## 3 Results and Discussion
### Influence of Climate on NPP
The regions with a positive correlation were concentrated in Hebei, Henan, Shandong, Qinghai, and Tibet, while the regions with a negative correlation were concentrated in Jilin, Liaoning, Inner Mongolia, Shaanxi, and Shanxi. Although temperature was one of the most important climatic conditions for the growth of vegetation, higher surface temperatures accelerated the evaporation of water in the regions with negative correlations between NPP and LST because of the lack of water resources. In addition, NPP and LST were negatively correlated in southwest Tibet. Precipitation, NPP, and LST showed significant positive correlations in Hebei, eastern Inner Mongolia, and western Qinghai. The change in LST and precipitation has bidirectional regulating effect on NPP. An increase in surface temperature promoted the growth of vegetation before reaching the critical point of heat required for photosynthesis. When the rate at which surface temperatures rise exceeds the appropriate threshold of vegetation photosynthesis, it would accelerate the consumption of nutrients and increase the amount of water evaporation of soil. Therefore, the rise of LST played a positive role in promoting the increase of NPP in the southeast of study area with a relatively good soil moisture and the Tibetan plateau. This can be attributed to the relative abundance of water resources in the abovementioned areas. However, NPP played an inhibitory role in the arid and semiarid areas in northwest China. The partial correlation coefficient of NPP and LST passed the significance test (\(p<0.01\)) over an area of \(7.25\times 10^{4}\) km\({}^{2}\), accounting for 2.39% of the study area. The area with a positive correlation accounted for 1.22% of the total, while the area with a negative correlation accounted for 1.17%. Areas with a positive correlation accounted for 4.16% of the study area, \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Province**} & \multirow{2}{*}{**NPP and Precipitation (R)**} & \multicolumn{3}{c}{**NPP and Precipitation**} & \multicolumn{3}{c}{**NPP and LST (R)**} & \multicolumn{3}{c}{**NPP and LST**} \\  & & & \multicolumn{3}{c}{**(Area, 10\({}^{8}\)km\({}^{2}\))**} & & & & & \\ \cline{2-10}  & **Max** & **Min** & **Mean** & **Positive** & **Negative** & **Max** & **Min** & **Mean** & **Positive** & **Negative** \\ \hline Heilongjiang & 0.67 & \(-0.84\) & \(-0.19\) & 0.32 & 0.69 & 0.90 & \(-0.57\) & 0.23 & 0.84 & 0.17 \\ Jilin & 0.96 & \(-0.96\) & \(-0.15\) & 20.18 & 52.09 & 0.97 & \(-0.94\) & 0.01 & 38.51 & 33.74 \\ Liaoning & 0.66 & \(-0.87\) & \(-0.33\) & 0.37 & 5.37 & 0.91 & \(-0.70\) & 0.19 & 4.58 & 1.16 \\ Hebei & 0.74 & \(-0.88\) & \(-0.12\) & 5.04 & 11.29 & 0.87 & \(-0.90\) & 0.00 & 8.38 & 7.95 \\ Beijing & 0.83 & \(-0.81\) & 0.00 & 6.77 & 7.44 & 0.89 & \(-0.86\) & \(-0.09\) & 5.07 & 9.14 \\ Tianjin & 0.81 & \(-0.88\) & \(-0.11\) & 2.71 & 6.88 & 0.86 & \(-0.77\) & 0.15 & 6.96 & 2.61 \\ Shandong & 0.94 & \(-0.94\) & \(-0.20\) & 12.31 & 36.04 & 0.91 & \(-0.89\) & 0.12 & 33.27 & 15.08 \\ Henan & 0.82 & \(-0.82\) & 0.09 & 2.76 & 1.25 & 0.87 & \(-0.79\) & 0.08 & 2.47 & 1.54 \\ Shanxi & 0.90 & \(-0.95\) & 0.02 & 34.07 & 31.74 & 0.92 & \(-0.94\) & \(-0.11\) & 21.27 & 44.50 \\ Shaanxi & 0.89 & \(-0.77\) & \(-0.27\) & 0.35 & 5.93 & 0.89 & \(-0.83\) & 0.11 & 4.40 & 1.87 \\ Inner Mongolia & 0.90 & \(-0.60\) & 0.34 & 7.13 & 0.56 & 0.86 & \(-0.79\) & \(-0.03\) & 3.23 & 4.47 \\ Ningxia & 0.91 & \(-0.89\) & 0.26 & 8.87 & 2.25 & 0.84 & \(-0.86\) & \(-0.19\) & 1.84 & 9.28 \\ Gansu & 0.77 & \(-0.84\) & \(-0.09\) & 2.69 & 6.22 & 0.87 & \(-0.78\) & 0.13 & 6.12 & 2.78 \\ Xinjiang & 0.73 & \(-0.48\) & 0.13 & 0.82 & 0.20 & 0.83 & \(-0.59\) & 0.24 & 0.90 & 0.13 \\ Sichuan & 0.81 & \(-0.60\) & 0.12 & 0.30 & 0.09 & 0.80 & \(-0.65\) & 0.16 & 0.30 & 0.09 \\ Qinghai & 0.80 & \(-0.76\) & 0.03 & 8.91 & 6.96 & 0.93 & \(-0.85\) & 0.17 & 11.61 & 4.27 \\ Tibet & 0.87 & \(-0.91\) & \(-0.18\) & 4.46 & 14.09 & 0.90 & \(-0.89\) & 0.00 & 8.70 & 9.85 \\ \hline \hline \end{tabular}
\end{table}