As mentioned in Sect. , aerosol particles in MADE3 are distributed across three log-normal size modes (Aitken, accumulation, and coarse modes), with three possible mixing states (soluble, insoluble, and mixed). Following the same notation as in K19, we indicate the MADE3 Aitken, accumulation, and coarse modes with the indices k, a, and c, respectively. Mixing states are indicated by s, i, and m for soluble, insoluble, and mixed, respectively. The relevant INPs considered in this study, namely BC and mineral dust (DU), are only present in the insoluble and mixed modes of MADE3, and mineral dust is only tracked in the accumulation and coarse modes. Of the nine modes normally required in MADE3 for each aerosol compound, only six are hence needed for BC (BCkm, BCki, BCam, BCai, BCcm, and BCci) and four for mineral dust (DUam, DUai, DUcm, and DUci).

The number concentration of INPs available for contact freezing in the mixed-phase cloud regime and for deposition nucleation in the cirrus regime are indicated by Ncnt(mp) and Ndep(c), respectively. Deposition nucleation in mixed-phase clouds is neglected, since observations show that this process is probably not important for ice formation in mixed-phase clouds . In K14, the number of particles available for immersion freezing in mixed-phase clouds was estimated as a fraction of the number of aerosol particles activated to form cloud droplets Nact. However, this approach is not suitable for cirrus, where immersion freezing occurs in mixed solution aerosols, i.e., aerosol particles that underwent hygroscopic growth, rather than in cloud droplets. A different approach for calculating the number concentration of INPs available for immersion freezing in mixed-phase (Nimm(mp)) and cirrus clouds (Nimm(c)) is therefore introduced as part of this study. All the number concentrations calculated in this section are checked for consistency in the code, to make sure that the estimated number concentrations in each mode are not larger that the total number concentration in the mode itself. To simplify the notation, this check is not explicitly included in the equations below.

We first estimate the number concentration of dust particles in each mode, starting from dust mass concentration and using the conversion function 2CDU(Dj,σj)=6π1Dj3exp⁡(4.5ln⁡2σj)ρ, with ρ=2500 kg m-3 for dust. Dj and σj are the log-normal size distribution parameters (median diameter and geometric standard deviation) of mode j, for which we follow the AeroCom recommendations : Da=0.42 µm and σa=1.59 for the accumulation mode, and Dc=1.30 µm and σc=2.0 for the coarse mode. The same parameters are also used to calculate the number of emitted dust particles in the model (see Sect. ). This means that we are neglecting the aging of the size distribution due to dust–dust coagulation. This process has a limited efficiency due to the comparatively small number concentration of mineral dust particles (no dust is present in the Aitken mode given the typically large sizes of mineral dust particles). The number of BC particles is then estimated based on the total number of particles and the number of dust particles as described below.

Since no dust is present in the mixed and insoluble Aitken modes, each particle of these modes contains BC. Note that organic carbon cannot generate BC-free particles in these modes since it is assumed to be emitted internally mixed with BC in the form of “soot” (K19). Furthermore, only the mixed-mode BC particles can be activated to form cloud droplets. For mixed-phase clouds, we therefore assume 3NBC,kimm(mp)=Nkmact. We do not include contact freezing of BC in the mixed-phase regime, as its effect is considered largely uncertain . For the cirrus regime, the number of potential Aitken-mode-sized INPs which could lead to immersion or deposition freezing coincides with the total number of particles in the mixed or insoluble Aitken modes, respectively: 4NBC,kimm(c)=NkmNBC,kdep(c)=Nki.

In the mixed and insoluble accumulation modes, dust is present in the typical accumulation-mode size (see above), since smaller dust particles are not considered and coarse dust particles can only reside in the coarse modes. In this case, we estimate the number of dust particles from their mass M using Eq. () and derive the number of potential dust INPs as follows: 5NDU,aimm(mp)=MDU,amCDU,aNamactNam6NDU,aimm(c)=MDU,amCDU,a7NDU,acnt(mp)=MDU,aiCDU,aNDU,adep(c)=MDU,aiCDU,a. It cannot be excluded that these potential dust INPs also contain BC as a consequence of coagulation. Due to the large size of the dust particles compared to BC, we assume, however, that dust dominates the ice nucleation properties of the particles. The remaining number of particles in the insoluble and mixed accumulation modes can then be ascribed to soot particles (internally mixed black and organic carbon): 8NBC,aimm(mp)=max⁡(0,Namact-NDU,aimm(mp))9NBC,aimm(c)=max⁡(0,Nam-NDU,aimm(c))10NBC,adep(c)=max⁡(0,Nai-NDU,adep(c)).

The insoluble coarse mode is dominated by dust, since it is unlikely that self-coagulation of insoluble accumulation-mode BC particles leads to growth into the insoluble coarse mode (BC mass is limited and the self-coagulation frequency is comparatively low). Hence, coarse dust particles are needed to form this mode. This results in 11NDU,ccnt(mp)=NciNDU,cdep(c)=Nci12NBC,cdep(c)=0.

In the mixed coarse mode, the mixing state is uncertain, since particles can be composed of dust from both the accumulation and the coarse size ranges, whose relative contribution is not known. Thus mass-to-number conversion is not as straightforward as in the accumulation-mode case. We need to distinguish two cases, based on the relative abundance of dust particles. We define the dust number fraction in this mode as 13fDU=MDU,cmCDU,cNcm. We use the conversion factor CDU,c of coarse dust particles, given in Eq. (), to estimate the number fraction, since these particles dominate the dust mass possible mass contributions of accumulation-mode dust are small, according to. Hence, an estimate of the coarse dust particle number based on the total dust mass in the mode appears to be a good approximation. It provides a minimum estimate of the number of dust-containing particles in the mode, since also many accumulation-mode-sized dust particles might be present in the mode due to coagulation. For dust-dominated regimes, e.g., at or in the vicinity of deserts, it can be expected that fDU is large and that also the non-coarse-dust particles in the mode contain many accumulation-mode-sized dust immersions. It can also be expected that BC has a comparatively small contribution under these conditions. Hence, all particles of the mode can be regarded as possible dust ice-nucleating particles. In the present study, we assume that mineral dust dominates in the mode where fDU≥0.7. In this case, the above assumptions result in 14NDU,cimm(mp)=Ncmact15NDU,cimm(c)=Ncm16NBC,cimm(mp)=0NBC,cimm(c)=0. If fDU<0.7, we assume that BC plays a major role and that the minimum estimate of the number of dust-containing particles applies. This results in 17NDU,cimm(mp)=MDU,cmCDU,cNcmactNcm18NDU,cimm(c)=MDU,cmCDU,c19NBC,cimm(mp)=max⁡(0,Ncmact-NDU,cimm(mp))20NBC,cimm(c)=max⁡(0,Ncm-NDU,cimm(c)). Despite the admittedly many assumptions required to estimate the number of coarse immersion INPs, we note that the resulting uncertainties are probably small, since the contribution of coarse particles to the number concentration of INPs is mostly small compared to the corresponding contribution of the accumulation mode. Sensitivity studies show little to no variation in ice water content and ice crystal number concentration for values of fDU ranging from 0.6 to 0.9.

Following a similar approach as in , we first analyze how sensitive the model performance in representing key cloud and radiation variables is when varying certain tuning parameters. We recall that the EMAC-MADE3 configuration being tuned in this work is nudged; i.e., meteorological variables such as temperature, winds, and the logarithm of surface pressure are relaxed towards reanalysis data. In line with the designed application target of this version of the model, this allows to run different simulations (such as perturbation experiments) with very similar meteorological conditions. Such a model setup is most suitable for short-term time-slice experiments that aim at isolating the effects of specific sources and processes, which would be statistically and numerically far more challenging without nudging. The use of the nudging technique has to be kept in mind while tuning the model, since nudging unavoidably impacts on the model climate, as it introduces a forcing component by modifying the model's temperature profile, which in turn perturbs the radiative balance . A previous study by based on the ECHAM6 model showed that temperature nudging may introduce a radiative imbalance around 5 W m-2 with respect to an otherwise identical configuration without nudging. In the following, we will apply our tuning procedure to the nudged setup. Once the optimal configuration is identified, we will additionally perform a control experiment in free-running mode to address the above issue and quantify the actual impact of nudging on the radiative balance in the tuned model configuration.

Our tuning approach focuses in particular on the enhancement factor of the rate of rain formation by autoconversion γr, the rate of snow formation by aggregation γs, the minimum cloud droplet number concentration CDNCmin, and the size of newly nucleated aerosol particles dnuc. The minimum CDNC is introduced in the model to avoid unrealistically low concentrations of cloud droplets in pristine conditions. The parameter dnuc is used to describe the initial growth of freshly formed sulfuric acid water clusters into larger sulfate aerosol particles. Since such nucleation and growth events frequently occur on spatial scales which cannot be resolved by the global model, the use of this parameter enables the implicit consideration of these subgrid-scale processes. In K19, a value of dnuc=10 nm was chosen, motivated by better agreement of simulated number concentrations with observations and supported by new particle formation measurements. Here, we explore how this parameter can also affect cloud and radiation variables. further considered the inhomogeneity factor of ice clouds and the entrainment rate for deep convection as tuning parameters, which in our configuration are set to 0.85 and 10-4 kg m-3 s-1, respectively, but their variation is not further explored. We tested five values for each of the four tuning parameters (γr, γs, CDNCmin, and dnuc), varying across a range of approximately 1 order of magnitude. We then calculated their effect on six cloud variables (total cloud cover, liquid water path (LWP) over the oceans, CDNC over the oceans, ice water content in cirrus clouds (IWCcirrus), ice crystal number concentration in cirrus clouds (ICNCcirrus), and precipitation), and three radiation variables (shortwave and longwave cloud radiative effects (SWCRE and LWCRE, as the difference between all-sky and clear-sky radiation fields), as well as the net radiative balance). Note that exploring the full parameter space, i.e., all possible combinations of the five values for the four tuning parameters, is not feasible, as it would require performing 54=625 model simulations. Thus, we only explore the model sensitivity for each single parameter while keeping the others fixed at a reference value, which corresponds to the median of the explored range, i.e., γr=8, γs=800, CDNCmin=10 cm-3, and dnuc=10 nm. This limits the numbers of simulations to be performed to 17 (i.e., 5×4=20 simulations minus three redundant cases). To further reduce the computational costs, the tuning simulations cover a period of only 3 years (1999–2001). To quantitatively characterize the impact of the four tuning parameters on the model variables, the normalized root mean square error (NRMSE) of the model with respect to the observations is calculated for each variable-parameter combination: 21NRMSE=∑i(Mi-Oi)2n∑iOin, where Mi and Oi represent the model and observational data, respectively. When comparing model and satellite data, the index i runs across all model grid boxes and the 12 timesteps resulting from the calculation of a monthly climatology. For the in situ data, the index i corresponds to the median value of the distribution for each 1 K temperature bins. In the case of gridded data, a weighting factor proportional to the grid box area and to the length of each month is also applied in Eq. ().

The results of this analysis are summarized in Fig. : each panel depicts the variation of a given variable over the range of values for the tuning parameter, with the black circles marking the corresponding NRMSE values (note that for the radiative balance, the globally averaged value is shown). To quantitatively describe this variation, each panel is color coded according to the relative standard deviation of the NRMSE (RSD=σNRMSENRMSE‾) for the variable-parameter combination shown in that panel. This helps to identify the combinations which display a low (RSD≤0.1), medium (0.1<RSD≤0.2), or high (RSD>0.2) variation with the value of tuning parameters.

The autoconversion rate (first column of Fig. ) controls the removal of liquid water from the clouds via precipitation and therefore has an impact on LWP in the model, also changing the radiative balance, while the effect on the other variables is less significant (RSD≤0.1). Choosing a high autoconversion rate minimizes the NRMSE of LWP but at the expense of a large radiative imbalance. A good compromise is γr=5, which limits the imbalance to 6.2 W m-2 while keeping the NRMSE of LWP reasonably low. Note that for values γr<5, the NRMSE of LWP grows rapidly, so this is the lowest among the explored γr values for which a reasonable deviation in both affected variables can be attained. Similarly, the aggregation rate (second column) controls the conversion of ice crystals to snow in ice clouds and consequently has a large (RSD>0.2) impact on IWC and ICNC in cirrus clouds, while its influence on the radiative balance is less pronounced than for the autoconversion rate. In this case, however, the two mostly affected variables behave similarly when varying γs, with a decreasing NRMSE for increasing values of γs, so that setting it to the maximum of the investigated range, γs=1300, seems to be the most appropriate choice. The minimum CDNC (third column) slightly impacts the NRMSE of ICNCcirrus and has an important effect on the radiative balance in the model. In ECHAM5-HAM and ECHAM6-HAM, this parameter was varied between 10 and 40 cm-3 . A high value would help to minimize both the NRMSE of ICNCcirrus and the radiative imbalance in EMAC-MADE3, but lower values for this threshold parameter are more consistent with the observations in pristine marine regions . Here, therefore, we choose CDNCmin=20 cm-3, to avoid tuning the model using unrealistic values, but at the price of a slightly worse representation of ICNC in cirrus and a slightly higher radiative imbalance. The size of newly nucleated particles dnuc (fourth column) has a significant impact on aerosol number concentrations, as shown by K19. Since aerosol particles serve as cloud condensation nuclei for cloud droplet formation, this parameter primarily controls CDNC in the model, hence impacting LWP, and ICNCcirrus, with a consequent effect on the radiative balance. As for the autoconversion rate, the tuning experiments reveal some trade-offs between these variables: large values of dnuc allow to minimize the NRMSE of LWP, ICNCcirrus, and (to a lesser extent) CDNC but again at the expense of the radiative balance, which grows rapidly over 10 W m-2 for dnuc>10 nm. A good compromise is dnuc=10 nm, which allows to keep the NRMSE of CDNC low and is also supported by K19, who found good agreement with aerosol number concentration measurements when choosing dnuc=10 nm.

In summary, this choice of the four parameters (γr=5, γr=1300, CDNCmin=20 cm-3, and dnuc=10 nm) represents our reference set and is used to perform a full 10-year simulation which is then evaluated in more detail in the next section. The NRMSE resulting from this choice of the tuning parameters is shown with the red circles in Fig. . Note that this set of the tuning parameters does not match any of the other sets marked with the black circles. This is because, as explained above, the tuning strategy adopted in this study aims at exploring the model's sensitivity to a set of tuning parameters, but it is limited to single-dimensional variation studies, in which the value of a single parameter is changed while the others are kept fixed at a reference value. Deciding on a reference set of tuning parameters always involves expert judgment and a compromise between certain basic principles , as the choice of priorities must be guided by the main application target of the model setup to be tuned. If, for instance, the model is to be coupled to an interactive ocean, a close-to-zero radiation balance at the top of the atmosphere must be the central goal of tuning. In this study, the first priority has been laid on providing reasonably good agreement with the observed values of the main cloud and radiation variables, although the model retains a radiative imbalance of 3.4 W m-2. A lower imbalance could be obtained by choosing a different set of tuning parameters but at the expense of worse agreement with the observations of other essential variables. This has been tested by performing two additional tuning simulations: increasing CDNCmin to 40 cm-3 and reducing dnuc to 5 nm with respect to the reference set, respectively. The results, shown by the blue markers in Fig. , demonstrate that this choice would improve the radiative balance to a value of 0.1 W m-2 in both cases but would also lead to larger errors in most of the other variables. As discussed above, however, a significant imbalance is introduced by temperature nudging, which is applied in all experiments shown here. To quantify this, a simulation with the tuned configuration but in free-running mode is performed, which encouragingly results in a radiative balance of -0.5 W m-2. Hence, while the nudged configuration – with its imbalance of 3.4 W m-2 – is well suited for its designed purpose, also the free-running model would meet the common requirements. We stress again that introducing a change of a few W m-2 on the radiative balance through nudging is fully consistent with the study by mentioned above.

Table  summarizes the results of the tuned simulation, compared with similar experiments performed with ECHAM5-HAM by K14, ECHAM6-HAM2 by , EMAC-GMXe by , NCAR-CAM5.3 by , and ECHAM6.3-HAM2.3 by . The performance of the EMAC-MADE3 coupled configuration is in line with these models and mostly close to the observed values given in the table.

In the rest of this section, we extend the analysis by further evaluating the mean state of cloud and radiation variables against satellite data using the diagnostics included in the Earth System Model Evaluation Tool (ESMValTool) v1.1.0 . Most of these observational datasets have already been used for the model-tuning procedure described above, but they are further analyzed to assess the performance of the tuned model configuration in representing specific aspects of the target variables and better quantify the remaining biases, by looking, for instance, at their spatial distribution. However, we complement these datasets by additional ones to provide a more robust and independent evaluation.

In Fig. a–c, multi-year average total cloud cover over the simulated time period (1996–2005) is compared with the European Space Agency (ESA) Climate Change Initiative (ESACCI) CLOUD satellite product, which is based on data from the passive imager sensors (AVHRR, MODIS, ATSR-2, AATSR, and MERIS; ). The overall pattern is very well reproduced by EMAC, with a small positive bias in the tropics and a negative bias in the stratocumulus regions off the coasts of South America and Africa. These features are quite common in many global models, e.g., those participating in the CMIP3 and CMIP5 intercomparisons , both in the Atmospheric Model Intercomparison Project (AMIP) and in the ocean-coupled configuration. Larger deviations between EMAC and the observations are found in polar regions, where, however, observational uncertainties are also larger . Note that total cloud cover is only weakly controlled by the specific coupling evaluated here and is rather a general feature of the core model, as demonstrated by the similar biases found by other studies using ECHAM5 and the cloud cover scheme, such as and K14.

In Fig. d–f, an analogous comparison is shown for LWP over the oceans against the Multisensor Advanced Climatology MAC;, which combines data from different satellite sources over the ocean, including SSM/I, TMI, AMSR-E, WindSat, SSMIS, AMSR-2, and GMI. Although the general pattern of LWP is reproduced by EMAC, several features are not consistent with observations: in particular, EMAC tends to simulate a higher LWP in the northern extratropics, with particularly high values in the western Pacific, and a lower LWP in the tropics, while it agrees better with the observations in the southern extratropics. Most striking is the high bias in the northwest Pacific Ocean, which may be related to a high bias in the cloud lifetime in this region. As it will be shown in the next section, CDNC is also biased high in this region in comparison to satellite data, which could in turn be the effect of a too-high concentration of cloud condensation nuclei. These biases could also be partly related to the tendency of EMAC to underestimate low cloud fraction in the tropics and overestimate it in the extratropics . Uncertainties in the prescribed emission fluxes could also contribute to these biases, especially in east Asia, where anthropogenic emissions in the year 2000 are higher than in other regions of the world and have further increased since then. As for the total cloud cover, similar deviations were found by in the CMIP5 multi-model mean, which is characterized by large biases in the same regions.

We evaluate CDNC using a compilation of in situ measurements provided by , integrated with the measurements performed during 12 research flights during the DACCIWA campaign Dynamics-Aerosol-Chemistry-Cloud Interactions in West Africa; in summer 2016 around Lomé (Togo). For this comparison, the model data are spatially colocated with the observations using a nearest-neighbor selection method for both the horizontal and the vertical coordinates. In the vertical, this is realized using the information provided for each location: either altitude (geopotential height in the model), pressure level, surface level (the lowermost hybrid model layer), or selecting the levels within the boundary layer as calculated by the model. The time selection is performed in a climatological way, by sampling the model output at a 5-hourly frequency for the same month(s) or season(s) as reported by each measurement, and averaging the selected time steps over the whole (10 years) simulation period. For comparison with the DACCIWA data, the model output is further filtered, by selecting only the cloud scenes with a liquid water content above 0.01 g m-3, which is the same criterion adopted in the measurements. Reported concentrations correspond to in-cloud values.

The result of this comparison is depicted as a scatterplot in Fig. : considering the observational uncertainties, EMAC simulates CDNC within a factor of 2 (i.e., factors in the range from 0.5 to 2) of the observations in most of the regions (i.e., 68 % of cases), but it generally tends to underestimate this quantity. This is in line with recent results by , who used the MARC global aerosol model and applied various cloud droplet activation schemes. Their global integrated CDNC in the range of 60–91 cm-3 is lower than the average value simulated by EMAC (151 cm-3), which is closer to the range of 75–135 cm-3 reported by for three models also using the parameterization for cloud droplet activation.

We also compare the simulated CDNC with satellite retrievals, which provide a unique global picture of this quantity, although these kinds of retrievals are still affected by considerable uncertainties . Here, we use a recent 13-year climatology by , based on MODIS Aqua retrievals. In-cloud CDNC, as reported in the observational dataset, are extracted from the model output with the same method used for comparing with in situ data but considering CDNC at cloud top, as observed by the satellite, i.e., by taking the CDNC in the highest model level with a liquid cloud. An alternative method, taking the average CDNC through the cloudy part of the column, provides very similar results (not shown). This is expected, since the representation of liquid cloud formation in the EMAC cloud scheme follows the adiabatic parcel theory, assuming that newly formed cloud droplets at the cloud base are equally distributed in the vertical by mixing, regardless of the aerosol concentrations. An identical assumption is also done in the retrieval process by . The results of this comparison are depicted in Fig. . In the Northern Hemisphere, EMAC captures the major spots of high CDNC over the Atlantic Ocean eastward of Canada and USA, over the Mediterranean and eastward of China, albeit with about 50 % higher CDNC than MODIS. These spots also have a wider horizontal extent over the oceans than in the observations. This could be due to the generally high CDNC over the continents (as shown by the in situ data in Fig. ) being too efficiently advected over the oceans or, as mentioned in Sect. , to a bias in the prescribed emissions, causing a too-high aerosol concentration and hence a too-high number of cloud condensation nuclei being activated. Another major bias is found at the Equator westward of central Africa, which could be due to biomass burning aerosol being transported over the Atlantic. Here again, uncertainties in emissions of aerosols and precursor species could play an important role in explaining such bias. In addition to deficiencies in the aerosol representation, misrepresentations of the model dynamics could also explain deviations from the observations. Another source of uncertainty is related to the retrieval errors in the MODIS products for effective radius and optical depth, which are used to derive CDNC. According to , this uncertainty is around 30 % in the stratocumulus regions and 60 %–80 % in the storm tracks, increasing towards the poles. Furthermore, this dataset is considered as highly uncertain for latitudes above 60∘ . To better characterize the observational uncertainties, we compare CDNC with another 13-year MODIS-based dataset (Fig. ), namely the climatology by based on the retrieval method of . The large positive bias of EMAC-MADE3 over the tropical oceans is significantly lower when compared with than with , while the negative bias over the extratropics is still present and also visible over most of the continents, thus confirming the conclusions from the comparison with the data collection shown in Fig. .

compared CDNC simulated by four global aerosol models with the dataset and found biases of similar magnitude as for EMAC-MADE3, albeit with different geographical patterns which are specific to each model. The same was done by for the CAM5.3-Oslo model with the OsloAero5.3 aerosol scheme, who found a very similar pattern of biases in CDNC to that in EMAC-MADE3, namely an overestimated (underestimated) CDNC over the tropical (extratropical) oceans. These authors also suggested that the lack of a satellite simulator in the model might affect the reliability of this comparison. evaluated CDNC in the HadGEM3 model with the same two MODIS-based satellite datasets used here and also found better agreement with the retrieval than with the one, although their model performance over the continents appears better than that for EMAC-MADE3. Finally, compared the Geophysical Fluid Dynamics Laboratory atmospheric model version 4.0 (GFDL-AM4.0) model with and reported significantly underestimated CDNC, especially along the coastlines in the outflow of large emission sources. In conclusion, the EMAC-MADE3 model's ability in simulating CDNC appears to be in line with the performance of other global models reported in the literature, although the relative limited amount of data available for evaluating this quantity and the large uncertainties still affecting the satellite retrievals warrant further investigations in the future.

The current version of EMAC-MADE3 also allows to calculate the supersaturation in liquid clouds based on the κ-Köhler theory as an alternative to the fitting function by . An additional sensitivity experiment performed with this alternative formulation reveals no significant differences in the resulting CDNC (see Figs. S3 and S4 in the Supplement).

Evaluating the microphysical properties of ice clouds by means of satellite data is a challenging task, due to the large uncertainties of satellite retrievals of such properties, mostly related to the difficulties in retrieving ice water content with passive instruments . Given also that this model configuration has been especially developed for studies of aerosol effects on cirrus clouds, to evaluate the model we use a collection of in situ measurements from 18 aircraft-based field campaigns compiled into a climatology by and further complemented with more recent data . A detailed description of the respective instruments is given in these publications. The campaigns took place in several locations including Europe, Australia, Africa, Seychelles, Brazil, USA, Costa Rica, and the tropical Pacific, i.e., in the latitude band between 75∘ N and 25∘ S, for a total of 113 flights. The measurements were performed in the cirrus regime between 182 and 243 K and include several cirrus properties such as ice water content (IWC, 127.5 h of measurements), number concentration of ice crystals (ICNC, 70.9 h), ice crystal radius (Rice, 65.9 h), as well as in-cloud and clear-sky relative humidity with respect to ice (RHice, 80.9 and 157.8 h, respectively). Consistent with the measurements, in the model, only the number concentration of ice crystals in the range of 3–960 µm in terms of mean-volume diameter is considered, where the mean-volume diameter is defined in analogy to Eq. (6) of .

The observational data are provided as probability distribution functions in bins of 1 K in the temperature range 182 to 243 K. Cloud variables in the model (IWC, ICNC, Rice, and RHice) are sampled in the same range, considering only pressure levels with p>100 hPa and selecting only the model grid boxes corresponding to the locations of the measurements used to generate the observational climatology. Following the same approach as K14, RHice is calculated by the cloud parameterization from air pressure p, air temperature T, specific humidity q, and saturation-specific humidity with respect to ice (qice) at each model time step: 22RHice=100qqice, with 23qice=0.622picep-0.378pice, where pice is the temperature-dependent saturation vapor pressure over ice, calculated according to . To distinguish between cloudy and cloud-free model grid boxes when comparing with the observations, the criterion IWC >0.5 mg kg-1 is adopted.

The results of this comparison are shown in Fig.  for five variables. IWC simulated by the model is in remarkably good agreement with the observations across the whole temperature range reported in the data. The observations are, however, characterized by a larger spread in the distribution of the IWC values in each temperature bin: this is not surprising, since the model cannot capture the small-scale variability due to its coarse resolution. The median value is also in very good agreement with the observations, with a normalized mean bias (NMB

The normalized mean bias is calculated as NMB=100∑i(Mi-Oi)/∑iOi, where Mi and Oi are the model and observation medians in each temperature bin, respectively.

These findings are further supported by a similar comparison to recent in situ cirrus measurements performed during the cirrus campaign in midlatitudes (ML-CIRRUS; ). Data from this campaign are also included in the cirrus climatology shown in Fig.  and discussed above see also but stem from a different set of instruments. The ML-CIRRUS climatology is based on more than 18 h of in situ cloud observations from 13 research flights in midlatitude cirrus clouds over Europe and the northern Atlantic. The ice crystal number concentration is determined from three cloud probes mounted on the wings of the aircraft: the Cloud and Aerosol Spectrometer with detector for polarization (CAS-DPOL; ), the Cloud Imaging Probe (CIP), and the Precipitation Imaging Probe (PIP; ). These three instruments cover the ice crystal size range between 3 and 6400 µm. IWC is calculated from enhancement-corrected total water measurements with the Water Vapor Analyzer () gas-phase observations as described by . Relative humidity with respect to ice is determined from gas-phase water vapor measurements with the Airborne Mass Spectrometer (AIMS; ). As for the global climatology, the ML-CIRRUS data for IWC, ICNC, and RHice are processed in 1 K bins but for temperatures between 203 and 243 K, as observed in midlatitudes. To account for different spatial resolutions of the cloud particle probes, measured ICNCs are averaged with a running mean of 5 s. The model output is processed and compared using the same method as for the global climatology but considering only spring months (March to May) over the simulation period. The results of this comparison are shown in Fig. : the agreement of simulated IWC and RHice with ML-CIRRUS data is very good (NMB=-17 % and 19 %, respectively), supporting the results from the global climatology, although the model shows a negative (positive) bias at temperatures below (above) 225 K for IWC. Also the high bias in modeled ICNC at temperatures above 225 K is confirmed for the meteorological conditions in midlatitude cirrus, although it is slightly lower (NMB=139 %) than in the global climatology. We further note that the ICNC measured by ML-CIRRUS is about a factor of 2 higher than in the global climatology: in the temperature range 203–243 K, the average of ICNC median values in ML-CIRRUS is 0.07 cm-3, while it is 0.03 cm-3 in the global climatology. This difference is also found in the model simulations, albeit with higher values due to the aforementioned bias (0.16 vs. 0.09 cm-3). This is an interesting difference, which could be due to the specific meteorological and dynamic conditions encountered during the ML-CIRRUS campaign with respect to the global climatology, and their seasonality, but might also be a signature of an aircraft-induced increase in ICNC above continental Europe and in the Northern Atlantic flight corridor see also. This will be further investigated in a follow-up study on aviation impacts on cirrus clouds.

An evaluation of model simulations against the same data from the climatology (see Fig. ) was also performed by for two different cirrus parameterizations implemented in the EMAC-GMXe global model. For temperatures above ∼225 K, the ICNC simulated by these two parameterizations is characterized by a high bias of about the same magnitude as the one found here. Biases are also found at lower temperatures, but they depend on the chosen parameterization. The same aircraft data were also used by to evaluate ICNC in the NCAR-CAM5.3 model, who found a significantly high bias around 200 K, relatively independent of the assumptions on the INP properties in their model. A previous version of the climatology was used by K14 to evaluate the ECHAM5-HAM model with the same cloud scheme implemented here: they also reported a bias in ICNC at temperatures T≳220 K but underestimating ICNC compared to the observations rather than overestimating it as EMAC-MADE3, and ascribed it to underestimated homogeneous freezing rates in the model, which in turn could be due to misrepresentation of temperature and/or vertical velocity. Although the two models share the same dynamical core (ECHAM5), differences in the dynamics could still arise due to the nudging mode adopted for the simulations in this study, as K14 performed their experiments in free-running mode.

The pattern of precipitation (Fig. ) is reproduced remarkably well by the model compared to the Global Precipitation Climatology Project – Satellite and Gauge data GPCP-SG;, based on GPI, OPI, SSM/I, and TOVS retrievals. Precipitation in EMAC is, however, characterized by a high bias in the tropics, especially over the Pacific and Indian oceans, and small negative bias in the extratropics; this is consistent with the biases found for liquid water path in Sect. , which anticorrelate with the precipitation biases, as expected. Interestingly, a very similar pattern of biases was found by for the models participating in ACCMIP (Atmospheric Chemistry Climate Model Intercomparison Project).

Figure  shows a similar comparison for radiation variables, namely shortwave (Fig. a–c) and longwave (Fig. d–f) cloud radiative effect compared to the CERES-EBAF satellite data based on MODIS, SNPP, and NOAA-20 retrievals . In the model, these quantities are given by the difference between the top-of-the-atmosphere all-sky and clear-sky fluxes, the latter being calculated via a second call to the radiation module which ignores the cloud effects. Although the general pattern is well captured by EMAC, the shortwave cloud radiative effect in the model is mostly weaker over the tropics and stronger at midlatitudes than the observations, a picture which is consistent with the aforementioned ECHAM5 bias in low cloud cover . As noted by , this is relatively independent of the cloud fraction scheme and can be ascribed to other model components, such as the convection scheme and the boundary-layer scheme see also. It is therefore not related to the specific model configuration which is being evaluated in this work. Longwave cloud radiative effect is also reasonably well represented in the model, although with a generally positive bias, which is strong over Central America.