## 1 Introduction  
Forests are important components of terrestrial ecosystems. Plants absorb CO\({}_{2}\) from the atmosphere by photosynthesis and lose water by transpiration, driving energy, and water cycling [1; 2; 3]. In this context, water-use efficiency (WUE) is a key parameter in connecting carbon fixation and evapotranspiration (ET) [4], defined as the ratio of gross primary productivity (GPP) to the ET of an ecosystem. The WUE indicates the water-use strategy among different species or at different life stages of plants at the stand scale [5]. At the ecosystem level, WUE can be used to quantify the coupling between carbon and water cycles. Water loss and C gain are highly complex at the ecosystem level. Various factors, including temperature (T), precipitation (P), vapor pressure deficit (VPD), leaf area index (LAI), and solar radiation (Rg), affect WUE by affecting ET and carbon exchange [6; 7; 8]. However, one factor affecting WUE may be masked or enhanced by the effects of other factors, resulting in considerable controversy in the research results [9]. For example, during droughs, WUE can first increase and then decrease [10]. Based on previous studies, the WUE does not significantly correlate with latitude because of the similar changes in GPP and ET with variations in latitude [10]. However, in other studies, the WUE of forest ecosystems increased or decreased with increasing latitude [11; 12; 13; 14]. Such controversy has also been observed regarding the relationships between WUE and the precipitation, temperature, VPD, LAI, and Rg [15; 16; 17; 18].  
Forest ecosystems occupy approximately 25% of the terrestrial surface, two to three times the total agricultural land area. The spatial patterns, magnitude, and factors affecting the carbon and water cycles of forest ecosystems are, however, not fully understood, mostly because of the lack of long-term flux data. The FLUXNET and the eddy covariance (EC) technique provide a platform and a method for determining carbon and water fluxes at the ecosystem level [19]. The FLUXNET is a reliable platform providing global ecosystem data, collected and processed in a unified manner [20]. Via FLUXNET, gross primary production (GPP) and evapotranspiration (ET) can be estimated at various time scales, allowing obtaining the WUE values for forest ecosystems. Recent studies have defined intrinsic water use efficiency (IWUE), which mainly considers the important impact of saturated water vapor pressure difference (VPD) on the carbon water coupling process on daily and hourly scales [21; 22; 23]. [PERSON] et al. [5] put GPP \(\times\) The ratio of VPD to ET is called IWUE, which is tested by using the data of 43 flux stations in different ecosystems around the world. It is confirmed that IWUE is more suitable than WUE for analyzing the carbon water coupling mechanism of the ecosystem on a daily scale.  
In this study, we selected flux observations from 67 EC flux sites encompassing a range of forest ecosystems worldwide to compare the WUEs of different forest ecosystems from longer time series and larger spatial scales. In the context of climate change, comparing the WUE of these forest ecosystems will help elucidate the ecosystem response and adaptation to climate change. The overall objective of this study was to examine the spatial patterns, magnitude, and climate rules of the inherent water-use efficiency (IWUE) of forest ecosystems. The following questions were answered: (1) what is the specific trend of the IWUE of forest ecosystems? (2) How does the IWUE response mechanism to environmental factors differ across forest ecosystems? The outcomes of this study provide a scientific basis for regional ecological construction and water and carbon management.