## 5 Discussion  
For a widely studied biome like deciduous broadleaf forest and for an extensively studied region like the eastern United States, the mismatches in the spatiotemporal patterns of derived annual GPP among satellite-based models are unexpected. Past satellite-based studies have largely focused on model development and evaluation on the 8-day or shorter time scale. Note that deciduous broadleaf forests have distinctive seasonality of leaf allocation dynamics [56] and, therefore, modeling intra-annual GPP variation is much easier than modeling interannual GPP variation as the influences of seasonality in GPP cancel out on the yearly basis. In addition, studies on the yearly basis require much longer and more persistent observation records than those on the weekly or shorter time scale. Existing modeling studies paid much attention to error metrics such as R\({}^{2}\) and RMSE but overlooked or even did not report the metric of model biases. For studies on the deciduous broadleaf forests, the MOD17 algorithm achieved an RMSE of 2.32 gC/m\({}^{2}\)/day as evaluated against the BigFoot GPP [57]. The VPM model achieved an R\({}^{2}\) of 0.92 at a 10-day time scale when assessed using flux tower data [46]. A recent study that used the FLUXNET dataset for model evaluation reported that the MOD17 algorithm achieved an R\({}^{2}\) of 0.88 and an RMSE of 12.61 gC/m\({}^{2}\)/8 day (or 1.58 gC/m\({}^{2}\)/day equivalently) and the TL-LUE model achieved an R\({}^{2}\) of 0.90 and an RMSE of 11.21 gC/m\({}^{2}\)/8 day (or 1.40 gC/m\({}^{2}\)/day equivalently) [50]. Comparative studies on global vegetation products using the FLUXNET dataset found that the BESS product achieved an R\({}^{2}\) of 0.72 with an RMSE of 2.59 gC/m\({}^{2}\)/day and the MOD17 product achieved an R\({}^{2}\) of 0.68 with an RMSE of 2.97 gC/m\({}^{2}\)/day for deciduous broadleaf forests [18]. The GPD model was found to achieve an R\({}^{2}\) of 0.787 and an RMSE of 2.25 gC/m\({}^{2}\)/day [26]. The EC-MOD model was reported to achieve an R\({}^{2}\) of 0.74 for the modeled GPP as evaluated using AmeriFlux data across biomes [58], and no biome-specific studies have been found. Despite different datasets and study regions, the model performance on the 8-day or shorter time scale in the above-mentioned studies is close to and comparable to that found in this study. Modeling annual GPP, however, requires paying more attention to the model bias because the cumulative biases could become considerable on a yearly basis, as shown in Figures 1 and 2, even when the model biases are small on the 8-day basis. Our study chooses to use existing parameter settings in the literature and supposes that the models have already been calibrated to achieve their best performance across space and time. Later studies may need to calibrate the models to balance the model performance in terms of bias and RMSE, or, otherwise, the modeling results could be misleading on the yearly basis. Beside appropriate model calibrations, studies that aim for model improvements need to investigate the potential mechanisms behind the unsatisfactory model performance on the yearly basis. One possible reason is that all models tested here apply biome-specific parameters but the canopy structure and tree species composition could vary greatly across sites and spaces even for the same biome of deciduous broadleaf forest. In our results, all models appear to underestimate GPP for the US-Ha1 and US-Oho sites. One possible reason is that understory LAI could contribute considerable GPP. Both field experiments and modeling studies are needed to understand why the model performance in these two sites is inconsistent with that in other sites. Accurate modeling of annual GPP greatly influences our understanding of the ecosystem processes as well as the climate-vegetation interactions. Even for deciduous broadleaf forests that have abundant observational sites available among ecosystems, the site-year flux tower data are still limited for comprehensive modeling studies on a yearly basis.