## 1 Introduction  
Over the past 20 years, China has undergone evident climate variations, such as temperature warming and decreasing solar radiation, as well as significant vegetation greening due to extensive anthropogenic activities (e.g., the \"Natural Forest Conservation Program\", \"Rocky Desertification Integrated Management\", \"Grain for Green Program\", and \"Three-North Forest Shelterbelt Program\") [1; 2; 3; 4]. Meanwhile, climatic change and vegetation greenness induced by anthropogenic activities have further influenced various terrestrial eco-hydrological processes over China [2; 5; 6]. Evapotranspiration (ET) and gross primary productivity (GPP) dominate the trade-off between water vapor and carbon accumulation. They represent two critical links of terrestrial eco-hydrological processes [7; 8]. ET consists of intercepting plant canopies, plant transpiration, and evaporation from the soil; it is a key link between natural carbon and water cycles [9]. GPP characterizes the ability of plant canopies to photosynthesize and is the basis of vegetation growth and human food supplies [8]. Generally, variations in climate factors have similar effects on ET and GPP [10]. For example, warming temperatures can reduce carbon sequestration and increase water ET; supplementary water can make vegetation greener and air more humid. Increased wind speeds may benefit the exchange of leaf stomatal carbon and water from vegetation to the atmosphere. Compared with climate factors, vegetation greenness has more complex effects on ET or GPP, especially in the case of the key biophysical parameter, the leaf area index (LAI) [6; 11; 12]. For instance, an increased LAI strengthens photosynthesis, which can improve GPP in regions with otherwise low to moderate LAI levels; however, an increased LAI may negatively affect GPP in regions where the LAI is already high [5; 6]. The LAI has different control levels on ET changes according to different inter-annual variabilities [13]. Anthropogenic activities, namely vegetation restoration programs, can significantly increase the coverage of plants performing photosynthesis and transpiration. Therefore, the controlling effect of anthropogenic activities on variations in ET and GPP can be quantitatively estimated by distinguishing the influences of climate and anthropogenic activities on plant greenness. Today, the residual method is often utilized to discern the influences of climatic factors and anthropogenic activities on vegetation changes [14; 15]. The mechanism at work between eco-hydroological processes and environmental factors is highly complex. Previous researchers show that vegetation greenness has improved ET over China [16; 17]. Rainfall and temperature regulate the latitudinal distributions of water and carbon fluxes in China [18]. Temperature acts as the predominant climatic element of Chinese GPP variability, followed by rainfall and radiation [19]. The precipitation amount, number of high-temperature days, and daily temperature range are the most important factors in carbon sequestration variability over China [20]. Human activities play a crucial role in positive ET trends [21]. Though informative, these studies solely reveal the influences of climate factors or vegetation restoration on the changes in ET or GPP; the contribution degrees of the controlling factors have not been comprehensively identified. Moreover, there has not yet been a simultaneous analysis of the degrees to which climate factors and anthropogenic activities distinctly affect ET and GPP from a national scale to climate zoning sub-regions. The spatiotemporal resolutions of remotely sensed vegetation products have continuously improved; remote sensing-based models are now widely employed tools to estimate ET or GPP [22; 23]. For instance, both the Priestley-Taylor Jet Propulsion Laboratory (PT-JPL) and Penman-Monteith-Leuning (PML) models, derived from remotely sensed data, are often used to simulate ET over large scales [24; 25; 26; 27].