## 4 Results
### Drought Spatial Distribution Pattern
#### 4.2.2 Drought Spatial Distribution Pattern for Clusters  
The clusters of the meteorological stations are shown in Figure 7a, and they are divided into three clusters in terms of geography (Figure 7b) as per city boundaries. Cluster 1 includes most of the western meteorological stations, Cluster 2 includes the northeast stations, and Cluster 3 includes the southern stations. This clustering result is consistent with the division of the economic zones and landform types of Hunan [53]. Cluster 1 is located in undeveloped economic conditions where landforms are dominated by mountains and plateaus. Cluster 2 is in less-developed economic conditions where landforms are surrounded by mountains and plains. Cluster 3 is located in well-developed economic conditions where landforms are dominated by basins and hills. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Cluster 1**} & \multicolumn{3}{c}{**Cluster 2**} & \multicolumn{3}{c}{**Cluster 3**} \\ \cline{2-10}  & **H(1)** & **H(2)** & **H(3)** & **H(1)** & **H(2)** & **H(3)** & **H(1)** & **H(2)** & **H(3)** \\ \hline DD & 0.25 & 0.38 & \(-\)0.47 & 0.46 & \(-\)0.21 & 0.02 & 0.39 & \(-\)0.13 & 0.42 \\ DS & 0.21 & \(-\)0.25 & 0.39 & 0.37 & \(-\)0.37 & 0.90 & 0.34 & \(-\)0.07 & \(-\)0.68 \\ DI & 0.39 & \(-\)0.38 & 1.13 & 0.33 & \(-\)0.16 & \(-\)0.27 & 0.44 & \(-\)0.02 & \(-\)0.14 \\ Latitude & 0.47 & \(-\)0.52 & 0.04 & 0.56 & 0.05 & \(-\)1.06 & 0.17 & \(-\)0.41 & \(-\)0.83 \\ Longitude & 0.69 & 0.73 & \(-\)0.13 & 0.34 & \(-\)0.78 & 0.31 & 0.34 & \(-\)0.50 & \(-\)0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Heterogeneity test results for different clusters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Clusters (k)** & \begin{tabular}{c} **Nbclust** \\ **(Number of** \\ **Indicators)** \\ \end{tabular} & \begin{tabular}{c} **Mclust** \\ **(Number of** \\ **Indicators)** \\ \end{tabular} & \
\begin{tabular}{c} **Elbow Rule** \\ **(SSE)** \\ \end{tabular} &
\begin{tabular}{c} **Calinsky** \\ **Criterion (VRC)** \\ \end{tabular} \\ \hline
2 & 4 & NA & 17.49 & 28.93 \\
3 & 7 & 4 & 13.63 & 30.36 \\
4 & 4 & NA & 11.20 & 30.42 \\
5 & 1 & 3 & 9.57 & 29.91 \\
6 & NA & NA & 8.56 & 28.4 \\
7 & NA & NA & 7.68 & 27.57 \\
8 & NA & NA & 6.87 & 27.45 \\
9 & NA & NA & 6.12 & 27.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantity evaluation measurements for different numbers of clusters. The investigation of the features of the centroid for each cluster shows that most of the drought events in Cluster 1 are slow droughts with low intensity and frequency. Cluster 2 has fast droughts with high intensity and frequency. Cluster 3 is highly susceptible to severe droughts. From the perspective of the features of ADD-ADS-ADI, the drought duration of Cluster 1 is long, but the intensity of each drought event is weak. Cluster 2 shows opposite drought characteristics relative to Cluster 1 (Figure 8a-c). The MDI value of Cluster 3 is large, which means that this area is prone to severe drought (Figure 8d). From the perspective of total drought duration and frequency, although Cluster 1 has the fewest drought events from 1965 to 2015, the duration of the events is the longest, whereas cluster 2 shows an opposite characteristic relative to Cluster 1 (Figure 8e,f). Figure 8: Box plot of station drought characteristics of the three clusters (average drought duration (**a**) (ADD), average drought severity (**b**) (ADS), average drought intensity (**c**) (ADI), max drought intensity (**d**) (MDI), total drought durations (**e**) (TDD), and total drought events (**f**) (TDE). Figure 7: Regionalization of meteorological stations: (**a**) Spatial distribution of clustering stations and (**b**) division of arid space according to the clustering stations. To explore the differences in the dry/wet transitions of the three clusters at the same time, we calculated the time series values of the three clusters of SPEI-12. The differences in the status of drought transitions in the three periods were determined.