# Response of Global Terrestrial Carbon Fluxes to Drought from 1981 to 2016
## 2 Materials and Methods  
### The Model Used to Simulate Global Carbon Fluxes  
Global GPP, NPP, ER, and NEP were simulated using the BEPS model [50], which includes photosynthesis, energy balance, hydrological, and soil biogeochemical modules [51]. This model was initially developed to calculate NPP for the Canadian landmass at daily time steps. In recent years, it has been improved in many aspects and applied to simulate regional terrestrial carbon fluxes in China [28; 52; 53; 54], North America [55; 56; 57; 58], Europe [59], East Asia [60; 61], and the globe [62; 63; 64]. Details about this model are described in references [53; 56] and in the supplementary Text S1 in reference [63]. We only highlight the major methodologies of the model related to the calculation of global terrestrial GPP, NPP, and NEP here.  
Canopy GPP is calculated as:  
\[\text{GPP}=\text{GPP}_{sunlit}LAI_{sunlit}+\text{GPP}_{shaded}LAI_{shaded} \tag{1}\]  
where \(\text{GPP}_{sunlit}\) and \(\text{GPP}_{shaded}\) are gross photosynthesis rates of sunlit and shaded leaves, respectively, and are calculated using the leaf level Farquhar model [65; 66]; \(LAI_{sunlit}\) and \(LAI_{shaded}\) are the leaf area indexes of sunlit and shaded leaves, respectively.  
NPP is calculated as the difference between GPP and autotrophic respiration:  
\[\text{NPP}=\text{GPP}-R_{g}-R_{m} \tag{2}\]  
where \(R_{g}\) and \(R_{m}\) denote growth respiration and maintenance respiration, respectively. The former is assumed to be 25% of GPP while the latter is calculated as a function of biomass, temperature, and the reference respiratory rate at a base temperature [56; 67]:  
\[R_{m}=\sum_{i=1}^{1}R_{m,i}=\sum_{i=1}^{1}M_{i}r_{m,i}Q_{10}{}^{(T-T_{b})/10} \tag{3}\]  
where \(M_{i}\) is the size of biomass carbon pool \(i\) (\(i\) = 1, 2, 3, 4, denoting leaf, stem, coarse root, and fine root carbon pools, respectively), \(r_{m,i}\) is the respiration rate at a base temperature \(T_{b}\), \(Q_{10}\) is the temperature sensitivity factor of maintenance respiration, and \(T\) is the temperature.  
NEP is calculated as:  
\[\text{NEP}=\text{NPP}-R_{h} \tag{4}\]  
where \(R_{h}\) is the heterotrophic respiration occurring in nine litter and soil carbon pools (i.e., surface structural litter, surface metabolic litter, soil structural litter, soil metabolic litter, coarse woody litter, and surface microbial, soil microbial, slow, and passive carbon pools). \(R_{h}\) is calculated using algorithms adopted from the CENTURY model [68].  
\[R_{h}=\sum_{j=1}^{9}\tau_{j}k_{j}C_{j} \tag{5}\]  
where \(\tau_{j}\) is the respiration coefficient of pool \(j\), \(k_{j}\) is the decomposition rate of pool \(j\), and \(C_{j}\) is the size of pool \(j\).  
In the BEPS model, soil water conditions affect photosynthesis by regulating stomatal conductance and heterotrophic respiration by modifying the decomposition rate \(k_{j}\). When soil water content is above field capacity, stomatal conductance and photosynthesis will not be limited. With the decrease in soil water content to wilting point, stomatal conductance will decrease to the minimum that limits photosynthesis. With the departure of soil water content from the optima (at approximately 60% of saturation), the decomposition rates of soil carbon and litter pools will decrease.