## 3 Spectral Radiance Inter-Comparison  
### Methodology of Spectral Radiance Inter-Comparison  
For statistical and trend analysis, we used the global dataset from September 2014 to March 2017. We selected five continuum points in each band as illustrated in Figure 2, each with very weak spectral absorption. We filtered out cloud contamination, ice or snow-covered surfaces, as well as the inhomogeneity of surface reflectance and terrain by visually checking all the CAM images for color contrast. This step was necessary because the cloud filter using the ABO2 band sometimes passes partially cloud contaminated scenes [31]. Besides, ice and snow surfaces have high reflectance in the ABO2 band but are almost black in the WCO2 and SCO2 bands. Figure 1: GOSAT and OCO-2 orbit direction and observation strategy. Figure 2: The wavelengths evaluated in each band; **(a)** ABO2; **(b)** WCO2 **(c)** SCO2 bands. As noted above, GOSAT and OCO-2 have different observation geometries and most of the land surface scenes are not perfect Lambertian reflectors. We corrected off-nadir viewing over land to nadir viewing spectra using the 1 km resolution MODerate resolution Imaging Spectroradiometer (MODIS) BRDF-Albedo Model Parameters product (MCD43B1) [32]. This product is made using cloud-free data measured by MODIS instruments on the Terra and Aqua satellites over 16-day periods [33]. The BRDF product applied MODIS Band 2 (841-876 nm), Band 6 (1628-1652 nm) and Band 7 (2105-2155 nm) to ABO2, WCO2 and SCO2 bands, respectively. Figure 3 shows BRDF plots of the ABO2 band, WCO2 band and SCO2 band for a non-Lambertian desert surface. Using these BRDF parameters, we corrected to nadir equivalent spectral radiance. The BRDF correction was applied to OCO-2 footprints individually using the nearest neighbor pixel of MODIS BRDF product. The BRDF corrected OCO-2 radiance averaged within the GOSAT IFOV. For GOSAT, the MODIS BRDF products were averaged within the GOSAT IFOV and applied for the GOSAT radiance. The BRDF corrected spectral radiances of GOSAT and OCO-2 were calculated as follows,  
\[\mathrm{L_{GOSAT\_nadir}}=\frac{\sum_{i}^{IFOV}(\mathrm{BRDF_{nadir}(i)})}{ \sum_{i}^{IFOV}(\mathrm{BRDF_{offnadir}(i)})}\mathrm{L_{GOSAT\_offnadir}} \tag{1}\]  
\[\mathrm{L_{OCO-2\_nadir}}=\sum_{j}^{IFOV}\biggl{(}\frac{(\mathrm{BRDF_{nadir} (j)})}{(\mathrm{BRDF_{offnadir}(j)})}\biggr{)}\mathrm{L_{OCO-2\_offnadir}(j)} \tag{2}\]  
where \(L_{GOSAT\_offnadir}\) and \(L_{OCO-2\_offnadir}\) are the off-nadir spectral radiances of GOSAT and OCO-2, respectively. \(BRDF_{nadir}\) and \(BRDF_{offnadir}\) are the nadir and off-nadir BRDF parameters calculated from the MODIS BRDF product. \(L_{GOSAT\_nadir}\) and \(L_{OCO-2\_nadir}\) are the corrected nadir equivalent spectral radiances. IFOV indicates summation within the GOSAT IFOV. The index \(i\) specifies the number of MODIS pixels within the GOSAT IFOV. The index \(j\) specifies the number of OCO-2 pixels within the GOSAT IFOV. Because of the cross-track viewing used for the GOSAT grid observations and nadir viewing for OCO-2, the BRDF difference can often exceed 10%. The correction errors remain due to the imperfect MODIS model. Details will be discussed in Section 5.1. We also adjusted the OCO-2 spectral dispersion to the GOSAT data by shifting and stretching the OCO-2 spectra. GOSAT measures two linear polarizations (P and S) with perpendicular directions, whereas OCO-2 measures one linear polarization. GOSAT used the FTS technology with polarization sensitivity lower than grating spectrometers and most of the observed scenes are not polarized. We averaged GOSAT P and S polarization vectors to produce an approximation of the total radiance which should  
Figure 3: Example of BRDF polar plots at the RRV desert surface on 30 July 2015 created from the MODIS MCD43B1 product. Latitude, longitude and solar zenith angle are 38.471 degrees, \(-\)115.653 degrees and 25 degrees, respectively. The radial direction is the viewing zenith angle where the center is for a nadir view angle (viewing zenith = 0 degrees).