## 2 Materials and Methods
### Satellite-Based ET Modeling Framework  
#### 2.3.1 TSEB-PT  
The two-source energy balance (TSEB) model was first described in [27], with improvements presented in [28]. The TSEB model partitions surface temperature into soil and vegetation canopy components using a local vegetation cover fraction (f\({}_{\rm c}\)) estimated from retrievals of leaf area index (LAI) and a clumping factor dependent on vegetation class (\(\Omega\); [30]) according to Equation (1). \[{\rm T_{r}=f_{c}T_{c}+(1-f_{c})T_{s}}, \tag{1}\]  
Initial temperature components are then used to initiate a temperature gradient-resistance system of equations designed to solve the surface-energy budget for the soil and vegetation components (Equation (2)). \[({\rm Rn_{s}+Rn_{c}})-G=(H_{s}+H_{c})+(\lambda E_{s}+\lambda E_{c}), \tag{2}\]  
In the above energy balance equation, \(R_{n}\) is the net radiation (W m\({}^{-2}\)), H is the sensible heat flux (W m\({}^{-2}\)), G is the soil heat flux (W m\({}^{-2}\)), and \(\lambda E\) is the latent heat flux (W m\({}^{-2}\)). Subscripts's' and 'c' represent fluxes associated with the soil and canopy components of the pixel, respectively. The soil and canopy components of \(R_{n}\) are estimated according to [62], and G is derived from a phase difference equation described by [63]. Following [27], we calculate \(H_{s}\) and \(H_{c}\) directly and \(\lambda E_{s}\) as the residual (details forthcoming). However, in order to do so, an initial estimate of \(\lambda E_{c}\) is obtained using the Priestley-Taylor approach [39]:  
\[\lambda E_{c\_PT}=\ \alpha f_{g}\frac{\Delta}{\Delta+\gamma}(Rn_{c}), \tag{3}\]  
where \(f_{g}\) is the fraction of green vegetation (set as 1.0), \(\alpha\) is the Priestley-Taylor parameter (\(\alpha\)-1.3), \(\Delta\) is the slope of the saturation vapor pressure-temperature curve, \(\gamma\) is the psychrometric constant, and \(R_{nc}\) is the divergence of net radiation in the canopy calculated as an initial estimate following [27]. Canopy and soil components of sensible heat flux are calculated assuming a series network as:  
\[H_{s}=\ \rho C_{p}*\left(\frac{T_{s}-T_{ac}}{r_{s}}\right), \tag{4}\]  
\[H_{c}=\ \rho C_{p}*\left(\frac{T_{c}-T_{ac}}{r_{x}}\right), \tag{5}\]  
where \(\rho C_{p}\) is the volumetric heat capacity of the air, \(T_{ac}\) is the air temperature within the air-canopy layer, \(r_{s}\) is the resistance to transport heat between the soil surface and a height representing the canopy, and \(r_{x}\) is the total boundary layer resistance of the complete canopy of leaves. Initial \(T_{c}\) values are estimated using a form of the Priestley-Taylor equation (Equation (6)), whereas initial \(T_{s}\) values are estimated as the residual to Equation (1). \[T_{c1}=T_{a}+\frac{R_{nc}r_{a}}{\rho C_{p}}\left[1-\alpha\frac{\Delta}{\Delta +\gamma}\right], \tag{6}\]  
Here, \(T_{a}\) is air temperature, \(\rho\) is the air density, \(C_{p}\) is the specific heat of air (assumed constant at 1013 J kg\({}^{-1}\) K\({}^{-1}\)), and \(r_{a}\) is the aerodynamic resistance, calculated from the stability corrected log profile equations for wind and temperature in the surface layer [64] and expressed as  
\[r_{a}=\frac{[\ln\left(\frac{z_{U}-d}{z_{M}}\right)-\Psi_{M}]\left[\ln\left( \frac{z_{T}-d}{z_{M}}\right)-\Psi_{H}\right]}{0.16U}, \tag{7}\]  
where \(z_{u}\) and \(z_{T}\) are the height of wind speed measurements (defined as 'U') and \(T_{a}\) measurements, respectively. Additionally, \(d\) is the displacement height (estimated as\(0.67\times\mathrm{h_{c}}\), where \(\mathrm{h_{c}}\) is canopy height), \(\mathrm{z_{M}}\) is the roughness length for momentum (estimated as 0.123 \(\times\)\(\mathrm{h_{c}}\)), 0.16 is the square of von Karmans constant taken as 0.4, and \(\mathrm{\Psi_{M}}\) and \(\mathrm{\Psi_{H}}\) are the stability correction functions for momentum and heat, respectively [64].