## 3 Results
### Geometric Features of the Warm Cloud Layers  
Since two warm cloud layers coexist in the warm-warm double layer structure, there are, in practice, four appearances for warm cloud layers that are present in the previous three categories of cloud systems. Besides single-layer warm clouds, the other three forms include the lower layer in a cold-warm double layer structure, the upper layer in a warm-warm double layer structure, and the lower layer in a warm-warm double layer structure. Although they all belong to the warm cloud category according to their cloud top phase, they get different treatment in passive measurements based remote sensing. Only single-layer warm clouds can be correctly identified. The ones that are embedded to the cold-warm double layer structures are mostly missed, while the two layers in the warm-warm double layer structure may have been mistaken as a single layer. Therefore, the occurrences of warm clouds would be underestimated. Based on the improved sampling of cloud layers by CPR, the geometric parameters, including cloud top height, cloud base height, and cloud layer thickness, are analyzed for the four kinds of warm cloud layers. The frequency distributions are displayed in Figure 5, with an interval of 240 m for the ordinate. The detailed statistical parameters are given in Table 1 for a straightforward comparison. The warm single layer clouds and lower layer of cold-warm double layer clouds have quite similar frequency distributions of the geometric parameters, as shown in Figure 5. The top height of these two types of warm cloud layers are mostly around 1.5-2.5 km, and their base heights are mostly around 0.5-1.5 km. The maximum, minimum, and average values are similar. At least for these geometric parameters, there is no difference between these two kinds of warm cloud layers, although they are involved in different cloud systems. Such a similarity suggests that the concurrence of a cold cloud layer at an upper level hardly impact the warm cloud layer at the lower level, and thus the two cloud layers in the cold-warm double layer system are independent to each other. In this way, those that are embedded in the cold-warm double layer system are indistinguishable from those appearing as a single layer system in terms of geometric properties. The upper and lower cloud layer in the warm-warm double layer system are found to have distinct features from the previous two kinds of warm cloud layers. Their geometric thickness is much smaller, especially the upper one that is only 0.5 km on average. When comparing the cloud top and base height with the previous two kinds of warm clouds, the upper (lower) cloud layer in the warm-warm double layer system tend to be higher (lower). Taking cloud top height as an example, those of the upper one appear around 3.0 km altitude,  
Figure 5: Frequency distribution of cloud top height (**a**), base height (**b**), and geometric thickness (**c**) of the four types of warm cloud layers. while those of the lower one tend to occur below 2.0 km, as provided in Table 1. In contrast to the independence between the two cloud layers in the cold-warm double layer system, these two cloud layers in the warm-warm double layer system are likely to be coupled, which makes the geometric properties of both these two cloud layers differ from those as a single layer system. The above statistics all are globally derived. When considering their distinct patterns of occurrences on the global scale, the cloud layer altitude and thickness characteristics may also be dependent on geographic regions. The averaged top height and thickness of these four kinds of warm cloud layers are shown in Figures 6 and 7, respectively. The regional dependence is found to be evident, but it is not alike that of the occurrences of each kind of clouds. There is a clear gradient from equator to the poles, with the maxima being located in the tropics. For all four kinds of cloud structures, without considering the absolute quantities, their spatial distribution patterns are similar.