## 4 Results
### Assessment of Modeled CO\({}_{2}\) Concentration
The TVP models for each continent are described below:  
Africa:  
\[\text{CO}_{2}=396.06-0.06\ \times\text{LST}+89.49\ \times\text{NDVI}-0.13\ \times\text{GPP}+0.23\ \times\text{NPP}-49.18\ \times\text{NG} \tag{5}\]  
Australia:  
\[\text{CO}_{2}=362.73+0.07\ \times\text{LST}+29.02\ \times\text{NDVI}+0.03\ \times\text{NPP}-23.90\ \times\text{NG}-0.07\ \times\text{GN} \tag{6}\]  
Eurasia:  
\[\text{CO}_{2}=277.93+0.40\ \times\text{LST}+95.04\ \times\text{EVI}-64.32\ \times\text{NDVI}-0.89\ \times\text{FPAR}+2.73\ \times\text{LAI}-0.03\ \times\text{GPP}-0.004\ \times\text{GN} \tag{7}\]  
North America:  
\[\text{CO}_{2}=321.04+0.23\ \times\text{LST}+48.44\ \times\text{EVI}-27.26\ \times\text{NDVI}-0.52\ \times\text{FPAR}+1.32\ \times\text{LAI}-0.03\ \times\text{GPP}-0.01\ \times\text{GN} \tag{8}\]  
South America:  
\[\text{CO}_{2}=634.59-0.49\ \times\text{LST}-9.49\ \times\text{EVI}-0.66\ \times\text{LAI}+0.11\ \times\text{GPP}-166.04\ \times\text{NG}- \tag{9}\]  
TVP models were run on a monthly time scale using the data of LST, EVI, NDVI, LAI, FPAR, GPP, NPP, GN and NG to predict CO\({}_{2}\) concentrations for the five continents. The TVP model performance was then evaluated using scatter plots (Figure 3) of the predicted versus TANSO-observed CO\({}_{2}\) concentrations from June 2009 to November 2011. Figure 3 shows that the correlation coefficient was not very high (R\({}^{2}\) = 0.57, RMSE = 0.73) in Australia. The TVP model provided better estimates of CO\({}_{2}\) concentration for Eurasia and South America (R\({}^{2}\) = 0.75 for both, RMSE = 1.16 and 1.17, respectively). The validation points of the TVP-modeled and TANSO-observed XCO\({}_{2}\) of Africa and North America were distributed closely around the 1:1 line (RMSE = 0.98 and 1.02, respectively). Satisfactory correlation coefficients were found in both Africa and North America (R\({}^{2}\) = 0.69 and 0.72, respectively). Thus, the results were very encouraging on all five continents. Notably, the higher R\({}^{2}\) values for the TVP-modeled CO\({}_{2}\) concentration in North America and South America do not necessarily indicate that the accuracy was higher for these continents. We found that in North and South America, the TANSO CO\({}_{2}\) points alone were inadequate (11,796 and 10,504, respectively) because the TANSO sensor is only able collect points under a clear sky (without clouds) [28]. As mentioned in Section 3.2 that the accuracy of TANSO XCO\({}_{2}\) is about 0.3\(\sim\)1% and it must increasing the uncertainty of the correlations between predicted and observed CO\({}_{2}\) concentrations if we presume TANSO XCO\({}_{2}\) as true value. Moreover, in  
different continents the bias of TANSO XCO\({}_{2}\) is different [28,72,73,76], which can also increase the uncertainly of Figure 3. These uncertainties have not necessarily weakened this study, in terms of achieving the targeted objectives. Figure 3: Comparison of TVP modeled with TANSO-observed CO\({}_{2}\) concentration in Africa (\(\bullet\)), Australia (\(\bullet\)), Eurasia (\(\bullet\)), North America (\(\bullet\)) and South America (\(\bullet\)). The dotted blue line is the 1:1 line between TVP derived and TANSO observed XCO\({}_{2}\). The black line is the regression line. Figure 3 also shows that the slope of predicted versus observed CO\({}_{2}\) concentration was significantly lower than the 1:1 line, suggesting that the TVP algorithm somewhat underestimates high CO\({}_{2}\) concentration and overestimates low CO\({}_{2}\) concentration. However, the over/underestimation of extreme values had only a small impact on the predicted value, with the largest RMSE at 1.17 in South America and the lowest at 0.73 in Australia.