**3. Results**

#### *3.1. Global Moran's I*

The results of the Global Moran's *I* are provided in Table 3. The values ranged between 0.37 and 0.59 and were all significantly positive (*p* < 0.01), which indicates the cluster e ffect of war (i.e., positive spatial autocorrelation or spatial dependency) and the feasibility of EHSA. In addition, except for agri-nomadic conflict between warm and cold phases, the statistics during all cold and dry intervals were larger than those in warm and wet stages. This illustrates that battles became more concentrated in cold and dry climate, but were slightly scattered in warm and wet conditions. The indexes for all war at any climatic mode were the largest, probably because each cell of the grid contains more battlefields. This is followed by rebellion, and agri-nomadic conflict had the smallest values (except that the value for rebellion in warm periods was the smallest), which means there seems to be a positive correlation between battle number and the degree of the concentration of war.

**Table 3.** The Global Moran's *I* for three kinds of war in all warm/cold and wet/dry intervals.


Note: \*\* *p* < 0.01.

#### *3.2. Mann–Kendall Trend Test*

Table 4 shows that except for wet periods, the hot spots for all war during the other climatic phases failed to pass the M–K test as the trend statistics were insignificant. The statistics for agri-nomadic conflict at any climatic stage were significantly positive compared with those for all war. The value for all warm intervals was the largest (8.446, *p* < 0.01) amongs<sup>t</sup> all statistics. For rebellion, the counterpart of all warm stages failed to pass the M–K test at the level of 0.05, whereas other statistics were positively significant, and the value for wet conditions was the largest (4.075, *p* < 0.01). Thus, the results of the trend test indicate that notwithstanding the di fference in climatic phase, the frequencies of agri-nomadic conflict and rebellion in imperial China basically increased through time.

**Table 4.** Trend statistic for three categories of war during all warm/cold and wet/dry phases


Note: \*\* *p* < 0.01, \* *p* < 0.05.

#### *3.3. EHSA Pattern and Explanation*

The explanations of the spatial patterns of EHSA involve many geographical names (Figure S2) and historical periods (Table S1) in China. Figure 3a shows that hot spots were preponderantly distributed in northern China, i.e., from the border between Qinghai and Gansu to western Liaoning, during all warm stages. Only a few oscillating hot spots were located in the Yangtze River Delta. Intensifying hot spots indicate that the areas were becoming increasingly hot (i.e., battles were becoming increasingly frequent). They were chiefly concentrated in central Shaanxi–eastern Gansu and southern 2020

Shanxi–the North China Plain and surrounded by other types. Beyond that, the south and north were predominantly occupied by historical versus sporadic and oscillating hot spots, respectively. As historical hot spots are hot most of the time but not hot in the most recent time, this situation implies the alteration of hot spots in history. To the north, probably along the Great Wall, battles were not as frequent as those in intensifying hot spots; therefore, they were categorized as sporadic or oscillating. Similarly, battles were occasionally clustered, but scattered or even absent sometimes in the Yangtze River Delta, which created oscillating hot spots.

**Figure 3.** EHSA patterns of all warm and cold periods for three types of war: (**<sup>a</sup>**,**b**) All war, (**<sup>c</sup>**,**d**) agri-nomadic conflict, and (**<sup>e</sup>**,**f**) rebellion. Only significant hot spots (*p* < 0.05) are shown (the same as Figure 4).

By contrast, intensifying hot spots moved massively southeastward to the Central Plain and more prominently to the Jianghuai region and the lower reaches of the Yangtze River during all cold intervals (Figure 3b). The original hot spots in warm periods turned into diminishing hot spots, along with a few sporadic or oscillating cells in central Shaanxi–eastern Gansu and the North China Plain. Since diminishing hot spots are opposite to intensifying hot spots in nature, this alteration indicates a less hot pattern of war (or less frequent battles) in northern China over time. Furthermore, the hot spots in all cold stages were generally situated farther south/southeast as they disappeared from northeastern Qinghai and central Gansu to the northern Loess Plateau and northern Hebei, whereas they appeared to the south of 30◦ N in a larger proportion. However, as battles in the middle–lower reaches of the Yangtze River–Yangtze River Delta and near the border of Hunan, Guangxi, and Guizhou were only concentrated during certain intervals, the hot spots in these areas were categorized as oscillating or sporadic.

Figure 3c,d visualize the EHSA patterns for agri-nomadic conflict over all warm and cold stages. In Figure 3c, there were only two sporadic hot spots, while others were oscillating hot spots, extending from central Gansu to western Liaoning. This pattern represents the confrontations between agricultural empires and nomadic tribes/regimes along the Great Wall in historical China. However, when carefully examining the time-series, the conflicts contained by oscillating hot spots were concentrated in two main periods: The Northern Song and Ming dynasties (Table S1). The war against the Liao and Western Xia for the former, and that against the Mongols for the latter, occupied the largest proportion, whereas battles during other stages were not intensive. This result is in line with the definition of oscillating hot spot, i.e., occasionally hot (highly clustered), occasionally cold (sparsely scattered), and the last time step (i.e., in the Ming dynasty) is hot.

In comparison, the hot spots for agri-nomadic conflict in cold climate principally shifted southeastward (Figure 3d). Although some cells remained in northern China, they do not match the scale in warm stages. Instead, hot spots (again prevailingly classified as oscillating) were more concentrated in the Jianghuai region, the lower reaches of the Yangtze River–Yangtze River Delta, and Fujian. Similarly, they are related to the distributions of battles during certain phases. Those in the Jianghuai region and the lower reaches of the Yangtze River–Yangtze River Delta resulted from N–S confrontations, such as northern dynasties versus southern dynasties and Jin versus Southern Song (Table S2). The hot spots in Fujian could be explained by the Ming–Qing war. Given that these oscillating hot spots emerged in different periods, the existence of this category is understandable.

The EHSA patterns for rebellion in all warm and cold stages are depicted in Figure 3e,f. In Figure 3e, the hot spots in all warm periods expanded outward and were clustered in four separate parts: Sichuan, the Central Plain, Taiwan, and Guangxi–Guangdong. Five kinds of hot spots were generated: new, diminishing, sporadic, oscillating, and historical. Historical and diminishing hot spots only emerged in the Central Plain, where rebellions were concentrated in earlier eras but gradually became less frequent. Oscillating hot spots mostly appeared in Guangxi and Guangdong, in which battles largely occurred in later eras but were not dense. Sporadic hot spots were distributed in the Chengdu Plain and its northwest, with a few adjacent to diminishing hot spots in northern China. Battles in these areas were concentrated, ye<sup>t</sup> they were occasionally intensive in some intervals. Finally, the new hot spots in western Taiwan may denote the recent revolts during the Qing dynasty.

The rebellion hot spots in all cold phases were more clustered (Figure 3f). The majority of them were oscillating hot spots, spreading from eastern Guizhou to northern Zhejiang and occupying the middle reaches of the Yangtze River. Another group in the Loess Plateau was adjacent to sporadic hot spots, which extended from Guanzhong to the Central Plain, with another part emerging in the Yangtze River Delta. Other types—such as consecutive, intensifying, and diminishing hot spots—appeared in northern China with a few cells only. Diminishing hot spots were situated north of intensifying hot spots, which implies the southward movement of the war focus through time. A comparison with the warm climate pattern showed that the hot spots in the northern Central Plain (southern North China Plain) changed from diminishing (sporadic) cells in all warm intervals to intensifying–consecutive (diminishing) ones in all cold phases. As a traditional warring zone in ancient China, the northern Central Plain became increasingly hot in recent time steps, particularly during the Ming–Qing transition and the late Qing dynasty. Sporadic hot spots in the Guanzhong–Central Plain and the Yangtze River Delta were not always hot. To the south, oscillating hot spots primarily included the rebellions during later cold stages, indicating the inward contraction of rebellion in cold periods.

The spatial patterns derived from EHSA during all wet and dry stages are visualized in Figure 4. Figure 4a presents the result of all wet periods for all war. Similar to Figure 3a, four types of hot spots (intensifying, diminishing, sporadic, and oscillating) dominated northern China and stretched from eastern Gansu to the North China Plain via Guanzhong, Shanxi, and the Central Plain. They also spread southeastward to the Jianghuai region, the lower reaches of the Yangtze River, and the Yangtze River Delta, but were exclusively covered by oscillating hot spots. Intensifying hot spots were clustered in most of the North China Plain, where battles became increasingly frequent through time. By contrast, in Guanzhong and the eastern Central Plain, the cells that belonged to diminishing hot spots became gradually less hot or not hot in the end, which implies a possible northward movement of battle over time. A striking contrast was observed between the patterns of all wet and dry stages. In Figure 4b, intensifying hot spots shifted to present-day Jiangsu, while the cells in the north mostly turned into diminishing hot spots. Others, such as sporadic and oscillating hot spots, laid in the north (along 40◦ N) and south (the lower reaches of the Yangtze River) respectively, with a few historical cells scattered around.

Figure 4c,d present the EHSA patterns for agri-nomadic conflicts in all wet and dry stages. The hot spots during wet periods were all clustered in northern China, i.e., from central Ningxia to eastern Hebei, and included three types: intensifying, sporadic, and oscillating. Oscillating hot spots were mainly distributed in Ningxia, northeastern Gansu, and northern Shaanxi, while intensifying hot spots in the North China Plain were surrounded by sporadic ones. The di fferences among them may have resulted from the proportions of time steps in three wet phases. Still, most hot spots were found in the north during all dry stages (Figure 4d), but their range elongated outward from two sides. The western end extended into central Gansu, while the eastern end extended into northern Liaoning. A few hot spots appeared in the lower reaches of the Yangtze River, which di fferentiates the patterns between wet and dry phases. All hot spots in northern China were oscillating, indicating the confrontations between agricultural and nomadic regimes along the Great Wall, which escalated in later times. Sporadic and new hot spots emerged in the lower reaches of the Yangtze River and coastal Fujian, respectively. Hence, the hot spots in southern China represent the southward nomadic invasions, and the new hot spot can be associated with the Manchu conquest during the Ming–Qing transitional period.

The EHSA results for rebellion in all wet and dry intervals are displayed in Figure 4e,f, which are similar to the patterns for all warm and cold stages in Figure 3e,f. The three separate parts in all wet phases indicate that hot spots were clustered in the Central–North China Plain, the lower reaches of the Yangtze River, as well as Guangxi and Guangdong (Figure 4e). The northern part, which was primarily occupied by sporadic hot spots, was surrounded by several oscillating ones, while the latter laid in the eastern and southern parts. For rebellions in sporadic hot spots, there were more time steps during the second wet period, but oscillating hot spots included more battles during the last wet stage. Thus, the hot spots in the north and south presented di fferent patterns. The hot spots during all dry phases were principally concentrated in the lower reaches of the Yangtze River–Yangtze River Delta and expanded southwestward to eastern Guizhou, part of Hunan and Guangxi, along with those from Guanzhong to the Central Plain (Figure 4f). Except for several diminishing hot spots in the north with surrounding sporadic ones, oscillating hot spots dominated the pattern. The di fference between sporadic and oscillating hot spots may be attributed to the proportions of time steps in di fferent dry stages. For diminishing hot spots, rebellions were less frequent in later periods, which implies the southward movement of rebellion focus through time.

2020

Figure 4. a b c d e f **Figure 4.** EHSA patterns of all wet and dry stages for three kinds of war. (**<sup>a</sup>**,**b**) All war, (**<sup>c</sup>**,**d**) agri-nomadic conflict, and (**<sup>e</sup>**,**f**) rebellion.
