## 4 Results
### Assessment of Modeled CO\({}_{2}\) Concentration  
In this study, we used the MODIS products of temperature (MOD11C3), vegetation cover (MOD13C2 and MOD15A2) and productivity (MOD17A2) as variables to measure land surface CO\({}_{2}\) concentration; thus, we named the model TVP. To select the indices of the TVP model, first, we calculated the correlation coefficient between each of these indices and the TANSO XCO\({}_{2}\) on each continent (Table 1). Then, we selected indices according to higher R\({}^{2}\), lower RMSE and significance value (P); if P was less than 0.05 (significance greater than 95%) and the index increased the correlation coefficient in the multivariate linear regression of the TVP model, then the index was selected. Finally, we selected seven indices for Eurasia and North America, six indices for South America and five indices for Africa and Australia. The results are shown in Table 1. EVI and NDVI, GPP and NPP and LAI and FPAR are pairs of indices that measure the same parameter and can, in some cases, be substituted for one another. Researchers found that a small number of indices is not sufficient to provide an accurate estimate of CO\({}_{2}\) flux [30]; thus, we also tested the use of a single \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & LST & EVI & GPP & NPP & NG & GN & NDVI & FPAR & LAI \\ \cline{2-10} Africa & R\({}^{2}\) & 0.24 & 0.09 & 0.47 & 0.61 & 0.40 & 0.01 & 0.39 & 0.23 & 0.19 \\  & P & 0.007 & 0.104 & 0.000 & 0.000 & 0.000 & 0.576 & 0.000 & 0.008 & 0.016 \\  & RMSE & 1.70 & 1.86 & 1.42 & 1.21 & 1.50 & 1.94 & 1.53 & 1.72 & 1.75 \\ \hline  & & LST & EVI & GPP & NPP & NG & GN & NDVI & FPAR & LAI \\ \cline{2-10}  & R\({}^{2}\) & 0.22 & 0.42 & 0.31 & 0.26 & 0.01 & 0.35 & 0.44 & 0.35 & 0.29 \\ Eurasian & P & 0.009 & 0.000 & 0.002 & 0.004 & 0.543 & 0.001 & 0.000 & 0.001 & 0.002 \\  & RMSE & 2.04 & 1.76 & 1.92 & 1.98 & 2.29 & 1.87 & 1.73 & 1.86 & 1.94 \\ \hline  & & LST & EVI & GPP & NPP & NG & GN & NDVI & FPAR & LAI \\ \cline{2-10}  & R\({}^{2}\) & 0.49 & 0.59 & 0.51 & 0.49 & 0.00 & 0.45 & 0.65 & 0.59 & 0.55 \\ North America & P & 0.000 & 0.000 & 0.000 & 0.000 & 0.796 & 0.000 & 0.000 & 0.000 & 0.000 \\  & RMSE & 1.37 & 1.23 & 1.35 & 1.37 & 1.92 & 1.42 & 1.15 & 1.23 & 1.30 \\ \hline  & & LST & EVI & GPP & NPP & NG & GN & NDVI & FPAR & LAI \\ \cline{2-10}  & R\({}^{2}\) & 0.41 & 0.13 & 0.00 & 0.16 & 0.35 & 0.20 & 0.38 & 0.11 & 0.04 \\ Oceania & P & 0.00 & 0.05 & 0.99 & 0.03 & 0.00 & 0.01 & 0.00 & 0.08 & 0.28 \\  & RMSE & 0.85 & 1.04 & 1.11 & 1.02 & 0.90 & 1.00 & 0.88 & 1.05 & 1.09 \\ \hline  & & LST & EVI & GPP & NPP & NG & GN & NDVI & FPAR & LAI \\ \cline{2-10}  & R\({}^{2}\) & 0.64 & 0.30 & 0.42 & 0.13 & 0.19 & 0.61 & 0.00 & 0.11 & 0.46 \\ South America & P & 0.000 & 0.002 & 0.000 & 0.048 & 0.016 & 0.000 & 0.777 & 0.080 & 0.000 \\  & RMSE & 1.39 & 1.94 & 1.77 & 2.16 & 2.09 & 1.46 & 2.32 & 2.19 & 1.71 \\ \hline \end{tabular}
\end{table} 
Table 1: [PERSON]’s correlation coefficient (R\({}^{2}\)) and the root mean square error (RMSE) between TANSO XCO\({}_{2}\) and MODIS-derived indices. Gray masked indices are selected for the TVP model. index for a given parameter (e.g., NPP but not GPP in Africa and NDVI but not EVI in Eurasia), but we found that the adjusted R\({}^{2}\) value was lower than that of the TVP model. At last, the index number that been selected for TVP model is 5 in Africa and Australia, 7 in Eurasia and North America and 6 in South America. After analyzing the R\({}^{2}\) and RMSE between MODIS products and the TANSO XCO\({}_{2}\), we employed MODIS-derived indices that were selected for each continent as independent variables and TANSO XCO\({}_{2}\) as dependent variables of multivariate linear regression in Microsoft Office 2010 to model the CO\({}_{2}\) concentration on each continent.