## 4 Postprocessing
### Bias Correction  
The basic assumption of the bias correction scheme is that on average XCO\({}_{2}\) has little variations on small scales so that correlations to more variable parameters can be used to quantify biases. As a consequence, the bias correction does not require any ground truth data except for the quantification of a globally constant offset. The final bias model consists of four components: a footprint bias \(B_{\text{f}}\), a land/sea bias \(B_{\text{ls}}\), a linear bias model \(B_{\text{lin}}\), and a globally constant bias \(B_{\text{g}}\):  
\[B=B_{\text{f}}+B_{\text{ls}}+B_{\text{lin}}+B_{\text{g}}\,. \tag{4}\]  
These four components are successively derived from analyses of the same two months data set (April and August 2015) used to determine the thresholds of the potential outliers filter (Section 4.1). The swath of OCO-2 consists of eight neighboring footprints across track. In order to determine the mean footprint anomaly, we used only soundings belonging to complete sets of eight neighboring soundings which all passed the post-filtering and which were entirely over land or sea. Figure 9 (right) shows the sampling of the roughly 180,000 soundings where this is the case. For each of these sets of \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Lower** & **Upper** & **Variance Reduction [\%]** \\ \hline \multirow{8}{*}{Land} & \(\Delta\) & 1.6669 & - & 38 \\  & \(\sigma\)XCO\({}_{2}\) [ppm] & - & 1.2963 & 17 \\  & \(\text{IL}_{\text{sq}}^{\text{sCO}_{2}}\) & - & 1.0022 & 16 \\  & \(\text{Pr}\) [Po] & \(-1.6435\times 10^{-1}\) & 2.2603 \(\times 10^{-1}\) & 11 \\  & \(\text{VCO}_{2}\) [ppm] & 5.2509 & 5.9995 & 11 \\  & \(\lambda_{\text{sq}}^{\text{wCO}_{2}}\) [mm] & \(-5.2186\times 10^{-4}\) & 3.9367 \(\times 10^{-5}\) & 2 \\  & \(\text{IL}_{\text{sq}}^{\text{wCO}_{2}}\) & - & 1.0041 & 1 \\  & \(\lambda\Omega\) [mm] & \(-\) & \(-2.5907\times 10^{-5}\) & 2 \\  & \(\lambda\Omega\) [mm] & \(-6.6146\times 10^{-4}\) & 9.2043 \(\times 10^{-4}\) & 1 \\  & \(\sigma\)XH\({}_{2}\)O [ppm] & - & 15.705 & 1 \\ \hline \multirow{8}{*}{Sea} & \(\lambda_{\text{sq}}^{\text{wCO}_{2}}\) [mm] & \(-3.1372\times 10^{-4}\) & \(-8.2869\times 10^{-5}\) & 32 \\  & \(\text{AP}_{\text{sq}}^{\text{sIF}}\) & \(-2.3184\times 10^{-3}\) & \(3.4846\times 10^{-3}\) & 20 \\  & \(\text{AP}_{\text{2}}^{\text{pD}_{2}}\) & - & \(1.7900\times 10^{-4}\) & 19 \\  & \(\lambda_{\text{sh}}^{\text{wCO}_{2}}\) [mm] & - & \(2.1023\times 10^{-3}\) & 9 \\  & \(\text{IL}_{\text{sq}}^{\text{sQ}}\) & - & 1.0175 & 4 \\  & \(\text{AP}_{\text{2}}^{\text{wCO}_{2}}\) & - & \(-2.1247\times 10^{-4}\) & 5 \\  & \(\text{AP}_{\text{2}}^{\text{wCO}_{2}}\) & \(3.2736\times 10^{-4}\) & - & 4 \\  & \(\text{I}_{\text{cont}}^{\text{wCO}_{2}}\) [\(1.25\times 10^{20}\) Ph/s/m\({}^{2}\)/mm] & \(5.6468\times 10^{-2}\) & - & 4 \\  & \(\lambda_{\text{sh}}^{\text{wCO}_{2}}\) [mm] & \(-3.4860\times 10^{-4}\) & - & 2 \\  & \(\hat{\text{A}}\) & 1.9014 & - & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thresholds and prorated variance reduction of the 10 parameters of the potential outliers filter for soundings above land (**top**) and sea (**bottom**). In total, the variance of \(\Delta\)XCO\({}_{2}\) is reduced from 2.05 ppm\({}^{2}\) to 1.68 ppm\({}^{2}\) above land and reduced from 1.22 ppm\({}^{2}\) to 1.09 ppm\({}^{2}\) above sea. See part 1 [23] and the main text for a description of the individual parameters. eight soundings, we compute the footprint anomaly and subsequently the average footprint anomaly of all sets which we then use as bias function. Figure 9 (left) shows the footprint bias pattern at the example of all soundings passing the post-filtering in August 2015 and the corresponding bias function depending on the footprint \(f\) is:  
\[B_{\text{f}}(f)=