## 3 Results
### Response of Tree Rings to GPP  
Correlation coefficients between spruce chronology and GLASS GPP and between spruce chronology and EC-LUE GPP were shown in Figure 4 and Figure S3. The results for GLASS GPP and EC-LUE GPP were basically the same. The GPP and tree-ring analysis based on both algorithms obtained the same results, indicating that the relationship between radial growth and canopy dynamics is reliable. Spruce radial growth was significantly positively correlated with the seventh and the eight 8-day GPP on a one 8-day scale (for GLASS GPP, \(r\) was 0.398 and 0.417, \(p<0.05\); for EC-LUE GPP, \(r\) was 0.400 and 0.417,  
Figure 2: Multi-year monthly climate data trends for meteorological stations in Yinchuan, 1982–2018. (Max-T, mean monthly maximum temperature; Min-T, mean monthly minimum temperature; Mean-T, mean monthly mean temperature; SPEI, mean monthly standardized precipitation evapotranspiration index; RH, mean monthly relative humidity; SD, mean monthly sunshine duration; Pre, mean monthly precipitation).  
\(p\) < 0.05) (Figures 4a and S3a). When considering the lag effect, significant positive correlations were detected on the 2-12 cumulative 8-day scale of the seventh-eighth 8-day (for cumulative GLASS GPP, \(r\) ranged from 0.320 to 0.445, \(p\) < 0.05; for cumulative EC-LUE GPP, \(r\) ranged from 0.326 to 0.589, \(p\) < 0.05) (Figure 4b and Figure S3b). This resulted in a significant positive correlation between GPP and spruce radial growth primarily in late February to early March; in a 2-year cumulative scale, spruce radial growth was significantly and positively correlated with cumulative GPP from November of the previous year to early March of the current year.  
The relationships between the Chinese pine chronology and the two GPP indices are shown in Figures 5 and S4. They also reveal similar results. Significant and positive correlations were observed with the 1-12 cumulative 8-day scales of the seventh-eighth 8-day (for GLASS GPP, \(r\) ranged from 0.322 to 0.419, \(p\) < 0.05; for EC-LUE GPP, \(r\) ranged from 0.348 to 0.405, \(p\) < 0.05) (Figures 5a and S4a), which is similar to the results between spruce and GPP. However, the Chinese pine was also positively correlated with the 1-10 cumulative 8-day scales of the 17 th-30 th GPP (for cumulative GLASS GPP, \(r\) ranged from 0.322 to 0.419, \(p\) < 0.05; for cumulative EC-LUE GPP, \(r\) ranged from 0.320 to 0.407, \(p\) < 0.05) (Figures 5b and S4b) from late March to the end of August.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \begin{tabular}{c} **Tree-Ring Width** \\ **(Mean \(\pm\) Standard** \\ **Deviation) (mm)** \\ \end{tabular} & \begin{tabular}{c} **Correlation** \\ **Coefficients** \\ **between Cores** \\ \end{tabular} & \begin{tabular}{c} **Standard** \\ **Deviation** \\ **Deviation** \\ **between Cores** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Sensitivity** \\ **between cores** \\ \end{tabular} & \
\begin{tabular}{c} **Expressed** \\ **Population** \\ **Signal** \\ \end{tabular} &
\begin{tabular}{c} **Variance in First** \\ **Eigenvector** \\ \end{tabular} \\ \hline spruce & 0.98 \(\pm\) 0.72 & 0.718 & 0.426 & 0.432 & 0.993 & 73.0\% \\ Chinese pine & 1.09 \(\pm\) 0.84 & 0.474 & 0.406 & 0.465 & 0.965 & 59.6\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristic of the standardized tree-ring width residual chronology.  
Figure 4: Correlation between residual chronology of spruce tree-ring and GLASS GPP ((**a**) 8-days scale (**b**) cumulative scale). The dotted line indicates the significant level of 0.95. (The color of each point maps to the spatial density of the point, with the density gradually increasing from green to red.)  
Figure 3: Chronology of tree-ring width residuals and sample size in the Helan Mountains ((**a**) spruce (**b**) Chinese pine).