## 5 Comparison and Validation
### Validation with TCCON  
In this section, we show validation results for one year (2015) of FOCAL v06 and NASA's operational OCO-2 L2 data and analyze the influence of the bias corrections. We used ground based TCCON [32] GGG2014 data obtained from [[http://tccon.ornl.gov](http://tccon.ornl.gov)]([http://tccon.ornl.gov](http://tccon.ornl.gov)) as reference data set and a similar validation protocol as [PERSON] et al. [19; 33]. We considered the column averaging kernels of all data products and co-located OCO-2 and TCCON measurements with a maximum time difference of 2 h, a maximum distance of 500 km, and a maximum surface elevation difference of 250 m. In cases with multiple TCCON measurements of the same site co-locating with an OCO-2 sounding, we averaged the TCCON measurements. In total we found about 179,000 and 378,000 co-locations for FOCAL and the NASA product, respectively.  
Figure 15 shows the co-locations of all 19 sites with more than 250 co-locations. Per site statistics (bias and scatter, i.e., single sounding precision measured by the standard deviation of the difference to TCCON) are shown from north to south in Figure 16. Note that global offsets have been removed for both figures (\(-0.29\) ppm, \(0.35\) ppm, \(-0.62\) ppm, and \(-0.94\) ppm for NASA, NASA not bias corrected, FOCAL, and FOCAL not bias corrected).  
Both algorithms show a somewhat similar bias site-to-site pattern regardless whether the bias correction is applied or not. The largest differences of the bias corrected satellite products can be found in Sodankyla and Tsukuba with larger than 1 ppm biases of the NASA product and FOCAL. The standard deviations of the site biases are 0.82 ppm and 0.67 ppm for the NASA product and FOCAL (0.69 ppm and 0.78 ppm if no bias correction is applied). These algorithm-to-algorithm differences are barely significant because TCCON's per site accuracy is about 0.4 ppm (1\(\sigma\)) [32].  
The analyzed algorithms also show a similar site-to-site pattern for the scatter with lowest values for the southern hemispheric sites probably due to smaller natural variability and, consequently, smaller representation errors. Both algorithms have a similar average scatter relative to TCCON before bias correction (1.62 ppm and 1.60 ppm for NASA and FOCAL) and after bias correction (1.31 ppm and 1.34 ppm for NASA and FOCAL). This means, both bias corrections primarily reduce the scatter rather than the site biases. However, according to Figure 12, the influence of the bias correction on the spatial bias pattern may be larger elsewhere.  
FOCAL's retrieved XH\({}_{2}\)O has also been initially compared with TCCON in the same manner. However, due to the much larger natural variability of water vapor (typically spanning a range from 500 ppm to 7000 ppm), we used stricter co-location criteria (1h maximum time difference and 150 km maximum distance) reducing the number of co-locations roughly by a factor of five. The global offset amounts to \(-150\) ppm, the standard deviation of the site biases is 206 ppm, and the average single sounding precision is 293 ppm. It should be mentioned that, in contrast to XCO\({}_{2}\), the agreement significantly reduces when relaxing the co-location criteria. Conversely, a significant part of the observed deviations could still be due to representation errors which are expected to reduce for even stricter co-location criteria. This, however, would also further reduce the number of co-locations.  
Figure 15: Validation of FOCAL v06 and NASA’s operational OCO-2 L2 product (both with and without bias correction) with TCCON data from sites with more than 250 co-locations. The sites are ordered from north (top/left) to south (bottom/right): Sodankylá [34], Bialystok [35], Bremen [36], Karlsruhe [37], Paris [38], Orleans [39], Garmisch-Partenkirchen [40], Park Falls [41], Lamont [42], Anneyondo [43], Tsukuba [44], Dryden [45], Pasadena [46], Saga [47], Ascension Island [48], Darwin [49], Reunion Island [50], Wollongong [51], and Lauder [52].