The ACE-FTS instrument (Bernath et al., 2005) is a solar occultation instrument on board the Canadian satellite SCISAT, which was launched into a highly inclined, non-sun-synchronous orbit in 2003. Since February 2004, ACE-FTS has been making observations of Earth's limb, providing profiles of atmospheric temperature and concentrations of over 30 trace species between altitudes of ∼ 5 and 150 km. The instrument is a high spectral-resolution (0.02 cm-1) infrared spectrometer detecting solar radiation between 750 and 4400 cm-1.

The O3 retrieval algorithm, described by Boone et al. (2005, 2013), is a global least-squares fitting technique that uses Levenberg–Marquardt iteration to converge on a solution without the need of a priori information. Version 3.5/3.6 data are used in this study, where the forward modelled spectra in 40 different microwindows between 829 and 2673 cm-1 are calculated using spectral parameters from the HITRAN 2004 (Rothman et al., 2005) database with some updates, as described by Boone et al. (2013). Ozone is retrieved between 5 and 95 km assuming horizontal homogeneity, and CFC-12, HCFC-22, CFC-11, N2O, CH4, HCOOH, and H2O, along with various isotopologues, are simultaneously retrieved as interfering species. The reported statistical fitting error, described by Boone et al. (2005; 2013), is typically on the order of 2 %–3 % in the 10–15 km range and ∼ 1.5 %–2 % in the 15–55 km range. Dupuy et al. (2009) validated the ACE-FTS v2.2 ozone data set using correlative data from multiple satellite, ground-based, and balloon-based instruments, and Sheese et al. (2017) compared v3.5 O3 data to correlative satellite data. In the upper troposphere to middle stratosphere, ACE-FTS v3.5 O3 tends to exhibit a slight positive bias on the order of a few percent and, near 45–60 km, a positive bias on the order of 10 %–20 %.

The OSIRIS instrument (Llewellyn et al., 2004) is a limb scatter detector on board the Odin satellite, which was launched into a sun-synchronous orbit in 2001 with a nominal ascending node of approximately 06:00 local time. Since November 2001, OSIRIS has been observing Earth's limb, producing standard data products of O3 and NO2 profiles between altitudes of ∼ 7 and 60 km, as well as various other atmospheric research products. The optical spectrograph is a grating spectrometer measuring between 275 and 810 nm with a spectral resolution of ∼ 2 nm and a vertical field of view of ∼ 1 km at the tangent point.

The O3 retrieval algorithm is described by Bourassa et al. (2012) and uses a multiplicative algebraic reconstruction technique (Roth et al., 2007; Degenstein et al., 2009). Version 5.07 O3 data are used in this study, where pressure and temperature profiles are obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF), and ozone is retrieved in number density, taking into account UV and visible absorption, and NO2 and aerosols are simultaneously retrieved as interfering species. The ECMWF pressure and temperature profiles are then used to convert the retrieved O3 densities to volume mixing ratios. The reported OSIRIS O3 uncertainties are typically on the order of 3 %–9 % in the 10–55 km range.

Adams et al. (2013) found that the v5.07 OSIRIS data were in excellent agreement with coincident Stratospheric Aerosol and Gas Experiment II (SAGE II) profiles throughout the stratosphere, typically within 5 %. Hubert et al. (2016) found there to be a statistically significant positive drift in the OSIRIS O3 data above 20 km with respect to ozonesonde and lidar data. The OSIRIS drift is on the order of 1 %–3 % per decade between ∼ 25 and 35 km and increases to 8 % per decade near 42 km; however, this drift has been corrected in the v5.10 release (Bourassa et al., 2018).

Three different models were used in this study: CMAM, EMAC, and WACCM, all of which used specified dynamics to relax, or “nudge”, different key atmospheric states (e.g., wind fields, temperature) to meteorological observations.

CMAM is a chemistry–climate model, described in detail by de Grandpré et al. (2000), Jonsson et al. (2004), and Scinocca et al. (2008). The CMAM30 simulation (McLandress et al., 2013), used in this study, is a 30-year run of the CMAM model with 6-hourly output from 1979 to 2010, on a 3.75∘ horizontal grid (linear T47 Gaussian grid). The model was run with 71 vertical levels up to 0.0007 hPa (∼ 95 km) with vertical resolution on the order of 1 km around the tropopause, increasing to ∼ 2.5 km in the mesosphere, and the data set used here is comprised of 6-hourly instantaneous model fields interpolated onto 63 constant pressure surfaces that span the full height range of the model. Below 1 hPa, temperatures and horizontal winds were nudged to 6-hourly values from ECMWF Interim Reanalysis (ERA-interim; Dee et al., 2011). CMAM simulations have been used in many studies to help understand the climatology and variations of stratospheric O3 and its effect on climate (e.g., Gillett et al., 2009; McLandress et al., 2011; Sakazaki et al., 2015; Froidevaux et al., 2019).

The global chemistry–climate model EMAC uses the general circulation model ECHAM version 5 as its base model in conjunction with MESSy version 2, which incorporates multiple sub-models, such as natural and anthropogenic emissions, land and ocean processes and interactions, and chemistry and transport (Jöckel et al., 2010, 2016). The simulations used in this study were on an approximate 2.8∘ horizontal grid (T42), with 90 vertical levels up to 0.01 hPa (∼ 80 km). Within the 30-year run (1980–2010), the calculated divergence, vorticity, temperature, and logarithm of surface pressure variables were nudged above the boundary layer up to 10 hPa (with transition layers) to ERA-interim data with nudging times between 6 and 48 h, depending on the variable. The data used in this study were from simulation RC1SD-base-10 (no nudging of global mean temperature), output every 5 h (Jöckel et al., 2016). Multiple studies focusing on O3 variations in the troposphere and stratosphere have used the EMAC model (e.g., Weber et al., 2011; Meul et al., 2014; Khosrawi et al., 2017).

WACCM is a climate chemistry model and is the atmospheric component of the National Center for Atmospheric Research's Community Earth System Model (Marsh et al., 2013). The simulations used in this study have horizontal resolutions of 1.9∘ latitude and 2.5∘ longitude and have 88 vertical levels up to 5.1 × 10-6 hPa (∼ 140 km). The model simulation spans 1979 to 2013, and below 50 km the temperature, pressure, zonal and meridional wind, and surface stress variables were nudged to NASA's Modern Era Retrospective-Analysis for Research and Applications (MERRA) reanalysis data (Rienecker et al., 2011) with a 50 h relaxation time constant. The WACCM model has been widely used to study O3 variability throughout the atmosphere (e.g., Merkel et al., 2011; Brakebusch et al., 2013; Chandran et al., 2014).

Another set of WACCM simulations was used in this study, with the same setup, the only difference being that the output model data were directly output at the ACE-FTS and OSIRIS observation times and geolocations (individual observation profiles were assumed to be at a single time, latitude, and longitude, taken as the 30 km tangent height values). The WACCM output at the instrument observed locations will from here onward be referred to as WACCMOL.

All three models used in this study are considered to be “state-of-the-art” stratosphere-resolving chemistry–climate models and regularly participate in multi-model intercomparisons, including the exhaustive model assessments performed for CCMVal-2 (SPARC CCMVal, 2010) and CCMI-1 (Morgenstern et al., 2017).

Coincidence criteria of within 6 h and 500 km were first chosen, yielding the profiles of mean O3 bias (ACE-FTS – OSIRIS) due to sampling and geophysical variability profiles (2σ variation) shown in Fig. 1. Also shown are the profiles of the actual measurement bias and 2σ variation of the differences at those criteria. All three models exhibit a small bias (within 0.02 ppmv, 0.5 %) between 12 and 29 km. Between 30 and 45 km, the model results indicate that ACE-FTS O3 values are expected to be systematically lower than OSIRIS. CMAM indicates a bias of up to ∼ 0.02 ppmv (0.5 %) in this region, EMAC indicates a bias of up to ∼ 0.06 ppmv (1.1 %), and WACCM indicates a bias of up to 0.13 ppmv (2.8 %). Above 48 km, all three models exhibit systematically larger concentrations of ACE-FTS O3 than OSIRIS O3. EMAC indicates a bias of up to ∼ 0.03 ppmv (2.1 %) in this region, CMAM indicates a bias of up to 0.05 ppmv (3.9 %), and WACCM indicates a bias of up to 0.10 ppmv (8.7 %). The more extreme values yielded by the WACCM simulations could in part be due to the finer horizontal resolution.

All three models agree well in terms of geophysical variability. In absolute terms, all three profiles of 2σ variation increase from ∼ 0.1 ppmv at 10 km to on the order of 0.5–0.6 ppmv near 30–40 km and then decrease with altitude to ∼ 0.2 ppmv near 55 km. In relative terms, all three decrease from within 27 %–32 % near 10 km to 7 %–9 % near 21 km. Between 21 and 52 km, the simulated geophysical variability profiles are typically on the order of 7 %–11 %, with WACCM exhibiting the largest variability of 12 % at 42 km. Above 52 km, variability increases with altitude to 10 %–12 % at 55 km.

In order to estimate the uncertainty introduced by model sampling uncertainties (interpolation uncertainties and uncertainties introduced by assuming ACE-FTS altitude–pressure values for OSIRIS), the standard run WACCM data that were linearly interpolated in time and bilinearly interpolated to the measurement geolocations were compared with WACCMOL profiles (i.e., profiles from a WACCM run with output directly at the satellite observation times and geolocations). In this specific case, both WACCM and WACCMOL assumed altitude-independent geolocations (30 km tangent height values). Figure 2 shows the 2σ variability between coincident ACE-FTS and OSIRIS O3 profiles as determined by WACCM and WACCMOL at coincidence criteria of within 6 h and 500 km. The difference in geophysical variability between WACCM and WACCMOL is typically within ±1 % between 11 and 38 km and within ±2 % between 10 and 47 km. Above 47 km, the difference increases sharply up to 7 % near 55 km; however between 30 and 55 km that difference in absolute terms is on the order of 0.04–0.06 ppmv. These results suggest that in the upper stratosphere the interpolation method may be underestimating the magnitude of the geophysical variation.

Simulated geophysical variability can also be determined for a range of coincidence criteria. Figure 3 shows the geophysical variability determined from CMAM, EMAC, and WACCM for all time difference criteria between within 1.5 h and within 12 h in 0.5 h increments and distance difference criteria between within 150 km and within 2000 km in 50 km increments. These were calculated for all three models at all altitude levels (10–56 km), and results are shown for altitude levels of 20.5, 40.5, and 55.5 km.

Again, all three models show very similar geophysical variability patterns for different coincidence criteria. At the lowest altitudes (e.g., 20.5 km), where there are relatively small diurnal variations, for any given distance criterion, geophysical variability tends to stay fairly constant regardless of the time criterion (up to within 12 h). Conversely, for any given time criteria, geophysical variability increases from ∼ 2 %–7 % at within 150 km to ∼ 16 %–23 % at within 2000 km. At the highest altitudes (e.g., 55.5 km), the opposite effect is seen. Since there is a significant diurnal effect, the simulated geophysical variability is fairly consistent at a given time criterion, regardless of the distance criterion; and at any given distance criterion, the geophysical variability typically increases from ∼ 6 %–12 % at within 1 h to 13 %–22 % at within 12 h. At intermediate altitudes (e.g., 40.5 km), where there is a moderate diurnal cycle, the geophysical variability tends to increase with both time and distance criteria. The variability increases from ∼ 2 %–5 % near within 1 h and 100 km to ∼ 12 %–15 % near within 12 h and 2000 km.

The mean of all three model results was taken to give ensemble mean values of the geophysical variability, shown in Fig. 4. These closely resemble the results described above, with geophysical variability being relatively independent of the time difference criterion at the lower altitude levels, relatively independent of the distance difference criterion at the higher altitude levels, and dependent on both at the intermediate altitude levels. When comparing O3 measurements between ACE-FTS and OSIRIS, these ensemble mean geophysical variability values can be used to optimize coincidence criteria. At each altitude level, “optimized” coincidence criteria can be chosen where there are the greatest number of coincident measured profiles with the estimated geophysical variability less than a desired value. For instance, the circle markers on the plots in Fig. 4 indicate “optimized criteria” where there are the greatest number of coincident ACE-FTS and OSIRIS profiles when the estimated geophysical variability is less than 10 %, and Fig. 5 shows results for comparisons between ACE-FTS and OSIRIS O3 profiles when using the optimized criteria for this chosen 10 % 2σ variability limit at each altitude. It should be noted that in Fig. 5, at some of the altitude levels below 17 km there were no coincidence criteria evaluated where geophysical variability was less than 10 %, and in those cases coincidence criteria of within 1.5 h and 150 km were used. The coincidence criteria can be optimized for any chosen limit of geophysical variability (10 % was chosen in this case), and naturally this could be done for any subset of seasons or latitudes within the collocated data. However, one drawback to having different coincidence criteria at each altitude, especially when making global comparisons, is that it can potentially add biases between altitudes due to changing seasonal and latitudinal sampling. Therefore, care must be taken to ensure that biases of this type are not being introduced.

These results can be used not only to constrain the inherent geophysical variability in comparisons between satellite measurements but also to increase the number of usable coincident profiles. Figure 6 shows results of comparisons between ACE-FTS and OSIRIS O3 profiles for five different coincidence criteria: within 2 h and 250 km, within 6 h and 500 km, within 8 h and 1000 km, within 12 h and 2000 km, and criteria optimized at each altitude. The optimized criteria were such that above 17 km the maximum estimated geophysical variability was 10 % and below 17 km it was 15 %. At most altitudes, the bias between the two instruments is relatively independent of coincidence criteria and the profiles exhibit similar variations with altitude. Above 20 km, the differences between the biases given different coincidence criteria are typically on the order of 1 %–4 %. These differences are slightly larger below 20 km, where the maximum difference is 8 % between the 2 h and 250 km criteria and the 12 h and 2000 km criteria. The 2σ standard deviations of the relative differences, shown in Fig. 6b, exhibit greater variability with coincidence criteria. Between 20 and 40 km, the optimized criteria yield standard deviations that are typically better than all the other criteria, with the exception of within 2 h and 250 km below 14 km and between 20 and 42 km. However, with the criteria of 2h and 250 km only 279 coincident profiles (Fig. 5c) are being compared, whereas with the optimized criteria, 1900–5900 profiles are used in the comparisons, leading to a more robust result with a consistent estimate on the geophysical variability uncertainty. The increase in coincident profiles may not be necessary in this exact case where global data are being compared but would be useful in specific regions where there are fewer coincident profiles with which to compare. The greatest improvement to the standard deviations is in the 13–20 km region, where the optimized criteria lead to standard deviations on the same order as the 2 h and 250 km criteria but making use of 2–7 times more profiles and, again, providing an estimate on the geophysical variability uncertainty.

It is also interesting to observe the difference in geophysical variability between the polar Northern Hemisphere (NH; poleward of 50∘ N) region and the polar Southern Hemisphere (SH; poleward of 50∘ S) region, where there is greater O3 variability in general. Figure 7 shows the same plots as those of Fig. 4 but for polar NH and SH data. At 20.5 km, at coincidence criteria of within 8 h and 1000 km, the ensemble mean geophysical variability in the NH is 8 %, whereas in the SH O3 concentrations are estimated to be over twice as variable, at 19 %.

Figure 8 shows the difference in ensemble mean bias and 2σ geophysical variability at coincidence criteria of 8 h and 1000 km binned by hemisphere and month. It shows that, unsurprisingly, there is a much larger difference between polar NH and SH in the stratosphere during the end of winter than at the beginning of summer. This is due to the stronger southern polar vortex.

Above 15 km in the summer months, when there is not a strong polar vortex, the NH and SH exhibit similar geophysical variability profiles, with variability on the order of 5 %–15 %. In the same altitude region in the SH spring, geophysical variability is much larger, due to the strong and prevalent southern polar vortex, which is just starting to break up with the onset of sunlight; and at laxer coincidence criteria, it is more likely that one instrument will be observing inside the southern polar vortex and the other outside the vortex, which can have different atmospheric conditions. The variability is on the order of 15 %–20 % above 22 km and peaks at 35 % near 18 km, where there is some of the most ozone depletion. As can be seen in Fig. 7a and d, in the lower stratosphere in the polar SH, the geophysical variability is more sensitive to the time coincidence criterion than in the polar NH. The NH geophysical variability above 30 km is also greater at the end of winter (∼ 5 %–10 %) than during the summer (∼ 10 %–15 %). This could be due to stronger planetary wave forcing in the NH (e.g., Butchart, 2014; de la Cámara et al., 2018) and/or stronger descent of NO and NO2 following sudden stratospheric warming events (e.g., Reddmann et al., 2010).

Figure 9 shows the estimated bias and the mean 2σ variability of the relative differences between ACE-FTS and OSIRIS O3 profiles in the polar SH for different coincidence criteria, including the optimized criteria for 10 % geophysical variability above 17 km and 15 % below 17 km. As with the global comparisons, the bias is largely unaffected by the choice of coincidence criteria. Between 20 and 42 km, all the coincidence criteria lead to similar variability profiles on the order of 15 %–20 %. Below 20 km, the optimized criteria tend to yield better variability results than the criteria of within 6 h and greater; however, they yield larger values than the 2 h and 250 km criteria. The benefits of the optimized criteria case in this region are that there is a consistent estimate of the geophysical variability and that it makes use of more coincident profiles – the 2 h and 250 km criteria have a maximum of only 54 profiles, whereas the optimized criteria make use of up to 307 profiles near 15 km.