## 2 Materials and Methods
### PML-V2.1 Model  
Version 2 of the Penman-Monteith-Leuning model (PML-V2) was developed by coupling the widely-used photosynthesis model [11] and a canopy stomatal conductance model [12] with the Penman-Monteith energy balance equation [13] to jointly estimate gross primary productivity (GPP), \(E_{c}\) and \(E_{s}\)[14; 15; 16; 17; 18]. The PML-V2 model also simulates the \(E_{i}\) based on a revised Gash-model scheme [19]. The PML-V2 model has been applied to successfully produce the MODIS LAI-based global GPP and ET products at a 500m and 8-day resolution from 2002 to present, which were noticeably better than most widely used GPP and ET products [16]. In this study, we incorporated modules of impervious surface evaporation (\(E_{u}\)) and open-water evaporation (\(E_{w}\)) into the PML model (PML-V2.1) to make it suitable for urban ecosystems. Key parameters used in the PML-V2.1 model are provided in Table 1. The following shows the detailed description for PML-V2.1.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Definition**} & \multirow{2}{*}{**Unit**} & \multicolumn{8}{c}{**Land Cover Classification (a)**} \\ \cline{3-11}  & & & **CRO** & **MIF** & **GRA** & **SHR** & **WET** & **WAT** & **IMP** & **BAR** \\ \hline \(\alpha\) & Surface albedo for shortwave radiation & \(-\) & 0.150 & 0.150 & 0.250 & 0.250 & 0.250 & 0.050 & 0.350 & 0.350 \\ \hline \(\varepsilon\) & Emissivity for longwave radiation & \(-\) & 0.960 & 0.990 & 0.950 & 0.950 & 0.960 & 0.990 & 0.940 & 0.940 \\ \hline \(D_{0}\) & Reference vapor pressure deficit at stomatal conductance reduction & kPa & 2.000 & 0.552 & 0.638 & 0.864 & 0.661 & 0.700 & 0.552 & 0.864 \\ \hline \(k_{Q}\) & Extinction coefficient of PAR & \(-\) & 0.721 & 0.386 & 0.595 & 0.230 & 0.996 & 0.600 & 0.386 & 0.230 \\ \hline \(k_{A}\) & Extinction coefficient of available energy & \(-\) & 0.899 & 0.899 & 0.900 & 0.888 & 0.888 & 0.700 & 0.899 & 0.888 \\ \hline \(S_{leaf}\) & Specific canopy rainfall storage capacity per unit leaf area & mm & 0.010 & 0.198 & 0.227 & 0.014 & 0.022 & 0.000 & 0.198 & 0.014 \\ \hline \(F_{ER0}\) & Specific ratio of evaporation rate over rainfall intensity per unit vegetation cover & \(-\) & 0.092 & 0.256 & 0.010 & 0.010 & 0.017 & 0.000 & 0.256 & 0.010 \\ \hline \(S_{U}\) & Specific canopy rainfall storage capacity per unit impervious surface area & mm & 0.014 & 0.014 & 0.014 & 0.014 & 0.014 & 0.014 & 0.014 & 0.014 \\ \hline \(LAI_{ref}\) & Reference LAI & m & 5.000 & 5.000 & 5.000 & 5.000 & 5.000 & 5.000 & 5.000 & 5.000 \\ \hline \(h\) & Canopy height & m & 1.000 & 10.00 & 0.5000 & 10.000 & 0.500 & 0.500 & 10.00 & 0.500 \\ \hline \(V_{m,25}\) & Maximum catalytic capacity of Rubisco per unit leaf area at 25\({}^{\circ}\)C & m\({}^{-2}\) & 22.560 & 28.450 & 29.560 & 18.770 & 24.440 & 0.000 & 28.450 & 18.770 \\ \hline \(\beta\) & Initial photochemical efficiency & \(-\) & 0.029 & 0.029 & 0.029 & 0.029 & 0.029 & 0.000 & 0.029 & 0.029 \\ \hline \(\eta\) & Initial value of the slope of CO\({}_{2}\) response curve & m\({}^{-2}\) & 0.069 & 0.040 & 0.026 & 0.024 & 0.069 & 0.000 & 0.040 & 0.024 \\ \hline \(m\) & Ball-Berry coefficient & \(-\) & 5.289 & 8.355 & 3.934 & 4.406 & 9.211 & 0.000 & 8.355 & 4.406 \\ \hline \(D_{min}\) & The threshold below which there is no vapor pressure constraint & kPa & 1.499 & 0.711 & 0.650 & 1.493 & 0.664 & 1.000 & 0.711 & 1.493 \\ \hline \(D_{max}\) & The threshold above which there is no assimilation & kPa & 6.500 & 3.500 & 5.199 & 5.797 & 5.188 & 6.500 & 3.500 & 5.797 \\ \hline \hline \end{tabular}  
* (a)CRO: cropland, MIF: mixed forest, GRA: grassland, SHR: shrubland, WET: wetland, WAT: water body, IMP: impervious surface and BAR: bare land.  
\end{table}
Table 1: Key parameters used in the PML-V2.1 model.