## 4 Simulated Profile Retrievals Using Radiosonde Data
### Comparative Retrievals Results for TES  
The plots in Figure 9a-f are similar to as in Figure 7a-f but different settings were applied for OEM retrievals as OEM performed inconsistently between different sensors (CrIS and TES, here) as we have discussed earlier. Although the solutions of RTLS for TES in Figure 9a,b are approximately similar to the previous example of CrIS simulated retrievals in Figure 7a,b, the OEM solutions are far off from the previous case study. Figure 9c for OEM with \"S\({}_{a}\) = exact, S\({}_{e}\) = exact\" indicates that the solutions essentially fallback to the a priori values. Performances in Figure 9d,e with arbitrarily tweaking both the error covariances while holding one at its original value shows that the results are comparable (and both are unsatisfactory) with slightly more bias in Figure 9e. Interestingly, however, by extreme tweaking of both S\({}_{a}\) and S\({}_{e}\) as shown in Figure 9f, the solutions are reasonably good. Recall that this last setting of CrIS (Figure 7f) which yields reasonable results, the settings for Figures 7f and 9f to achieve reasonable result using OEM are different. This confirms the performance of OEM are inconsistent for different characteristics of sensors. It is often reported in satellite retrieval literature e.g., [5; 6; 7] that there are inconsistencies in retrieved datasets from different sensors for a given trace gas. It is often argued that the measurement characteristics of different instruments are the primary cause for that. However, this study confirms that different tweakings of OEM are the root cause for final results. Moreover, using another experiment for the very selective dataset by fine tweaking of error covariances (chance success), one may attempt to show that OEM is a better inverse method compared to RTLS for a particular case study. However, fundamental assumptions to derive any stochastic inverse method are based on a random process, which prevents in investigating and understanding the cause and effect. This hinders further science development. For example, the residual analysis of a deterministic inverse provides an excellent opportunity to further improve the forward model whereas a stochastic inverse conceals these residuals inside the error covariances and bias correction. Figure 10 is similar as Figure 8 but for the TES instrument. The RMSE of retrieval using RTLS (Figure 10a) for all profiles is 0.007 K, which is one order magnitude lesser than that for CrIS. The information content for RTLS is slightly improved for TES (Figure 10b) as compared to CrIS (Figure 8b), which is expected because SNR and spectral resolution of TES are higher than those of CrIS. For different OEM settings, the one corresponding to Figure 9d (i.e., S\({}_{a}\) = 100%, S\({}_{e}\) = exact) has slightly more information than Figure 9e (i.e., S\({}_{a}\) = exact, S\({}_{e}\) = 1000%). Repeatedly, this tweaking-related improvement does not warrant any scientific discussions as the reason is unclear. Tweaking both covariance errors surprisingly yields better solutions, but again the reason for it has no scientific basis. Figure 8: **(a) Retrieval errors in surface temperature vs. true values, using RTLS and OEM; (b) Information content of the retrievals using various RTLS and OEM scheme. **Figure 10: (**a**) Shows the retrieval errors of ST using various retrieval schemes. The RMSE of retrieval using RTLS for all profiles is 0.007 K, whereas the same using OEM with stochastically correct a priori error is 0.05 K. The OEM error is one order magnitude higher than that using RTLS. The dispersion of ST retrieval using OEM is more than \(\pm\)2 K, and for RTLS it is only \(\pm\)0.2 K. (**b**) shows that the information content for LFDO (RTLS1) and LSDO (RTLS2). Figure 9: Bivariate density scatter plots between the individual points of simulated TES retrievals and 277 true zoonesonde profiles. (**a**,**b**) similar to Figure 7a,b; (**c**–**f**) OEM with two different a priori (S\({}_{a}\)) and two different measurement error covariances (S\({}_{c}\)).