## 5 Discussion  
Ecosystem models can provide a description of the complex vegetation dynamics of the ecosystem, but only by a simplified presentation of the actual situation. There are many approximations, assumptions, and uncertainties that will increase the uncertainties in the terrestrial GPP estimates. Data assimilation methods have been used to improve the performance of the processed model and reduce errors in model simulation [15; 16; 70; 71; 72; 17]. Most studies regarding assimilating observation data into the ecosystem models mainly focused on the evaluation of the EnKF approach for ecological forecasting. Though EnKF can give an optimum estimate of GPP at the next moment of model simulations, it does not provide an analytical solution of overall balance. Other assimilation algorithms, like 4 DVar, may be adopted so that the entire model trajectory will be affected by the observations and an analytical solution of overall balance will be obtained [18]. To make productivity estimates more precise, a combination of different assimilation approaches should be considered. The PODEn4 DVar adopted by this paper complements the advantages and disadvantages of EnKF and 4 DVar well, which can simultaneously assimilate multi-time and multi-source observations, providing the overall balance analysis solution and the error estimates with flow-dependence [21]. The results of statistical analysis indicate that the simulated GPP from the LPJ-POD scheme has been improved significantly compared with the LPJ and LPJ-EnKF schemes. This study is generally encouraging for the further  
Figure 8: Spatial distribution of gross primary productivity (GPP) in China for year: (**a**) 2003; and (**b**) 2012. Figure 7: Spatial distributions of (**a**) annual averaged gross primary productivity (GPP); and (**b**) standard deviation (_SD_) of GPP during 2003–2012 in China. application of the PODEn4 DVar method integrating with dynamic vegetation models, to reduce uncertainty of terrestrial carbon flux estimates at different scales. The performance of data assimilation schemes may also be affected by the quality of observation data. Currently, most studies have investigated the capability of assimilating MODIS LAI product into the process-based models [72; 73; 74]. However, the MODIS LAI product lacks adequate stable profiles, especially for the growing seasons [44]. [PERSON] et al. [72] have adopted a Savizky-Golay filter to resolve the discontinuous performance of MODIS LAI arising from snow cover, cloud, and sensor errors during the crop growth stages, but the filter has brought new errors which will decrease the higher LAI and create abnormal lower values when involving the universal low LAI values. [PERSON] et al. [44] proposed a method for retrieving a long time series GLASS LAI product from multi-temporal data. The retrieval algorithm used annual observations to generate the LAI annual profile, which can remove abrupt spikes and dips effectively and produce temporally continuous LAI product. Therefore, we assimilated high-quality GLASS LAI sequentially into the LPJ model to renew the FPC that is related to photosynthesis. The better performance for GLASS LAI than the MODIS LAI were validated through the quantitative comparison at site of different biomes [44]. Though our LPJ-POD scheme successfully improved the modeling accuracy, and explicitly described the spatial distributions of GPP in China during the period 2003-2012, there were still some uncertainties. For six selected sites, overestimated and underestimated GPP remained at a few site-years. This discrepancy also raised the inaccuracy of the temporal and spatial features of the simulated GPP at the regional scale. The uncertainty was partly owing to the model structure. First, one limitation is that many critical parameters provided as default values in LPJ will induce uncertainty in simulating ecosystem carbon fluxes [75; 76; 77].