## 3 Retrieval Adaptations
### Zero Level Offset Correction  
We define as zero level offset (ZLO) an additive fit window-wide radiance offset. An apparent or effective ZLO can have various reasons such as residual calibration errors or unconsidered spectroscopic effects. Many of these effects can be expected to result in ZLOs being approximately proportional to the fit window's continuum radiance. In order to study potential ZLOs, we used the same modified FOCAL setup as in the last section but with the just defined noise model. The simultaneous retrieval of ZLOs reduce the uncertainty reduction for XCO\({}_{2}\) and renders the SIF retrieval impossible. Therefore, we aimed at a ZLO correction rather than a ZLO retrieval per sounding. We analyzed the same 24 days of OCO-2 data as in the last section but filtered for potential contamination with chlorophyll fluorescence because in the SIF fit window it is not possible to disentangle ZLO and SIF (Figure 5). For this purpose, we used monthly L3 MODIS Aqua chlorophyll-a data (obtained from [[https://modis.gsfc.nasa.gov/data/dataprod/chlor_a.php](https://modis.gsfc.nasa.gov/data/dataprod/chlor_a.php)]([https://modis.gsfc.nasa.gov/data/dataprod/chlor_a.php](https://modis.gsfc.nasa.gov/data/dataprod/chlor_a.php)), [28]) over ocean and normalized difference vegetation index (NDVI) data over land (obtained from [[https://modis.gsfc.nasa.gov/data/dataprod/mod13.php](https://modis.gsfc.nasa.gov/data/dataprod/mod13.php)]([https://modis.gsfc.nasa.gov/data/dataprod/mod13.php](https://modis.gsfc.nasa.gov/data/dataprod/mod13.php))).  
Figure 4: Root mean square noise to signal ratio NSR versus root mean square residual to signal ratio RSR for all four fit windows. **red points**: 2.28 th percentile within bins with more than 500 samples (35 bins in total). **orange points**: 15.9 th percentile. **green points**: expectation value estimated from the 2.28 th and 15.9 th percentile. **solid green line**: RSR as computed from the RSR model (Equation (1)). **gray points**: RSR model plus 2\(\sigma\) estimated from the 2.28 th and 15.9 th percentile. **gray line**: outlier threshold. **gray dots**: potential outliers. **dashed green line**: one-to-one line.  
Figure 6 shows that we find a reasonably linear relationship (with correlations around 0.9) between the retrieved ZLO and the continuum radiance within the SIF and both CO\({}_{2}\) fit windows hinting at ZLOs in the range of 0.8-1.8% of the continuum radiance. In the following, we use the fitted linear relationship as ZLO correction for these three fit windows. In the O\({}_{2}\) fit window, the correlation between ZLO and continuum radiance is poor and the linear fit suggests a small negative slope. Therefore, we decided to not apply a ZLO correction for this fit window.  
Figure 5: Sampling of all pre-filtered soundings analyzed in order to determine the ZLO correction. The data set consists of all pre-filtered OCO-2 soundings of 24 days in 2015 (13.01., 15.01., 14.02., 16.02., 10.03., 20.03., 03.04., 19.04., 08.05., 23.05., 08.06., 24.06., 15.07., 16.07., 15.08., 16.08., 15.09., 16.09., 15.10., 16.10., 15.11., 17.11., 12.12., 18.12.) additionally filtered for potential contamination with chlorophyll fluorescence (see main text).  
Figure 6: _Cont._