2.1.1. Climate

Derived from Ge et al. [32], the paleotemperature anomalies were reconstructed with the partial least squares regression method based on multi-proxies (lake sediments, stalagmites, historical documents, tree rings, and ice cores) from five regions (northeast, central east, southeast, northwest, and the Tibetan Plateau) of China during 5–1995 CE. Due to the relatively coarse decadal resolution, the data were linearly interpolated into an annual sequence. The original data were smoothed with a five-point fast Fourier transform (FFT) filter to represent the 50-year variation. Similarly, in this study, the FFT filter was set to 50 points (via OriginLab 2018) to obtain the same low-frequency signal.

The paleoprecipitation series during 300 BCE–2000 CE was synthesized by Zhang et al. [15] from 38 document-based single-proxy hydroclimatic datasets at an annual resolution, using the composite plus scale method [33]. This is the first-published long precipitation sequence that spans the past 2000 years on the national scale. A 300-year Butterworth low-pass filter was applied to retrieve the multi-centennial cycle [15]. In this study, the imperial age 1–1911 CE was taken for consistency, and the average of this sequence was calculated to facilitate comparisons.

#### 2.1.2. Division of Climatic Cycles

On the basis of a few criteria, the temperature and precipitation series were divided into di fferent warm–cold and wet–dry cycles.

#### Temperature: Seven Warm–Cold Cycles

The paleotemperature anomalies reconstructed by Ge et al. [32] were originally divided into four warm (5–200, 551–760, 951–1320, and 1921 CE–present) and cold (201–350, 441–530, 781–950, and 1321–1920 CE) intervals. These do not cover the entire period, as this division scheme does not indicate whether 351–440, 531–550, and 761–780 CE belonged to warm or cold periods. In this study, by referencing the definitions of warm and cold phases from Zhang et al.'s [1] first study on the relationship between climate change, social unrest, and dynastic transition in historical China, the start and end of a warm or cold stage were placed in the midpoint between the highest and lowest temperature anomalies. Based on this criterion, the procedure of cyclic division was as described below:

(1) Determination of the maxima and minima over the temperature sequence: The maximum in 575 CE and minimum in 615 CE were excluded due to the short duration of the resultant warm (530–594 CE) and cold (595–659 CE) periods that lasted for only 65 years. The maximum in 1911 CE was disregarded, as the warm phase in 1873–1911 CE would have been too short to avoid any possible bias otherwise. Another minimum in 95 CE and maximum in 115 CE had a slight di fference in temperature anomalies and were not considered. Accordingly, seven pairs of extrema were identified during 5–1911 CE.

(2) Calculation of the midpoint for each pair of extrema: The midpoint from a maximum to a minimum was set as the end of a warm stage, and the year after was treated as the start of a cold phase. By contrast, the midpoint from a minimum to a maximum was set as the end of a cold period, and the year after was treated as the start of a warm stage. The maximum of 1911 CE was excluded in the calculations.

Therefore, seven temperature cycles were defined according to this division scheme (Figure 1a). Each warm and cold phase is listed in Table 1. The duration of all warm periods was 916 years, while cold periods covered 991 years in total. Hence, the warm and cold intervals were relatively balanced compared with the results from Ge et al. [32], in which there were 855 and 1010 years of warm and cold stages, respectively.

#### Precipitation: Three Wet–Dry Cycles

The paleoprecipitation reconstruction from Zhang et al. [15], which was used to discuss the interactions between agriculturalists and pastoralists in imperial China, was divided into three "Yang" (agriculturalist empires took control of the hinterland) and "Yin" (nomadic tribes invaded and established their own regimes on agricultural region) periods. The Yang–Yin division scheme is actually dynasty-oriented rather than climate-based. Specifically, Yin 1 happened from the Eastern Jin dynasty in 317 CE until the end of the Southern and Northern dynasties in 589 CE, Yin 2 occurred during the Southern Song–Yuan dynasty (1127–1368 CE), and Yin 3 coincided with the Qing dynasty (1644–1911 CE). Here, a new criterion for re-delimiting the precipitation curve was established, in which a wet (dry) phase can be defined when the 300-year smoothed precipitation is above (below) the average of the series (about 666.7 mm/year). Hence, three precipitation cycles were determined, and

over the study period, the lengths of all wet and dry periods lasted for 826 and 1085 years, respectively (Figure 1b and Table 1). 2020

Figure 1. a b **Figure 1.** (**a**) Paleotemperature anomaly under the seven-cycle scheme. Note: The annual and 50-year FFT-smoothed series are colored in yellow and red, respectively. Seven cold phases are highlighted in cyan bars. (**b**) Paleoprecipitation reconstruction under the three-cycle scheme. Note: The annual and 300-year curves (smoothed by Butterworth low-pass filter) are shown in cyan and blue, respectively. Three dry intervals are marked by yellow bars.


Table 1. **Table 1.** Divisions of warm (W)/cold (C) and wet (W)/dry (D) cycles in ancient China, 1–1911 CE.
