## 2 Analytical Method
### Selection of Geometrically Matched-Up Data  
The GOSAT spacecraft is in a sun-synchronous orbit at an altitude of 666 km, with a descending node local time between 12:46 p.m. and 12:55 p.m., and a revisit cycle of three days. OCO-2 flies at the head of the 705 km A-train, in an ascending orbit with a nodal crossing time between 13:35:30 and 13:36:20. Table 2 summarizes geometric information of GOSAT and OCO-2. The local time of the descending GOSAT sun-synchronous orbit and the ascending OCO-2 differ by between about 40 and 50 min.  
Since August 2010, the GOSAT 2-axis pointing mechanism has executed a nominal 3-point cross-track scan mode over land. GOSAT uses a target mode to acquire observations over large emission sources and calibration/validation sites, and uses a glint mode over ocean. OCO-2 has four Earth-surface observation modes: Nadir, Glint, Transition and Target. For nominal science operations, the spacecraft points the instrument at the local nadir, which provides more useful, cloud-free samples over land, or near the glint spot, which provides much higher signal-to-noise ratios (SNR) over the ocean. In addition to the nadir and glint observing modes, OCO-2 has a target mode that points the instrument's boresight at a specified surface target, such as a vicarious calibration site or TCCON validation site to acquire thousands of observations near that target as the spacecraft flies over. When OCO-2 is near the southern terminator, where the slit is oriented almost perpendicular to the ground track, each of the eight cross-track footprints has dimensions of 1.29 km \(\times\) 2.25 km across a 10.6 km swath at nadir. However, the orientation of the slit rotates along the orbit track to maintain a constant orientation with respect to the principal plane, defined by the sun, the surface footprint, and the spacecraft aperture, such that the swath has a minimum width \(<\)0.3 km about 30 degrees north of the sub-solar latitude.  
The much larger GOSAT circular footprint covers dozens of OCO-2 footprints, as illustrated in Figure 1. A single GOSAT pixel includes a maximum of 40 OCO-2 pixels with nadir or glint mode, and more than one thousand in target mode. These OCO-2 pixels were averaged to yield one OCO-2 sample. We compared spectral radiances and retrieved XCO\({}_{2}\) for a single GOSAT footprint with this averaged OCO-2 sample as one match-up point. The broad spectral coverage of the GOSAT TANSO-FTS covers all the OCO-2 narrow spectral bands. GOSAT has slightly better spectral resolution as shown in Table 1, but OCO-2 has higher spectral contrast, such that both GOSAT and OCO-2 have enough spectral resolution to distinguish each absorption line from the continuum.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Satellite** & **GOSAT** & **OCO-2** \\ \hline
**Orbit Height** & 666 km & 705 km \\ \hline
**Inclination** & 98.1 degrees & 98.2 degrees \\ \hline
**Local Time** & 12:46–12:55 LT & 13:35:30–13:36:20 LT \\ \hline
**Recurrent Period** & 3 day & 16 day \\ \hline
**Repeat Orbits** & 44 & 233 \\ \hline
**Swath** & \(\pm\)35 degrees & 10.6 km (nadir) \\ \hline
**Pointing** &
\begin{tabular}{c} Multiple targets with a 2-axis \\ pointing mechanism \\ \end{tabular} & Nadir, Glint, Transition or Target \\ \hline
**Footprint (Nadir, Nominal)** & Circle of 10.5 km diameter & Parallelogram of 1.29 km \(\times\) 2.25 km \\ \hline \hline \end{tabular}
\end{table}
Table 2: Orbit and observation geometry of GOSAT and OCO-2.  
In this work, we compared spectral radiance and retrieved XCO\({}_{2}\) at temporally coincident and spatially collocated points. We selected \(\pm\)1 h match-up time and made a correction for solar zenith angle (SZA) differences by dividing by cosine of the local solar zenith angle.