# Satellite-Observed Global Terrestrial Vegetation Production in Response to Water Availability
## 3 Results
### Vegetation Productivity Loss Probability under Different Drought Scenarios  
We first fitted GPP's optimal marginal distribution during different months based on the Kolmogorov-Smirnov test. According to the criterion that the smaller the SED, RMSE, and AIC values, the better the copula function's fit effect, we fitted the optimal copula function with the GPP and SPEI in each grid. We set GPP's damage degree to four levels, the 10 th, 20 th, 30 th, and 40 th percentile values of GPP in different seasons. Figure 7 shows the spatial distribution of the LUE GPP values at the four percentiles over the globe in March-May, and those in June-August, September-November and December-February are provided in Figures S4-S6. It can be seen that there are obvious differences in the level of global GPP damage during different seasons. At the same time, three drought scenarios were set based on SPEI, moderate (\(-1.5<\text{SPEI}\leq 1\)), severe (\(-2<\text{SPEI}\leq-1.5\)) and extreme (\(\text{SPEI}\leq-2\)). In this way, the temporal and spatial distribution characteristics of the probability of different degrees of damage to vegetation productivity under different drought scenarios were studied to determine areas around the globe susceptible to drought during different seasons. As Figure 8d,h,i shows, the proportion of high-probability areas in the global terrestrial ecosystem increases with the increase in drought intensity when the GPP is lower than the 40 th percentile in March-May. Under moderate drought conditions, the area with a probability of occurrence higher than 75% covers only 5.04% of the global terrestrial vegetation area, while under extreme drought conditions, the proportion increases to 27.78%. Further, when the GPP is lower than the 10 th, 20 th, and 30 th percentiles, it still shows the same characteristics of change (the area with a probability of occurrence higher than 75% increases from 0.005% to 2.13%, from 0.12% to 9.24%, and from 1.65% to 18.71%). In other seasons, as the degree of drought increases, the conditional probabilities that GPP will be damaged at different levels increase as well (Figures S7-S9). Under the same drought severity with different levels of GPP damage, drought's influence on GPP loss probabilities weaken gradually as the GPP damage level increases (Figure 8a-d). We explored the seasonal evolution in vegetation productivity's loss probability further under the same drought scenario and the same level of damage of GPP. Using Figure 8h, Figures S7h, S8h and S9h as examples, it can be seen that under severe drought conditions, the area with a conditional probability higher than 75% was 17.48, 21.89, 17.37, and 14.25% in March-May, June-August, September-November, and December-February respectively,  
Figure 7: Spatial distribution of global LUE GPP values at 10 th (**a**), 20 th (**b**), 30 th (**c**) and 40 th percentiles (**d**) during March–May. in which vegetation productivity was more sensitive to drought in June-August. The primary reason for this phenomenon is drought's effect on GPP in mid- and high-latitude regions of the Northern hemisphere, as this period is the growing season of vegetation in those regions. The occurrence of drought during the growing season reduced the carbon sequestration capacity of vegetation greatly, and increased the GPP loss probability thereby. Further, we analyzed the conditional probabilities of vegetation productivity losses under different drought scenarios in various climatic regions. Take the conditional probability when GPP is less than the 40 th percentile from March to May as an example (as shown in Figure 9). Under the moderate drought scenario, the conditional probabilities of GPP loss are 0.54, 0.49, 0.45, and 0.44 in arid, semi-arid, semi-humid, and humid regions, respectively. (They are 0.74, 0.67, 0.56, and 0.56 under the severe drought scenario, and are 0.81, 0.72, 0.59, and 0.58 under the extreme drought scenario).