## 5 Conclusions  
This study introduced fractal theory to analyze the spatiotemporal distribution characteristics of WUE in Anhui Province using multi-source data, including remote sensing and meteorological data, from 2001 to 2021. The findings were as follows:  
(1) Temporal scale: The WUE in Anhui Province showed significant interannual variation, with an overall upward trend. Monthly changes in WUE exhibited an inverted \"V\" shape, with the highest average WUE in summer and the lowest in winter.  
Spatial scale: In terms of the natural terrain, the highest average WUE was found in the hilly and mountainous regions of southern Anhui and the Dabie Mountains in western Anhui. Brown soil exhibited the highest WUE, whereas southern paddy soils exhibited the lowest. The most significant WUE changes were observed in the northern Huaihe Plain and southern Jianghuai hills.  
(2) WUE data across multiple spatiotemporal scales displayed clear multifractal characteristics. Specifically, the multifractal features of WUE were similar across different temporal scales, with the most pronounced characteristics observed in summer, especially in August. This suggests that the WUE was less evenly distributed during summer than the other seasons. The spatial distribution of WUE is more complex in mountainous and hilly areas than in the plains. The multifractal characteristics of WUE were evident in regions with brown soil and were often associated with higher self-similarity.  
(3) Precipitation was identified as the primary factor influencing WUE in this region. However, when analyzed separately, evapotranspiration played a significant role in central Anhui, whereas precipitation had a greater impact in northern and southern Anhui. These patterns also correspond to the spatial distribution of the soil types.  
In conclusion, the introduction of fractal theory into WUE research helps to clarify the complexity across different scales. However, the scales used in the study were not exhaustive. Future research plans include studying WUE across different crop types, growth stages, and vegetation types, and expanding the study area to test the universal fractal characteristics of WUE.  
T.Z.: conceptualization, methodology, software, validation, formal analysis, investigation, data curation, resources, writing--original draft, writing--review and editing, visualization. Y.W., Y.Z., Q.W., P.W., H.Y. and Z.H.: methodology, resources, writing--review and editing. J.L.: resources, writing--review and editing, supervision, project administration, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Open Fund of the Key Laboratory of JiangHuai Arable Land Resources Protection and Eco-restoration [grant number ARPE-OF2024-KF02], and the Key Natural Science Research Project of Higher Education Institutions in Anhui Province [grant number2023 AH051013], and the National Natural Science Foundation of China [grant number 42271381, 42101381, 41571400], and the New Era Education Quality Engineering of Anhui Province (2022 zywjx-alk039, 2021 xxkc038).  
**Data Availability Statement**: The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest**: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.