## 1 Introduction  
Carbon and hydrological processes are integral components of the terrestrial ecosystem cycle [1]. Understanding the driving factors behind the interactions between terrestrial environmental systems and climatic shifts is crucial, especially the global rise in temperatures and the rising occurrence of severe weather phenomena [2; 3]. Vegetation carbon use efficiency (CUE) and water use efficiency (WUE), as key indicators characterizing the carbon-water cycles of terrestrial ecosystems, have consistently been focal topics in studies related to climate variability and environmental change [4; 5; 6; 7]. CUE is commonly defined as the ratio of net primary productivity (NPP) to gross primary productivity (GPP), reflecting the capacity of ecosystems to capture and retain carbon [7]. WUE represents the amount of water lost for each unit of carbon assimilated by vegetation, typically reflected as the ratio of vegetation productivity (e.g., NPP or GPP) to evapotranspiration (ET), and serves as an indicator of an ecosystem's carbon sequestration capacity per unit area, characterizing its response to water resource changes [8]. With the intensification of global warming, the potential for vegetation carbon sequestration is expected to accelerate, alongside an increase in water evaporation [9; 10]. In the context of ongoing environmental shifts, terrestrial ecosystems are undergoing systemic alterations in both their carbon and water cycles, posing significant threats to ecosystem stability and sustainability [11]. Therefore, exploring the factors influencing CUE and WUE and their relationships with environmental variables is crucial for tackling environmental issues, preserving ecosystem integrity, and optimizing resource allocation while promoting sustainable socioeconomic development. Traditionally, research on vegetation CUE and WUE at finer scales utilized observational techniques like eddy covariance and thermal diffusion methods [12; 13; 14]. Vegetation CUE can be estimated through various approaches, including ground-based measurements, eddy covariance techniques, and biogeochemical models [12; 13]. Similarly, vegetation WUE can be derived using plant-scale experiments, remote sensing-based inversion, eddy covariance methods, and stable isotope analysis [14]. These diverse methodologies have been widely applied and validated across varying spatial scales and ecological contexts, offering robust theoretical and technical support for advancing our understanding of carbon-water coupling in ecosystems. Recently, advancements in satellite-based observation technologies have provided long-term remote sensing datasets, offering new perspectives for research on carbon and water cycles [15]. Numerous studies have utilized satellite observation data to examine the patterns of variation and the driving forces behind vegetation carbon and water use efficiency across different geographical extents and timeframes [16; 17]. At the regional level, [PERSON] et al. [16] found a slight increasing trend in annual vegetation CUE across China from 2000 to 2013, with greater values in the west and smaller values in the east; grasslands exhibited the highest CUE (0.21) and shrubs the lowest (0.06). Using CMIP5 models to simulate the future CUE of China's terrestrial biotic communities and analyze its potential changes, the results indicated that the future CUE is projected to range between 0.332 and 0.617, with a slight decline over time [18]. In central Asia, the mean WUE value from 2001 to 2021 was 3.011 g C kg\({}^{-1}\) H\({}_{2}\)O, showing a general decline in WUE over time [18]. At smaller scales, such as a watershed, the long-term average CUE (0.458) and WUE (0.682 g C kg\({}^{-1}\) H\({}_{2}\)O) in the Poyang lake basin showed a moderate decrease from 2000 to 2014, with grasslands having the highest CUE and forests the highest WUE [19]. In addition, [PERSON] et al.