## 3 Methodology  
### The Surface Energy Balance System (SEBS)  
The SEBS is an advanced single source model developed by [PERSON] [23] for estimating turbulent heat fluxes based on energy balance (EB) and employs an evaporative fraction (ETF) for estimating actual ET (AET) by accounting for water limiting (wet-limit and dry-limit) cases (wetness and dryness). Briefly, the SEBS consists of the functions of land surface parameters derived from remote sensing data, a model of dynamic roughness lengths with a reference to heat transfer, and the determination of ETF. Abiding by the theories of EB, bulk atmospheric similarity (BAS) [68] and MOS [39], based on a combination of physical land surface parameters obtained from remote sensing data and meteorological forcing data, the SEBS has been proven to be a reliable remote sensing-based ET model in numerous studies conducted over multiple ecosystems and under various climate and landscape conditions [69; 70; 71; 72; 73; 74]. However, few studies have focused on forests [75; 76; 77], especially those located in cold and arid regions. Figure 1: The location and sub-reaches of the Heihe River Basin (HRB). A concise description of the SEBS algorithm is provided below. Details can be found in Su [23]. Basically, the surface energy balance is expressed as follows:  
\[R_{n}=G_{0}+H+\lambda E \tag{1}\]  
where \(G_{0}\) is the soil heat flux, \(R_{n}\) is the net radiation, \(H\) is the sensible heat flux, and \(\lambda E\) is the latent heat flux (\(\lambda\) is the latent heat of vaporization (\(\mathrm{J}\cdot\mathrm{g}^{-1}\)) and E is the AET). Surface available energy (\(H+\lambda E\)) is generally used to partition the energy exchange for heat and water vapor. The unit for Equation (1) is watts per square meter (\(\mathrm{W}\cdot\mathrm{m}^{-2}\)). To derive sensible and latent heat fluxes, the theory of BAS (for the mixed layer of the atmosphere) or MOS (for the atmospheric surface layer (ASL)) was employed. In most cases, MOS relationships for profiles of mean wind speed, \(u\) (\(\mathrm{m}\cdot\mathrm{s}^{-1}\)), and mean temperature, \(\theta_{0}-\theta_{a}\), were applied within the SEBS and the integral form was written as follows [39]:  
\[u=\frac{u_{\ast}}{k}\left[\ln(\frac{z-d}{z_{0m}})-\Psi_{m}(\frac{z-d}{L})+\Psi _{m}(\frac{z_{0m}}{L})\right] \tag{2}\]  
\[\theta_{0}-\theta_{a}=\frac{H}{ku_{\ast}\rho c_{p}}\left[\ln(\frac{z-d}{z_{0h} })-\Psi_{h}(\frac{z-d}{L})+\Psi_{h}(\frac{z_{0h}}{L})\right] \tag{3}\]  
where \(u_{\ast}\) is the friction velocity (\(\mathrm{m}\cdot\mathrm{s}^{-1}\)) calculated as \((\tau_{0}/\rho)^{1/2}\); \(\tau_{0}\) is the surface shear stress (\(\mathrm{kg}\cdot\mathrm{m}\cdot\mathrm{s}^{-2}\)); \(\rho\) is the air density (\(\mathrm{kg}\cdot\mathrm{m}^{-3}\)); \(k\) = 0.41 is [PERSON]'s constant; \(z\) is the height of the measurement; \(d\) is the zero displacement height (m); \(z_{0m}\) is the aerodynamic roughness length for momentum transfer; \(\theta_{0}\) is the potential temperature (K) at the surface; \(\theta_{a}\) is the potential air temperature (K) at \(z\); \(c_{p}\) is the specific heat capacity of air at constant pressure (\(\mathrm{J}\cdot\mathrm{kg}^{-1}\cdot\mathrm{K}^{-1}\)); \(z_{0h}\) is the roughness height for heat transfer (m); and \(\Psi_{m}\) and \(\Psi_{h}\) are the stability correction functions for momentum and heat transfer. \(L\) is the Obukhov length (m). Obviously, both the zero-plane displacement height (\(d\)) and the roughness lengths (\(z_{0m}\) and \(z_{0h}\)) are critical parameters for determinations of momentum and heat transfer between the land surface and the atmosphere.