## 3 Results  
### Optimized Model Parameters  
Table 3 shows the averages of optimized \(\varepsilon_{m}\), \(\varepsilon_{max}\), \(\varepsilon_{msu}\) and \(\varepsilon_{msh}\) for 6 different vegetation types at half-hourly, daily and 8-day temporal scales, respectively. \(\varepsilon_{m}\) was generally larger than \(\varepsilon_{msh}\), \(\varepsilon_{msu}\), and \(\varepsilon_{max}\). It increased sizably when the temporal scales increasing from half-hourly to 8-day, especially for CROP. CROP always had the highest \(\varepsilon_{m}\) in all the three temporal scales. At the half-hourly scale, three forest types, including BF, MF and NF, had lower \(\varepsilon_{m}\) values than CROP and SHRUB, but higher than GRASS. Through metadata analysis for more than 100 published datasets, [PERSON] _et al._[99] reported that CROP has the highest \(\varepsilon_{m}\) (about 5.17 g C MJ\({}^{-1}\)) at the half-hourly scale, followed by forests (about 4.37 g C MJ\({}^{-1}\), mainly BF sites), and GRASS has the smallest one (about 2.71 g C MJ\({}^{-1}\)), similar to the identified changes of \(\varepsilon_{m}\) with vegetation types here. Optimized \(\varepsilon_{max}\) was in between \(\varepsilon_{msh}\) and \(\varepsilon_{msu}\) for all vegetation types and at all temporal scales. \(\varepsilon_{msh}\) is larger than \(\varepsilon_{msu}\) and \(\varepsilon_{max}\) due to the fact that shaded leaves are only exposed to diffuse radiation, which enters a canopy from all directions and distributes more evenly than direct radiation within the canopy [107,108]. The intensity of light absorbed by shaded leaves is normally lower than light saturation point. Thus, they have higher light use efficiency than sunlit leaves. The values of \(\varepsilon_{max}\), \(\varepsilon_{msu}\) and \(\varepsilon_{msh}\) showed smaller variations than \(\varepsilon_{m}\) across three temporal scales (Table 3). As expected, CROP had the highest \(\varepsilon_{max}\), \(\varepsilon_{msu}\), and \(\varepsilon_{msh}\) values, which are 1.78, 1.21 and 5.23 g C MJ\({}^{-1}\) at the half-hourly scale, 1.80, 0.95 and 4.67 g C MJ\({}^{-1}\) at the daily temporal scale, and 1.80, 0.96 and 4.26 g C MJ\({}^{-1}\) at the 8-day scale, respectively. MF had the second largest ones, followed by BF and NF. GRASS had the lowest \(\varepsilon_{max}\), \(\varepsilon_{msu}\) and \(\varepsilon_{msh}\) values among all 6 vegetation types. The \(\varepsilon_{max}\), \(\varepsilon_{msu}\) and \(\varepsilon_{msh}\) of GRASS were lower than half of the corresponding values of CROP at the three temporal scales, respectively. In general, the average optimized \(\varepsilon_{max}\) was close to the default values used in the MOD17 algorithm (Table 2) for all vegetation types except CROP, which had much higher optimized \(\varepsilon_{max}\) than the default (0.604 g C MJ\({}^{-1}\)). Many studies have indicated that the underestimation of CROP GPP by the MOD17 algorithm is mainly due to the low value of \(\varepsilon_{max}\) used [109]. It has been reported that the mean LUE of croplands can approach 2.80 g C MJ\({}^{-1}\)[110,111,112], slightly higher than the average value of about 2.0 g C MJ\({}^{-1}\) optimized in this study. The parameter \(\beta\) in the TL-LUEn model showed complex changes with temporal scales and vegetation types. At the half-hourly scale, non-forest types had a relatively higher \(\beta\) value than forests, which is consistent with the findings reported by [PERSON] _et al._[99] and [PERSON] _et al._[6]. At the daily temporal scale, GRASS had the highest \(\beta\) (286.28 \(\upmu\)g C m\({}^{-2}\) s\({}^{-1}\)), followed by CROP, NF, MF, SHRUB and BF.