## 4 Results
### Spatiotemporal Patterns of the CCD in the Five Periods of 2004, 2007, 2010, 2013, and 2016  
The \(K\)-means clustering method is one of the most widely used algorithms in clustering analysis. \(K\)-means clustering aims to divide \(n\) observations into \(k\) clusters, and each observation belongs to the cluster that is closest to the mean value, which serves as the prototype of the cluster [82; 83]. The \(K\)-means clustering method is an efficient heuristic algorithm that quickly converges to the local optimum [84]. Thus, we conducted the \(K\)-means clustering method and used ArcGIS spatial visualization to analyze the spatial patterns of the CCD between urbanization and urban residents' livelihood level in Mongolia, as shown in Figure 3. Based on relevant research [19; 32], the CCD is divided into four stages of moderate disorder (\(0.355\leq D\leq 0.472\)), mild disorder (\(0.473\leq D\leq 0.545\)), low-level coordination (\(0.546\leq D\leq 0.616\)), and high-level coordination (\(0.617\leq D\leq 0.748\)). The spatial patterns of the CCD were highly heterogeneous in the five periods of 2004, 2007, 2010, 2013, and 2016. In 2004 and 2007, the average CCD values existed in the moderate disorder stage. The high values of the CCD were clustered in the central part, while the low values of the CCD were clustered in the west and northeast of Mongolia. This result was approximately consistent with the spatial distribution of the level of urbanization. Some central regions have developed industries and are rich in infrastructure, and had both relatively high levels of urbanization and high livelihood levels of urban residents, such as Ulaanbaatar, Dundgovic, and Umunugovic. Thus, the values of the CCD in these regions were relatively high. However, in most of the west and northeast regions (e.g., Uvs, Bayan-Ulgii, Khovd, Knentili, and Dornod), where the economy is mainly based on animal husbandry [85; 86; 87], the livelihood levels of urban residents and the levels of urbanization were low. Although some Aimags with trade ports have improved their residents' livelihood level through foreign trade (e.g., Govi-Altai and Zavkhan), their urbanization levels were still in the preliminary stage (Figure 2A,F). Therefore, the values of the CCD in the west and northeast regions were low. In 2010, the average CCD value improved to reach 0.505, which reflected mild disorder. The spatial trend of the CCD data was less obvious in 2010 than in 2004 and 2007. Moreover, the spatial trend of the CCD was not consistent with the spatial distribution of the level of urbanization and urban residents' livelihood level. The high CCD values were mainly clustered in the central and border areas of Mongolia (e.g., Ulaanbaatar, Tov, Govisumber, Govi-Altai, Ummugovic, and Sukhbaatar), while the low values were only clustered in the northwest and northeast (Figure 3C). Although the urbanization levels of Ulaanbaatar and Tov were not the highest, the CCD values of the two regions were the largest, which may be attributable to their residents' relatively higher livelihood level. In contrast, although the urbanization level of Ummugovic was the highest, its CCD value was not the largest, which may be attributable to its low residents' livelihood level. Furthermore, although the urban residents' livelihood levels of several western Aimags were high, their urbanization levels were in the preliminary stage (e.g., Zavkhan, Arkhangai, and Bulgan). Thus, their CCD values were still lower than the central Aimags. The spatial trend of the CCD data was much more obvious in 2013 and 2016, and the average CCD values increased to 0.522 and 0.521, respectively, but still exhibited mild disorder. In 2013 and 2016, the spatial patterns of the CCD were basically consistent with the spatial distribution of the level of urbanization. In 2013, the high CCD values were only clustered in the middle of Mongolia, including Ulaanbaatar, Tov, Dundgovic, and Ummugovic.