**3. Results**

#### *3.1. The Spatiotemporal Pattern of Temperature*

In order to understand the temperature variations during the period of 1980–2012 in the YRD, we first analyzed the overall trend of temperature variation by using the linear trend method, and the linear slope is used to identify the trend of temperature changes. If the linear slope is greater than 0, it indicates that temperature is increasing, if the linear slope is equal to 0, it means that temperature is not changing, and, if the linear slope is less than 0, it indicates that temperature is decreasing. It showed a significant increasing trend during the period of 1980–2012 (Figure 5), and this trend may continue in the future. We can see that the temperature rose 1.53 ◦C with the average rising rate of 0.465 ◦C/10 years and passed the significance test during the period of 1980–2012. However, in the most recent 50 years, the global average rising rate only has reached about 0.13 ◦C/10 years [35]. We can conclude that the increase in temperature in the YRD was not only the result of global warming, but also other regional factors.

**Figure 5.** The trend of temperature during the period of 1980 to 2012.

Then, we showed the spatial distribution of TS during the period of 1980–2012 (Figure 6). The ordinary Kriging method was used during the interpolation, in which a spherical model is used when selecting the semi-variogram model, and its parameters are system default parameters. We can see that the temperature rose in all regions. In addition, among the dense areas of population and urban, the temperature rose quickly, while the temperature in the sparse areas of population and urban rose slowly.

**Figure 6.** Temperature slope (change rate of temperature) during the period of 1980–2012.

#### *3.2. The Spatiotemporal Complexity of Temperature*

#### 3.2.1. The Temporal Complexity of Temperature

Based on meteorological data, we analyzed the chaotic dynamics with fractal characteristic for the temperature dynamics by using the G–P method [36]. Firstly, we randomly selected six meteorological stations (i.e., Bozhou, Nanjing, Nantong, Wuhu, Hangzhou, Dongtou) with annual time series data for a pilot study. The relationship between different embedding dimension (*m*) and correlation exponent (*d*) was shown in Figure 7.

**Figure 7.** The plots of correlation exponent (*d*) versus embedding dimension (*m*) for the time series of annual data from the selected six meteorological stations

It can be seen from the trend of the six meteorological stations in Figure 7 that, as the embedding dimension increases, the correlation exponent increases continuously and eventually stabilizes, and the saturated correlation exponent, namely, the correlation dimension, was obtained when *m* ≥ 10.

Then, we calculated the CD on the daily, seasonal and annual temporal scales of each station in the same way. Table 1 shows the CD values of several representative stations and average CD values of all stations at different temporal scales. It can be seen from Table 1 that each CD is not an integer, which indicates that the temperature process at different temporal scales is a chaotic dynamic system with a fractal characteristic, and it is sensitive to the changes of initial conditions.


**Table 1.** The Correlation Dimension (CD) values at daily, seasonal, and annual scales for 68 meteorological stations.

Note: MCD is the mean of correlation dimensions for all meteorological stations.

It can be seen from the mean of correlation dimensions (MCD) at different temporal scales in Table 1 that the ordering of the CD is: annual (2.32) > seasonal (2.08) > daily (1.73). We can conclude that the temperature process over a larger temporal scale is more complicated than the temperature process at a small temporal scale. Figure 8 showed the temperature anomalies of daily range and temperature anomalies of annual range. It could be seen from the maximum, minimum, and variance that the annual temperature fluctuated greatly, which proved that the temperature process on the annual scale was more complicated. Table 1 also shows that, even at the same temporal scale, the CD values of different stations are different. It is mainly related to the different locations of each station, which makes the driving factors of each station different. The values of MCD on the seasonal and annual scales are greater than 2, with 2.2 and 2.4, respectively, indicating that at least three independent variables are needed to describe the dynamics of temperature process on the seasonal and annual scale; and the value of MCD for daily is 1.73, indicating that at least two independent variables are needed to describe the dynamics of temperature process on the daily scale.

**Figure 8.** (**a**) anomalies of the daily range and (**b**) anomalies of the annual range.

3.2.2. The Spatial Distribution Complexity of Temperature

Table 1 gives the CD values of the temperature on different temporal scales, showing temperature dynamics on the daily, seasonal and annual scales. What is the spatial distribution of the CD values of different stations? We show the spatial distribution of CD values on the daily, seasonal, and annual scales (Figure 9). The ordinary Kriging method was used during interpolation, in which a spherical model is used when selecting the semi-variogram model, and its parameters are system default parameters.

**Figure 9.** The spatial pattern of complexity of the temperature process at daily (**a**), seasonal (**b**), and annual (**c**) scales.

Figure 9a shows the spatial distribution of CD values on the daily scale, with values between 1.46 and 1.87. High value is mainly distributed in the northwest and southwest of the entire region, while low values are mainly distributed in the eastern coastal areas. Figure 9b presents the spatial distribution of CD values on the seasonal scale, which shows that all CD values are between 1.51 and 2.34. High value is mainly distributed in the northwest of the entire region, while low values are mainly distributed in the eastern coastal areas. Figure 9c shows the spatial distribution of CD values on the annual scale. All CD values are between 1.73 and 2.99, and the spatial pattern is similar with the spatial pattern on the seasonal scale. As we all know, the eastern coastal areas, especially Shanghai, Suzhou, and Hangzhou, are densely populated and have high levels of urbanization, and the CD value of this area is relatively low, while the areas located in the northwest of the YRD, such as Bozhou, Xuzhou, and Fuyang, the large outflow of people results in a relatively small population in these areas, and the urbanization level is relatively low, and the CD value in this area is relatively high. It can be seen that the population density and the urbanization level are related to CD.

In general, on different temporal scales, the high values of CD are mainly distributed in the sparse areas of population and urban, while the low values of CD are mainly distributed in the dense areas of population and urban.

3.2.3. The Influences of Driving Factors and Their Interactions on Temperature Slope

From the above results, we can see that the spatial distribution of TS is different, and what is the reason for this result? In order to answer this question, we choose some driving factors (AT, NDVI, UD, GDP, and NL) that affect the temperature to explore the reasons of this phenomenon by using the Geogdetector method.

The factor detector is used to detect whether the driving factors affect TS and the size of their influences. In addition, the greater the value of *q*, the greater the influence of this factor on TS. Table 2 shows the result of the factor detector. On the whole, the influence, in order of size, of each factor is: UD (0.323) > GDP (0.234) > NL (0.218) > NDVI (0.118) > AT (0.047). In addition, all driving factors pass the significant test, which means that these five factors have significant effects on TS. In addition, we can see that the contribution rate of socioeconomic factors (UD, GDP, NL) is greater than natural factors (NDVI, AT).


**Table 2.** The result of factor detectors.

Note: GDP represents the gross domestic product; AT represents the altitude; NL represents the night light; UD represents the urban density; NDVI represents the normalized difference vegetation index.

Whether the factor has a significant difference in the spatial distribution affecting the TS is achieved by an ecological detector. A test with a significance level of 0.05 indicates that the two factors are different influencing the distribution of TS; otherwise, there is no significant difference. The result of an ecological detector is shown in Table 3.


**Table 3.** The result of an ecological detector.

Note: Y indicates that the two factors have significant differences in the spatial distribution of temperature slopes, N indicates no significant difference, and the confidence is 95%. And GDP represents the gross domestic product; UD represents the urban density; NL represents the night light; AT represents the altitude; NDVI represents the normalized difference vegetation index.

The result shows that there is a significant difference between UD and GDP; there is no significant difference between AT, NL, NDVI, and GDP, indicating that the effects of AT, NL, NDVI, and GDP on the spatial distribution of TS are similar. In addition, there is a significant difference between UD and NL, AT, and there is no significant difference between UD and NDVI. Similarly, there is a significant difference between NL and AT, while NL is not significantly different from NDVI. For AT and NDVI, there is also a significant difference between them. We can also conclude that the influences of various driving factors on the TS are different.

Table 2 indicates that the contribution rate of each factor alone to the TS is different. Thus, there is an interaction between them, and, if so, what is the interaction result? In order to answer this question, we give the results of interaction detector as Table 4.



Note: # indicates that the interaction is a bi-enhancement, i.e., *q* (*X1*∩*X2*) > Max(*q*(*X1*), *q*(*X2*)); \* indicates that the interaction is a nonlinear enhancement, i.e., *q* (*X1*∩ *X2*) > *q*(*X1*) + *q*(*X2*). And GDP represents the gross domestic product; UD represents the urban density; NL represents the night light; AT represents the altitude; NDVI represents the normalized difference vegetation index.

Table 4 shows that only AT and GDP have a nonlinear enhancement effect (*q* (GDP∩ AT) > *q*(GDP) + *q*(AT)) on TS, and the interactions between remaining driving factors have the bi-enhancement effect on TS. It shows that the effect of interaction of any two factors is greater than the effect of a single factor. Among them, the interaction effect between GDP and UD (*q* (GDP ∩ UD) = 0.464) is the largest, and the interaction effect between UD and NL (*q* (UD∩ NL) = 0.420) is second, followed by the interaction effect between UD and NDVI (*q* (UD∩NDVI) = 0.393) and the interaction effect between GDP and NL (*q* (GDP∩ NL) = 0.391), while the interaction effect between AT and NDVI (*q* (AT∩NDVI) = 0.146) is the smallest. In general, the interaction effect between socioeconomic factors is the largest, the interaction effect between socioeconomic factors and natural factors is second, followed by the interaction effect between natural factors.
