective of the campaign was to investigate cirrus clouds, most aerosol measurements in Fig.  were performed in the upper troposphere, at altitudes above the 400 hPa pressure level. At lower altitudes, particularly at high latitudes, the median values show less robust results due to limited data availability. At low pressure levels below 500 hPa, the integrated aerosol concentrations for the three size modes do not differ much between high and mid-latitudes. However, a consistent trend emerges at pressure levels above 500 hPa: aerosol concentrations across all three size modes are higher at mid-latitudes than at high latitudes.

The mid-latitude profile of the aerosol concentration of particles with D> 12 nm (Naer, D> 12 nm) aligns with previous studies during the spring and summer seasons, when wildfire activity is typically higher . Our aerosol observations at high latitudes are in good agreement with the measurements from conducted near Kiruna, Sweden. In addition, our results are also consistent with the tropospheric profiles from the INCA campaign in the Northern Hemisphere and the LACE 98 campaign . In contrast to our study, reported lower aerosol concentrations in the tropical upper troposphere. Vertical profiles from in the remote upper troposphere show an order of magnitude higher accumulation mode particle concentrations compared to our measurements. This difference can be attributed to their lower cut-off diameter of 80 nm for the accumulation mode particles, which results in higher reported concentrations.

Statistically, cirrus clouds at mid-latitudes were observed at higher altitudes than those at high latitudes, as shown in Fig. e. However, the altitudes observed relative to the tropopause were similar for both latitude ranges. This result is expected, since the tropopause is generally higher at mid-latitudes than at high latitudes . In fact, the altitudes observed relative to the tropopause were similar for both latitude regions. At pressure levels below 225 hPa, high-latitude data is sparse, requiring careful interpretation of the median values of cirrus properties. Given the lower tropopause heights at high latitudes, this range corresponds to the lower and drier stratosphere, where cirrus are rare.

Figure a shows that mid-latitude (ML) cirrus contain approximately one order of magnitude more ice crystals than high-latitude (HL) cirrus along the whole pressure profile. The ice water content is slightly higher in ML cirrus at lower altitudes, but overall the difference in IWC between high and mid-latitudes is not pronounced. This is because the higher number concentration at mid-latitudes is compensated by the presence of fewer but larger ice particles at high latitudes, as shown in Fig. b, leading to similar IWC . RHice is generally higher by 9 % in median in HL cirrus than in ML cirrus across all pressure levels. observed an increase in the frequency of ice supersaturation with latitude in the Arctic, while linked high Arctic supersaturations to warm air intrusions. In addition, a relaxation of the relative humidity towards saturation values is observed in ML cirrus at the highest measured altitudes, which is likely influenced by contrail and contrail cirrus .

The central finding of this section is that the difference in aerosol concentrations between high and mid-latitudes does not directly correspond to the observed difference in ice crystal number concentration. While the difference in median aerosol concentrations varies by factors of 2 to 4 at the lower altitudes and converges at higher altitudes, ice crystal number concentrations in cirrus differ by an order of magnitude between high and mid-latitudes. That being said, it is important to note that INPs represent only a small fraction of total aerosol number concentration. Previous studies have used the number of aerosol particles with diameters larger than 500 nm (Naer, D> 500 nm) as a proxy for INP concentrations in the cirrus temperature regime . The median Naer, D> 500 nm in our measurements is generally below 0.5 cm-3 at cirrus altitudes, which represents an upper bound of the ice crystal number concentration (assuming heterogeneous nucleation). Considering the full particle size distribution measured by the OPC, the vertical profile of Naer, D> 250 nm shows a similar pattern to that of Naer, D> 500 nm, with no clear differences between high- and mid-latitude in the upper troposphere and with a maximum median difference of a factor of 3 at altitudes close to the ground (see Fig. S1 in the Supplement).

Based on these observations, we conclude the following: while liquid origin cirrus clouds form at lower altitudes, where aerosol (and potentially INP) concentrations differ more distinctly between high and mid-latitudes, this alone cannot account for the factor of 10 difference in ice crystal numbers. The substantial difference in ice crystal number concentration between high and mid-latitude is probably not driven by the total number of INPs available at the measurement location. Therefore, we investigate in Sect.  the properties and distribution of available INP types for each latitude region along backward trajectories and the number concentrations of ice crystals formed from these mechanisms relying on simulations from EMAC.

This section presents the results from the direct comparison of in situ measurements of ice particles and aerosols from the CIRRUS-HL campaign with EMAC S4D diagnostic output along the flight tracks, as described in Sect. . This study primarily serves as a descriptive and qualitative intercomparison between in situ observations and the EMAC model rather than a comprehensive evaluation of model performance. A more thorough assessment would require additional measurements across different regions and seasons. However, the CIRRUS-HL campaign covered a diverse range of meteorological conditions, including remote areas and regions influenced by significant anthropogenic emissions from ground sources and aviation, providing a comprehensive data set for comparison. In addition, the following analyses provide valuable context for the analysis in Sect. , where aerosol–cirrus interactions observed during the CIRRUS-HL campaign are further discussed using model data.

Performing a direct, one-to-one comparison between observations and model output is challenging mainly due to differences in spatial resolution and an inherent sampling bias in the observations. As explained in Sect. , to enhance comparability with the model grid-box averages, the observational data were averaged over the model's 15 min time resolution. Additionally, only ice crystals with diameters smaller than 200 µm are considered in the calculation of cirrus microphysical properties to ensure consistency with the model, where ice crystals larger than 200 µm are transferred to snow crystals, which are assumed to be removed within one model time step by precipitation . This threshold, while necessary to avoid model instabilities which may arise due to a too-fast sedimentation of large ice crystals , introduces an additional uncertainty which should be explored in future studies.

The analysis in Fig.  is constrained to higher altitudes (above the 400 hPa pressure level), where data density is highest (as shown in Fig. ), allowing for the application of 15 min averages. In Fig. , darker colors represent profiles from the observations, while lighter colors indicate the model output. Overall, the model mostly shows reasonable agreement with the observations for both size ranges and latitude groups. The cut-off diameter of 12 nm in the model was selected to match the estimated cut-off from the measurements. Variations in the cut-off diameter of ± 2 nm result in maximum differences of ± 10 % in Naer,D>12±2nm in the model. A particularly good alignment is observed in Naer,D>12nm at both mid- and high latitudes. However, the model exhibits a modest underestimation for D> 500 nm at high latitudes between 350 and 200 hPa, with a maximum discrepancy of half an order of magnitude at 300 hPa.

The magnitude of these differences across the pressure range is examined in more detail in Fig. a and b, where it is represented as the order of magnitude of the ratio between observed and modelled medians for mid- and high latitudes in both size ranges. The vertical range in Fig.  is extended down to < 500 hPa to illustrate the trend at lower altitudes. Additionally, Fig. c compares temperature profiles from both observations and the model, showing a reasonable alignment.

Further examining the trend in Naer,D>12nm the difference between observed and modelled values varies with altitude. At the highest altitudes, the model slightly overestimates aerosol concentrations, followed by close agreement in the upper troposphere and increasing discrepancies at lower altitudes. The model's overestimation at high altitudes might result from an overestimation of the upward transport of particles or of the particle nucleation rate . An underestimation of smaller particles in the lower troposphere has been reported in previous studies , likely due to an underrepresentation of natural aerosol sources and new particle formation from precursor gases in the model. Near the surface (not shown here), the difference becomes more pronounced at mid-latitudes, which could be attributed to a higher density of emission sources compared to high latitudes, which are not fully represented in the emissions data set.

Ice cloud properties from observations and model as a function of temperature are compared in Fig. . The overall medians (Fig. a, d, and g) are dominated by mid-latitude data points due to lower data coverage at high latitudes. At high latitudes, there is more variability and fewer data points in both observations and the model, leading to higher uncertainty. However, a general alignment between model and observations is observed in the three cloud properties, indicating lower ice crystal number concentration, lower ice water content, and higher relative humidity over ice at high latitudes compared to mid-latitudes. Model climatological averages of these properties for June and July over the period 2014–2021 confirm this trend (see Fig. S2 in the Supplement) and also serve as reference to contextualize the specific CIRRUS-HL episode. However, both model outputs should not be directly compared due to the different methodological approaches applied.

In general, the observed ice properties at mid-latitudes in the cold regime (< 220 K) are mostly well captured in the model. At the lowest temperature of the measurements (≈ 212 K), the model predicts Nice and RHice comparable to the observations but, as at warmer temperatures, it systematically overestimates IWC. The improvement in the agreement of Nice is explained by the steep decrease in Dice in the observations, which converges to the model values (see Fig. S3 in the Supplement). High Nice and low Dice at mid-latitudes for this temperature regime in the observations are potentially connected to contrail formation dominating the 15 min averages. indicated that identifiable aged contrails and contrail cirrus appeared in the dataset as outliers, but their influence was likely greater than assumed, since the conservative selection criteria only accounted for cases clearly distinguishable from natural cirrus and the significant overlap in their microphysical properties made further separation difficult. However, this mechanism is not represented in the EMAC simulations, as the current microphysical scheme does not incorporate the physical processes associated with contrail ice nucleation. As a result, the comparability between model and observations in this temperature range is inherently limited.

For warmer cirrus (T> 220 K), the model consistently overestimates both Nice and IWC, and underestimates Dice (see comparison of Dice in Fig. S3 in the Supplement). This discrepancy is particularly evident in Nice, where the model exceeds observations by one to two orders of magnitude. A similar bias in this temperature range has been reported in previous studies, potentially linked to an underestimation of ice crystal sizes in the model, which translates into artificially high number concentrations . Specifically, observed this bias when comparing model results with climatology data sets from and , and with the observations from the ML-CIRRUS campaign . Figure S3 in the Supplement compares the ML-CIRRUS and CIRRUS-HL median number concentrations from both observations and model output from climatological averages over the corresponding periods, revealing similar profiles between campaigns.

It is important to note that we compare the model output from ML-CIRRUS only with the corresponding climatological average for CIRRUS-HL, and not with the S4D model output used in this study. As in , the climatological model data were averaged vertically and horizontally over the relevant campaign region, potentially leading to a smoothing effect on the medians, whereas the S4D output along the flight tracks allows for a more direct one-to-one comparison with the observations. It should also be noted that these campaigns occurred under different meteorological conditions and seasons. The CIRRUS-HL campaign meteorology was influenced by strong convective activity during summer . Previous studies by have reported an overestimation of ice crystal number concentration in the ECHAM-HAM model compared to observations, particularly for ice crystals detrained from convective events. This overestimation may be due to inadequately represented microphysical processes, such as collision-coalescence, aggregation, or sedimentation, which reduce ice crystal number concentrations while increasing particle size during convective outflow . We analyse the influence of detrainment from convection on the Nice in Sect.  in more detail. In addition to the microphysical cirrus properties shown in Fig. , we also compare the updraft velocities between the model and the observations in Fig. S3 in the Supplement, showing, in general, a good agreement.

Secondary ice production (SIP) has been shown to substantially increase ice crystal number concentrations not only in mixed-phase clouds but also in convective outflows feeding cirrus anvils (e.g., ). As explained in Sect. , the EMAC model represents some SIP mechanisms, subject to certain limitations. However, we did not perform a dedicated analysis of SIP effects in our observations. While we acknowledge a potential influence on cirrus formed from convective detrainment, the events with high particle concentrations analysed in this study were mostly associated with observations of aged contrails and contrail cirrus.

showed that high-latitude cirrus exhibit on average lower number concentrations but larger ice crystal sizes compared to mid-latitude cirrus, along with higher supersaturation. Here, we investigate whether these differences in cirrus microphysical properties could result from a reduced availability of INPs at higher latitudes. To gain further insights into the life cycle of the observed cirrus and their interaction with aerosol, we use global simulations of INP concentrations from the EMAC model (with hourly output), as described in Sect. , after having validated in Sect.  the model's ability to reproduce the CIRRUS-HL observations with reasonable accuracy. We focus on heterogeneous nucleation processes as the main driver of the observed cirrus properties, because the analysis of both measured vertical updrafts and derived vertical updrafts along the backward trajectories (interpolated from ERA5) indicated a negligible influence of homogeneous nucleation in our data set. The hourly model output along the backward trajectories further confirms that only a few homogeneous nucleation events occurred in the analysed time period in the model (see Fig. S5 in the Supplement).

Figure  illustrates the methodology for determining INP concentrations (DU, BCav, and BC) and newly formed ice crystal concentrations (Ni,DU, Ni,BCav, and Ni,BC) along backward trajectories for two cirrus types: M-M (formed and measured at mid-latitudes) and H-H (formed and measured at high latitudes). found that high-latitude cirrus could be divided into two groups depending on their latitude at formation. When air masses originated from mid-latitudes, the resulting cirrus at high latitudes (M-H) exhibited higher number concentrations and smaller ice crystals. Given that we aim to explore influences along the cirrus life cycle, we further distinguish cirrus by their latitude of origin and, for simplicity, consider only “pure” mid-latitude or high-latitude cirrus (M-M and H-H).

In Fig. b, d and f, we present absolute frequency distributions of all INP-induced nucleation events occurring at each model time step (every hour) along the backward trajectories of M-M (orange) and H-H (blue) cirrus. The absolute frequency values serve as a reference for comparison, as they depend on the time step (shorter intervals result in higher frequencies) and the length of the trajectories. M-M and H-H cirrus have similar median lifetimes of approximately 16 and 22 h, respectively.

Examining the frequency of events for each INP type, it becomes evident that ice crystals predominantly form on mineral dust particles due to their strong freezing potential and higher concentration at lower latitudes , as reflected by the broad distributions in Fig. b. Freezing on DU can initiate at lower supersaturations compared to BCav or BC. However, under suitable conditions, freezing on BCav and BC can also occur. As shown in Fig. a, mineral dust availability is higher at mid-latitudes, making it likely that cirrus forming at these latitudes are more influenced by these nucleating particles. Figure b further highlights a clear difference between the distributions of ice crystals nucleated by DU in M-M and H-H cirrus, with a pronounced second mode at approximately 0.1 cm-3 for M-M cirrus. Generally, the interplay of ambient conditions and the freezing efficiency of INPs is more important than total aerosol availability. evaluate the influence of various parameters on cirrus properties and also find that RHice plays a more decisive role than the total concentrations of both larger aerosol particles (> 500 nm) and smaller ones (> 100 nm).

Interestingly, the influence of BC from ground sources is minimal in H-H cirrus in terms of absolute frequency of events, whereas BCav appears to have a comparable effect in both M-M and H-H cirrus. BCav exhibits a stronger influence in M-M cirrus, where the median Nice is an order of magnitude higher than in H-H cirrus. It is important to note that the ice crystal number concentrations and the frequency of freezing events from aviation soot ice-nucleation are very likely overestimated, as suggested by recent findings by . However, these results are still useful for assessing the potential role of BCav as an INP. If BCav was an efficient INP, it would have a noticeable impact on cirrus formed at high latitudes, while BC from other sources than aviation seems less relevant. This difference arises because BCav and BC from ground sources differ not only in their ice-nucleating properties but also in their spatial distributions, leading to different interactions with cirrus clouds and, consequently, different climate effects. Soot from ground sources is likely to be aged (i.e., coated) by the time it reaches the upper troposphere, which limits its ice-nucleating ability. While black carbon concentrations from ground sources decrease with altitude and needs efficient vertical transport mechanisms, aviation emissions create a distinct concentration peak of BCav at cruise altitudes , precisely where in situ cirrus form and evolve. This local source is continuously renewed through flight activities e.g. in the North Atlantic Flight corridor. H-H cirrus are mainly of in situ origin (≈ 90 %, , ), which form and remain at high altitudes where the relative abundance of BCav compared to other INPs is higher. However, any potential impact would be limited if BCav is assumed to have low ice-nucleating efficiency.

It should be noted that while the role of homogeneous nucleation in ice crystal formation during CIRRUS-HL was neglected, we cannot exclude a contribution from contrails to the overall ice crystal number concentration, as discussed in Sect. .

In Sect. , we identified an overestimation of ice crystal number concentration by the model at mid-latitudes at warm temperatures (above 220 K). This is likely connected to the higher frequency of convective events at mid-latitudes, while this influence was minimal at high latitudes. In this section, we examine the role of convection in the model overestimation of Nice in more detail and focus our analysis on the temperature region above 220 K.

In EMAC, the ice crystal number concentration from convective detrainment is calculated based on the radius parameterization for convective ice crystals of . In Fig. , we compare this approach with two alternative ice crystal radius parametrizations derived from CIRRUS-HL measurements during convective events over the Alps (flights F12 and F15, excluded from the main analysis in the previous sections). Based on targeted EMAC simulations, we then assess how these new fits affect the model output compared to the reference case using the fit (denominated as “ref”).

Figure a shows the convective ice crystal radius as a function of temperature. The reference fit from is shown with a solid red line, and the two CIRRUS-HL-derived fits are represented by rot dashed and purple dotted lines. The CIRRUS-HL fits are only valid for the temperature regime > 220 K and smooth transitions to the fit are implemented at this temperature threshold to account for the colder temperature regime (using a sigmoid logistic function with a steepness parameter of k=1). These new parameterizations are based on the mean volume diameter of the ice crystal populations per sample period, as defined in . The mean volume diameter is calculated after using two different methods to estimate the diameter of individual ice particles: (fit1) the maximum dimension of each ice crystal, calculated as the minimum enclosing circle; and (fit2) the area-equivalent diameter, derived from the projected surface area of the ice crystals . The resulting particle size distributions are used to calculate mean volume diameters, which are then binned and fitted as a function of temperature to produce the final parameterizations. Fit1 consistently yields larger radii than fit2, and both considerably exceed the values from the fit. This could be due to the fact that data sets from the early 2000s are likely affected by the ice crystal shattering phenomenon described in many studies, e.g., , which artificially increases the number of small ice crystals, leading to an underestimation of the mean volume diameter.

Figure b shows the absolute frequency distribution of newly formed ice crystals from convective clouds (Ni,CV), computed along backward trajectories, analogous to the analysis in Fig. b, d, and f for DU, BC, and BCav, respectively. At high latitudes, the influence of convective detrainment is negligible. However, at mid-latitudes, the median Ni,CV for the reference case is around 1 cm-3, significantly higher than the concentrations of newly formed ice crystals from DU, BC, and BCav. Both fit1 and fit2 reduce the median Ni,CV by one to two orders of magnitude, with fit1 having a stronger effect due to its larger estimated radii. This reduction results from distributing the same ice mass among fewer, but larger crystals.

Finally, Fig. c illustrates the impact of the different radius fits on the comparison between modelled and observed total ice crystal number concentrations as a function of temperature for mid-latitude cirrus, as in Fig. b. Both alternative fits improve the model estimates compared to the reference case at temperatures above 220 K. Fit1 may lead to an overcorrection of Nice because the minimum enclosing circle method systematically overestimates particle volume and ice mass when ice crystals have irregular or complex shapes. Fit2, however, relies on the area-equivalent diameter to calculate the mean volume diameter, providing a more realistic approximation of the actual ice crystal volume. This makes fit2 the more accurate choice, particularly in conditions where non-spherical ice shapes are prevalent . Figure S6 in the Supplement also shows an improved model representation of RHice and Dice. In contrast, the new parametrizations have little effect on IWC, as expected.

In addition to the CIRRUS-HL specific comparison shown in Fig. c, we also compare the simulated ice cloud microphysical properties (Nice, IWC, Dice, and RHice) to measurement data from a climatology derived from various flight campaigns compiled by in a similar manner as presented in (see Fig. S7 in the Supplement). This comparison also shows an improved agreement of the simulated results with the observations for temperatures above 220 K when using the alternative fits. Hence, this model refinement represents a valuable way to improve the model representation of cirrus clouds also for other regions and cloud conditions.

These findings allow us to close the loop in our study by improving the model based on observational data. We demonstrate the strong sensitivity of simulated ice crystal number concentrations in EMAC to the model representation of convective ice crystals and show that applying fits based on CIRRUS-HL measurements substantially improves model accuracy in the temperature range above 220 K.