The First Global Insight of Cirrus Clouds Characterized by Hollow Ice Crystals From Space‐Borne Lidar

Cirrus clouds often contain numerous hollow ice crystals, which are distinct in scattering properties from solid ice crystals, and will be challenging to microphysical retrieval and radiative forcing assessment. Currently, hollow ice crystals have not been observed by remote sensing methods, and the estimation of their hollowness is a complex task. To address this issue, the Mixed Modal Hollow Columns (MMHC) model for hollow ice crystals is introduced, and its backscattering properties are computed using the physical optics approximation method. Through comparison with spaceborne lidar observations, we identify a specific type of cirrus associated with the MMHC model for the first time. The visible optical depth of this cirrus is less than or equal to 0.1, and the temperature is between −60 and −40°C. The MMHC characteristic cirrus clouds are prevalent in middle and high latitudes but less comm+on in low latitudes. They exhibit distinct patterns in terms of sea and land distribution as well as seasonal variation.


Introduction
Cirrus clouds coverage can reach up to 30% in the mid-latitudes, and even exceed 60%-80% in tropical regions (Baran, 2012).The radiative impact of cirrus on the earth system is significant and cannot be disregarded (Liou, 1986), particularly within the current global climate change trajectory.Cirrus clouds exhibit a limited capacity to reflect significant amounts of solar short-wave radiation back into space, instead, they absorb longwave radiation emitted by the earth's surface or lower-level clouds.Consequently, their climatic impact is akin to that of greenhouse gases (Gasparini & Lohmann, 2016;Lohmann & Gasparini, 2017).
From a macroscopic point of view, the radiative properties of cirrus clouds are related to the cloud optical depth (COD) (Choi & Ho, 2006).But it's essentially driven by the sizes, shapes and orientations of the ice crystals (Baran, 2009;Borovoi et al., 2013Borovoi et al., , 2014a;;Liou & Yang, 2016;Yang et al., 2013).These crystals can generally be categorized into four classes: plates, columns (including hexagonal columns, rosettes, etc.), droxtals (Lawson et al., 2019;Woods et al., 2018;Yang et al., 2001), and aggregates (Voronoi) (Ishimoto et al., 2012;Letu et al., 2016;Sato & Okamoto, 2023).Typically, plates exhibit quasi-horizontal orientation and tend to concentrate in the lower layers of cirrus clouds, while columns display a random orientation tendency at altitudes below 40°C (Bailey & Hallett, 2009;Kokhanenko et al., 2020).In higher cirrus clouds, particularly near the tropopause, crystals tend to become nearly quasi-spherical (droxtals), which is attributed to the sublimation and the decrease in atmospheric water vapor content, leading to slower vapor deposition rates (Woods et al., 2018).Following the growth of ice crystals through vapor deposition, variations in falling or rising speed result in collisions and adhesion, leading to the formation of aggregates (Gasparini et al., 2023;Sölch & Kärcher, 2011).The newly introduced Voronoi model has demonstrated greater suitability for retrieving microphysical properties and conducting radiative assessments of ice clouds compared to the plates and columns aggregation models employed in the past (Letu et al., 2016;Li et al., 2022).In recent years, the backscattering properties of these crystals have been solved (Okamoto et al., 2019(Okamoto et al., , 2020) ) through physical optical approximation (PO) method (Borovoi et al., 2014b;Konoshonkin et al., 2017).The global distribution of these crystals has also been estimated, utilizing spaceborne lidar observations (Sato & Okamoto, 2023).
However, within actual cirrus clouds, a significant proportion of ice crystals are hollow, typically accounting for more than 50% and exhibiting columnar structures (Schmitt & Heymsfield, 2007;Walden et al., 2003).The scattering properties of these hollow ice crystals markedly differ from those of solid ice crystals, which has significant effects on the retrieval of the effective radius of ice crystals and the estimation of radiative forcing (Smith et al., 2015;Takano & Liou, 1995;Yang et al., 2008).But in most remote sensing, especially in lidar observation experiments, hollow ice crystals are frequently overlooked.This oversight can impact the accuracy of lidar retrievals concerning cirrus characteristics.Hence, we introduce randomly oriented Modal Hollow Columns (MHC) and examine their backscattering properties, which offers a theoretical foundation for lidar observations (Zhu et al., 2023).
The primary objective of this study is to integrate the latest theoretical calculations of MHC backscattering properties with spaceborne lidar observations of cirrus clouds.We analyze the types of cirrus clouds that align with the theory and discuss their global distribution characteristics.

Mixed Modal Hollow Columns
In previous scattering databases of hollow ice crystals, the degree of hollow was treated as a constant value relative to the length (L) of columns (Yang et al., 2013).However, in reality, its mean value varies with temperature and L (Schmitt & Heymsfield, 2007).We employ the Hollow Hexagonal Column model, where the degree of hollow is defined as k = 2 h/L (h is the height of the cavity cone) (Chiruta, 2005) and establish an empirical relationship between n (mean value of k) and L based on the in situ observation results of Schmitt and Heymsfield (2007). (1) By using Equations 3 and 4, the backscattering Mueller matrix of the Hollow Hexagonal Column which is calculated through the PO method is derived as a weighted average, leading to the determination of the MHC backscattering Mueller matrix (Zhu et al., 2023).In Equation 3, the parameter s is standard deviation which is defined as 0.05 in order to correspond to the in situ observation results, and the p is the probability density function which will be used in Equation 4. The parameter M is the backscattering Mueller matrix of Hollow Hexagonal Column and the M is for MHC in Equation 4.
In nature, MHC does not occur independently and is typically combined with Solid Hexagonal Columns (SC).Thus, we define the Mixed Modal Hollow Columns (MMHC) for this purpose.The backscattering properties of MMHC are derived by superimposing the backscattering Mueller matrix of the SC and the MHC in a specific proportion after accounting for the spectrum distribution of the effective crystal radius.Although a significant number of rosettes are present in cirrus clouds, particularly in in situ cirrus formation (Bailey & Hallett, 2009;Lawson et al., 2019), Timofeev et al. (2023) indicated that a single column and a combination of columns exhibit nearly identical backscattering properties, and their disparity in scattering cross-sections in various directions is

Geophysical Research Letters
10.1029/2024GL109852 primarily influenced by the number of columns.This discovery eliminates the need to construct a separate model to characterize rosettes when utilizing MMHC for studying columnar ice crystals.
Considering computational efficiency, we have currently calculated the MMHC with L ranging from 10 to 316 μm, in which the maximum dimension is approximately 340 μm.This range, supported by in situ observations, is representative of typical columnar ice crystals (Lawson et al., 2019).The depolarization ratio and color ratio, utilized for comparing lidar observations, are obtained from the backscattering Muller matrix of MMHC.
Figure 1 shows the theoretical calculation results calculated at 532 and 1,064 nm wavelengths, there are large gaps between the patterns of 95% MHC and 100% MHC attributed to the nature of SC.Only when proportion of SC is infinitely small, these gaps can be filled.Meanwhile, there is no evidence supporting the assertion that the proportion of MHC in cirrus clouds can reach 100%.From Figure 1 in this paper and Figure 8a of Okamoto et al. (2020), we also can notice that if MHC accounted for more than 95%, the theoretical calculated value of MMHC will be close to that of droxtals and Voronoi.Therefore, we assume that the proportion of MHC in MMHC does not exceed 95%.The dashed black rectangle in Figure 1 which is defined as MMHC approximation region represents the depolarization ratio ranged from 0.22 to 0.39 and the color ratio ranged from 0.48 to 0.74, which are obtained from theoretical calculations of the MMHC model.

Satellite Data
To enable global observations of clouds and aerosols, the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite was launched in 2006 (Winker et al., 2010).The onboard Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) lidar is able to identify cirrus clouds in view of the globe (Sassen et al., 2008).We used data identified as cirrus clouds by the version 4.20 CALIOP level-2 Merged layer 5 km product from 2016 to 2019.

Comparison With Spaceborne Lidar Observations
The CALIOP data set provides only the attenuated color ratio of cirrus clouds.Generally, the corrected color ratio of cirrus is slightly higher than the attenuated color ratio, although the difference is minimal (Tao et al., 2008).In this study, we analyze a sufficiently large number of cirrus samples about 79,437,361, and considering the combined effects of observation errors in the CALIOP system we choose to overlook this factor.
Figure 1.The relationship between depolarization ratio and color ratio of MMHC with different mixing degree.The depolarization ratio is calculated at 532 nm wavelength and the color ratio is calculated at 1,064 and 532 nm wavelengths.
The distribution characteristics of cirrus clouds and the types of ice crystal within them depend on latitude (Sassen et al., 2008;Sato & Okamoto, 2023).Therefore, we examined the correspondence between cirrus samples and MMHC globally, as well as specifically in low ( 30°-30°), middle (30°-60°and 60°-30°), and high (60°-90°a nd 90°-60°) latitudes.From the perspective of in situ observation, cirrus clouds can be broadly classified into three layers.Regions with temperatures above 40°C are predominantly characterized by plates and aggregates formed through collision, adhesion and sedimentation in the lower part.In the temperature range between 60 and 40°C, rosettes are prevalent.Ice crystals below 60°C typically exhibit quasi-spherical and irregular shapes (Bailey & Hallett, 2009;Yang et al., 2001).As depicted in Figures 2i-2l, the percentage of cirrus samples within MMHC approximation regions concentrated in the temperature range of 60 to 40°C is higher compared to the total samples for each latitude region.This finding aligns with the characteristic distribution of columnar ice crystals observed in situ.
Without restricting COD, the depolarization ratio of cirrus clouds in various latitudes predominantly fall within the range of 0.2-0.5, while the attenuated color ratio is primarily situated between 0.8 and 1.2 (Figures 2a-2d).
The COD of cirrus clouds is typically related to their life cycle.Initially, in the formation stage, the COD is minimal.As the ice crystal nucleation rate rises and the ice crystal number concentration increases, the COD subsequently grows following vapor deposition.However, during the mature stage of cirrus clouds, larger ice crystal particles within the cloud may descend to lower layers leading to a reduction in number concentration and COD (Baran, 2012;Kärcher et al., 2009).Meanwhile, the variation in COD can influence the geometric thickness of cirrus clouds, typically showing a positive correlation between them.In our statistical samples, for thicker cirrus clouds, such as COD values above 0.3, typically exhibit a temperature difference exceeding 20°C between the cloud base and the cloud top.The types of ice crystal within these cirrus clouds exhibit noticeable diversity, often forming distinct layers.The vertical motion process of crystals in cirrus clouds is also associated with COD.
Cirrus clouds with larger COD exhibit more vigorous vertical development, resulting in stronger vertical ascending or descending air motion inside.This dynamic environment is more conducive to the collision and adhesion process of ice crystals, leading to the formation of aggregates (Sölch & Kärcher, 2011).
As depicted in Figures 2e-2h, we observe that when the COD of cirrus clouds is less than or equal 0.1, with the exception of low-latitude regions, the core region with the maximum frequency of cirrus cloud samples in the two-dimensional histogram closely corresponds to the MMHC approximation region.And this correspondence will diminish when 0.1 ≤ COD ≤ 0.2.We find that as COD increases, the final characteristics tend to resemble those in Figures 2a-2d.Based on our statistics, cirrus cloud samples with COD ≤ 0.1 make up nearly 50%.We estimate in these thin cirrus clouds the degree of ice crystal collision and adhesion is not strong and they still exhibit the optical properties associated with simple ice crystal types (columns, droxtals etc.).While the color ratio of aggregates is typically higher than that of columns and closely resembles quasi-spherical shapes (Okamoto et al., 2019(Okamoto et al., , 2020)), which also explains the performance characteristics of cirrus samples with higher COD in Figures 2a-2d.
As evident in Figures 2b and 2f, a significant number of cirrus clouds with quasi-spherical ice crystal characteristics are observed at low latitudes, where the cirrus cloud temperature is lower than 60°C (Figure 2j), and both the depolarization ratio is greater than 0.4 and the attenuated color ratio is greater than 0.8.This is particularly noticeable in the thin cirrus samples with COD ≤ 0.1 (Figure 2f).This phenomenon is associated with the abundance of tropical tropopause layer (TTL) cirrus clouds generated by circulation and gravity waves in the tropics (Gasparini et al., 2023;Sassen et al., 2009).
In Figure 2i, the proportion of samples with the temperature of 60 to 40°C (columnar ice crystal characteristic temperature) exceeds 55% in the statistics of cirrus samples with COD ≤ 0.1 in MMHC approximation region, which indicates a good consistency with the MMHC model.To investigate characteristic cirrus clouds corresponding to the MMHC model, we extracted samples with COD ≤ 0.1 and temperatures ranging from 60 to 40°C, as illustrated in Figure 3.These cirrus clouds constitute approximately 20% of all observed cirrus clouds.Compared with Figures 2e and 3a, the samples exhibiting quasi-horizontal orientation characteristics (depolarization ratio is less than 0.1) of ice crystals in cirrus clouds are significantly reduced when temperature conditions are constrained.And according to our statistics, these samples have decreased by about 81%.In low latitudes, the correspondence between sample frequency and the MMHC model is also improved, as seen by comparing Figures 2f and 3b, and the proportion of cirrus samples in MMHC approximation region increased from 11% to 17%.
Meanwhile, due to the high convective intensity at low latitudes, the influence of MMHC collision and adhesion cannot be entirely disregarded in thin cirrus clouds (Baum et al., 2011).In comparison with low and middle latitudes, the correspondence between the model and observation is less favorable.However, considering the limited number of samples available at low latitudes, approximately 18.6% of all latitudes, and the global representation of this cloud type, as depicted in Figure 3a, remains highly consistent with the MMHC model.In the future, the accuracy of radiative forcing estimation and remote sensing retrieval for such thin cirrus clouds is expected to be further improved by using this model with taking into account ice crystal surface roughness and deformation factors (Borovoi et al., 2015;Saito & Yang, 2023).

Global Distribution
The global geographic distribution of MMHC characteristic cirrus clouds is statistically studied using 4-year CALIOP observation data.We interpolate the satellite orbit data into a 5°× 5°latitude and longitude grid and calculate the occurrence frequency of such cirrus clouds at each grid point during different months, as illustrated in Figure 4.
In general, the Intertropical Convergence Zone (ITCZ) and the monsoon circulation in lower latitudes generate more deep convective activities, leading to a substantial occurrence of injection cirrus.Cirrus clouds appear much more frequently near the equator compared to the poles (Sassen et al., 2008).While Figure 4 illustrates that low latitudes display seasonal variation characteristics similar to most cirrus clouds, the global distribution perspective reveals contrasting features.Such cirrus clouds are abundant in high latitudes where the average frequency is as high as 15%, whereas the sample size is relatively small in low latitudes where the average frequency is only 6%.In autumn (SON) and winter (DJF), MMHC characteristic cirrus occurs more frequently in the high latitudes of the northern hemisphere than in the high latitudes of the southern hemisphere, and the difference of average frequency can reach 2%-4%.In spring (MAM) and summer (JJA), the opposite trend is observed.This may be related to seasonal variations in convective intensity at high latitudes.Furthermore, the spatial distribution of MMHC characteristic cirrus differs between land and sea, with a higher frequency observed over land, particularly in high latitude regions.As shown in Figure 4, Antarctica, Siberia, and Greenland exhibit the highest frequency of such cirrus which can reach more than 24%.In summary, the impact of such cirrus on the radiative forcing of the Earth system is significantly greater at high latitudes than at low latitudes.

Conclusion
This study presents the first remote sensing observation of cirrus features associated with hollow ice crystals.The characteristic cirrus of MMHC is identified by comparing the color ratio and depolarization ratio of the MMHC model, calculated using the PO method, with 4 years of CALIOP data.Cirrus clouds of this type, characterized by COD ≤ 0.1 and temperatures between 60 and 40°C.The observed MMHC characteristic cirrus accounts for approximately 20% of all observed cirrus clouds, and its impact on radiative forcing throughout the earth system cannot be ignored.The formation of such cirrus clouds is also related to the strength of convection, as convection facilitates the collision and adhesion of ice crystals leading to the formation of aggregates.Consequently, the frequency of MMHC characteristic cirrus in low latitudes is relatively low, and the correspondence between observational results and theoretical calculations is even less favorable compared to middle and high latitudes.
The seasonal global distribution of MMHC characteristic cirrus shows distinct patterns.In autumn and winter, the high latitudes of the northern hemisphere exhibit higher frequency compared to those in the southern hemisphere, which is opposite in spring and summer.The distribution of such cirrus also varies between land and sea, especially at high latitudes where they occur more frequently on land such as in Antarctica, Siberia, and Greenland.
In the future, with comprehensive consideration of surface roughness and deformation factors, we can make a more accurate estimation of the scattering properties of such cirrus clouds.This approach is more conducive to the retrieval of cirrus microphysical properties and the evaluation of radiative forcing.While achieving this may pose challenges, it is undoubtedly a priority that needs to be addressed in the future.
Figure2illustrates the comparison between the statistical samples of cirrus observed by CALIOP and the MMHC model over a span of 4 years.To facilitate comparison, we apply min-max normalization to the frequency of cirrus samples collected in the two-dimensional histogram and the dashed black rectangles are MMHC approximation regions.The CALIOP data contains temperature at the layerattenuated backscatter centroid altitude.In Figures2i-2l, we calculated the probability density distribution of this temperature for cirrus samples with different COD, as well as those specifically within MMHC approximation regions for each latitude area.