## 5 Discussion
In terms of GPP estimation accuracy alone (R\({}^{2}\) and RMSE), EC-LUE was comparable to PAR-LUE in GPP estimation. However, the PAR-LUE mitigated the underestimation of high GPP, which is a nonnegligible contribution to an accurate estimate of total annual GPP. The constant \(\mathcal{E}_{\mathrm{max}}\) in the EC-LUE model, as a special case of dynamic \(\mathcal{E}_{\mathrm{max}}\), is one of the reasons for its comparable ability to estimate GPP (especially R\({}^{2}\)) with the PAR-LUE model. On the one hand, the GPP values at the beginning and end of the growing season were relatively small, so only a minor difference existed between the GPP estimated by the constant and dynamic \(\mathcal{E}_{\mathrm{max}}\). For example, in the comparison of the seasonal variation in GPP at typical sites in the Northern Hemisphere (Figure 7), EC-LUE and PAR-LUE showed similar R\({}^{2}\) values, but the seasonal dynamics of PAR-LUE GPP were closer to the observed GPP. On the other hand, the accuracy of other input parameters in the LUE model may inhibit the ability of dynamic \(\mathcal{E}_{\mathrm{max}}\) to improve the accuracy of GPP estimation. In addition, compared with the spatial dynamics of \(\mathcal{E}_{\mathrm{max}}\)-based D-VPM, PAR-LUE has two advantages in addition to the improvement in precision. First, PAR drives vegetation photosynthesis more directly than albedo, the \(\mathcal{E}_{\mathrm{max}}\) constructed by PAR is more theoretical than that of albedo, and \(\mathit{PAR}\)-\(\mathcal{E}_{\mathrm{max}}\) has bothspatial and temporal dynamic characteristics. Second, the estimation of spatial dynamic _RS_-\(\mathcal{E}_{\max}\) requires remote sensing data in a whole growing season (it requires the maximum EVI and minimum albedo of the whole growing season), which limits its application in near-real-time GPP estimation, while _PAR_-\(\mathcal{E}_{\max}\) is not affected by this. The accuracy validation results showed the reasonableness and reliability of _PAR_-\(\mathcal{E}_{\max}\). However, PAR-LUE still has room for improvement. First, the accurate estimation of _PAR_-\(\mathcal{E}_{\max}\) requires a large number of high-quality observations. Limited by site representativeness and data quality, _PAR_-\(\mathcal{E}_{\max}\) may have some errors in the specific values. A large number of high-quality observations will help to improve the performance of the PAR-LUE model. Second, _PAR_-\(\mathcal{E}_{\max}\) characterizes the \(\mathcal{E}_{\max}\) of all vegetation, and it was thought that the EVI-based FPAR could constrain the differences in _PAR_-\(\mathcal{E}_{\max}\) across vegetation types in the PAR-LUE model. However, from the performances of PAR-LUE in estimating vegetation GPP (Figures 5-7), FPAR was able to partly characterize differences in vegetation types, but its ability to constrain _PAR_-\(\mathcal{E}_{\max}\) was still limited. Obviously, the _PAR_-\(\mathcal{E}_{\max}\) of different vegetation types can be obtained based on vegetation type data, but it will be limited by the quality of vegetation type data, and it is difficult to characterize the spatially continuous variation in terrestrial vegetation with vegetation type data. It is hoped that further research can introduce a factor that can characterize the spatially continuous variation in vegetation photosynthetic capacity in PAR-LUE to improve the theory of the PAR-LUE model and the accuracy of GPP estimation. Finally, the effect of other input parameters of the LUE model on the accuracy of GPP estimation needs to be further analyzed to reduce the interference from other input parameters on the contribution of \(\mathcal{E}_{\max}\) parameter optimization to the improvement of GPP estimation.