## 2 Materials and Methods
### Crop Evapotranspiration Algorithm  
#### 2.2.1 Two-Source Surface Energy Balance (TSEB)  
The TSEB estimates LE as follows (Equations (3)-(5)):  
\[\rm{LE}=\rm{LE}_{\rm c}+\rm{LE}_{\rm soil} \tag{3}\]  
\[\rm{LE}_{\rm c}=\rm{Rn}_{\rm c}-\rm{H}_{\rm c} \tag{4}\]  
\[\rm{LE}_{\rm soil}=\rm{Rn}_{\rm soil}-\rm{G}-\rm{H}_{\rm soil} \tag{5}\]  
where the subscripts \"c\" and \"soil\" refer to the \"canopy\" and \"bare soil\" conditions, respectively. All terms in Equations (3)-(5) have W/m\({}^{2}\) units. The LE is converted from W/m\({}^{2}\) to hourly ET\({}_{\rm a}\) (mm/h) using Equation (6):  
\[\rm{ET}_{\rm ah}=\rm{C}_{\rm f}\times\rm{d}_{\rm f}\times\frac{\rm{LE}}{\rm{ \lambda}_{\rm v}\rho_{\rm a}} \tag{6}\]  
where ET\({}_{\rm ah}\) is the hourly instantaneous actual crop ET\({}_{\rm a}\) (mm/h); d\({}_{\rm f}\) is a time-scale factor in seconds (e.g., 1 h = 3600 s); \(\rm{\lambda}_{\rm v}\) is the latent heat of water vaporization (J/kg); \(\rho_{\rm a}\) is the air density (kg/m\({}^{3}\)); C\({}_{\rm f}\) is a length scale conversion factor (e.g., 1000 mm/1 m). \begin{table}
\begin{tabular}{c c c c c} \hline
**Maize Growing** & **Research Field** & **Number of Irrigation** & **Cumulative Gross** & **Cumulative Rainfall** \\
**Season** & **Events** & **Irrrigation (mm)** & **(mm)** \\ \hline
2020 & F & 7 & 1620 & 34 \\ \cline{2-5}  & D & 5 & 870 & \\ \hline
2021 & F & 8 & 1081 & 104 \\ \cline{2-5}  & D & 4 & 1064 & \\ \hline \end{tabular}
\end{table} 
Table 2: Cumulative soil wetting events (irrigation and rainfall) at IIC Fields F and D in 2020 and 2021. The G model used was the soil heat flux (Equation (7)) approach recommended by [21], which is a fraction of the net radiation from the soil layer (Rn\({}_{\text{soil}}\)) during midday conditions coinciding with most spaceborne RS platform overpass times. \[\text{G}=0.35\text{Rn}_{\text{soil}} \tag{7}\]  
The Rn\({}_{\text{c}}\) and Rn\({}_{\text{soil}}\) terms (appearing later in Equations (18) and (19)) are calculated following the approaches by [19; 21] and indicated by Equations (8) and (9), respectively:  
\[\text{Rn}_{\text{c}}=(1-\Omega_{\text{solar}})(1-\alpha_{\text{c}})\text{R}_{ \text{s}}+\exp(-0.95\text{LAI})\text{L}_{\text{sky}}+[1-\exp(-0.95\text{LAI})] \epsilon_{\text{c}}\sigma\text{T}_{\text{cK}}^{4}-\epsilon_{\text{soil}}\sigma \text{T}_{\text{soilK}}^{4} \tag{8}\]  
\[\text{Rn}_{\text{soil}}=\Omega_{\text{solar}}(1-\alpha_{\text{soil}})\text{ R}_{\text{s}}+[1-\exp(-0.95\text{LAI})]\Big{[}\epsilon_{\text{a}}\sigma\text{T}_{ \text{aK}}^{4}+\epsilon_{\text{soil}}\sigma\text{T}_{\text{soilK}}^{4}-2 \epsilon_{\text{c}}\sigma\text{T}_{\text{cK}}^{4}\Big{]} \tag{9}\]  
where \(\Omega_{\text{solar}}\) is the solar atmospheric transmittance (dimensionless); \(\alpha_{\text{c}}\) and \(\alpha_{\text{soil}}\) are the canopy and bare soil albedo (dimensionless), respectively; \(\epsilon_{\text{c}}\) is the canopy thermal emissivity (dimensionless); \(\epsilon_{\text{soil}}\) is the bare soil thermal emissivity (dimensionless); \(\epsilon_{\text{a}}\) is the air emissivity (dimensionless); T\({}_{\text{cK}}\) is the canopy temperature (K); T\({}_{\text{Scilk}}\) is the soil temperature (K); T\({}_{\text{AK}}\) is the air temperature (K); L\({}_{\text{sky}}\) is the longwave radiation from the sky (W/m\({}^{2}\)); \(\sigma\) is the Stefan-Boltzmann constant (5.67 \(\times\) 10\({}^{-8}\) W/m\({}^{2}\)/K\({}^{4}\)); LAI is the leaf area index (m\({}^{2}\)/m\({}^{2}\)); R\({}_{\text{s}}\) is the incoming shortwave solar radiation (W/m\({}^{2}\)). The \(\alpha_{\text{c}}\) and \(\alpha_{\text{soil}}\) were calculated following the approaches by [29] and [30], respectively. The study by [29] gave an exponential model that relates maize albedo and green LAI for a semi-arid climate region. The study by [30] provided a multivariate model that relates \(\alpha_{\text{soil}}\) and the visible surface reflectance bands of the light spectrum (RED, GREEN, and BLUE).