## 2 Materials and Methods
### Retrieval Algorithms
#### 2.2.3 Stratospheric NO\({}_{2}\) Vertical Profiling  
The vertical distribution of stratospheric NO\({}_{2}\) can be retrieved from ground-based measurements of the zenith-scattered sunlight. Basically, at visible wavelengths where NO\({}_{2}\) absorption is measured, the mean altitude at which Rayleigh scattering occurs increases with increasing SZA. During twilight, the mean scattering altitude scans the stratosphere rapidly, yielding height-resolved information on the absorption by stratospheric NO\({}_{2}\) (see Figure 3). Through linear optimal estimation (OEM), vertical profiles of stratospheric compounds can be derived from zenith-sky DOAS observations at twilight [12; 34]. \begin{table}
\begin{tabular}{l l} \hline Wavelength range & 450–540 nm \\ \hline Wavelength calibration method & Based on the reference solar atlas of [PERSON] [27] \\ \hline Absorption cross-sections: & \\ O\({}_{3}\) (223 K and 243 K) & [28]; 243 K orthogonalised to 223 K \\ NO\({}_{2}\) (220 K and 298 K) & [29]; 298 K orthogonalised to 220 K; I\({}_{0}\) effect-corrected \\ O\({}_{4}\) (293 K and 203 K) & [30]; 203 K orthogonalised to 293 K \\ H\({}_{2}\)O & [31] \\ Ring effect & Pseudo-absorber [32; 33] \\ Polynomial & Order 5 (6 coefficients) \\ Intensity offset correction & Order 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Spectral retrieval settings for ozone in the Chappuis band. The algorithm implemented in the FRM4 DOAS system is based on the work by [12]. It allows for retrieving sunrise and sunset NO\({}_{2}\) stratospheric profiles in the altitude range of 20-40 km, representative of conditions at 90\({}^{\circ}\) SZA. The details of the OEM algorithm are described in [12], and therefore, only a summary of its main features is presented here, with a focus on deviations resulting from the FRM4 DOAS implementation. As for ozone retrievals, the first step of the evaluation consists of a spectral fitting using the QDOAS algorithm to produce dSCDs. Settings currently adopted for FRM4 DOAS are given in Table 4.  
The second step consists of retrieving stratospheric NO\({}_{2}\) profiles from the measured dSCDs. The profiling algorithm applied in FRM4 DOAS is based on the OEM and is fully described in [12]. To reproduce the rapid variation of NO\({}_{2}\) at twilight, the forward model includes a stacked box photochemical model (PSC-Box [35]) initialised with meteorological and chemical fields at the location of the station obtained with the 3D-CTM SLIMCAT [36]. Based on these simulations, NO\({}_{2}\) slant columns (and corresponding weighting functions) are calculated using the pseudo-spherical radiative transfer model UVSPEC/DISORT [37], which has been validated in several past studies [38; 39]. To provide the FRM4 DOAS processing system with the capability to retrieve NO\({}_{2}\) stratospheric vertical profiles at globally distributed stations, a set of LUTs of weighting functions (WFs) were calculated for 10\({}^{\circ}\) latitude bands between 90\({}^{\circ}\)S and 90\({}^{\circ}\)N.  
Although the core of the algorithm remains identical to the one described in [12], recent developments described in the FRM4 DOAS technical documentation ([https://frm4 doas.aeronomie.be/index.php/documents/deliverables](https://frm4 doas.aeronomie.be/index.php/documents/deliverables), accessed on 27 November 2024) but not yet implemented in the current version of the processor have led to major improvements in the stability of the retrievals. In particular, it was shown that improved retrievals can