# Evaluation of Clumping Effects on the Estimation of Global Terrestrial Evapotranspiration
## 2 Modeling Methodology
### ET Modeling
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameters \({}^{\bullet}\)** & **ENF \({}^{\circ}\)** & **DNF \({}^{\circ}\)** & **DBF \({}^{\circ}\)** & **EBF \({}^{\circ}\)** & **MP\({}^{\circ}\)** & **Grass** & **Crop** & **Shrub** & **Others** & **References** \\ \hline \(V_{\rm{max}}^{\rm{255}}(\rm{(mmol\,m^{-2}s^{-1})}\) & \(48.2\pm 5.7\) & \(44.6\pm 2.7\) & \(72.7\pm 14.7\) & \(53.6\pm 14.7\) & \(60.5\pm 10.2\) & \(88.7\pm 20.9\) & \(82.7\pm 15.2\) & \(57.4\pm 31.0\) & \(90.0\pm 89.5\) & [23; 34] \\ Na (g m\({}^{-2}\)) & \(4.45\) & \(2.45\) & \(2.45\) & \(2.97\) & \(3.5\) & \(2.38\) & \(2.38\) & \(2.70\) & \(2.38\) & [23] \\ \(\chi_{a}\) (m\({}^{2}\)g\({}^{-1}\)) & \(0.33\) & \(0.56\) & \(0.59\) & \(0.48\) & \(0.47\) & \(0.60\) & \(0.60\) & \(0.57\) & \(0.60\) & [23] \\ \(m\) & \(8\) & \(8\) & \(8\) & \(8\) & \(8\) & \(4\) & \(4\) & \(8\) & \(8\) & [23] \\ \(\rm{g_{0}}\) (mol m\({}^{-2}\)s\({}^{-1}\)) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & \(0.001\) & [23] \\ \(RASH_{a}\) & \(0.976\) & \(0.966\) & \(0.966\) & \(0.962\) & \(0.966\) & \(0.952\) & \(0.961\) & \(0.978\) & \(0.966\) & [35] \\ \(RASH_{a}\) & \(0.6\) & \(0.6\) & \(0.885\) & \(0.575\) & \(0.6\) & \(0.495\) & \(0.6\) & \(0.6\) & \(0.6\) & [36] \\ \(a\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.04\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & [36] \\ LAI & \(3.60\pm 2.14\) & \(3.43\pm 1.96\) & \(3.61\pm 2.01\) & \(3.98\pm 2.25\) & \(4.39\pm 2.01\) & \(1.64\pm 1.36\) & \(2.27\pm 1.60\) & \(1.71\pm 1.33\) & \(1.87\pm 1.64\) & [37] \\ \(\rm{LA_{u}}\) & \(0.03\) & \(1.04\) & \(0.96\) & \(0.03\) & \(0.06\) & \(0.01\) & \(0.01\) & \(0.01\) & \(0.01\) & [38] \\ CI & \(0.58\pm 0.10\) & \(0.60\pm 0.11\) & \(0.60\pm 0.11\) & \(0.58\pm 0.12\) & \(0.57\pm 0.11\) & \(0.66\pm 0.14\) & \(0.68\pm 0.13\) & \(0.65\pm 0.14\) & \(0.66\pm 0.14\) & [39] \\ \hline \hline \end{tabular} \({}^{\bullet}\) V\({}_{\rm{max}0}\)n00 is leaf maximum carboxylation rate at the top of the canopy at 25 \({}^{\circ}\)C; N\({}_{0}\) is leaf nitrogen content at the top of canopy; \(\chi_{a}\) is the slope of V\({}_{\rm{max}}\)n variation with leaf nitrogen content; \(m\) and g\({}_{0}\) are the slope and intercept in the BWB equation. \(\beta\) is the simple numerical index of rooting distribution based on the asymptotic equation \(p(z)=1-\beta^{z}\), where p(z) is the proportion of roots from the surface to the depth (z). \(RASH_{a}\) is the threshold of relatively available soil moisture. \(a\) is the fitted slope in the equation of accumulated soil water deficit (ASWD) adjusted V\({}_{\rm{max}}\) ratio (Appendix A). The peak LAI during the growing season and the annual mean clumping index are given as the mean and standard deviation for each FET. \({}^{\rm b}\) ENF: evergreen needleleaf forests; DNF: deciduous needleleaf forests; DBF: deciduous broadleaf forests; EBF: evergreen broadleaf forests; MF: mixed forests.  
\end{table} 
Table 1: Physiological and canopy structural parameters are used in the BEPS model for various PFTs. In BEPS, leaf transpiration is coupled with leaf photosynthesis rate through stomatal conductance, which is estimated based on the Ball-Woodrow-Berry (BWB) stomatal conductance model [41]:  
\[g_{sw}=m\frac{Ah_{s}}{C_{s}}+g_{0} \tag{4}\]  
where \(g_{sw}\) is stomatal conductance to water vapor (mol m\({}^{-2}\) s\({}^{-1}\)). \(h_{s}\) is relative humidity (RH) at the leaf surface. \(C_{s}\) represents CO\({}_{2}\) concentration (\(\mu\)mol mol\({}^{-1}\)) at the leaf surface. \(m\) is a slope (dimensionless) and \(g_{0}\) is a small intercept term (mol m\({}^{-2}\) s\({}^{-1}\)). The \(m\) values are highly variable among plant functional types (PFTs) [42]. We choose the most frequently used values in this study (Table 1). The values of \(g_{0}\) are usually very low and treated invariant for all PFTs (Table 1).