Optical remote sensing systems measure the surface reflectance, the fraction of solar energy that is reflected by the Earth’s surface. For a given wavelength, different land cover types may have different reflectance [16]. As a part of the National Aeronautics and Space Administration (NASA)-centered international Earth Observing System (EOS), two MODIS instruments (Terra and Aqua) have been launched (in 1999 and 2002, respectively) to provide information for global studies of atmospheric, land and ocean processes. The MODIS instrument strengths include its global coverage, high radiometric resolution and dynamic ranges and accurate calibration in the visible, near-infrared and thermal infrared bands [38].

MODIS, which is a key instrument aboard the Terra (AM) and Aqua (PM) satellites is one of the most reliable data sources on the global scale [21]. Terra and Aqua MODIS can view the entire Earth’s surface every 1 to 2 days, acquiring data in 36 spectral bands ranging in wavelength from 0.4 μm to 14.4 μm. The MODIS data have been used to generate science data products for more than eleven years and these science data products are available to the public free of charge. More than 10 types of products are retrieved from the 36 MODIS bands. In this study, we selected four product types, MOD11C3, MOD13C2, MOD15A2 and MOD17A2, to develop a CO₂ concentration prediction model.

The GOSAT was launched on January 23, 2009 from Tanegashima Island, Japan, and is a joint project of the Japan Aerospace Exploration Agency (JAXA), the Ministry of the Environment of Japan (MOE) and the National Institute for Environmental Studies (NIES) of Japan. The primary purpose of the GOSAT project is to accurately estimate the emissions and absorptions of GHG on a subcontinental scale to assist environmental administrations in evaluating the carbon balance of land-based ecosystems and to provide assessments of regional emissions and absorptions [66]. The GOSAT main sensor (TANSO) is a nadir-looking Fourier Transform Spectrometer (FTS) with four spectral bands, from the visible to thermal infrared. GOSAT is the World’s first spacecraft designed to measure XCO₂ and XCH₄, the two major GHG concentrations, from SWIR bands with global coverage every three days [67]. GOSAT is a sun-synchronous orbit with a local overpass time of 13:00 [68,69]. It derives the CO₂ and CH₄ column amounts by observing ground-surface scattered solar spectra in the 1.6 and 2.0 μm regions, which contain suitable CO₂ and CH₄ absorption bands, and the satellite also measures vertical profiles higher than approximately 2 km by measuring thermal emission spectra from the atmosphere [8].

TANSO FTS SWIR Level 2 Version 02.00 and 02.11 (stored column abundances of CO₂ and CH₄ retrieved from the radiance spectra in bands 1 through 3 of FTS) data from June 2009 to November 2011 were used in this study. The relative accuracy of TANSO FTS Level 2 data is 0.3–1% (1∼4 ppm) for CO₂[70]. The GOSAT FTS SWIR Level 2 data are point data and the footprint is a circle with 10.5 km diameter at nadir [71]; thus, we obtained the monthly CO₂ concentration easily. Moreover, in this study, we assumed that the TANSO XCO₂ were the true value without bias. TANSO XCO₂ data were also used to check the accuracy of the modeled CO₂ concentration from MODIS derived products.

MOD11C3, MOD13C2 and MOD15A2 were downloaded from the NASA homepage [74], and MOD17A2 was downloaded from the University of Montana [65]. Regarding the spatial resolution of these MODIS products, MOD11C3 and MOD13C3 have 0.05-degree spatial resolutions; MOD15A2 and MOD17A2 have 1-km resolutions. All of these products are sinusoidally projected, and all data are monthly except MOD15A2 (8-day). To use these data in one model, we must unify them into the same projection, the same spatial resolution and the same temporal resolution.

First, all data were reprojected and masked from a sinusoidal projection to the Geographic WGS84 projection as a 0.05-degree pixels using the MODIS Reprojection Tool [75]. Then, MOD15A2 LAI/FPAR was monthly stacked. We employed the maximum value composite (MVC) method that selected the highest pixel value to represent the composting period [17,49].

The spatial variability of GPP and NPP over the global is enormous, ranging from approximately 1,000 g C m⁻² for evergreen tropical rain forests to less than 30 g C m⁻² for deserts. For bare areas such as the Sahara Desert in North Africa and deserts in central-eastern Asia and western China, there are no calculated GPP data, and the values were defined as 0 in the present study.

For the TANSO CO₂ data, we averaged all of the TANSO FTS Level 2 points in each month for each continent as the monthly value. From June 2009 to November 2011, there were 66,126 CO₂ points in Africa, and the point numbers were 21,088, 37,651, 11,796 and 10,504 in Australia, Eurasia, North America and South America, respectively.

The correlation coefficient (R), also called the Pearson correlation coefficient, provides an index of the degree of correlation between two datasets. In the present work, R² was used to indicate the strength of the correlation between the modeled data set and the observations. The present work also employed the root mean square error (RMSE) to analyze the error between predictions and observations. The RMSE was used to evaluate the error of the predicted and the uncertainty relative to the TANSO-observed XCO₂. The RMSE and R², provide information on the regional performance and uncertainty of the modeled CO₂ concentration.

MODIS-derived indices have different variations on different continents (Figure 2). In Eurasia and North America, all indices (LST, NPP, NDVI and LAI) change seasonally, with maximum values in summer (July or August) and minimum values in winter (January or February). The LST in Australia has the opposite trend from that found in Eurasia and North America, but the seasonal change is not as obvious. The fluctuation of NPP, NDVI and LAI are quite small in Africa, Australia and South America. South America always has the largest value of NPP, NDVI and LAI.

Eurasia and North America are located in Northern Hemisphere and the seasonal sensitivity of plant green-up and snow events are the main reasons of the changes in the indices. Australia is located in Southern Hemisphere, with a large percentage of bare areas leads to the small fluctuation of NPP, NDVI and LAI. The Amazon River Basin in South America has the highest vegetation cover in the world; thus, the NPP, NDVI and LAI are all higher in South America. The LST is closely associated with land-cover type, especially in bare areas [39], which is the main reason for higher value in of this parameter in Africa and Australia.

The R² and RMSE between TANSO XCO₂ and MODIS-derived indices were analyzed across months on each continent. The following nine indices were considered in the analysis: LST (of MOD11C3), EVI and NDVI (of MOD13C2), LAI and FPAR (of MOD15A2), GPP, NPP, GN (GPP minus NPP) and NG (NPP/GPP) (of MOD17A2).

Different correlation coefficients between TANSO XCO₂ and MODIS-based indices were found on different continents (Table 1). In Africa, the highest correlation coefficients were between XCO₂ and NPP (R² = 0.61 and RMSE = 1.21). Although the values between XCO₂ and NDVI and LST were not very high (R² = 0.39 and 0.24, RMSE = 1.53 and 1.70, respectively), but they meet the model indices select standard (see Section 4.3). In Australia, because the higher rate of bare areas can increase the reflectance of background, the highest correlation coefficient was between XCO₂ and LST (R² = 0.41, RMSE = 0.85). Although the bare areas in Eurasia are also extensive, the forests in Siberia and southern China increase the correlation between XCO₂ and NDVI and EVI (R² = 0.44 and 0.42, RMSE = 1.73 and 1.76, respectively). In North America, the correlation coefficients between XCO₂ and NDVI reached R² = 0.65 (RMSE = 1.15) and the lowest values that were selected for the TVP model is R² = 0.49 (between XCO₂ and LST and NDVI). In South America, the highest correlation coefficients were between XCO₂ and LST (R² = 0.64, RMSE = 1.39). The index of NG (R² = 0.19, RMSE = 2.09) were also selected for the model build.

The different values indicate that CO₂ concentration was influenced by different factors associated with different climate and land-cover types [2]. Table 1 also shows that LST was important in all five continents, which indicates that LST is an important factor in CO₂ concentration research. With regard to the selected indices in the five continents, only Australia had an average RMSE lower than 1; Eurasia had the highest averaged RMSE (1.87).

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 CO₂ 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 XCO₂ on each continent (Table 1). Then, we selected indices according to higher R², 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 CO₂ flux [30]; thus, we also tested the use of a single 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 R² 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 R² and RMSE between MODIS products and the TANSO XCO₂, we employed MODIS-derived indices that were selected for each continent as independent variables and TANSO XCO₂ as dependent variables of multivariate linear regression in Microsoft Office 2010 to model the CO₂ concentration on each continent. The TVP models for each continent are described below:

Africa: (5) CO 2 = 396.06 − 0.06 × LST + 89.49 × NDVI − 0.13 × GPP + 0.23 × NPP − 49.18 × NG

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 CO₂ concentrations for the five continents. The TVP model performance was then evaluated using scatter plots (Figure 3) of the predicted versus TANSO-observed CO₂ concentrations from June 2009 to November 2011.

Figure 3 shows that the correlation coefficient was not very high (R² = 0.57, RMSE = 0.73) in Australia. The TVP model provided better estimates of CO₂ concentration for Eurasia and South America (R² = 0.75 for both, RMSE = 1.16 and 1.17, respectively). The validation points of the TVP-modeled and TANSO-observed XCO₂ 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 (R² = 0.69 and 0.72, respectively). Thus, the results were very encouraging on all five continents. Notably, the higher R² values for the TVP-modeled CO₂ 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 CO₂ 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 XCO₂ is about 0.3∼1% and it must increasing the uncertainty of the correlations between predicted and observed CO₂ concentrations if we presume TANSO XCO₂ as true value. Moreover, in different continents the bias of TANSO XCO₂ 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 also shows that the slope of predicted versus observed CO₂ concentration was significantly lower than the 1:1 line, suggesting that the TVP algorithm somewhat underestimates high CO₂ concentration and overestimates low CO₂ 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.

Figure 4 shows the seasonal variation of CO₂ concentration and the differences between TVP-modeled and TANSO-observed CO₂ concentration. The TANSO XCO₂ time series showed a more pronounced seasonal variation and the extreme values appeared in different months on different continents. In Africa, the observed CO₂ concentration ranged between a maximum of 384.13 ppm and a minimum of 376.00 ppm between June 2009 and November 2011. The maximum and minimum appeared in March and September, respectively. The CO₂ concentration estimated by TVP model were overestimated before September 2010 and underestimated in 2011. The largest difference between the modeled and observed CO₂ concentration was −2.43 ppm, which occurred in September 2009. In Australia and South America, the maximum value of CO₂ concentration was usually in June or July and the minimum value appeared around December. Moreover, Figure 4 shows that the fluctuation of CO₂ concentration from June 2009 to December 2011 was very mild in Australia, where the difference between minimum and maximum value of TANSO XCO₂ was 4.17 ppm. This low fluctuation mainly results from the land-cover types in Australia, where bare areas covered 41.79%. The amount of CO₂ sequestered by desert soils is lower than by other soils [77]. Lack of plant photosynthetic is the main reason for the mildly seasonal change of CO₂ concentrations. The largest differences between TVP-modeled and TANSO-observed CO₂ concentration was 1.24 ppm in Australia and the average value is 0.62 and 0.95 ppm in Australia and South America, respectively. In Eurasia and North America, the minimum values of CO₂ concentration appeared in August and the maximum values appeared in April or March. The difference between minimum and maximum value of TANSO XCO₂ was 9.46 and 8.39 ppm in Eurasia and North America, respectively. In Eurasia, overestimating of CO₂ concentration by TVP model was found from June 2009 to April 2010 and underestimating appeared after December 2010. In North America, the overestimating happened from June 2009 to April 2010 (except December 2009) and from then on underestimating happened (except December 2010). The average difference between TANSO-observed and TVP-modeled CO₂ concentration was 0.97 and 0.84 ppm in Eurasia and North America, respectively. In Africa, the maximum overestimating of TVP model was 2.43 ppm in September 2009 and the maximum underestimating value was 1.86 ppm in February 2011.

Figure 4 also shows that in the study time scale, TANSO XCO₂ clearly increased in all the study areas. The maximum slope was in Eurasia (slope = 0.13) and the minimum slope was in Australia (slope = 0.09).

Some studies have used ground-based data to validate the CO₂ concentration estimated by TANSO and SCIAMACHY and found different results in different regions. TANSO XCO₂ with six ground-based Total Carbon Column Observing Network [78] sites around the world have been compared and found that the average bias of TANSO XCO₂ was 2.80 ppm [28]. Researchers also found that the computed errors of TANSO XCO₂ varied between 1.20 and 3.20 ppm [72]. With regard to the accuracy of SCIAMACHY CO₂ concentration, some researchers found that the global single-measurement precision amounted to 2.50 ppm [29,79]. In the present study, we used TANSO XCO₂ as the observed value to check the accuracy of TVP model and found that the accuracy in the study area was between −2.56∼3.14 ppm. Australia exhibited the lowest difference, at −1.24∼1.19 ppm, and the largest difference was in South America, at −2.09∼3.14 ppm. It indicates that the accuracy of TVP model is similar with the SCIAMACHY and TANSO.

Despite the encouraging performance of the TVP model in estimating CO₂ concentration from MODIS products, these estimates still contain significant uncertainties and are a long way from reliably estimating CO₂ concentration from remote sensing data. Although random error is usually considered less serious than uncertainties [31], there can be many sources of error that create a high overall uncertainty. The CO₂ exchange between terrestrial ecosystems and the atmosphere has been mainly dominated by three factors: climate, land-cover type and human activities [4,80–82]. With regard to the TVP model in the present study, there are several sources of uncertainty associated with the CO₂ concentration estimates: uncertainly in the TANSO accuracy, uncertainty in land cover, uncertainty in the input data and uncertainty regarding the extent and nature of climate change in different regions. Thus, there remains a great deal of research is still required to ensure the accuracy of CO₂ concentration estimated based on remote sensing data.

Although the TVP model itself has some shortcomings but it is a meaningful explore in CO₂ calculate using remote sensing data. The same as used MODIS, we can also use NOAA AVHRR data combine with ground stations data to derive CO₂ and CH₄ concentrations at regional or global scale. Using the TVP model we can derive global CO₂ concentration from 1981 to 2002 when there was no GHG satellite. In fact, we can also use TVP model to identify the spatial distribution of GHG concentrations which is also an important issue nowadays. Moreover, in the future, with the launching of other GHG observe satellites, e.g., Orbiting Carbon Observatory 2 (OCO-2), Carbon Monitoring Satellite (CarbonSat) and GOSAT-2, the accuracy of TVP model will increasing.