## 1 Introduction  
Ecosystem water use efficiency (eWUE), the ratio of gross primary production (GPP, the total amount of carbon fixation by vegetation through photosynthesis) and evapotranspiration [1]. The total amount of carbon fixation is \(\sim\) 100  
spiration (ET, the sum of evaporation from soil and transpiration through plant leaves), is a critical indicator connecting the terrestrial carbon and water cycles and reflecting multiple ecosystem functions [1; 2]. Cultivated cropland accounts for approximately 12% of the Earth's non-ice-covered land surface and provides indispensable survival supplements (e.g., food and fiber) for human beings [3; 4]. Accurate quantification of eWUE over agro-cosystems is therefore pivotal for the management of water resources and assurance of food security. The satellite-based remote sensing (RS) technique has been recognized as the most practical and feasible means to derive the long-term eWUE at a global scale. With the aid of the RS technique, plenty of eWUE-related research obtained the eWUE at local, regional, and global scales through the free combination of various RS-based GPP and ET products. Essentially, the contemporary GPP and ET products can be categorized into (1) the uncoupled products (e.g., the Moderate Resolution Imaging Spectroradiometer (MODIS) [5], Vegetation Photosynthesis Model (VPM) [6], SateILite Only Photosynthesis Estimation (SLOPE) [7], FLUXCOM [8] products for GPP estimates, the MODIS [9], Global Land Evaporation Amsterdam Model (GLEAM) [10], Global Land Surface Satellite (GLASS) [11], and FLUXCOM [12] products for ET estimates) and (2) the coupled products (e.g., the Penman-Monteith-Leuning version 2 (PMLv2) [13], Boreal Ecosystem Productivity Simulator (BEPS) [14], and Breathing Earth System Simulator (BESS) [15] products for both GPP and ET estimates). The uncoupled products commonly treat vegetation photosynthesis and transpiration as two independent processes and simulate GPP and ET based on various individual algorithms (e.g., the light use efficiency model for GPP estimation and the Penman-Monteith equation for ET estimation). However, the photosynthesis and transpiration of vegetation are intrinsically coupled because the stomata on the surface of plant leaves can simultaneously regulate the exchange of water and carbon in the vegetation-atmosphere interface. Over the past decades, relying on the assumption that the stomatal conductance is positively and linearly correlated with the carbon assimilation rate, mounting stomatal conductance models have been developed, such as the Ball-Berry [16], Ball-Berry-Leuning [17], optimality-based unified stomatal optimization [18], and best-fitted [19] models. Using these stomatal conductance models, the coupled products can couple the estimation of vegetation photosynthesis and transpiration and simulate GPP and ET collectively. Previous findings revealed that the coupled products outperformed the uncoupled products in both GPP and ET estimations [13; 15]. However, the evaluation of eWUE is much more complicated than that of individual GPP or ET, mainly because the error in GPP and ET estimates could be offset or expanded to some extent in the ultimate eWUE estimates (for example, the underestimation of both GPP and ET may lead to an unbiased estimate of eWUE) [2]. Therefore, it is imperative to assess the performance of the coupled and uncoupled products in eWUE estimations. Moreover, the coupled products (i.e., PMLv2 and BESS) have been proven to achieve better results in eight-day and annual eWUE estimations than the uncoupled products (e.g., MODIS) for different plant functional types (PFTs) [2; 13]. However, these studies mainly focused on a PFT level, and few evaluations of the performance of the coupled and uncoupled products in eWUE estimations were conducted at a species level (i.e., C4 and C3). Relative to C3 plants, C4 plants are more adaptable to the conditions of high light intensity, high temperature, and low water supplements [20].