## 2 Analytical Method
### Spectral Radiance Data and Retrieved XCO\({}_{2}\) for the Inter-Comparison
The slow degradation term is caused by a reduction in the throughput of the solar diffuser, perhaps associated with degradation of the gold coatings on its active inner surfaces. The current V7 L1B product (OCO2_L1B_Science.7) has an ABO2 band-degradation correction term applied, without discrimination between the fast and slow degradation. In total, the radiometric performance is determined using the solar diffuser, lamp diffuser, the Moon, and well-characterized vicarious calibration targets. OCO-2 produces two sets of L1B and Level2 (L2) products. The \"forward\" products (OCO2_L1B_Science.7) are distributed within one week of acquisition. This product uses calibration information based on extrapolations of calibration data that were collected in the recent past. The \"retrospective\" products, (OCO2_L1B_Science.7r) use interpolated calibration data, which is expected to be more reliable, and is distributed approximately one month later after data acquisition. Basically, the retrieval algorithms of GOSAT and OCO-2 used here are the same ([PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] et al., 2016). XCO\({}_{2}\) is retrieved with the full physics algorithm. GOSAT retrievals used Build 7.3 (V7.3) of the Atmospheric CO\({}_{2}\) Observations from Space (ACOS) algorithm while OCO-2 retrievals used Version 7 of the OCO-2 retrieval algorithm. The solution of inverse method is the state vector with maximum a posteriori probability, given the measurement. The inverse method employs the Levenberg-Marquardt modification of the Gauss-Newton method. The solar spectrum used in the forward model is comprised of a pseudo-transmittance spectrum, which was developed by [PERSON] and colleagues ([PERSON] et al., 2016), and a solar continuum spectrum, which is based on polynomial fits to the low-resolution extra-terrestrial solar spectrum acquired by the Solar Spectrum (SOLSPEC) instrument ([PERSON] et al., 2016). The algorithm adopted absorption coefficient (ABSCO) tables, which consider line mixing, speed dependent line shape, and collision induced absorption (CIA). The CO\({}_{2}\) a priori profiles are from a climatology based on the GLOBALVIEW dataset at the time of year and the latitude of the site. A single CO\({}_{2}\) covariance matrix is used for all retrievals. This covariance has been constructed by assuming a root-mean-square variability of XCO\({}_{2}\) of 12 ppm. For the XCO\({}_{2}\) comparison analysis, we mainly use the GOSAT/ACOS_L2_Lite_FP.7.3 (GOSAT/ACOS Lite V7.3) product and GOSAT/ACOS_L25.7.3 (GOSAT/ACOS Full V7.3) product from GOSAT L1B V201 and OCO2_L2_Lite_FP.7r (OCO-2 Lite V7r) product from OCO2_L1B_Science.7r. Both GOSAT/ACOS V7.3 and OCO-2 V7 algorithms were developed by the JPL/OCO-2 team, and are identical except for use of specific instrument-dependent parameters and individual bias correction. This allows the comparison of GOSAT/ACOS and OCO-2 data without consideration of algorithm differences. The retrieved state vector contains the CO\({}_{2}\) mole fraction at 20 layers, surface pressure, aerosol profile, two aerosol types, cloud water, cloud ice, albedo, albedo slope and wind speed over ocean. The details are described in Table 2 of [PERSON] et al. (2016). Because the O\({}_{2}\) dry air mole fraction is well known, measurements from the GOSAT Band 1 and OCO-2 ABO2 band are used to retrieve surface pressure, P\({}_{\text{surf}}\), and to estimate light attenuation and scattering by thin clouds and aerosols. The GOSAT/ACOS product was validated with TCCON ([PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] et al., 2016). GOSAT has taken measurements in the vicinity of all TCCON sites with high gain, except for Armstrong Flight Research Center (AFRC) TCCON, where medium gain is used. We used the GOSAT/ACOS V7.3 Full Product without bias correction and with the recommended filtering, only for medium gain data, and GOSAT/ACOS V7.3 Lite, with bias correction and recommended filtering for high gain data. The XCO\({}_{2}\) bias level of the medium gain data has not been evaluated yet.