## 3 Methods
### The Eddy Covariance and MODIS Data-Driven Model  
The eddy covariance and MODIS data-driven model (EC-MOD) applies a data-driven approach that simulates vegetation GPP using the eddy covariance flux tower data, MODIS data streams, micrometeorological reanalysis data, stand age, and aboveground biomass data [54]. The EC-MOD dataset that provides gridded carbon and water fluxes over North America was downloaded from the Global Ecology Group at University of New Hampshire ([[http://globalecology.unh.edu/](http://globalecology.unh.edu/)]([http://globalecology.unh.edu/](http://globalecology.unh.edu/))). The EC-MOD dataset consists of gross primary productivity (GPP), net ecosystem exchange (NEE),  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model Name** & **Equations** \\ \hline Canopy radiative transfer & \([\text{PAR}_{\text{i}},\text{R}_{\text{in}},\text{R}_{\text{sn}}]=f(\text{R}_{ \text{g}},\text{R}_{\text{d}},\theta,\text{LAAI},\Omega)\) \\ Leaf photosynthesis & \(\text{A}_{\text{n}}=f(\text{PAR}_{\text{i}},\text{T}_{\text{j}},\text{Photo}, \text{SWC}_{\text{p}},\text{P}_{\text{atm}},\text{g}_{\text{s}},\text{c}_{ \text{i}})\) \\ Leaf conductance & \([\text{g}_{\text{s}},\text{g}_{\text{b}},\text{c}_{\text{i}}]=f(\text{A}_{ \text{n}},\text{VPD},\text{P}_{\text{atm}},\text{u},[\text{CO}_{2}])\) \\ Leaf transpiration & \([\text{AE}_{\text{i}},\text{T}_{\text{j}}]=f(\text{R}_{\text{in}},\text{T}_{ \text{a}},\text{VPD},\text{P}_{\text{atm}},\text{g}_{\text{s}},\text{g}_{ \text{b}})\) \\ Soil evaporation & \(\text{\lambda E}_{\text{s}}=f(\text{R}_{\text{sn}},\text{T}_{\text{a}},\text{ VPD},\text{P}_{\text{atm}})\) \\ \hline \hline \end{tabular} Note: \(\text{PAR}_{\text{i}}\) denotes the radiation absorbed by either sunlit or shaded leaves per leaf hemi-surface area at the photosynthetically active radiation wavelength; \(\text{R}_{\text{in}}\) denotes the net shortwave radiation at the leaf surface; \(\text{R}_{\text{in}}\) denotes the net shortwave radiation at the soil surface; \(f\) denotes the function with input arguments in parentheses; \(\text{R}_{\text{g}}\) denotes daily total incoming solar radiation at the canopy top; \(\text{R}_{\text{d}}\) denotes daily diffuse radiation at the canopy top; \(\theta\) denotes solar zenith angle; \(\text{LAI}\) denotes leaf area index; \(\Omega\) denotes foliage clumping index; \(\text{A}_{\text{n}}\) denotes the leaf net photosynthetic rate; \(\text{T}_{\text{i}}\) denotes daily mean leaf temperature; Photo denotes daily photoperiod for a given day of the year at a given geolocation; SWC denotes the root zone soil water content; \(\text{P}_{\text{atm}}\) denotes daily atmospheric pressure; \(\text{g}_{\text{s}}\) denotes the leaf stomatal conductance; \(\text{g}_{\text{b}}\) denotes the leaf boundary layer conductance; \(\text{c}_{\text{i}}\) denotes the intercellular CO\({}_{2}\) partial pressure; VPD denotes daily vapor pressure deficit; \(\text{u}\) denotes the wind speed; \([\text{CO}_{2}]\) denotes atmospheric CO\({}_{2}\) concentration; \(\text{AE}_{\text{i}}\) denotes the latent heat at the leaf surface; \(\text{T}_{\text{a}}\) denotes daily mean air temperature; and \(\text{\lambda E}_{\text{s}}\) denotes the evaporation rate for the soil surface.  
\end{table}
Table 2: The generalized equations for the growing production day (GPD) model to simulate canopy photosynthesis and evapotranspiration.  
ecosystem respiration (ER), and evapotranspiration (ET) at 1000 m spatial resolution [48], and only yearly data were accessible when the study was conducted.