^Research Square

Preprints are preliminary reports that have not undergone peer review. They should not be considered conclusive, used to inform clinical practice, or referenced by the media as validated information.
Fingerprinting the Robust Recovery of Antarctic Ozone
Peidong Wang
pdwang@mit.edu

Massachusetts Institute of Technology
Susan Solomon
Massachusetts Institute of Technology
Benjamin Santer
Woods Hole Ocreanographic Institution
https://orcid.org/0000-0002-6491-7171
https://orcid.org/0000-0002-2020-7581
https://orcid.org/0000-0002-9717-460X
Douglas Kinnison
National Center for Atmospheric Research
Qiang Fu
University of Washington
Kane Stone
Massachusetts Institute of Technology https://orcid.org/0000-0002-2721-8785
Jun Zhang
National Center for Atmospheric Research
Gloria Manney
NorthWest Research Associates
Luis Millan
Jet Propulsion Laboratory, California Institute of Technology
Physical Sciences - Article
Keywords:
Posted Date: August 20th, 2024
DOI: https://d0i.0rg/l 0.21203/rs.3.rs-4876981/v1
License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.
Read Full License
Additional Declarations: There is NO Competing Interest.
Version of Record: A version of this preprint was published at Nature on March 5th, 2025. See the published version at https://doi.org/10.1038/s41586-025-08640-9.
Abstract
The Antarctic ozone “hole" was discovered in 19851, and its primary cause is man-made ozone-depleting substances (ODS)2. Following reductions of ODSs under the Montreal Protocol3, signs of ozone recovery have been reported, based largely on observations and broad yet compelling model-data comparisons4. While such approaches are highly valuable, they do not establish levels of overall confidence that account for the temporal and spatial structure of Antarctic ozone trends as well as uncertainties in internal climate variability. Here, we rely on trend pattern information as a function of month and height to separate anthropogenically forced ozone responses from internal variability, using pattern-based detection and attribution (D&A) methods as employed in climate change studies5-11. The analysis uses satellite observations together with both single-model and multi-model ensemble simulations to identify and quantify the month-height Antarctic ozone recovery "fingerprint”12. We demonstrate that the data and simulations show remarkable agreement in the fingerprint pattern of the ozone response to decreasing ODS forcing since 2005. We also show that ODS forcing has enhanced ozone internal variability during the austral spring, influencing detection of forced responses and their time of emergence. Our results provide robust statistical and physical evidence that actions taken under the Montreal Protocol to reduce ODSs are indeed resulting in Antarctic ozone recovery.
Introduction
Initial-condition large ensembles (LEs) generated with fully coupled global climate models offer a unique opportunity to "fingerprint" the anthropogenic influence in detection and attribution (D&A) research. For example, they provide valuable information on the characteristic space and time signatures of the climate responses to different external forcings5-12. While multiple linear regression approaches are commonly used in ozone studies to isolate underlying forced trends by fitting ozone time series to known sources of variability (such as the solar cycle, El Nino-Southern Oscillation, Quasi-Biennial Oscillation, volcanic activities, etc.)4,13, LEs do not require assumptions that the response is a linear combination of independent predictor variables14. Although some D&A methods have been applied to global ozone depletion and the time of emergence of total column recovery using multi-model ensembles8,15-17, previous studies were limited by shorter data records, and have not fully utilized the pattern-based technique. Furthermore, single-model LEs now reliably quantify modelled forced signals and intrinsic variability, whereas multi-model ensembles can sample large inter-model differences in forcing, response, and variability, thus hampering the identification of ozone recovery15,16.
Observed and model-simulated ozone trends
Figure 1 shows the observed and simulated month-height trend patterns over 2005 to 2018 for Antarctic ozone data spatially averaged over 66°-82°S. Observations from MLS18 (Microwave Limb Sounder) are compared with two different sets of model results: 1) the multi-model ensemble mean computed using one run of each of the 19 models that participated in the CCMI-119 (phase 1 of the Chemistry-Climate
Model Initiative); and 2) the single-model ensemble of 10 different realizations of CESM-WACCM20,21 (Community Earth System Model-Whole Atmosphere Community Climate Model; referred to as WACCM for short). Time series used for calculating trends are presented for illustration for four selected months and heights, and the periods of recent exceptional events, including the unusual 2019 sudden stratospheric warming22 (SSW), 2020 Australian wildfire23-25, and 2022 Hunga volcanic eruption26-29 are marked with dashed lines.
The WACCM (and some of the CCMI) ensemble comprises free-running coupled ocean-atmosphere simulations forced by time-evolving changes in greenhouse gases (GHG) and ozone-depleting substances (ODS), specified under the refC2 scenario (detailed descriptions of the models and scenarios are in the Methods section). The smaller amplitudes in WACCM and CCMI modelled mean trends in Figure 1d-e compared to the single real-world realization provided by MLS are partly due to the fact that the model ensemble means are averages over many different realizations with varying phasing of internal variability superimposed on the forced response. Because the internal variability in different realizations and models is uncorrelated (except by chance), averaging reduces its amplitude.
For comparison, Extended Data Figures 1 and 2 show the ozone trends in 2005-2018 from individual WACCM realizations and CCMI model runs (respectively). Some individual members display monthheight trend patterns that are more similar to MLS while others are less similar, reflecting differences in the phasing of internal variability. Nonetheless, nearly all realizations preserve some common features, likely reflecting the "fingerprint" of GHG and ODS forcings on ozone recovery.
Ozone recovery in the lower stratosphere (at altitudes below the pressure level of ~30 hPa) during the austral spring is mainly due to the reduction in ODS concentrations3, leading to less heterogeneous ozone depletion2. The seasonal signature of the ozone hole in August-December is apparent in this region (Figure 1d,e). Recovery of upper stratospheric ozone (above ~10 hPa) also varies seasonally but maximizes in March-May30 and is due to both increased GHG and a decrease in ODS31, with each forcing roughly contributing equally (see Extended Data Figure 3). Increasing GHGs induce a large temperature decrease in the upper stratosphere32, slowing down the gas-phase ozone depletion; decreasing ODSs also lead to a reduction in gas-phase ozone depletion via reduced reactive chlorine at these altitudes33. In the descending circulation of the polar winter, the increased ozone in the upper stratosphere propagates down to the mid-stratosphere. This combined month- and height-resolved pattern characterizes the "fingerprint” of GHG and ODS forcings on Antarctic ozone recovery.
Noise of ozone variability and ODS forcing
Signal-to-noise analyses in D&A climate studies typically use natural internal variability ("noise") estimated from long pre-industrial control runs5-11. We rely on several different noise estimates here (a detailed description of signal and noise calculations is provided in the Methods section). One source is from a WACCM simulation representing atmospheric conditions prior to the onset of large ozone losses in the 1980s. Such conditions were specified in the "historical" scenario, in which both GHG and ODS concentrations evolve over 1955 to 1974. A second source of noise information is from the WACCM refC2 scenario, in which the GHG and ODS levels are comparable to present-day conditions. Figure 2a-b show the month-height patterns of noise, defined here as the standard deviation of ozone trends in the two separate 10-member WACCM historical and refC2 ensembles. The amplitude of internal variability in these 14-year ozone trends (2005-2018) varies markedly as a function of altitude and month. The noise patterns of the ozone trends in the CCMI models under the refC2 scenario are qualitatively similar to those of WACCM, but the CCMI multi-model ensemble also reflects different model responses and possible errors34-36 which can inflate noise compared to a single-model ensemble (see Extended Data Figure 4a).
Although generated with the same physical climate model, the WACCM historical and refC2 simulations exhibit certain notable differences in the amplitude of the internal variability of ozone trends. This is especially important in the austral spring in the lower stratosphere where the ozone "hole" typically occurs (marked with the white dashed boxes in Figure 2). This indicates that the forcing differences in the two scenarios directly affect internal noise. Our results highlight the importance of accounting for forced changes in variability when examining ozone recovery. The enhanced ozone variability can affect the estimated statistical significance of the observed ozone trends.
For accurate analysis of the statistical significance of ozone recovery, it is critical that the model-based noise is realistic. Figure 2c shows the distributions of ozone monthly anomalies from MLS and model simulations (after removing the mean forced response) relative to the present-day MLS climatology, in the region highlighted by the white dashed boxes in Figure 2a,b. This information is displayed in Figure 2d in the form of distributions of the absolute ozone monthly mixing ratios. The distributions of internal variability of monthly ozone in MLS and in the WACCM refC2 scenario are virtually identical in Figure 2c,d. Interestingly, there is a striking enhancement in ozone variability under the refC2 scenario; the standard deviation is increased by 130% compared to the historical scenario. GHG forcing alone (the fODS scenario, with low ODS but high GHG) yields a narrow spread in ozone variability similar to the historical case, confirming that the variability enhancement is primarily driven by ODS forcing. Such enhancement can be understood by noting that the weak (strong) Brewer-Dobson circulations associated with internal variability can be expected to lead to large negative (positive) temperature anomalies37-39. The heterogeneous chemistry and the ozone depletion due to ODS are more effective under colder conditions2, extending the lower tail of the distribution of absolute ozone concentration40 (Figure 2d). Because low ozone concentrations are confined within the vortex41, vortex variations (e.g., changes in size, shape, and position) can also contribute to the ozone internal variability when concentrations are spatially averaged over a fixed latitude range. This sensitivity to the choice of averaging area extends from austral spring to austral summer when the vortex breaks up42. A similar enhancement in simulated ozone variability under high ODS was reported in the Arctic, albeit with a model that does not have an interactive ocean43. This enhancement in ozone variability due to ODS forcing sheds light on a potential pathway for external forcing to modulate specific modes of natural internal variability, such as the Southern Annular Mode44.
Signal-to-noise analysis of ozone changes: local and overall pattern
Figure 3d shows the "local" (at individual months and heights) signal to noise (S/N) ratio inferred from WACCM for a trend length of 14 years (2005 to 2018). In Figure 3c, the mean forced signal from WACCM is replaced by the MLS observed trend, which contains both the forced response and internal variability. A larger local S/N ratio indicates increased likelihood that the ozone trend is anthropogenically forced, with 95% and 90% confidence indicated by backslashes and dots (respectively). Based on the WACCM S/N for the refC2 scenario, ozone recovery (as a forced response to GHG and ODS forcing) can be detected with high confidence by 2018 in certain months and heights. In the upper stratosphere, recovery is significantly larger than internal variability in every month except during winter, when it propagates to the middle stratosphere due to polar descent. There is also a relative maximum in local S/N in September in the lower stratosphere in MLS and in the WACCM ensemble mean. The overall pattern of local S/N is similar in CCMI, but statistical significance is lower in several key regions (Extended Data Figure 5). This is expected given that the multi-model CCMI noise does not reflect intrinsic variability alone and is larger than in single-model WACCM refC2.
The WACCM simulations used here do not include major volcanic eruptions thought to have influenced observed ozone after 2012 (e.g., Calbuco and Hunga eruptions), nor do they account for exceptional wildfires, such as those in Australia in 2020. To explore the impact of the later events, we performed a local S/N analysis over a longer period (2005-2023; see Extended Data Figure 6). The month-height local S/N pattern over 2005-2023 shows many features similar to those in Figures 3c,d, but also pronounced differences between WACCM and MLS, especially in the mid-stratosphere in October-December. Note that Antarctic ozone trends in the mid-stratosphere in these months are particularly sensitive to the end points, and that may be exacerbated by changes in the vortex. As illustrated for example in Extended Data Figures 7 and 8, visual inspection of time series and maps illustrates how a shift of the vortex off the pole affects how it is sampled in a spatial average calculated with fixed latitudinal boundaries. Our results indicate that ozone trends may be highly sensitive to the choice of domain for spatial averaging, and to how well a given domain samples temporal changes in vortex location and shape. Consideration of such sampling issues, together with simulations that account for the exceptional forcings26,45,46, would be expected to provide better agreement with the observed ozone trends.
In addition to the "local" S/N analysis described above, we also performed a S/N analysis using the overall month-height fingerprint pattern of Antarctic ozone trends since 2005 (see Methods section). The local S/N analysis (Figure 3) and the S/N analysis of the similarity of this fingerprint pattern (Figure 4) provide strong evidence that the observed time-space structure of ozone changes over Antarctica is consistent with time-evolving ODS and GHG forcing. And the observed changes during 2005-2018 are inconsistent with natural internal variability alone (with 95% confidence for the observed MLS pattern projected on both WACCM and on CCMI month-height fingerprints). Although the exceptional ozone years in and after 2020 lower the overall S/N in Figure 4, MLS trends projected on WACCM results (which neglect these events as well as the sampling concerns as noted above), nonetheless remain significant at the 90% confidence level as late as the end of 2023.
Antarctic springtime total ozone recovery
Signs of total column ozone recovery are often sought during the Antarctic spring4, the season when the ozone hole maximizes in depth and extent. The emergence of ozone recovery after 2005 in September occurs around 2018 both in terms of ozone at a single illustrative level (82.5 hPa) in Figure 3e and in terms of the total column ozone (TCO) in Extended Data Figure 9a, where the observed TCO is from the OMI47 (Ozone Monitoring Instrument). Even with exceptionally low ozone in and after 2020 (which may be related to unusual wildfire and volcanic emissions lofted into the stratosphere), the total ozone healing signal from the satellite data is still outside the noise with a 95% confidence in September.
A recent study raises the concern that October ozone in the middle stratosphere as well as the column ozone has significantly decreased48. We note that although the TCO trend in October is negative, the trend is well within the internal variability (Extended Data Figure 9b). The emergence of ozone recovery due to GHG and ODS forcing (based on the WACCM ensemble mean signal) in both October and November had been expected around 2021 under typical conditions (Extended Data Figure 9b,c). However, the unusually low ozone years in and after 2020 may have delayed detection in the observations. This underscores the importance of maintaining a long observation record to ensure high confidence in detecting and attributing future ozone recovery at this time of year.
Summary and outlook
Here we have provided a pattern-based fingerprint analysis for Antarctic ozone recovery, analogous to fingerprinting anthropogenic climate change5-12. We find that the local and overall pattern similarity of the S/N ratio between MLS and single or multiple model ensembles gives high confidence that the observed Antarctic ozone trends are primarily due to forced responses rather than natural variability, reflecting three coherent features of the fingerprint: 1) the upper stratospheric ozone increases in all seasons except winter; 2) middle stratospheric ozone recovery during winter; 3) and lower stratospheric ozone increases in September.
Further, we have shown that the amplitude of lower stratospheric ozone variability is greatly enhanced in a present-day simulation relative to the amplitude of ozone variability in a "pre-ozone depletion" simulation. This enhancement is due to the higher present-day levels of ODS. It is crucial to consider this modulation of internal variability by ODS forcing when evaluating the statistical significance of ozone trends. A significant ODS-driven signal of local ozone recovery in October and November has yet to emerge in the observations, likely due to the exceptionally low ozone years in and after 2020. These low ozone years are at least partly due to known volcanic and wildfire forcings not included in the available simulations. While October ozone exhibits a decreasing trend in the middle stratosphere48, this time and location is subject to only a small healing signal (Figure 1) and substantial noise (Figure 2), implying that trends with weak statistical significance here may well be spurious. October ozone trends in the middle stratosphere are also affected by sampling: we have shown that the noise in this month and region is very sensitive to polar vortex variations.
Some caveats of the current analysis should be noted. Only one model with 10 members is examined in detail in this work. To improve confidence in the detection and attribution of forced responses versus natural variability in future ozone recovery assessments, it would be beneficial to use larger initial condition ensembles from multiple single models rather than relying on single realizations from many different models11,15,16. The forced response in this study considers GHG and ODS only, and does not include known forcings from important volcanoes and major wildfires after 2012; future ensemble runs including these forcings from 2020 onward would likely improve S/N of the results. The projected long- lasting stratospheric water vapor from the Hunga eruption28,49 or future volcanic forcing50,51 could reduce the future ozone recovery signal. Indeed, even the large S/N ratio we now see in the upper stratosphere could be temporarily obscured by uncertainties in future GHG emissions52 and solar proton events30.
Our work shows how fingerprinting and pattern similarity establishes quantitative confidence in Antarctic ozone recovery. It also shows why it is crucial to maintain global height-resolved observations over extended periods to identify patterns of signals that emerge from noise, raising concerns about the impending satellite data gap in stratospheric measurements53. A long observational record can ensure a sufficient S/N ratio that is less sensitive to short-term episodic perturbations, thereby providing high confidence in detecting and attributing trends5.
Declarations
Acknowledgments
We thank Clara Deser and Pu Lin for helpful discussions. We also thank Larry Horowitz and Meiyun Lin for providing GFDL model data for this analysis. S.S. and P.W. gratefully acknowledge support from the atmospheric chemistry division of the National Science Foundation under grant 2316980 and 2128617. B.D.S. was supported by the Francis Ε. Fowler IV Center for Ocean and Climate at Woods Hole Oceanographic Institution (WHOI). D.E.K. was financed in part by NASA grant 80NSSC19Κ0952. Q.F. was in part supported by NSF Grant AGS-2202812. The Community Earth System Model (CESM) project is supported by the National Science Foundation and the Office of Science of the U.S. Department of Energy. We gratefully acknowledge high-performance computing support from Cheyenne (https://doi.Org/10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory (CISL), sponsored by the National Science Foundation.
Data Availability
MLS and OMI satellite data are publicly available at https://disc.gsfc.nasa.gov. CCMI model outputs are available at https://archive.ceda.ac.uk, and the CESM model outputs are available at https://www.earthsystemgrid.org. All the pre-processed model data (e.g., monthly mean ozone averaged over 66°-82°S from CCMI and WACCM and interpolated onto MLS vertical coordinates) and the code used to generate all the figures in this analysis are available at Zenodo (https://d0i.0rg/l 0.5281/zenodo.13257908).
Author Contributions
P.W., S.S., B.D.S. designed the study. D.E.K. designed and performed the WACCM simulations. P.W. analyzed the data and produced the figures. P.W. and S.S. drafted the initial text. B.D.S., Q.F, K.A.S., J.Z., G.L.M., and L.F.M. contributed significantly to the interpretation of findings.
Competing Interests
The authors declare no competing interests.
Correspondence and requests for materials
Peidong Wang (pdwang@mit.edu) and Susan Solomon (solos@mit.edu)
References
1.		Farman, J. C., Gardiner, B. G. & Shanklin, J. D. Large losses of total ozone in Antarctica reveal seasonal CIOx/NOx interaction. (1985).
2.		Solomon, S., Garcia, R. R., Rowland, F. S. & Wuebbles, D. J. On the depletion of Antarctic ozone. 4 (1986).
3.		Johannes C, L. & Susann, T. Scientific Assessment of Ozone Depletion: 2022, Chapter 1: Update on Ozone-Depleting Substances (ODSs) and Other Gases of Interest to the Montreal Protocol. 509 (2022).
4.		Chipperfield, M. P. & Santee, M. L. Scientific Assessment of Ozone Depletion: 2022, Chapter 4: Polar Stratospheric Ozone: Past, Present, and Future. 509 (2022).
5.		Santer, B. D. et al. Exceptional stratospheric contribution to human fingerprints on atmospheric temperature. Proc. Natl. Acad. Sci. U.S.A. 120, e2300758120 (2023).
6.		Terray, L. et al. Near-Surface Salinity as Nature’s Rain Gauge to Detect Human Influence on the Tropical Water Cycle. Journal of Climate 25, 958-977 (2012).
7.		Stott, P. A., Sutton, R. T. & Smith, D. M. Detection and attribution of Atlantic salinity changes. Geophysical Research Letters 35, 2008GL035874 (2008).
8.		Gillett, N. P., Fyfe, J. C. & Parker, D. E. Attribution of observed sea level pressure trends to greenhouse gas, aerosol, and ozone changes. Geophysical Research Letters 40, 2302-2306 (2013).
9.		Christidis, N. & Stott, P. A. Changes in the geopotential height at 500 hPa under the influence of external climatic forcings. Geophysical Research Letters 42, (2015).
10.		Shi, J.-R., Santer, B. D., Kwon, Y.-O. & Wijffels, S. Ε. The emerging human influence on the seasonal cycle of sea surface temperature. Nat. Clim. Chang. 14, 364-372 (2024).
11.		Santer, B. D. et al. Robust Anthropogenic Signal Identified in the Seasonal Cycle of Tropospheric Temperature. Journal of Climate 35, 6075-6100 (2022).
12.		Klaus Hasselmann. Optimal Fingerprints for the Detection of Time-dependent Climate Change. Journal of Climate 6, 1957-1971 (1993).
13.		Hassler, Β. & Young, P. J. Scientific Assessment of Ozone Depletion: 2022, Chapter 3: Update on Global Ozone: Past, Present, and Future. 509 (2022).
14.		Santer, B. D. et al. Accounting for the effects of volcanoes and ENSO in comparisons of modeled and observed temperature trends. J. Geophys. Res. 106, 28033-28059 (2001).
15.		Dhomse, S. S. et al. Estimates of ozone return dates from Chemistry-Climate Model Initiative simulations. Atmos. Chem. Phys. 18, 8409-8438 (2018).
16.		Zeng, G. et al. Attribution of Stratospheric and Tropospheric Ozone Changes Between 1850 and 2014 in CMIP6 Models. JGR Atmospheres 127, e2022JD036452 (2022).
17.		Robertson, F. et al. Signal-To-Noise Calculations of Emergence and De-Emergence of Stratospheric Ozone Depletion. Geophysical Research Letters 50, e2023GL104246 (2023).
18.		Waters, J. W. et al. The Earth observing system microwave limb sounder (EOS MLS) on the aura Satellite. IEEE Trans. Geosci. Remote Sensing 44, 1075-1092 (2006).
19.		Morgenstern, 0. et al. Review of the global models used within phase 1 of the Chemistry-Climate Model Initiative (CCMI). Geosci. Model Dev. 10, 639-671 (2017).
20.		Marsh, D. R. et al. Climate Change from 1850 to 2005 Simulated in CESM1 (WACCM). Journal of Climate 26, 7372-7391 (2013).
21.		Garcia, R. R., Smith, A. K., Kinnison, D. E., Camara, A. D. L. & Murphy, D. J. Modification of the Gravity Wave Parameterization in the Whole Atmosphere Community Climate Model: Motivation and Results. Journal of the Atmospheric Sciences 74, 275-291 (2017).
22.		Wargan, K., Weir, B., Manney, G. L., Cohn, S. E. & Livesey, Ν. J. The Anomalous 2019 Antarctic Ozone Hole in the GEOS Constituent Data Assimilation System With MLS Observations. JGR Atmospheres 125, e2020JD033335 (2020).
23.		Santee, M. L. et al. Prolonged and Pervasive Perturbations in the Composition of the Southern Hemisphere Midlatitude Lower Stratosphere From the Australian New Year's Fires. Geophysical Research Letters 49, (2022).
24.		Solomon, S. et al. On the stratospheric chemistry of midlatitude wildfire smoke. Proc. Natl. Acad. Sci. U.S.A. 119, e2117325119 (2022).
25.		Bernath, P., Boone, C. & Crouse, J. Wildfire smoke destroys stratospheric ozone. Science 375, 12921295 (2022).
26.		Wang, X. et al. Stratospheric Climate Anomalies and Ozone Loss Caused by the Hunga Tonga- Hunga Ha'apai Volcanic Eruption. JGR Atmospheres 128, e2023JD039480 (2023).
27.		Zhang, J. et al. Chemistry Contribution to Stratospheric Ozone Depletion After the Unprecedented Water-Rich Hunga Tonga Eruption. Geophysical Research Letters 51, (2024).
28.		Wohltmann, I., Santee, M. L., Manney, G. L. & Millan, L. F. The Chemical Effect of Increased Water Vapor From the Hunga Tonga-Hunga Ha'apai Eruption on the Antarctic Ozone Hole. Geophysical Research Letters 51, e2023GL106980 (2024).
29.		Manney, G. L. et al. Siege in the Southern Stratosphere: Hunga Tonga-Hunga Ha'apai Water Vapor Excluded From the 2022 Antarctic Polar Vortex. Geophysical Research Letters 50, e2023GL103855 (2023).
30.		Stone, K. A., Solomon, S. & Kinnison, D. Ε. On the Identification of Ozone Recovery. Geophysical Research Letters 45, 5158-5165 (2018).
31.		Chipperfield, M. P. et al. Detecting recovery of the stratospheric ozone layer. Nature 549, 211-218 (2017).
32.		Manabe, S. & Wetherald, R. Τ. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. Journal of the Atmospheric Sciences 24, 241-259 (1967).
33.		Molina, M. J. & Rowland, F. S. Stratospheric sink for chlorofluoromethanes: chlorine atom-catalysed destruction of ozone. Nature 249, 810-812 (1974).
34.		Deser, C. et al. Insights from Earth system model initial-condition large ensembles and future prospects. Nat. Clim. Chang. 10, 277-286 (2020).
35.		Kay, J. Ε. et al. The Community Earth System Model (CESM) Large Ensemble Project: A Community Resource for Studying Climate Change in the Presence of Internal Climate Variability. Bulletin of the American Meteorological Society 96, 1333-1349 (2015).
36.		Solomon, A. et al. Distinguishing the Roles of Natural and Anthropogenically Forced Decadal Climate Variability: Implications for Prediction. Bull. Amer. Meteor. Soc. 92, 141-156 (2011).
37.		Fu, Q., Solomon, S., Pahlavan, H. A. & Lin, P. Observed changes in Brewer-Dobson circulation for 1980-2018. Environ. Res. Lett. 14, 114026 (2019).
38.		Poivani, L. M. et al. Large Impacts, Past and Future, of Ozone-Depleting Substances on Brewer- Dobson Circulation Trends: A Multimodel Assessment. JGR Atmospheres 124, 6669-6680 (2019).
39.		Lin, P., Fu, Q., Solomon, S. & Wallace, J. M. Temperature Trend Patterns in Southern Hemisphere High Latitudes: Novel Indicators of Stratospheric Change. Journal of Climate 22, 6325-6341 (2009).
40.		Solomon, S., Portmann, R. W., Sasaki, T., Hofmann, D. J. & Thompson, D. W. J. Four decades of ozonesonde measurements over Antarctica. J. Geophys. Res. 110 2005JD005917 (2005).
41.		Schoeberl, M. R. & Hartmann, D. L. The Dynamics of the Stratospheric Polar Vortex and Its Relation to Springtime Ozone Depletions. Science 251, 46-52 (1991).
42.		Lawrence, Z. D., Manney, G. L. & Wargan, K. Reanalysis intercomparisons of stratospheric polar processing diagnostics. Atmos. Chem. Phys. 18, 13547-13579 (2018).
43.		Akiyoshi, H., Kadowaki, Μ., Yamashita, Υ. & Nagatomo, Τ. Dependence of column ozone on future ODSs and GHGs in the variability of 500-ensemble members. Sci Rep'X'i, 320 (2023).
44.		Thompson, D. W. J. et al. Signatures of the Antarctic ozone hole in Southern Hemisphere surface climate change. Nature Geosc/ 4, 741-749 (2011).
45.		Solomon, S. et al. Emergence of healing in the Antarctic ozone layer. Science 353, 269-274 (2016).
46.		Solomon, S. et al. Chlorine activation and enhanced ozone depletion induced by wildfire aerosol. Nature 615, 259-264 (2023).
47.		Levelt, P. F. et al. The ozone monitoring instrument. IEEE Trans. Geosci. Remote Sensing 44, 10931101 (2006).
48.		Kessenich, H. E., Seppala, A. & Rodger, C. J. Potential drivers of the recent large Antarctic ozone holes. Nat Commun 14, 7259 (2023).
49.		Zhou, X. et al. Antarctic Vortex Dehydration in 2023 as a Substantial Removal Pathway for Hunga Tonga-Hunga Ha'apai Water Vapor. Geophysical Research Letters 51, e2023GL107630 (2024).
50.		Eric Klobas, J., Wilmouth, D. M., Weisenstein, D. K., Anderson, J. G. & Salawitch, R. J. Ozone depletion following future volcanic eruptions. Geophysical Research Letters 44, 7490-7499 (2017).
51.		Chim, M. M. et al. Climate Projections Very Likely Underestimate Future Volcanic Forcing and Its Climatic Effects. Geophysical Research Letters 50, e2023GL103743 (2023).
52.		Revell, L. E., Bodeker, G. E., Huck, P. E., Williamson, Β. Ε. & Rozanov, E. The sensitivity of stratospheric ozone changes through the 21st century to Ν20 and CH4. Atmos. Chem. Phys. 12, 11309-11317 (2012).
53.		Chipperfield, Μ. Ρ. & Bekki, S. Opinion: Stratospheric ozone - depletion, recovery and new challenges. Atmos. Chem. Phys. 24, 2783-2802 (2024).
Methods
Satellite data
MLS provides daily observations since August 2004, and the data has been extensively validated54,55. Here we use MLS version 5 monthly level 3 ozone mixing ratios on pressure coordinates from 100 hPa to 1 hPa. The level 3 product covers latitudes from 82 °S to 82 °N, using a 4° latitude bin. Ozone is averaged over 66°-82°S in this paper, weighted by cosine latitude to account for the reduction in area further poleward. We use the monthly mean starting from 2005 (excluding the latter half of 2024) so that every month in the trend analysis has the same number of time samples.
Satellite TCO observations are from the OMI47 version 3 daily level 3 product, which is onboard the same satellite as MLS. TCO from OMI is also averaged by month starting from 2005 and in the latitude range from 66°-82°S (weighted by cosine latitude).
Model and scenario descriptions
A total of 19 different models participated in the CCMI-1, with a total of 33 realizations for the refC2 scenario15,19. This scenario characterizes ODS emissions following WMO (2011)56, and other GHG emissions following RCP6.057 from 1960 to 2100. To prevent biasing towards models with more ensemble members, we only use the first realization from each model.
We also used the fully coupled CESM1-WACCM420’21 in this analysis, which incorporates coupled oceanatmosphere processes with interactive chemistry. Our primary focus is on a 10-member WACCM initial condition ensemble run generated with the refC2 scenario employed by the CCMI-1 models. We also consider three other WACCM initial condition ensembles, referred to as fODS, fGHG, and historical. fODS fixes ODS forcing at the 1960 level, while GHG concentrations evolve as in the refC2 runs. Alternately, fGHG fixes GHG concentrations in 1960, while ODS levels evolve as in refC2 runs. The historical scenario involves temporal changes in both GHG and ODS from 1955 to 197958. The CCMI and WACCM simulations are vertically interpolated to MLS pressure levels (linear interpolation in log pressure), and are also averaged over 66°-82°S and cosine-weighted for consistency with MLS.
Although the WACCM runs analyzed here are less than 30 years in length (from 1995 to 2024 for refC2, fODS, and fGHG, and from 1955 to 1979 for the historical scenario), an advantage of the set of simulations is that each scenario has 10 realizations that are slightly perturbed in their initial conditions35. This facilitates reliable estimation of both the underlying forced response (the ensemblemean) and internal variability. In contrast, multi-model ensembles convolve internal variability estimates with inter-model differences or errors in forced responses, and/or with model differences in the amplitude and patterns of internal variability34-36. For example, not all of the 19 CCMI models are fully coupled to an interactive ocean19, likely introducing large inter-model differences in forced responses and natural variability.
As shown here, the WACCM historical and refC2 initial condition ensembles can also be used to explore whether external forcing modulates internal variability - a key issue in signal detection. Using the WACCM fully-coupled chemistry climate model can be expected to improve upon multiple linear regression approaches for estimating the anthropogenic component of ozone trends, since no prior assumptions are required regarding the relationships between different predictor variables (such as the El Nino-Southern Oscillation, Southern Annual Mode, Quasi-Biennial Oscillation, solar cycle, etc.). Any nonlinear interactions between ozone and climate internal variability are inherent in the model simulations.
Although large initial condition ensembles from multiple single-models are preferred for analyzing the interactions between atmospheric chemistry and natural internal variability, the high computational cost may be a barrier to generating such ensembles, at least for some models34.
Signal and noise definition and uncertainty estimation
The "local" signal and noise denotes an analysis at individual months and heights. We define the local signal as the linear trend in ozone (starting in 2005, ending years can vary from 2009 to 2023) at each month and pressure level, derived from a linear fit of ensemble-mean forced model simulation data. To calculate the "local" noise, we first subtract the ensemble-mean ozone time series from each individual model realization; the resulting residuals then characterize the internal variability34. Noise is defined as the standard deviation of the ozone trends (with the same trend length as the signal) in these residuals. The noise represents the spread in ozone trends that is primarily due to internal variability. Both the local signal and the local noise have units of ppm/decade (parts per million by volume per decade). The statistical significance of ozone trend is determined by the signal-to-noise ratio, S/N. A 95% confidence level is associated with local S/N larger than 1.96, and a 90% confidence level is associated with local S/N larger than 1.645, for two-tailed tests.
In addition to the local S/N analysis at individual months and heights, we also applied a conventional "fingerprint" method5 to the overall simulated and observed month-height patterns of ozone changes. The key point here is that the entire month-height pattern is employed to distinguish a forced response from internal variability. The overall signal is the uncentered covariance between the month-height ozone trend patterns in MLS and in the WACCM ensemble-mean (or between the trend pattern in MLS and the CCMI multi-model mean). Fingerprinting is performed over the same space-time ranges used in the local S/N analysis: i.e., using spatially averaged ozone changes between 66°-82°S at altitudes from 100 hPa to 1 hPa and in the 12 months from January through December. This is essentially equivalent to projecting the observed month- and height-resolved trend pattern onto the forced response5. Similarly, the overall noise is the standard deviation in the uncentered covariance between internal variability in individual realizations and the mean forced response. The increase in the overall S/N in Figure 4 with increasing trend length suggests that the observed overall month-height ozone recovery pattern is unlikely to be explained by internal variability alone.
Vortex coverage calculation
Vortex-averaged ozone in Extended Data Figure 7 is from the MLS level 3 monthly VortexAvg product on potential temperature (theta) surfaces. Vortex edge in MLS is determined by the sPV (scaled potential vorticity) from the derived meteorological products59-61 (DMPs) and a height-dependent sPV threshold42. The DMPs are calculated from the NASA GMAO (Global Modeling and Assimilation Office) using meteorology from MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) and are interpolated to the same time and location as MLS level 2 products. For consistency with MLS vortex average products, we vertically interpolated sPV from pressure level to theta level (linear interpolation from log pressure to log theta). To estimate the monthly polar vortex coverage at each grid point on the MLS level 3 grid (with 4°x5° horizontal resolution), we count the total number of MLS overpasses in each grid box for every month. We then calculate the fraction of these measurements that meet the vortex threshold based on the sPV value42.
Additional references for the Methods section
54.		Hubert, D. et al. Ground-based assessment of the bias and long-term stability of 14 limb and occultation ozone profile data records. Atmos. Meas. Tech.9, 2497-2534 (2016).
55.		Froidevaux, L. et al. Validation of Aura Microwave Limb Sounder stratospheric ozone measurements. J. Geophys. Res.113, 2007JD008771 (2008).
56.		WMO (World Meteorological Organization). Scientific Assessment of Ozone Depletion: 2010. 516 pp (2011).
57.		Meinshausen, M. et al. The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Climatic Change109, 213-241 (2011).
58.		Stone, K. A., Solomon, S., Thompson, D. W. J., Kinnison, D. Ε. & Fyfe, J. C. On the Southern Hemisphere Stratospheric Response to ENSO and Its Impacts on Tropospheric Circulation. Journal of Climate35, 1963-1981 (2022).
59.		Manney, G. L. et al. Solar occultation satellite data and derived meteorological products: Sampling issues and comparisons with Aura Microwave Limb Sounder. J. Geophys. Res.112, 2007JD008709 (2007).
60.		Millan, L. F. et al. Multi-parameter dynamical diagnostics for upper tropospheric and lower stratospheric studies. Atmos. Meas. Tech.16, 2957-2988 (2023).
61.		Manney, G. L. et al. Jet characterization in the upper troposphere/lower stratosphere (UTLS): applications to climatology and transport studies. Atmos. Chem. Phys.11, 6115-6137 (2011).
Figures

Figure 1
Month-height patterns of ozone trends in observations and simulations. The middle row shows the leastsquares linear trends in ozone over 2005-2018 as a function of pressure and month in the MLS observations, the WACCM 10-member ensemble mean, and the CCMI 18-model ensemble mean. Results are for spatial averages over 66°-82°S. We also show the time series of ozone at four illustrative locations (indicated by different markers on the contour figure) on the top and bottom rows (plotted as anomalies relative to the 2005-2018 mean). Thick blue and red lines are the model ensemble means, while the thin lines are the ozone time series in individual model realizations. The black solid line is from MLS. Time series after 2018 are shown as dashed lines because of likely impacts of exceptional perturbations from the 2019 SSW, 2020 Australian wildfire, and 2022 Hunga eruption.

Figure 2

historical (N=3360) fODS (N=336) refC2 (N=3360) MLS (N=3360)
Ozone variability modulated by external forcing. Panels a-b show the month-height patterns of the standard deviation of ozone trends (averaged over 66°-82°S) in the WACCM historical and refC2 scenarios. The standard deviation is a measure of the trend uncertainty arising from internal variability among the 10 WACCM ensemble members. Both scenarios have the same trend length of 14 years: the historical scenario analysis period is from 1955 to 1968 and the refC2 analysis period is from 20052018. Panel c shows (for the white dashed box in the top panels), the internal variability in WACCM and MLS ozone after first removing the mean forced response of monthly ozone. Results are expressed as percent changes relative to the MLS climatological mean. The thick lines are the Gaussian fits to the distributions. Panel d displays the same distributions shown in panel c, but in terms of the absolute

monthly ozone mixing ratios. The number of data points in each distribution is indicated in the legend. A similar figure for CCMI models is shown in Extended Data Figure 4.

Trend length (year)

Figure 3

The local signal-to-noise pattern of ozone recovery. The middle panels show the month-height patterns of the observed ozone trends in MLS (panel c) and the WACCM 10-member ensemble mean refC2 trends (panel d) divided by the internal variability noise in refC2 trends (which are given in Figure 2b). Results are for trends over 2005-2018; Extended Data Figure 5 similarly displays local S/N for trends calculated over 2005-2023. Hatched regions indicate that the local trend exceeds the noise with 95% confidence (backslashes) and with 90% confidence (dots). The top and bottom panels provide the local signal and noise as a function of timescale at the same four illustrative months/heights shown in Figure 1. The thin gray lines are the trends due to internal variability in each model realization, and the gray shading indicates the 95% distribution of that spread. Thick lines are the trends from MLS (black) and the

WACCM ensemble mean (red). The error bars on the red line indicate ±1 standard deviation in the

Signal-to-noise characteristics for the overall month-height fingerprint pattern. The overall S/N for MLS ozone trends projected onto the WACCM (red) or CCMI (blue) ensemble-mean month-height ozone trend pattern exceeds the 95% confidence level after around 2016, indicating that the similarity between the observed trend pattern and the model-predicted forced response is unlikely to be due to internal variability alone. S/N increases to higher values by 2018 but falls after 2020, following exceptional events that apparently had large impacts on observed ozone changes but are not included in the simulations. Despite the neglect of these unusual post-2020 forcings, S/N for WACCM remains above the 90% threshold even at the end of 2023.
Supplementary Files
This is a list of supplementary files associated with this preprint. Click to download.
• ExtendedDataFigures.docx