## 2 Materials and Methods
### Crop Evapotranspiration Algorithm
#### 2.2.1 Two-Source Surface Energy Balance (TSEB)
The \(\Omega_{\text{solar}}\) variable was calculated using the nonlinear model from [31], in which the \(\Omega_{\text{solar}}\) is a function of LAI, surface absorptivity factor [32], light extinction coefficient, and the fraction of incident photosynthetically active radiation or PAR [33; 34; 35]. The T\({}_{\text{cK}}\) and T\({}_{\text{soilK}}\) are calculated through an iterative approach using Equation (10) below [21]:  
\[\text{T}_{\text{SK}}\cong\Big{[}\ell_{\text{c}}(\varphi)\text{T}_{\text{cK}}^ {4}+\Big{(}1-\ell_{\text{c}}(\varphi)\text{T}_{\text{soilK}}^{4}\Big{)}\Big{]} ^{0.25} \tag{10}\]  
where T\({}_{\text{sK}}\) is the equivalent nadir-looking surface temperature calculated from plant and soil temperature composites (K); f\({}_{\text{c}}(\varphi)\) is the fractional green vegetation cover for a radiometric field-of-view angle \(\varphi\)[21]. The TSEB Series Approach for H Estimation  
In the TSEB series algorithm (TSEB\({}_{\text{Ser}}\)), the heat exchange between soil, plant, and air is assumed to be interconnected [21]. The expressions for calculating H using the TSEB\({}_{\text{ser}}\) approach are given by Equations (11)-(13) below [21]:  
\[\text{H}^{\text{[ser]}}=\text{H}_{\text{c}}^{\text{[ser]}}+\text{H}_{\text{soil }}^{\text{[ser]}} \tag{11}\]  
\[\text{H}_{\text{c}}^{\text{[ser]}}=\rho_{\text{a}}\text{C}_{\text{pa}}\Bigg{(} \frac{\text{T}_{\text{c}}-\text{T}_{\text{o}}^{\text{[ser]}}}{\text{r}_{\text{ x}}}\Bigg{)} \tag{12}\]  
\[\text{H}_{\text{soil}}^{\text{[ser]}}=\rho_{\text{a}}\text{C}_{\text{pa}}\Bigg{(} \frac{\text{T}_{\text{soil}}-\text{T}_{\text{o}}^{\text{[ser]}}}{\text{r}_{ \text{soil}}}\Bigg{)} \tag{13}\]  
where T\({}_{\text{c}}\), T\({}_{\text{soil}}\), and T\({}_{\text{o}}^{\text{[ser]}}\) are the canopy, bare soil, and TSEB\({}_{\text{ser}}\) aerodynamic temperatures (K), respectively; r\({}_{\text{x}}\) and r\({}_{\text{soil}}\) are the total boundary layer resistance of canopy leaves (s/m) and the soil resistance (s/m), respectively. The superscript [ser] refers to the TSEB\({}_{\text{ser}}\) (series) algorithm. More details on how to calculate these resistance terms and other auxiliary variable inputs for the TSEB can be found in Appendices A and B. The air parameters \(\rho_{a}\) and \(C_{pa}\) are calculated as indicated by Equations (14) and (15), respectively (as used in [36]):  
\[\rho_{a}=\bigg{(}\frac{P}{R_{d}T_{a}}\bigg{)}\bigg{(}1-\frac{0.378e_{a}}{P}\bigg{)} \tag{14}\]  
\[C_{pa}=1004.7\times\bigg{(}1+\frac{0.522e_{a}}{P}\bigg{)} \tag{15}\]  
where P is the local atmospheric pressure (Pa); \(e_{a}\) is actual vapor pressure (Pa); \(R_{d}\) is the gas constant for dry air (\(\approx\)287.04 J/kg/K). The air parameters \(\rho_{a}\) and \(C_{pa}\) are given in kg/m\({}^{3}\) and J/kg/K units, respectively. The \(T_{o}\)[ser] (given in K) is calculated as indicated by Equation (16) [21]:  
\[\text{G}=0.35\text{Rn}_{\text{soil}} \tag{7}\]0  
In this study, we followed the improved TSEB\({}_{ser}\) approach from [18] and used the modified Penman-Monteith (PM) approach instead of the Priestley-Taylor (PT) modified model (as described in [21]) to calculate an initial \(T_{c}\) value to derive the surface temperature composites (\(T_{c}\) and \(T_{soil}\)). The modified PM approach for an initial \(T_{c}\) value is indicated by Equation (17):  
\[\text{G}=0.35\text{Rn}_{\text{soil}} \tag{7}\]1  
where \(T_{cO}\) is the initial guess for canopy temperature (K); \(\gamma\) is the psychometric constant (kPa/\({}^{\circ}\)C); \(r_{c}\) is the bulk canopy resistance (s/m); \(\Delta\) is the slope of the saturation vapor pressure curve (kPa/\({}^{\circ}\)C); \(e_{s}\) and \(e_{a}\) are the saturated and actual vapor pressures in kPa, respectively. The calculation of \(r_{c}\) is described in Appendix B. The TSEB Parallel Approach for H Estimation  
The TSEB parallel (TSEB\({}_{par}\)) assumes that the processes that derive the heat transfer among plants, soil, and the air above are independent and can be modeled with two separate resistances for heat transfer [18; 21].