## 3 Data and Methodology
### Methodology  
#### 3.2.1 Glo-Pem  
In this study, the Global Production Efficiency Model (GLO-PEM), which was based on light use efficiency, was applied to simulate the NPP of forests in Northeast China. This model fully considered the characteristics of plant growth and abiotic environmental factors that could regulate plant photosynthesis, such as temperature, soil and water conditions. The NPP estimated by the GLO-PEM (Figure 2) was mainly determined by considering the absorbed photosynthetic active radiation (_APAR_) and the light use efficiency (\(\varepsilon\)), using Equation (1) [36; 45; 46; 47; 48]:  
\[\mathrm{NPP(x,\,t)}=\,\mathrm{APAR(x,\,t)}\,\times\,\varepsilon(x,\,t) \tag{1}\]  
where NPP(x, t) represents net primary productivity of pixel x at time t, APAR(x, t) refers to the absorbed photosynthetic active radiation of that and \(\varepsilon\)(x, t) indicates light use efficiency under the same conditions. The APAR mainly depends on the following two variables:  
\[\mathrm{APAR(x,\,t)}\,=\,\mathrm{FPAR(x,\,t)}\,\times\,\mathrm{PAR(x,\,t)}. \tag{2}\]  
where PAR(x, t) refers to photosynthetically active radiation of pixel x at time t, FPAR(x, t) is fraction of absorbed photosynthetically active radiation of that. _Photosynthetically Active Radiation_ (PAR)  
In this study, PAR was estimated by considering the geographic location of typical sites in the study area, including longitude, latitude, elevation and the sunshine hours as the input data for the crop mode [36; 49; 50]. (1) Solar radiation top of atmosphere (H\({}_{0}\))  
\[\mathrm{H_{0}}=\,(1/\pi)\,\times\,\mathrm{G_{SC}}\times\mathrm{E_{0}}\times( \cos\phi\mathrm{cos}\,\delta\sin\,\mathrm{W_{S}}+(\pi/180)\,\times\,\sin\Phi \sin\,\delta\,\times\,\mathrm{W_{S}}). \tag{3}\]  
where G\({}_{\mathrm{SC}}\) is the solar constant with value equal to 1367 W\(\cdot\)m\({}^{-2}\) that is equivalent to 118.108 MJ\(\cdot\)m\({}^{-2}\).d\({}^{-1}\). \(E_{0}\) represents eccentricity correction factor of the earth's orbit; \(\Phi\), \(\delta\), \(\mathrm{W_{s}}\) indicate latitude, declination of the sun and time Angle, respectively. (2) Solar radiation in clear sky (H\({}_{\rm L}\))  
According to existing studies [51], the transparency coefficient of total radiation in the atmosphere is usually about 0.8 under ideal conditions, i.e., clear sky, and it is different under specific environmental conditions. \[{\rm H_{L}}=\ 0.8\,\times\,{\rm H_{0}} \tag{4}\]  
(3) Daily solar radiation (H)  
\[{\rm H}\ =\ {\rm H_{L}}\times({\rm a}\ +\ {\rm b}\ \times\ {\rm S/S_{L}}) \tag{5}\]  
where \(H\) is the daily solar radiation; \(H_{\rm L}\) is solar radiation in clear sky; \(S\) and \(S_{\rm L}\) are sunshine hours and sunshine days, respectively; and a and b are empirical parameters generally obtained by regression simulation based on measured values of solar radiation. According to the average value of total daily solar radiation, the sunshine percentage and the solar radiation in clear sky in different regions of China. [PERSON] et al. [52] and [PERSON] et al. [53] calculated that a was equal to 0.248, and b was equal to 0.752. PAR is calculated based on the daily solar radiation; the formula is expressed as Equation (6). \[{\rm PAR}\ =\ 0.5\,\times\,{\rm H} \tag{6}\]  
_Light-Use Efficiency_ (\(\varepsilon\))  
The light-use efficiency under realistic conditions (\(\varepsilon\)) refers to the light use efficiency under the stress of environmental driving factors such as temperature and vapor pressure, which can be extracted from meteorological indicators [28; 29; 30; 45; 46]. \(\varepsilon\) is calculated by using Equation (7):  
\[\varepsilon({\rm x},\ {\rm t})\ =\ {\rm T_{\varepsilon 1}({\rm x},\ {\rm t})}\, \times\,{\rm T_{\varepsilon 2}({\rm x},\ {\rm t})}\,\times\,{\rm W_{\varepsilon}({\rm x},\ {\rm t})}\,\times\varepsilon* \tag{7}\]  
where \({\rm T_{\varepsilon 1}({\rm x},\ {\rm t})}\) and \({\rm T_{\varepsilon 2}({\rm x},\ {\rm t})}\) represent the stress coefficients of high temperature and low temperature on light utilization efficiency, respectively.