## 4 Results  
### Accuracy Assessment of Simulated GPP  
In this experiment, we assimilated ten years of GLASS LAI products into the LPJ-DGVM to update FPC beginning in 2003. The temporal trends of estimated and assimilated results of FPC at six sites are given in Figure 3, depicted as: \(FPC_{L}\) (FPC simulated from LPJ-DGVM), \(FPC_{LE}\) (FPC simulated from the assimilated LPJ-DGVM using the EnKF), and \(FPC_{LP}\) (FPC simulated from the assimilated LPJ-DGVM using the PODEn4 DVar). \(FPC_{G}\) represented GLASS FPC (calculated from GLASS LAI products using Equation (1)). Notably, the estimation of FPC with assimilation has great improvement in most sites. We can see that the simulated FPC with assimilation at Figure 3a obviously corrected the modelling tracks of the LPJ-DGVM, improving the original model which overestimates in peak value and slightlyunderestimates in winter. Figure 3b,c showed higher estimated FPC compared with \(FPC_{G}\), especially at the peak of the growing season, but the assimilated FPC followed GLASS FPC closer than the simulated FPC and can capture the variation of FPC exactly at these two sites. As shown in Figure 3d-f, the simulated results without assimilation clearly overestimated after the peak of the growing season, while results with assimilation significant decreased margin between estimated and remote-sensed values. It is noticeable that \(FPC_{LP}\) performed much better than \(FPC_{L}\) and \(FPC_{LE}\), and the estimated results are quite consistent with the \(FPC_{G}\), especially for the growing season of forests (Figure 3a-c). The seasonal variations of estimated and observed GPP at six sites in China during 2003-2010 are given in Figure 4a-f. \(GPP_{EC}\), \(GPP_{L}\), \(GPP_{LE}\), and \(GPP_{LP}\) were the abbreviations of GPP from eddy-covariance observations and Lund-Potsdam-Jena (LPJ), LPJ-Ensemble Kalman Filter (LPJ-EnKF), and LPJ-proper orthogonal decomposition (LPJ-POD) schemes. The results showed that schemes with assimilation can exactly retrieve \(GPP_{EC}\) by integrating remote-sensed information. At the CN-Din and CN-Qia sites (Figure 4a,b), good agreement was shown for both \(GPP_{LE}\) and \(GPP_{LP}\) with \(GPP_{EC}\). Both tracked the seasonal dynamics of \(GPP_{EC}\) well but underestimated the value when it captured the peak of the growing season in 2004. At the CN-Qia site, there was an apparently underestimation for \(GPP_{L}\), but was improved greatly with the PODEn4 DVar method. At the CN-Cha site (Figure 4c), \(GPP_{LP}\) was much closer to the observed values at the peak of the growing season. However, data assimilation did not show obvious advantages at the CN-Dan site (Figure 4d), with three schemes having higher GPP values than observations. This was consistent with results shown in Figure 3d, with all schemes displaying higher FPC than \(FPC_{G}\). The estimated GPP showed  
Figure 3: (**a–f**) Comparison of simulated eight-day FPC (\(FPC_{L}\), \(FPC_{LE}\), and \(FPC_{LP}\)) and GLASS FFC (\(FPC_{G}\), calculated from GLASS LAI). \(FPC_{L}\) represents FPC simulated from LPJ-DGVM, \(FPC_{LE}\) and \(FPC_{LP}\) represent FPC obtained from the assimilated LPJ-DGVM using the EnKF and PODEn4 DVar, respectively, and \(FPC_{G}\) represents GLASS FPC. later initiation, but captured the cessation of the growing season for the CN-HaM site (Figure 4e). \(GPP_{L}\) overestimated GPP to a large extent after August for the CN-Cng site (Figure 4f), indicating that assimilation can accurately retrieve GPP by adding remotely sensed LAI. Before and after the peak of the growing season at the CN-Cng site, all of the estimated GPP values were significantly overestimated. The \(GPP_{LE}\) values were very close to \(GPP_{L}\) at several site-years (e.g., CN-Dan 2004, CN-Cng 2008), which indicated that the EnKF method did not make significant improvements. However, the \(GPP_{LP}\) for these site-years showed greater consistency with \(GPP_{EC}\) and were significantly closer to the observed GPP.