## 3 Methodology
### The Surface Energy Balance System (SEBS)
The SEBS parameterizes roughness height based on a semi-empirical model using the following equations:  
\[\beta=C_{1}-C_{2}\mathrm{exp}\left(-C_{3}C_{4}\times LAI\right) \tag{4}\]  
\[n_{ec}=\frac{(C_{d}\times LAI)}{2\beta^{2}} \tag{5}\]  
\[\frac{d}{h}=1-\frac{1}{2n_{ec}}[1-\mathrm{exp}(-2n_{ec})] \tag{6}\]  
\[\frac{z_{0m}}{h}=[1-\frac{d}{h}][\mathrm{exp}(\frac{-k}{\beta})] \tag{7}\]  
where \(\beta\) is the ratio of friction velocity to wind speed at canopy height; \(C_{1}\), \(C_{2}\), and \(C_{3}\) are constants related to the bulk surface drag coefficient; \(C_{\mathrm{d}}\) is the foliage drag coefficient; and \(n_{\mathrm{ec}}\) is the wind speed profile extinction coefficient within the canopy. The roughness model utilizes a proportional relationship between canopy height and roughness height [78]. Obviously, canopy height is also a critical parameter by which \(z_{0m}\) and \(d_{0}\) are directly prescribed. In the SEBS, if canopy height information is not available, it can be also derived using an empirical equation, as follows:  
\[h=h_{\mathrm{min}}+\frac{NDVI_{\mathrm{reg}}-NDVI_{soil}}{NDVI_{\mathrm{reg}}+ NDVI_{soil}}\times(h_{\mathrm{max}}-h_{\mathrm{min}}) \tag{8}\]where \(h_{\text{min}}\) and \(h_{\text{max}}\) are the minimal and maximal canopy heights, respectively; \(NDVI_{max}\) and \(NDVI_{min}\) are the NDVI values of fully vegetated and bare soil. The \(kB^{-1}\) model proposed by [PERSON] [23] was used in this study and it links \(z_{\text{0m}}\) and \(z_{\text{0h}}\), as follows:  
\[z_{\text{0h}}=\frac{z_{\text{0m}}}{\exp(kB^{-1})} \tag{9}\]  
where \(kB^{-1}\) is a scalar heat transfer coefficient called the inverse Stanton number. The energy balance of a limiting case at dryness and wetness are then used to estimate the relative evaporative fraction (\(\Lambda_{r}\)), as follows:  
\[R_{n}=G_{0}+H+\lambda E \tag{1}\]0  
where \(H_{\text{tot}}\) is \(H\) at wetness and \(H_{dry}\) is dryness. Both were estimated as described in [PERSON] [23]. The evaporative fraction (\(\Lambda\)) is calculated, as follows:  
\[R_{n}=G_{0}+H+\lambda E \tag{1}\]1  
where \(\lambda E_{wet}\) is \(\lambda E\) at wetness. Finally, \(\lambda E\) is determined by the following equation:  
\[R_{n}=G_{0}+H+\lambda E \tag{1}\]2  
In practice, the remote sensing data used in the SEBS represents instantaneous information for the land surface. The evaporative coefficient is assumed to be constant throughout the day, and, finally, daily evapotranspiration is expressed, as follows:  
\[R_{n}=G_{0}+H+\lambda E \tag{1}\]3  
where \(E_{daily}\) is the daily ET (mm\(\cdot\)d\({}^{-1}\)), and \(\overline{R_{n}}\) and \(\overline{G_{0}}\) are the mean daily net radiation (Wm\({}^{-2}\)) and mean daily soil heat fluxes that can be assumed to be negligible for the entire day. In brief, the SEBS generally requires two sets of driven data, remotely sensed land surface parameters (for example, the surface Albedo, Emissivity, temperature, LAI, NDVI, and roughness lengths) and meteorological data (for example, air temperature, wind speed, air and vapor pressures, and downwelling shortwave and long-wave radiations).