## 1 Introduction  
Water use efficiency (WUE) is the term used to describe the ratio of gross primary productivity (GPP) to evapotranspiration (ET) and is fundamental to understanding the balance between the carbon gain and water loss in ecosystems under different climatic conditions [1, 2]. Under the expansion of global climate change, the water cycle in several ecosystems has accelerated, significantly affecting the WUE and leading to regional water resource scarcity and ecosystem stress [3, 4]. Therefore, it is crucial to delve deeper into the patterns of WUE variation and climatic factors to better predict the response of carbon and water cycles to future climate changes [5, 6]. Research into WUE can be divided into different scales: leaf-level, whole-plant, crop-level, and ecosystem-level [7]. Many scholars have investigated the impact that climatic factors have on WUE at the ecosystem level, with results indicating specific patterns of spatiotemporal variation observed in the WUE of different ecosystems [8, 9]. Moreover, the results vary on different scales, as is apparent from studies that have investigated WUE in specific forest or farmland ecosystems, compared WUE across different climatic zones, or assessed the spatiotemporal characteristics of WUE in natural agricultural zones [5; 10; 11]. These studies have provided new perspectives for understanding WUE at specific scales. Research into WUE has indicated that the differences associated with WUE on various scales are significant [8; 9; 12], with many studies exploring the spatiotemporal distribution characteristics and driving factors of WUE from a global or national perspective leading to the determination of the spatial distribution characteristics of WUE. However, the relatively large spatial scale of such studies renders it difficult to accurately describe the results in detail [8; 9; 13]. Other studies have used flux tower observation data from China to investigate the variation characteristics and driving factors of WUE on the site scale, allowing the WUE of China's terrestrial ecosystems to be explored and the seasonal variation in WUE to be analyzed. Although precise in terms of temporal accuracy, the influencing factors are complex, and information on the spatial distribution characteristics is lacking [14; 15]. Some studies have divided regions into ecosystems, vegetation types, and natural regions, which is conducive to analyzing changes in WUE at smaller scales and has led to the identification of regional patterns [10]. However, accounting for the various patterns observed in different regions remains challenging. Commonly used methods for analyzing spatiotemporal variation in WUE include isotope analysis (e.g., carbon isotope discrimination), remote sensing (using satellites and drones), ecosystem modeling (process models and statistical models), long-term monitoring networks (the eddy covariance method, meteorological station data), and data assimilation [16; 17; 18]. However, these methods are limited when addressing small-scale variation, nonlinearity, and complex systems, and their applicability is often constrained by data availability and quantity. Therefore, a method that can simultaneously address scale variation and nonlinear issues via spatiotemporal variation analysis is required. Multifractal analysis can be used to describe heterogeneity and self-similarity at multiple scales in complex systems, providing a more accurate characterization of the multiscale and multi-intensity fluctuations that occur in nature and complex systems [19]. The fractal dimension is an important metric for describing the complexity of fractals. Multifractal analysis is widely used in environmental and ecological studies to capture the spatial and temporal variabilities of processes that do not conform to simple, linear, or homogeneous patterns [20].