3.3.1 Maximum temperature
Figure 2 shows the spatial distribution of statistically significant trends in the annual average amplitude (A0), amplitudes of the annual (A1) and semi-annual cycles (A2), and phases of the annual (F1) and semi-annual cycles (F2) for monthly maximum temperature (Txmax) and monthly average maximum temperature (Txmean). Complimentarily, a summary of areas with significant trends is presented in Fig. 3.
The amplitude variation in the maximum temperature was mainly positive, and the phase variation was negative over mainland China, as shown in Fig. 2. In 1979–2020, the maximum temperatures in most parts of mainland China had a significant increase, and there was no significant decrease. The A0 of Txmax and Txmean increased significantly in 84.5% and 93.2% of areas, respectively. The regions without significant change mainly occurred on the Tibetan Plateau and South China (Fig. 2a, Fig. 2b, and Fig. 3). Studies have revealed that the South is one of the regions with the weakest warming trend in China, and the warming trend on the Tibetan Plateau ranks first among the eight major regions in China (Editing Commission of the Third National Report on Climate Change of China, 2015). In addition, the daily maximum temperature of the Tibetan Plateau from 1961 to 2015 had a warming trend (Jin et al. 2020). The areas where Txmax and Txmean significantly changed in A1 accounted for 10.0% and 9.3% of the total area of mainland China, respectively. Among them, Txmax decreased significantly, mainly on the Tibetan Plateau and Tarim Basin. The area where Txmean decreased significantly was slightly smaller than the area where it increased significantly. They appeared on the southeastern Tibetan Plateau, Tianshan Mountains and Junggar Basin (Fig. 2c, Fig. 2d, and Fig. 3). This indicates that the annual range of maximum temperature has not changed significantly in most areas over mainland China, while the annual range of maximum temperature in some areas on the Tibetan Plateau had been smaller, and that in the Tianshan and Junggar Basins had become larger. Since the amplitude of the nonzero semi-annual is not easy to interpret, it may be related to the difference in the semi-annual period or annual curve shape in the seasonal curve (Cogliati et al. 2021). Therefore, this paper only provides the results without analysis. Figure 2e and Fig. 2f show that A2 of the maximum temperatures was approximately 1/3, showing a significant positive trend and mainly distributed in the northwestern region and Yangtze River Basin.
F1 of the maximum temperature in mainland China, approximately 30% of the area, had a significant negative trend. Among these areas, Txmax mainly occurred in northwestern China and north of the Yangtze River, while Txmean had a pattern of ‘shrinking in the north and expanding in the south’, the area with a significant decrease in North China decreased, and the area with a significant decrease to the south of the Yangtze River increased (Fig. 2g and Fig. 2h). F1 reflects the time when the sine waves reached a peak, which indicates that the time when the maximum temperature appeared in the above areas in the last 42 years was delayed. Some people think that the phase change was related to a variety of mechanisms, but the influence of the change in thermal mass was greater. Thermal mass on land is largely modulated by soil moisture. If soil moisture decreases, it will produce a positive phase shift (Stine et al. 2009). Because of the lack of long-term and spatial high-resolution soil moisture datasets, it is very difficult to find conclusions supporting the above soil moisture and temperature changes from the existing studies on soil moisture changes in mainland China. The significant trend of F2 was also dominated by a negative trend, with 28.3% of Txmax decreasing significantly, mainly in the Yangtze River Basin and North China. The area where Txmean decreased significantly was approximately 1/3 of Txmax (Fig. 2i and Fig. 2j).
The above results show that the maximum temperature had a significant positive trend in mainland China. What was the spatial pattern of the trend rate? Was the change trend based on monthly temperature consistent with the annual mean temperature?
Figure 4 shows the trends in Txmax and Txmean in the 1979–2020 period (Fig. 4a and Fig. 4b) together with the trends in A0 (Fig. 4b and Fig. 4d). We can see that Txmax and Txmean in mainland China had a positive trend, and the spatial distribution and magnitudes of the trend were very consistent with their A0. They had a significant linear relationship with a coefficient of determination of 0.92. This indicates that A0 from the seasonal trend analysis method, as a representative index of annual average temperature, is also suitable for the analysis of interannual temperature. From the perspective of spatial distribution, both Txmax and Txmean had a strong warming trend on the northeastern edge of the Tibetan Plateau, eastern coast, and Inner Mongolian Plateau. In addition, combined with Fig. 2 and Fig. 4, the trend rates of the regions where the maximum temperature change was not significant were also small.
The five parameters of seasonal trends together represent the temporal dynamics of climate factors, up to 243 combinations. Were there one or several combinations with certain advantages in mainland China? What was their spatial distribution? Therefore, this paper selects the first three significant combinations from five parameters to examine the main classes and spatial distribution of the seasonal trend of each temperature element.
Figure 5 shows the first three classes of significant changes in Txmax and Txmean, which were characterized by a significant increase dominated by A0. The seasonal trend of Txmax was very distinct in mainland China, and only 9.6% of the areas did not change significantly. There were 63 significant change combinations, and the first three accounted for 46.9% of the total area. A total of 28.7% (+ 0000, red) had a significant increase in A0 and no significant increase in other parameters, mainly distributed in the northeastern and southeastern coastal areas and the Tibetan Plateau, indicating that the extreme maximum temperature in these regions increased synchronously with an insignificant temperature range, and the occurrence time of the maximum value did not change significantly. The second combination accounted for 60%, with A0 increasing significantly, while F1 and F1 decreased significantly (+ 00–, green), which was mainly distributed in the eastern Northwest China, northern Huang-Huai, and Jiang-Huai regions, indicating that the extreme maximum temperature in these regions generally increased and that the time was delayed. Both A1 and A2 also increased by 9.1% (+ 0 + 00, blue) and were mainly distributed in Northwest China and the northern margin of the Tibetan Plateau (Fig. 5a).
There were 51 combinations with significant seasonal variations in Txmena in mainland China, accounting for 96.3%. The first three classes were when A0 increased significantly (+ 0000), A0 and A2 increased significantly (+ 0 + 00), A0 and A2 increased significantly, and F1 decreased significantly (+ 0+-0), accounting for 34.8%, 16.2%, and 13.0% of the total area of mainland China, respectively. The first class was distributed mainly in Northeast China, North China, the Tibetan Plateau, and the southeastern coast. The second was mainly in the Northeast and Northwest, and the third appeared in the middle and lower reaches of the Yangtze River and Northwest (Fig. 5b). It can be concluded that in some regions of Huang-Huai and Jiang-Huai, the maximum temperature not only had a significant upward trend but also the time at which its maximum value appeared was significantly delayed. These two places are one of the main grain-producing regions in China, which provides some ideas for follow-up studies on the effect of temperature increases on grain yield.
A grid is randomly selected from the first three types of Txmax and Txmena, and the monthly dynamics of the start year (1979, black curve) and end year (2020, red curve) are fitted (Fig. 6). We can see that the shapes of the curves are different due to different parameter combinations. Even if the same class was different due to locations and elements, the seasonal trend of the same class of curves, regardless of their shapes, was consistent. For example, when A0 increased significantly (+ 0000), the overall value in 2020 was higher than that in 1979. When F1 decreased significantly, the peak time was obviously delayed (+ 00–, + 0+-0). However, the curve of a significant increase only in A0 of Txmax seems to have been significantly delayed in 2020, but the statistical test is not significant, which should be related to the large difference in the time of the maximum at this grid.
3.3.2 Minimum temperature
Similar to the maximum temperature, the minimum temperature also had a significant increase in mainland China. The A0 of monthly minimum temperature (Tnmin) and monthly average minimum temperature (Tnmean) increased significantly in 92.4% and 97.9% of areas, respectively. From this point of view, the warming of the minimum temperature was larger than that of the maximum temperature, which is consistent with existing studies (Wang et al. 2018; Wu et al. 2017), but the time variation of its minimum value was slightly smaller than that of the maximum temperature (Fig. 7g and Fig. 7h). The regions where A0 of the minimum temperature did not change significantly were scattered on the Tibetan Plateau, Northwest China, and Northeast China (Fig. 7a and Fig. 7b). In contrast, the minimum temperature in the mid-lower reaches of the Yellow River, Yangtze River Basin, Jiang-Nan, South, and eastern Southwest China showed a positive trend in the last 42 years. The above regions are major agricultural areas in China. The regions where A1 of Tnmin and Tnmean increased and decreased significantly were bounded by the 400 mm isohyet in mainland China, i.e., the temperate continental and plateau mountain climatic areas mainly increased, while the monsoon climatic areas mainly decreased (Fig. 4c and Fig. 4d). Comparing the spatial distribution of the parameters of maximum temperature and minimum temperature, we can find that A0, A1, A2, and F1 of maximum temperature; A0, A1, F1, and F2 of minimum temperature; and their trend of Txmax/Tnmin and Txmean/Tnmean had similar spatial patterns. However, A2 of minimum temperature was an exception. Tnmin showed no change in most regions, while Tnmean showed a significant increasing trend in northern China (Fig. 7e and Fig. 7f).
F1 of Tnmin had a significant change in 8.6% of the area, and the area with a significant increase was slightly smaller than that with a significant decrease (Fig. 7g). F1 of Tnmin decreased significantly in 14.4% of the area and increased significantly in 3.1% of the area (Fig. 7h). The area where F2 changed significantly was further reduced, accounting for 3.2% and 3.7%, respectively (Fig. 7i and Fig. 7j).
In the last 42 years, the spatial distribution and magnitude of the trend of minimum temperature were also similar to the trend of A0, and their linear regression determination coefficients were 0.96 and 0.94, respectively. The warming trends of Tnmin and Tnmean were generally higher in the north and lower in the south. The warming trend rate for most parts of the North was 0.04 ~ 0.08°C·a− 1, and that for the South was not more than 0.04°C·a− 1. The spatial patterns of the warming trends of Tnmin and Tnmean were also similar, and the warming trend rate of the former was higher than that of the latter (Fig. 8).
The seasonal trend of Tnmin was very distinct in mainland China, and all were mainly characterized by significant changes in amplitude, which was somewhat different from the maximum temperature. A total of 94.7% of the areas had significant changes, including 57 combinations. The first three classes of significant change accounted for 78.1% of mainland China, and the first class (+ 0000) was the most distinct, accounting for 67.6% of the total area. The A0 and A1 classes increased ( + + 000) and the A0 increase and A1 decrease (+-000) accounted for 5.3% and 5.1%, respectively, and they appeared in the western and central regions, respectively (Fig. 9a and Fig. 10).
The first three classes with significant seasonal trends in Tnmean were also dominated by amplitude, and all had increased significantly. A0 increased significantly (+ 0000), and both A0 and A2 increased significantly (+ 0 + 00). The three amplitudes all increased significantly (+++00), accounting for 52.2%, 12.6% and 5.8% of mainland China, respectively, and the latter two mainly appeared in northwestern China (Fig. 9b and Fig. 10).
From the three fitting curves, we can see the seasonal trends of Tnmin and Tnmean. Because these three classes are amplitude combinations, the phase change was insignificant at the beginning year and the end year; that is, the time of peak appearance was no different (Fig. 10).