Supplement of Synergy of Using Nadir and Limb Instruments for Tropospheric Ozone Monitoring (SUNLIT)

Abstract. Satellite measurements in nadir and limb viewing geometry provide a
complementary view of the atmosphere. An effective combination of the limb
and nadir measurements can give new information about atmospheric
composition. In this work, we present tropospheric ozone column datasets
that have been created using a combination of total ozone columns from OMI (Ozone Monitoring Instrument) and
TROPOMI (TROPOspheric Monitoring Instrument) with stratospheric ozone column datasets from several available
limb-viewing instruments: MLS (Microwave Limb Sounder), OSIRIS (Optical Spectrograph and InfraRed
Imaging System), MIPAS (Michelson Interferometer for Passive Atmospheric Sounding), SCIAMACHY (SCanning Imaging Spectrometer for Atmospheric CHartographY), OMPS-LP (Ozone Mapping and Profiles
Suite – Limb Profiler), and GOMOS (Global Ozone Monitoring by Occultation of Stars). We have developed further the methodological aspects of the assessment of
tropospheric ozone using the residual method supported by simulations with
the chemistry transport model SILAM (System for Integrated modeLling of Atmospheric coMposition). It has been shown that the accurate
assessment of ozone in the upper troposphere and the lower stratosphere
(UTLS) is of high importance for detecting the ground-level ozone patterns. The stratospheric ozone column is derived from a combination of ozone
profiles from several satellite instruments in limb-viewing geometry. We
developed a method for the data homogenization, which includes the removal
of biases and a posteriori estimation of random uncertainties, thus making
the data from different instruments compatible with each other. The high-horizontal- and vertical-resolution dataset of ozone profiles is created via
interpolation of the limb profiles from each day to a 1∘×1∘ horizonal grid. A new kriging-type interpolation method, which
takes into account data uncertainties and the information about natural
ozone variations from the SILAM-adjusted ozone field, has been developed. To
mitigate the limited accuracy and coverage of the limb profile data in the
UTLS, a smooth transition to the model data is applied below the tropopause.
This allows for the estimation of the stratospheric ozone column with full coverage of
the UTLS. The derived ozone profiles are in very good agreement with
collocated ozonesonde measurements. The residual method was successfully applied to OMI and TROPOMI clear-sky
total ozone data in combination with the stratospheric ozone column from the
developed high-resolution limb profile dataset. The resulting tropospheric
ozone column is in very good agreement with other satellite data. The global
distributions of tropospheric ozone exhibit enhancements associated with the
regions of high tropospheric ozone production. The main datasets created are (i) a monthly 1∘×1∘ global tropospheric ozone column dataset (from ground to 3 km below the tropopause) using OMI and limb instruments, (ii) a monthly 1∘×1∘ global tropospheric ozone column dataset using TROPOMI and limb instruments, and (iii) a daily 1∘×1∘ interpolated stratospheric ozone column from limb instruments. Other datasets, which are created as an intermediate step of creating the
tropospheric ozone column data, are (i) a daily 1∘×1∘ clear-sky and total ozone column from OMI and TROPOMI, (ii) a daily 1∘×1∘ homogenized and interpolated dataset of ozone profiles from limb instruments, and (iii) a daily 1∘×1∘ dataset of ozone profiles from SILAM simulations with adjustment to satellite data. These datasets can be used in various studies related to variability and trends in ozone distributions in both the troposphere and the
stratosphere. The datasets are processed from the beginning of OMI and
TROPOMI measurements until December 2020 and are planned to be regularly
extended in the future.


1 S1. Feasibility studies on residual method to retrieve tropospheric ozone Correction of upper tropospheric column by monthly zonal mean Correction of upper tropospheric column using TpO3 climatology

S2. Adjusted SILAM ozone field
The simulated ozone field by the chemistry-transport model is an attractive source of information for various feasibility and sensitivity studies. This additional source of information is of especial importance in the UTLS, where the accuracy of satellite data is rather poor and the covered altitude range is not uniform over the globe. It is instrument-specific, therefore the resulting fields solely based on retrievals may be not accurate.
The SILAM model has proved to produce realistically distribution of ozone field, including the special events like ozone hole and mini-holes (Sofiev et al., 2020), https://en.ilmatieteenlaitos.fi/news/1140594517; https://en.ilmatieteenlaitos.fi/tiedote/1276664372, last access 7.04.2022). In addition, we have studied the small-scale ozone variability by the structure function method using OMI and SILAM total ozone column data and have found that they are in a very good agreement (Supplement, Sect S3). However, the model field is biased with respect to satellite data.
One possible approach to make the model data consistent with observations is data assimilation but this approach is critically dependent on the amount of data used for assimilation. In particular, changing satellite missions can affect the long-term stability of the assimilated data. We apply a different approach: we adjust SILAM data to MLS observation by computing space-resolving daily biases. These biases are evaluated as a weighted mean of model deviations from the observations in 10x30 latitude-longitude bin, for each pressure level and each grid-point. As an example, MLS observations, original SILAM data, and the adjusted SILAM data for 20 June 2018 are shown in Figure S5.
The size of latitude-longitude box for evaluation of SILAM bias is relatively large, so that the small-scale structure of the model field is preserved in the adjusted field. For example, one can notice interesting small-scale perturbations in Figure S5.
The uncertainty associated with the bias correction is estimated as the interpolated absolute difference between MLS and SILAM adjusted data. In majority of locations, the estimated uncertainty is a few percent (an example is shown in Figure S5, right bottom panel).   (Sofieva et al., 2017(Sofieva et al., , 2021b using adjusted SILAM ozone profiles (left) and MLS data (right). All trends are shown by colored contours, while the statistically significant at 95% level trends are shown by shades.
Compared to the data assimilation methods, the model is much tighter nudged to the observations, so that the potentially wrong trends in the model do not affect the resulting dataset (The problems of using assimilated data for trend analyses are discussed in ( e.g., Simmons et al., 2014;Stauffer et al., 2019)). At the same time, changes in the data availability do not affect the very smooth bias corrections as long as the varying amount of retrievals do not bring any systematic bias themselves. This is illustrated in Figure S6, which compares the zonal mean ozone trends in 2004-2018 from MLS and from adjusted SILAM dataset. As observed in Figure S6, these trends are nearly identical, as expected.
Since MLS profiles are recommended for use at altitudes above 250 hPa, we apply a fast 3 -point linear transition to original SILAM ozone profiles at lower altitudes: at 250 hPa, the adjusted model is used, at next level below (300 hPa) -the mean of original and adjusted data, and 350 hPa and below -original SILAM data. This step is justified by a more extensive evaluation of SILAM in the troposphere than in the stratosphere (see, e.g., Copernicus regional evaluation at https://atmosphere.copernicus.eu/index.php/regional-services, visited 03.07.2021, in particular, evaluation at elevated stations (Douros et al., 2021), first approaches to evaluation in Asia Petersen et al., 2019), etc.).

S3. Analysis of small-scale ozone variability using OMI and SILAM data
For the analyses, we used SILAM daily-mean ozone fields and OMI data. For selection of the tropospheric and the stratospheric ozone columns, we used the thermal tropopause/ozonepause definition as described in the main text. The OMI retrievals were gridded with 1 x 1 resolution. It was assumed that the stratospheric ozone column in the retrievals corresponds to the cloudy conditions, i.e. we used columns where clouds overshadowed the tropospheric part.
All ozone columns -total, stratospheric and tropospheric -have large temporal variability. Analogously to (Sofieva et al., 2021a), we characterized the variability of the ozone field by the structure function (Tatarskii, 1961): where and are two locations and . This concept assumes that the random field is locally homogeneous, which is the spatial equivalence of a random process with stationary increments. In spatial statistics, () D ρ is called the variogram (Wackernagel, 2003). The structure functions in latitude and in longitude are evaluated for different seasons and broad latitude bands for years 2005-2017, for both total and stratospheric columns and experimental and simulated ozone fields. The TOC structure functions are shown in Figures  S7 and S8, for OMI and SILAM data, respectively. The analogous structure functions for SOC are shown in Figures S9 and S10.   Figure S7, but for SILAM TOC. Figure S9. As Figure S7, but for SOC using OMI data. Figure S10 As Figure S7, but for SOC using SILAM data.
The obtained morphology of ozone variability is quite expected: it is overall much smaller in the tropics than at middle and high latitudes, where it has a pronounced seasonal cycle. In polar regions in winter and spring the ozone variability is very strong, even for small separations. The structure functions are evidently anisotropic nearly everywhere, with stronger variability in latitudinal direction. The only exceptions are latitudes 60-90 N in all seasons and 60-90 S in March-May. As expected, the structure functions for total ozone and for stratospheric ozone look similar.
The overall morphology -latitudinal dependence, latitude-longitude anisotropy, seasonal cycle -is similar for OMI and SILAM, for both total and stratospheric ozone column. . For total ozone column, the experimental and modelled structure functions are very similar for almost all latitudinal zones. Some disagreement in seasonal cycle is observed for polar winter conditions (for example 60-90S in June-Aug, Figs S7 and S8). This disagreement is quite expected: OMI cannot measure in polar night conditions. The shape of structure functions and the growth with separation distance are similar in Figs S7 and S8, but some difference in absolute values exists and is expected; it comes from biases between model and observations (note that the structure functions are presented in absolute values).
For stratospheric ozone column, the comparison is more complicated, because we could use only cloudy pixels of OMI, which have limited coverage. This results in less reliable estimates of structure function from the OMI data. For example, limited amount of data at large separations (> 500-1000 km), resulted in different shapes of experimental and model-based the structure functions in the equatorial zone. Although the seasonal cycle and latitudelongitude anisotropy are qualitatively similar in Figures S9 and S10, mid-and high-latitude structure functions tend to group somewhat differently. Therefore, comparison of the stratospheric ozone column structure functions in Figs S9 and S10 should be considered as indicative only.
Since the stratospheric ozone has a bulk contribution to the total ozone (for which observational and modelled structure functions are similar), and with the above notes, we conclude that the ozone small-scale variability is realistically represented by SILAM.

S4. Uncertainties of the interpolated ozone profiles
The estimation of uncertainties associated with the interpolated dataset of ozone profiles are illustrated in Figure S11. Firstly, we used the error propagation to evaluated uncertainty after the kriging step ( Figure S11, top right). In addition, we estimated the interpolation uncertainty using the SILAM data: we run the same interpolation but on the SILAM fields sub-sampled at the measurements locations, and evaluated the error as the absolute difference of true and interpolated data ( Figure S11, bottom left). The final uncertainty is the root-mean-square of error propagation and model-assessed interpolation errors ( Figure S11, bottom right).

S5. Compatibility of ozone data from limb and nadir instruments.
We compared OMI and TROPOMI measurements in cloudy conditions (the ghost column removed) with the integrated ozone profiles from the cloud-top height. For this comparison, we selected cloudy pixels with cloud fraction >0.8 and cloud-top pressure less than 350 hPa and the corresponding limb profiles from the SILAM adjusted field. The example of the comparison for September 2018 is shown in Figure S12. The best region for evaluation of limb-nadir compatibility is over Indonesia, where high clouds are frequently observed. In other locations, there might be contributions from the upper troposphere due to partially cloudy scenes. Additional discrepancy can result from an uncertainty in cloud top height definition or from the fact that the clouds are not a purely reflecting layer and radiation penetrates into the cloud to a certain depth.