## 3 Results  
### Effects of \(T_{spring}\) Anomalies on Current and Post-season GPP  
Pearson's correlations between \(T_{spring}\) and \(GPP_{spring}\) showed similar spatial patterns in all three GPP products (Figure 2a-c). A high positive correlation dominated the mid- and high latitudes. Only the southwestern part of North America and South Asia showed a negative correlation. The same pattern was seen in all three products, however, NIRv-GPP had fewer significant correlations, resulting in a sparser pattern. Figure 1: The diagram of the study workflow. The input data (depicted in orange color) underwent pre-processing and statistics calculations (depicted in blue color), eventually leading to the main results (depicted in green color). \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{1}{c}{**X: Predictive**} & **Y** & **Type** \\ \hline Spring: T & Spring: GPP & Pearson, Direct \\ Spring: T & Summer: GPP & Pearson, Direct \\ Spring: T & Autumn: GPP & Pearson, Direct \\ Spring: T, GPP, Summer: T, SM, VPD & Summer: GPP & Pearson, Partial \\ Spring: T, GPP, Summer + Autumn: T, SM, VPD & Autumn: GPP & Pearson, Partial \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Direct correlations between spring temperature and GPP anomalies, as well as two sets of variables (pertaining to summer and autumn GPP anomalies) were used in correlation analysis. All variables were converted into anomalies based on Equation (1) before [PERSON]’s correlations were performed. Lagged effects of \(T_{spring}\) anomalies on \(GPP_{summer}\) showed fairly similar effects on certain land areas, and a larger difference among different GPP products was noticeable in the Arctic tundra and North Eurasia (Figure 2d-f). All three GPP products showed negative correlations in North America as well as Southeast Eurasia. The Arctic displayed clear positive effects in GOSIF-GPP and FluxSat-GPP, whereas negative effects dominated the response in NIRv-GPP. Legacy effects from \(T_{spring}\) anomalies on \(GPP_{autumn}\) were consistent to legacy effects from summer in the large southern areas (Figure 2g-i). However, GOSIF-GPP showed positive effects in North America, where negative effects were found in NIRv-GPP and FluxSat-GPP. Particularly, PW (Hudson Bay and West Siberia) showed strong negative effects in FluxSat-GPP. Some sporadic patches of positive correlations in Eurasia were also found in NIRv-GPP and FluxSat-GPP. Latitudinal distributions for legacy effects of \(T_{spring}\) anomalies on \(GPP_{summer}\) and \(GPP_{autumn}\) were quantified based on their [PERSON]'s correlation coefficients (mean and one standard deviation) calculated across all the longitudes at each latitude interval of 0.05\({}^{\circ}\) (Figure 3). As the legacy effects largely oscillated in the high latitudes, the results were shown based on a moving average of every five pixels along the latitude. In general, all three GPP products showed positive legacy effects in most areas at north of 70\({}^{\circ}\) and negative legacy effects in lower latitudes. GOSIF-GPP and NIRv-GPP had a fairly similar  
Figure 2: Pearson’s correlations (\(p<0.05\)) between \(T_{spring}\) anomalies and \(GPP_{spring}\) (**a–c**)/\(GPP_{summer}\) (**d–f**)/\(GPP_{autumn}\) (**g–i**). distribution of the legacy effects on \(GPP_{summer}\), however, NIRv-GPP and FluxSat-GPP had a similar distribution of the legacy effects on \(GPP_{autumn}\). FluxSat-GPP differed from the other two in regards to \(GPP_{summer}\), where positive legacy effects began to dominate further south, at \(\sim\)43 degN compared to >60 degN for GOSIF-GPP and NIRv-GPP. FluxSat-GPP also displayed a strong negative peak at 55 degN-60 degN for \(GPP_{autumn}\), which almost has an inverse pattern of the legacy effects seen in summer. Effects of \(T_{spring}\) Anomalies on \(GPP_{spring}\), \(GPP_{summer}\), and \(GPP_{autumn}\) for Each Biome  
Effects of \(T_{spring}\) anomalies on \(GPP_{spring}\), \(GPP_{summer}\) and \(GPP_{autumn}\) were aggregated for each biome based on all three GPP products (Figure 4).