## 4 Simulated Profile Retrievals Using Radiosonde Data
### Profile Retrievals Using RTLS  
First, two distinctly different profiles are considered from this database to understand the different aspects of retrieval from realistic atmospheric measurements (ozonesonde). One of them is an extreme  
Figure 4: (**a**) A set of representative O\({}_{3}\) profiles obtained from ozonesonde measurements. (**b**) Distribution of deviation from IG in percentage and logarithmic scale.  
profile and the other one is comparatively simpler or close to straight-line profile. Although RTLS, usually uses a first derivative LFDO, it is intrinsically capable of also using a Laplacian second derivative operator (LSDO). In Figures 1 and 2, TP1 has a sharp peak and LSDO is not applicable (by definition it must fit a line through three consecutive updates and the presence of a sharp peak violates this requirement). However, in our experiment involving realistic radiosonde data (Figure 4a), there are no extreme peak as was shown in simulated profile in Figure 1. Therefore, we consider it worthwhile to test both LFDO and LSDO for improved understanding of the regularization process. The retrievals from two different IGs, two different derivative operators and two different instruments using RTLS are shown in Figure 5a-d (Figure 5a,b are for CrIS and Figure 5c,d are for TES). The two different IGs are chosen to represent a worst-case (vertical straight line in solid green) and a reasonable IG (dash blue line) as we defined earlier that is shown in Figure 4a. The retrievals employing LFDO (RTLS1) and LSDO (RTLS2) are shown in red and cyan colors, respectively. A retrieval shown in solid line corresponds to the use of the worst-case IG and a retrieval in dashed line is from the reasonable IG.  
From Figure 5a,b, one can notice that the solution from extreme IG1 (solid green) improves using LSDO (solid cyan), as compared to LFDO (solid red). However, for a reasonable IG2 (dashed blue), the improvement is not noticeable. The failure of the LFDO solution from IG1 is following reason. LFDO solution unable to reconstruct the shape of the true profile when IG is far from truth (~2400%) because RTLS using LFDO is comparatively high regularize solution. Now coming to the true profile shapes, to resolve the extreme profile (Figure 5a) more than at least eight pieces of information are required, whereas regularized retrieval can provide maximum 2 to 3 pieces of information. Therefore, efficient regularization scheme smooths the solution adjusting the information content of the retrieval. Put another way, the measurement has all the information without regularization, but there is no solution without regularization due to the constraints of ill-conditioned inversions as discussed in our earlier publications [13; 14; 15]. The advantage of using RTLS is that it inherently determines the  
Figure 5: Retrievals employing both LFDO and LSDO in RTLS for two different true profiles and from two different IGs. Upper-panels (**a,b**): CrIS; Lower-panels (**c,d**): TES. Colors: true profiles in black; two IGs in solid green and dashed blue; retrievals using LFDO in red and LSDO in cyan.  
regularization strength compromising the information content of the retrieval and no noticeable oscillations observed in the solution around the inflection points. On the other hand, reasonable solutions are obtained from two different IGs using both LFDO and LSDO for a true profile devoid of major inflections (Figure 5b). Analogous analyses for TES are shown in Figure 5c,d and the results are very similar to those of CrIS, with an expected higher accuracy. The improvement of TES results for extreme true profile from both IGs is significant as shown in Figure 5c.