## 6 Conclusions  
In this study, we developed a GPP assimilation system based on EnKF and PODEn4 DVar algorithms. Eddy covariance flux datasets of six sites provided by FLUXNET2015 were adopted for validating the performances of GPP values estimated by two assimilation methods (\(GPP_{LE}\), \(GPP_{LP}\)) and no assimilation method (\(GPP_{L}\)). The optimal method was applied to assess the spatial distribution of GPP values in China during the period 2003-2012. Results showed that the EnKF and PODEn4 DVar methods were reasonable for application to the LPJ model, showing better correlation and smaller \(RMSD\). The LPJ-POD scheme performed better, with an \(r\) of 0.923 and \(RMSD\) of 32.676 gC/m\({}^{2}\)/month compared with the LPJ-EnKF scheme values of \(r\) = 0.887, 38.531 gC/m\({}^{2}\)/month and the LPJ scheme with \(r\) = 0.840, 45.410 gC/m\({}^{2}\)/month. According to the results of the optimal method, the LPJ-POD scheme, the annual GPP values in China from 2003 to 2012 varied between 5.92 PgC/yr (2003) and 6.67 PgC/yr (2012) with a mean of 6.35 PgC/yr.  
This study demonstrated that integrating remotely-sensed data with dynamic global vegetation models through data assimilation methods has potential for simulation optimization and that the LPJ-POD scheme showed better performance in improving GPP estimations. However, our developed LPJ-POD scheme still has uncertainties both in the magnitude and spatial distribution of the GPP at the national scale. To improve process-based models and obtain better simulated results, integrating with a remote sensing model, such as CASA, to calibrate ecophysiological parameters of the LPJ model is a further step for future study.  
**Acknowledgments:** This study was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 41271372), the Innovation Team Program of Hainan Natural Science Foundation (Grant No. 2016 CXTID015), and the Major Programs of High-Resolution Earth Observation System (Grant No. 32-Y2-0A17-9001-15/17). The work used eddy covariance data acquired and shared by the FLUXNET community, including ChinaFlux and USCCC networks. The authors would also like to thank to the Center for Global Change Data Processing and Analysis of Beijing Normal University for providing the GLASS LAI products. The authors appreciate the constructive comments on the manuscript offered by anonymous reviewers and editors.  
**Author Contributions:** [PERSON] conducted the experiments, processed the data, analyzed the results, and wrote the majority of the manuscript. [PERSON] designed the main concept of the study, supervised and provided instructions for the research work, and contributed to the manuscript structure and discussions. [PERSON] developed the PODEn4 DVar method and helped with discussions and modification of the manuscript. [PERSON]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **GPP (PgC/yr)** & **Period** & **Reference** \\ \hline CASA & 5.14–5.92 & 1982–2003 & [PERSON] et al. (2008)[81] \\ GLOPEM & 5.52–6.62 & 1981–2000 & [PERSON] et al. (2008)[81] \\ TEPC & 7.356 & 1993–1999 & [PERSON] et al. (2001)[82] \\ RSM & 12.26 & 1990 & [PERSON] et al. (2001)[83] \\ EC-LUE & 5.63–6.39 & 2000–2009 & [PERSON] et al. (2013)[63] \\ VPM & 4.87–5.16 & 2006–2008 & [PERSON] et al. (2014)[84] \\ BEPS & 5.26–5.68 & 2000–2010 & [PERSON] et al. (2013)[64] \\ LPJ-POD & 5.92–6.67 & 2003–2012 & this study \\ \hline \hline \end{tabular}
\end{table}
Table 4: Estimation of total gross primary productivity (GPP) values in China with different terrestrial models.  
contributed to the experiments and helped with discussions. [PERSON], [PERSON] and [PERSON] helped with discussions and revisions. [PERSON] provided and processed the GLASS LAI products for the experiments.  
The authors declare no conflict of interest.