The 2017 release of the ESA Ozone_cci Climate Research Data Package contains 13 nadir ozone profile products in total, as listed in Table 1, and a description of their associated uncertainties. The latter are included in the comparison results discussion presented in Sect. 5. The time span of the products is indicated in Table 2. All five Level-2 (L2) backscatter UV–VIS instrument retrievals are performed by the RAL algorithm, while the infrared thermal emission measurements of the IASI instruments are processed by a collaboration between the ULB and LATMOS, using their FORLI algorithm. All instruments listed in Table 1 are on satellite vehicles with a Sun-synchronous low Earth orbit, resulting in fixed local solar overpass times (also see Sect. 3.3).

Monthly averaged Level-3 (L3) products and assimilated Level-4 (L4) atmospheric fields of the ozone profile are produced from the L2 UV–VIS data by the Royal Meteorological Institute of the Netherlands (KNMI). The L4 product is generated by assimilation of the L2 GOME and GOME-2A products (NP_GOME and NP_GOME2A). Version 0004 of the L3 and L4 products has been considered in this work (see Table 1). For the thermal infrared IASI instrument on Metop-A, only a tropospheric L3 product (prefix TTC instead of NP in Table 1) has been generated by the ULB–LATMOS team, of which the first release (version 0001) is under study in this work.

Full time series of the ERS2 GOME (1996–2011), Envisat SCIAMACHY (2002–2011), Metop-A GOME-2 (2007–2013), Metop-B GOME-2 (2013–2015), and AURA OMI (2004–2015) nadir ozone profile data were retrieved at the RAL using version 2.14 of its RAL retrieval system. Each ozone profile is provided in volume-mixing ratio (VMR) and number density (ND) units on a fixed vertical grid with 20 levels ranging between 0 and 80 km, while the values of the 19 intermediate partial ozone column layers are provided as well. The RAL retrieval is a three-step process (Munro et al., 1998; Siddans, 2003; Miles et al., 2015).

In the first step, the vertical profile of ozone is retrieved from Sun-normalized radiances at selected wavelengths of the ozone Hartley band, in the range 265–307 nm, which primarily contains information on stratospheric ozone. Prior ozone profiles come from the McPeters–Labow–Logan (McPeters et al., 2007) climatology, except in the troposphere where a fixed value of 1012 ozone molecules per cubic metre is assumed. A prior correlation length of 6 km is applied to construct the covariance matrix. The surface albedo, a scaling factor for the Ring effect, and the dark signal are retrieved jointly. In the second step, the surface albedo for each of the ground pixels is retrieved from the Sun-normalized radiance spectrum between 335 and 336 nm. Then, in step three, information on lower stratospheric and tropospheric ozone is added by exploiting the temperature dependence of the spectral structure in the ozone Huggins bands. The wavelength range from 323 to 334 nm is used in conjunction with ECMWF ERA-Interim meteorological fields (Dee et al., 2011). Each direct Sun spectrum is thereby fitted to a high-resolution (0.01 nm) solar reference spectrum to improve knowledge of wavelength registration and slit function width. In this step the a priori ozone profile and its error are the output of step one, except that a prior correlation length of 8 km is imposed.

RAL's radiative transfer model (RTM) is derived from GOMETRAN (Rozanov et al., 1997), but the original code has been modified substantially in order to increase its efficiency without losing accuracy. Within the RTM there is no explicit representation of clouds, but their effects are incorporated as part of the Lambertian surface albedo (from step two of the retrieval). Therefore a negative bias in retrieved ozone is to be expected where high or thick cloud is extensive and there is limited photon penetration (no “ghost column” is added). The linear error analysis of the RAL retrieval is additionally complicated by the three-step retrieval approach. Particularly as the ozone prior covariance used in step three is not identical to the solution covariance output from step one. This is handled by linearizing each step and propagating the impact of perturbations in parameters affecting the measurements through to the final solution. The estimated standard deviation of the final retrieval is taken to be the square root of the step-three solution covariance.

In this work, all nadir ozone profile screening of RAL retrievals follows the recommendations as outlined in the latest version of RAL's Ozone Profile Algorithm Product User Guide (PUG). As summarized in Table 3, the filtering requires that the normalized cost function is less than 2, the convergence flag equals 1, all ozone profile values are positive, the solar zenith angle (SZA) is below 80∘, and the effective cloud fraction (ECF) below 20 %. Additionally, for GOME-2A and B the band 1 slant column density must stay below 500 DU, and the OMI outer two pixels from each swath are rejected (see product-specific criteria in Table 3). Back-scan measurements are never considered.

The Ozone_cci Metop-A and Metop-B IASI nadir ozone profile data for 2008–2015 and 2013–2015, respectively, were generated in a near-real-time mode using the FORLI-O3(Fast Optimal Retrievals on Layers for IASI Ozone) latest version 20151001 (see Hurtmans et al., 2012 for a full description of the retrieval parameters and performances). FORLI-O3relies on a fast radiative transfer and a retrieval algorithm based on the optimal estimation method (Rodgers, 2000). In the current version of FORLI-O3, look-up tables (LUTs) were precomputed to cover a larger spectral range (960–1105 cm-1) using the HITRAN 2012 spectroscopic database (Rothman et al., 2013) and correcting numerical implementation, especially with regard to the LUTs at higher altitude compared to the previous version. Ozone is retrieved using the 1025–1075 cm-1 spectral range, which is dominated by ozone absorption with only few overlapping water vapour lines and a weak absorption contribution of methanol. The a priori information used in the FORLI algorithm consists of a single global ozone prior profile. The prior variance–covariance matrix is built from the McPeters–Labow–Logan climatology (McPeters et al., 2007), as for RAL. A purely diagonal wavenumber-dependent effective noise at a value around 2 × 10-8 W cm-1 sr-1 is considered in the retrievals (Hurtmans et al., 2012).

The FORLI-O3product consists of a vertical profile retrieved on a uniform and fixed 1 km vertical grid on 40 layers from the surface up to 40 km, with an extra residual layer from 40 km to the top of the atmosphere (60 km in practice). Associated averaging kernels and relative total error profiles are provided on the same vertical grid. A posteriori filtering of the data – performed by ULB–LATMOS before data distribution – is applied to keep only the more reliable data, by removing those corresponding to poor spectral fits (root mean square of the spectral fit residual higher than 3.5 × 10-8 W cm-1 sr-1) or incomplete water vapour retrievals. Additionally, quality flags rejecting biased or sloped residuals, suspect averaging kernels, and violations of the maximum number of iterations are applied (see Table 3). Cloud-contaminated IASI scenes characterized by a fractional cloud cover above 13 % are also filtered out, as identified using cloud information from the EUMETCast operational processing (August et al., 2012). Upon discussion within the Ozone_cci community, it has been decided in this work to also reject FORLI ozone profiles whose ratios of the 0–6 km integrated column to the fully integrated column exceed 0.085. These provisional fixes, however, are corrected for in the online Ozone_cci nadir ozone profile product release.

For the thermal infrared IASI instrument on Metop-A, a tropospheric L3 product (prefix TTC instead of NP in Table 1) has been generated by the ULB–LATMOS team from their quality-screened L2 nadir ozone profile retrievals directly. This product consists of horizontally gridded (1∘ latitude by 1∘ longitude) monthly averages of the 0 to 6 km vertically integrated IASI-A ozone observations.

Monthly averaged L3 profile products are produced from the filtered RAL v2.14 GOME, GOME-2A, SCIAMACHY, and OMI data by the KNMI. Version 0004 of the KNMI L3 products has been used in this work (see Table 1). The KNMI L3 data consist of monthly ozone profile averages, also on a 1 × 1∘ latitude–longitude grid, containing 19 layers between 20 fixed pressure levels at each grid point. The algorithm that calculates the monthly averaged ozone fields assumes that the L2 satellite ground pixel vertices (labelled ABCD) are ordered as indicated in Fig. 1. Each pixel's across-track direction is defined by the lines AD and BC, while the along-track direction is defined by the lines AB and DC. The satellite pixel is divided into 25 subpixels, 5 in the along-track direction and 5 in the cross-track direction, and each subpixel is assigned to the L3 grid cell (the boundaries are indicated with the dashed lines in Fig. 1) containing the subpixel. The subpixel values xi are weighted by the square inverse of their uncertainties (σi-2), so the weighted mean grid cell value xc and the corresponding standard deviation σc are given by xc=σc2∑ixiσi-2, and σc=∑iσi-2-12, respectively.

Assimilated L4 ozone fields are produced from the screened Ozone_cci UV–VIS nadir ozone profile data by the KNMI by use of its chemical transport model TM5. The resulting L4 assimilated fields consist of 44 ozone layers (surface to 1 hPa) on a 2 × 3∘ latitude–longitude grid for four times a day (0, 6, 12, 18 h). Version 0004 of the L4 products has been used in this work, meaning that the assimilation input is limited to the L2 GOME (1 January 1996 to 31 May 2011) and GOME-2A (1 May 2007 to 30 June 2013) products (NP_GOME and NP_GOME2A in Table 1).

A complete description of KNMI's assimilation algorithm can be found in van Peet et al. (2018). The covariance matrices and the averaging kernel matrices from the L2 optimal estimation retrievals are thereby used. For the atmospheric model, the covariance matrix must be specified as well. The observations and the model data are combined using a Kalman filter technique. The averaging kernel matrix (AKM) is incorporated into the observation operator and the observation and model covariance matrices are used in the Kalman equations to calculate the analysis fields. In order to reduce biases between multiple instruments, an ozonesonde-based bias correction has been developed. For this correction, only sondes collocated with cloud-free retrievals (i.e. cloud fraction < 0.2) have been used. This correction is applied to the L2 data before the assimilation, meaning that the ozonesonde measurements involved (from 64 stations) cannot be used for the Ozone_cci L4 comparative validation exercise (see Sect.  5.6) as FRM used for comparisons have to be independent of the validated product.

This work adopts the exhaustive seven-step satellite data QA approach presented in Keppens et al. (2015), as schematized in its Appendix A. This approach includes (1) satellite data collection and post-processing, (2) dataset content study, (3) information content study, (4) FRM data selection, (5) co-located datasets study, (6) harmonization of data representation in terms of vertical sampling and units, and (7) comparative analyses including dependences on physical influence quantities of relevance. The satellite data collection and post-processing (mainly L2 profile screening) is described by the previous section. The L2 datasets have, however, been reduced to 300 km ground station overpass datasets for the quality assessment in this work in order to reduce the total amount of data processing (i.e. satellite pixels must be within a 300 km radius from a FRM station). The FRM data selection, co-located dataset study, and data harmonization are therefore included as the successive subsections within this section. The satellite data content studies and information content studies are discussed in Sect. 4. These include statistics on the L2 station overpass data screening and spatiotemporal coverage as well as averaging-kernel-based information content measures. The comparative analysis with both spatially and temporally co-located FRM data follows later in Sect. 5.

Ground-based data records from the well-established Network for the Detection of Atmospheric Composition Change (NDACC), Southern Hemisphere Additional Ozonesonde programme (SHADOZ), and other ozonesonde and lidar stations contributing to the World Meteorological Organisation's Global Atmosphere Watch (WMO GAW) networks are used as a transfer standard against which the nadir ozone profile retrievals are compared. Like for the satellite data, and prior to searching for co-locations with satellite ECV data, data screening has been applied to the FRM. The recommendations of the ground-based data providers to discard unreliable measurements are thereby followed, both on entire profiles and on individual vertical levels. Measurements with unrealistic pressure, temperature, or ozone readings are rejected automatically. Ozonesonde measurements at pressures below 5 hPa (above 30–33 km) and lidar measurements outside of the 15–47 km vertical range are rejected as well. The raw ozonesonde profiles retrieved from the public NDACC, SHADOZ data archives, and World Ozone and UV Data Centre (WOUDC) are moreover quality-screened according to the criteria outlined in Hubert et al. (2016) for a similar analysis on space-borne limb observations of atmospheric ozone: entire FRM profiles are discarded when more than half of the levels are tagged bad or when less than 30 levels are tagged good. The resulting spatiotemporal distribution of ground-based observations is summarized in Fig. 2. Despite the higher concentration of FRM in the northern mid-latitudes (20–60∘) and before 2014, the distribution is sufficiently homogeneous to consider global comparison statistics and to enable drift assessments.

The uncertainties related to the sonde and lidar FRM used in this work are discussed in Keppens et al. (2015) and Hubert et al. (2016). Essentially, ozonesondes measure the vertical profile of ozone partial pressure with order of 10 m vertical sampling (100–150 m actual vertical resolution) from the ground up to the burst point of the balloon, usually between 30 and 33 km. Their estimated bias is smaller than 5 %, and the precision remains within the order of 3 %. Above 28 km the bias increases for all sonde types. Below the tropopause, due to lower ozone concentrations, the precision decreases slightly to 3–5 %, depending on the sonde type. The tropospheric bias also becomes larger, between 5 and 7 %. Stratospheric ozone lidar systems are sensitive from the tropopause up to about 45–50 km altitude with a vertical resolution that declines with altitude from 0.3 to 3–5 km. The estimated bias and precision are about 2 % between 20 and 35 km and increase to 10 % outside this altitude range where the signal-to-noise ratio is smaller.

From all quality-approved L2 nadir ozone profile data, only those that are located within a certain radius of an NDACC, SHADOZ, or GAW ozonesonde or stratospheric lidar station location are retained for further analysis. This radius is adapted to the ground pixel size of each spaceborne instrument, in such a way that the ground-based station is roughly located within the satellite pixel (see Table 4). The possible satellite pixel index (SPI) values within each cross-track scan and the resulting number of pixels per scan are provided for each instrument in Table 4 (taking into account pixel co-adding, see Sect. 2). Additionally, only co-locations with a maximal time difference of 6 h for ozonesondes and 12 h for lidars are allowed. These time windows are chosen to generally have at least one satellite co-location with each FRM, given the satellite's fixed local solar time (LST, also see Sect. 2.1) and the fact that ozonesondes are typically launched around local noon, while lidar measurements are taken during the night. When multiple L2 satellite pixel co-locations with one unique ground-based measurement occur, only the closest satellite measurement is kept. For the L3 and L4 nadir ozone profile data, only the grid cell that overlaps with the ground-based station location is considered. All FRM within this grid cell and within the relevant month are included in the analyses for the L3 comparisons. For the 6-hourly assimilated L4 data, the unique, temporally closest, ground-based reference measurement is always less than 3 h away.

Calculating difference profiles also requires harmonization of the satellite and reference ozone profiles in terms of at least their unit representation and vertical sampling (Keppens et al., 2015). While ozonesondes report measurements in partial pressure, easily converted into VMR units and into ND using the on-board PTU measurements, the lidar data are given in ND and in general the files do not provide associated temperature profiles for a beforehand ND-to-VMR conversion. The latter has therefore been accomplished by consistently applying pressure and temperature fields that were extracted from the latest ERA-Interim reanalysis. Moreover, when there are no GPS altitude data in the ozonesonde data files, the altitude scale is reconstructed via the hydrostatic equation from the pressure and temperature recordings by the radiosonde attached to the ozonesonde. The ND profiles are integrated to partial column profiles by use of these corresponding altitude grids. The partial column profiles are then converted to the fixed satellite vertical grids by use of mass-conserved regridding, meaning that the integrated ozone column between the outer vertical edges is conserved (Langerock et al., 2015).

The optimal estimation method used in the RAL and FORLI retrieval systems consists in minimizing the difference between the measured atmospheric spectra and spectra simulated by a radiative transfer code (forward model). Since the retrieval is performed at higher vertical sampling than the actual amount of independent pieces of profile information available from the measurement, the retrieval is in general underconstrained and consequently unstable. Retrieval schemes therefore include additional constraints, e.g. in the form of a priori information on the profile, its shape, and its allowed covariance. As a result, the retrieved quantity is a mix of information contributed by the measurement and of a priori information, as represented in its vertically correlated averaging kernels. In this work, the satellite L2 and ground-based profiles' vertical smoothing is by default harmonized (i.e. reducing the vertical smoothing difference error) by smoothing of the FRM with the co-located averaging kernel (Keppens et al., 2015). The mass-conservation regridded ground-based profile xg is thereby converted into its vertically smoothed form xg′ by multiplication with the satellite profile's AKM A (in partial column units), yet taking into account the kernel's sensitivity to the prior profile xp of the optimal estimation retrieval: xg′=Axg+(I-A)xp. The reference profile hence becomes a vertically smoothed combination of the ground-based measurement (by multiplication with A) and the prior profile (by multiplication with I - A, with I being the unit matrix of dimensions A) (Rodgers, 2000).

The nadir ozone profile CRDP L2 data content study focuses on the spatiotemporal distribution and the effect of screening of the retrieved satellite profiles in the first place, next to the regular file structure, file content, and value checks for the quantities of highest relevance (also see Table 3). Figure 3 displays the latitude–time distribution per 10∘ latitude band and per month of the percentage of screened profiles for all NP L2 station overpass (300 km) datasets (except for IASI on Metop-B). The data that are screened fail the filtering criteria suggested to data users as described in Table 3 and are therefore omitted from further analysis. Where the screening goes from 0 % (all data passes, in blue) to 100 % (no data passes, in red), one could equally insightfully interpret the plots as showing the spatiotemporal coverage of the satellite data ranging between 100 % (full coverage, in blue) and 0 % (no coverage left, in red), respectively.

The screening for the GOME and SCIAMACHY instrument retrievals is quite high (60–80 % on average), mainly due to the cloud screening that rejects all effective cloud fractions above 20 %. The lack of GOME data in the southern mid-latitudes from 2003 onwards is due to severe screening of L2 overpass data for ground stations that are all located near the South Atlantic Anomaly (SAA). The ECF has less impact on the GOME-2 and OMI instruments, but the SZA screening (if higher than 80∘) still causes meridian and seasonal coverage variations. Moreover, a latitudinal striping can be observed for all UV–VIS instrument distributions, although this is partially due to the satellite pixel co-adding before retrieval and the 300 km station overpass data selection afterwards. The decreased GOME-2B availability from June 2015 onwards points at a retrieval issue and justifies additional screening, as shown in Table 3. The IASI screening, in contrast, appears very low, but this is due to the pre-screening by the product providers before data delivery, i.e. mainly the IASI cloud screening (if the fraction is higher than 13 %) cannot be observed from the plots, but is roughly of the same order as the UV–VIS data screening. Only the seasonality of the tropospheric ozone screening (ratio of the 6 km integrated column to total integrated column > 0.085) becomes clear near the Antarctic. The IASI-B availability is fully similar to IASI-A (and overlapping in time) and therefore not shown.

The baseline output of the L2 validation exercises consists of median absolute and relative nadir ozone profile differences at individual stations or within latitude bands for the entire time series. This median difference is a robust (against outliers) estimator of the vertically dependent systematic error, i.e. the bias, of the satellite data product. The bias profiles for the entire list of stations are then combined and visualized as a function of several influence quantities in order to reveal any dependences of the systematic error. The influence quantities considered in this work are latitude (for meridian dependence), quarter (for seasonal dependence) – being December–January–February (DJF), March–April–May (MAM), June–July–August (JJA), and September–October–November (SON) – total ozone column, DFS, SZA, scan pixel index (SPI), (effective) cloud fraction (for the UV–VIS products), TC (for the TIR products), and time. The latter actually results in drift studies, i.e. the annual or decadal bias change of the satellite product with respect to the ground-based reference time series.

Besides the median difference, the Q84–Q16 or 68 % interpercentile spread (IP68) on the differences is also calculated as a robust estimator of the random errors in the satellite data product, i.e. the precision profile. However, this spread on the differences will also include contributions from ground-based random uncertainties (limited to a few percent, as indicated in Sect. 3.2) and representativeness (sampling and smoothing) differences between the satellite and reference measurements, and therefore in fact provides an upper limit on the actual satellite uncertainty. In case of a normal distribution of the ozone differences, median and IP68 are equivalent to mean and standard deviation, but they offer the advantage to be much less sensitive to occasional outliers.

The long-term stability of the systematic errors in the ozone data products is a key user requirement. Robust linear regressions including an uncertainty estimate based on a bootstrapping approach (Hubert et al., 2016) are performed on the satellite–ground difference profiles for all stations within the predefined latitude bands or on the global scale. The uncertainty on the global drift that is as such introduced by inhomogeneities across the ground-based network is of the order of about 5 % decade-1, but in fact partially covered by the confidence interval obtained by the bootstrapping. This value was estimated from the standard deviation on the ensemble of single-station drift estimates in ground-based comparisons with limb-sounding instruments by Hubert et al. (2016), who use the same quality-checked selection of FRM stations. To avoid spurious effects due to a seasonal cycle in the differences, only time series of 5 years or longer are used for this drift assessment. Therefore Metop-B GOME-2 and IASI instruments are excluded from the drift studies (indicated with an asterisk in Table 4). Moreover, only fully available years of the satellite datasets have been considered for comparative analysis in order not to introduce seasonal effects at the beginning and the end of each time series.

Due to the availability of assimilated global ozone fields every 6 h, the L4 comparative validation approach is fully similar to the L2 statistics described above. The strongly reduced amount of parameters in the L4 data product files, however, reduces the number of influence quantity dependences that can be studied. These have therefore been limited to the latitude, quarter, and time (drift). Next to that, as vertical averaging kernel matrixes are only available for the L2 retrieved data, no averaging kernel smoothing can be applied before comparison. Yet as mentioned in Sect. 2.5, the L2 averaging kernel matrices are incorporated into the equations to calculate the analysis fields. Also remember that the satellite instrument bias correction by use of ozonesonde measurements, the 64 stations involved are not used for the L4 comparative validation exercise.

The situation is quite different for the validation statistics of the L3 monthly gridded averages. No L2 averaging kernels are used for the data generation and no merging or bias correction are implemented. The satellite-based and 1 × 1∘ gridded NP L3 data xsL3 can be compared with spatially co-located ground-based reference profiles xr directly or with monthly (gridded) averages 〈xr〉 of the latter (i.e. a ground-based L3-type dataset). Yet both approaches introduce similar spatial and temporal representativeness errors into the difference statistics because taking (monthly) averages as a bias estimator 〈Δx〉 yields comparable outcomes: 〈Δx〉=Nm-1xsL3-xr,1+xsL3-xr,2+…+xsL3-xr,m=xsL3-〈xr〉. For sufficiently fine-gridded L3 data, the comparisons can therefore be limited to direct differences with ground-based reference measurements, if one additionally only considers ground-based stations with a sufficient number Nm of valid measurements per month. This number has been set to six (per month, or about at least one measurement every 5 days) in the L3 validation presented in this work. As such, an implicit averaging of at least six ozonesonde or lidar measurements per month is introduced in the comparison statistics. The 1 × 1∘ box that overlaps with the ground measurements is thereby taken as the co-located measurement. Due to this high horizontal resolution of the Ozone_cci L3 satellite nadir ozone profile products and the constraint on the temporal representativeness of the ground-based data, representativeness errors are thus kept to a minimum.

In this section comparison results between L2 RAL v2.14 nadir ozone profiles and ground-based ozonesonde and lidar measurements are reported in the form of statistics on the median relative difference (bias) and 68 % interpercentile spread of ozone differences as a function of several influence quantities. Figures 6 to 10 contain the results for GOME, SCIAMACHY, GOME-2A, GOME-2B, and OMI, respectively, as a function of latitude, quarter, total ozone column, DFS, SZA, SPI, and effective cloud fraction. Note that the number of comparisons (shown in each plot title) is higher for the latter as the ECF filter has been switched off. Estimates of the relative satellite errors provided with the RAL v2.14 products have been added to the graphs (grey lines) in order to discuss them with respect to the ozone differences and spreads. In each plot the third subgraph displays the median sensitivity of the retrieved ozone profile as a function of altitude (and the relevant influence quantity), as calculated from the fractional RAL v2.14 vertical averaging kernels.

Before discussing the comparison results in terms of influence quantities, it is interesting to note that the vertical smoothing of the ground-based reference data with averaging kernels mostly yields qualitatively similar bias and spread estimates as when merely the regridded data are considered (not included). The comparisons from regridded reference data, however, show a vertically oscillating structure (as smoothing difference error) that largely disappears for the kernel smoothed comparisons. This structure is strongest around the tropics, yielding significant differences between the regridded and smoothed data, mostly due to a positive bias peek just below 20 km for the regridded data. The corresponding comparison spreads indicate that the random uncertainty on the bias is reduced by about 10 % on average by applying the averaging kernel smoothing. This value provides a rough estimate of the vertical smoothing difference error between the ground-based reference data on the one hand and the satellite data on the other hand.

Focussing on the comparisons involving averaging kernel smoothed partial column profiles, one observes that generally the five RAL v2.14 UV–VIS retrieval products agree similarly with the ground-based data, showing a rather typical Z curve with zero biases approximately at 5 and 25 km altitude (the third around 55 km is not on the plots because of the sparseness of the FRM data availability above 50 km). The negative bias peak in the UTLS and above (5 to 25 km) and the positive bias peak in the upper stratosphere (between 25 and 55 km) both amount to about 20 to 40 %. Comparison results for the 0–6 km subcolumn show that the bias again shifts towards 40 % positive values in that layer, with the exception of the OMI instrument that keeps its median tropospheric bias within 10 %. The sensitivity for this lowest layer, however, is reduced to about 0.5, meaning that generally about 50 % of the retrieval information comes from the prior profile rather than from the measurement. In the 0 to 45 km altitude range, the UV–VIS nadir ozone profile comparison uncertainties in terms of the 68 % interpercentile spread display a U-shaped curve with a minimum of about 10 % around 25 km. The uncertainty increases to roughly 40 % at 45 km, to slightly decrease again above, but rises even more strongly where the sensitivity profile peaks and towards the ground.

The individual L2 UV–VIS comparison graphs also contain information on the validity of ex ante uncertainties provided for the satellite nadir ozone profile retrievals (thin grey lines). The relative random error reported in the RAL v2.14 data files amounts to about 5 % at the altitude of the ozone maximum, up to about 10 % at higher altitudes, and up to 40 % in the lower troposphere. In theory the IP68 spread should be close to the combined uncertainty of the satellite data, the ground-based data, and metrology errors due to remaining differences in vertical and horizontal smoothing of atmospheric variability (including co-location mismatch errors). The latter is difficult to assess, but one can expect that the bias and spread estimates resulting from the comparisons, including AK smoothing, are close to the combined uncertainty of satellite and ground-based data, or at least the ex ante satellite uncertainty in practice (Miles et al., 2015). The plots in Figs. 6 to 10 show that this is hardly the case (also see the discussion in the previous section). The satellite measurement uncertainties provided in the product files do not cover the systematic and random uncertainties obtained by FRM comparisons (subtraction of the FRM uncertainties discussed in Sect. 3.2 does not make a difference). This means that the total satellite measurement and retrieval uncertainty is typically underestimated in the RAL v2.14 nadir ozone profile products, because the ex ante uncertainty under consideration only includes random noise errors. Only for the OMI tropospheric ozone data with a bias within 10 % does the combined uncertainty come close to the ex ante uncertainty. The total ex post satellite uncertainty is an unknown number because of precision ignorance, but can be estimated to range in between the combined (quadratic sum) bias and satellite random uncertainty and the combined bias and comparison spread (although the latter contains error contributions that are not part of the satellite observation, like co-location mismatch).

Looking at the dependence of the L2 UV–VIS product comparison results on the eight influence quantities shown in Figs. 6 to 10, one can observe that the latitude band and total ozone column have the biggest impact on the RAL v2.14 retrieval performance. Especially in the UTLS and the troposphere the comparison variability is very high, which is also reflected in the strong differences in spread between different influence quantity ranges. Smaller biases are typically obtained in the Northern Hemisphere and for intermediate to larger total ozone columns. Larger ozone columns are indeed expected to result in an improved satellite measurement and retrieval sensitivity, and thus more stable averaging kernel behaviour with smaller vertical dependences. In contrast, the DFS and SZA behaviour is somewhat smaller and, as one can again expect for UV–VIS observations, rather similar, with the higher SZAs typically corresponding to the larger DFS values (mainly from the stratosphere), the largest stratospheric biases, and the smallest tropospheric biases. The latter could be due, however, to a somewhat reduced tropospheric sensitivity, bringing the retrieved profile closer to the prior profile. This effect is most clear for the GOME and SCIAMACHY instruments though, while the overall DFS dependence for the other instruments is less obvious. For all UV–VIS instruments except GOME-2B, however, some satellite profiles with very low DFS, nearly zero stratospheric sensitivity, and high bias occur (mainly in the SAA, see previous sections). These profiles result from retrievals without stratospheric measurement information (hence the low DFS) and should appropriately be screened by users accordingly, e.g. using a DFS < 3 flag. Nadir ozone profiles flagged as such should then only be considered for tropospheric ozone monitoring or fully rejected because of the increased bias.

Again more or less in line with nadir ozone profile retrieval expectations, the comparison results depend little on the surface albedo and effective cloud fraction, except for the lowermost 0 to 6 km retrieval layer. Higher ozone concentrations logically correspond with lower cloud fractions and higher albedos. Note, however, that the ECF and surface albedo dependence is also reflected, yet inversely, in the UTLS, due to the typically high sensitivity peak in this region and the low compensation above. This effect is most clearly visible for the GOME-2B and OMI instruments. Instead of the full-profile effective cloud screening suggested by the RAL team now, one could thus apply layer screening up to the UTLS instead. Finally, for the UV–VIS retrievals under consideration the quarter and scan pixel index have hardly any effect on the comparison results, meaning that the RAL v2.14 retrieval algorithm copes with ozone seasonality and instrument viewing angle effects very appropriately.

Median relative differences and 68 % interpercentile spreads for comparison of L3 GOME, SCIAMACHY, GOME-2A, and OMI data with ground-based reference measurements are presented in Fig. 11. The same difference statistics are redistributed for each instrument over two influence quantity ranges, with the influence quantities being the latitude and quarter. Note the high numbers of co-locations in the title of each plot, as for each ground-based reference measurement an overlapping L3 data grid cell can be identified. As can be expected, the median relative differences roughly follow the bias features of the respective L2 datasets for their comparison with ozonesonde and lidar data. These features, together with the corresponding spreads, seem to be enlarged due to larger differences in spatiotemporal representativeness. The latter results from the lack of averaging kernel smoothing that reduces vertical smoothing difference errors and the limited amount of reference data measurements per month (although at least six, see previous sections). Note, however, that the lack of kernel smoothing instead reduces the L3 spread for the lowest level, which has a strongly reduced sensitivity in comparison with the levels above.

GOME L3 data show an above-tropopause bias of 5–10 % positive to negative, with strong outliers around 70 and 8 hPa, especially in the tropical UTLS and Antarctic local spring (up to 50 %) due to ozone hole's vortex conditions. The corresponding spread is of the order of 10–30 %, with again outliers at the same two scenes. Especially during Antarctic spring (SON) the spread explodes to the order of 100 %. Below the tropopause (100–200 hPa), GOME L3 data show stronger negative and positive biases ranging between 10 and 30 %. Exceptions can be observed in the Arctic winter (DJF) and Antarctic spring (SON), with outliers ranging up to 60 and -50 %, respectively. Corresponding spread values are of the order of 20–40 %, with the highest values again in Arctic winter.

The SCIAMACHY L3 bias and spread values are very similar to those of the GOME L3 comparison results. Only exceptions are the strong positive Arctic spring (MAM) bias in the troposphere (up to 40 %) and the availability of Antarctic winter (JJA) data showing a strong negative bias in the UTLS and above (-30 to -40 %). Also the GOME-2 instrument on board Metop-A shows a performance that is very similar to the GOME instrument in terms of L3 bias and spread. The only significant difference is in the bias during the northern and southern DJF quarter: GOME-2A outliers are much more negative (up to -50 %) for the lowest partial columns. OMI's L3 bias and spread again are very similar to those of the other three instruments, with the difference that the negative tropical tropospheric bias is more pronounced (-40 %) and a positive tropospheric bias (30–50 %) is introduced in the Southern Hemisphere during local winter (JJA).

Overall one could state that between about 10 hPa and the tropopause (100–200 hPa), relative differences and spreads are of the order of -5 and 10–30 %, respectively, for all four instruments, while the troposphere shows a 10–40 % bias (both positive and negative) and spread. Strong outliers do occur, typically in the troposphere of the Arctic winter (DJF), in the equatorial UTLS (order of 50 % positive for all seasons and instruments), and in the Antarctic local winter (JJA) and spring (SON) due to strong ozone variability around the polar vortex.

Relative decadal drift and 68 % interpercentile spreads for comparisons of L2 and L3 GOME, SCIAMACHY, GOME-2A, and OMI data with ground-based reference measurements are collected in Fig. 12. As discussed in the previous section for their bias and spread behaviour, the similarity between the L2 and L3 UV–VIS drift results for the same instrument appears very clearly. Again, however, features in the L2 statistics are enlarged for the L3 data due to larger differences in spatiotemporal representativeness (except for the lowest-level spread, see previous section).

The GOME L2 and L3 stratospheric drift typically do not exceed 10 % decade-1 values, with the exception of an almost 20 % decade-1 positive drift near the South Pole lower stratosphere and an equally large L3 peak around 35 km. Only the latter is clearly significant in terms of the corresponding 95 % drift confidence interval (CI, as horizontal error bars). This can also be observed from the highly peaked (> 60 %) IP68 spread on the differences (right-hand panel in each plot of Fig. 12). This peak indeed partially reflects the instrument's drift, as the spread is not determined from the drift residuals but with respect to the overall median difference. A large drift will as such contribute to a large spread. The negative drift values appearing above 45 km are considered less trustworthy because of the sparseness of the lidar reference data. The GOME tropospheric drift equals about -5 % decade-1 on average, but at the lowest altitudes ranges from -20 % decade-1 at the South Pole to 20 % decade-1 near the Equator. Yet again the L2 drifts remain within the CI and are therefore insignificant.

SCIAMACHY drift results strongly differ from the GOME observations: although still mostly insignificant, the above-tropopause drift is of the order of -10 % decade-1 and shows the same L3 outlier at 35 km. Below the tropopause, however, the drift ranges from about 20 % decade-1 at the poles to 50–60 % decade-1 towards the Equator. This entails that in the mid-latitudes (both north and south) and tropics this drift is significant. The GOME-2A drift results come close to the SCIAMACHY drift performance, although the sub-tropopause drift is even stronger (around 50 % decade-1) and significant globally. Besides, a significant negative drift of the order of 30 % decade-1 also appears in the UTLS, which is strongest around the Equator, reaching -70 % decade-1 around 100 hPa.

Despite the occurrence of insignificant negative drifts in the Northern Hemisphere, the OMI L3 tropospheric drift is significantly positive (around 40 % decade-1 on average) in the Southern Hemisphere and the tropics, resulting in a global average L3 tropospheric drift of the order of 15 % decade-1 (see Fig. 12). The L2 tropospheric drift equals about 5 to 10 % decade-1 only and is close to insignificant. It is remarkable that the OMI L3 drift is typically 10 % negative in the UTLS (with -40 % decade-1 values around the Equator), while in the stratosphere above an average 10 % decade-1 positive drift can be observed. Both L2 and L3 show a negative close to 20 % decade-1 value just below 40 km. These results and their significance are in qualitative agreement with Huang et al. (2017) on the OMI PROFOZ retrieval product.

On the global scale, as shown in Fig. 12, the decadal drift is order of 5 % negative and insignificant for GOME and order of -15 and 10 % insignificant (except for the tropics) for OMI's L2 stratosphere and troposphere, respectively. A significant positive drift of the order of 40 % decade-1 is observed for SCIAMACHY and GOME-2A below the tropopause. GOME-2A moreover shows a significant 30 % decade-1 negative drift in the UTLS at all latitudes.

The L4 1996–2013 data, constructed by data assimilation at KNMI from merged RAL v2.14 GOME and GOME-2A observations, can be compared with ground-based reference profiles directly. The single 2 × 3∘ box that overlaps with the ground measurement within 3 h is thereby taken as the co-located measurement. The number of co-locations and stations, however, is smaller than for the L3 data, as data from 64 ozonesonde stations (that have been used for satellite bias correction during assimilation) are omitted from the comparative analysis. Median relative differences and 68 % interpercentile spreads for comparison of the L4 assimilated nadir ozone profile data with ground-based reference measurements are collected in Fig. 13, redistributed over two influence quantity ranges (latitude and quarter). The corresponding relative decadal drift and overall 68 % interpercentile spread profiles are added as well.

The most remarkable result that can be observed from the UV–VIS L4 comparison statistics is that, as a result of the model assimilation, the typical Z-shape of the L2 bias has disappeared. The L4 bias typically remains below 10 % (positive and negative) with the exception of a strong positive outlier around 5 hPa (as for the L3 data) and the surface boundary layer and a 20 % positive to negative fluctuation around the UTLS that is strongest in the tropics (∼ 50 % positive for all seasons, with a similar but only positive bias feature in the Southern Hemisphere). This entails that the L2 and L3 comparison features in the Antarctic spring (SON) with ozone hole conditions and in most of the troposphere have been strongly reduced. The L4 spread remains close to the L2 and L3 values, though with an even stronger reduction (to 20 %) in the troposphere than the L3 comparisons as no monthly averages are considered. Moreover, due to the ozonesonde-based bias correction the remaining L4 drift is of the order of a few percent only and insignificant, i.e. within the 95 % CI, for all altitudes up to about 40 km globally.

Similarly to the L2 RAL v2.14 UV–VIS retrievals, Figs. 14 and 15 contain the median relative differences, 68 % interpercentile spreads, and vertical sensitivities for the comparison of FORLI v20151001 retrieved IASI profiles with ground-based reference measurements (IASI-A for 2008–2015, IASI-B for 2013–2015). Difference and information statistics are again redistributed in each plot over several influence quantity ranges, with the influence quantities now being the latitude, quarter, total ozone column (DU), DFS, SZA, SPI, and TC. For IASI-A in Fig. 14, the corresponding relative decadal drift and overall 68 % interpercentile spread are also added.

As already pointed out in the information content studies, the IASI-A and IASI-B results are very similar, showing no significant differences between their respective statistics. Overall the FORLI v20151001 IASI retrieval data products show a less than 10 % and insignificant stratospheric bias, a 10 to 30 % positive bias in the UTLS, and an order of 10 % negative bias in the troposphere. The latter is in agreement with an initial IASI tropospheric ozone (also retrieved with FORLI v20151001) validation exercise using ozonesonde reference measurements performed by Boynard et al. (2016). Possible reasons for the UTLS bias are discussed in Dufour et al. (2012). Taking into account the FRM uncertainties discussed in Sect. 3.2, the ex ante IASI uncertainties provided in the product files (light grey lines in the plots) are typically of the order of the bias, except in the UTLS. The ex post random uncertainty, as estimated by the spread, is roughly twice as large, except for the lower tropics. This means that overall the total satellite measurement and retrieval uncertainty is underestimated in the IASI FORLI v20151001 nadir ozone profile products. The comparison results show hardly any scan angle dependence or seasonality, except for some larger systematic differences around the Antarctic ozone hole that can be partially attributed to co-location errors at the edge of the polar vortex. The remaining meridian dependences are typically limited to stronger UTLS bias fluctuations in the tropics.

Both the polar sub-tropopause and tropical UTLS outliers seem to go together with a TC dependence of the differences (clearer for IASI-A than for IASI-B) that also agrees with the sensitivity dependence. One would expect the TC to be mainly influential in the lowermost layers, but the information content studies on the IASI product have indeed demonstrated that the corresponding averaging kernels show significant vertically interdependent oscillations. Therefore the polar sensitivity outliers around 30 km altitude can be related to the strongly negative thermal contrasts and typically go together with very low DFS values (below two, suggesting screening upon this threshold) and strong ozone overestimations. The latter is again clearer for the longer IASI-A time series, wherein the highest total ozone column profiles have the lowest DFS values. Finally, differences can be observed between the IASI daytime (SZA < 83∘) and nighttime (SZA > 91∘) measurements, which are most clear for the largest SZAs (140 to 180∘). Due to the small numbers of co-locations for the latter, however, it is difficult to attribute any significance to these differences.

Looking at latitude-resolved drift studies for the Ozone_cci IASI-A nadir ozone profiles (not shown), a significant decadal negative drift of the order of 25 % or higher can be observed in the Antarctic UTLS and the northern hemispheric troposphere. On the global scale (see Fig. 14), the significance of these drifts remains in terms of the corresponding 95 % drift confidence intervals (horizontal error bars) and is again reflected in the peaked UTLS IP68 spread on the differences (40 %) as the spread is not determined from the drift residuals but with respect to the overall median difference. A less pronounced positive drift is detected around 30 km altitude. Part of the overall negative tropospheric drift of the FORLI v20151001 IASI retrievals could, however, be due to a change in the processing of the IASI L2 processor (e.g. temperature profile) at EUMETSAT that changed to version 5.0.6 in September 2010. This idea is supported by Boynard et al. (2017), who have observed that the IASI-A FORLI v20151001 tropospheric drift becomes statistically insignificant if calculated from the September 2010 to 2016 period retrievals only.

Time series of median relative differences (in solid blue), spreads (in dashed blue), and linear drift (green) for direct comparisons of the IASI-A L3 monthly gridded mean tropospheric ozone column data (integrated from 0 to 6 km) with integrated ozonesonde reference data (at stations with at least six valid measurements per month) are determined within five latitude bands and plotted in Fig. 16. The yearly linear drift value and its 95 % confidence interval as an uncertainty estimate on the derived slope are both determined from a bootstrapping technique using 1000 subsamples and are added in the lower-left corner of each graph.

The IASI-A TIR monthly gridded tropospheric ozone column data for January 2008 to December 2012 show a strong seasonal variation in their comparison with the integrated ozonesonde data, ranging up to 100 %, especially around the South Pole. Despite this strong seasonality, and in agreement with the IASI-A L2 comparison statistics, median relative differences throughout the whole time series range between 25 % negative in the northern mid-latitudes and 30 % positive in Antarctica, with a nearly zero overall bias around the Equator. The corresponding spread decreases from about 25 % in the tropics to about 5–10 % towards the poles. The drift, however, increases from less than 1 % per year negative in the tropics to up to -4 % per year around the South Pole. In contrast with the IASI-A L2 drift study results, none of these drifts are significant, as the 95 % confidence intervals in combination with the comparison spreads indicate: where the confidence interval is fully negative, as is the case for the mid-latitudes, the distance of the confidence interval from zero drift is much smaller than the average spread on the differences. This difference between the IASI L2 and L3 significance of the drift is mainly due to their difference in spatiotemporal representativeness with respect to the ground-based reference data (averaging kernel smoothing, vertical integration, and monthly averaging).