## 4 Discussion
### The Responses of LUE to \(T_{a}\), \(R_{g}\), and VPD in the H-LUE Model  
Whether in conventional LUE models or in the H-LUE model developed in this study, meteorological factors are essential input data that play a crucial role in ensuring the  
Figure 8: (**a**) H-LUE, (**b**) EC-LUE, (**c**) VPM, and (**d**) VPRM estimations of daily gross primary productivity (GPP) on 11 sites of the test dataset. The color bars represent the density of points within a circle area with a radius of 1.0 gC m\({}^{-2}\) d\({}^{-1}\). accuracy of GPP simulation. The MLP can accurately model LUE and, therefore, can be applied to systematically understand the responses of LUE to meteorological factors. Figure 9 shows the density plot of the LUE modeled by MLP with the three meteorological factors \(\rm T_{a}\), \(\rm R_{g}\), and VPD for the test dataset. As expected, the LUE increased sharply as \(\rm T_{a}\) increased, especially when \(\rm T_{a}\) was higher than \(-5\)\({}^{\circ}\)C. When \(\rm T_{a}\) was lower than \(-5\)\({}^{\circ}\)C, the LUE was very low and changed slowly, which indicated the inhibitory effect of low temperatures on plant photosynthesis. In general, chill could induce stomatal closure, precipitating a decline in photosynthesis [53]. LUE decreased with VPD, which indicates that high VPD can inhibit photosynthesis. An increase in VPD results in an enhanced transpiration rate, and stomata then respond by partially closing to reduce the water loss of plants [54], which leads to a decline in photosynthesis. As the light level increases, the canopy LUE decreases because of the light saturation effect [55]. However, the LUE showed insignificant responses to \(\rm R_{g}\) variations (Figure 8b), likely because other environmental factors can be covarying at the same time--for instance, \(\rm R_{g}\) can increase during reduced cloud cover while temperature can also increase. Moreover, previous studies found that an increased fraction of diffuse radiation during cloudy days enhanced plant photosynthesis [55; 56]. Therefore, the variations of the fraction of diffuse radiation caused by changes in clouds and aerosols can also interfere with our observation of the response of LUE to \(\rm R_{g}\) variations. We further investigated the responses of LUE to the three meteorological factors in different PFTs on the test dataset, as shown in Figures 10 and 11. In multiple PFTs, the LUE shows a phenomenon of increasing first and then decreasing as \(\rm T_{a}\) increases. For example, in DBF, EBF, ENF, GRA, MF, SAV, and SHR, the optimum temperature for vegetation photosynthesis is shown; that is, when \(\rm T_{a}\) reaches this value, the LUE will reach a peak, and then the LUE gradually decreases as \(\rm T_{a}\) increases. The global terrestrial average value of ecosystem-scale optimum temperature for photosynthesis is estimated to be 23 \(\pm\) 6 \({}^{\circ}\)C, with large spatial heterogeneity [57]. Additionally, the ecosystem-scale optimum temperature for photosynthesis varies across vegetation types [58]. In our study, for example, in ENF, when \(\rm T_{a}\) reached about 17 \({}^{\circ}\)C, LUE reached a peak value (Figure 10(a5)), while in SAV, LUE reached a peak at 24 \({}^{\circ}\)C (Figure 11(a3)). As for the response of the LUE to \(\rm R_{g}\) variations, in multiple PFTs such as DBF, EBF, ENF, and MF, the LUE showed a decreasing trend with an increase in \(\rm R_{g}\), which is caused by a light saturation effect. In most PFTs, the LUE tended to decrease as VPD increased. In addition, it was evident that the LUE of C4 crops is higher than that of C3 crops (Figure 10). This conclusion is supported by previous studies [48; 59], which found that under the same climate conditions, C4 crops had greater photosynthetic capacity than C3 crops. Figure 9: Density plot of the LUE modeled by MLP with (**a**) \(\rm T_{a}\), (**b**) \(\rm R_{g}\), and (**c**) VPD on the test dataset.