## 2 Material and Methods
### Two ET Models Based on ANN  
In this study, two models were trained based on the PM equation, and the difference lies in the _Gs_ calculation. The following two summaries introduce the two methods in detail. The formula of the PM equation is as follows:  
\[\lambda\mathrm{E}=\frac{(Rn-G)\cdot\Delta+\rho\cdot\mathrm{C}p\cdot\mathrm{D} \cdot Ga}{\Delta+\gamma(1+Ga/Gs)} \tag{1}\]  
where \(\lambda\mathrm{E}\) is evapotranspiration, \(Rn\) is net radiation, \(G\) is soil heat flux, \(\Delta\) is the gradient of the saturation vapor pressure versus atmospheric temperature, \(\rho\) is air density, \(Cp\) is the specific heat at constant pressure of air, \(D\) is the vapor pressure deficit of the air, \(Ga\) is the aerodynamic conductance, and \(\gamma\) is the psychometric constant.  
In order to test the effects on the accuracy of using different combinations of input variables, different combinations of input variables in the ANN are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Site Code** & **Latitude** & **Longitude** & \
\begin{tabular}{c} **Mean Annual** \\ **Temperature (\({}^{\circ}\)C)** \\ \end{tabular} &
\begin{tabular}{c} **Mean Annual** \\ **Precipitation (mm)** \\ \end{tabular} & **Years** & **Reference** \\ \hline BE-Lon & 50.55 & 4.75 & 11.41 & 766.50 & 2004–2014 & [PERSON] et al. [35] \\ CH-Oe2 & 47.29 & 7.73 & 9.56 & 2062.25 & 2004–2014 & [PERSON] et al. [36] \\ DE-Geb & 51.10 & 10.91 & 9.67 & 532.90 & 2001–2014 & [PERSON] et al. [37] \\ DE-Kli & 50.89 & 13.52 & 7.77 & 810.30 & 2004–2014 & [PERSON] et al. [38] \\ DE-RuS & 50.86 & 6.45 & 10.80 & 551.15 & 2011–2014 & [PERSON] et al. [39] \\ DE-Seh & 50.87 & 6.45 & 10.29 & 573.05 & 2007–2010 & [PERSON] et al. [40] \\ FR-Gri & 48.84 & 1.95 & 10.96 & 598.60 & 2004–2014 & [PERSON] et al. [41] \\ IT-BCi & 40.52 & 14.96 & 17.88 & 1197.20 & 2004–2014 & [PERSON] et al. [42] \\ IT-CA2 & 42.38 & 12.03 & 14.84 & 766.50 & 2011–2014 & \\ US-ARM & 36.60 & \(-\)97.49 & 15.27 & 646.05 & 2003–2012 & [PERSON] et al. [43] \\ US-CRT & 41.63 & \(-\)83.35 & 10.85 & 810.30 & 2011–2013 & [PERSON] et al. [44] \\ US-Ne1 & 41.1651 & \(-\)96.477 & 10.54 & 846.80 & 2001–2013 & [PERSON] et al. [45] \\ US-Ne2 & 41.1649 & \(-\)96.470 & 10.26 & 876.00 & 2001–2013 & [PERSON] and [PERSON] [46] \\ US-Ne3 & 41.1797 & \(-\)96.440 & 10.38 & 697.15 & 2001–2013 & [PERSON] and [PERSON] [46] \\ US-Tw2 & 38.1047 & \(-\)121.643 & 15.23 & 386.90 & 2012–2013 & [PERSON] et al. [47] \\ US-Tw3 & 38.1159 & \(-\)121.647 & 16.00 & 343.10 & 2013–2014 & [PERSON] et al. [48] \\ US-Twt & 38.1087 & \(-\)121.653 & 14.75 & 357.70 & 2009–2014 & [PERSON] et al. [49] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of flux sites.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Formula** \\ \hline NDVI & \(\mathrm{NDVI}=\frac{2-\gamma 1}{\gamma 2+\gamma 1}\) \\ NIRv & \(\mathrm{NIRv}=\mathrm{NDVI*}\)\(\mathrm{\tau}\)\(\mathrm{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Calculation of vegetation index. _rx_ represents the reflectivity of MODIS (\(x=1\)–\(\gamma\)), NDVI is the normalized difference vegetation index, NIRv is near-infrared reflectance of vegetation.