# Evapotranspiration in Dynamic of Highland Barley Using PML ET Product in Tibet
## 2 Materials and Methods
### Analysis Method  
(1) PML-V2 Model  
The PML-V2 model used total primary productivity and atmospheric CO\({}_{2}\) concentration to estimate canopy conductance, thereby realizing a joint estimation of ET and total primary productivity. ET was divided into three main components: vegetation transpiration (Ec), soil evaporation (Es), and canopy interception evaporation (Ei) [1,21].  
\[ET=Ec+Es+Ei \tag{1}\]  
\[Ec=\frac{\varepsilon A_{c}+\left(\frac{\rho C_{p}}{\gamma}\right)D_{a}G_{a}}{ \varepsilon+1+G_{a}/G_{c}} \tag{2}\]  
\[Es=\frac{f\varepsilon A_{s}}{\varepsilon+1} \tag{3}\]  
\[Ei=\left\{\begin{array}{l}f_{p}P,\hskip 56.905512 ptP<P_{wet}\\ f_{p}P_{wet}+f_{v}(P-P_{wet}).P\gg P_{wet}\end{array}\right. \tag{4}\]  
where \(\varepsilon=s/\gamma\), in which \(\gamma\) is the psychrometric constant (kPa/\({}^{\circ}\)C), and \(s\) is the slope of the curve relating saturation water vapor pressure to temperature (kPa/\({}^{\circ}\)C); \(A\) is the available energy absorbed by the surface (MJ/(m\({}^{2}\)-day))--that is, net absorbed radiation minus soil heat flux; \(As\) and \(Ac\) are the available energy of the soil and vegetation canopy, respectively; \(\rho\) is the density of air (g/m\({}^{3}\)); \(C_{p}\) is the specific heat of air at constant pressure (MJ/(g\({}^{\circ}\)C)); \(D_{a}\) is the water vapor pressure deficit of the air (kPa); \(G_{a}\) is the aerodynamic conductance (m/s); \(Gc\) (m/s) is the canopy conductance; \(f\) is a dimensionless variable that determines the water availability for soil evaporation; \(f_{v}\) is canopy leaf area; \(P\) is the daily precipitation (mm/d); \(P_{wet}\) is the threshold of precipitation when the canopy is enough wet.  
(2) Unitary Linear Regression Model  
A unitary linear regression model was used to describe the interannual change trend in ET components of highland barley, and the trend rate (k) was calculated as  
\[k=\frac{n\times\sum_{i=1}^{n}(i\times ET_{i})-\sum_{i=1}^{n}i\sum_{i=1}^{n} ET_{i}}{n\times\sum_{i=1}^{n}i^{2}-\left(\sum_{i=1}^{n}i\right)^{2}} \tag{5}\]  
where \(ET_{i}\) is the ET components of highland barley for the \(i\)th year, and \(n\) is the number of years.  
F-test was used to measure the significance of the linear trend as follows:  
\[F=\frac{U}{Q/(n-2)}\,\sim F(1,n-2) \tag{6}\]  
\[U=\sum_{i=1}^{n}\bigl{(}ET_{i}-\overline{ET}\bigr{)}^{2} \tag{7}\]  
\[Q=\sum_{i=1}^{n}\bigl{(}ET_{i}-\overline{ET}_{i}\bigr{)}^{2} \tag{8}\]where \(U\) and \(Q\) are the sum of regression squares and the sum of residual squares, respectively; n is the sample size; \(ET_{i}\) is the ET components of highland barley from PML product; \(ET_{i}\) is the estimated ET components by the linear regression model; \(\overline{ET}\) is the average ET components of highland barley. Python was used to calculate \(k\) and \(F\) values for the three components.  
(3) Pearson Correlation Analysis  
Pearson correlation coefficient (R) was used to explore the relationship between the variations in ET components and meteorological variables. It was calculated using the following equation:  
\[\text{R}=\frac{\text{n}\sum\text{x}_{i}\text{y}_{i}-\sum\text{x}_{i}\sum \text{y}_{i}}{\sqrt{\text{n}\sum\text{x}_{i}^{2}-\left(\sum\text{x}_{i} \right)^{2}}\sqrt{\text{n}\sum\text{y}_{i}^{2}-\left(\sum\text{y}_{i}\right)^{ 2}}} \tag{9}\]  
where \(x_{i}\) and \(y_{i}\) are the ET components and meteorological variables, respectively, and n is the sample size. The metric R varying between \(-1\) and \(1\) was adopted to measure the degree of linear correlation between two variables; a higher absolute value of R suggests a stronger correlation. The Pearson correlation between ET components and meteorological variables was calculated by SPSS software.