# Evaluation of Remote Sensing-Based Evapotranspiration
## 3 Methodology
### Evaluation Indices  
Multiple statistical indices are used to evaluate the accuracy of the three remote sensing-based ET datasets and their performance in improving hydrological model performance. These indices include R, PBIAS, ME, RMSE, and KGE [42; 43]. The five indices are defined as follows:  
\[\text{R}=\frac{\sum\limits_{i=1}^{n}{(O_{i}-\overline{O})(S_{i}-\overline{S})}} {\sqrt{\sum\limits_{i=1}^{n}{(O_{i}-\overline{O})}^{2}\cdot\sqrt{\sum\limits_ {i=1}^{n}{(S_{i}-\overline{S})}^{2}}}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Meaning** & **Unit** & **Abbreviation** & **Range** \\ \hline Rain LAI multiplier & Multiplier for LAI to determine & & & & \\  & interception capacity for rain & m & Rj & & \\ \hline Lateral conductivity (CL) & Lateral conductivity for clay loam, & & & & \\  & used to calculate movement of & m/s & K (CL) & & 0.00001–0.09 \\  & lateral runoff & & & & \\ \hline Porosity (CL) & Porosity for clay loam, soil & & & & \\  & moisture content when soil & m\({}^{3}\)/m\({}^{3}\) & \(\varphi\) (CL) & & 0.35–0.6 \\  & is saturated & & & & \\ \hline Field capacity (CL) & Field capacity for clay loam, used & & & & \\  & to estimate available water for & m\({}^{3}\)/m\({}^{3}\) & \(\theta\)fc (CL) & & 0.16–0.4 \\  & subsurface layers & & & & \\ \hline Wilting point (CL) & \
\begin{tabular}{c} Wilting point for clay loam, used \\   to calculate evapotranspiration \\ \end{tabular} & m\({}^{3}\)/m\({}^{3}\) & \(\theta\)wp (CL) & & 0.05–0.25 \\ \hline Understory monthly & Understory leaf area index & & & & \\ LAI (CrL) & for cropland & m\({}^{2}\)/m\({}^{2}\) & ULAI (CrL) & & 0.3–3 \\ \hline Understory minimum & Understory minimum stomatal & & & & \\ resistance (CrL) & resistance for cropland & & & & \\ \hline Soil moisture & Soil moisture threshold above & & & & \\ threshold (CrL) & & & & \\  & restrict transpiration for cropland & & & & \\ \hline Root zone depth (CrL) &
\begin{tabular}{c} These are in effect the depths of \\ the various soil layers for cropland \\ \end{tabular} & m & D (CrL) & & 0.1–0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Range, meaning, unit, and abbreviation of eight highly sensitive parameters for parameter calibration. \[\text{PBIAS}=abs\left(\frac{\sum\limits_{i=1}^{n}\left(S_{i}-O_{i}\right)}{\sum \limits_{i=1}^{n}O_{i}}\times 100\%\right) \tag{2}\]  
\[\text{RMSE}=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}\left(S_{i}-O_{i}\right)^{2 }}} \tag{3}\]  
\[\text{ME}=\frac{1}{n}{\sum\limits_{i=1}^{n}\left(S_{i}-O_{i}\right)} \tag{4}\]  
\[\text{KGE}=1-\sqrt{\left(r-1\right)^{2}+\left(a-1\right)^{2}+\left(b-1\right) ^{2}} \tag{5}\]  
For assessing the accuracy of the three sensing-based ET datasets, \(O_{i}\) and \(S_{i}\) in the above equations denote in situ observations and remote sensing-based ET datasets, respectively. \(\overline{O}\) and \(\overline{S}\) are the mean values of these two datasets, respectively. For KGE, \(r\) is the linear correlation coefficient between in situ observations and remote sensing-based ET datasets, \(a\) is the ratio of the standard deviation of remote sensing-based ET datasets to the mean of in situ observations. For evaluating these remote sensing-based ET datasets' performance in improving hydrological model performance (runoff and ET simulations), \(O_{i}\) and \(S_{i}\) in the above equations denote observed runoff (remote sensing-based ET datasets) and simulated runoff (simulated ET), respectively. \(\overline{O}\) and \(\overline{S}\) are the mean values of observed runoff (remote sensing-based ET datasets) and simulated runoff (simulated ET), respectively.