## 5 Discussion  
### Error in BRDF Correction  
One possible reason why GOSAT high gain observations have larger bias and standard deviation in radiance spectra over land than over ocean is BRDF variability. Over land match-up observations do not always have similar geometry, whereas over ocean both GOSAT and OCO-2 target the glint point with similar geometry. For coincident observations over RRV, while GOSAT has only four scenes per orbit, OCO-2 acquires thousands of observations by maneuvering the satellite. The RRV site is located between GOSAT paths 36 and 37 and OCO-2 paths 137 and 139. We can analyze the effect of the BRDF correction by comparing the data targeted from the east and west. We selected two cases; 29 June 2015, when both GOSAT and OCO-2 viewed the RRV target from the sun direction (West), and 1 July 2015, when both GOSAT and OCO-2 viewed RRV from the direction opposite to the sun (East). The former case has a backward scattering geometry and BRDF changes rapidly with viewing angle. Figures 10 and 11 show the OCO-2 and GOSAT spectra radiance plotted against sensor azimuth and zenith angles during RRV target observations on 29 June 2015 and 1 July 2015, respectively. As shown in these figures, OCO-2 targeted RRV with sensor zenith angles from 10 to 75 degrees. The spectral radiances  
Figure 9: \(\Delta\)XCO\({}_{2}\) as a function of (**a**) GOSAT/ACOS retrieved AOD at 0.755 \(\upmu\)m; (**b**) GOSAT/ACOS retrieved surface pressure and (**c**) OCO-2 ABO2 \(\sigma_{allbda}\) over land with high gain. The lower panels (**d–f**) show same parameters as the above panels over land with medium gain. All match-up data were plotted with gray marks. The green and red plots and bars are the average value and standard deviation within each bin. The bin sizes are (**a**) 0.05; (**b**) 20 hPa and (**c**) 0.02. The upper panel shows over land with high gain and the lower panel shows medium gain. are plotted at wavelengths of (a) 0.768 \(\upmu\)m in the ABO2 band, (b) 1.606 \(\upmu\)m in the WCO2 band and (c) 2.061 \(\upmu\)m in the SCO2 band. The lower figures (d-f) represent BRDF corrected spectral radiances at the same wavelengths as the upper figures. The BRDF correction was applied to both GOSAT and OCO-2 using the MODIS BRDF product [32]. The spectral radiance variation of OCO-2 spectral radiance within the GOSAT IFOV is larger than forward scattering. After the BRDF correction, the variation of spectral radiance within the GOSAT IFOV becomes small but still is not constant. As the MODIS BRDF model is more accurate between 0 to 55 degrees, we selected the data with the sensor zenith angle of less than 55 degrees [39]. In addition, we selected the GOSAT sensor zenith angles of 38 degrees and 28 degrees on 29 June 2015 and on 1 July 2015, respectively. Table 3 summarizes the spectral radiance of GOSAT and averaged OCO-2 with and without BRDF correction and selected data with the truncated sensor zenith angles. Table 4 shows the standard deviation of spectral radiance divided by the average. The deviation becomes smaller than 5% after applying the BRDF correction and the truncated sensor zenith angle. Figure 12 shows the OCO-2 and GOSAT retrieved XCO\({}_{2}\) on (a) 29 June 2015 and (b) 1 July 2015. The current retrieval algorithm has yet to take account of the BRDF correction, but it can help to minimize the uncertainties of XCO\({}_{2}\) retrieval, especially in large off-nadir viewing geometry scenes.