Following the usual sequence of retrieval steps, the temperature and the tangent altitude information retrieved in a previous step from V8R spectra are included in the O3 retrieval. This version of the temperature retrieval includes, in addition to the level-1b spectra, several updates and improvements with respect to the V5R version. Among them, the most important are as follows: the a priori temperature above 43 km (updated from NRLMSISE-00 to SD-WACCM4), the atomic oxygen (updated from the NRLMSISE-00 model to the SD-WACCM4 model at MIPAS geolocations and corrected with MIPAS V5R climatology) and the CO2 concentration now taken from the SD-WACCM4 climatology (see , and , for more details).

In nominal-mode retrievals, where high-altitude temperatures depend largely on a priori assumptions, the new temperature retrieval led to a significant improvement in polar lower-mesosphere O3 during large stratospheric warnings . This effect, however, is small in the current MA-mode O3, because in this mode the retrieved temperature at higher altitudes does not depend that much on a priori assumptions.

A further improvement of the preceding retrieval of temperature in V8R is the inclusion of its variability along the line of sight (LOS). This was considered by including an a priori 3D field with its horizontal structure provided by a priori information and its vertical structure scaled by the retrieved temperature . Following our sequential retrieval approach, the resulting 3D temperature field was used in the forward calculations of O3 limb radiances. Likewise, this temperature field was used to correct the non-LTE populations along the LOS. In the previous O3 version, the variations in temperature along the LOS were implemented more approximately by retrieving a linear horizontal temperature gradient around the tangent point .

The IMK–IAA processor retrieves, jointly with the O3 abundance, a background continuum radiation and a zero-level calibration offset. Both the continuum and the offset are retrieved at each microwindow (MW) and altitude.

The uppermost altitude of the continuum retrieval has been extended from 50 to 60 km. The background continuum is strongly constrained to zero above 60 km (we used 50 km in the previous version), and the vertical-offset profiles for the microwindows in band A (MW nos. 1–30) and band AB (MW nos. 31–38) (see Table ) are strongly regularized towards the a priori values taken from the empirically determined offset correction profiles by . See more details in .

Further, in this version, the abundance of H2O is also jointly retrieved with those parameters. This is done in order to avoid the propagation of uncertainties in the a priori H2O. Note, however, that these jointly retrieved H2O profiles are not used further because they are of sub-optimal quality since the spectral range was selected for the retrieval of ozone but not for H2O .

As for temperature and other gases, in the retrieval of O3 we use small spectral regions (microwindows) covering ro-vibrational emissions of the main O3 isotope. These MWs vary with tangent altitudes in order to minimize errors and optimize computation time. have shown that the O3 spectroscopic data in MIPAS band A (685–980 cm-1) and those in the AB band (1010–1180 cm-1) are inconsistent. Further, found that the use of microwindows in the AB band, instead of in band A, leads to a positive bias in MIPAS ozone profiles in the upper troposphere and lower stratosphere. Thus, whenever possible, we used MWs in band A. However, in the mesosphere and lower thermosphere, the O3 lines in band A are too weak and the spectra are noisy; hence the use of MWs in the AB band was necessary.

The MWs used in this version are essentially the same as in the previous version and are listed in Table  for easy reference. Only minor changes were made. In particular, MW no. 8 (720.75–723.688 cm-1) was excluded due to CO2 line mixing, and MW nos. 37 and 38 near 1053 and 1055 cm-1 were slightly reduced to remove the radiance contribution of CO2 laser band lines. The MWs used below 50 km are the same as those used in the NOM O3 retrieval (all located in the A band), and those used between 50 and 70 km are very similar (both from the AB band) .

The O3 spectroscopic data from the HITRAN 2008 database used in the previous version of the O3 retrieval were replaced with those of the MIPAS pf3.2 database . This change was motivated by the MIPAS spectroscopic database having smaller inconsistencies between the line strengths in the spectral range of the MIPAS A and AB bands and by there being, in the HITRAN dataset, an unrealistically large change in the air-broadening coefficients near 797 cm-1 . For the interfering species, we used HITRAN2016 . CO2 line-mixing coefficients have been re-calculated for the new spectroscopic data.

Another less important change included in this version is the different concentrations of the interfering species. While in the previous version we used a specifically tailored climatology, here we constructed the interfering species dataset based on previous V5R version results see. The CO2 concentration is taken from the SD-WACCM4 climatologies (see , and ).

In the current version, we used an internal spectroscopic grid in the forward model, wgrid, of 0.0009765625 cm-1, instead of the finer grid of 5 × 10-4 cm-1 used in the previous version. For convenience, wgrid was chosen as that which is closer to 10-3 cm-1 and fulfils the criterion that 0.0625/wgrid = 2N, where 0.0625 (cm-1) is the spectral resolution before apodization and N is an integer number; N = 6 in our case. Tests performed show that the use of that coarser spectral grid has a negligible effect on the retrieved O3. That is, it adequately accounts for the mesospheric O3 Doppler line shape. In turn, it allows us to reduce the CPU time consumed by the retrieval. On the other hand, the wider frequency range for the Norton–Beer “strong” apodization of calculated spectra used now contributes to increasing the CPU time.

The retrievals are performed from the surface to 120 km over a fixed altitude grid of 1 km up to 50 km, at 72–75 km and at 77–88 km; of 2 km at 50–72, 75–77 and 88–102 km; and of 5 km from 105 up to 120 km. Contrary to the retrievals from the nominal observation mode , which are linear in the volume mixing ratio (VMR), in the middle-atmospheric measurement modes we retrieve the logarithm of VMR. Forward calculations are performed using the same grid. As this grid is finer than the MIPAS vertical sampling of 3 km (except in the NLC mode at 78–87 km, where it is 1.5 km), we used a regularization, a Tikhonov-type first-order smoothing constraint in our case . The regularization used in this version has not changed since version 5.

The a priori O3 in the mesosphere and lower thermosphere has changed significantly and affects principally the upper-mesosphere daytime O3 mixing ratio. We recall that the Tikhonov regularization chosen does not systematically push the retrieved ozone profile towards the a priori but only constrains the shape of the vertical profile.

In the previous version we used the 2D field from , which had the O3 daytime secondary maximum at altitudes lower than those of recent measurements . Here, the O3 a priori is essentially a MIPAS O3 V5R zonal-mean climatology (obtained from MA and UA monthly composites, 10∘ resolution, and linearly interpolated in between). This climatology has been modified to account for the poorer MIPAS vertical resolution in the upper mesosphere by correcting with O3,corr = O3,uncorr × [O3,W/O,W_AK], where O3,W is taken from the SD-WACCM4 climatology, the Whole Atmosphere Community Climate Model Version 4 (WACCM4) simulations of a specified dynamics run , and O3,W_AK is the same O3,W climatology but with the MIPAS averaging kernels applied. With this correction, the MIPAS climatology remains essentially unaltered below ∼ 70 km. Above, the overall magnitude of the MIPAS V5R ozone abundances is maintained, while unresolved profile features are incorporated from the Whole Atmosphere Community Climate Model (WACCM) climatology.

The ozone non-LTE model used in this version is described in detail by ; see Sect. 2 and Tables 1 and 2 in that work. We describe here the major changes in the model that apply to this version. First, we discuss the collisional rates and, later on, the species abundances required by the non-LTE model and not measured by MIPAS, i.e. the atomic oxygen and hydrogen concentrations.

The major uncertainty in the O3 non-LTE model is the deactivation of O3(v1,v3) by atomic oxygen, either by chemical quenching, O3(v1,v3)+O→O2+O2, or by inelastic collisions, O3(v1,v2,v3)+O→O3(v1′,v3′)+O+ΔE, process kvt,O in Table . The uncertainty comes not only from the rates themselves but also from the uncertain amount of atomic oxygen, which is not measured but derived or constrained by the retrieved O3 in an iterative process . For larger rates or larger O concentrations, the deactivation is stronger, which leads to lower populations for the emitting O3 states and hence larger O3 abundances.

In the validation of the previous version of O3, we found that the nighttime upper-mesosphere O3 was larger by ∼ 20 % than in most of the other instruments . Thus, to obtain a better agreement, we reduced the relaxation of O3 by O, O3(v1,v3)+O, kvt,O, by a factor of 2, i.e. 4.65 × 10-12 cm3s-1. Note that the chemical quenching, O3(v1,v3)+O→O2+O2, was already neglected in the previous version, as suggested by . The assumed rate is within the uncertainties in the laboratory measurements but at the lower limit measured by see the discussion in. More recently, have measured the thermal relaxation of the lower-energy v2 mode

The 9.6 µm emission used here to retrieve O3 in the mesosphere and lower thermosphere comes from the Δv3 and Δv1 bands.

As shown above, the retrieval of O3 mixing ratios under non-LTE conditions requires knowledge of the atomic oxygen concentration, [O]. In our retrieval, we constrain [O] by assuming that O3 is in photochemical equilibrium with O and using the O3 abundance retrieved in the previous iteration of the inversion (daytime) or from the previous version (nighttime). This is a reasonable approach above around 60 km during the daytime and ∼ 80 km at nighttime because of the rapid timescales for ozone production and loss in this region. Below those altitudes, collisions with O are negligible.

Taking into account the major photochemical reactions affecting O3 in the mesosphere and lower thermosphere (see Table ), the O concentration for daytime conditions can be well approximated by 1[O]d=(JO3+k2[H])[O3]k1[O2],[M]-k3[O3]≈JO3[O3]k1[O2][M]-k3[O3], where the chemical loss of O3 by H has been neglected. In summary, for the daytime, the required [O] is computed by using this equation and the O3 retrieved in the previous iteration.

The photo-absorption coefficient JO3 is calculated by using the TUV model version 5.3.2,

https://www2.acom.ucar.edu/modeling/tropospheric-ultraviolet-and-visible-tuv-radiation-model (last access: 9 November 2023).

During the nighttime, the photochemical equilibrium of O3 leads to 2[O]n≈k2[H][O3]k1[O2][M]-k3[O3].

In the previous version we calculated [O]n from Eq. () and taking [H] from the NRLMSIS-00 model . Here [H] was inferred from MIPAS daytime and nighttime O3 measurements in the altitude range where the O VMR is free of photochemically induced diurnal variations (above ∼ 80 km). In that region, the atomic oxygen VMR has no significant diurnal variations except those caused by tides, which we consider related by Ovmr,n=Ovmr,d×ft, where ft is a tidal correction factor. Thus, by combining Eqs. () and (); using ft; and defining the chemical losses for the daytime (10:00), Ld=k1,d[O2]d[M]d-k3,d[O3]d, and nighttime (22:00), Ln=k1,n[O2]n[M]n-k3,n[O3]n, we obtain 3[H]n=JO3k2,nLnLdO3,vmr,dO3,vmr,nft, where we consider different densities and temperatures for the daytime and nighttime. The tidal correction factor ft for atomic oxygen can be constructed by making use of the pressure difference Δp between 10:00 and 22:00 at a given potential temperature level by 4ft=1+O3,vmr,d(p-Δp)O3,vmr,d(p).

Unfortunately, MIPAS did not measure daytime and nighttime O3 at the same geolocations. This means that information on [H]n can be obtained from MIPAS only on a climatological basis, e.g. from O3 VMR day- and nighttime climatologies. In order to incorporate the transient variability, we employ SD-WACCM4 simulations (see Sect. ) sampled at MIPAS geolocations, [HW]n(geo), e.g. 5[H]n(geo)=[HW]n(geo)fc, where, to be consistent with the climatological MIPAS [H]n, they were corrected by the climatological MIPAS-to-WACCM ratio 6fc=[HMIP]n(month,p,lat)/[HW]n(month,p,lat).

This method for generating the a priori [H] has two caveats. First, SD-WACCM4 is free-running above the stratopause, resulting in deviations from the observed meteorology. However, larger perturbations of mesosphere and lower-thermosphere dynamics caused by wave propagation from the lower atmosphere, which may have a noticeable impact on atomic hydrogen, are still represented reasonably well in comparison to a merely climatological a priori. Secondly, the correction factor fc is based mainly on MIPAS V5R O3 data. It might change if derived from the V8R reprocessed ozone data, which would then raise the necessity for iteration. To sort this out, we computed fc factors from the resulting V8R ozone data. Differences in the updated fc are generally smaller than 15 %, except in the tropics, where deviations can be as large as 30 %. The nighttime [H] concentration derived from MIPAS V5R data in the 80–100 km altitude range agrees well, within 20 %–25 %, with the [H] from the NRLMSIS 2.0 empirical model for all latitudes and seasons, except in the tropics where the differences are within 20 % and 50 %, with [H] derived from MIPAS being smaller.

The atomic oxygen described above is available in the region where we retrieve O3. Above approximately 97 km, we used the atomic oxygen from SD-WACCM4 simulations see.

Even if we tried to avoid CO2 lines in the MW selection (see above), to be on the safe side, we also included the contribution of CO2 lines in the forward model. The CO2 bands are also considered in non-LTE. A detailed description of the CO2 non-LTE model and all the required input parameters can be found in .

The measurement errors include the spectral noise of MIPAS, the uncertainty in the gain calibration, the instrument line shape uncertainty, inaccuracies in the frequency calibration and pointing errors.

The propagation of the spectral noise was estimated by using Eq. (5) of . The mapping of the other measurement errors in the O3 error was evaluated from sensitivity studies performed for the representative atmospheric conditions discussed above.

The measurement noise is typically 30–33 nW(cm2srcm-1)-1 in the MIPAS A band and 5.4–9.6 nW(cm2srcm-1)-1 in the AB band. Both values refer to the apodized spectra. The mapping of those errors in the retrieved O3 single profiles is shown in Fig.  for solstice conditions (top row) and equinox conditions (bottom row). As mesospheric O3 is significantly different during the day- and nighttime, and so is MIPAS sensitivity (see Fig. ), we distinguish between daytime (left panels) and nighttime (right panels). Typical values (1σ) for daytime (left column of Fig. ) are smaller than 5 % below ∼ 60 km, 5 %–10 % between 60 and 70 km, 10 %–20 % at 70–90 km, and about 30 % at 95 km. For nighttime (right column of Fig. ), the O3 noise errors are very similar to those during the daytime below around 70 km but significantly smaller above, being 10 %–20 % at 75–95 km, 20 %–30 % at 95–100 km (except near the tropics where the errors are smaller) and larger than 30 % above 100 km.

The 1σ gain uncertainties were estimated to be 1.1 % and 0.8 % for the A and AB bands, respectively see. The response of retrieved ozone to the gain calibration is, to first order, multiplicative. Hence, in the band-A spectral region, the gain uncertainties in the retrieved ozone mostly compensate for the gain uncertainty in the temperature and tangent altitude errors, since these are retrieved from the same band. This occurs approximately for the O3 retrieved below about 50 km.

The instrument line shape (ILS) uncertainties and the spectral shift residual error have been evaluated as described in and are based on the estimates of modulation loss through self-apodization and its uncertainties. We also considered a residual frequency calibration error which resulted in 0.0003 cm-1 in bands A and AB.

In the ozone retrieval of the MA, UA and NLC modes, we used the information of temperature and tangent altitude previously retrieved from the 15 µm region. Thus, the different sources of errors affecting the retrieved temperature and tangent altitude (T + LOS) are implicitly taken into account by propagating their uncertainties into the O3 retrieval. The major sources of temperature are the following. The random component, mainly instrumental noise, is typically less than 1 K below 60 km, 1–3 K at 60–70 km, 3–5 K at 70–90 km, 6–8 K at 90–100 km, 8–12 K at 100–105 km and 12–20 K at 105–115 km . Its systematic part is dominated by the CO2 spectroscopic data errors below 75 km and by the uncertainties in the non-LTE model parameters and CO2 concentration above ∼ 80 km. The systematic uncertainties are smaller than 0.7 K below 55 km, 1 K at 60–80 km, 1–2 K at 80–90 km, 3 K at 95 km, 6–8 K at 100 km, 10–20 K at 105 km and 20–30 K at 115 km .

The uncertainties in the spectrally interfering molecules with ozone, i.e. N2O, CH4, NO2, NH3, HNO3, ClO, OCS, HCN, CH3Cl, H2O2, C2H2, C2H6, COF2, C2H4, F-22, CCl4, CFC-113, CFC-114, N2O5, HCFC-141b, HCFC-142b, ClONO2, CH3CCl3, CH3OH, acetone and PAN, which are not jointly fitted, as well as their vertical covariances, are estimated from the error covariance matrices of previous MIPAS data version V5R. These values are considered more accurate than the climatological mean values for the actual atmospheric conditions of the measurements. For those interfering species which are not available from previous MIPAS versions, we used climatological data and estimate the effects of their errors in the retrieved O3 from the perturbed spectra with their 1σ estimated uncertainties. We should note that, overall, the errors in O3 due to the uncertainties in the interfering species are very small. This is due to the high spectral resolution of MIPAS, which allows us to choose microwindows where essentially only O3 contributes to the measured radiance. The errors caused by the uncertainties in H2O are not explicitly included in the error budget as H2O is jointly fitted with O3 and as H2O uncertainties are implicitly taken into account during the propagation of measurement errors. Further, CO2 uncertainties contribute to the O3 error budget not only because of spectral CO2 interferences (for which we also include CO2 levels in non-LTE; see Sect. ), but also mainly through its propagation via the preceding temperature retrieval from band A see. CO2 was taken from WACCM4 simulations, and their 1σ uncertainties are listed in Table 3 of .

In Sect.  we discuss the concentrations of the atomic oxygen and atomic hydrogen, which are not measured by MIPAS but required for the calculations of the non-LTE population of the O3 levels. The atomic oxygen uncertainty contributes to the O3 error budget in two ways: one, directly, through the non-LTE population of the emitting levels, as described above, and the other, indirectly through its impact on the kinetic temperature retrieval see. It is worthwhile noting that both errors are partially compensated when propagated to the retrieved O3. Thus, in the upper mesosphere, a larger [O] induces a larger retrieved kinetic temperature and hence a larger population of the O3 emitting levels. On the other hand, a larger [O] gives rise to a larger collisional deactivation of the O3(v1,v3) levels and hence lower populations. In the lower thermosphere, the effects are swapped but with a similar compensating effect.

As described above, the daytime atomic oxygen is obtained from the retrieved O3 below 95 km. It is then inherently retrieved together with O3, and it is not by itself an independent source of errors. The uncertainties incurred by this approach are those introduced by the collisional and kinetic rates, which are described below in Sect. . During the nighttime, the [O] uncertainty is driven by that of atomic hydrogen. The uncertainties in [H] have been estimated by using Eq. (), and the errors in the entering parameters which have been discussed above. They result in mean values ranging between 20 % and 40 % from 70 to 100 km, being larger in the tropics (40 %–60 %) and smaller at high latitudes (10 %–30 %) (see Fig. 4).

In the region of 95–120 km, where [O] is taken from WACCM, we use the same uncertainties (5 %–30 %) as those used in the kinetic temperature retrieval (see Fig. 6 in ).

The “indirect” error induced by O through the temperature retrieval has been neglected. First, it is partially compensated by its direct effect on the populations of O3. Secondly, the effect of the [O] error in the temperature uncertainty is much smaller than the effects of other parameters (e.g. of kCO2-O; ) already included. Further, we should note that the propagation of the temperature errors onto O3 is considerably weakened in the mesosphere since the emitting levels are in non-LTE, e.g. far away from the population dictated by the local kinetic temperature.

The spectroscopic errors are in general not so well characterized as would be required for a thorough error assessment of remotely sensed data. In particular, information about the confidence limits (e.g. 68 %, 95 % or other) of the error margins (1σ or 2σ) or about error covariances between spectral lines and bands is not available. The spectroscopic errors for O3 are described in detail by ; see Table 2 in that work. In summary, for the stronger ozone lines, we assume uncertainties in their intensities in the range of 2 %–4 %. The broadening coefficients were parameterized as a function of the rotational quantum number, and their uncertainties vary from 3.5 %, 7.5 % and 15 % to 20 %, depending on the ozone band considered. In this respect, we were rather conservative and assumed that all errors in the lines of a given band are completely correlated.

The uncertainties in the non-LTE model are an important source of systematic error for O3 above the mid-mesosphere. Their most important components are the uncertainties in the collisional rates and, as discussed above, uncertainties in the atomic oxygen concentration. The errors in the collisional rates were discussed in , and their values have not changed in this version. In summary, we considered the following uncertainties: (1) 10 % for the three-body reaction rate of O3 formation (k1 in Table ); (2) 20 % for the thermal relaxation of O3(v1,v3) by N2 and O2; and (3) 50 % for the collisional relaxation (and/or chemical reaction) of O3(v1,v3) with atomic oxygen (k3 in Table ), the latter based on . The error in the photo-absorption coefficient JO3, required in the photochemical model described above, was estimated to be 7 %.

In line with the recommendation of TUNER, we consider random errors those that explain the standard deviation of the differences in co-located measurements taken by two instruments of the same state variable .

We identified the following error sources as contributing to the random error: measurement noise, gain calibration uncertainties, offset calibration noise, T + LOS errors, uncertainties in the abundance of interfering species and the residual frequency calibration errors. Further, we also include in the random error the random variations in retrieval responses to systematic uncertainties so-called “headache errors”; see.

The random components of the errors in Fig.  are shown in Fig. . The major component of the random error is measurement noise. Zonal-mean distributions of the ozone error due to noise for the solstice and equinox, and for the daytime and nighttime, are discussed above in Sect.  and are shown in Fig. . The noise error (+) and the total random error (thick red line) (see Fig. ) are practically overlaid above ∼ 70 km, reflecting the predominance of noise in the random error budget at these altitudes. Above ∼ 80 km, some further contributions are made by the offset uncertainty; the random component of the NLTE error; and for some atmospheric conditions, the random component of the propagated T + LOS error. Between ∼ 70 km and ∼ 50 km, the propagation of the temperature and LOS random errors significantly contribute. Below ∼ 50 km, both T + LOS errors and the random component of the spectroscopic errors contribute significantly to the total random error.

The random component of the gain calibration error is very small, and the values shown in Fig.  are mainly of systematic nature. The errors induced by the uncertainties in the abundance of interfering species are significant only below about ∼ 30 km. Errors produced by the residual frequency calibration uncertainty are negligibly small and are not shown.

The total random error varies between ∼ 1 %–2 % near 30 km and increases with altitude, reaching 20 %–30 % in the upper mesosphere–lower thermosphere. In this region, it is larger in the daytime than at nighttime. In the lower stratosphere, due to the temperature decrease, it also increases see more details in. The random O3 error is generally larger than the total systematic uncertainty above around ∼ 60 km.

The sources of systematic errors in MIPAS O3 retrievals from middle-atmosphere measurements are as follows: uncertainties in spectroscopic data, instrument line shape uncertainties, the gain calibration error and non-LTE-related uncertainties. The systematic components of the errors in Fig.  are shown in Fig. . The systematic error is dominated by the spectroscopic data error below ∼ 60 km. In this region, the ILS also contributes significantly and, to a lesser extent, the gain calibration uncertainty. Above ∼ 60 km the systematic errors are dominated by the non-LTE uncertainties, which are discussed below, but the spectroscopic data error also contributes significantly, being in some cases comparable to or even larger than the non-LTE errors. The ILS contribution is also appreciable at very high altitudes, above ∼ 90 km.

The non-LTE error includes both uncertainties in the collisional and kinetic rate constants and uncertainties in the abundances of atmospheric species required for the non-LTE modelling, namely, atomic oxygen (O) and hydrogen (H). Abundances of these species are uncertain due to uncertainties in the kinetic constants of the photochemical model used to infer them or due to biases in the trace gas climatologies used. Both errors are primarily systematic, i.e. bias-generating, while their random component is less relevant. Only in a few conditions and at a few altitudes is the random component of the non-LTE significant, e.g. near 95 km during the daytime in the tropics and in the northern polar summer (see Fig. ).

The different components of the non-LTE errors corresponding to the atmospheric conditions of Fig.  are shown in Fig. . Non-LTE errors are only significant above ∼ 70 km and are in the range of 1 % to 10 %. In the region of 65–85 km the non-LTE error is dominated by the uncertainty in the thermal relaxation of O3(v1,v3) by N2 and O2, process 5, kvt,M, in Table , and above ∼ 85 km the non-LTE error is dominated by the errors in the collisional relaxation reaction of O3(v1,v3) with atomic oxygen, process 6, kvt,O, in Table , and by uncertainties in the abundances of atomic hydrogen. The latter is the largest contributor above ∼ 90 km under nighttime conditions at tropical and middle latitudes. The error component due to atomic oxygen abundances in the region where it is not retrieved (z ≳ 95 km) contributes moderately at the highest altitudes. The error contribution of the reaction rate of O3 formation (k1 in Table ) is negligible during the nighttime and below 2 % during the daytime. The error due to the photo-absorption coefficient is hardly 1 % near 80 km during the daytime. Overall, the non-LTE errors are typically negligible (smaller than 1 %) below 60 km, 2 %–8 % at 60–85 km and slightly larger at 5 %–12 % above 85 km.

SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) is a broadband radiometer flying on board NASA's Thermosphere ⋅ Ionosphere ⋅ Mesosphere ⋅ Energetics and Dynamics (TIMED) satellite, launched in December 2001 and starting operations in January 2002 . It measures from 83∘ S to 52∘ N and from 52∘ S to 83∘ N alternatively every 2 months. A 24 h local time coverage is completed in ∼ 60 d. The instrument measures the ozone limb emission at 9.6 µm during the daytime and nighttime, and the ozone concentration is retrieved from 10 to 100 km using a non-LTE model . Here we use version 2.0 of O3 retrieved from the 9.6 µm channel, publicly available at http://saber.gats-inc.com (last access: 9 November 2023). SABER's ozone precision is ∼ 1 %–2 % in the stratosphere and ∼ 3 %–5 % in the lower mesosphere . The systematic errors range from 22 % in the lower stratosphere to ∼ 10 % in the lower mesosphere. The vertical resolution of SABER ozone is approximately 2 km. Given the MIPAS O3 coarser vertical resolution, particularly in the daytime mesosphere, we used the MIPAS averaging kernels and a priori O3 to smooth SABER O3 profiles.

The Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument was a stellar occultation spectrometer on board the ESA's Envisat space platform and operated from August 2002 to April 2012. GOMOS took measurements at 250-692 nm, and O3 nighttime density profiles were derived from 10 to 110 km. The latitudinal coverage is uneven, providing data at low latitudes at around 22:00–23:00 LST and eventually reaching the poles and slightly varying throughout the year. We used here ESA Instrument Processing Facilities (IPF) version 6.01, which is described in and . These data are available from the ESA Earth Online portal (https://earth.esa.int, last access: 9 November 2023). Unreliable profiles have been removed following the recommendations of the GOMOS/6.01 Level 2 Product Quality Readme File.

GOMOS O3 vertical resolution changes from 2 km in the lower stratosphere to 3 km in the upper stratosphere and above. Because this resolution is better than that of MIPAS, we applied MIPAS averaging kernels to the GOMOS profiles. Because GOMOS provides O3 number density, we compare the GOMOS and MIPAS O3 number densities. Random errors due to measurement noise and scintillations are 0.5 %–4 % in the stratosphere and 2 %–10 % in the mesosphere. Systematic errors are smaller than 2 %, mainly induced by the O3 spectroscopic data .

The Microwave Limb Sounder (MLS) was launched in July 2004 on NASA's Earth Observing System Aura satellite . The ozone dataset used here is version 5.0–1.1a, downloaded from GES DISC and described by . One of the major differences in this data version compared to previous ones is that the ozone retrieval uses larger a priori errors at high altitudes, making the retrieved O3 less dependent on the a priori. Thus, it can be used up to higher altitudes, to 0.002 to 0.001 hPa (∼ 90 km). We used here daytime and nighttime O3 profiles from the stratosphere up to 0.001 hPa (∼ 90 km; see https://mls.jpl.nasa.gov (last access: 9 November 2023). This is an important difference with respect to the previous comparison carried out by , where it was limited to ∼ 72 km.

The vertical resolution of MLS ozone profiles is 3 km in the stratosphere, 6 km in the middle mesosphere and 9 km in the upper mesosphere. The estimated systematic uncertainty is 5 %–10 % in the stratosphere, 10 %–20 % in the lower mesosphere and 20 %–40 % in the middle mesosphere (with a larger error of 100 % near 80 km) see Table 3.18.2 in. Since the MLS O3 vertical resolution in the mesosphere is larger than that of MIPAS, we have applied MLS averaging kernels and a priori information to the MIPAS ozone.

The Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) on the International Space Station (ISS) operated between October 2009 and April 2010 . It measured ozone profiles in the altitude range of 16 to 85 km during the daytime and up to 96 km during the nighttime . The latitudinal coverage is 38∘ S and 65∘ N. Version 3.2 of the data was used here (http://darts.isas.jaxa.jp/stp/smiles/, last access: 9 November 2023). The vertical resolution is 3 km in the stratosphere, 4 km in the lower and middle mesosphere, and 6 km at 95 km. MIPAS and SMILES O3 vertical resolutions are similar, and hence no averaging kernels were applied. Previous versions of SMILES O3 (v2.2) agree with other measurements within 10 % in the stratosphere and 30 % in the mesosphere .

The Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) is an infrared solar occultation Michelson interferometer flying on the Canadian Space Agency (CSA) Atmospheric Chemistry Experiment (ACE), launched in August 2003 . It measures atmospheric absorption from the cloud top to 150 km at sunrise and sunset. ACE covers the tropical, mid-latitude and high-latitude regions in approximately 3 months. Ozone profiles are retrieved from microwindows between 829 and 2673 cm-1 . We use here version 4.1 of the data. ACE-FTS ozone retrievals are limited to a 5–95 km altitude range. The vertical resolution is 3-4 km.