## 3 Results  
### Change Trends of SPEI and Ecosystem Function Indicators  
Figure 2 shows the temporal trends of the SPEI, LAI, ET, and GPP for the period of 2000-2020 using a linear regression equation. Four variables showed increasing trend, of which ET had the highest slope of 0.0386 mm/month (\(p\) < 0.05). The rest followed a descending order of SPEI > LAI > GPP. The spatial distribution of the trend derived from the Theil-Sen + MK method is illustrated in Figure 3. The trends were classified into three major types owning a total of nine characteristics (Table 1). Spatially, SPEI showed different degrees of increasing trend. Centering on the central region, the trend of SPEI decreased gradually towards the north-south direction, while it increased along the east-west direction. The most remarkable trend of increasing SPEI was found in the central grassland, wetland, and cropland. LAI tended to be unchanged, accounting for 88.34% of the total area (Figure 4). The pixels with trend value of \(-1\) were scattered throughout the study area (taking up 9.43%) and were more concentrated in the northeastern fringe and the central areas. In the central area, the pixels of insignificantly decreasing trend were mixed with those of insignificant increasing trend. ET showed an increasing trend overall (occupying about 24.87% of the total pixels). We found that ET radiated outward from the mid-west of the study area (mainly covered by grassland), and the increasing trend decreased gradually. In the forest of the northeastern fringe, ET showed an insignificant decreasing trend, which was similar to LAI. From 2000 to 2020, the pixels with an increasing trend of GPP accounted for 54.94%. Compared with LAI and ET, the number of pixels showing no change in GPP were smallest (taking up 44.55% of the total pixels). In southwestern grassland, the pixels of significant increase and extremely significant increase in GPP (i.e., trend types 3 and 4) were clustered. In the north of the study area, GPP showed no change trend, and pixels with decreasing trend only occupied about 0.51% of the total pixels.  
Figure 3: The spatial distribution of SPEI, LAI, ET and GPP trends from 2000 to 2020. LAI, ET and GPP are expressed using the same color table. SPEI shows significant increase trend (\(p<0.05\)) throughout the study area, expressed in a stretched mode.  
Figure 2: Trends of SPEI (**a**), LAI (**b**), ET (**c**), and GPP (**d**) from 2000 to 2020 (\(p<0.05\)).  
The spatial distribution of the causality between SPEI and GPP was not consistent. Moisture condition had an impact on the photosynthesis in more areas, taking up 52.8% of the total pixels (\(p<0.05\)), especially concentrated in the northern region (Figure 5c). Conversely, the area where vegetation photosynthesis affected moisture conditions was  
Figure 5: The significance level (\(p\)-value) of Granger causality. (**a,b**) interactions between SPEI and LAI; (**c,d**) interactions between SPEI and ET; (**e,f**) interactions between SPEI and GPP. The pixels with insignificant trends are in grey color.  
Figure 6: The proportion of pixels at different significance levels in Granger causality of four variables.  
small with scattered pixels (Figure 5f). In the three groups of bidirectional experiments, SPEI had a greater influence on GPP, with more significant pixels. Compared with ET and GPP, the areas of SPEI response to LAI changes were larger. Spatially, the pixels that were affected by drought changes or had a regulating effect on external moisture showed highest aggregation in the northern cropland.