## 1 Introduction  
Water use efficiency (WUE) is a key metric of carbon-water coupling maintaining the trade-off between photosynthesis and water vapor loss on plant function, which is often defined as the ratio of gross primary production (GPP) and evapotranspiration (ET) on the ecosystem scale [1, 2, 3, 4, 5, 6]. Previous studies have reported that the global forest WUE shows an upward trend with the rise in atmospheric carbon dioxide concentration as shown in Figure 1a,c [7, 8]. However, based on satellite observations, the global average WUE has showed a significant downward trend before 2010, which is possibly due to the change in land use, and this phenomenon is improved during 2011-2014 as shown in Figure 1b [9]. As an independent ecological variable of the ecosystem responding to global changes, WUE is a key measurement to link the carbon and water cycle of ecosystems. Various researches have investigated the underlying mechanism of WUE at a single site by measuring flux with simple weather condition-driven models [10; 11; 12; 13]. To reveal the effect of global change on the interaction of water-carbon cycles in ecosystems, several studies upscaled WUE from a single site to the regional/global scale through remote sensing techniques and ecological models [2; 4; 7; 9; 14; 15; 16; 17]. The retrieval of spatial-temporal variability and control mechanism of WUE on regional scale ecosystems is helpful to evaluate and predict the impact of global changes on ecosystem water and carbon processes [18]. However, issues concerning the inconsistent response to environmental factors and indistinct carbon-water coupling mechanisms need to be resolved for effectively evaluating ecosystem functions with a higher requirement of long-lasting continuous and consistent spatial measurements to capture changes in water-carbon cycles. Indirect methods (i.e., based on remote sensing products and output of process models) [4; 19], empirical models (i.e., based on meteorological variables, flux observations, and remotely sensed vegetation indices) [9; 20], and analytical models [8] are applied to estimate the WUE and to analyze the response to environmental factors. Although an increasing trend exists in global forest WUE based on the result of site observation and process-based models, the global mean WUE from satellite observation was decreasing--before the year 2010--and then increased. However, satellite-observed WUE has uncertainties for validation at the site scale. Therefore, the applied remote sensing product(s) should be improved by precise remote sensing algorithms or to develop a more precise product(s). Here, we review the current progress in WUE remote sensing and guiding steps for the  
Figure 1: Trends of global water use efficiency (WUE). (**a**) The annual change in WUE (\(W_{ei}=\) WUE \(*\) VPD, gC kg\({}^{-1}\) H\({}_{2}\)O hPa. VPD is atmospheric vapor pressure deficit), calculated using daytime fluxes from summer months at 21 flux towers of temperate and boreal forest ecosystems (discussed in Section 2.2.1). The red line indicates mean trend over all sites and grey dots and black lines represent the trends of each site. Adapted with permission from ref. [7]. Copyright 2013 Nature Publishing Group, a division of Macmillan Publishers Limited ([[https://www.nature.com/](https://www.nature.com/)]([https://www.nature.com/](https://www.nature.com/)). Accessed on 15 April 2021). (**b**) Change in global annual mean WUE, calculated using satellite remote sensing data (discussed in Section 2.2.3). The dashed line represents the mean value of WUE. Reprinted with permission from ref. [9]. Copyright 2014 The authors. (**c**) Global WUE anomalies, calculated using output of an analytical ecosystem WUE model (discussed in Section 2.3). The blue line represents the linear trend of WUE and the error bars are standard deviation (Source: [PERSON] et al., 2017 [8]). Adapted with permission from ref. [8]. Copyright 2017 The authors. improvement in WUE estimation.