## 4 Discussion
### Application Analysis of Multifractals in WUE  
The choice of multifractal analysis to study water use efficiency (WUE) is primarily based on the widespread presence of fractal characteristics in nature. Meteorological variables closely associated with WUE, such as temperature, precipitation, and the standardized precipitation index (SPI), often exhibit multifractal properties [26; 30; 69]. Applying multifractal analysis allowed for a comprehensive understanding of the complexity and fractal patterns within the study area, providing insights into the variations in WUE across temporal and spatial scales.  
On a temporal scale, segmenting WUE into annual, seasonal, and monthly intervals enables a precise observation of its nonlinear variability over time. Fractal theory is an effective tool for describing nonlinear characteristics in time series data, with multifractal spectra capturing dynamic nonlinear patterns within WUE fluctuations [69; 70]. On a spatial scale, the mountainous regions of southern Anhui, which are characterized by rugged terrain and diverse ecosystems, exhibit pronounced multifractal properties. The topographical features of the area align closely with the fractal characteristics of sloped landscapes [71; 72]. In regions with significant elevational changes, multifractal spectra can effectively reveal spatial heterogeneity in WUE. WUE distribution in the hilly areas of southern Anhui displays a right-skewed multifractal spectrum (\(\Delta\)f(\(\alpha\)) \(<\) 0), suggesting relatively uniform WUE within localized areas but significant differences across varying topographies, highlighting heterogeneity at a broad scale [72; 73; 74].  
The Huaibei Plain, a key agricultural zone in Anhui, displays distinct multifractal characteristics that are predominantly influenced by human agricultural activities. Extensive farming and irrigation practices have had a considerable impact on the spatial distribution of WUE in this area. The plain is largely devoted to staple crops, such as wheat and maize, with irrigation mainly reliant on groundwater and river sources. Variations in irrigation methods significantly influence the efficiency of water resource utilization. In the multifractal analysis of this region, the WUE spectrum also exhibits a right-skewed pattern (\(\Delta\)f(\(\alpha\)) \(<\) 0), reflecting a relatively consistent WUE at localized scales but noticeable differences in WUE across larger spatial scales among different fields [74; 75]. This spatial complexity likely stems from differences in crop water requirements, irrigation management, and the spatial heterogeneity of soil types.  
Soil type also plays a crucial role in shaping the multifractal characteristics of WUE. The WUE distribution across different soil types exhibits significant spatial heterogeneity. In particular, soils with high mineral contents and active biological properties tend to show pronounced multifractal characteristics [76; 77]. Across five different regions, WUE consistently exhibits a right-skewed multifractal spectrum, where a right-skewed multifractal spectrum (\(\Delta\)f(\(\alpha\)) \(<\) 0) suggests WUE homogeneity within larger regions but significant differences between distinct areas [75]. Thus, the multifractal analysis revealed the complexity and heterogeneity of WUE at different spatial scales, comprehensively capturing the variation patterns within each area.