## 3 Results
### Time-Lag Response of the GPP to Meteorological Variables during the Vegetation Growing Season  
Since the impact of the climate on vegetation photosynthesis is not immediate, this study focused on the lagged response of the China's regional Gross Primary Productivity (GPP) to climate during the vegetation growing season from 2000 to 2018 (May to September). The detrended GPP and its periodic interactions with climate factors are represented by the monthly total GPP values and normalized monthly average temperature and precipitation values for China during 2000-2018 (Figure 6). Temperature, precipitation, and radiation fluctuations exhibit stable periodicity across the entire region. GPP fluctuations show trends similar to the meteorological factor curves, but the normalized GPP curve does not always align with the meteorological factors. A certain degree of delay compared to the meteorological factors can be observed over the entire study period. This serves as evidence of the lag effect in GPP response to meteorological factors. By analyzing the correlation coefficients between GPP and meteorological variables within different time periods, specifically the lag and cumulative effects in the 0-3 months prior to the vegetation growing season, this study aimed to explore the sensitivity of GPP changes to climate variables. For example, a lag of 1-0 (one-month lag, zero-month accumulation) for a given year implies that the total GPP for May to September is correlated with meteorological variables for April to August. A lag of 1-1 (one-month lag, one-month accumulation) means that the GPP for May to September is correlated with meteorological variables for March and April to July and August. Figure 5: The interannual change rates of PRCP (**a**), SR (**c**), and TEMP (**e**) from 2000 to 2018, and boxplots of interannual changes in PRCP (**b**), SR (**d**), and TEMP (**f**) in different regions. This research investigated the maximum correlation coefficients between GPP and meteorological variables at different lag periods within the growing season based on the vegetation pixel scale to discuss the spatial distribution of lag effects (Figure 7). GPP values show significant correlations with meteorological elements in over 90% of the vegetation area (\(p<0.05\)) during the growing season. The maximum correlation coefficients between GPP and temperature are greater than zero in 88% of the vegetation regions, especially in the western part of Region I, the eastern part of Region III, and the northern part of Region VI (Figure 5a). In these areas, abundant lakes and rivers provide vegetation with ample sources of soil moisture, reducing vegetation's dependence on precipitation and making temperature the primary limiting factor for vegetation growth in these regions [45; 46]. The maximum correlation coefficients between GPP and rainfall are greater than zero in 78% of the vegetation regions, primarily concentrated in Northern China (Figure 7a). In 73% of the vegetation regions, there are maximum correlation coefficients greater than zero between GPP and radiation, with these regions mainly concentrated in local areas within Regions III and VI. These areas share a common characteristic of having a significant amount of forest cover, where sunlight provides the primary energy source for plants. Compared to other vegetation types, forests with larger canopy cover might absorb more energy, which is likely an important reason for the sensitivity of radiation variables in some parts of the southwest and northeast. In the western part of the Region IV, there is a clear negative correlation between the GPP and temperature. This region experiences a relatively arid climate and is largely influenced by water supply; as a result, vegetation growth in this area is strongly correlated with precipitation. During the growing season, there is a strong negative correlation between vegetation and rainfall in the northern part of Region I, where the region is predominantly covered by forests and farmland.