## 4 Retrieved XCO\({}_{2}\) Product Inter-Comparison
### Retrieved XCO\({}_{2}\) Inter-Comparison Result  
Figure 6 shows the global map of retrieved XCO\({}_{2}\) differences between GOSAT/ACOS and OCO-2 at matched-up points with (a) high gain and (b) medium gain. The number of match-up points is  
Figure 5: (**a**) The fractional difference in spectral radiance for GOSAT and OCO-2 is shown as a function of the GOSAT radiance amplitude. Blue and red dots represent high and medium gains, respectively; (**b**) Spectral radiance ratio at the center of wavelengths shown in Figure 2. For both panels (**a,b**), the upper, middle and lower figures represent the ABO2, WCO2 and SCO2 bands, respectively. 934 for high gain and 296 for medium gain. We define \(\Delta\)P\({}_{\text{surf}}\) and \(\Delta\)XCO\({}_{2}\) as follows to analyze the difference in retrieved parameters:  
\[\Delta\)P\({}_{\text{surf}}=\text{P}_{\text{surf}_{\text{GOSAT/ACOS}}}-\text{P}_{ \text{surf}_{\text{OCO-2}}} \tag{3}\]  
\[\Delta\)XCO\({}_{2}=\text{XCO}_{\text{2 GOSAT/ACOS}}-\text{XCO}_{\text{2 OCO-2}} \tag{4}\]  
There are some large differences (\(>\)5 ppm), especially over land. Figure 7 shows the correlation between GOSAT/ACOS XCO\({}_{2}\) and OCO-2 XCO\({}_{2}\) for matched observations (a) over land with high gain, (b) over ocean with high gain, and (c) over land with medium gain, respectively. Figure 7d shows the histogram of the above three cases. The mean biases and standard deviations are (a) \(-\)0.57 \(\pm\) 3.33 ppm, (b) \(-\)0.17 \(\pm\) 1.48 ppm and (c) \(-\)0.19 \(\pm\) 2.79 ppm. Both bias and standard deviation are lower over ocean than over land. The GOSAT FTS analog circuits all have flat frequency-dependent responses, with the exception of high gain Band 1 [1]. The GOSAT FTS medium gain does not require nonlinearity correction, which may cause biases in \(\Delta\)P\({}_{\text{surf}}\) and \(\Delta\)XCO\({}_{2}\). Even though the bias corrected GOSAT/ACOS V7.3 Lite products are not available for medium gain, we expect much lower bias in the non-bias corrected GOSAT/ACOS V7.3 Full product over the bright desert target. Figure 6: The plots show \(\Delta\)XCO\({}_{2}\) between GOSAT/ACOS and OCO-2 with (a) high gain and (b) medium gain observations. Figure 8 shows the time series of \(\Delta\)XCO\({}_{2}\) and \(\Delta\)P\({}_{\text{surf}}\) for high gain over land, high gain over ocean and medium gain over land. There is no significant time dependent variation of \(\Delta\)XCO\({}_{2}\) for either high or medium gain. However, there are small quasi-periodic structures in \(\Delta\)P\({}_{\text{surf}}\) below the uncertainty level. The time dependent structures suggest the possibility of an estimation error in the \"fast\" degradation of the OCO-2 ABO2 band, imperfect radiance degradation correction of GOSAT and or OCO-2, seasonal cycle, zero-level offset in the GOSAT Band 1 or the effect of solar induced chlorophyll fluorescence [37]. To investigate the root cause of the \(\Delta\)XCO\({}_{2}\) bias, Figure 9 shows \(\Delta\)XCO\({}_{2}\) plotted as a function of GOSAT/ACOS retrieved Aerosol Optical Depth (AOD) at 0.755 \(\upmu\)m, GOSAT/ACOS retrieved surface pressure and the standard deviation of OCO-2 retrieved ABO2 albedo within the GOSAT IFOV over land with both high gain and medium gain. We compared the GOSAT/ACOS retrieved AOD with AERONET data at optically thick sites such as Beijing, Paris and Pasadena [38]. The AERONET AOD does not have AOD at 0.755 \(\upmu\)m, therefore we converted the value using Angstrom index between 0.870 \(\upmu\)m and 0.675 \(\upmu\)m. The slope with linear regression of GOSAT/ACOS and AERONET AOD at three sites are 0.818, 0.547 and 0.606, respectively. The squares of the Person correlation coefficient, R\({}^{2}\), are 0.470, 0.568, and 0.243, respectively. The trend of both products agrees well.