3.1 The S/N in annual temperature extremes during 850−2005 in China relative to the pre-industrial level
3.1.1 Mean temperature
First, time series of area-weighted regional mean S/N in annual mean temperature during 850−2005 over the land grid point of China for bias-corrected six CMIP5 models and their multi-model median relative to the pre-industrial level are shown in Fig. 1a. The S/N in annual minimum and maximum temperatures have similar features to annual mean temperature during 850−1850 (Fig. S4a). Before 1850, regional mean multi-model median S/N in annual mean temperature over the whole China are from –0.8 to 0.1. In other words, regional mean changes in annual mean temperature over China do not exceed natural variability during 850−1850 at the level of S/N > 1, based on the multi-model median S/N.
Nevertheless, annual cold signals in periods 1245−1303, 1446−1461, 1597−1614, 1647−1650, 1684−1727, and 1801−1829 emerge from natural variability at the level of S/N > 1 at local scale (Fig. 2a). For example, during 1245−1303, 1684−1727, and 1801−1829, the proportions of the areas where the multi-model median S/N in annual mean temperature are smaller than –1 to the whole country are from 0.4% to 25.1%, from 0.4% to 11.0% and from 0.5% to 4.9%, respectively. These large S/N may be driven by volcanic events (Fig. 1d), particularly after the large eruptions in 1257, 1452, 1600, and 1815 (Hartl-Meier et al. 2017). The results from six individual models are similar to the multi-model median except CSIRO-Mk3L-1-2, which has some warm signals in annual mean temperature during 850−1850. In addition, CCSM4, IPSL-CM5A-LR, and MPI-ESM-P have stronger signals than multi-model median and the other three models with respect to volcanic forcing during 850−1850 (Fig. 1a and Fig. 2a).
During the period 1851−2005, regional mean signal in annual minimum, mean, and maximum temperature begins to be larger than natural variability in 1971, 1972, and 1980 at the level of S/N > 1, respectively (Fig. 1a and Fig. S4a). At local scale, the warm signals in annual mean, minimum and maximum temperatures begin to emerge in 1929, 1933, and 1944 at the level of S/N > 1, respectively, and occur in most of China until 2005 (Fig. 2a and Fig. S4a). These warm signals are mainly caused by greenhouse gas forcing (Fig. 1a and Fig. 1d, Schmidt et al. 2011). All six individual models have warm signals in the 20th century, and the time of emergence in signals in annual temperature for IPSL-CM5A-LR is earlier than that for other five models at the level of S/N > 1 (Fig. 1a).
Next, S/N in annual mean temperature from CMIP5 models are compared with that from LMR. On one hand, median signals in annual mean temperature of LMR over China do not emerge from natural variability at the level of S/N > 1, either (Fig. 1a). Specifically, median regional mean S/N in annual mean temperature from LMR over China during 850−1850 are in the range of –0.7 to 0.6. Moreover, the correlation coefficient between median S/N in annual mean temperature from CMIP5 models and that from LMR during 1400−1850 (0.25) is higher than that during 850−1399 (–0.30). In addition, both of them show that the early 19th century is a cold period. However, local signals from the median runs of LMR do not emerge from natural variability during 850−1850 after the volcanic forcing in the CMIP5. On the other hand, during period 1851−2005, both CMIP5 simulations and LMR have the increasing trend for S/N in annual mean temperature, and their correlation coefficient is 0.87 (Fig. 1a). Nevertheless, the time of emergence in median regional mean signals of annual mean temperature over China for LMR is 10 years later than that for CMIP5 models at the level of S/N > 1.
3.1.2 Cold extremes
The temporal information of annual cold nights (TN10p) is consistent with annual mean temperature variations in China, with larger (smaller) S/N in cold (warm) climatic conditions before 1850 (Fig. 1a and Fig. 1b). The regional mean S/N in annual cold nights range from 0.1 to 1.5 before 1850. Specially, during both 1247−1276 and 1810−1828, regional mean S/N in annual cold nights in China are larger than 1. At local scale, the increasing signals in annual cold nights emerge from natural variability in the 13th century and from the end of 16th century to the first half of 19th century at the level of S/N > 1. It is worth mentioning that during 1261−1276 and 1817−1827 the increasing signals in annual cold nights emerge from natural variability in more than half of China at the level of S/N > 1. The correlation coefficient between S/N of cold nights and radiative forcing from volcanic aerosols is –0.50, –0.95, and –0.54 during the period 900−1200, 1201−1449, and 1450−1850, respectively, and the correlation coefficients between multi-model median S/N of cold nights and other radiative forcings are low (Table 3). The results from six individual models are also similar to the multi-model median during 850−1850 except that CSIRO-Mk3L-1-2 has some warm signals in annual cold nights, and that CCSM4, IPSL-CM5A-LR, and MPI-ESM-P have stronger signals than multi-model median and the other three models with respect to volcanic forcing at the level of S/N > 1 (Fig. 1b and Fig. 2b).
During 1851−2005, regional mean median S/N in annual cold nights in China are from –1.2 to 0.4, with decreasing signals exceeding natural variability from 1984 (Fig. 1b). All six individual models also have decreasing signals in annual cold nights, and the time of emergence in signals of annual cold nights for IPSL-CM5A-LR is earlier than that for other five models (Fig. 1b). Local decreasing signals in annual cold nights emerge from noise in 1970s for multi-model median (Fig. 2b).
The other cold extreme indices, such as cold days (TX10p), frost days (FD), and icing days (ID) have similar features to cold nights (TN10p), but their absolute values of S/N are generally smaller than that of cold nights (Fig. S4c−S4d). To be specific, regional mean increasing signals in annual cold nights and cold days over China emerge from natural variability during 1247−1276 and 1810−1828, and there are no regional mean signals in other temperature extremes for the whole country before 1850. At local scale, the increasing signals in annual cold nights, cold days, frost days, and icing days exceed natural variability in the second half of the 13th century and in the early 19th century. The local increasing signals in annual cold nights and cold days are outside natural variability from the end of the 16th century to the end of the 18th century.
Compared to the identification about the extreme cold winter events in southern China during 1650−2000 from Zheng et al. (2012), it is consistent that low frequency cold nights (TN10p) in winter in southern China occurs in 1730−1800 and in the second half of the 20th century (Fig. S5a). Both of them show that high frequency cold nights in winter in southern China occurs in 1800−1850 (Fig. S5a), but simulation presents that the first half of this period has more cold nights than the second part has, and that is opposite to Zheng et al. (2012). In addition, they find the intensities of some cold events in southern China are strong, such as those during 1653–1654, 1670, 1690, 1861, 1892 and 1929. The simulation can reproduce that both in 1690 and in 1892, with a weak magnitude (Fig. S5b–S5c).
3.1.3 Warm extremes
The warm extreme indices, such as warm days (TX90p), summer days (SU), tropical nights (TR), hottest day (TXx), and warmest night (TNx) have similar features to warm nights (TN90p), but their absolute values of multi-model median S/N are generally smaller than that of warm nights (Fig. S4b−S4d). Consistent with annual mean temperature changes, larger (smaller) absolute values of multi-model median S/N in warm nights occur in cold (warm) climatic conditions during 850−1850 (Fig. 1a and Fig. 1c). However, there are no regional mean multi-model median signals in these warm extremes for the whole country before 1850, with regional mean multi-model median S/N in annual warm extremes being from –0.6 to 0.03. At local scale, the decreasing signals in annual TNx and TR exceed natural variability in the second half of the 13th century and in the early 19th century. The local decreasing signals in annual TNx are also larger than natural variability in the middle of the 15th century. For individual models, CCSM4, IPSL-CM5A-LR, and MPI-ESM-P have decreasing signals in warm nights with respect to volcanic forcing during 850−1850 (Fig. 1c and Fig. 2c).
As for multi-model median results, regional mean increasing signals in annual warm nights, warm days, and tropical nights for the whole country emerge from natural variability during 1851−2005, with the regional mean signals first occurring in 1969 for annual warm nights (Fig. 1c, and Fig. S4c−S4d). There are some local signals in almost all annual warm extremes during 1851−2005, with local signals first occurring in 1929 for annual warm nights (Fig. 2c, and Fig. S4b−S4d). The local increasing signals in annual warm nights emerge from natural variability until 1989 for all grid points of the whole country (Fig. 2c). All six individual models also have increasing signals in annual warm nights, and the time of emergence in signals of annual warm nights for IPSL-CM5A-LR is earlier than that for other five models (Fig. 1c, and Fig. 2c).
According to the research of Zhang and Gaston (2004), the northern China heat wave in summer 1743 is severe, and another strong case is in 1215. From the view of S/N, the signals of summer maximum temperatures in 1215 and 1743 do not exceed natural variability over China based on simulation (Fig. S6). Moreover, models cannot capture the features of hot events in 1215, but represent a weakly warmer summer in northern China in 1743 (Fig. S6b−S6c). The other warm extreme indices have similar results with summer maximum temperature (Fig. S6d−S6e).
3.2 The S/N in annual temperature extremes in subregion of China relative to the pre-industrial level
We examine the spatial patterns of S/N in temperature extremes by dividing China into four roughly equal area land regions, including northwestern China (NWC), northeastern China (NEC), Tibet Plateau (TP), and southern China (SC) (Fig. 3). On one hand, the noise variance decreases with averaging (Hawkins and Sutton 2012). On another hand, these regions were determined by annual mean temperature (Fig. 3a), noise of temperature extremes (Fig. 3b−3c), administrative boundaries and societal and geographical conditions.
Time series of area-weighted regional mean S/N in annual mean temperature, cold nights, and warm nights during 850−2005 over the land grid point of four regions in China for multi-model median relative to the pre-industrial level are shown in Fig. 4. The multi-model median S/N in annual mean and extreme temperatures in subregions of China during 850−1850 have similar features to that in China (Fig. 4−5). The annual mean and extreme temperatures have some differences among four regions with respect to volcanic forcing during 850−1850 (Fig. 4−5). For example, northeastern China has local signals in annual cold nights with respect to strong volcanic forcing, such as after the large eruptions in 1257 and 1815; northwestern China, Tibet Plateau, and southern China have local signals in annual cold nights with respect to both weak and strong volcanic forcing (Fig. 1d and Fig. 5b). The other cold extremes, such as cold days, frost days, and icing days, have similar regional features during 850−1850, but their areas where signals emerge from natural variability are smaller than that for cold nights (Fig. S7). Compared our results with the reconstruction by Li et al. (2021), both of them show that the early 19th century is a cold period in Tibet.
As for warm signals during the 20th century, the time of emergence in signals of annual warm nights in Tibet Plateau, southern China, and northwestern China is earlier than northeastern China (Fig. 4−5). All the time of emergence in signals of the other temperature indices is latter than that of warm nights in each region of China (Fig. S7−S8).