## 3 Methodology  
### Model of Remote Sensing-Based LE Estimation  
The surface energy balance describes the transfer of energy between the land surface and the atmosphere. The land surface energy balance equation is the basis of remote sensing-based _LE_ estimation, and it is commonly expressed as follows:  
\[R_{n}=G+H+LE \tag{1}\]  
\(H\) is the flux caused by the temperature gradient between the land surface and the air, whereas _LE_ is the change in energy due to evapotranspiration or condensation. Atmospheric turbulence at the boundary layer is the motivation for the heat transfer between the land surface and the atmosphere. _LE_ can be derived as the residual of the energy balance equation after \(R_{n}\), \(G\) and \(H\) are known. The models that permit estimation of \(R_{n}\), \(G\) and \(H\) using remote sensing data are introduced below. \(R_{n}\) is the main energy source of land surface heat and mass transfer and exchange, such as evaporation. The estimation of \(R_{n}\) is of great importance in the remote sensing-based estimation of land surface heat fluxes. It is the difference between incoming and outgoing radiation, and it is calculated as follows:  
\[R_{n}=R_{s}\downarrow-R_{s}\uparrow+R_{L}\downarrow-R_{L}\uparrow=(1-\alpha)R _{s}\downarrow+\varepsilon_{s}R_{L}\downarrow-\varepsilon_{s}\sigma T_{s}^{4} \tag{2}\]  
where \(R_{n}\) is the surface net radiation (W\(\cdot\)m\({}^{-2}\)), \(R_{s}\downarrow\) is the downward shortwave radiation (W\(\cdot\)m\({}^{-2}\)), \(R_{s}\uparrow\) is the shortwave radiation reflected by the surface (W\(\cdot\)m\({}^{-2}\)), \(R_{L}\downarrow\) is the downward atmospheric longwave radiation (W\(\cdot\)m\({}^{-2}\)), and \(R_{L}\uparrow\) is the upward longwave radiation emitted by the surface (W\(\cdot\)m\({}^{-2}\)). \(\alpha\) is the surface albedo, \(\varepsilon_{s}\) is the emissivity of the land surface, \(R_{L}\downarrow=\varepsilon_{a}\sigma T_{a}^{4}\), \(\varepsilon_{a}\) is the effective emissivity of the atmosphere, \(\sigma=5.67\times 10^{-8}\) W\(\cdot\)m\({}^{-2}\)\(\cdot\)K\({}^{-4}\) is the Stefan-Boltzmann constant, \(T_{a}\) is the air temperature, and \(T_{s}\) is the surface radiation temperature. \(G\) is the heat exchange between the surface and the soil deeper underground, and it is related to the exchanges of water and heat within the soil. Generally, heat is transferred from depth to the surface at night. Studies have found that soil heat flux is correlated with \(R_{n}\) and can be derived using land surface parameters [24; 49]. Because canopies exert a significant influence on \(G\), the fractional canopy coverage \(f_{c}\) is used to determine the ratio of \(G\) to \(R_{n}\) as follows [24]:  
\[G=R_{n}\times[\Gamma_{c}+(1-f_{c})\times(\Gamma_{s}-\Gamma_{c})] \tag{3}\]  
where \(\Gamma_{c}=0.05\) and \(\Gamma_{s}=0.315\) represent the ratio of \(G\) to \(R_{n}\) for full canopy coverage and bare soil. \(H\) is the turbulent heat transfer between the surface and the atmosphere that is derived using the temperature gradient between them. According to gradient diffusion theory:  
\[H=\rho C_{p}\frac{T_{zero}-T_{a}}{r_{ac}} \tag{4}\]  
where \(\rho\) is the air density (kg\(\cdot\)m\({}^{-3}\)), \(C_{p}\) is the specific heat of air at a constant pressure (J\(\cdot\)kg\({}^{-1}\)\(\cdot\)K\({}^{-1}\)), \(T_{zero}\) is the radiative surface temperature (K), \(T_{a}\) is the air temperature at a reference height (K), and \(r_{ac}\) is the aerodynamic resistance (s\({}^{-1}\)\(\cdot\)m), which is determined using the zero plane displacement height and the roughness length. \(r_{ac}\) was calculated based on the Monin-Obukhov similarity theory (MOST) using a stability correction function [12; 50; 51]. Because remote sensing-based methods cannot obtain \(T_{zero}\), the value of \(T_{zero}\) is usually replaced by the radiative surface temperature (\(T_{s}\)). It should be noted that \(T_{s}\) is not strictly equal to \(T_{zero}\) in Equation (4).