Effects of Thermodynamics, Dynamics and Aerosols on Cirrus
Clouds Based on In Situ Observations and NCAR CAM6 Model

Abstract. Cirrus cloud radiative effects are largely affected by ice microphysical properties, including ice water content (IWC), ice crystal number concentration (Ni) and mean diameter (Di). These characteristics vary significantly due to thermodynamic, dynamical and aerosol conditions. In this work, a global-scale observation dataset is used to examine regional variations of cirrus cloud microphysical properties, as well as several key controlling factors, i.e., temperature, relative humidity with respect to ice (RHi), vertical velocity (w), and aerosol number concentrations (Na). Results are compared with simulations from the National Center for Atmospheric Research (NCAR) Community Atmosphere Model version 6 (CAM6). The differences between simulations and observations are found to vary with latitude and temperature. Specifically, simulations are found to underestimate IWC by a factor of 5–30 in all regions. Simulated Ni is overestimated in most regions except Northern Hemisphere midlatitude and polar regions. Simulated Di is underestimated, especially for warmer conditions (−50 °C to −40 °C) and higher Na, possibly due to less effective ice particle growth/sedimentation and weaker aerosol indirect effects, respectively. For RHi effects, the frequency and magnitude of ice supersaturation is underestimated in simulations for clear-sky conditions, and the simulated IWC and Ni show maximum values at 80 % RHi instead of 110 % as observed. For w effects, both observations and simulations show variances of w (σw) decreasing from tropics to polar regions, but simulations show much higher σw for in-cloud condition than clear-sky condition. These findings provide an observation-based guideline for improving simulated ice microphysical properties and their relationships with key controlling factors at various geographical locations.


of misrepresenting the prerequisite condition of cirrus clouds -ice supersaturation (ISS, where relative humidity with respect to ice (RHi) > 100%) -can lead to an average bias of +2.49 W/m 2 at the top of the atmosphere. Other modelling studies found large differences in the net cloud radiative forcing depending on the fraction of activated ice nucleating particles (INPs) and the nucleation mechanisms (i.e., homogeneous and heterogeneous nucleation) through which the clouds form (Liu et al., 2012;Storelvmo and Herger, 2014). The large uncertainties in cirrus cloud radiative forcing illustrate the need for 35 further study on cirrus cloud microphysical properties as well as their controlling factors in various geographical locations.
Ideally, a comprehensive quantification of cirrus cloud microphysical properties globally based on high-resolution, in situ observations would mitigate many uncertainties. However, challenges remain in field measurements to achieve such spatial coverage. Previously, efforts have been made to understand cirrus cloud properties based on their geographical locations. Diao et al. (2014b) performed a hemispheric comparison of in situ cirrus evolution and found little difference in the clear-sky 40 heterogeneous nucleation on mineral dust and metallic particles. Anthropogenic aerosols, such as secondary organic 65 aerosols, were found to be less effective INPs compared with mineral dust (Prenni et al., 2009). Based on remote sensing data, Zhao et al. (2018Zhao et al. ( , 2019 showed that the correlations between ice crystal sizes and aerosol optical depth can be either positive or negative depending on the meteorological conditions in convective clouds. Chylek et al. (2006) showed an increase in ice crystal size during the more polluted winter months compared with cleaner summer months over the eastern Indian Ocean. Using a global-scale dataset of multiple flight campaigns, Patnaude and Diao (2020) isolated individual 70 effects on cirrus clouds from temperature, RHi, vertical velocity (w) and aerosol number concentrations (Na). They found that when Na is 3 -10 times higher than average conditions, it shows strong positive correlations with cirrus microphysical properties such as IWC, Ni and number-weighted mean diameter (Di). These aerosol indirect effects are also susceptible to whether or not thermodynamic and dynamical conditions are controlled, demonstrating the importance of conducting a comprehensive analysis of various key controlling factors altogether. 75 More recently, in situ observations have been used to evaluate and improve cirrus cloud parameterizations in global climate models (GCMs). Two types of simulations have been frequently used for model evaluation, i.e., free-running (Eidhammer et al., 2014(Eidhammer et al., , 2017Wang and Penner, 2010;Zhang et al., 2013) and nudged (D'Alessandro et al., 2019;Kooperman et al., 2012;Wu et al., 2017) simulations. For free-running simulations, a comparison on statistical distributions of ice microphysical properties is often used for model validation (e.g., Penner et al., 2009). The nudged simulation would nudge certain 80 meteorological conditions towards reanalysis data, such as horizontal wind and temperature (e.g., D'Alessandro et al., 2019;Wu et al., 2017). These nudged simulations can also be output to similar location and time as those of the aircraft observations. Given the importance and limited understanding of how aerosols interact with cirrus clouds, much attention has been dedicated to the parameterization of aerosol indirect effects Lohmann, 2002, 2003;Kuebbeler et al., 2014;Wang et al., 2014). Shi et al. (2015) added the effects of pre-existing ice into the Community Atmosphere Model 85 Version 5 (CAM5) and found a decrease in Ni due to the reduction of homogeneous nucleation frequency. Other studies also investigated the effect of updraft velocity on simulated Ni and aerosol indirect effects (Zhou et al., 2016;Penner et al., 2018).
This study aims to bridge the knowledge gap on how cirrus clouds vary depending on geographical locations and environmental conditions by using a comprehensive in situ observation dataset that includes seven U.S. National Science 90 Foundation (NSF) flight campaigns. Observations were collected onboard the NSF/National Center for Atmospheric Research (NCAR) Gulfstream-V (G-V) research aircraft. Descriptions of the seven flight campaigns, instrumentations, model configurations of the NCAR Community Atmosphere Model version 6 (CAM6) are provided in Section 2. Both observations and simulations are used to examine the regional variations in the statistical distributions of cirrus microphysical properties, including IWC, Ni and Di (Section 3). Impacts of several key controlling factors, i.e., temperature, 2 Data and Methods

In situ observations and instrumentations
In this study, in situ airborne observations at 1 Hz are provided by instruments onboard the NSF High-Performance 100 Instrumented Airborne Platform for Environmental Research (HIAPER) G-V research aircraft. A comprehensive global dataset is compiled based on seven major flight campaigns funded by the NSF, including START08 (Pan et al., 2010), HIPPO deployments 2-5 (Wofsy et al., 2011), PREDICT (Montgomery et al., 2012), TORERO (Volkamer et al., 2015), DC3 (Barth et al., 2015), CONTRAST (Pan et al., 2017), and ORCAS (Stephens et al., 2018). Table 1  For this study, ice particle measurements are provided by the Fast 2-Dimensional Cloud particle imaging probe (Fast-2DC) with a 64-diode laser array for a range of 25 µm -1600 µm. Larger particles can be reconstructed up to 3200 µm. The mass-Dimensional relationship of Brown and Francis (1995) is used to calculate IWC for the Fast-2DC probe, which was 110 previously used in other studies of the Fast-2DC probe onboard the NSF G-V aircraft (Diao et al., 2014a(Diao et al., , 2014b(Diao et al., , 2015. Number-weighted mean diameter (Di) is calculated by summing up the size of particles in each bin using the bin center, and then dividing it by the total number of particles. In order to mitigate the shattering effect, particles < 62.5 µm (i.e., first two bins) are excluded in the Fast-2DC measurements when calculating IWC, Ni and Di. The Rosemount temperature probe was used for temperature measurements, which has an accuracy and precision of ~ ±0.3 K and 0.01 K, respectively. All analyses 115 are restricted to temperatures £ -40°C, in order to exclude the presence of supercooled liquid droplets in this study.
Laboratory calibrated and quality-controlled water vapor data were collected using the Vertical Cavity Surface Emitting Laser (VCSEL) hygrometer (Zondlo et al., 2010), with an accuracy of ~6% and precision of £ 1%. Both temperature and water vapor are used at 1-Hz resolution for this analysis. Aerosol measurements were collected from the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS), which uses 100 logarithmically spaced bins ranging from 0.06 -1 µm. RHi is 120 calculated using saturation vapor pressure with respect to ice from Murphy and Koop (2005). The combined RHi uncertainties from the measurements of temperature and water vapor range from 6.9% at -40ºC to 7.8% at -78ºC.
The vertical profiles of observed in-cloud temperature, clear-sky potential temperature (Θ), and their correlations are shown in Figure 2. The observations sampled temperatures from -78ºC to -40ºC and altitudes from 5 -15 km, while a previous study of Krämer et al. (2020) sampled -91ºC to -30ºC and 5 -19 km (their Figure 2). The lowest temperatures are found in the tropical regions and at the highest altitudes, whereas polar regions show more observations at lower altitudes that satisfy temperature ≤ -40ºC. Distributions of cirrus cloud properties (i.e., IWC, Ni, Di), in-cloud and clear-sky RHi, and clear-sky water vapor mixing ratio for the observation dataset are shown in Figure 3. Di increases with decreasing altitudes, IWC slightly increases with decreasing altitudes, and Ni is almost independent of altitudes. Clear-sky RHi and water vapor mixing 135 ratio both increase with decreasing altitudes, while in-cloud RHi is centered around 100% and shows smaller dependency on altitudes. Compared with Figure 3 in Krämer et al. (2020), 48% of their ice particle samples have Di < 40 μm, which is below the size cut-off used in this study. The higher Di in this study also leads to lower range of Ni (0.01 -1000 L -1 ) and higher range of IWC (10 -5 -10 g m -3 ) compared with that previous study (i.e., Ni from 0.1 -10 5 L -1 and IWC from 10 -7 -1 g m -3 ). 140

Climate model description and experiment design
This study uses model simulations based on the NCAR CAM6 model. Compared with its previous version -the CAM5 model, CAM6 implemented a new scheme, the Clouds Layers Unified by Binomials (CLUBB) for representations of boundary layer turbulence, shallow convection and cloud macrophysics (Bogenschutz et al., 2013). CLUBB is a higher-order turbulence closure scheme that calculates prognostic higher-moments based on joint probability density function (PDFs) for 145 vertical velocity, temperature, and moisture (Golaz et al., 2002). An improved bulk two-moment cloud microphysics scheme has been implemented (Gettelman and Morrison, 2015) that replaces diagnostic treatment of rain and snow with prognostic treatment of all hydrometeors (i.e., rain, snow, graupel, hail). This is coupled with a 4-mode aerosol model (MAM4)  for simulations of aerosols and aerosol-cloud interactions. It allows ice crystals to form via homogeneous freezing simulation show very minor differences in the statistical distributions of cirrus microphysical properties and the correlations with their controlling factors when selecting different years, seasons, and days in a month.
In-cloud conditions in simulations are defined by concurring conditions of IWC > 10 -5 g m -3 and Ni > 10 -2 L -1 , which are the 165 lower limits from observations. In addition, analysis of simulated cirrus clouds is restricted to similar pressure ranges as those measured in the seven campaigns. An additional constraint on cloud fraction > 10 -5 was applied to CAM6-free to exclude extremely low values. A summary of the ranges of meteorological conditions and ice microphysical properties for in situ and simulation data is shown in Table 2. Simulated ice and snow are restricted to > 62.5 µm based on the size cut-off of the Fast-2DC probe. Note that due to the ice crystal size constraint, some thin cirrus may not be detected. IWC, Ni and Di 170 values are re-calculated by combining snow and ice for their mass and number concentrations based on a similar method from Eidhammer et al. (2014), which also combined snow and ice to compare with in situ data. In addition, simulated aerosols number concentrations are further categorized by diameters > 500 nm and > 100 nm (i.e., Na500 and Na100, respectively), by summing the size-restricted concentrations of the Aitken, accumulation and coarse aerosol modes.
Previously, field experiments found that Na500 correlates well with INP number concentrations (DeMott et al., 2010). Even 175 though that correlation was only determined based on observations warmer than -36ºC, the separation of Na500 and Na100 can help to examine the effects of larger and smaller aerosols in this work.

Cirrus cloud microphysical properties with respect to temperature
Three cirrus cloud microphysical properties, IWC, Ni and Di are examined in relation to temperature at six latitudinal 180 regions ( Figure 4). The observations of IWC and Ni in the NH indicate clear latitudinal differences with the highest values occurring in the midlatitudes, followed by tropics, then polar regions for temperatures between -40ºC and -60ºC, while for colder temperatures the NH tropical region shows the highest IWC. In the SH, the highest IWC and Ni occur in the tropics, followed by the polar regions and midlatitudes. Comparing the two hemispheres, IWC and Ni show significant reductions by ~1 order of magnitude from NH midlatitude to SH midlatitude ( Figure 5). The IWC, Ni and Di are relatively similar between 185 NH and SH tropical regions, while IWC and Di are higher in the SH polar region than NH polar regions. CAM6-nudg data show similar trend of average IWC, Ni and Di with respect to temperature as seen in observations, that is, the average IWC increases with increasing temperature consistent with previous observational studies (Krämer et al., 2016;Luebke et al., 2013;Schiller et al., 2008), average Ni shows no clear trend with temperature, and average Di increases with increasing temperature. Differing from observations, CAM6 produces the highest IWC and Ni in the tropical regions, 190 followed by midlatitudes then polar regions for both hemispheres. The simulated Di also shows little difference between hemispheres and latitudes. Overall, the major problem of the simulation is the underestimation of average IWC by a factor of 2 -10, which leads to the underestimation of average Di by a factor of 1.2 -2. The comparison of Ni shows relatively better results, with the simulated average Ni being higher than observations in the tropics at -55ºC to -40ºC and in SH extratropical regions, but lower than observations in the NH midlatitude. This result indicates "too many" and "too small" simulated ice in 195 most regions, except for "too few" and "too small" simulated ice in the NH midlatitude. The larger differences in average Di occur in the temperatures closer to -40ºC, which indicates possible misrepresentation of ice particle growth and sedimentation into the relatively warmer regions in the model parameterization. 3rd generation) by comparing with in situ observations of multiple aircraft field campaigns from 75ºN to 25ºS (Krämer et al., 2009(Krämer et al., , 2016(Krämer et al., , 2020. That study showed low biases of simulated Di at 190 -243 K, low biases of simulated IWC at 205 -235 K, as well as high biases of simulated Ni above 225 K, which are generally in the same direction as the biases we found in CAM6 model. Note that Righi et al. (2020) implemented different cloud microphysics parameterizations compared with the CAM6 model, including a two-moment cloud microphysics scheme of Kuebbeler et al. (2014) and the ice nucleation 205 parameterization for cirrus clouds (T < 238.15 K) from Kärcher et al. (2006) which account for both homogeneous and heterogeneous nucleation and the competition between the two mechanisms. More future intercomparison studies of these models are warranted to examine the reasons behind the similar biases. while almost no simulated RHi data exceed the homogeneous freezing threshold. The higher RHi observed in the NH tropical region was also observed by Krämer et al. (2009). Such feature can be explained by the competition between higher updrafts seen in the tropics and the depletion of water vapor from newly nucleated ice particles as discussed in Kärcher and 220 Lohmann (2002). For the polar regions, in-cloud RHi is skewed towards ISS in both observations and simulations, indicating less effective water vapor depletion likely due to lower Ni values (Figure 5 f).

RHi and σw distributions for in-cloud and clear-sky conditions
Regional distributions of the variance of w (σw) for in situ observations and CAM6 nudged simulations are shown in Figures   8 and 9, respectively. σw in the observations is calculated as the variance of w within each 200 seconds of data, which corresponds to a horizontal scale of ~46 km, similar to the horizontal grid scale of the CAM6 simulations. The σw in 225 simulations is based on the "wsub" variable, which is calculated from the square root of turbulent kinetic energy (TKE) (Gettelman et al., 2010). in-cloud condition. However, a secondary peak is shown in simulations at 80% RHi, which is likely due to the parameter of RHimin for ice cloud fraction calculation being set at 80% for representing variance of humidity in a grid box (more details on 240 RHimin are described in Gettelman et al. (2010)). In addition, the maximum RHi values are 170% and 180% for in-cloud and clear-sky conditions in the observations, while the CAM-nudg simulations show lower values at 160% and 150%, respectively. The CAM-free data show higher maximum RHi values than CAM-nudg data, likely due to additional data from tropical regions at temperatures below -70ºC (Figure 10 c). When using a lower size cut-off (1 μm) of ice particles for the simulation data, the number of in-cloud samples increases (supplementary Figure S1). However, negligible differences are 245 seen in the PDFs of temperature, RHi and σw for the two simulations between Figures 10 and S1. Specifically, the steeper decrease of probability for RHi > 100% is consistently shown in the simulations regardless of the ice particle size range.

Effects of RHi and σw on ice microphysics
The relationships between ice microphysical properties and RHi are examined in Figure 11. For the observations, the maximum IWC and Ni occur slightly above ice saturation at 110% RHi, while the maximum Di occur at 130% RHi. The average IWC and Ni increase 1.5 orders of magnitude from 40% to 110% RHi, and decreases 0.5 order of magnitude (i.e., a 255 factor of 3) from 110% to 130% RHi. The maximum IWC and Ni do not occur at the highest RHi most likely due to the consumption of water vapor by ice deposition. High Di values at lower RHi (~30%) are likely a result of sedimenting large ice crystals, which has been previously observed by Diao et al. (2013) when investigating the evolutionary phases of cirrus clouds.
In contrast to observations, both CAM6-nudg and CAM6-free simulations show a primary peak of average IWC and Ni at 260 80% RHi and a secondary peak at 100% RHi, with a local minimum at 90% RHi. The peak at RHi 80% is likely produced by the RHimin parameter reflecting sub-grid scale RHi variance as mentioned above (Gettelman et al., 2010). Smaller increases in IWC and Ni are shown in the simulations (i.e., 0.5 order of magnitude) compared with observations as RHi increases from 40% to 100%. Increases of average IWC and Ni are seen in the simulations as RHi increases from 110% to 140%, differing from the decreasing trend seen in the observations. The simulations may underestimate water vapor depletion rate since the 265 average IWC and Ni in the simulations are lower than the observations by 0.5 order of magnitude at 110% -140% RHi. For Di -RHi correlations, both simulations show similar results to the observations, with the maximum Di around 130% RHi and some large ice particles in the subsaturated conditions. The large variability of observed ice microphysical properties is also significantly underestimated in the model for ISS conditions. Standard deviations are 0.5 -1 order of magnitude lower for IWC and Ni and a factor of 2 lower for Di compared with observations. 270 Comparing the correlations with σw (Figure 12), the simulations show increasing IWC and Ni with higher σw, which agree with observations. The simulated Di is relatively constant with increasing σw, which differs from the observed positive correlation between Di and σw. This positive Di -σw correlation is likely due to the growth of ice particles as cirrus clouds evolve with continuous updrafts that supply excess water vapor above ice saturation, which was previously discussed in a cirrus cloud evolution analysis (Diao et al., 2013). The simulations may overlook this positive correlation due to several 275 reasons, such as the lack of temporal resolution to resolve cirrus evolution in the growth phase, the lack of vertical velocity sub-grid variabilities (as discussed in Zhou et al. (2016)), and a dry bias (i.e., lower RHi) in the model (as discussed in ).

Aerosol indirect effects
The effects of larger and smaller aerosols (i.e., Na500 and Na100) on ice microphysical properties are further examined for 280 observations and CAM6-nudg data ( Figure 13). Cloud fraction is calculated in each temperature -Na bin by normalizing the number of in-cloud samples with the total number of samples in that bin. For three cirrus microphysical properties (i.e., IWC, Ni and Di), positive correlations are seen in observations with respect to Na500 and Na100. In addition, higher Na500 (>10 cm -3 ) and Na100 (>100 cm -3 ) values are associated with significant increases in cloud fraction. At -70ºC to -60ºC, higher IWC, Ni and cloud fraction are seen when Na500 is observed, with positive correlations of IWC and Ni with respect to Na500. 285 This finding indicates that larger aerosols provide an effective pathway of ice particle formation for colder conditions. The higher IWC and Ni are only shown in much higher Na100 (>100 cm -3 ) between -70ºC and -60ºC, demonstrating that larger aerosols facilitate ice formation more effectively than smaller aerosols at this temperature range, possibly due to the activation of larger aerosols as INPs for heterogeneous nucleation.
The CAM6-nudg simulation shows increasing average IWC, average Ni and cloud fraction with increasing Na500, consistent 290 with the observations. But at temperatures below -60ºC, simulated IWC and Ni do not show a sudden increase when Na500 exists as shown in the observations. The simulated Di slightly decreases with increasing Na500, differing from the increasing trend seen in observations. For aerosol indirect effect analysis based on Na100, the comparison results are similar to Na500, that is, CAM-nudg simulation is able to represent positive correlations of Ni and cloud fraction with respect to Na100, but underestimates the average IWC, underestimates Ni below -60ºC, and misses positive correlations between Di and Na100. 295

Discussion and conclusions
In this study, we investigate the statistical distributions of cirrus cloud microphysical properties (i.e., IWC, Ni, and Di) as well as several key controlling factors (i.e., temperature, RHi, σw and Na) using a comprehensive in situ observational dataset and GCM simulations. Regional variations of cirrus cloud microphysical properties are examined for six latitudinal regions in two hemispheres. Two types of CAM6 simulations are evaluated, i.e., nudged and free-running simulations. 300 Regarding the regional variations at warmer conditions (i.e., -55ºC to -40ºC), the highest and lowest IWC values were observed in NH midlatitude and SH midlatitude, respectively, while the polar regions show the lowest Ni and highest Di (Figures 4 and 5). The hemispheric differences between NH and SH midlatitudes indicate a possible role of anthropogenic aerosols in controlling ice microphysical properties. The tropical regions show the highest IWC and Ni at temperatures below -55ºC possibly due to convection anvils with the droplet freezing from down below or homogeneous nucleation in 305 gravity waves generated by convection. This feature is corroborated by the fact that tropical regions show the highest RHi values for both clear-sky and in-cloud conditions (Figure 6), while the midlatitude and polar regions show fewer samples exceeding the homogeneous nucleation threshold. The higher RHi values in tropics are likely contributed by higher updrafts (indicated by higher σw in Figure 8). These results demonstrate the important roles of these controlling factors on cirrus clouds at different latitudinal and temperature ranges. 310 Evaluating the model simulations of cirrus microphysical properties, different model performance results are seen in different regions. For example, simulations underestimated the IWC and Ni in NH midlatitude (Figures 4 and 5), possibly due to model dry bias to form ice clouds (as discussed in Wu et al. (2017)) and/or smaller aerosol indirect effects on IWC and Ni in the simulations (Figure 13). For RHi distributions, the simulations represent a similar peak position at ice saturation for in-cloud RHi PDFs compared with observations but underestimate the frequency and magnitude of ISS for 315 clear-sky condition. For σw distributions, simulations represent similar regional variations of σw compared with observations, with σw decreasing from lower to higher latitudes. However, larger biases are seen in the simulations for the effects of RHi and σw on ice microphysical properties, including the simulated average IWC and Ni maximize at 80% RHi instead of 110% RHi as observed, and the simulation misses the increasing average Di with increasing σw as observed.
For aerosol indirect effects, the simulations underestimate IWC, Ni, Di as well as cloud fraction at colder conditions conditions. The observations also show higher Di than simulations by a factor of 3 -4 at warmer temperatures (-50ºC to -40ºC), indicating inefficient ice particle growth and/or sedimentation in the simulations. In addition, the observed IWC, Ni and Di show significant increase at higher Na500 (>10 cm -3 ) and Na100 (>100 cm -3 ), while simulations do not show such significant increase. This result indicates that aerosol indirect effects may be underestimated especially for higher Na values. 325 Overall, the global-scale observational dataset used in this study provides statistically robust distributions of cirrus cloud microphysical properties, which can be used to evaluate the effects of thermodynamics, dynamics and aerosols on cirrus clouds in a global climate model. Extending from previous studies that investigated climate model sensitivity to individual cirrus cloud controlling factors, i.e., w Liu, 2016), RHi (D'Alessandro et al., 2019), water vapor , and aerosols (Wang et al., 2014), this study provides a comprehensive analysis of all factors. In addition, further attention 330 was given towards evaluating these factors in the simulations based on geographical locations. Even though small ice particles (< 62.5 μm) are excluded in this study, correlations between ice microphysical properties and these key controlling factors are still clearly seen in the observation dataset. This study underscores the importance of correctly representing the thermodynamic, dynamic and aerosol conditions in climate models at various regions, as well as accurately simulating their correlations with ice microphysical properties. Failing to do so may result in biases of cirrus cloud microphysical properties 335 depending on different regions and temperatures, leading to biases in cirrus cloud radiative effects on a global scale.

Data Availability
Observations from the seven NSF flight campaigns are accessible at https://data.eol.ucar.edu/.

Competing interests
The authors declare that they have no conflict of interest.   In-cloud Clear sky Clear sky  Table 2 for the full ranges). 590

Clear sky
In-cloud  humidity and temperature, based on the equation of saturation vapor pressure with respect to ice from Murphy and Koop (2005).

Clear sky
In-cloud In-cloud Clear sky   observations and CAM6-nudg data, examined for (left two columns) log10(Na500) and (right two columns) log10(Na100). 630 Number of samples is shown in the bottom row. Cloud fraction is calculated as the number of in-cloud samples over the total number of samples for a given temperature and Na bin.