# XCO\({}_{2}\) Fusion Algorithm Based on Multi-Source Greenhouse Gas Satellites and CarbonTracker
## 4 Results and Analysis
### Fusion of XCO\({}_{2}\) Datasets Based on the TC Algorithm  
Due to the errors from the satellite inversion algorithm, the limitations of the Earth's surface and atmospheric conditions, the CO\({}_{2}\) concentrations obtained by satellite have a certain deviation. The CT model obtains the CO\({}_{2}\) concentrations through the data assimilation method, which leads to its excessive dependence on the surface observation data. The CO\({}_{2}\) concentrations obtained in high latitudes and other areas where it is difficult to obtain the observation data have larger deviations, so there are certain random errors in the CO\({}_{2}\) concentrations observed by the satellite and assimilation model. In this study, the  
Figure 1: Distribution of coverage of OCO-2 and GOSAT XCO\({}_{2}\) for the first half of the month (**left graphs**) and a full month (**right graphs**) in January 2018. The satellite observation data are displayed in dark blue, and the interpolated data are displayed in light blue.  
Figure 2: Half-monthly XCO\({}_{2}\) data coverage before and after interpolation of OCO-2, GOSAT, and CT in 2018.  
TC algorithm was used to evaluate the uncertainty of three XCO2 products of interpolated OCO-2, GOSAT, and CT. In order to reveal the influence of the time length of the input dataset on obtaining the random error, this study compared the random errors obtained from three different time series of one year, two years, and one month. As shown in Table 4, the differences in random errors between the two-year time series of OCO-2, CT, and GOSAT and the one-year time series are 0.0082, 0.0081, and 0.0349, while the differences in random errors between the two-year time series and the one-month time series are 0.0646, 0.0632, and 0.1505. It shows that the length of the time series has an important impact on the stability of the TC algorithm. When the time series of input data is short, the robustness of the TC algorithm is poor. In this study, the data from 2017 to 2018 were selected as the input dataset. The random errors obtained are CT of 0.5273 ppm, OCO-2 of 0.6346 ppm, and GOSAT of 0.7995 ppm from small to large. The traditional arithmetic average method cannot minimize the random error of the combined results, and the equal weighting coefficient will lead to the introduction of large random errors from GOSAT data, which are particularly obvious in high latitudes. Therefore, the fusion weight should be determined according to the characteristics of the data. Based on the least square principle, combined with the random error based on TC estimation, the weights of the three datasets were calculated by Equation (11). The weights of CT, OCO-2, and GOSAT are 0.4015, 0.3337, and 0.2648, respectively, as shown in Table 5. Among them, the CT with the smallest random error has the largest weight, followed by OCO-2 and GOSAT. This means that the XCO2 dataset generated by fusion depends more on CT data. When a \(1^{\circ}\times 1^{\circ}\) grid fails to simultaneously have the three XCO2 data, it is filled with the CT data. Otherwise, it is filled with a new XCO2 value according to the obtained weights. The results of the TC algorithm fusion in 2018 are shown in Figure 3.  
Figure 3: XCO2 distribution of fusion dataset in 2018.