2.1 TROPOMI

TROPOMI (TROPOspheric Monitoring Instrument) is a nadir-viewing spectrometer and the only instrument on the Sentinel-5 Precursor (S5P) satellite launched in October 2017. S5P is part of the Copernicus Earth observation programme and is designed to prevent a potential gap in global atmospheric monitoring that could arise between existing missions such as OMI and GOME-2 and the upcoming Sentinel-4 and Sentinel-5 (Fletcher and McMullan, 2016). S5P is in a sun-synchronous orbit with an Equator crossing time of 13:30 local time (LT). TROPOMI consists of four spectrometers in the UV, UVIS, NIR and SWIR spectral range. For the ozone profile retrieval, UV1 and UV2 bands are used. Both are located on the same CCD detector. The wavelength range of UV1 extends from 267 to 300 nm and that of UV2 from 300 to 332 nm. The spectral resolution of both bands is 0.5 nm, and the sampling is 0.065 nm. The high spatial resolution of TROPOMI is worth mentioning. One measurement pixel in the middle of the swath covers 28.8×5.6 km² (across track × along track) in UV 1 and 3.6×5.6 km² in UV2. The difference between the two channels comes from the different binning factors that are already applied on board. As the intensity of the measured radiation below 300 nm is much lower, the detector pixels in UV1 have to be binned to get an adequate signal-to-noise ratio (SNR). For the ozone profile retrieval, the sampling of UV1 and UV2 has to be matched. To further improve the SNR in both bands, additional binning is applied before the retrieval.

In the middle of the swath 1 UV1 pixel and 8 UV2 pixels are binned in the across-track direction, while in the along-track direction 8 pixels are binned for both UV1 and UV2. At the far end of the swath, the UV1 pixels have half size in the across-track direction, and therefore 2 UV1 pixels have to be binned here to obtain the same size of the 8 UV2 pixels. That results in a spatial sampling of about 45×45 km² for all pixels. This additional binning reduces the computation time per satellite orbit.

In this study, we use the L1B product of an updated processor version (version 2.0), which is available from the end of 2019. Details of the pre-launch calibration and of the V2 update can be found in Ludewig et al. (2020). Only the V2 update is of sufficient quality for the ozone profile retrieval. At the moment, only a limited data set of version 2.0 is available. The data have not yet been officially released. Modifications in V2 data are still possible until the official release. Between June 2018 and October 2019, data from 2 weeks every 3 months are processed (all in all around 12 full weeks). TROPOMI, like all instruments of this type, also shows drift and degradation effects in the UV channels. Since the same optical path is used for measuring radiance and solar irradiance, these effects cancel to a large degree in the retrieval using sun-normalised radiances. Remaining uncertainties due to errors or changes in the absolute radiometric calibration need to be corrected for. This calibration correction was performed for UV1 and UV2 bands by comparisons with OMPS solar data. The measured TROPOMI irradiance in the wavelength range between 270 and 332 nm is between 5 % and 15 % lower and was corrected by these values in version 2 of the L1B product (Ludewig et al., 2020).

For the ozone profile retrieval, all ground pixels are used which do not have an error flag above 15 for “measurement_quality” or a “ground_pixel_quality” flag greater than 32. The meaning of the flag values is described in the S5P Level 1B data documentation (Kleipool, 2018). In this study, pixels with error flags like “sun glint possible” or “South Atlantic Anomaly” are included. Besides the measured radiance and irradiance, the signal-to-noise ratios contained in the L1B product are used. Here, only single pixels which have a mean SNR(UV1) >20 or SNR(UV2) >50 are accepted. These low SNR limits of the single pixels are then increased by binning (with n pixels) as described above. A Gaussian approach is used for the increasing binning factor: ${\text{SNR}}_{\mathrm{binned}}=\sqrt{\mathrm{1}/n\cdot {\sum }_{i=\mathrm{1}}^n{\text{SNR}}_i^{\mathrm{2}}}$.

2.2 MLS

MLS is a forward-looking microwave limb sounder aboard Aura that was launched in July 2004. It measures millimetre and submillimetre emissions using seven radiometers which cover a spectral region between 118 GHz and 2.5 THz (Waters et al., 2006). Aura is moving on a sun-synchronous orbit with an equatorial passing time of 13:45 LT. MLS has a spatial sampling of ∼6 km across track and ∼200 km along track. Although TROPOMI and MLS do not operate on the same satellite, their measurements are quite close. The maximum distance between the closest MLS and TROPOMI pixels is 1000 km and 1.5 h.

MLS is an extensively characterised and validated instrument measuring among others vertical ozone profiles (Froidevaux et al., 2008; Livesey et al., 2008). The temporal stability was also shown by comparison with, for example, lidar measurements (Nair et al., 2012). The approved vertical range in which the ozone profiles may be used is between 9 and 75 km. The vertical resolution varies from 2.5 to 3.5 km from the upper troposphere to the middle mesosphere. The precision is estimated to be 5 %–100 % at 9–20 km, 2 %–4 % at 20–45 km, and 7 %–30 % at 45–60 km (Livesey et al., 2020). The accuracy varies from 7 % to 10 % in the troposphere and is around 5 % in the stratosphere. The level 2 product version 4.23, which we use, differs very little from the previous versions, especially in the stratosphere.

2.3 OMPS

Another data set suitable for comparison with TOPAS ozone profiles is provided by the Ozone Mapping and Profiler Suite (OMPS) that was launched on board of the Soumi National Polar-orbiting Partnership (SNPP) at the end of 2011. SNPP has a sun-synchronous orbit with the ascending node at 13:30 LT. That means TROPOMI and OMPS operate in a loose formation at a distance of less than 5 min. The measurements used for the ozone profiles retrieval are taken from the limb profiler (LP) and have been available since 2012 (Flynn et al., 2014).

We compare the ozone profiles from TOPAS retrieval with the OMPS-LP profiles retrieved at IUP Bremen by Arosio et al. (2018). The vertical resolution of the OMPS-LP ozone profiles varies from 1.5 to 4.5 km. The retrieval error resulting from the measurement noise is 1 %–4 % above 25 km increasing up to 10 %–30 % in the upper troposphere. The accuracy varies from 5 %–10 % in the whole altitude range, except in the lower tropical stratosphere where a bias of 10 % with respect to ozonesondes is observed.

2.4 Ozonesondes

Balloon-borne ozonesondes provide a well-established data set of in situ measured ozone profiles in the troposphere and lower stratosphere. Ozonesondes can be operated up to an altitude of approximately 35 km and have a vertical resolution of 100–150 m depending on the design and environmental conditions. The measurement precision is 3 %–5 %, and the accuracy is 5 %–10 % (Deshler et al., 2008; Johnson, 2002; Smit et al., 2007). Ozonesondes have been used in many studies on tropospheric and stratospheric ozone and especially for the validation of satellite data (e.g. Kroon et al., 2011; Jia et al., 2015; Huang et al., 2017; Hubert et al., 2020).

The ozonesondes' data for the validation come from the World Ozone and Ultraviolet Radiation Data Center (WOUDC) (WOUDC Ozonesonde Monitoring Community et al., 2021) and the Southern Hemisphere Additional Ozonesondes (SHADOZ) (Witte et al., 2017, 2018; Thompson et al., 2017; Sterling et al., 2018). During the validation period (June 2018 to October 2019) data from 26 WOUDC and 9 SHADOZ stations were available. The stations are displayed in the map in Fig. 1. The collocation criteria for comparison with TROPOMI are 100 km maximum distance and 24 h maximum time difference. Within the 100 km radius of the ozonesonde site, only the closest pixel in time is taken for the validation. SHADOZ profiles were filtered to exclude data that displayed “dropoffs” larger than 5 % (Stauffer et al., 2020). In total, 231 WOUDC and 22 SHADOZ sonde profiles were compared with TROPOMI ozone profiles.

Figure 1Global distribution of ozonesondes (WOUDC and SHADOZ) and lidar measurements used for comparison with the TROPOMI ozone profiles. The exact number and position can be found in Table S1 in the Supplement.

2.5 Ozone lidar

For the validation of ozone profiles, particularly in the upper stratosphere, stratospheric lidar measurements are recommended. The high-power differential absorption lidars (or DIALs) are designed for precise measurements of stratospheric ozone concentration from 20 to 50 km altitude. They use two or more laser wavelengths with strong and weak ozone absorption to measure the backscattered radiation and determine the ozone concentration in the atmospheric layer from their difference. In general, the estimated accuracy of the lidar ozone profiles is 5 % in the 15–50 km range (Leblanc et al., 2016). Like the ozonesondes, lidar measurements are regularly used to validate satellite ozone profiles (e.g. Rozanov et al., 2007; Jiang et al., 2007; Hubert et al., 2016).

For our validation, we used measurements from five lidar stations that are part of the NDACC network (de Mazière et al., 2018). They are marked green in Fig. 1: Hohenpeissenberg (Germany), Lauder (New Zealand), Mauna Loa (Hawaii), Table Mountain (California), and Observatoire de Haute Provence (France). For lidar measurements, we used the same collocation criteria as for ozonesondes and found a total of 177 collocation matches during the validation period.

3.1 Inversion technique

The IUP Bremen retrieval algorithm, which will be referred to as TOPAS, is based on the first-order Tikhonov regularisation approach (Tikhonov, 1963), as described in detail by Rodgers (2002). The relationship between the state vector x that contains the atmospheric quantities to be retrieved and the measurement vector y is given by the forward model operator F(x): $\mathit{y}=F\left(\mathit{x}\right)+\mathit{ϵ}$, where ϵ represents all errors. For the linearisation of the problem, the derivative K of the forward model is needed, that is called the Jacobian or weighting function matrix:

The linearised expression with the a priori state vector x_a is then

The inverse problem is ill-posed and can be solved by minimising the following norm:

Here S_y is the measurement error covariance matrix, and S_r is the regularisation matrix. The latter contains contributions from both the zeroth- and first-order Tikhonov terms, given by

where the zeroth-order Tikhonov term is represented by the a priori covariance matrix, ${\mathbf{S}}_{\mathrm{a}}^{-\mathrm{1}}$ (see, for example, Rodgers, 2002), S_t is the first-order derivative matrix (see, for example, Rozanov et al., 2011a) and γ a scaling factor.

Since the problem is not linear, an iterative approach is necessary. Here, a Gauss–Newton iteration scheme is used as described in detail by Rodgers (2002). It should be noted that in the first iteration, x₀=x_a. In the subsequent iterations, x₀ is replaced by the solution obtained from the previous iteration, while x_a remains fixed. The solution at iteration step i+1 is given by

As in the TOPAS algorithm the relative deviations from the a priori state are retrieved, the appropriate transformation of the state vectors and Jacobian and regularisation matrix is done:

where 1 is the unity vector, and X_a=diag{x_a}. Equation (5) is then written as

We note that this transformation also affects the retrieval error matrix, S_e, and the averaging kernel matrix, A. The matrices for the transformed variables are related to those for the standard inversion described by Rodgers (2002) as follows:

3.2 Retrieval algorithm

The TOPAS retrieval approach is structured as follows: first, the a priori information in the first iteration or the results from the previous iteration serve as input to the forward simulations with the radiative transfer model (RTM) in the next iteration. A polarisation correction given by a lookup table (LUT) is applied to the simulated intensities and will be described later in this section. In a subsequent preprocessing step, the calibration correction spectrum, the rotational Raman scattering, and an offset correction are fitted to the radiance spectrum and a first-order polynomial is subtracted. Finally, the vertical ozone profile and a Lambertian (scalar) surface albedo are retrieved using Eq. (7). An overview about the relevant retrieval parameters is given in Table 1.

Table 1Overview of the ozone profile retrieval settings.

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The inversion of the ozone profile is an ill posed mathematical problem. Consequently, the retrieval needs to be constrained by a priori information. Information on total ozone is needed because it helps to determine the ozone profile selected from the climatology as a priori.

The a priori profiles for ozone are taken from the ozone climatology of Lamsal et al. (2004), which contains ozone profiles averaged from sonde and satellite data depending on latitude, season, and total ozone. For each processed profile, the a priori ozone profile is scaled with an initial value for the total ozone. In order to obtain the best possible starting point, the total ozone and the effective scene albedo from the WFDOAS retrieval (Coldewey-Egbers et al., 2005; Weber et al., 2018) applied to TROPOMI is used. For the total ozone amount a positive bias of 2 % in comparison to Brewer and Dobson instruments was found (Orfanoz-Cheuquelaf et al., 2021). Pressure and temperature profiles are taken from the ERA5 reanalysis (Hersbach et al., 2020). The effective scene height accounts for cloud effects and is calculated using surface height, cloud coverage and cloud-top-height. The cloud parameters are part of the operational ESA data product (Loyola et al., 2018). The cloud fraction and cloud-top-height are taken from the offline total ozone S5P product, which contains the OCRA (Optical Cloud Recognition Algorithm) cloud fraction and ROCINN_CRB (Retrieval Of Cloud Information through Neural Networks, cloud as reflecting boundary) cloud altitude matched to the UV3 channel. The cloud-top-height and surface height are weighted according to cloud coverage to determine the effective scene height (Coldewey-Egbers et al., 2005). That enables cloudy and cloudless pixels to be retrieved without a need to account for clouds implicitly in the RTM.

The radiative transfer model SCIATRAN V4.1 is used for the forward simulations (Rozanov et al., 2011a). The radiance in the wavelength range from 270 to 329 nm is simulated with the spectral resolution and sampling of TROPOMI. Polarisation and rotational Raman scattering are omitted for reasons of computing time and are accounted for using a lookup table . Instead of a full-spherical atmosphere, a pseudo-spherical atmosphere is assumed, which accelerates the calculation even more. In this approximation, the direct solar beam is calculated for a fully spherical atmosphere, while for the scattered light, a plane-parallel atmosphere is assumed (Rozanov et al., 2000). This might, however, result in larger errors for larger viewing angles. In this study we use the fact that these errors are largely mitigated if the forward model is run using the angles (viewing, solar zenith, and azimuth) at the surface rather than those at the top of the atmosphere (de Beek et al., 2004).

The radiance spectrum calculated by the RTM is corrected for polarisation using a wavelength-dependent scaling factor. To determine this factor, simulated spectra with and without polarisation are taken from the LUT with appropriate values for albedo, total ozone, geometric height, and viewing geometry. These spectra are then convolved with the TROPOMI instrument response function (ISRF) (ESA/KNMI, 2021b). The ratio of both is then used as a correction factor to account for the polarisation effects.

To account for atmospheric and instrumental effects which are not included in the forward modelling, the preprocessing fit procedure includes three pseudo-absorbers and accounts for a possible misalignment of the wavelength grids of the measured and modelled spectra by performing shift and squeeze correction (Rozanov et al., 2005). During the preprocessing step, the original wavelength range is divided into three spectral windows: 270–300 nm (UV1 for TROPOMI), 300–310 nm (lower UV2) and 310–329 nm (upper UV2). For each of these spectral windows, pseudo-absorbers and shift/squeeze corrections were fitted independently. The first pseudo-absorber used in the fit, which accounts for the missing contribution from the rotational Raman scattering in the forward model, is the Ring spectrum. The Ring spectrum is obtained from LUT using the same procedure as for the polarisation correction spectrum (ratio of convolved radiances modelled with and without rotational Raman scattering contribution). The second pseudo-absorber represents the calibration correction, which accounts for errors in the stray-light correction and other systematic errors in the radiometric calibration parameters. The calibration correction spectrum is determined using the radiances modelled with ozone information from collocated MLS/Aura measurements as described in details below. This pseudo-absorber, as shown in Fig. 5, indicates a discontinuity around 300 nm. In the second spectral window (300–310 nm), the scaling of the recalibration term is not sufficient to remove the discontinuity near the channel boundary. Therefore, in this spectral window, a linear polynomial is fitted by least squares and subtracted for each fitting term separately. The third pseudo-absorber accounts for a wavelength-independent offset in the radiance spectra. To this end, the inverse of the solar spectrum is scaled to the radiance spectra for each of the three spectral windows (Rozanov et al., 2011b).

The Tikhonov regularisation was proven to be very efficient in dealing with non-linear ill-posed problems (e.g. Hasekamp and Landgraf, 2001). The Tikhonov regularisation is particularly effective in smoothing oscillations, which are typical of retrievals at a fine vertical grid.

In the main retrieval step, the first-order Tikhonov regularisation is employed, which ensures that the ozone profile retrieval remains stable and converges, even if the number of independent pieces of information is much lower than the total number of retrieval grid levels. As the zeroth-order Tikhonov term, the inverse a priori covariance matrix, ${\mathbf{S}}_{\mathrm{a}}^{-\mathrm{1}}$, is used. The a priori variance, which is intended to keep the solution within the natural variability from its a priori value (Rodgers, 2002), is set to 0.3 for both the Lambertian surface albedo and ozone number densities at all altitude levels. The assumed a priori variance for ozone is in generally good agreement with the findings of Lamsal et al. (2004), who reported the variability of ozone to be generally less than 30 % in the upper stratosphere and up to 60 % in the troposphere. In this study, we preferred to use the altitude-independent (constant) a priori variance for ozone rather than the values from the climatology as the latter might introduce vertical irregularity in the retrieval sensitivity, distorting the shape of averaging kernels and occasionally resulting in retrieval artefacts. The strength of the first-order Tikhonov term is controlled by the altitude-independent scaling factor γ (see Eq. 4), which is set to 0.007. The optimum value for this scaling factor is unknown, but through empirical studies we found that this value has the largest information content in the retrieval, and the rms between the measurement and forward model is the smallest. The measurement error covariance matrix, S_y, was filled with squared signal-to-noise ratio (SNR) values, which for the TROPOMI instrument are reported for each spectral measurement in the level 1B product. The noise is a measure for the 1 standard deviation random error of the radiance measurement, and it is assumed to be spectrally uncorrelated; i.e. all off-diagonal elements of the noise covariance matrix are set to zero.

The state vector comprises the ozone number densities at the retrieval grid levels and the effective Lambertian surface albedo. The vertical grid of the retrieval ranges from the effective scene height to the top of the atmosphere (at 60 km) in steps of 1 km. Within each iterative step, the ozone profiles and the effective surface albedo are retrieved independently; i.e. no crosstalk between these parameters is considered. For the ozone profile retrieval, the wavelength range from 270 to 329 nm is used, while the albedo retrieval is done using the 310–329 nm spectral range. A wavelength-independent (constant) surface albedo retrieved from the wavelengths above 310 nm is used in the next iterative step for the entire spectral range. This is done because the radiation at shorter wavelengths barely reaches the ground, and, thus, the surface albedo for wavelengths below 310 nm is much more challenging to determine. We note that the retrieved effective Lambertian surface albedo is not merely the surface reflection but also includes contribution from the backscattering of the radiation by aerosols and clouds. The combined use of the effective scene height and effective albedo eliminates the need to include the contributions from the tropospheric aerosols and clouds in the forward modelling. The iterative process ends when one of the two convergence criteria is fulfilled: the change of the ozone number density in a selected height range or the change of the spectral fit rms (the difference between the measured and modelled radiances) from the corresponding values at the previous iterative step is below 2 %.

4.1 Synthetic retrievals of ozone profiles

One of the widely used approaches to check the self-consistency of the retrieval, investigate its sensitivity, and estimate uncertainties and biases in the retrieved parameters is to undertake sensitivity studies. We call the data sets, used in these sensitivity studies, synthetic retrievals of ozone profiles. To this end, the radiances are simulated using the forward model for a representative set of geophysical scenarios. The retrieval algorithm then runs with the simulated radiances instead of the measured ones. The advantage of this approach it that the true state of the atmosphere is known, which is never the case for the real data.

In this study, the radiances are simulated in the spectral range from 270 to 329 nm (TROPOMI UV1 and UV2 bands). The spectral resolution and sampling are set to 0.5 and 0.065 nm, respectively, which is in accordance with the specifications of the TROPOMI instrument. All spectra are simulated assuming a fully spherical atmosphere and multiple scattering. The solar irradiance spectrum from Chance and Kurucz (2010) convolved with the TROPOMI instrument response function is used in the simulations. To investigate the uncertainty associated with the usage of LUTs to account for the polarisation and the rotational Raman scattering (see Figs. S1–S4 in the Supplement), the simulated radiances were calculated with the following settings: (i) without both the Ring effect and polarisation, (ii) with polarisation only (no Ring effect), and (iii) including the Ring effect only (no polarisation). Furthermore, the effect of the viewing and illumination geometry as well as of the surface albedo on the resulting retrieval uncertainties is investigated. The ozone profiles used to calculate the simulated radiances are taken from the CAMELOT study (Levelt and Veefkind, 2009), whose general objective was to establish the quality requirements for air quality and climate monitoring by satellites. Three ozone profile scenarios were selected: European background, China polluted, and south polar. Furthermore, two variants of the European ozone profile with enhanced tropospheric pollution were created: one limited to enhancement in the planetary boundary layer and the other enhanced uniformly over the entire troposphere. The pressure and temperature profiles were also taken from the CAMELOT scenarios. In Table 2, a complete overview of the parameters used in this study is given. In total, 1500 synthetic spectra were generated.

Table 2Input parameters for the generation of synthetic spectra.

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The settings for the synthetic retrieval are kept as close as possible to those of the real TROPOMI retrieval. However, a few settings needed to be adjusted. Instead of a measured solar spectrum, we use in the synthetic retrieval the solar spectrum from Chance and Kurucz (2010) convolved with the measured instrument response functions. The signal-to-noise ratio is set in accordance with SNR values extracted from selected TROPOMI measurements. For each scenario, a TROPOMI measurement at possible closest conditions was selected to extract the SNR values. Depending on the wavelengths and viewing and illumination geometry, typical SNR values for binned TROPOMI pixels vary between 100 and 600 in the UV1 band and between 200 and 4000 in the UV2 band. The noise sequences are created with a Gaussian random noise generator available within the SCIATRAN package. For each scenario, 50 independent noise spectra are generated. The synthetic retrievals use the same a priori ozone profiles as for the real TROPOMI retrievals, while the initial guess for the surface albedo is set to a fixed value of 0.5. Since neither calibration errors nor offsets are included in the simulations, and the same RTM is used in the simulation and retrieval, the calibration correction pseudo-absorber is turned off in the synthetic retrievals.

4.2 Sensitivity study

An overview of the ozone profiles resulted from the synthetic retrieval is shown in Fig. 2. The results for the five CAMELOT profile scenarios for all viewing geometry settings and both albedos are shown there. The three European profiles differ only at altitudes below 20 km and are intended to assess the sensitivity of the retrieval to the tropospheric pollution. In the stratosphere, the ozone profile retrieval can reproduce true values very well. For the south polar (panel d) and Chinese profiles (panel e), the a priori profiles deviate from the true values by more than −25 % or up to $-\mathrm{1}\times {\mathrm{10}}^{\mathrm{18}}$ molec m⁻³. Despite the large differences between a priori and true profiles, the retrieval results are in a good agreement with the true profiles. The retrieval in the stratosphere seems to be nearly independent of the a priori profile values, as indicated by the measurement response of about 1 (not shown). Since the vertical resolution is limited, a dependence on the shape of the a priori ozone profile remains.

Above 50 km, the sensitivity of the retrieval decreases and the deviations increase. This is explained by the fact that the maximum of the ozone weighting functions at the shortest wavelength lies at about 50 km. Below 25 km, the retrieval results strongly depend on the ozone profile scenario used. In general, the closer the a priori profile is to the true profile, the smaller the retrieval error is. In scenarios with small differences between the a priori and true profiles in the troposphere, the retrieval results seem reasonable. Between 20 and 25 km, all profiles show small negative deviations. Here, the vertical gradient of the ozone profiles is particularly strong, and the retrieval is challenging because the averaging kernels have strong contributions from the ozone peak located above. Below 10 km, the deviations are within 25 % for the European profiles, (panel k) to (panel m), while for the other two profiles, (panel n) and (panel o), the a priori seems to be too far from the truth, so that the retrieval results cannot reach the true values. For the same reason, somewhat larger disagreement between the retrieved and true profiles is observed in the lowermost stratosphere (18 to 25 km).

When the retrieval results are compared to observations or data products having a higher vertical resolution, the latter are usually convolved with the averaging kernels of the former. This also applies to the CAMELOT profiles used here as they have a finer vertical structure than can be resolved by the TOPAS algorithm. The convolution with the averaging kernels is done as follows:

where x and $\widehat{x}$ represent the original and the convolved CAMELOT profiles, respectively, x_a is the a priori ozone profile, and $\stackrel{\mathrm{̃}}{\mathbf{A}}$ is the averaging kernel matrix corresponding to the retrieval with the transformed variables (see Eq. 6). In Fig. 2, $\widehat{x}$ is shown in green. By applying the averaging kernels, the comparison profiles are smoothed with the strongest changes occurring in the troposphere, where the vertical resolution of the retrieval (as shown in Fig. 3) is lower. The difference between the retrieval results and averaging kernel smoothed comparison profiles is significantly smaller than that without applying the averaging kernels. Overall, the deviations are below ±10 % over the entire altitude range.

Figure 2Retrieval results for the five CAMELOT scenarios (true); all settings are listed in Table 2. The upper row, (a–e), shows the retrieved (orange), a priori (black), and true profiles (red), as well as the true profiles convolved with the averaging kernels (green). The middle and bottom rows present the absolute (f–j) and percentage (k–o) mean differences between the retrieval results and the true profiles (orange), the mean differences between the retrieval results and true profiles convolved with the averaging kernels (green), and the differences between the a priori and true profiles.

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As a next step, we analyse essential retrieval diagnostics, i.e. averaging kernel matrix (AK matrix), vertical resolution, and precision. They are shown for the European background profile (solar zenith angle (SZA) 30^∘, viewing angle (VA) 20^∘, relative azimuth angle (RAZ) 0^∘, albedo: 0.1) in Fig. 3. The averaging kernel matrix consists of 61×61 entries, the averaging kernels (AKs), one for each altitude level. For the sake of clarity, AKs at every 5 km layers are shown in panel (c). At altitudes between 20 and 45 km, the peaks are clearly pronounced and centred at the nominal altitudes of AKs. Above and below this region, the AK shapes are strongly asymmetric. For example, at 15 km there is no clear maximum. At this altitude, the retrieved profile is affected by changes of the true profile in a wide range of altitudes with the strongest contribution from the 12–21 km altitude region and non-negligible influence from altitudes below 25 km to the ground. For the layers below 20 km, a double peak shape of AKs is observed. The averaging kernels for 0 and 5 km do not differ much, which means that no vertical structure can be resolved in the lower troposphere.

The vertical resolution of the retrieval calculated as the inverse of the main diagonal of the AK matrix (Purser and Huang, 1993) is shown in Fig. 3d. The best vertical resolution of about 6 km is reached in the stratosphere between 30–40 km. Above 50 km, the vertical resolution strongly degrades. As a consequence, we perform the TROPOMI retrieval only up to 60 km. In the upper troposphere at about 9 km, the vertical resolution locally degrades to about 20 km and then improves again with the decreasing altitude down to the boundary layer.

Figure 3e illustrates the influence of the measurement noise on the retrieval results. The noise retrieval error calculated in the linear approximation using the Rodgers formalism (Rodgers, 2002; Sect. 3.4.2, Eq. 3.30) is plotted in blue and is around 0.2 %. The error is relatively small because the SNR values from binned TROPOMI pixels are used. In green, the standard deviation of the ozone profiles retrieved from synthetic spectra with different noise sequences added is plotted. It agrees well with the noise retrieval error. Following von Clarmann et al. (2020), we interpret our results as an estimate of the smoothed truth and thus do not consider the smoothing error as an error component.

Figure 3Retrieval diagnostics for the European background profile, SZA of 30^∘, VA of 0^∘, RAZ of 0^∘, and albedo of 0.1. (a, b) Profiles and relative mean differences for 50 noisy spectra. (c) Averaging kernels for every 5 km altitude levels. (d) Vertical resolution of the retrieval. (e) Retrieval noise error (blue) as defined by Rodgers (2002) and the standard deviation of the retrieval results from simulated spectra with 50 noise realisations (green).

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Figure 4 shows the vertical resolution of the retrieval for all geometries and albedos for one true profile (polluted Chinese case). Each of the four panels shows the results for 25 combinations of the viewing angle (VA) and solar zenith angle (SZA) used in the sensitivity study. On the left, the retrieval results for low surface albedo (0.1) are shown, which simulates cloud and ice-free pixels. On the right, the high-albedo (0.8) scenarios are shown. The top and bottom panels show the vertical resolution of the retrieval for azimuth angles of 0 and 180^∘, respectively. Between 18 and 50 km, the vertical resolution is similar for all geometries and surface albedos and ranges from 5 to 10 km. In the troposphere, the vertical resolution degrades to about 15 km (between 1 and 18 km altitude) but improves again in the 5 km altitude region. With exception of the uppermost and lowermost altitudes, the worst retrieval resolution of about 20 km is found at 10 km altitude. Differences between the vertical resolutions for the ground scenes with low and high albedo are most pronounced in the lower troposphere. The best vertical resolution in this altitude range is achieved for high surface albedo and small SZA. It should be noted, however, that a high albedo in the UV spectral range occurs only above clouds or snowy/icy surfaces. Ozone hidden below clouds can of course not be retrieved.

In general, the vertical resolution is determined by the influence of the ozone absorption in each particular altitude region on the total strength of the ozone absorption signal registered by the instrument. Two factors are essential here and both depend on the observation and illumination geometry. These are the length of the effective light path through the altitude layers of interest and the amount of light originating from these layers. While the latter depends on the amount of the incident light and scattering properties of the atmosphere, the light paths always increase with the geometrical angles (SZA, VA, and AA). Furthermore, the simulations were done using TROPOMI-specific SNR values for each viewing geometry, which also influences the sensitivity of the retrieval. The solar zenith angle (different colours) strongly affects the vertical resolution below about 17 km as less light penetrates into the lower atmosphere at large solar zenith angles. The best vertical resolution is obtained at the smallest SZA (blue), where more light is scattered back to the instrument. The vertical resolution is also impacted by the viewing angles (plotted with different line styles) and the azimuth angles. Below about 17 km and at large SZA, there is a degrading vertical resolution with increasing VA for very high AA, which is most probably related to an increased light path of the direct solar light through the troposphere, thus decreasing the amount of light to be scattered. On the contrary, for lower AA the vertical resolution is improving with larger VA. The troposphere becomes invisible for the retrieval at large SZAs (>85^∘). Depending on the viewing angle, this might be the case already at 75^∘ SZA for large azimuth angles.

Figure 4Vertical resolution of the retrieval for all simulations with the Chinese polluted ozone profile. The panels show the different combinations of the surface albedo (0.1 and 0.8) and relative azimuth angles (0 and 180^∘). Each panel displays the results for 25 combinations of VA and SZA.

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A measure for independent pieces of information in the retrieved ozone profiles is provided by the number of degrees of freedom (DOF) determined from the trace of the averaging kernel matrix ($\text{DOF}=\text{tr}\left(\stackrel{\mathrm{̃}}{A}\right)={\sum }_{i=\mathrm{1}}^n{a}_{ii}$). About 6.5 independent variables (from 6.3 for the south polar scenario to 6.7 for the polluted China case) can be retrieved in the altitude range between 0 and 60 km. This corresponds to a mean vertical resolution of about 9 km. Between 0 and 18 km, the synthetic retrievals show around 1.5 DOF. This means that somewhat more information than the total ozone content can be determined in the troposphere. In summary, profile information in the troposphere is severely limited and thus dependent on the a priori ozone profile.

It should be noted here that the number of independent variables might change in the retrievals using real TROPOMI data because of additional pseudo-absorbers which cannot be applied to the synthetic data. These pseudo-absorbers serve to compensate for inestimable calibration errors in the measured radiation.

6.1 Ozonesondes

Figure 7 shows the results of the comparison of TROPOMI ozone profiles with ozonesonde measurements. Here, the relative mean difference Δ and its standard deviation SD(Δ) are shown, which are defined by

where r_i and s_i are the data from the ith collocated pair of TROPOMI and sonde measurements, respectively. The relative mean deviation between the TOPAS retrieval results and high-resolution ozonesonde data from all collocations (panel a, black curves) is about 5 % down to about 13 km increasing to about 10 % below. The standard deviation varies between 10 % and 20 % in the lower stratosphere (18–30 km) and between 25 % and 50 % below 18 km. The comparison of the retrieved O₃ profiles from TROPOMI and ozonesondes convolved with the TOPAS averaging kernels (panel a, red curves; see Eq. 9) shows that the relative difference is below ±5 % for all altitudes. The difference between the black and red curves is particularly large in the altitude range, where the retrieval is less sensitive (8–18 km).

Figure 7Comparison of the ozone profiles retrieved from TROPOMI and those from ozonesondes for different zonal bands. The relative mean difference between the retrieval results and the high-resolution sonde data (solid line), as well as the standard deviation of the differences (dashed line), is shown in black. The comparison with the sonde profiles convolved with the TOPAS averaging kernels is shown in red. In grey the relative difference between the a priori ozone profiles and high-resolution ozonesonde profiles is displayed, along with the corresponding standard deviations.

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The results for the northern latitudes and tropics (panels d to f), where the number of available sonde measurements are the highest, look very similar to one another. Above 18 km and below 8 km the relative mean differences are below about ±10 % with 15 % standard deviation. At high and middle southern latitudes (panels b and c), the results are somewhat poorer in the troposphere and lower stratosphere. Between 8 and 18 km differences of +40 % and above can occur.

Also noticeable are the larger differences between the a priori and sonde profiles. As shown in Fig. 2, the results in the altitude range between 8 and 18 km are strongly dependent on the a priori ozone profile. A better choice of the a priori in southern latitudes could possibly improve the retrieval results. With increasing latitudes the viewing geometries change, and especially the SZA becomes larger. There is a connection between SZA and vertical resolution so that at larger angles the vertical resolution between 8 and 18 km strongly decreases. As a consequence, the retrieval remains close to the a priori.

In the lower troposphere (around 5 km) an agreement with the raw ozonesonde profiles within 10 % is observed in all latitude bands, which coincides with the increased vertical resolution found in the altitude range around 5 km; see Fig. 4. As the difference of the a priori to the sonde profiles (grey) is generally larger than that for the retrieved profiles, we can say that the retrieval improves the ozone knowledge in this altitude range for all latitude bands. But we have to note that the standard deviation, in comparison to the a priori, remains almost the same.

Figure 8Scatter plot of collocated TROPOMI and ozonesonde profiles, the latter with and without convolving with TOPAS averaging kernels (red and black, respectively) for different altitudes (note different scales). The comparison between a priori and sonde profiles is shown in grey. The solid lines show the linear fit. The R value is indicated in the top left corner of each panel (also black and red). The ideal 1:1 curve is plotted as a dashed line.

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Figure 8 illustrates the quality of the retrieval at different altitudes in a scatter plot. Again, the retrieval is compared with ozonesondes with (red) and without the convolution with the TOPAS averaging kernels (black). The linear regression is plotted as a solid line (red and black), and the dashed line marks the ideal 1:1 curve. At 1 and 5 km altitude the scatter is wide, and also the R value is small. At 10 km the convolution of the sonde profiles with TOPAS AKs improves the comparison because here the information content is the lowest. The best agreement is found at altitudes 15, 20, and 30 km. The R value here is above 0.8 (0.9 after convolving with AKs), and the linear regression is close to the 1:1 line. At 25 and 33 km the scatter is a little bit larger, but with R values larger than 0.7 the agreement is still good. The slope of the linear regression lines (black and red) improves for each altitude shown in comparison to the a priori slope (grey). In regions where the information content is very limited (10 and 15 km), only the comparison to ozonesondes with applied AKs shows improvement.

6.2 Lidar

Figure 9 shows the relative mean differences (solid line) and the standard deviations (dashed line) between the retrieved profiles form TROPOMI and lidar data (black) for five individual stations and the all-station average (panel a). In addition, the difference between the TOPAS results and the collocated MLS ozone profiles (convolved with TOPAS averaging kernels) is shown in green. When all stations are considered, the deviations between 15 and 45 km are below ±5 % (grey bar). There is a small positive bias between 25 and 45 km that comes mainly from the Table Mountain station data set, which contains the largest number of comparison profiles. The standard deviation of the differences is about 10 % in the range of 20 to 40 km. The comparison with lidar profiles convolved with TOPAS averaging kernels (red) shows nearly the same results for the mean relative difference but a smaller standard deviation above 40 km and below 20 km. A closer look at the individual station reveals generally good agreement but also individual station-dependent deviations. For OHP, Hohenpeißenberg, and Lauder, no larger differences are identified. At Table Mountain there is a stronger negative peak of −9 % around 20 km. Above this altitude a positive bias of up to +10 % increasing with height is observed. The comparison to MLS also shows the negative peak at 20 km but does not show the positive bias at higher altitudes. At Mauna Loa there is a positive bias of +10 % between 25 and 30 km that is also present in the comparison with MLS.

Figure 9Comparison between TROPOMI ozone profile retrieval and the results from five different lidar stations and all-station average. The colours are the same as in Fig. 7 but for lidar instead of ozonesonde data. In addition, the difference between the TROPOMI ozone profile retrieval and MLS results convolved with the TOPAS averaging kernels is shown in green. Only collocated MLS profiles are used (distance <1000 km and time <2 h).

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Scatter plots at individual altitude layers are presented in Fig. 10. The colours and lines are assigned in exactly the same way as for the ozonesonde validation shown in Fig. 8. From the scatter plots (Fig. 10), it is evident that in the altitude range between 15 and 40 km the agreement is very good, with R values above 0.6 both with and without convolving with TOPAS averaging kernels. An exception is the altitude of 25 km, where the spread gets larger and the R value lower. At altitudes above 45 km the sensitivity of the TOPAS retrieval decreases, and the agreement after convolving the lidar data with TOPAS averaging kernels is much better. It is notable that above 40 km the TOPAS retrieval shows smaller variability than lidar data. It is not yet known if this is a consequence of the lower sensitivity of the TOPAS retrieval or the lower precision of lidar measurements. Similar to the ozonesonde results, the slope of the linear regression is improving in comparison to the a priori.

Figure 10Same as Fig. 8 but for comparison of TROPOMI ozone profiles with lidar measurements.

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