## 1 Introduction  
Ecosystem water use efficiency (WUE), typically defined as the ratio between gross primary productivity (GPP) and evapotranspiration (ET), is typically used to indicate tradeoff between carbon uptake and water losses in land ecosystems. Many studies have shown that changes in WUE are related to variations in a variety of environmental factors including aerosol loading [1], land use change [2; 3],climate change [4], and nitrogen deposition [5]. When transpiration (\(T\)) dominates ET, variations in WUE reflect how plants regulate carbon-water exchange processes through stomata. However, WUE also varies with vapor pressure deficit (VPD) [6; 7], which complicates correlations between WUE and plant conditions. Recently, more physiologically meaningful formulations have been proposed to quantify the interrelationship between carbon and water cycles. Intrinsic WUE (WUE\({}_{i}\)), which is defined as the ratio between GPP and surface conductance (Gs), was introduced [8; 9]. Gs that is used to represent water loss from ecosystems is usually estimated by inverting the Penman-Monteith equation [10; 11] (hereinafter referred to as P-M equation). Studies have shown that WUE\({}_{i}\) is more appropriate to describe the capacity of different plants to regulate how much water is lost per unit carbon acquired [12; 13], because Gs implicitly considers the impacts of related environmental factors. However, it is hard to estimate WUE\({}_{i}\), especially at a large spatial scale, because a large number of difficultly measured variables are needed to calculate Gs. Furthermore, Gs also contains the effects of canopy architecture, which is not related to stomatal closure. After some simplifying assumptions, [PERSON] et al. [14] proposed a much more simplified formulation called inherent water use efficiency (IWUE) as a proxy for the WUE\({}_{i}\). IWUE, which is defined as the product of VPD and WUE, significantly removes obscurities induced by variations in VPD. IWUE is more reflective of carbon and water exchanges via stomata [14] than WUE, and it has been wildly used to quantify the responses of plants to environmental controls including drought stress [15], nitrogen deposition [16], and rising CO\({}_{2}\) concentration [17]. Note that IWUE was developed by assuming the ratio of inner leaf over ambient partial pressure of CO\({}_{2}\) (\(C_{i}\)/\(C_{a}\)) to be constant. However, studies have shown that VPD may change \(C_{i}\)/\(C_{a}\)[6; 18]. To account for the effect of VPD on \(C_{i}\)/\(C_{a}\), [PERSON] et al. [19] proposed underlying water use efficiency (uWUE), which is defined as uWUE = GPP*VPD\({}^{0.5}\)/ET and they showed that uWUE is more related to plant physiological regulation of carbon uptake and water losses at the sub-daily time scale [20]. Although IWUE and uWUE are relatively simple and have a potential to describe mechanisms controlling carbon and water exchanges through stomata, their estimation at large spatial scales is still challenging. At regional or global scales, both GPP and ET are estimated from either processed-based or semi-empirical models, which use remotely sensed and/or meteorological variables as inputs [21; 22]. However, their performances may suffer from uncertainties in assumptions, inputs, and parameters. For example, it is common that estimated ET has an error greater than 50% [22; 23; 24]. Satellite-based estimates typically capture less than 60% of the variance in WUE even at sites with accurate measurements [25]. Thus, efforts on pursing other efficient ways in estimating large scale WUE are highly needed. More recently, studies have shown that solar-induced chlorophyll fluorescence (SIF) emission has a close correlation with carbon assimilation [26; 27; 28; 29]. Plants convert captured incoming solar radiation into three different pathways: assimilating carbon from the atmosphere into organic compounds (i.e., photosynthesis), heat dissipation (i.e., non-photochemical quenching (NPQ), and SIF emission.