## 3 Results
### Partial Correlations between WUE and Phenological Factors  
Figure 3 provides the spatial distributions of coefficients of partial correlation (\(r\)) between yearly fluctuations of seasonal WUE and phenological factors during 2001-2014, where r is significant when the absolute value of \(r\) is higher than 0.60. Negative partial correlations between WUE and SOS (i.e., WUE enhanced with earlier SOS or WUE decreased with later SOS) dominate the spring (96.08% pixels), and 67.33% of these are statistically significant (\(P<\) 0.05) mainly in the mid- and high latitudes (over 50\({}^{\circ}\)N), southwestern China and mid-western North America (Figure 3a). At the PFT level, our statistics show in general, the negative partial correlations between spring WUE and SOS enhance from warm climates to cold climates (Figure 4a). The PFT-level average partial correlation coefficient between them ranges from \(-\)0.28 in dry climates (B) to \(-\)0.80 in continental subarctic climates (D2), with the strongest correlation of \(-\)0.87 (\(\pm\)0.10) in D2-WSA. The panel analysis shows similar results (Table S2). When SOS advances a 10-day, the spring WUE will increase on average by 0.05, 0.04, 0.21 and 0.06 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\) in dry climates (B), temperate/mesothermal climates (C1, C2 and C3), continental/microthermal climates (D1 and D2) and Polar and alpine climates (E), respectively. During summer, both negative and positive correlations between WUE and SOS are found (Figure 3b), with 16.64% of valid pixels having significant negative correlations (\(P<\) 0.05) mainly at high latitudes (e.g., northern Siberia, northeastern Canada and mid-western United States) and 4.14% significant positive correlations (\(P<\) 0.05) mainly in mid-eastern United States, most Europe, north-eastern China and central Siberia. D1-DBF shows the strongest positive partial correlations between summer WUE and SOS with a coefficient of 0.45 (\(\pm\)0.28) (Figure 4b), and decreases by an average value of 0.11 (\(\pm\)0.01) g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\) with a 10-day advancement of SOS (Table S2). E-SHR and D2-SHR show the strongest negative partial correlation (\(r=-\)0.51 \(\pm\) 0.28) (Figure 4b) and the lowest regression coefficient of panel analysis (coef = \(-\)0.15 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\) 10-day\({}^{-1}\)) between summer WUE and SOS, respectively (Table S2), indicating significant promotions of earlier SOS to summer WUE in extreme cold regions. Positive correlations between autumn WUE and EOS are mainly observed in 86.67% of valid pixels (Figure 3c), and 32.40% of these are statistically significant (\(P<\) 0.05) mainly at high latitudes (e.g., northern North America and northern Eurasia). Similar to spring, the partial correlations between autumn WUE and EOS of PFTs in cold regions are generally stronger than those in warm areas (Figure 4c). However, the correlations are weaker overall, ranging from 0.12 in humid subtropical climates (C2) to 0.43 in continental subarctic climates (E) on average. Moreover, some areas with a significant correlation in spring (e.g., eastern North America, north Europe and West Siberia) exhibit no significant correlation in the autumn, indicating differences in ecological effects of different phenological changes observed in a changing climate. Figure 4: Relationships between the phenological factor (SOS/EOS) and WUE during (**a**) spring (March–May); (**b**) summer (June–August) and (**c**) autumn (September–November) at the plant functional type (PFT) level. Partial correlation coefficient is calculated after controlling the environmental factors (including temperature, precipitation, insolation and CO\({}_{2}\) concentration), which is significant (\(P<0.05\)) when the absolute value of coefficient is higher than 0.60.