## 2 Materials and Methods
### Retrieval Algorithms
#### 2.2.2 Total Ozone Retrieval  
Total ozone column is retrieved from zenith-sky twilight observations using the NDACC standard approach described in [13]. The procedure involves two steps. The first one consists of obtaining the gas density along the optical path or differential slant column density (dSCD) by means of a DOAS spectral fitting. In FRM4 DOAS, this spectral fit is based on the QDOAS software, version 3.4.7, 3 February 2021 [26]. The DOAS parameters for O\({}_{3}\) dSCD retrieval are defined according to [13] with some adaptations reflecting recent updates in spectroscopy and new practices to account for temperature dependence effects.  
Figure 2: From top to bottom: slope, intercept, regression coefficient and root mean squares (RMSs) of a linear regression between true and retrieved total aerosol optical thickness derived from O\({}_{4}\) dSCDs at 360 nm and 477 nm and HCHO and NO\({}_{2}\) tropospheric total columns for each of the algorithms. Dots show all data; circular symbols represent pie charts that quantify the fraction of data flagged as valid. Intercept and RMS values are in dimensionless units for aerosols and 10\({}^{16}\) molec cm\({}^{-2}\) for HCHO and NO\({}_{2}\). This figure is adapted from (Figure 18 in [25]).  
The settings currently adopted for FRM4 DOAS are given in Table 3. They include specifications for the spectral fitting range, the absorption cross sections of the active gases in the chosen spectral range and some operational parameters for the DOAS fitting.  
The second step is the conversion of the dSCD into a vertical column density (VCD), which directly follows [13]. For the selection of the solar zenith angle (SZA) range representative of twilight conditions, the best compromise between accuracy and precision is achieved in the 86-91\({}^{\circ}\) SZA range. The retrieved VCD is obtained at an effective SZA, which is usually fixed at 90\({}^{\circ}\).  
For zenith-sky twilight observations, the observed air mass is not exactly located over the observation site, but it is horizontally shifted towards east in the morning and towards west in the evening. The average horizontal displacement can reach up to 500 km from the station in the stratosphere during twilight. This horizontal displacement must be considered to make a correct comparison with satellite measurements. In the FRM4 DOAS processing system, lookup tables (LUTs) of the horizontal displacement depending on SZA angle and altitude are used in combination with the solar azimuth angle to report the mean location of the effective air mass corresponding to the total O\({}_{3}\) columns and stratospheric NO\({}_{2}\) profile.  
Sources of uncertainties in zenith-sky twilight total ozone retrievals are documented in [13]. They mainly originate from random errors associated with the fitting procedure, systematic uncertainties related to the ozone absorption cross-sections and pseudo-random errors related to the calculation of the air mass factor that is used to convert dSCDs into VCDs. The overall uncertainty on the vertical column derivation is estimated to be 5.9% at 90\({}^{\circ}\) SZA. Note that clouds have a small impact on zenith-sky ozone measurements at twilight, which is an advantage of the technique. Another advantage is the possibility of measuring under most weather conditions (excluding fog and heavy rain) and at all latitudes even in polar regions.