# Estimation of Global Vegetation Productivity from Global LAnd Surface Satellite Data
## 2 Materials and Methods  
### Method  
#### 2.1.1 Estimation of GPP and NPP  
A flowchart of GPP and NPP estimation and validation is shown in Figure 1. To estimate global daily GPP/NPP by integrating remote sensing data and eco-physiological processes, the Multi-source data Synergized Quantitative (MuSyQ) NPP algorithm [22] was adopted in this paper. The MuSyQ-NPP algorithm is essentially a LUE model; thus, daily GPP could be described as:  
\[\text{GPP}=\varepsilon\times\text{FPAR}\times\text{PAR} \tag{1}\]  
where \(\varepsilon\) is the LUE, and PAR is the photosynthetically active radiation (PAR), which could be obtained from Global Land Data Assimilation System (GLDAS) incident shortwave radiation R using the following equation:  
\[\text{PAR}=0.5\times\text{R} \tag{2}\]  
LUE may be influenced by many environmental stressors, such as low temperature and water shortage. In this condition, \(\varepsilon\) could be described as:  
\[\varepsilon=\varepsilon_{max}\times f_{1}(T)\times f_{2}(\beta) \tag{3}\]where \(\varepsilon_{max}\) is the biome-specific potential of LUE, and \(f_{1}(T)\) and \(f_{2}(\beta)\) are the down-regulation effects of temperature and water conditions on \(\varepsilon_{max}\), respectively. A biome-specific potential \(\varepsilon_{max}\) Look-Up Table (LUT) was established by referring to land cover categories according to the Biome Properties Look-Up Table (BPLUT) of the MODIS GPP/NPP algorithm [23]. It is noted that a potential \(\varepsilon_{max}\) value of 1.5 g C MJ\({}^{-1}\) for crops was used in the algorithm. \(f_{1}(T)\) was calculated according to the CASA model [17]. The effect of water conditions on plant photosynthesis \(f_{2}(\beta)\) could be described as:  
\[f_{2}(\beta)=0.5+0.5 ET/ET_{P} \tag{4}\]  
where \(ET\) represents actual evapotranspiration, which is estimated from a modified P-M approach, LAI and Fcover products [22; 24; 25]. \(ET_{P}\) represents potential evapotranspiration, which is estimated using the Priestley and Taylor (PT) equation [26]. NPP is the net flow of carbon from the atmosphere to plants, which is defined as the balance between GPP and autotrophic respiration. \[NPP=GPP-R_{a} \tag{5}\]  
where \(R_{a}\) is autotrophic respiration. Autotrophic respiration (\(R_{a}\)) could be separated into two parts: maintenance respiration \(R_{m}\), which refers to the energy necessary to maintain biomass, and growth respiration \(R_{g}\) which refers to the energy needed for converting assimilates into new structural plant constituents. \[R_{a}=R_{m}+R_{g} \tag{6}\]  
When estimating \(R_{m}\), non-forest and forest lands were estimated separately. For non-forest land, \(R_{m}\) was estimated with LAI and specific leaf area (SLA). \[R_{m}=LAI/SLA\times 0.5\times 2^{(T-T_{b})/10} \tag{7}\]  
where SLA was obtained from the BPLUT of MODIS GPP/NPP algorithm [23] in our model. For forest land, \(R_{m}\) was obtained by summing the maintenance respiration of leaves, stems, and roots [22]. \[R_{m,i}=M_{i}r_{m,i}Q_{10,i}^{T-T_{b}/10} \tag{8}\]  
where \(M_{i}\) is the biomass of plant component \(i\), \(r_{m,i}\) is maintenance respiration coefficient for component \(i\), \(Q_{10,i}\) is the temperature sensitivity factor, \(T\) is the daily average temperature and \(T_{b}\) is the base temperature, \(r_{m,i}\) is the maintenance respiration coefficient. Forest lands are classified into four classes: needle-leaf forests, broadleaved forests, mixed forests and others, and \(Q_{10,i}\) and \(r_{m,i}\) for each class are obtained according to the BPLUT of MODIS GPP/NPP algorithm [23]. Specifically, leaf mass is estimated from LAI and SLA:  
\[M_{1}=LAI/SLA \tag{9}\]  
Stem and root mass are obtained using:  
\[\text{GPP}=\varepsilon\times\text{FPAR}\times\text{PAR} \tag{1}\]0  
\[\text{GPP}=\varepsilon\times\text{FPAR}\times\text{PAR} \tag{1}\]1  
where \(y\) is the ecophysiological biome-specific constant obtained from the Boreal Ecosystem Productivity Simulator (BEPS) model [27].