## 2 Background of WUE Estimation by Remote Sensing
### Indirect WUE Estimation by Measuring GPP and ET at the Ecosystem Level  
#### 2.2.1 Measurements Using Eddy Covariance Observations  
The eddy covariance (EC) technique has enabled long-term and continuous measurements of water and CO\({}_{2}\) flux in recent decades [23]. Based on the EC technique, the flux tower can obtain a continuous time series data of carbon and water flux at a siteThe light use efficiency (LUE) model was a widely used method of GPP estimation based on the fact that GPP is directly related to absorbed photosynthetically active radiation (APAR), in which LUE represents the efficiency of vegetation in converting solar energy to biomass through absorption and photosynthesis [41]. An LUE model has become one of the main tools for studying ecosystem GPP and its temporal and spatial variation characteristics using remote sensing information. The current background of most light use efficiency models goes back to a canopy-scale GPP modeling approach [41]. The basic assumption of this idea considers the vegetation canopy as a large leaf. The LUE has nothing to do with the direction and canopy structure of the canopy. The GPP has a simple linear relationship with photosynthetically active radiation (PAR) entering the canopy as follows:  
\[\mathrm{GPP}=\varepsilon_{\mathrm{max}}\times f(\cdot)\times\mathrm{PAR} \times\mathrm{FPAR}, \tag{3}\]  
where, \(\varepsilon_{\mathrm{max}}\) (gC MJ\({}^{-1}\)) represents the maximum LUE of the plant, \(f(\cdot)\) is the environmental stress factor, and FPAR represents the proportion of PAR utilized by the canopy. Typical LUE models for estimating GPP are shown in Table 2.  
Empirical models (i.e., based on remote sensing data) and process-based models (i.e., using remote sensing data as the main inputs) are the main methods for estimating ET. In this regard, empirical models are mainly comprised of regression models [48] and models based on machine learning methods [49; 50; 51]. Additionally, the process-based models are mainly transferred by the Penman-Monteith equation, such as the PM-MOD16 model [52], PM-Yuan model [53]), and Priestley-Taylor model (PT-JPL) [54]. The typical process-based models of ET estimation are shown in Table 3.  
ET modeling involves complex physical processes controlled by several factors, leading to a more complicated estimation by remote sensing, especially for crop ecosystem. Dryland river basins frequently support both irrigated agriculture and riparian vegetation and remote sensing methods are needed to monitor water use by both crops and natural vegetation in irrigation districts [59]. Crop evapotranspiration (ETc) represents crop water requirements, which is affected by weather and actual crop conditions [60; 61]. A useful method to estimate ETc or crop water requirements is to multiply reference evapotranspiration (ETr) by a crop coefficient (\(Kc\)). \(Kc\) is typically taken from literature values and is affected by crop variety and growth stage. ETc is actually estimated from site measurements or satellite-based remote sensing methods. Using a satellite remote sensing-based vegetation index in combination with site measurements have shown a certain degree of accuracy for the estimation of ET with spatial and temporal distribution at different scales, i.e., regional or field scales [62]. Remote sensing methods for estimating ET losses