## 1 Introduction  
Evapotranspiration (ET), which is a combined process of evaporation and transpiration, is crucial to the hydrological cycle. It links energy and water exchanges among the hydrosphere, atmosphere and biosphere [1; 2; 3; 4; 5]. ET is the largest outgoing water flux from the earth's surface; most precipitation is lost in the form of ET with the percentage varying from region to region globally. In semi-arid regions, the amount of ET is roughly equivalent to the precipitation [6]. Therefore, the accurate quantification of ET is critical to developing a greater understanding of local and global energy and water cycles, global climate change, land atmosphere interactions and ecosystem processes, and beneficial to improving applications in many fields, such as water resources management, drought monitoring and assessment [7], irrigation scheduling, hydrological modeling, weather forecasts and so on [8; 9; 10; 11; 12; 13]. Ground-based observations of ET have some advantages but the required ground instrumentation is available in a limited number of places and can only obtain localized values of ET, which often cannot satisfy the needs of regional-scale studies. In addition, the employment of instrumentations is always time consuming, labor intensive and sometimes subject to instrument failure [9]. Recent developments in remote sensing have made it possible to acquire crucial variables for characterizing land surface interactions. Over the last two decades, the requirement of quantifying ET at a regional scale, together with the recent advances in satellite remote sensing technology, has led to many studies on mapping large-scale ET [9; 11; 14; 15]. The surface energy balance algorithm based on the energy balance equation (SEB; Equation (1)), is one of the most widely used approaches for obtaining regional estimates of remotely sensed ET at multiple temporal and spatial scales [9]. Energy and mass are exchanged between the land surface and the atmosphere [16; 17]. When the heat fluxes that are transported by horizontal advection and consumed by photosynthetic vegetation are not considered, the one-dimensional form of the surface energy balance equation on an instantaneous time scale can be expressed as:  
\[R_{n}=G+H+LE \tag{1}\]  
where \(R_{n}\) (W/m\({}^{2}\)) is the net surface radiation, \(G\) (W/m\({}^{2}\)) is the soil heat flux, \(H\) (W/m\({}^{2}\)) is the sensible heat flux, and \(LE\) (W/m\({}^{2}\)) is the latent heat flux. In Equation (1), sensible heat flux can be calculated using the remotely sensed surface temperature, air temperature and a series of conductance formulas; estimates of \(R_{n}\) and \(G\) are available using remote sensing or ground data, and hence, the latent heat flux is taken as a residual term of Equation (1) [16; 17]. Based on how the sinks or sources of heat fluxes are parameterized between the earth's surface and the atmosphere, SEB models can be divided into two categories: the single-source models and two-source models, or multi-source models [18]. Single-source SEB models consider vegetation and soil to be a single unit and often utilize land surface temperature (LST) and empirical resistance corrections to derive the latent heat flux [19]. Since they are highly dependent on empirical corrections, single-source SEB models are inappropriate for application over areas with partial vegetation cover, where significant errors would be found [20; 21; 22]. To overcome the limitations associated with single-source SEB models in partially vegetated areas [22], it is necessary to apply a two-source SEB model that separately simulates the heat and water exchange and the interactions between soil and atmosphere and between vegetation and atmosphere. Thus, in two-source SEB models, the component \(H\) is partitioned between the soil and vegetation, and the component \(LE\) is treated as the sum of evaporation from the soil surface and transpiration from vegetation.