## 4 Postprocessing  
### Filtering  
First of all, we check for convergence, i.e., the state vector increment has to be small compared to the a posteriori uncertainty, the maximum number of iterations must not exceed 15, and \(\chi^{2}\) must not exceed 2 (for more details, see part 1[23]).Convergence is achieved in about 74% of all pre-filtered OCO-2 soundings. Many non-converging soundings can be found near the SAA, the Saharan desert, and the Arabian peninsula (Figure 7). In the next step, we check for each fit window if the RSR is smaller than the threshold for potential outliers defined in Section 3.1. The throughput of this filter, which is most active above the tropical oceans (Figure 7), is about 68%. Additionally, we filter for potential outliers by parameters that have a unexpectedly large influence on the retrieved local XCO\({}_{2}\) variability. For the example data shown in Figure 7, this filter is most active in high latitudes and has a throughput of about 84%. This filter bases on the idea that XCO\({}_{2}\) outliers increase the local retrieved XCO\({}_{2}\) variability and are likely correlated with extreme values of some of the candidate parameters: XCO\({}_{2}\) uncertainty \(\sigma\)XCO\({}_{2}\), lowermost layer of the CO\({}_{2}\) column averaging kernel, XH\({}_{2}\)O, XH\({}_{2}\)O uncertainty \(\sigma\)XH\({}_{2}\)O, XH\({}_{2}\)O difference to the a priori, continuum radiance in the O\({}_{2}\) (I\({}_{\mathrm{cont}}^{\mathrm{O_{2}}}\)), wCO\({}_{2}\) (I\({}_{\mathrm{cont}}^{\mathrm{wCO_{2}}}\)), and sCO\({}_{2}\) (I\({}_{\mathrm{cont}}^{\mathrm{sCO_{2}}}\)) fit window, gradient between first and second CO\({}_{2}\) layer \(\
abla\)CO\({}_{2}\), albedo difference between the O\({}_{2}\) and sCO\({}_{2}\) fit window, and all non CO\({}_{2}\) and H\({}_{2}\)O state vector elements [23]. For a representative two months data set (April and August 2015), we estimated the local retrieved XCO\({}_{2}\) variability VAR(AXCO\({}_{2}\)) as follows: For each sounding, we computed the difference \(\Delta\)XCO\({}_{2}\) between XCO\({}_{2}\) and its \(5^{\circ}\times 5^{\circ}\) daily median and subsequently, we computed the variance of all \(\Delta\)XCO\({}_{2}\) values falling in grid boxes with more than 100 samples. Now we searched for an upper or lower threshold for that candidate parameter which reduces VAR(\(\Delta\)XCO\({}_{2}\)) most when removing 1% of all data points. We repeated this until 15% of all data points were removed. In order to reduce the complexity of the postprocessing filter procedure, we now identified the 10 most promising parameters separately for land and ocean and repeated the whole exercise to find filter thresholds for these 10 parameters. Figure 6: Retrieved zero level offset (ZLO) versus continuum radiance (I\({}_{\mathrm{cont}}\)) for all four fit windows. gray dots: potential outliers, (i.e., no convergence, \(\chi^{2}>2\), or RSR exceeding threshold (see Figure 4)). green line: linear fit. Figure 8 shows (especially for land) that the decrease in variability somewhat reduces after the removal of the first 5-10%. A potential interpretation is that in this range indeed primarily outliers are removed. After the removal of approximately 15% the decrease in variability is relatively constant over a larger range before it drops to zero when the last data points are removed. As the curves do not show a distinct kink, the choice to remove 15% of all data points is a bit arbitrary but seems to be a good compromise. Figure 8: Variance versus filter throughput for the 10 most promising parameters identified for the potential outliers filter. The colors represent the prorated variance reduction of the individual parameters. See part 1 [(23)] and the main text for a description of the individual parameters. (**left**) Land; (**right**) Sea. Figure 7: Post-filtering statistics for April and August 2015. The filters are applied in the order: convergence, residual, and potential outliers (see main text for a description).