## 3 Results  
### Spatiotemporal Distribution and Variation of GPP  
Figure 3a shows that the GPP ranges from 350 to 1100 g C/m\({}^{2}\), where the high values are mainly concentrated in the northern and western Tai-hang Mountains, and the GPP ranges from 600 to 850 g C/m\({}^{2}\). The areas with low values are mainly concentrated in coastal and urban areas. The northwest and the southern Plains range from 300 to \begin{table}
\begin{tabular}{c c} \hline
**q Value Comparison** & **Interaction** \\ \hline \(\text{q}(\text{X}_{1}\cap\text{X}_{2})<\text{Min}(\text{q}(\text{X}_{1}), \text{q}(\text{X}_{2}))\) & Non-linear weakening \\ Min(\(\text{q}(\text{X}_{1})\text{q}(\text{X}_{2}))<\text{q}(\text{X}_{1}\cap\text{X}_{2})<\text{ Max}(\text{q}(\text{X}_{1}),\text{q}(\text{X}_{2}))\) & Single-factor nonlinear attenuation \\ \(\text{q}(\text{X}_{1}\cap\text{X}_{2})>\text{Max}(\text{q}(\text{X}_{1}), \text{q}(\text{X}_{2}))\) & Two-factor enhancement \\ \(\text{q}(\text{X}_{1}\cap\text{X}_{2})=\text{q}(\text{X}_{1})+\text{q}(\text{ X}_{2})\) & Independent \\ \(\text{q}(\text{X}_{1}\cap\text{X}_{2})>\text{q}(\text{X}_{1})+\text{q}(\text{ X}_{2})\) & Non-linear enhancement \\ \hline \end{tabular}
\end{table} 
Table 1: The five types of interaction detector. 500 g C/m\({}^{2}\). The effect of topography and vegetation type on GPP distribution can be clearly seen. Figure 3b shows the spatiotemporal variation of the annual growth rate of GPP: in the plains area, the growth rate of GPP is between 0 and 15 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\), and in the mountainous forest area in the northwest and north, the growth rate is between 15 and 20 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\). The mountainous forest area is significant, while the non-significant area is distributed in the central and southern plains area. This may be related to land use type. Over the whole region, the proportion of the area with a growth trend is 68.73%, while the area with a decreasing trend is 0.44%, and the rest is 30.83%. We calculated the mean value of GPP in the whole region and processed the mean value of GPP every year by way of linear fitting, as shown in Figure 4. The overall trend of GPP from 2000 to 2020 was increased at a rate of 2.07 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\). In the 21 years, the maximum value of GPP appeared in 2016 and the minimum value in 2001. According to the seasonal classification of GPP, spring is from March to May, summer is from June to August, autumn is from September to November, and growing season is from April to October [33]. Figure 5 shows that the growth rate is the fastest in the summer season from 2000 to 2020, with an increase rate of 4.26 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\). The growth trend of the whole growing season is slightly slower than that of summer. The growth rate in spring is 2.62 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\), and the growth trend in autumn is the slowest at only 1.78 g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\) per year. It is speculated that the growth rate is related to vegetation phenology. In summer, vegetation grows heavily and there is a large gap with spring and autumn. In autumn, crop harvesting and defoliation in broad-leaved forests will lead to a sharp decline in GPP and slow down the growth rate. Figure 3: Spatial distribution of (**a**) average of accumulated gross primary productivity (GPP) (unit: g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\)) and (**b**) inter–annual GPP trend (unit: g C\(\cdot\)m\({}^{-2}\cdot\)yr\({}^{-1}\)) during 2000–2020. Figure 4: Inter-annual variation trends of GPP in the BTH from 2000 to 2020. Figure 5: Inter-annual variation trends of GPP in the BTH from 2000 to 2020. ((**a**) spring; (**b**) summer; (**c**) autumn; (**d**) growth). Correlation Distribution of GPP with Precipitation, Temperature and Downward Surface Shortwave Radiation  
Figure 6 shows that in the north and the west of the BTH, GPP presents a low correlation with LST, with the correlation coefficient being between 0 and 0.2.