# Generation of High Resolution Vegetation Productivity from a Downscaling Method
## 2 Materials and Methods
### Methods
#### 2.3.2 Estimation of GPP and NPP  
To estimate high resolution GPP and NPP by integrating remote sensing data and eco-physiological processes, the Multi-source data Synergized Quantitative (MusyQ) GPP/NPP algorithm [5,44] was adopted in this paper. The MusyQ GPP/NPP algorithm is essentially a LUE model. GPP could be described as [49]:  
\[\mathrm{GPP}=\mathrm{FPAR}\times\mathrm{PAR}\times\varepsilon_{max}\times f_{1} (T)\times f_{2}(\beta), \tag{1}\]  
where PAR is the photosynthetically active radiation (PAR), and \(\varepsilon_{max}\) is the biome-specific potential LUE, which could be obtained through a biome-specific potential \(\varepsilon_{max}\) Look-Up Table (LUT) by referring to land cover categories of the Biome Properties Look-Up Table (BPLUT) of the MODIS GPP/NPP algorithm [50], shown in Table 1.  
\(f_{1}(T)\) and \(f_{2}(\beta)\) are the down-regulation effects of temperature and water conditions on \(\varepsilon_{max}\), respectively. \(f_{1}(T)\) could be calculated according to the Carnegie, Ames, Stanford Approach (CASA) [51]. \(f_{2}(\beta)\) was calculated by [52]:  
\[f_{2}(\beta)=\frac{1+NDWI}{1+NDWI_{max}}, \tag{2}\]  
\[NDWI=\frac{\rho(NIR)-\rho(MIR)}{\rho(NIR)+\rho(MIR)}, \tag{3}\]  
where NDWI is the normalized difference water index, \(NDWI_{max}\) is the maximum NDWI in the growing season, and \(\rho(NIR)\) and \(\rho(MIR)\) are the reflectance in near-infrared band and mid-infrared band, respectively. NPP is the net flow of carbon from the atmosphere to plants, which is defined as the balance between GPP and autotrophic respiration [5,44,51]. \[NPP=GPP-R_{a}, \tag{4}\]  
where \(R_{a}\) is 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 [5,44]. \[R_{a}=R_{m}+R_{g}. \tag{5}\]  
\(R_{m}\) were estimated separately for non-forest and forest lands. For non-forest land, \(R_{m}\) was estimated with LAI and specific leaf area (SLA) [5,44]. \[R_{m}=LAI/SLA\times 0.5\times 2^{(T-T_{b})/10}, \tag{6}\] \begin{table}
\begin{tabular}{c c} \hline
**Landcover** & \(\varepsilon_{max}\)**(g C/M)** \\ \hline C3 crops & 1.300 \\ C4 crops & 1.700 \\ Deciduous broadleaved forest (DBF) & 1.165 \\ Evergreen broadleaved forest (EBF) & 1.268 \\ Deciduous needle-leaf forest (DNF) & 1.086 \\ Evergreen needle-leaf forest (ENF) & 0.962 \\ Mixed forest & 1.051 \\ Grass & 0.860 \\ Wetland & 0.860 \\ \hline \end{tabular}
\end{table} 
Table 1: Biome-specific potential LUE for different landcover types. where SLA was obtained from the BPLUT of MODIS GPP/NPP algorithm [50] in our model. For forest land, \(R_{m}\) was defined as the summation of the maintenance respiration of leaves, stems, and roots [5; 44]. \[R_{m,i}=M_{i}r_{m,i}Q_{10,i}^{T-T_{b}/10}, \tag{7}\]  
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 as four classes, needle-leaf forests, broadleaved forests, mixed forests and others, and \(Q_{10,i}\) and \(r_{m,i}\) for each classes are obtained according to the BPLUT of MODIS GPP/NPP algorithm [50]. Specifically, leaf mass is estimated from LAI and SLA [5; 44]:  
\[M_{1}=LAI/SLA, \tag{8}\]  
Stem and root mass are obtained using [5; 44]:  
\[M_{2}=biomass/(1+y), \tag{9}\]  
\[M_{3}=y\times M_{2}, \tag{10}\]  
where \(y\) is the ecophysiological biome-specific constant obtained from the Boreal Ecosystem Productivity Simulator (BEPS) model [53]. The leaf, stem, fine root and coarse root respiration items were calculated separately according to the BEPS model.