## 3 Results
### The Inter-Annual Variability of the Carbon and Water Fluxes  
The correlations between the simulated variables from three experiments (\"_prior_\", \"_co\({}_{2}\)\", and \"_sm + co\({}_{2}\)\") and moderate-to-strong ENSO events were used to depict the model  
Figure 3: The RMSE of monthly NEP and GPP from the (**a**) “_prior_\", (**b**) “_co\({}_{2}\)_”, and (**c**) “_sm + co\({}_{2}\)_” experiments against CarboScope NEP and FLUXCOME GPP (**d**–**f**). Values attached with figure stand for the global mean RMSE values. Figure 2: Comparisons of RMSE of monthly soil moisture from the (**a**) “_prior_”, (**b**) “_co\({}_{2}\)_”, and (**c**) “_smt + co\({}_{2}\)_” experiments against ESA-CCI soil moisture, as well as (**d**) the difference between “_smt + co\({}_{2}\)_” and “_co\({}_{2}\)_”. Values in each figure denote the global mean RMSE values in “_prior_”, “_co\({}_{2}\)_”, and “_smt + co\({}_{2}\)_” experiments. performance in representing the inter-annual variability at global scale. Our results suggest that the \"\(sm+co_{2}\)\" experiment obtained the correlations between soil moisture anomalies from 30\({}^{\circ}\)N to 60\({}^{\circ}\)N (others are detailed shown in Figure A2) and MEI/Nino 3.4 (Figure A3a) of 0.78/0.76 (\(p<0.001\)), respectively (Figure A3b), with a time lag of 3 months (Figure A4a). The correlations between the \"\(sm+co_{2}\)\" optimized NEP anomaly and MEI/Nino 3.4 are \(-0.60/-0.64\) (\(p<0.001\), Figure A3c), respectively. The time lags of the \"\(sm+co_{2}\)\" optimized NEP and the Jena CarboScope inversed NEP to MEI/Nino 3.4 are 6 months and 8 months, respectively (Figure A4b). The optimized global CO\({}_{2}\) growth rate (CGR) shows the correlation with the MEI/Nino 3.4 as 0.52/0.41 (\(p<0.001\)), respectively (Figure A3d), with a time lag of 5 months (Figure A4c). The CCDAS-optimized GPP from 30\({}^{\circ}\)N to 60\({}^{\circ}\)N shows tighter correlation to the two ENSO indices than the FLUXCOM GPP (\(-0.29/-0.39\) vs. 0.01/\(-0.05\), \(p<0.001\), Figures A3e and A5b). In Figure A6, we presented the power spectrum of the CCDAS output variables, e.g., GPP, NEP, and surface soil moisture (0-5 cm). The power spectra show the features of variability of GPP, NEP, and soil moisture in the frequency domain. Overall, the ENSO-band variations of all variables are characterized by a relatively larger amplitude at low/mid latitudes (e.g., 30\({}^{\circ}\)N-60\({}^{\circ}\)N and 0-30\({}^{\circ}\)S) and a smaller amplitude at high latitudes (60\({}^{\circ}\)N-90\({}^{\circ}\)N). CCDAS-optimized surface soil moisture (0-5 cm) and GPP show contrasting relations over the six continents (Figure 4a,b). Overall, for North America, Europe, and Asia, which are mainly north of 30\({}^{\circ}\)N, all aggregated moderate-to-strong El Nino/La Nina events result in lower GPP but higher soil moisture, while for South America, Africa, and Oceania, which are mainly south of 30\({}^{\circ}\)N, all aggregated moderate-to-strong El Nino/La Nina events result in the same trend of GPP and soil moisture. GPP decrease during moderate-to-strong and strong El Nino events in Asia (\(-0.26/-0.39\) PgC yr\({}^{-1}\)) and Europe (\(-0.23/-0.20\) PgC yr\({}^{-1}\)) is accompanied by an increase in surface soil moisture (0.32/0.23 \(\times\) 10\({}^{-1}\) mm and 0.26/0.29 \(\times\) 10\({}^{-1}\) mm, respectively). In North America, an increase in GPP during moderate-to-strong and strong El Nino events (0.20/0.34 PgC yr\({}^{-1}\)) is mainly caused by an increase in surface soil moisture (0.52/0.68 \(\times\) 10\({}^{-1}\) mm). In South America, the El Nino events contribute to an increase in GPP (0.90/1.00 PgC yr\({}^{-1}\)) accompanied by an increase in surface soil moisture (0.88/0.95 \(\times\) 10\({}^{-1}\) mm). In South Africa and Oceania, a decrease in GPP during El Nino (\(-0.47/-0.59\) PgC yr\({}^{-1}\) and \(-0.43/-0.33\) PgC yr\({}^{-1}\)) is accompanied by a positive surface soil moisture anomaly (\(-0.57/-0.86 \(\times\) 10\({}^{-1}\) mm and \(-1.47/-0.95 \times\) 10\({}^{-1}\) mm).