## 3 Results
### Geometric Features of the Warm Cloud Layers
The relatively low cloud top and corresponding small thickness both arise in the several oceanic regions near the west coast of continents. Such a pattern may be correlated to the global pattern of the sea surface temperature, which determines the lower-tropospheric stability to a large extent, and in turn dominates the evolution of warm clouds [25]. The above coastal regions have cold sea surface temperatures, forcing the cloud layer to be thin. In the ITCZ and warm pool regions, all of the warm clouds tend to reach higher levels. As for the cloud top comparison among the four types, for any given location, upper layer and lower layer clouds in the warm-warm double layer system have the highest and lowest cloud top, respectively. In particular, the cloud top of upper layer ones reaches about 3.5 km in many regions. As for the thickness, warm single layer clouds and lower layer of cold-warm double layer clouds have the largest thickness, and followed by lower layer of warm-warm double layer clouds. The upper layer of warm-warm double layer clouds has the smallest thickness. In terms of grid averaging, there is no region with cloud layer thickness exceeding 720 m. In contrast, there are extensive regions with a cloud thickness above 1440 m for warm single layer clouds. The warm-warm double layer system manifests as a distinctive appearance of warm clouds. The two warm cloud layers are notably different from those in the form of a single layer or embedded in the cold-warm double layer system. Although these appearances of warm clouds account for a small part of oceanic warm clouds, they represent a subset of warm clouds that have very different geometric properties. Beside the individual geometric parameters of each layer, the cloudless spacing between the two cloud layers in such a double system was also examined, which may reflect the potential correlation of these two concurrent cloud layers. The sampling frequencies and separation distance in the two-dimensional parameter space were calculated and the results are given in Figure 8. The thickness of two cloud layers pose a constraint on the thickness of cloudless gap between the two cloud layers since the available space for warm-warm double layer system is strictly limited to the lower troposphere below freezing level as shown in Figure 5a. Taking this into account, the separation distance is found to be weakly dependent on cloud thickness. For any cloud thickness, the number of occurrences notably decreases with increasing separation distance. Most double layer systems \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Cloud Top Height**} & \multicolumn{3}{c}{**Cloud Base Height**} & \multicolumn{3}{c}{**Cloud Thickness (km)**} \\ \cline{2-10}  & \multicolumn{3}{c}{**(km)**} & \multicolumn{3}{c}{**(km)**} & \multicolumn{3}{c}{**(km)**} & \multicolumn{3}{c}{**(km)**} \\ \cline{2-10}  & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** \\ \hline Warm single layer cloud & 6.2 & 0.9 & 2.1 & 5.5 & 0.4 & 1.1 & 5.3 & 0.2 & 1.0 \\ \hline Lower cloud of cold-warm & \multirow{2}{*}{6.2} & \multirow{2}{*}{0.9} & \multirow{2}{*}{2.2} & \multirow{2}{*}{5.5} & \multirow{2}{*}{0.4} & \multirow{2}{*}{1.2} & \multirow{2}{*}{5.5} & \multirow{2}{*}{0.2} & \multirow{2}{*}{1.1} \\ double layer structure & & & & & & & & & \\ \hline Upper cloud of warm-warm & \multirow{2}{*}{6.2} & \multirow{2}{*}{1.4} & \multirow{2}{*}{3.0} & \multirow{2}{*}{5.9} & \multirow{2}{*}{1.1} & \multirow{2}{*}{2.5} & \multirow{2}{*}{4.1} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.5} \\ double layer structure & & & & & & & & & \\ \hline Lower cloud of warm-warm & \multirow{2}{*}{5.5} & \multirow{2}{*}{0.9} & \multirow{2}{*}{1.9} & \multirow{2}{*}{4.7} & \multirow{2}{*}{0.7} & \multirow{2}{*}{1.1} & \multirow{2}{*}{4.8} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.8} \\ double layer structure & & & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Statistics of geometric features for the four kinds of warm cloud layer.