## 2 Materials and Methods
### Remote Sensing Data and its Processing  
#### 2.3.1 Introduction to MODIS Productivity Data  
The MODIS satellite sensor is one of the major sensors of the U.S. Earth Observation System (EOS). Generalized MODIS data cover 44 types of products. The MODIS data used in this study came from the MOD17A2 eight-day PSNnet (net photosynthesis) product, with a resolution of 1  km, which is a global land vegetation net productivity product calculated by model [25] and has been validated and widely used in studies on productivity and biomass in different regions of the world [26, 27, 28, 29].  
The MOD17 product is a land productivity product calculated using the BIOME-BGC model and a light use efficiency model, in combination with remote sensing data. The essence of the core science in the MOD17 algorithm is the application of radiation conversion efficiency logic to predictions of daily GPP (Gross Primary Productivity) using satellite-derived FPAR (Fraction of Photosynthetically Active Radiation, from MOD15) and independent estimates of PAR (Absorption Ratio of Photosynthetically Active Radiation) and other surface meteorological fields (from the DAO). The subsequent estimates of maintenance and growth respiration terms are subtracted from GPP to arrive at NPP (Net Primary Productivity). The principles underlying daily PSNnet estimation are as follows:  
\[\varepsilon=\varepsilon_{\text{max}}\times\text{TMIN\_Scalar}\times\text{VPD\_Scalar} \tag{1}\]  
where, \(\varepsilon\) is the light use efficiency, \(\varepsilon_{\text{max}}\) is the maximum light use efficiency obtained from the Biome Parameter Look-Up Table (BPLUT) provided by NASA; TMIN_Scalar is the daily minimum temperature scalar, and VPD_Scalar is the daily average vapor pressure deficit scalar, which are used to calculate the scalars that attenuate \(\varepsilon_{\text{max}}\) to produce the final \(\varepsilon\) used to predict GPP.  
\[\text{IPAR}=\text{SWRad}\times\text{0.45} \tag{2}\]  
\[\text{APAR}=\text{IPAR}\times\text{FAR} \tag{3}\]  
\[\text{GPP}=\varepsilon\times\text{APAR} \tag{4}\]  
where, SWRad is the incident shortwave radiation provided by the Data Assimilation Office (DAO) of NASA; IPAR is the photosynthetically active radiation incident on the vegetative surface; FAR is the absorption ratio of photosynthetically active radiation; and APAR is the photosynthetically active radiation absorbed by vegetation.  
\[\text{Leaf\_Mass}=\text{LAI/SLA} \tag{5}\]  
where, LAI is the leaf area index obtained from the MOD15, and SLA is the projected leaf area for a given pixel obtained from the BPLUT.  
\[\text{Leaf\_MR}=\text{Leaf\_Mass}\times\text{leaf\_mr\_base}\times\text{Q10\_mr} ^{\text{(Tavg-20.0)/10.0]}} \tag{6}\]  
where, leaf_mr_base is the maintenance respiration of leaves obtained from the BPLUT and Tavg is the average daily temperature ( \(\text{C}\)) estimated from the DAO meteorological data; Leaf MR is the leaf autotrophic respiration consumption.  
\[\text{Froot\_Mass}=\text{Leaf\_Mass}\times\text{Froot\_leaf\_ratio} \tag{7}\]  
\[\text{Froot\_MR}=\text{Fine\_Root\_Mass}\times\text{froot\_mr\_base}\times \text{Q10\_mr}^{\text{(Tavg-20.0)/10.0]}} \tag{8}\]where, \(\text{Froot\_leaf\_ratio}\) is the ratio of fine root to leaf mass obtained from the BPLUT; \(\text{Froot\_mr\_base}\) is the maintenance respiration per unit of fine roots at 20 \(\text{\textdegree C}\) obtained from the BPLUT; and \(\text{Froot\_MR}\) is the fine root autotrophic respiration consumption.  
Finally, \(\text{PSNnet}\) (\(\text{kg\textdegree C\text{-}day}^{-1}\)) can be calculated from GPP using Equation (9):  
\[\text{PSNnet}=\text{GPP-Leaf\_MR}-\text{Froot\_MR} \tag{9}\]  
The process for the estimation of the MOD17A2 GPP (gross primary productivity) and PSNnet (net photosynthesis) products is illustrated in Figure 2.