## 2 Materials and Methods  
### Model Description  
The SWH model simulates plant transpiration and soil water evaporation separately with algorithms based on the Penman-Monteith equation [8]. A full description of the SWH model is available in Appendix A and in [PERSON] et al. [14]. Five resistances are necessary to estimate ET with the SWH model (Figure 1, Appendix A), i.e., soil surface resistance (\(r_{\text{ss}}\)), canopy stomatal resistance (\(r_{\text{sc}}\), the reverse of canopy stomatal conductance), the aerodynamic resistances encountered by the water flux leaving leaf lamina (\(r_{\text{ac}}\)) or soil surface (\(r_{\text{as}}\)) before being incorporated into the mean canopy flow and the transfer resistance between the hypothetical mean canopy flow and the reference height (\(r_{\text{aa}}\)). \(r_{\text{ss}}\) and \(r_{\text{sc}}\) are the most critical for model performance among the five resistances. \(r_{\text{ss}}\) was estimated as a function of soil water content [23; 24]:  
\[r_{\text{ss}}=b_{1}(\frac{SWC_{\text{s}}}{SWC})^{b_{2}}+b_{3} \tag{1}\]where \(SWC\) and \(SWC_{s}\) are the soil water content and saturated water content in the surface soil (m\({}^{3}\cdot\)m\({}^{-3}\)) and \(b_{1}\) (s\(\cdot\)m\({}^{-1}\)), \(b_{2}\) and \(b_{3}\) (s\(\cdot\)m\({}^{-1}\)) are empirical constants. \(b_{1}\) is fixed as 3.5 s\(\cdot\)m\({}^{-1}\)[23]. Using the scheme of the Biome-Biogeochemical(Biome-BGC model) [24], SWC was estimated using a one-layer bucket model in which soil water storage was estimated as the balance of water input (i.e., precipitation and snowmelt) and output (i.e., ET, runoff and sublimation). Runoff was calculated as the surplus precipitation overpassing the water storage at the point of the saturated and field-holding capacity. Snowmelt and sublimation were calculated as functions of air temperature and solar incident radiation. Thereafter, SWC was calculated using soil water storage and the parameter 'effective soil depth' (\(d\)), which is determined by parameterization, explained below. Due to the insensitivity of the model output, the same empirical values of 0.45 and 0.35 m\({}^{3}\cdot\)m\({}^{-3}\) were used for saturated water content and field-holding capacity, respectively, for all ecosystems. Details for calculating the SWC are available in the Biome-BGC handbook ([[http://www.ntsg.umt.edu](http://www.ntsg.umt.edu)]([http://www.ntsg.umt.edu](http://www.ntsg.umt.edu))). We estimated \(r_{\mathrm{sc}}\) by introducing the Ball-Berry model in our study[21]:  
\[r_{\mathrm{sc}}=\frac{1}{g_{0}\ +\ \frac{a_{1}p_{\mathrm{s}}h_{\mathrm{s}}}{c_{s}}} \tag{2}\]  
where \(g_{0}\) and \(a_{1}\) are empirical parameters, \(P_{n}\) (\(\mathrm{\upmu mol\cdot m^{2}\cdot s^{-1}}\)) is the photosynthetic rate and \(h_{\mathrm{s}}\) is the leaf surface relative humidity, which was approximated using the air relative humidity. \(C_{S}\) is the leaf surface CO\({}_{2}\) content. \(C_{S}\) should vary seasonally and inter-annually, considering it is insensitive to model simulation; hence, we simplified it as a constant (390 ppm). Note that a varying CO\({}_{2}\) must be used if long-term trend analysis is to be conducted. Figure 1: Flowchart of evapotranspiration (ET) estimation with the SWH model. The meanings of the acronyms in this figure are available in Abbreviation. \(P_{\rm n}\) is a key driving variable in the estimation of \(r_{\rm sc}\). We used GPP, which was estimated using a satellite-based light-use efficiency model, to replace this variable [22]:  
\[\rm GPP=\varepsilon\times PAR\times FPAR. \tag{3}\]  
where PAR is the incident photosynthetically-active radiation (\(\upmu mol\cdot m^{-2}.s^{-1}\)) and FPAR is the fraction of PAR absorbed by the canopy, which was estimated as a function of NDVI [25] (FPAR = 1.24 NDVI \(-\) 0.168). At the very beginning, we used the MODIS LAI/FPAR product directly, finding many outliers or no data available at many sites, which hampered the job of parameterization. Therefore, we used NDVI to estimate FPAR and LAI.