## 3 Results
### WUE Analysis of the Five Natural Terrain Areas
#### 3.2.2 Multiple Fractal Analysis of WUE in Different Natural Terrain Regions  
The fractal characteristics of the WUE in the different natural regions were obtained using the differential box-counting method, as seen in Figure 11. The log(r)-log(Nr) double logarithmic plots for these regions show a linear relationship, with fitting ranges between 0.9987 and 0.9997 for the absolute slopes of the least squares fitted line indicating high fitting coefficients, suggesting fractal characteristics and self-similarity for the WUE in the five regions. The fractal dimension D, derived from the slopes, varied between 1.7546 and 1.8539, indicating different degrees of complexity in the spatial distribution of the WUE in these regions. The fractal dimensions from highest to lowest are as follows: the hilly and mountainous region of southern Anhui (1.8539), the Huaibei Plain (1.8525), the Dahie Mountain area of west Anhui Province (1.8486), the Jianghuai hilly region (1.8008), and the plain alongside the river (1.7546). The highest fractal dimension in the hilly and mountainous region of southern Anhui indicates a more complex and uneven spatial distribution in this region, while the lowest fractal dimension observed for the plains alongside the river suggests a more uniform spatial distribution in this area. The relationship between the partition function and box size for the WUE factors in the five different natural regions of Anhui Province can be seen in Figure 12. The relationship curves, Xq(\(\epsilon\))-\(\epsilon\), are displayed in double logarithmic plots, with similar patterns observed across the five regions. In this study, the q values range from \(-\)10 to 10 in integer steps. The double logarithmic curves obtained for the partition function and box size exhibit a good linear relationship, indicating a certain degree of self-similarity for WUE across multiple scales. The different arrangements of log(r) on the axis for various q values indicates significant variation, suggesting a scale dependency with changes in q. When q \(>\) 0, the data points incline upward with a positive slope and the slope increases more rapidly,  
Figure 10: Temporal trends in WUE, ET, and the GPP in the five regions of Anhui Province: (**a**) the Huaibei Plain, (**b**) Jianghuai hilly region, (**c**) plain alongside the river, (**d**) Dabie Mountain area in west Anhui Province, and (**e**) hilly and mountainous region of southern Anhui. indicating regions with high WUE on larger scales. Conversely, when q < 0, the data points decline downwards with a negative slope, and the slope increases more slowly, indicating that smaller regions are exhibiting low WUE. Figure 11: Fractal dimensions of different natural terrain subdivisions in (**a**) the Huaibei Plain, (**b**) Jianghuai hilly region, (**c**) hilly and mountainous region of southern Anhui, (**d**) Dabie Mountain area, and (**e**) plain alongside the river. Figure 12: The double logarithmic chart for different natural terrain partitions: (**a**) the Huaibei Plain, (**b**) Jianghuai hilly region, (**c**) hilly and mountainous area of southern Anhui, (**d**) Dabie Mountains, and (**e**) plain alongside the river. The relationship between moment order q and mass index \(\tau\)(q) in the Huaibei Plain, the Jianghuai hilly region, the hilly area in southern Anhui, the Dabie Mountains, and the plain alongside the Yangtze River can be seen in Figure 13. The function relation of all of \(\tau\)(q) to q is increased, indicating that for a positive q, the overall heterogeneity increases and a high WUE is more significant. An increasing q is associated with a higher growth rate for \(\tau\)(q), indicating that all five regions have multifractal characteristics. The multifractal spectrum curves of WUE for each region and their fitted curves are shown in Figure 14. The calculation curves for the five regions were fitted using a quadratic polynomial, and the curves were found to be similar.