## 3 Results
### Partial Correlations between EVI and Climate Variables  
EVI\({}_{a}\) showed very high partial correlations with both wet-year (\(0.57\pm 0.01\)) and growing-season precipitation (\(0.55\pm 0.02\)) for the grassland patches (Figures 5a and 6). There are 210 and 200 grassland patches exhibiting the positive partial correlations significant at \(p<0.05\) (one-tail test) with wet-year (\(0.72\pm 0.01\)) and growing-season precipitation (\(0.72\pm 0.01\)), respectively. For the deciduous-broadleaved forest patches, EVI\({}_{a}\) also showed mostly positive partial correlations with wet-year (\(0.19\pm 0.01\)) and nongrowing-season precipitation (\(0.21\pm 0.01\)), especially those patches in the southern part. There are 96 and 94 forest patches having positive partial correlations significant at \(p<0.05\) between EVI\({}_{a}\) and precipitation in wet year and nongrowing season with coefficients of \(0.57\pm 0.01\) and \(0.68\pm 0.01\), respectively. Maximum EVI (EVI\({}_{m}\)) of the grassland patches also showed positive correlations with both wet-year (\(0.39\pm 0.02\)) and growing-season precipitation (\(0.31\pm 0.02\)) (Figure 6), and 147 and 65 grassland patches showed positive correlation significant at \(p<0.05\) (one-tail test) with wet-year and growing-season precipitation at coefficients of \(0.65\pm 0.01\) and \(0.64\pm 0.01\), respectively. The histograms of significant partial correlations detected as greater than 0 or lower than 0 at \(p<0.025\) (one-tail test) are shown in Appendix A Figure A2 for reference. Figure 4: Trends of total precipitation (**a**), average minimum temperature (**b**), and average maximum temperature (**c**) during wet year (prior October to September), growing season (May to September), and nongrowing season (prior October to April) in 2001–2015 for the grassland (GRASS) and deciduous-broadleaved forest (DBF) patches. Right columns are histograms, and red bars on the left side of the dashed line indicate those trends significantly lower than 0 while those on the right side of the dashed line indicate those trends significantly greater than 0 (\(p\)-value \(<\) 0.05, one-tail test). Figure 5: Partial Correlation between EVI\({}_{a}\) and climate variables of precipitation (**a**), minimum temperature (**b**), and maximum temperature (**c**) during wet year, growing season, and nongrowing season in 2001–2015 for the grassland (GRASS) and deciduous-broadleaved forest patches (DBF). Right columns are histograms of partial correlation coefficients, and red bars on the left side of the dashed line indicate those partial correlations significantly lower than 0 while those on the right side of the dashed line indicate those partial correlations significantly greater than 0 (\(p\)-value \(<\) 0.05, one-tail test). The partial correlation between \(\text{EVI}_{a}\) and growing-season \(T_{\text{min}}\) (Figure 5b) showed distinct spatial heterogeneity among forest patches: 115 patches in the north showed significant positive correlations with coefficient of \(0.66\pm 0.01\) whereas 61 patches in the south showed mostly significant negative correlation with coefficient of \(-0.70\pm 0.01\). There are 33 forest patches showing significant negative partial correlations between \(\text{EVI}_{a}\) and nongrowing-season \(T_{\text{min}}\) with coefficient of \(-0.67\pm 0.01\). \(\text{EVI}_{m}\) of forest patches also showed heterogeneous partial correlation with growing-season \(T_{\text{min}}\): 122 patches have significant positive coefficient of \(0.67\pm 0.01\) and 48 patches have significant negative coefficient of \(-0.67\pm 0.01\). For grassland patches, both \(\text{EVI}_{a}\) and \(\text{EVI}_{m}\) showed a barely negative partial correlation with growing-season \(T_{\text{min}}\) with coefficients of \(-0.06\pm 0.02\) and \(-0.13\pm 0.02\), respectively, but positive correlation with nongrowing-season \(T_{\text{min}}\) with coefficients of \(0.04\pm 0.02\) and \(0.10\pm 0.02\), respectively.