## 3 Results
### Drought Impacts on Continental GPP  
The tightest correlation between the optimized GPP from CCDAS and SPEI among 12 drought durations (1, 3, 6, 9, 12, 15, 18, 21, 24, 30, 36, 48) was identified as the optimal drought duration. The percentage of droughts' duration identified by the CCDAS-optimized GPP was 48%, which is the maximum among 12 durations (Figure 5a). Additionally, a total of 68% of droughts of less than 9 months' duration were identified by the CCDAS-optimized GPP. This suggested that the CCDAS could better capture the response of GPP to sub-annual drought durations (less than 9 months) by assimilating both CO\({}_{2}\) and soil moisture. The TRENDY GPP had the highest percentage at the 48-month drought duration with 34% (Figure 5b) and the percentage of 80% for droughts greater than 12 months' duration, which showed that TRENDY GPP was not good at capturing sub-annual drought durations (9 months and below) but could capture long-term drought durations (12 months and above) very well. Similar to TRENDY, GPP proxies NDVI and SIF derived from remote sensing also had the highest percentages at 48 months with 22% and 31% (Figure 5c,d), as well as the total percentages of 66% and 77%, respectively, for droughts of a duration greater than 12 months. Since CCDAS identified the 9-month drought duration best, the next analyses related to SPEI were based on SPEI-9. Figure 4: Continually aggregated soil moisture (**a**), GPP (**b**) anomaly differences during El Niño/La Nña period, and (**c**) the GPP relation to TWS from GRACE-REC. Hatches in the bars with slash and backslash denote results during aggregated moderate-to-strong El Niño/La Nña event periods and during aggregated strong El Niño/La Nña event periods, respectively. Values next to each bar denote the anomalies during aggregated El Niño (up) and La Nña (down) event periods, respectively. Symbols in (**c**) denote aggregated GPP and GRACE-REC TWS anomalies for different levels and types of El Niño/La Nña events in each continent. The regressions (black line) are based on the solid dots. The empty dots denote data from South America during different El Niño/La Nña events. The spatial distributions of drought-aggregated GPP anomalies for CCDAS and TRENDY and NDVI anomalies for GIMMS3g from SPEI-9 with SPEI < -1 were similar in most areas (Figure 6). As can be seen in Figure 6a-c, CCDAS, TRENDY, and NDVI all show a trend of reduced vegetation growth (decreased GPP and NDVI) when drought occurs in most areas south of the 30\({}^{\circ}\)N latitude. For most regions north of 30\({}^{\circ}\)N, especially northern North America and northern Asia, both CCDAS GPP and NDVI show a trend of increased vegetation growth (increased GPP and NDVI) when drought occurs, but TRENDY shows a trend of a decrease in these regions. Further, the CCDAS-optimized GPP showed a weak increase in the Amazon rainforest region (Figure 6a), which is in agreement with TRENDY (Figure 6b), but disagreement with NDVI and SIF, which show lower values in the tropical rainforest region (Figure 6c,d). That is, the CCDAS-optimized GPP showed that GPP increased in mid- and high-latitude regions in response to drought and weakly decreased in tropical rainforest regions (Figure 6a). Figure 5: Drought duration identification using the correlation between GPP, NDVI, SIF, and SPEI. a, the optimal drought duration (month) that is best identified (with the tightest correlation among 12 durations) with respect to the Pearson correlations between SPEI from different durations and the GPP from CCDAS. The inset denotes the percentage for each drought duration. (**b**), same as (**a**), but for TRENDY multi-model mean (S3, 6 models) GPP. (**c**), same as (**a**), but for the NDVI from GIMMS3g. (**d**), same as (**a**), but for SIF from LT_SIF. To further prove the rationality of the CCDAS results, we calculated the correlation between the CCDAS-optimized GPP and SPEI-9 as well as the region of drought changes identified using SPEI-9.