## 4 Postprocessing
### Bias Correction
\begin{cases}-0.974\,\text{ppm}&\text{if $f=1$,}\\ -0.336\,\text{ppm}&\text{if $f=2$,}\\ -0.234\,\text{ppm}&\text{if $f=3$,}\\ -0.315\,\text{ppm}&\text{if $f=4$,}\\ -0.856\,\text{ppm}&\text{if $f=5$,}\\ 1.013\,\text{ppm}&\text{if $f=6$,}\\ 0.484\,\text{ppm}&\text{if $f=7$,}\\ 1.219\,\text{ppm}&\text{if $f=8$.}\\ \end{cases}  \tag{5}\]  
In order to determine the land/sea bias, we corrected all post-filtered results for the footprint bias and analyzed all coastline overpasses with a maximum duration of 120 s (\(\approx\)800 km along track), at least 100 soundings, and a land fraction between 30% and 70%. For each of these coastline overpass (162 with about 102,000 soundings, Figure 10, right) we computed the land/sea anomaly and hence the average land/sea anomaly (\(\pm\)0.8986 ppm). Figure 10 (left) shows the land/sea bias pattern corresponding to the bias function  
\[B_{\text{ls}}(l)=0.8986\,\text{ppm}\,\,(2\,l-1) \tag{6}\]  
with \(l\) being the land/sea fraction. Figure 9: FOCAL v06 OCO-2 footprint bias pattern (Equation (5)) at the example of August 2015 (**left**) and sampling of soundings used to determine the footprint bias (**right**). In addition to the footprint and land/sea biases, we found a small correlation (\(\rho=0.16\)) between small scale anomalies of XCO\({}_{2}\) and the retrieved ILS squeeze in the wCO\({}_{2}\) fit window ILS\({}_{\text{sq}}^{\text{wCO${}_{2}$}}\). The small scale anomalies have been computed from 60 s chunks (\(\approx\)400 km) of post-filtered and footprint and land/sea bias corrected OCO-2 orbit data with more than 10 soundings. In total about 5000 chunks with one million soundings (Figure 11, right) have been analyzed to compute the linear bias model (Figure 11, left):  
\[B_{\text{lin}}(\text{ILS}_{\text{sq}}^{\text{wCO${}_{2}$}})=107.936\,\text{ppm }\cdot\text{ILS}_{\text{sq}}^{\text{wCO${}_{2}$}}-107.862\,\text{ppm}\,. \tag{7}\]  
Finally, we correct for a global offset in respect to the optimized CO\({}_{2}\) concentration fields of the CAMS (Copernicus Atmosphere Monitoring Service) greenhouse gas flux inversion model [29] obtained from [[http://apps.ecmwf.int](http://apps.ecmwf.int)]([http://apps.ecmwf.int](http://apps.ecmwf.int)). CAMS is the CO\({}_{2}\) atmospheric inversion product of the European Union programme Copernicus that develops information services based on satellite Earth observation and other data ([[http://www.copernicus.eu/](http://www.copernicus.eu/)]([http://www.copernicus.eu/](http://www.copernicus.eu/))). The product is released twice per year and each time covers the full period from 1979 until the year before the release. It results from an analysis of CO\({}_{2}\) surface air sample measurements over the corresponding period and consists of optimized CO\({}_{2}\) surface fluxes over the globe and of associated 3D CO\({}_{2}\) concentrations. Version 15r4 used here analyzed 37 years of surface measurements (1979-2015). Its spatial resolution is of 3.75\({}^{\circ}\) in longitude and 1.875\({}^{\circ}\) in latitude, with 39 hybrid layers in the vertical. A full description of v15r4 is given by [PERSON] [30], showing also, among other validation results, that its root-mean-square fit to TCCON  
Figure 11: FOCAL v06 bias pattern of the linear bias model (Equation (7)) at the example of August 2015 (**left**) and sampling of soundings used to determine the linear bias model (**right**). Figure 10: FOCAL v06 land/sea bias pattern (Equation (6)) at the example of August 2015 (**left**) and sampling of soundings used to determine the land/sea bias (**right**). measurements is usually close to 1 ppm. The global offset of FOCAL v06 relative to the CAMS model amounts:  
\[B_{\mathrm{g}}=-1.673\,\mathrm{ppm}\,. \tag{8}\]  
Figure 12 (left) shows an example of the total bias pattern consisting of all four components (footprint bias, land/sea bias, linear bias model, global bias). As can be seen, the large scale pattern of the total bias is dominated by the land/sea bias followed by the footprint bias and the linear bias model plays only a minor role.