Total ozone column retrieval from OMPS-NM measurements

A scientific total ozone column product from the Ozone Mapping and Profiler Suite Nadir Mapper (OMPS-NM) observations and its retrieval algorithm are presented. The retrieval employs the Weighting Function Fitting Approach (WFFA), a modification of the Weighting Function Differential Optical Absorption Spectroscopy (WFDOAS) technique. The total ozone columns retrieved with WFFA are in very good agreement with other datasets. A mean difference of 0.6 % with respect to ground-based Brewer and Dobson measurements is observed. Seasonal and latitudinal variations are well represented and in 5 agreement with other satellite datasets. The comparison of our product with the scientific product of OMPS-NM indicate a mean bias of around 0.1 %. The comparison with the Tropospheric Monitoring Instrument products (S5P/TROPOMI) OFFL and WFDOAS, shows a persistent negative bias of about -0.5 % for OFFL and -2 % for WFDOAS. Larger differences are only observed in the polar regions. This data product is intended to be used for trend analysis and the retrieval of tropospheric ozone combined with the OMPS limb profiler data. 10


Introduction
The majority of the ozone's atmospheric load (O 3 ) resides in the stratosphere. The strong absorption of the Ultraviolet (UV) B and C radiation by O 3 shields the biosphere from biologically damaging UV radiation. O 3 heats the atmosphere and creates the temperature inversion, which characterizes the stratosphere. In turn, this plays a key role in determining the tropopause height and influences tropospheric weather. On the other hand, O 3 is toxic, and anthropogenic emissions lead to its production in the track field of view (FOV) and 110°across-track FOV divided into 36 cross-track bins. The two central FOVs cover 20 km x 60 50 km and 30 km x 50 km, the rest, approximately 50 km x 50 km each (Flynn et al., 2004(Flynn et al., , 2014Seftor et al., 2014).
For the retrieval of OMPS TOC, the level 1 data, version 2.0 (L1b V2.0), of OMPS-NM were used (Jaross, 2017a). Since the ultimate goal of our nadir TOC product is the match with OMPS limb profiles to derive tropospheric ozone columns, only the central FOV bins, 17 to 20, were processed (approximately corresponding to a 150 x 50 km swath). Only pixels with a cloud fractions under 0.1, and solar zenith angles smaller than 80°were used. At the moment, the limb ozone profiles can be 65 only retrieved from the central of the three vertical slits (Arosio et al., 2018). The period retrieved comprises the years 2012 to 2018. Later data were not considered because of systematic errors in measured radiances of OMPS-LP (Kramarova et al., 2018) that lead to a significant drift in OMPS-LP ozone, which would affect the tropospheric ozone. The cloud fraction and topography information from OMPS-NM Level 2 (L2) version 2.1 product was used as input in the retrieval.

A priori ozone profile climatology 70
It is well known that a good knowledge of the ozone profile shape helps to increase the quality of TOC retrievals from nadir measurements in the UV spectral range. As discussed by Lamsal et al. (2007), differences in the retrieved total ozone due to a priori ozone profile might go up to 10 %. Most of the ozone climatologies available so far were created from periods before the year 2012 Paul et al., 1998;Lamsal, 2004;McPeters et al., 2007;Labow et al., 2015;Yang and Liu, 2019). Therefore, it was decided to create a new ozone profiles database to have a consistent input for the time frame of this 75 retrieval, by using OMPS-LP (Arosio et al., 2018) and ozonesonde observations between January 2012 and December 2018.
The ozone profiles are provided as a function of latitude band, season, and total ozone content as in the ozone climatology from Lamsal (2004). Therefore, the ozone database consists of zonally and latitudinally averaged profiles for five regions: northern polar region (np, 60°-90°N), northern mid-latitudes (nm, 30°-60°N), tropics (trop, 30°N-30°S), southern midlatitudes (sm, 30°-60°S), and southern polar region (sp, 60°-90°S). Due to the typical annual cycle of the total ozone column, 80 the profiles have been classified in two groups considering the season: winter/spring (ws) and summer/fall (sf), except for the tropics, where no seasonality was considered. The final profiles were grouped and averaged by their total ozone column amount in intervals of 30 DU. For each ozone profile, a temperature profile is provided as well but is not used in the retrieval.
As the total ozone retrieval is sensitive to changes in the ozone profiles in both the stratosphere and the troposphere (Wellemeyer et al., 1997), the database was built by combining stratospheric profiles from OMPS-LP and ozonesonde measurements 85 for the troposphere. The limb profiles are from the scientific zonal average Level 3 product from OMPS-LP provided by Arosio et al. (2018), that contains gridded monthly means between January 2012 and December 2018. These profiles are zonal averages, every 5°in latitude, for 53 altitudes from 8.5 to 60.5 km with a sampling of 1 km. Here, the profiles from 12.5 km altitude up to the top-of-the atmosphere were used. The ozonesondes data used are from the World Ozone and Ultraviolet Data Center (WOUDC) (Fioletov et al., 1999) and from the Southern Hemisphere Additional Ozonesondes (SHADOZ) (Thompson 90 et al., 2007). All stations with data between 2012 and 2018 were used, 29 stations from WOUDC and 14 from SHADOZ (Fig. 1). Each ozonesonde profile was convolved using a Gaussian function with 3.3 km FWHM, to obtain a resolution similar to that of the OMPS-LP profiles (Arosio et al., 2018), and sampled onto a grid of 1 km from 0.5 to 20.5 km.
Every ozone profile in the database was created using the ozonesonde profile up to 11.5 km and the zonal monthly mean limb profile above 20.5 km. In the transition zone between 12.5 and 20.5 km, the merged profile results from a linear weighted 95 average between the ozonesonde and the limb profile. Each ozonesonde profile was joined with the corresponding zonal monthly mean stratospheric profile, matching the latitude and the month of the ozonesonde. These merged profiles were averaged considering their total ozone content, date, and latitude according to the description above. The resulting ozone climatology profiles are shown in Fig. 2.

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The retrieval algorithm used here, is a modification of the Weighting Function Differential Optical Absorption Spectroscopy algorithm (WFDOAS) which has been developed for the retrieval of trace gases in the near-infrared spectrum range, from SCIAMACHY measurements (Buchwitz et al., 2000). It was adapted and successfully applied for TOC retrieval from nadir viewing measurements of GOME (Coldewey-Egbers et al., 2005), GOME2 and SCIAMACHY .
The algorithm approximates the measured atmospheric optical depth by a Taylor expansion around a first guess atmospheric 105 state. Also, contributions from interfering species, not included in the forward model, and a polynomial are included in the fit (Coldewey-Egbers et al., 2005):  The coarse resolution of the OMPS instrument was found to result in unstable retrievals when using the WFDOAS approach for small UV spectral windows in the Huggins band. To adapt the retrieval technique, it was decided to use a lower order polynomial, a wider spectral window, and every second spectral point from the input radiance. In the WFDOAS approach, a 120 cubic polynomial is usually used to account for all broadband contributions; consequently, the total column ozone information is obtained from the differential absorption structure only. For OMPS, the fit parameters' correlation is too high when using only the differential structure, which results in large differences in the total ozone retrieved from adjacent ground pixels in the across-track direction. Therefore, a zero degree polynomial (a constant) is used instead of the cubic one and the slope of the ozone absorption signature is fitted as well. To reduce the differential structure's impact in the fit, the spectral window was 125 chosen to be 316-336 nm, which is wider than typically used in WFDOAS (325 to 335 nm). In addition, only the odd-numbered detector readouts are used in the retrieval, using a one-based index. Even with a wider spectral window, the use of either all spectral points or of the even-numbered detector readouts results in significant discrepancies in the retrieved TOCs from ground pixel to ground pixel, and in a negative bias of around 2 % with respect to the actual selection. With these changes, we now refer to the retrieval method as the Weighting Function Fitting Approach, WFFA. Apart from using a low-order polynomial 130 and the wider spectral fit windows, WFFA is similar to WFDOAS (Coldewey- Egbers et al., 2005). Some further modifications have been implemented as described below.
The fitting procedure follows an iterative scheme. First, the synthetic radiance and all weighting functions needed in Eq. (1) are computed with a radiative transfer model (RTM). To account for a possible wavelength misalignment between the earthshine spectrum and the solar reference spectrum, the earthshine spectrum's wavelength axis is adjusted through an iterative non-linear 135 fit of the shift and squeeze of the wavelength axis. In a second step, the unknown fit parameters in Eq. (1) (V ,T , SCD N O2 , SCD Ring and the constant C) are estimated using a linear least-squares minimization. The resulting total ozone is then passed to the RTM to start the next iteration. The iterative process is terminated when the retrieved ozone column differs by less than 1 DU from the result of the previous iteration.
The reference intensities, as well as the weighting functions, are computed with the RTM SCIATRAN V4.2 (Rozanov et al.,140 2014), using the ozone profile climatology described in Section 3, for a given total ozone, zonal band, and season. During the iterative procedure a new ozone profile is selected according the retrieved total ozone amount. For each ground pixel, the pressure and temperature profiles are obtained from ECMWF ERA5 (Hersbach et al., 2020). For solar zenith angles (SZA) larger than 40°the pseudo-spherical approximation is employed, whereas for smaller SZAs the plane parallel atmosphere is used, which is faster. The pseudo-spherical approximation solves the radiative transfer equation for a plane parallel atmosphere, 145 however the single-scattering source function is calculated considering the spherical shape of the atmosphere. The ground level viewing geometry is used in the forward model. Compared with the spherical mode , the use of this approach yields almost identical results (de Beek et al., 2004).
The selected initial guess value of total ozone for the first pixel processed per FOV is 300 DU. The following pixels use as initial value the TOC from the previous one. The ozone absorption cross-sections from Serdyuchenko et al. (2014) and the in WFDOAS, the effective scene albedo is retrieved near 377 nm using the Lambert equivalent reflectivity (LER) approach (Coldewey-Egbers et al., 2005). The aerosol effect is largely accounted for with the effective scene albedo.
The Ring effect is estimated using the difference in the optical depths calculated by the SCIATRAN model with and without Raman scattering (Rozanov and Vountas, 2014). Lookup tables (LUT) of the optical depths accounting for the Ring effect, i.e.

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infilling of Fraunhofer lines and molecular absorption bands, were simulated using SCIATRAN V4.2 and implemented in the retrieval scheme. With the pixel's viewing geometry information, total ozone, surface albedo, and altitude, the LUT are read and interpolated to obtain the corresponding Ring spectrum at high spectral resolution. After convolution of the LUT radiances with and without Ring effect with the instrument response function, the logarithm of the ratio of both convolved radiances is used as the Ring spectrum in Eq. (1). A second lookup table provides modelled sun-normalized radiances calculated with and 160 without polarisation. From these correction factors are determined to convert the observed (polarised) radiances into scalar radiances. With the LUTs, the time-consuming RTM modelling of the Ring and polarisation effects during the retrieval can be avoided. As the Ring effect and polarisation depend on ozone, the inputs from the LUT are updated in each iteration.

Validation datasets
In order to evaluate our scientific product, a comparison with other total ozone column measurements was performed. The

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NASA product from OMPS-NM, the operational OFFL and scientific WFDOAS products from the Tropospheric Monitoring Instrument on board of Copernicus Sentinel-5 Precursor (S5P/TROPOMI), and ground-based Brewer and Dobson measurements, were used.

Ground-based measurements
The comparison with ground-based data was performed using daily means of total ozone columns from 12 Dobson (Basher,170 1982) and 34 Brewer (Kerr, 2002) stations, obtained from the WOUDC dataset. Only ozone data derived from direct sun (DS) measurements are included in the analysis as they are the most accurate (Vanicek et al., 2003).

Version 2 OMPS-NM total ozone column
The operational OMPS-NP Level 2 (L2) version 2.1 total ozone column product is generated using NASA's V8.5 total column retrieval algorithm (Jaross, 2017b). This algorithm uses a pair of wavelengths to retrieve cloud fraction and ozone, 317.5 and nm) is used to estimate ozone. The measured radiances are compared with a pre-calculated set of radiances using various ozone and temperature profiles, and the TOC is obtained using piece-wise linear interpolation (Bhartia, 2002). eter that provides measurements in the ultraviolet, visible, near-infrared and short wave infrared spectral bands. TROPOMI has a ground pixel resolution of 3.5 km x 7 km, covering 2600 km across-track (Veefkind et al., 2012).
The L2 product of S5P/TROPOMI used in this study is the offline (OFFL) Total Column Ozone product, the reprocessed version (RPRO) which includes a cloud correction (Lerot et al., 2020). S5P/TROPOMI OFFL is obtained using the GODFIT version 4 retrieval. The algorithm performs a direct comparison with simulated radiances through non-linear least-square in-195 version, using the sun-normalized measured radiance from 325 to 335 nm. The modelled radiances and Jacobians are obtained with the RTM LIDORT (Heue et al., 2016).
A validation for S5P/TROPOMI OFFL TOC with global ground-based measurements during the period from April to November 2018, showed a mean bias of 0 % to 1.5 % and standard deviations between 2.5 % and 4.5 % for monthly mean collocations (Garane et al., 2019).

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A scientific S5P/TROPOMI product generated with the WFDOAS v4 algorithm was also used. The WFDOAS set up is identical to WFFA described above except for the narrower wavelength window (325-335 nm) and a third-degree polynomial used (Eq. (1)). Furthermore, WFDOAS uses temperature profiles from the ozone profile climatology rather than reanalysis data as in WFFA. Figure 3 shows a comparison of S5P/TROPOMI WFDOAS results with daily ground-based measurements between November 2017 and September 2019. S5P/TROPOMI-WFDOAS shows a bias of 2.0 % with 1σ of 1.9 % for Brewer 205 instruments, and 2.1 % bias with 2.3 % standard deviation for Dobson instruments.
To perform the comparison with ground data and between the S5P products, both datasets, OFFL and WFDOAS, have been binned into 0.3°×0.3°boxes and averaged daily. These gridded data were used for the comparison with OMPS-WFFA retrieval. Figure 4 shows the latitude-time comparison between TROPOMI OFFL and WFDOAS, exhibiting a global mean difference of 1.5 % with 0.7 % standard deviation, with WFDOAS being higher than OFFL. Almost no seasonal variability is observed 210 in the differences, larger differences occur in the southern hemisphere polar region during winter/spring.
The S5P-WFDOAS product is retrieved using the recommended Serdyuchenko et al. (2014) cross-sections. For the WF-DOAS approach, the use of the Bass-Paur (BP, shifted by 0.23 nm) and BDM ozone absorption cross-sections (Paur and Bass, 1985;Malicet et al., 1995) leads to retrieved total ozone being lower by 2 − 3 %. The WFFA approach with a wider spectral window and subtraction of a low order polynomial is only weakly sensitive to the use of different ozone absorption    In the southern hemisphere, over the subpolar region, the maximum in TOC during austral spring (SON) is weaker than its counterpart in the northern hemisphere. The minimum over the Antarctic during austral spring ("ozone hole") is observed. Over 225 complex topography areas, like the Himalayas in Asia and the Andes in South America, lower ozone amounts are observed.

Comparison with ground-based measurements
Daily mean ground-based data for 46 stations were compared with daily satellite data averaged in the grid box that contains the station. Since only cloud-free satellite ground pixels were retrieved, the number of co-located days to be compared at a given station is rather low. Only stations with co-located data of at least 50 days were selected to have a sufficient sample for 230 the comparison. With these criteria, 12 Dobson and 34 Brewer stations were available for the validation during the analyzed period.
Daily relative differences between WFFA TOC and the ground-based data were calculated. The mean relative differences      (Feister, 1994;Vanicek, 2006). Overall, the bias between WFFA and ground-based measurements is positive, 0.5 % for Brewer and 1.0 % for Dobson instruments, with a mean standard deviation of 1.3 % and 1.5 %, respectively. For

Comparison with OMPS-NM operational product and S5P/TROPOMI
WFFA results have been compared to the operational total ozone column product of OMPS-NM (OMPS-L2), and two different 250 retrievals from S5P/TROPOMI (OFFL and WFDOAS) as introduced in Section 5.
A comparison for one orbit on June 10, 2018, is shown in Fig. 8. The upper panels show the TOC of the central FOV (18) against latitude and SZA for all datasets. The lower panels show the percentage differences of WFFA results with respect to the comparison datasets. The ozone total column reaches a minimum in the tropics increasing towards the poles, with local maxima at 40°S and 70°N. The absolute maximum is observed at 50°N. All satellite data show very good agreement in the variation 255 of TOC with latitude and SZA. The mean bias with respect to OMPS-L2 is 0.39 %. The differences with respect to S5P OFFL and WFDOAS data, are -0.36 % and -2.48 %, respectively. S5P WFDOAS exhibits more ozone than the other datasets along the entire orbit. This is expected considering the direct comparisons between the two S5P datasets shown above (Section 5.3).
Between -70°to 40°SZAs (approximately 40°S to 60°N in latitude), differences with respect to OMPS L2 and S5P OFFL data vary around ±1 %. For larger SZAs, WFFA results differ by less than 2 % with respect to the three comparison datasets, 260 except for the first pixel of the considered orbit. A difference between hemispheres is observed, for the northern hemisphere WFFA shows more ozone than S5P OFFL and OMPS-L2, while for the southern hemisphere WFFA TOCs are lower. The standard deviations of the differences are similar for all three comparison datasets, varying between 1.1 % for OMPS-L2 and 1.4 % for S5P WFDOAS.
To carry out a more general comparison, by looking at seasonal and global averages, the three comparison datasets were 265 gridded in the same way as WFFA data. For OMPS-L2 the same orbits and ground pixels as those for WFFA were selected (ground pixels with cloud fraction less than 0.1, SZA smaller than 80°and only central FOVs from 17 to 20), from 2016 to 2018. For S5P all available data (all FOVS as well as cloudy scenes included) were gridded. The regular production of the    The comparison between WFFA and S5P/TROPOMI results is shown in the right panels of Fig. 9. Striping is seen in the differences to S5P most likely due to differences in the grid boxes' sampling. For S5P, the topography distinction is seen over For a more detailed analysis, TOC time series for five zonal bands were calculated: high northern latitudes (60°-90°N), northern mid-latitudes (30°-60°N), tropics (30°N-30°S), southern mid-latitudes (30°-60°S), and southern high latitudes (60°-90°S), as shown in Fig. 10. The mean relative differences in these zonal bands are summarised in Table 1. In general, the four different datasets follow the same seasonality and short-term variability, generally showing very good agreement. However S5P products, OFFL and WFDOAS, are typically higher than OMPS-L2 and WFFA, particularly higher in the tropics and in 300 the southern mid-latitudes. A persistent mean negative bias is observed with respect to S5P WFDOAS as it was seen in the comparison for one sample orbit in Fig. 8.
Strong daily variations are observed at northern latitudes, particularly during boreal winter. Nevertheless, the mean differences are mostly less than 1 %. At northern mid-latitudes, WFFA shows a bias of approximately 0.3 % with respect to OMPS-L2, -0.4 % with respect to S5P-OFFL, and -2.0 % with respect to S5P-WFDOAS. In th tropics, the differences be-305 tween the datasets are fairly constant with time, with biases of 0.5 % for OMPS-L2, -0.5 % for S5P-OFFL and -2.2 % for S5P-WFDOAS; the standard deviations are below 0.7 %. WFFA shows less ozone than OMPS-L2 during winter at southern mid-latitudes, by about -6 %. The relative difference decreases in autumn and spring and becomes slightly positive during the summer. The same pattern is observed when comparing with S5P, with the mean relative differences ranging from -1.3 for OFFL to -3.4 % for WFDOAS. At high southern latitudes, WFFA results show similar seasonal behaviour as in the mid-310 latitudes. Overall there is a zero bias with respect to OMPS-L2, and the standard deviation is 0.6 %(1σ). Very good agreement (bias -0.3 %) of both WFFA and OMPS-L2 with S5P-OFFL is observed at high southern latitudes.
In this study we present a new scientific TOC product from OMPS-NM observations using the WFFA technique, which is a modified retrieval approach adapted from WFDOAS algorithm. A new ozone profiles climatology was generated for the 315 retrieval, using OMPS-LP profiles (Arosio et al., 2018) and ozonesondes.
The comparison with ground-based measurements shows a mean bias below 1 % for 26 of a total of 46 stations. For 30 stations, the standard deviations of the mean differences are under 3 %. In total, a mean bias of +0.6 % and a standard 320 deviation of 1.4 % were found. These values are similar to those reported by the operational product of OMPS-NM and by S5P/TROPOMI (Section 5).
All comparisons between WFFA TOC and other satellite products are consistent, concerning seasonality and variability with latitude. WFFA TOC presents a yearly global mean bias of about +0.1 % with respect to OMPS-L2, -0.5 % with respect to S5P OFFL and -2 % with respect to S5P WFDOAS. The standard deviations of the differences are around 1.3 % for all satellite 325 validation datasets. Larger differences were found for polar regions and larger SZAs.
It is shown that the WFFA OMPS-NM total ozone dataset is suitable for retrieving tropospheric ozone columns using the limb-nadir matching technique in combination with OMPS-LP data.
Author contributions. All authors contributed to the design of the study. Andrea Orfanoz-Cheuquelaf developed the retrieval algorithm, performed the computer calculations and made the comparisons supervised by Mark Weber, Alexei Rozanov and Annette Ladstätter-

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Weißenmayer with John P. Burrows providing scientific conceptual input and oversight. Carlo Arosio provided vertical ozone profiles used in the study from inversions of OMPS-LP observations. Andrea Orfanoz-Cheuquelaf led the preparation of the manuscript. All authors contributed to the writing, editing and and evolution of the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. This research has been funded in parts by the University and the State of Bremen, in parts by ESA-Ozone-CCI+, BMBF SynopSys-Ozone, and the German Research Fundation (DFG) through the research unit VolImpact (FOR2820) and project VolARC. Carlo Arosio acknowledges the support by the PRIME programme of the German Academic Exchange Service (DAAD) via funds from the German Federal Ministry of Education and Research (BMBF) and ESA's Living Planet Fellowship SOLVE.