## 4 Results
### Accuracy Assessment of Simulated GPP
Figure 5 quantifies the similarity between simulated and observed GPP in terms of their correlation, normalized centered \(RMSD\), and relative amplitude of variations represented by normalized \(SD\)s by withholding 17 site-years (No. 1 to No. 17, Figure 5a) and four PFTs (A to D, Figure 5b) including EBF, ENF, MF, and GRA. Only the site-years or PFTs with \(p\)-values \(<\)0.05 were considered. An ideal model manifested as \(NSD\) of 1.0 and \(r\) of 1.0. The points between the two black dashed lines in the figure represented the site-year or PFTs with \(0.7\leq NSD\leq 1.3\). The excluded site-years were CN-Din 2003 (No. 1, \(GPP_{LP}\), \(p\)-value \(>\) 0.05) and CN-Dan 2005 (No. 11, \(NSD\)\(>\) 2.0). Points lying on the red solid line indicated estimated GPP having variations similar to those of the observations. The position of each point on the two plots quantified the agreement between simulated GPP and observations. Sites with large or small \(NSD\) showed inconsistency between simulated and observed GPP. Therefore, we considered that the points between two dashed lines (with \(0.7\leq NSD\leq 1.3\)) had similar variability with the observations, and we further grouped them into three levels based on the correlation values: I (\(0.7<r\leq 0.8\)), II (\(0.8<r\leq 0.9\)), III (\(0.9<r\leq 1.0\)). All of these points showed better performance than other points (with \(NSD<0.7\) or \(NSD>1.3\) and \(r\leq 0.7\)), and the higher correlation coefficient presented better consistency with the observations. Figure 4: (**a–f**) Seasonal dynamic of tower-based and estimated gross primary productivity (GPP) from Lund-Potsdam-Jena (LPJ), LPJ-Ensemble Kalman Filter (LPJ-EnKF), and LPJ-proper orthogonal decomposition (LPJ-POD) for each site during the study period. Figure 5: Statistics of three models (LJP-DGVM, LJP-EnKF and LPJ-POD) for the six selected tower sites (Table 1) by withholding the **(a)** site-year and (b) plant functional type (PFT). As shown in Figure 5 the GPP values with data assimilation behaved better in terms of correlation, especially for III (0.9 \(<r\leq\) 1.0) with correlations of 7/17 (seven points meet the requirement in 17 site-years) for both of two assimilation methods. For all site-year, the total proportion within the scope of 0.7 \(\leq NSD\leq\) 1.3 and \(r\) > 0.7 increased by 87.5% from both \(GPP_{L}\) (8/17) to \(GPP_{LE}\) (15/17), and \(GPP_{LP}\) (15/17). \(GPP_{LP}\) performed better with higher proportion (8/17) than \(GPP_{L}\) (4/17) and \(GPP_{LE}\) (4/17) for II (0.8 \(<r\leq\) 0.9). Moreover, the correlation of certain site-years (e.g., CN-Din) was substantially improved by more than 0.2 when using the PODEn4 DVar method, and exhibited stronger correlations (generally \(r\) > 0.85) with the site observations than the values from LPJ and LPJ-EnKF schemes (Table 2). For four PFTs, a similar situation is shown in Figure 5b. The results with data assimilation generally agreed well with observations, with higher correlation and \(NSD\) closer to 1. Point A (PFT: EBF), apparently, had been greatly improved by using assimilation method (improving r by 0.141 and 0.249 for \(GPP_{LE}\) and \(GPP_{LP}\), respectively, and \(NSD\) getting closer to 1) (Figure 5b, Table 3). Point D (PFT: GRA, \(GPP_{L}\)) did not exist between the two dashed lines owing to its higher \(NSD\), which increased the distance from the red solid line, but it had been improved by PODEn4 DVar method with a higher correlation and lower \(RMSD\). Overall, \(GPP_{LP}\) had a higher proportion and higher correlation with 0.7 \(\leq NSD\leq\) 1.3; all of the PFTs were present between the dashed lines. This showed obvious improvement in all statistical indices over values without assimilation, especially for evergreen needleleaf forest and mixed forest, with \(r\) > 0.94 (Table 3).