## 3 Results  
### Occurrences of the Three Categories of Cloud Systems  
Warm cloud layers are present in three distinct structures, i.e., warm single layer cloud system, cold-warm double layer cloud system, and warm-warm double layer cloud system. Figure 3 shows the respective occurrences of these three categories of cloud systems. The fraction of warm single layer clouds is about 77%, which indicates that most warm cloud layers occur as isolated ones, without concurrent cloud layers in the same atmospheric column. Cold-warm double layer clouds account for about 20% while warm-warm ones account for 3%. The inability of CPR to detect clouds near the sea surface may have some effects on the above individual proportions, but the quantitative contrast among these three parts should be meaningful. In the lower troposphere, two independent warm cloud layers are possible to overlap with each other. Such occurrences account for about 13% in the total double layer cases that involve a warm cloud component and represent a distinctive appearance of warm clouds. It is apparent that, by using the cloud top temperature of 273 K to identify warm clouds, the samples contain merely warm single layer and warm-warm double layer clouds. Cold-warm double layer ones, approximately 20% of the total, would be excluded, and thus the warm cloud layer at the lower portion in these systems cannot be involved in the sampling of warm clouds. Figure 4 shows the spatial distributions on the global scale for the three cloud system types that contain warm cloud layer. When considering the notable differences of sample volumes among the three categories, the global distribution of each category are normalized, which means that the global sum of all local frequencies is a unit. Such a pattern emphasizes the spatial distributions of each cloud system, rather than the occurrence differences among the three cloud systems at a certain geolocation. Since at least one warm cloud layer is present, the required atmospheric temperature conditions that lead to most of the three cloud systems are distributed in the zone between 60\({}^{\circ}\) N and 60\({}^{\circ}\) S.  
As for the specific geographic pattern, the differences are prominent among the three categories. The spatial pattern of cold-warm double layer clouds that is shown in Figure 4 resembles that of the total cloud cover shown in Figure 2a, where the few occurrences are correlated with relatively low surface sea temperature and large-scale subsidence that jointly inhibit the development of vigorous cloud systems. When compared to the other two categories, cold-warm double layer clouds tend to be more evenly distributed throughout global oceans, without notable maximum centers. The majority of frequencies are around 0.03% and the local maxima are below 0.05%. The rather weak regional differences for cold-warm double layer clouds are shown to be mostly dependent on latitude. Such relatively even distributions imply that excluding these samples from the warm cloud  
Figure 3: Occurrences of the three kinds of profiles containing warm cloud layer. ensemble does not strongly affect the global distribution pattern of warm clouds. There are three appreciable oceanic regions, with very few occurrences of cold-warm double layer clouds, all being located in low latitudes of southern hemisphere, i.e., central Indian Ocean, southeastern Pacific Ocean, and southern Atlantic Ocean. As a contrast, these three regions all have very large occurrences of warm single layer clouds, as shown in Figure 4a. The frequencies of warm single layer clouds within these regions exceed 0.07%, while they are below 0.03% at the other regions. Especially, in the low latitudes, the occurrences of warm single layer clouds lowest in the equatorial western Pacific warm pool and the ITCZ. There exists a marked zonal gradient, where the occurrences reach the maximum nearly at the east boundary of oceans and gradually decrease westward.