## 3 Results
### Response Patterns of WUE to Phenology  
Here, spatial distributions of the six response patterns of WUE to photosynthetic phenology are shown in Figure 5. The results show that Pattern I (R\({}_{\text{WUE}}<0\), R\({}_{\text{GPP}}<0\), R\({}_{\text{ET}}<0\)) and Pattern II (R\({}_{\text{WUE}}<0\), R\({}_{\text{GPP}}<0\), R\({}_{\text{ET}}>0\)) are widespread (about 54.87% and 36.83% of the valid pixels, respectively) in the high and mid latitudes during spring (Figure 5a). This indicates that the negative response of spring WUE to the advance in SOS is mainly because the negative sensitivity of GPP to SOS is relatively strong in magnitude compared to that of ET, or GPP negatively responds to SOS while ET positively responds to SOS during spring. In other words, an increasing spring WUE with earlier SOS, for example, is mainly shown by a steeper increase in GPP than ET, or by an increase in GPP accompanied by a decrease in ET resulting from an advance in SOS. However, for some PFTs in dry or Mediterranean climates (e.g., B-SHR and C1-WSA) (Figure 6a), both spring GPP and ET exhibit a positive correlation with variations in SOS, leading to an increase or decrease in WUE according to their changing magnitudes.  
The response patterns of summer WUE to SOS give a different picture (Figure 5b), with only 15.05% and 27.13% of pixels showing Pattern I (R\({}_{\text{WUE}}<0\), R\({}_{\text{GPP}}<0\), R\({}_{\text{ET}}<0\)) and Pattern II (R\({}_{\text{WUE}}<0\), R\({}_{\text{GPP}}<0\), R\({}_{\text{ET}}>0\)), respectively, mainly in regions of north of 60\({}^{\circ}\)N, northeastern Canada and East and South China. Areas with Pattern III (R\({}_{\text{WUE}}<0\), R\({}_{\text{GPP}}>0\), R\({}_{\text{ET}}>0\)) and Pattern VI (R\({}_{\text{WUE}}>0\), R\({}_{\text{GPP}}>0\), R\({}_{\text{ET}}>0\)) (about 20.00% and 18.98% of the valid pixels, respectively) are widespread in the mid latitudes (including most PFTs in dry climates, Mediterranean climates and continental climates with warm summers) (Figure 6b), indicating that summer GPP and ET positively respond to advance in SOS, whereas summer WUE increases or decreases are determined by the changing magnitudes of GPP and ET.  
Figure 5: Spatial distribution of response patterns of seasonal WUE to phenological factors (SOS/EOS). R\({}_{\text{WUE}}\), R\({}_{\text{GPP}}\), R\({}_{\text{ET}}\) indicate the partial correlation coefficients of WUE, gross primary productivity (GPP), evapotranspiration (ET) with the phenological factor after controlling the environmental factors (including temperature, precipitation, insolation and CO\({}_{2}\) concentration), respectively. The partial correlation coefficients are calculated in (**a**) spring (March–May); (**b**) summer (June–August) and (**c**) autumn (September–November), respectively. The white areas denote invalid satellite-image pixels in this study.  
During autumn, Pattern VI (R\({}_{\text{WUE}}>0\), R\({}_{\text{CPP}}>0\), R\({}_{\text{ET}}>0\)) and Pattern V (R\({}_{\text{WUE}}>0\), R\({}_{\text{GPP}}>0\), R\({}_{\text{ET}}<0\)) are observed in 50.61% and 31.16% of valid pixels, respectively (Figure 5c). These response patterns of autumn WUE to EOS indicate that an increased autumn WUE resulting from a delayed EOS is mainly associated with an enhanced GPP, with either a relatively slight increase in ET or a decrease in ET. Nevertheless, in parts of central United States, Inner Mongolia and southwest China and east Siberia, the contrast patterns are observed; there is a negative relationship between autumn WUE, and EOS is associated to with a negative correlation of autumn GPP with EOS.