Stratospheric ozone trends for 1985–2018: sensitivity to recent large variability

The Montreal Protocol, and its subsequent amendments, has successfully prevented catastrophic losses of stratospheric ozone, and signs of recovery are now evident. Nevertheless, recent work has suggested that ozone in the lower stratosphere (<24 km) continued to decline over 1998– 2016, offsetting recovery at higher altitudes and preventing a statistically significant increase in quasi-global (60◦S – 60◦N) total column ozone. In 2017, a large lower stratospheric ozone resur5 gence over less than 12 months was estimated (using a chemistry-transport model; CTM) to have offset the long-term decline in the quasi-global integrated lower stratospheric ozone column. Here, we extend the analysis of space-based ozone observations to December 2018 using the BASICSG ozone composite. We find that the observed 2017 resurgence was only around half that modelled by the CTM, was of comparable magnitude to other strong inter-annual changes in the past, and re10 stricted to southern hemisphere mid-latitudes (SH; 60◦S–30◦S). In the SH mid-latitude lower stratosphere, the data suggest that by the end of 2018 ozone is still likely lower than in 1998 (probability ∼80%). In contrast, tropical and northern hemisphere (NH) ozone continue to display ongoing decreases, exceeding 90% probability. Robust tropical (>95%, 30◦S–30◦N) decreases dominate the quasi-global integrated decrease (99% probability); the integrated tropical stratospheric column (1– 15 100 hPa, 30◦S–30◦N) displays a significant overall ozone decrease, with 95% probability. These decreases do not reveal an inefficacy of the Montreal Protocol. Rather, they suggest other effects to be at work, mainly dynamical variability on long or short timescales, counteracting the positive effects of the Montreal Protocol on stratospheric ozone recovery. We demonstrate that large inter-annual mid-latitude (30◦–60◦) variations, such as the 2017 resurgence, are driven by non-linear 20 quasi-biennial oscillation (QBO) phase-dependent seasonal variability. However, this variability is not represented in current regression analyses. To understand if observed lower stratospheric ozone decreases are a transient or long-term phenomenon, progress needs to be made in accounting for this dynamically-driven variability.

Abstract. The Montreal Protocol, and its subsequent amendments, has successfully prevented catastrophic losses of stratospheric ozone, and signs of recovery are now evident. Nevertheless, recent work has suggested that ozone in the lower stratosphere (<24 km) continued to decline over 1998-2016, offsetting recovery at higher altitudes and preventing a statistically significant increase in quasi-global (60 • S -60 • N) total column ozone. In 2017, a large lower stratospheric ozone resur-5 gence over less than 12 months was estimated (using a chemistry-transport model; CTM) to have offset the long-term decline in the quasi-global integrated lower stratospheric ozone column. Here, we extend the analysis of space-based ozone observations to December 2018 using the BASIC SG ozone composite. We find that the observed 2017 resurgence was only around half that modelled by the CTM, was of comparable magnitude to other strong inter-annual changes in the past, and re-10 stricted to southern hemisphere mid-latitudes (SH; 60 • S-30 • S). In the SH mid-latitude lower stratosphere, the data suggest that by the end of 2018 ozone is still likely lower than in 1998 (probability ∼80%). In contrast, tropical and northern hemisphere (NH) ozone continue to display ongoing decreases, exceeding 90% probability. Robust tropical (>95%, 30 • S-30 • N) decreases dominate the quasi-global integrated decrease (99% probability); the integrated tropical stratospheric column (1-15 100 hPa, 30 • S-30 • N) displays a significant overall ozone decrease, with 95% probability. These decreases do not reveal an inefficacy of the Montreal Protocol. Rather, they suggest other effects to be at work, mainly dynamical variability on long or short timescales, counteracting the positive effects of the Montreal Protocol on stratospheric ozone recovery. We demonstrate that large inter-annual mid-latitude (30 • -60 • ) variations, such as the 2017 resurgence, are driven by non-linear 20 quasi-biennial oscillation (QBO) phase-dependent seasonal variability. However, this variability is not represented in current regression analyses. To understand if observed lower stratospheric ozone decreases are a transient or long-term phenomenon, progress needs to be made in accounting for this dynamically-driven variability.
1 Introduction 25 Ozone in the stratosphere acts as a protective shield against ultraviolet radiation that may harm the biosphere, and leads to cataracts, skin damage, and skin cancer in humans (Slaper et al., 1996;WMO, 2014WMO, , 2018. In the latter half of the 20 th century, the emission of long-lived halogen-containing ozone depleting substance (hODSs) led to ∼5% loss in quasi-global (60 • S-60 • N) integrated total column ozone (WMO, 2014), which represents the combined changes in tropospheric and strato-30 spheric ozone contributions. The 1987 Montreal Protocol and its amendments and adjustments led to a reduction in hODSs that resulted in a halt in total column ozone losses around 1998-2000 (Harris et al., 2015;Chipperfield et al., 2017).
However, there is still no evidence of a statistically significant increase in total column ozone since 1998 (Chipperfield et al., 2017;Weber et al., 2018;Ball et al., 2018), despite a significant 35 2 increase in upper stratospheric ozone (1-10 hPa) (Ball et al., 2017;Steinbrecht et al., 2017;Ball et al., 2018;Petropavlovskikh et al., 2019). Ball et al. (2018) and  presented evidence, using OMI/MLS tropospheric column observations for 2005-2016, that tropospheric ozone had also increased significantly. However, large uncertainties remain in quasi-global tropospheric ozone trends, and the recent Tropospheric Ozone Assessment Report (TOAR) shows that different 40 tropospheric ozone products give a wide range of trends, some even indicating negative changes (Gaudel et al., 2018). The importance of considering tropospheric and stratospheric changes separately to understand changes in total column ozone has also been highlighted in recent studies using chemistry climate models (CCMs) (Meul et al., 2016;Keeble et al., 2017;Dhomse et al., 2018). If tropospheric and upper stratospheric ozone have indeed both increased, then the observed flat trend 45 in total column ozone implies that middle and lower stratospheric ozone should have decreased.
To assess trends in stratospheric ozone, compositesof observations must be formed by merging multiple ozone observational timeseries into a long, multi-decadal record from which variability can be attributed, and long-term trends determined. Composites are subject to artefacts from merging different observing platforms. Multiple papers (Tummon et al., 2015;Harris et al., 2015;Steinbrecht 50 et al., 2017;Ball et al., 2017Ball et al., , 2018) and a SPARC report (Petropavlovskikh et al., 2019) review, discuss, and attempt to account for the artefacts in the uncertainty budget. Ball et al. (2018) integrated ozone over the whole stratosphere, i.e. the ozone layer, quasi-globally for pressure levels from 147-1 hPa (∼13-48 km) at mid-latitudes (30 • -60 • ), and 100-1 hPa (∼16-48 km) between the sub-tropics (30 • S-30 • N), and found ozone to be lower in 2016 than in 1998 55 in multiple ozone composites. In their analysis, the lower stratosphere (147/100-32 hPa, ∼13/17-24 km) was driving this decrease. The most significant decreases were in the tropics, but negative trends extended out into the mid-latitudes (Fig. 1d). Other studies have subsequently confirmed these negative trends (Zerefos et al., 2018;Wargan et al., 2018;Chipperfield et al., 2018). Evidence points towards dynamical variations driving changes (Chipperfield et al., 2018), perhaps in the form of 60 enhanced isentropic mixing (Wargan et al., 2018). Part of the negative trends in northern hemispheric stratospheric ozone in the 1980s and 1990s at higher latitudes have been previously attributed to synoptic and planetary waves (Hood and Zaff, 1995;Hood et al., 1999) inducing large localised (e.g. over Europe) wintertime decreases in ozone that might in turn be driven by sea surface temperature and eddy flux changes on decadal or longer timescales, although most of these studies are limited 65 to the end of the last century when ODSs remained an established primary driver of the decrease.
The El Niño Southern Oscillation (ENSO) and Quasi-Biennial Oscillation (QBO) are known to influence the dynamical variability in the lower stratosphere and may be a main player in driving inter-annual and decadal variability in this region (Diallo et al., 2018(Diallo et al., , 2019. Nevertheless, these dynamical changes do not in themselves determine a specific underlying driving force, however the 70 effect of increasing anthropogenic greenhouse gases (GHGs) (Hood and Soukharev, 2005;Peters and Entzian, 1999) on specific mechanisms needs further study (Ball et al., 2018). On the other hand,  Stone et al. (2018) showed that negative ozone trends could be simulated in the lower stratosphere over the same period in two of nine ensemble members of a coupled CCM as a result of natural variability interfering in the (linear) trend analysis although none of the ensembles displayed the 75 same widespread negative trends as detected in observations Ball et al. (2018). They suggested that an additional seven years of observations would lead to negative signals disappearing in favour of positive trends. The implication is then that the observed negative trend over the relatively short 19 year timeframe may be a temporary result from large natural variability (in the single realisation) of the real-world, rather than a response to increasing GHGs. 80 Chipperfield et al. (2018) used a chemistry transport model (CTM) to reconstruct ozone variability close to past real-world behaviour; transport in the CTM is driven by ERA-Interim (Dee et al., 2011) reanalysis fields. The results showed changes similar to those presented by Ball et al. (2018) up to December 2016. They extended their CTM analysis by an additional 12 months to find that the 1998-2016 ozone decline in the lower stratosphere (∼2 DU; Ball et al. (2018)) was offset by a sudden 85 increase of ozone in 2017, exceeding 8 DU quasi-globally. This was attributed almost entirely to dynamical changes and was primarily located in the southern hemisphere; Froidevaux et al. (2019) have noted that ozone trends derived from Aura/MLS data over a shorter period (2005-2018) have a tendency towards slightly positive values in the SH, but not so elsewhere within the extra-polar regions. Chipperfield et al. (2018) suggested that the lower stratospheric ozone decrease was a result 90 of large natural variability that biased the trend analysis, and that the variability could be attributed to dynamics and not to chemical or photolytic changes, although the source of dynamical perturbations was not identified or the impact on trends quantified. Thus, an assessment of this recent variability on trends, and an update to 2018 is needed and is a key aim of this study.
Here, we update the observational analysis of Ball et al. (2018) to include data to the end of 95 2018 (Section 3.1). This allows us to assess the impact of the 2017 ozone increase in the lower stratosphere on the trend analysis, and to consider additional changes over 2018. We show that large ozone-increase events, with a duration and magnitude similar to that of 2017 (Chipperfield et al., 2018) have occurred regularly since 1985 at mid-latitudes (Section 3.2), and find the events are linked to a seasonally-dependent QBO effect (Section 3.3). We update partial column ozone  (Ball et al., 2017) to account for artefacts in merged composites and improve trend estimates. These data were referred to as 'Merged-SWOOSH/GOZCARDS' by Ball et al. (2018), but we refer here to it as BASIC SG . To briefly place the SWOOSH and GOZCARDS datasets in the context of BASIC SG , Figure S1 of Ball et al. (2018) 115 presented 1998-2016 changes using SWOOSH or GOZCARDS alone; this figure reveals that these ozone composites show generally similar changes on large spatial scales, though there are clear differences on small scales, e.g. in the tropical upper stratosphere, and in the southern hemisphere lower stratosphere. Figure S2 of Ball et al. (2018) importantly demonstrates at 100 hPa in the tropical lower stratosphere that there are significant differences between SWOOSH and GOZCARDS in 120 the late 1990s; this figure also shows that BASIC SG is able to account for the differences in a principled way that is not simply the averaging of the two products, which is particularly important for having confidence in an assessment of ozone in the lower stratosphere. We extend BASIC SG from Ball et al. (2018)  We only consider BASIC SG here for the following reasons. First, as discussed in Ball et al. (2018), compared to the other composites it had the least apparent artefacts within the timeseries. The Stratosphere-troposphere Processes And their Role in Climate (SPARC) Long-term Ozone Trends 5 and Uncertainties in the Stratosphere (LOTUS) report (Petropavlovskikh et al., 2019) indicates this 130 method to be more robust to outliers than other composites. Second, BASIC SG is resolved in the lower stratosphere, which is not the case for all composites; for further discussion see Ball et al. (2018) and the SPARC LOTUS report (Petropavlovskikh et al., 2019). Additionally, SWOOSH and GOZCARDS are currently two of the most up-to-date composites available. Finally, we are interested here in the sensitivity of stratospheric ozone changes to different end years and, since 135 Aura/MLS is arguably one of the best remote sensing platforms for ozone currently in operation (Petropavlovskikh et al., 2019), focusing only on BASIC SG provides an analysis, discussion, and interpretation that is free from the complications of considering multiple composites that have multivariate reasons for displaying different behaviour.
Our DLM approach models the ozone timeseries as a (dynamical) linear combination of the following components: two seasonal components (with 6-and 12-month periods respectively), a set 145 of regressor variables (i.e., proxy timeseries describing various known drivers), an auto-regressive (AR) process, and a smooth non-linear (non-parametric) background trend. DLM differs from traditional multiple linear regression (MLR) approaches in a number of key ways. Firstly, while MLR fits for a fixed (constant-in-time) linear combination of seasonal, regressor, and trend components, DLM can allow the amplitudes of the various components to vary dynamically in time, capturing 150 richer phenomenology in the data. Here, we allow the amplitude and phase of the seasonal components to be dynamic, but keep the regressor amplitudes constant in time; we do this because the seasonal cycle in the observational composites can change over time either as a physical feedback of changing temperature and ozone, or due to different observations exhibiting different seasonal amplitudes (not shown) that are a result of the observing instruments 'seeing' slightly different parts 155 of the atmosphere or having different sampling. Due to the seasonal cycle having the largest variability of all modes we expect that, if left unaccounted for, the time varying seasonal modulation might have an influence on the regression. In principle other regressor amplitudes could also have some time modulation for similar reasons; we leave an investigation of more flexible DLM models with dynamic regressor amplitudes to future work where a physically-motivated justification for 160 such freedom can be investigated. Secondly, MLR that does not assume a driver for the long-term trends, e.g. for the influence of ODSs or GHGs) typically assumes a fixed prescription for the shape of the background trend, e.g., a piecewise-linear or independent-linear trend with some fixed, prechosen inflection-date. These assumptions are both restrictive and give a poor representation of the smooth background trends we expect from nature (Laine et al., 2014;Ball et al., 2017). DLM ad-165 6 dresses this by instead modelling the trend as a smooth, non-parametric, non-linear curve, where the 'smoothness' of the trend is controlled by a free parameter that is included in the fit (see supplementary materials Fig. S1). Thirdly, in practice MLR is often performed by first subtracting an estimated mean seasonal cycle, fitting the trend and regressor variables to the anomalies, and then making a post-hoc correction for auto-regressive residuals, although many do fit annual and semi-170 annual components. This procedure typically does not propagate the errors on the seasonal cycle and AR parameters in a rigorous way, leading to misrepresentation of uncertainties. DLM addresses this by inferring all components of the model simultaneously, and formally marginalizing over the uncertainties in all other parameters when reporting uncertainties on e.g., the trend. We use the same prior assumptions as described in Ball et al. (2018).

175
Probabilities of an overall increase (decline) in ozone between two dates (Figs. 1, 7, and Table 1) are computed as the fraction of Monte Carlo Markov Chain (MCMC) samples that show positive (negative) change. Credible intervals (Figs. 6,8,9) are computed as the central 95 and 99 percentiles of the MCMC samples. The use of 'confidence' or 'significance' is used in this paper interchangeably with 'probability' and refers specifically to Bayesian probabilities; it does not refer to the application In previous analyses, we considered the Arctic and Antarctic Oscillation, AO/AAO 2 , as proxies for 185 Northern and Southern surface pressure variability only for partial column ozone analysis in their respective hemisphere; here we also consider them for the spatially-resolved analysis and in all cases use both AO and AAO simultaneously -they have little affect outside their respective regions, but we do not limit the possibility they may influence some variability in either hemisphere (Tachibana et al., 2018). We use a first order autoregressive (AR1) process (Tiao et al., 1990) to consider auto-190 correlation in the residuals. We remove a three year period following the Pinatubo eruption, i.e. June 1991 to May 1994, which is a year longer than the previous analysis, to avoid any effects of the eruptions that may have persisted. Another key point regarding the SAOD proxy is that, unlike the other proxies that have been fully updated to the end of 2018 for this analysis, the SAOD is currently not extended beyond 2016, so we repeat the year 2016 for 2017 and 2018; if any deviations in the 195 SAOD occurred during this period, our analysis will not account for this. Nevertheless, as can be seen in Fig. 1d here, in comparison to Fig. 1b of Ball et al. (2018), all of these adjustments to the procedure from Ball et al. (2018) have little impact on the estimated mean changes in ozone.

Stratospheric ozone changes since 1998
200 Figure 1d shows the pressure-latitude, spatially-resolved 1998-2016 ozone change, reproducing the sensitivity of ozone trends to six consecutive end years. These end years give insight into the sensitivity of the trends to large inter-annual variability. In particular, these six years encompass periods of both negative/Easterly and positive/Westerly phases of ENSO/QBO. These modes are major contributors to stratospheric variability (Zerefos et al., 1992;Tweedy et al., 2017;Toihir et al., 2018;Garfinkel et al., 2018;Diallo et al., 2018Diallo et al., , 2019, and any sensitivity of the end year to the 220 state of these drivers should be encapsulated in the set of spatial responses depending on the end year only (Fig. 1), particularly if these modes were not well-captured by DLM predictors (Fig. 1).
A lower stratosphere negative ozone trend is persistent for all end years. For 1998-2013, there is a highly probable negative trend in ozone in the SH lower stratosphere; the probability is retained until 2016, after which it reduces. The opposite is seen in the NH, where only a small region of probable 225 ozone decrease exists for 1998-2013, and this strengthens with each panel until 2016, after which a highly probable decrease of ozone remains stable. There is no apparent switch from negative to positive ozone changes in these regions for any of the six end years.
The reduced probability of a SH decrease is related, as we will see in Section 3.2, to the rapid 2017 increase in SH mid-latitude lower stratospheric ozone reported by Chipperfield et al. (2018) using 230 a CTM. However, Fig. 1 also confirms in observations that this is localised to south of 30 • S and does not reveal coherent or consistent behaviour over time with the NH, suggesting that there may be large, hemispherically independent variability interfering with the trend estimates. Nevertheless, there are no signs as yet of an ozone increase underway in the quasi-global lower stratosphere.
8 Further, the decrease in ozone in the tropical lower stratosphere increases in magnitude and signif-235 icance as more data are added. The tropical lower stratospheric ozone is projected to decrease by the end of the century in all CCMs (Dhomse et al., 2018), due to enhanced upwelling from the Brewer Dobson circulation (BDC) as a result of changes to stratospheric dynamics from increasing GHGs (Polvani et al., 2018). It is possible that this is a detection of the expected tropical lower stratosphere decline in ozone, earlier than expected (WMO, 2014). However, whilst the data show a significant 240 decline, it remains to be seen if this can be attributed to the anthropogenic GHG induced upwelling of the BDC.  Fig. 2b-d) show that the large increases in the SH are normal, occurring regularly. They also occur in the NH, but not as regularly, and the tropical variability is much smaller than the mid-latitude variance. In addition to the large increases, there are also comparatively large negative swings in both SH and NH timeseries -one in the NH beginning in 2002 exceeds 24 DU. In the following 265 section we argue that these large, rapid changes are driven by a non-linear seasonal-QBO effect. sphere where the lifetime of ozone is long. Given that the contributions from each sub-region 270 (Fig. 2b-d) add up to the quasi-global change in 2017, it is reasonable to assume that dynamics controls much of the sub-decadal variability there too. The peaks (or troughs) in the SH are 2-3 years apart; the QBO has a similar periodicity and is known to have the largest inter-annual dynamical impact on ozone in the stratosphere (see Gray and Pyle (1989), Zerefos et al. (1992), and Toihir et al. (2018), and references therein) . Labelling each month in Fig. 2 with the 30 hPa QBO-Easterly 275 or Westerly phase in yellow or blue dots, respectively, reveals that the large SH negative anomalies are almost always associated with a Westerly phase, while positive anomalies are associated with an Easterly phase; Bodeker et al. (2007) previously identified large SH negative anomalies in 1985, 1997 and 2006 and related these to the QBO-Westerly phase. This also appears to be the case in the NH, but the variability is less regular, unsurprisingly since the NH stratosphere is known to have 280 additional variability, a consequence of greater sea-land contrast and more orography than in the SH. The NH thus exhibits stronger large scale wave activity and polar vortex and stratospheric variability (see Butchart (2014) and Kidston et al. (2015) and references therein). Equatorial variability in ozone related to the QBO phase at 30 hPa shows the opposite behaviour to that at mid-latitudes: decreases in ozone generally appear to occur with the Easterly phase and vice versa, and the return influence of polar variability on the 30 • -50 • band, and isolates the equatorial region to where the QBO variability is strongest; we note that the act of forming partial columns of ozone may reduce the integrated variability compared to counter-varying layers that would otherwise be resolved by 300 pressure level. We find the use of the QBO phase at 15 hPa also better separates the events in this additional analysis. We find negative and positive ozone excursions in the lower stratosphere become clear in 13-month segments when they are bias-shifted to zero in March (a,b) and September (c,d) and then colour coded according to their QBO phase in April or October, respectively (vertical dotted line). The largest deviations are found to occur four or five months later (vertical dashed line), 305 at the onset of hemispheric autumn (Holton and Tan, 1980;Dunkerton and Baldwin, 1991). It is also interesting to note that the only large, positive QBO-Westerly anomaly that peaks four months later, in either hemisphere, occurs in the SH in 2002. This year is famous for having the only observed sudden stratospheric warming in the southern hemisphere, and indicates that while the QBO-phase appears to dominate this distribution of anomalies, other processes can also sometimes dominate. We reiterate that the separation of positive and negative anomalies into those related to Easterly or Westerly QBO phases is clearest for the SH (Fig. 4a) and the corresponding, opposing, equatorial changes (Fig. 4b). The anti-correlated behaviour of anomalies between mid-latitude and equatorial regions is consistent with previous studies investigating the relationship between the QBO and midlatitude ozone variability (Zerefos et al., 1992;Randel et al., 1999;Strahan et al., 2015). We sum-315 marise the dynamical concept, in the context of these results, in the following (see Baldwin et al. (2001) and Choi et al. (2002) for detailed discussion). The QBO consists of downward propagating equatorial zonal winds; in the lower stratosphere this consists of a Westerly above an Easterly, or vice versa. For Westerly above Easterly (i.e. the 15 hPa QBO is Westerly as identified by blue lines in Fig. 4) leads to a shear that induces a anomalously downward motion of air, and adiabatic 320 warming ( Fig. 1 of Choi et al. (2002)) and also to an anomalous increase in ozone; for an Easterly above a westerly, this leads to anomalously rising air and adiabatic cooling together with an associated ozone decreases; an equator-to-mid-latitude circulation forms to conserve mass (Randel et al., 1999;Polvani et al., 2010;Tweedy et al., 2017). At sub-tropical and mid-latitudes, the return of this meridional circulation draws ozone-rich air from above down into ozone poor regions, anomalously 325 enhancing ozone (yellow, Fig. 4a,c). When Easterlies lie over Westerlies (blue, Fig. 4), the opposite circulation is set up, and ozone anomalies reverse.

Contribution of QBO to mid-latitude ozone variability
The 2017 increase is highlighted in Fig. 4, with November 2016 to January 2017 shown as a dotted red line, and January to October 2017 as a red dashed line. Focusing on Fig. 4a in the SH, the increase onset during the Easterly phase is large, but as noted earlier larger excursions have occurred 330 before and regularly (Fig. 2). A prolonged Westerly phase, following the breakdown of the expected barring no further QBO breakdown, decrease again in 2019 in the SH mid-latitudes; the last three months of 2018 hint at such a decrease (Fig. 2).
Despite this variability, Fig. 1 indicates that the lower stratospheric negative trends in ozone could already be identified throughout the lower stratosphere before, and after, 2016. As such, the QBO breakdown event is likely not the primary cause of the negative ozone trends reported by Ball et al. 340  (2018), but does appear to affect the robustness of the trend depending on the end year. We will investigate this end-year sensitivity in section 3.5.

Latitude-integrated lower stratospheric ozone trend estimates
While Chipperfield et al. (2018) applied ordinary least squares trend fits to timeseries using a single linear trend, this cannot be compared to multi-variate regression approaches, e.g. DLM and MLR. 345 This is because the former simply asks what the trend in the data is, regardless of the forcing agents, while the latter attempts to separate known (usually quasi-periodic) drivers to distill out the trend that has (usually unknown) drivers of its own. The DLM non-linear trend estimates presented here are the first multivariate analysis applied to ozone timeseries that include the large ozone increase witnessed in 2017. It is important to be clear that long-term trends cannot be compared with single 350 year changes; indeed, the processes governing each timescale are likely quite different. While large short-term increases will likely bias the whole trend-line for that period under MLR analyses (with piecewise linear and independent linear trends -PWLT or ILT), DLM promises to be more robust in the sense that asymmetric fluctuations will only influence part of the smooth trend over a timescale fixed by the smoothness parameter σ trend that controls how rapidly the trend is allowed to evolve 355 (see Ball et al. (2017) and Fig. S1).
The DLM trends in lower stratospheric ozone estimated over 1985-2018 in Fig. 2 continue to be negative, monotonic trends up to 2018 in the quasi-global, tropical and NH regions, while the SH trend reaches a minimum in ∼2013 before slowly rising. All integrated regions suggest the mean remains below the 1998 level (see Table 1; an extended supplementary materials Table S1 provides 360 changes in DU, %, and %}decade for 1985-2018, 1985-1997, and 1998-2018), though the probability of an overall decrease is 99% in the quasi-global, dominated by the tropics (99%), with probabilities of a decrease of 80% and 76% in the SH and NH respectively. Except in the SH, monotonic  Fig. 2). This agrees with Chipperfield et al. (2018) who suggested the large rapid increase of 2017 affected trends, although this was mainly in the SH and has subsequently showed little change over 2018. However, it has done little to reduce the overall probability of a decrease in the quasi-global timeseries (99%). Furthermore, the shape of the DLM curve is affected only near the end years, such that the period away from the end-date is relatively insensitive to a change in the end year and be-370 comes 'locked-in' 3 ; this is a good example of the inadequacy of using linear trends to describe these data. As the DLM-estimated changes in ozone relative to 1998 in years prior to 2010 are essentially unaffected by the addition of 2017 and 2018, the data show robustly that lower stratospheric ozone did continue to decrease until at least 2010 in all regions. We speculate that the shift back to a QBO-Westerly phase will again decrease ozone at mid-latitudes in 2019 (which appears to have begun in 375 October 2018, see Fig. 2). If that happens it is therefore possible that the non-linear trend estimates will likely decrease again, and the emergent 2013 minimum in the DLM non-linear trend estimate seen in Fig. 2b is likely to shift to a later date or disappear.

Sensitivity of DLM trends to the end year and non-linear seasonal-QBO effects
Since mid-latitude ozone excursions depend on the QBO-seasonal interaction, i.e. the QBO phase Due to the magnitude of the mid-latitude, seasonally-dependent QBO ozone variability on short (two to three year) timescales, ILT or PWLT applied to the relatively short post-1997 timeseries will be sensitive to these large swings in ozone. For the smooth DLM trends on the other hand, we expect the last few years of the curve will be primarily affected, with the rest of the trend being stable. We the end year are presented in Fig. 6 with 95% (dark grey shading) and 99% credible intervals. The results specifically for the 1998-2018 change are combined and presented in Fig. 7 as probability distributions, in the same manner as in Fig. 2 of Ball et al. (2018), where blue and red colours represent negative and positive changes respectively, and numbers above each distribution are the 400 probability of the change (fraction of the probability distributions) being negative.
From the panels of Fig. 5, it is clear that ozone trends in the middle-stratosphere exhibit the largest sensitivity to the end year and the uncertainties in the change from 1998 are consistently large (Fig. 6); quasi-globally the change since 1998 is negative for all end years, but does not exceed 95% probability. The upper stratosphere is also sensitive to the end year in the tropics (Fig. 5), and the end 405 year shifts the estimated ozone change from negative to positive with increasing end year, although the uncertainty always remains large (Fig. 6); at mid-latitudes uncertainties in the change since difference. The quasi-global lower stratospheric ozone continues to exhibit a monotonic decline that is still highly confident with 99% probability (Fig. 7 and Table 1), and ozone abundances integrated 415 over the whole stratosphere continues to remain lower in 2018 than in 1998, though this is now with a probability of 86%; these trends are dominated by the tropical contribution (58%, latitude weighted) to the quasi-global change, whereas the NH and SH contribute 21% each. Even so, the NH changes do not appear affected by the recent large seasonally-dependent QBO variability. QBO with ozone reducing sharply as it has done in the past (Fig. 2). We expand the idea of inferring the likely earliest minimum using the DLM with spatially-resolved data in the Supplementary Materials.

Update on ozone profiles
Briefly, in Fig The aim of this work is to assess the current state of, and trends in, stratospheric ozone. Improved knowledge of such trends, and the relevant forcing mechanisms and associated variability, will help to better constrain CCM projections of ozone to the end of the 21 st Century. Chemistry models 470 resolving the stratosphere are one of the best tools for attribution and long-range studies of ozone, but different types exist: free-running CCMs generate their own model-dependent internal climate and variability; chemistry transport models (CTMs) use wind, temperature and surface pressure fields fully prescribed by reanalyses; and specified-dynamics CCMs (SD-CCMs) use reanalyses to nudge the internally-generated variability of the model closer to the historical variability in the real 475 atmosphere while attempting to retain model dependent processes and internal consistency. CTMs and SD-CCMs can be useful for attributing historical changes in ozone to evolving concentrations of CO 2 and ODSs (Solomon et al., 2016), or the Sun (Ball et al., 2016), by accounting for dynamical variability in observations.
A recent study (Chipperfield et al., 2018) used a CTM to reconstruct the ozone timeseries beyond 480 the observational record available at the time to 2017 and found that that model simulated a lower stratospheric ozone increase in 2017 back to 1998 levels; this was attributed to dynamical variability.
Indeed, chemistry and photochemistry play a dominant role over dynamical perturbations in the upper stratosphere as ozone lifetimes are short (∼days), while ozone lifetimes of ∼6-12 months in the lower stratosphere means that equator-to-mid-latitude transport of similar timescales plays an 485 important (dominant) role there (London, 1980;Perliski et al., 1989;Brasseur and Solomon, 2005).
CTMs can provide insight as to whether the changes might be driven by photochemistry, chemistry, or dynamics. However, because the dynamical fields are prescribed, the CTM cannot provide insight into the underlying dynamical driver of the long-term decreases or the 2017 increase. We show here that the 2017 increase simulated by the CTM (Chipperfield et al., 2018) was more than 60% larger 490 than that observed, and that the 1998-2017 and -2018 ( Fig. 1e and f) change remains negative (60 • S-60 • N), and significant in the tropics and some sub-regions of the NH (Fig. 1f). Neither free-running CCMs (WMO, 2014), nor SD-CCMs (Ball et al., 2018), have so far been demonstrated to accurately reproduce the long-term changes estimated from observations in lower stratospheric ozone (Fig. 6).
The effect of the ozone increase in 2017 was small and the probability of an overall ozone decrease 495 in the lower stratosphere remains at 99% for 1998-2018 (-1.7 DU, or 2.0%; see Table S1). We note that the lower stratospheric ozone trends are dominated by the tropical regions (30 • S-30 • N) where the decrease is robust to the end year over 2013-2018, with a probability of 99% (-2.1 DU, -3.5%) that it was lower in 2018 than in 1998. Nevertheless, mid-latitudes out to 50 • N also indicate that the decrease persists (-1.9 DU, -1.7%). We also find that the 2017-2018 addition enhances the estimated 500 magnitude of the upper stratospheric ozone positive trend, but that the quasi-global (60 • S-60 • N) ozone layer still displays a reduction since 1998, though the confidence in this has reduced from 95% in 2016 (Ball et al., 2018) to 86% in 2018 (-1.1 DU, -0.4%). Given the high probability of a decrease in tropical middle (94%) and lower (99%) stratospheric ozone, the whole tropical stratospheric ozone column indicates a highly probable decrease (95%) over 1998-2018 (-1.9 DU, -0.8%).

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In general, uncertainties on changes since 1998 in partial columns have changed little over 2013-2018 (Fig. 6), a result likely due to the large fraction of unaccounted variance in the standard set of predictors used in regression analysis. Our analysis shows that ozone continued to decrease until a minimum in at least 2013 in the SH, and has continued to decrease at all latitudes north of 30 • S. By comparing the phase of the QBO with large, 2-3 year inter-annual variability at mid-latitudes, the 510 implication is that these large mid-latitude changes are related to the seasonal-dependence of ozone on the QBO, i.e. a non-linearity; if true, this could explain why regression models cannot capture this variability, since such non-linear behaviour is not included. The clarification of the origin of these large mid-latitude changes -occurring every few years -is a high priority.
CCMs are consistent in the sign of their projections, although lower stratospheric ozone variabil-515 ity can differ with observations and there is a large spread in their sensitivity to hODSs (Douglass et al., 2012(Douglass et al., , 2014, and therefore their return dates, i.e. a return of ozone to the level it was in 1980 (WMO, 2014;Dhomse et al., 2018;WMO, 2018). CCMs do a good job on many timescales, but due to historically different internal variability, and parametrized sub-grid scale processes and numeri- Future projections tend to focus on how stratospheric ozone will evolve under a given global warming scenario; this is important given that the changing climate due to anthropogenic GHG emissions may impact inter-annual dynamical variability (Osprey et al., 2016;Newman et al., 2016;530 Tweedy et al., 2017), and changes in the large-scale circulation in the stratosphere are likely to modify future distributions of ozone (Chipperfield et al., 2017). Further, ozone is not a passive tracer, but dynamics responds to ozone changes Polvani et al., 2018;Abalos et al., 2019), as has been demonstrated most notably in the SH following ozone depletion and strengthening of the ozone hole (WMO, 2014(WMO, , 2018; as ozone is expected to recover in the coming decades, the 535 dynamics of the stratosphere are also expected to respond. The overall expectations are that total column ozone levels will return to 1980s levels globally by ∼2050, in the Antarctic by 2100, and by ∼2030 and ∼2050 in Northern and Southern mid-latitudes, respectively, continuing on to a 'superrecovery', i.e. that ozone will be higher by the end of the 21 st Century than prior to 1980s levels (Dhomse et al., 2018;WMO, 2014WMO, , 2018, although this is predicated on future scenarios of hODSs 540 decreases continuing as expected (Montzka et al., 2018). However, it is neither clear whether the recent increase in SH lower stratospheric ozone will remain at higher levels or will reduce again in 2019 as the QBO shifts to a Westerly phase, nor why the NH continues to show a persistent decrease.
Nonetheless, we note that the signal is small compared to the (i) large inter-annual variability, (ii) pre-2000 changes induced by ozone depleting substances, and (iii) ozone loses that would have 545 occurred without the Montreal Protocol being enacted.
The ongoing negative trend of ozone in the lower stratospheric component of the total column also continues to pose a problem for global trends in tropospheric ozone. If tropospheric ozone has really increased over the last two decades, and stratospheric ozone was not decreasing or remained flat, then some component of the total column ozone must have been decreasing to balance the 550 ozone budget since it appears that total column ozone has remained steady in the past 5-10 years.
Alternatively, it is possible that the solution simply lies in very large observational uncertainties (Harris et al., 2015;Gaudel et al., 2018;Petropavlovskikh et al., 2019) and/or the inadequacies of linear regression techniques to attribute variability and identify trends. In addition to potential future improvements in merged observational records, this calls for a community push to improve detection 555 and attribution techniques to solve an issue that is of great importance to the health of society, the biosphere, and the climate.