*2.2. Three-Temperature Model*

The three-temperature model estimates vegetation ET by introducing a reference leaf with no ET [34,48].

$$LE = R\_n - R\_{np} \frac{T\_c - T\_a}{T\_p - T\_a} \tag{1}$$

where *LE* is the latent heat consumed by vegetation ET. *Rn* and *Rnp* are the net radiation on the vegetation and reference leaf, respectively (W m<sup>−</sup>2). *Tc* and *Tp* are the surface temperature of the vegetation and reference leaf (◦C). The surface temperature could be obtained by thermal images, and the maximum *Tc* in the image is regarded as *Tp* [37,38]. *Ta* is air temperature (◦C). *Rn* and *Rnp* could be estimated according to [49].

$$R\_n = (1 - \alpha\_c)R\_s + \Delta R\_l \tag{2}$$

where *Rs* is solar radiation (W m<sup>−</sup>2). αc is the albedo of the vegetation canopy. To simplify the calculation, the empirical coefficient αc = 0.22 was used in this study [37]. Δ*Rl* is the net long-wave radiation (W m<sup>−</sup>2), which could be estimated by [50,51]

$$
\Delta R\_l = \left( 0.4 + 0.6 \frac{R\_\varepsilon}{R\_{so}} \right) \left( \varepsilon\_d \sigma T\_a^4 - \varepsilon\_c \sigma T\_c^4 \right) \tag{3}
$$

where *Rso* is the clear day solar radiation (W m<sup>−</sup>2), which is assumed to equal to *Rs* in this study as all the experiment were conducted in clear sunny days [41]. *εc* the canopy emissivity, and empirical coefficient *εc* = 0.98 was used here [37]. *σ* is the Stefan–Boltzman constant (5.67 × 10−<sup>8</sup> W m<sup>−</sup><sup>2</sup> <sup>K</sup>−4). *εa* is the atmospheric emissivity and could be estimated according to [52]

$$
\varepsilon\_a = 0.92 \times 10^{-5} T\_a^2 \tag{4}
$$

If αc, *<sup>ε</sup>c*, and *Tc* are replaced by <sup>α</sup>cp, *<sup>ε</sup>cp* and *Tcp* in Equations (2) and (3), then *Rnp* could be estimated. As we use the leaf with the highest surface temperature in the canopy as the reference leaf in this study, αc, *εc* are assumed to be same to <sup>α</sup>cp, *<sup>ε</sup>cp*.

The analysis procedures were written into a software named "A system to estimate evapotranspiration by infrared remote sensing and the three-temperature model", which can be downloaded and used freely from https://pan.baidu.com/s/19iuz5PIVjZOR96iVObYBqA.
