## 3 Results  
### Soil Moisture Assimilation Performance  
As seen in Figure 1, in the \"_prior_\" experiment, the difference between the simulated CO\({}_{2}\) concentration results and the observations gradually grows with increasing simulation time. This issue is resolved in the \"\(co_{2}\)\" and \"\(sm+co_{2}\)\" experiments, where the optimized CO\({}_{2}\) concentrations are closer to the observations. Table 1 displays the RMSEs of these  
Figure 1: The methodology framework of this study. The blue-shaded part denotes the setup of three experiments adopted in CCDAS. The orange-shaded part denotes the CCDAS and its inputs. The purple-shaded part denotes the validation of assimilation performance compared with the ISO observations, ESA-CCI observations, Jena CarboScope NEP, and FLUXCOM GPP with simulated CO\({}_{2}\) concentrations, surface layer soil moisture, NEP, and GPP, respectively. The inter-annual variability representation of model through calculating the correlation of simulated variables with ENSO indices (green). The gray-shaded part denotes the relationship of GPP and SPIE to reflect the response of GPP to drought. three experiments. For each of the eight flask sampling stations, the \"\(sm+co_{2}\)\" simulation demonstrates large improvements in the simulated atmospheric CO\({}_{2}\) concentrations compared with the prior simulations. Assimilation of CO\({}_{2}\) concentrations and ESA-CCI soil moisture lowers RMSE from 15.56 and 15.77 ppm for _\"prior\"_ to 1.13 and 0.89 ppm for _\"co\({}_{2}\)\"_ and 0.89 and 0.31 ppm for _\"sm +co\({}_{2}\)\"_ experiments at BHD and SMO sites, respectively. At the CHR site, the RMSE obtained for the _\"sm +co\({}_{2}\)\"_ experiment was identical with that of the _\"co\({}_{2}\)\"_ experiment, both at 1.12 ppm. As expected, slightly higher RMSE values than the _\"co\({}_{2}\)\"_ experiment were recorded at some sites. At the ALT, BRW, KUM, MLO, and SPO stations, the \"\(sm+co_{2}\)\" achieves the RMSE of 2.07, 2.54, 1.77, 1.42 ppm, and 1.29 ppm, respectively; whereas in the _\"co\({}_{2}\)\"_ experiment, the RMSE is 1.54, 1.71, 1.28, 0.97 ppm, and 0.80 ppm, respectively. In Figure 2, the comparison between simulated surface layer soil moisture content from three experiments and the ESA-CCI observations is displayed. The global mean soil moisture RMSE decreases from 4.24 mm for _\"co\({}_{2}\)\"_ experiments to 2.57 mm for _\"sm +co\({}_{2}\)\"_ experiments as a result of the simultaneous assimilation of CO\({}_{2}\) concentrations and ESA-CCI soil moisture, respectively (Figure 2 b,c). The global mean soil moisture RMSE for _\"sm +co\({}_{2}\)\"_ is slightly higher than the _\"prior\"_ RSME of 2.26 mm (Figure 2a). Reductions from _\"co\({}_{2}\)\"_ to _\"sm +co\({}_{2}\)\"_ experiments are shown for mainly north of the 30\({}^{\circ}\)N latitude, with overall values reduced by \(-\)1.67 mm globally, but with a little degradation in tropical regions (Figure 2d). In the _\"co\({}_{2}\)\"_ simulation and the _\"sm +co\({}_{2}\)\"_ simulation, the global mean RMSE of the simulated NEP is reduced from 23.55 gC/m\({}^{2}\)/month in the _\"prior\"_ simulation to 22.95 gC/m\({}^{2}\)/month and 21.93 gC/m\({}^{2}\)/month (Figure 3a-c). Middle and high latitudes of Eurasia and North America, where an RMSE decline in NEP primarily occurs, are where soil moisture has also shown large improvements (Figure 3c). In areas such as the Amazon, Sahara, and Australia, where soil moisture is not greatly enhanced, a slight increase in RMSE can be seen. For GPP, the global mean RMSE values decreased from 68.60 gC/m\({}^{2}\)/month to a value of 57.76 gC/m\({}^{2}\)/month in _\"sm +co\({}_{2}\)\"_, a 13.41% decline (Figure 3a,d), whereas in the _\"co\({}_{2}\)\"_ experiment, the RMSE is 68.68 gC/m\({}^{2}\)/month. In most regions, the RMSE for GPP has been reduced rather greatly, particularly in the Amazon, Africa, North America, Central Europe, and Australia.