Analyzing the Thermodynamic Phase Partitioning of Mixed Phase Clouds Over the Southern Ocean Using Passive Satellite Observations

The thermodynamic phase transition of clouds is still not well understood, therefore, the partitioning of ice and liquid in mixed phase clouds is often misrepresented in numerical models. We use 12 years of cloud observations from the geostationary Spinning Enhanced Visible and InfraRed Imager over the Southern Ocean to detect clouds which contain both liquid and ice pixels at their tops and we retrieve microphysical and radiative properties in each cloud object. The results show that large cloud droplet effective radius coincides with high ice fraction and high ice optical thickness for cloud top temperatures higher than −8 °C. We also found that the density of ice pixel clusters increases with the cloud ice fraction, for ice fraction lower than 0.5, suggesting a multiplication of ice pockets in line with previous studies, particularly efficient for clouds with high perimeter fractal dimension.

higher for simulations in which the phase partitioning is constrained by satellite observations. The authors have also shown that the cloud glaciation process is sensitive to the spatial distribution of phase within the clouds, that is, the presence of ice and liquid pockets or homogeneously mixed ice crystals and liquid droplets (Tan & Storelvmo, 2016).
The Southern Ocean is one of the cloudiest region on Earth and the frequency of mixed phase clouds is high (Korolev et al., 2017;Wang et al., 2003). The cloud thermodynamic phase partitioning has been determined as essential to simulate and quantify the cloud radiative impact in the Southern Ocean (Vergara-Temprado et al., 2018). Gettelman and Sherwood (2016) attributed the cloud phase as a key process to determine cloud feedback effect in the Southern Ocean. Many field campaigns took place in the Southern Ocean to study cloud microphysical and radiative properties (McFarquhar et al., 2020). Mace, Protat, et al. (2020) have shown that Southern Ocean clouds tend to be thicker with smaller and more numerous hydrometeors than other latitudes. With airborne measurements, Ahn et al. (2017) showed that 38.5% of the clouds contained ice, mainly from mixed-phase clouds, and they suggested that these clouds were considered as ideal for the Hallet-Mossop secondary ice production process. Mace, Benson, and Hu (2020) studied mixed phase clouds in the Southern Ocean with active satellite measurements and showed that they are associated with precipitation, suggesting efficient secondary ice processes. Noh et al. (2019) developed an algorithm to study the mixed phase clouds using passive satellite observations. Korolev et al. (2017) differentiate mixed-phase clouds using different scales from in situ, active remote sensing and passive remote sensing observations. They highlighted that there is not a consensus to define mixed-phase clouds and it depends on the considered instruments. In situ and radar data have smaller averaging scale than passive satellite observations, thus they are difficult to compare.
All the different cited studies analyzed the vertical structure of clouds to define the mixed phase category. Horizontal cloud phase inhomogeneities have not been in the focus of analyses for any Southern Ocean campaign to our knowledge, in contrast to arctic clouds (Curry et al., 2000;Schäfer et al., 2018). Since the phase partitioning and the spatial distribution of the ice and liquid within clouds are important for the radiative properties and the evolution of clouds but not well understood nor represented in numerical models, we take a new perspective and we consider the horizontal inhomogeneity on cloud top to define the mixedphase category. The present study analyses how clouds transition from mainly liquid to mainly ice. We also aim to describe and quantify the impact of cloud parameters on the ice fraction and we speculate about the potential reasons. We use 12 years of mixed phase cloud properties from a passive space-based sensor over the Southern Ocean and we analyze the ice and liquid fraction at the cloud top for each cloud for different regimes of cloud droplet radius, optical thickness, and cloud top temperature. The study does not aim to retrieve liquid and ice properties within the same pixel, but rather considering mixed-phase clouds at the pixel scale, considering the pixel as strictly liquid or ice. We also analyze the spatial distribution of ice and liquid pixels within mixed phase cloud top to understand how clouds evolve from dominantly liquid to dominantly ice.

Data Sets
The Spinning Enhanced Visible and Infrared Imager (SEVIRI), on board the geostationary METEOSAT second generation satellites, provides measurements with a temporal resolution of 15 min and measures in the visible and infrared. The SEVIRI disk is centered at 0° and covers the European and African continents and parts of the eastern edge of South America. The spatial resolution is 3 km at the sub-satellite point for 11 channels in the visible and infrared and for the High Resolution Visible (HRV) channel the resolution is 1 km at the sub-satellite point. The CLoud property dAtAset using SEVIRI -edition 2 (CLAAS-2, Benas et al., 2017;Stengel et al., 2014) retrieves cloud properties from recalibrated measurements following Meirink et al. (2013). The data set does not include measurements with a solar zenith and viewing zenith angles greater than 84° to mitigate potential uncertainties (Grosvenor & Wood, 2014) (See Text S1 in the supporting information for more details). Details are given in Benas et al. (2017) but we summarize hereafter the methods used to retrieve parameters relevant to our study.
Cloud top pressure uses the infrared measurements compared with clear-sky and cloudy radiative transfer simulations from the Radiative Transfer model for Television infrared observation satellite Operational COOPMAN ET AL.
The cloud top phase is determined by a decision tree using a combination of five spectral channels from 6.2 to 13.4 μm and simulated clear and cloudy sky radiances from RTTOV. The decision tree classifies cloud phase into six categories: liquid, supercooled, opaque ice, cirrus, overlap, and overshooting. The six categories are converted to liquid or ice (Benas et al., 2017).
For our analysis, we use instantaneous CLAAS-2 data at native spatiotemporal SEVIRI resolution and projection from 2004 to 2015.

Method
We define cloud objects as clusters of fully cloudy pixels surrounded by clear sky and we consider cloud objects containing both liquid and ice pixels at cloud tops: These clouds are considered in this study as mixed phase, but it is important to note that it does not include vertically mixed-phase clouds, for example, liquid top with ice below clouds. We set a minimum size for the considered cloud objects of 30 pixels (a schematic of a typical cloud and examples of such clouds observed by SEVIRI are shown in Figure S1 in the supporting information and described in Text S2). Mace and Protat (2018) have shown from field campaign measurements that cloud occurrence in the Southern Ocean is dominated by low-level layers but high clouds can also be present. Only cloud objects with a difference in top temperature of less than 10 °C are considered in order to exclude multi-layer clouds detected as one cloud object. The choice for the threshold is ad-hoc but represent a good compromise between the number of analyzed cloud objects avoiding multilayer clouds. We determine the cloud properties associated with each cloud object: the mean CTT, the mean liq e r and ice e r , the mean τ for the liquid and ice pixels, and the ice fraction defined as: with N ice and N liq the number of ice and liquid pixels, respectively. For each mixed phase cloud object, the mean size and the number of so-called ice and liquid pockets, which are respectively clusters of ice and liquid pixels, are calculated.
Clouds in the Southern Ocean can be associated with cold and warm fronts (Naud et al., 2010), stratus clouds (Hudson et al., 1998), cumulus, frontal, cirrus, and stratocumulus (Bodas-Salcedo et al., 2012). There are several criteria which enable to differentiate these cloud types, such as their fractal dimension estimated as the area-perimeter relation and defined as (Batista-Tomás et al., 2016;Lovejoy, 1982): with A the cloud area, P the perimeter, and D(P) the perimeter fractal dimension. It is important to note that P represents the boundary between the cloudy and clear-sky pixels. If there are clear-sky pixels within the cloud object, they affect P and D(P). For a circle or a square, D(P) is equal to one but increases when the cloud shape is more complex. In the present study, to estimate the shape of each cloud object, we consider that: If D(P) is low, the cloud object shape is similar to a cumulus clouds but if D(P) is high, the cloud object shape is similar to a frontal cloud (see Text S2 and Figure S1 in the supporting information for more information).
Cloud property retrieval algorithm for passive satellites do not treat mixed phase clouds as a separate category, therefore, cloud properties are retrieved considering pixels as only-liquid or only-ice. Coopman et al. (2019) have shown that pixels detected as ice by the retrievals are likely to be contaminated by liquid droplets and have an artificially low ice e r . On the opposite pixels detected as liquid but potentially contaminated by ice crystals have an artificially high liq e r . As our data set includes cloud objects for which ice pixels are in contact with liquid pixels, liquid pixels are potentially contaminated by ice crystals and vice-versa. To reduce this bias, we do not consider pixels that are at the interface between liquid and ice phase pockets within the cloud objects to reduce the likelihood of being contaminated by particle of the other phase. These pixels are not considered in retrieving cloud optical properties nor the ice fraction (cf. Equation 1). Moreover, pixels for which the uncertainty on the phase does not allow to retrieve cloud properties are discarded from the study. Figure 1 shows the mixed phase cloud fraction defined as the number of mixed phase cloud objects divided by the number of all cloud objects over the SEVIRI disk for the four seasons in 2010. The spatial distribution of mixed phase at cloud top is similar to the global phase distribution shown by Korolev et al. (2017) based on CloudSat and CALIPSO observations. In the tropics, mixed phase clouds are associated with deep convective clouds and mid-level stratiform clouds. There is also a high fraction of mixed phase clouds at high latitudes already observed by previous studies (e.g., Intrieri, 2002;Shupe et al., 2001;Shupe et al., 2005). Mixed phase clouds are also common over the Southern Ocean (e.g., Hu et al., 2010;Huang et al., 2012;Kanitz et al., 2011) with an averaged fraction between 42% (Winter) and 48% (Spring). We focus our study on mixed phase clouds over the Southern Ocean with latitudes ranging from −60° to −40° and longitudes ranging from −60° to 60°. At these latitudes, the spatial resolution of the CLAAS-2 data set is between COOPMAN ET AL.   r is 16.0 μm for χ ice from 0.46 to 0.99. Larger cloud droplets associated with higher χ ice have already been observed in previous studies (e.g., Coopman et al., 2018Coopman et al., , 2019Rangno & Hobbs, 2001;Rosenfeld & Lensky, 1998;Rosenfeld et al., 2011). It has been suggested that large cloud droplets are more prone to secondary ice production  via rime splintering for temperatures between −8 °C and 0 °C (Hallett & Mossop, 1974). Also, large cloud droplets freeze to large ice crystals which are more prone to ice shattering. An other possible explanation is that ice is more absorbing than liquid in the near infrared so a contamination of ice crystals within a liquid-detected pixel would artificially increase the size of liquid droplets following the Nakajima and King (1990). In the current article, we do not focus on the freezing temperature (given by χ ice as a function of temperature) but a short discussion can be found in Text S3 and Figure S2.

Results and Discussion
The secondary ice processes are associated with an ice multiplication mechanism (Hobbs & Rangno, 1990;Koenig, 1963) and, therefore, an increase in the ice crystal concentration (Hobbs & Rangno, 1998;Mossop, 1970;Rangno & Hobbs, 2001), which is not retrieved by algorithms based on passive sensor measurements. For liquid clouds, τ is related to droplet number concentration (N c ), mean cloud droplet size (r ) and cloud geometrical thickness (h) as (Petty, 2006): assuming that cloud parameters do not vary within the cloud and that r is much larger than the wavelength. Similarly, we can assume that τ of ice clouds is also proportional to the number concentration of ice crystals, r and h. So, if we constrain for ice e r , a variation in optical thickness of ice pixels has to be associated with a variation in the cloud geometrical thickness and/or ice crystal concentration. The constrain for temperature COOPMAN ET AL.  ranges limits the impact of geometrical height on τ but we cannot rule out this dependence with the available information. It is important to note that ice number concentration cannot be retrieved from passive satellite measurements only, therefore we cannot estimate the primary nor the secondary ice number concentration. Clouds with larger cloud droplets are associated with higher ice fraction which has been speculated to be a sign of the secondary ice production by previous studies. Therefore, to support this theory, the increase in high ice fraction should be associated with an increase in ice number concentration associated here with the optical thickness of ice pixels. Figure 3 shows the optical thickness of the ice pixels as a function of liq e r of the same cloud objects for three temperature ranges and constrained for ice e r considering the first and third quartiles as thresholds to choose a narrow interval: from 21.0 to 25 μm. We observe that the optical thickness of ice pixels is increasing with liq e r for the temperature bins from −20 °C to −8 °C and from −8 °C to 0 °C and for the two regimes of ice e r . For example, for CTT between −8 °C and 0 °C, τ ice increases from 0.7 for liq e r between 3 and 9 μm to 1.4 for liq e r between 14 and 34 μm. In contrast, for CTT between −30 °C and −20 °C, the optical thickness variation is smaller than for the other CTT ranges but it should be noted that the range of mean τ ice is larger for the coldest CTT range than for the two other CTT ranges. We did the same analysis considering the measurement uncertainties in the optical depth rather than the upper and lower quartiles of the distributions and it did not change the conclusions (for more information, see Figure S3 and Text S4 in supporting information).
When regimes of liq e r lower than 9 μm and greater than 14 μm are compared, τ ice increases on average by 31% for CTT between −30 °C and −20 °C, by 50% for CTT between −20 °C and −8 °C, and by 95% for CTT between −8 °C and 0 °C. Therefore, we speculate that the increase in ice crystal concentration with  efficient for CTT between −8 °C and 0 °C confirming the hypothesis of active secondary ice processes associated with large cloud droplets.
We defined the ice pocket density as the number of ice pockets divided by the pixel number of the cloud (see Text S2 and Figure S1 in the supporting information for more details). Figure 4a shows the ice pocket density as a function of χ ice for four regimes of liq e r . We observe that for each bin of liq e r , the increase in χ ice is associated with an increase in the ice pocket density, reaches a maximum of 0.063 ice pockets per pixel for χ ice between 0.4 and 0.6, and then decreases. The increase in χ ice is not associated with a spread of glaciated cloud phase from pixel to pixel but rather there are multiple ice pockets not connected to each other. When χ ice is greater than 0.5, ice pockets merge decreasing the ice pocket density.
We observed that higher liq e r is associated with higher ice fraction but we do not know if liq e r stimulates the number of ice pockets. Figure 4a shows that the maximum difference in ice pocket density is 0.01 per pixel for χ ice between 0.8 and 1 comparing  In the aim to better understand the evolution of ice pocket density with χ ice for different types of clouds, Figure 4b shows the ice pocket density as a function of χ ice for four regimes of shape parameter D(P). Similarly to Figure 4a, the ice pocket density increases with χ ice and reach a maximum for χ ice from 0.4 to 0.6 and then decreases. We also observe that the larger D(P), the higher the ice pocket density. For χ ice between 0.4 and 0.6, the ice pocket density is equal to 0.05 per pixel for D(P) lower than 1.96 and 0.08 per pixel for D(P) greater than 2.13. Clouds with ragged boundaries are associated with a higher ice pocket density than clouds with regular boundaries. There is a correlation between the cloud size and the ice pocket density (not shown) which could explain the link between D(P) and the ice pocket density. But, when the data are constrained for D(P), there is no correlation between the cloud size and the ice pocket density (see Text S5 and Figure S4 in the supporting information for more details). Therefore, results from Figure 4b, do not depend on either resolution effect nor on cloud size. As the optical thickness decreases when pixels transition from liquid to ice, the pixels can become undetectable by satellite observations. D(P) will increase if parts of ice pockets are undetected.
The ice pocket density increases with χ ice but is the increase in density enough to explain the variation in χ ice or does the ice pocket increase in size? Figure 4c shows the median pocket size for different χ ice considering ice and liquid pockets. The mean ice pocket size increases from 50 to 217 km 2 with χ ice increasing from 0 to 0.6 and then the ice pocket size increases to 977 km 2 for χ ice equal to 0.99. The median liquid pocket size decreases from 1,667 to 183 km 2 with the χ ice increasing from 0 to 0.6 and then the ice pocket size decreases to 53 km 2 for χ ice equal to 0.99. When χ ice is lower than 0.05, one liquid pocket and one ice pocket represents 44% and 1% of the cloud size respectively. When χ ice ranges between 0.45 and 0.55, one liquid pocket and one ice pocket represents 8% and 7% of the cloud size respectively. When χ ice is greater than 0.95, one liquid pocket and one ice pocket represents 2% and 40% of the cloud size respectively (see Text S6 and Figure S5 in the supporting information for more information).
From Figure 4b and 4c, we observe that the median ice pocket size and the ice pocket density increase with χ ice when χ ice is less than 0.6. When χ ice is greater than 0.6 and the ice pocket density decreases, the increase in the median ice pocket size as a function of the χ ice is steeper. On the opposite, the median liquid pocket size decreases when χ ice increases and the increase in size is more rapid, possibly when the ice pockets merge with each other for χ ice greater than 0.6.

Conclusion
We analyzed 12 years of space-based observation from the geostationary sensor SEVIRI to analyze the thermodynamic phase partitioning of the top layer of clouds over the Southern Ocean. Our results show that clouds with large droplets are associated with a higher χ ice for different cloud top temperature ranges in line with previous studies (Coopman et al., 2018;Coopman, Hoose, & Stengel, 2020;Coopman, Riedi, et al., 2020;Rosenfeld & Lensky, 1998;Rangno & Hobbs, 2001;Rosenfeld et al., 2011). For the temperature ranges from −20 °C to −8 °C, and from −8 °C to 0 °C, large cloud droplets are also associated with higher optical thickness of ice pixels, while the effective radius of ice crystals is constrained, which can be used as a proxy of geometrical height or ice crystal concentration. We speculate that χ ice increases with large cloud droplets can be associated with secondary ice processes for CTT ranging from −8 °C to −0 °C but further analysis are needed to confirm and quantify this effect.
We also analyzed the distribution of the ice and liquid pixels within mixed phase clouds by defining ice pockets as cluster of ice pixels. Large cloud droplets are not associated with higher density of ice pockets but clouds with a high perimeter fractal dimension are. We quantified the size of the ice pockets for different χ ice . When χ ice increases, the ice pocket size increases in the same time as new ice pockets are forming. When χ ice is greater than 0.5, the ice pocket size increases rapidly with χ ice and the ice pockets are merging, decreasing their density.
Satellite observations allow to hypothesize on causes and consequences. We hypothesize that a variation in optical thickness of ice pixels is associated with a variation of ice crystal concentration if it is constrained for ice e r . The product liDAR-raDAR (DARDAR) based on CALIPSO and CloudSat observations retrieves ice crystal concentration (Sourdeval et al., 2018) and can quantify the increase in ice crystal concentration associated with larger cloud droplets. Our data set and the analysis of mixed phase cloud top could be used for the evaluation and constrain of models in particular convection-permitting models to better understand the causes and the consequences of the effects discussed related to mixed phase clouds.