Springtime arctic ozone depletion forces northern hemisphere climate anomalies

Abstract

Large-scale chemical depletion of ozone due to anthropogenic emissions occurs over Antarctica as well as, to a lesser degree, the Arctic. Surface climate predictability in the Northern Hemisphere might be improved due to a previously proposed, albeit uncertain, link to springtime ozone depletion in the Arctic. Here we use observations and targeted chemistry–climate experiments from two models to isolate the surface impacts of ozone depletion from complex downward dynamical influences. We find that springtime stratospheric ozone depletion is consistently followed by surface temperature and precipitation anomalies with signs consistent with a positive Arctic Oscillation, namely, warm and dry conditions over southern Europe and Eurasia and moistening over northern Europe. Notably, we show that these anomalies, affecting large portions of the Northern Hemisphere, are driven substantially by the loss of stratospheric ozone. This is due to ozone depletion leading to a reduction in short-wave radiation absorption, when in turn causing persistent negative temperature anomalies in the lower stratosphere and a delayed break-up of the polar vortex. These results indicate that the inclusion of interactive ozone chemistry in atmospheric models can considerably improve the predictability of Northern Hemisphere surface climate on seasonal timescales.

Main

In the Southern Hemisphere (SH), polar stratospheric ozone has declined drastically since the late 1970s due to anthropogenic emissions of gases such as chlorofluorocarbons (CFCs) and bromine-containing halons, resulting in the yearly formation of an ozone hole over the Antarctic in austral spring¹. This decrease in ozone not only is critical for human health and ecosystems^2,3 but has been linked to large-scale climatic changes in the SH^4,5,6,7. While long-term changes in SH surface climate have been clearly attributed to radiative and dynamical impacts of Antarctic ozone depletion⁸, recent studies also show a clear connection between the state of the Antarctic ozone layer in spring and subsequent surface climate on seasonal timescales^6,9,10.

Owing to stronger planetary wave fluxes in the Northern Hemisphere (NH), which result in increased transport of ozone-rich air into the polar regions and less-favourable conditions for ozone depletion compared with the SH, the observed relative trend in Arctic stratospheric ozone is much smaller than over the Antarctic. Yet drastic springtime ozone losses with magnitudes typical for the Antarctic can also occur in the Arctic stratosphere, most recently in spring 2020^11,12. Observations and model simulations suggest that such low springtime Arctic ozone concentrations are followed by surface anomalies resembling a positive phase of the Arctic Oscillation (AO)^13,14, consistent with observations in the SH. Some analyses argue that this ozone–surface climate connection could be useful for statistical and model predictions^15,16 of NH climate.

However, it remains difficult to disentangle the potential downward influence of ozone extremes from extreme dynamical events in the stratosphere, for which a surface impact is well established^17,18,19. Surface patterns coincident with ozone depletion might be caused entirely by dynamical variability in the lower stratosphere, with ozone simply acting as a passive tracer of such dynamical variability^20,21. Conversely, some studies based on models and observations conclude that ozone extremes actively influence surface climate^13,14. Inconclusive results arise from both a lack of model studies that explicitly isolate the ozone feedbacks and the specific analysis methods used in past studies. Until now, neither has there been robust evidence for a causal link between springtime stratospheric ozone and NH surface climate nor has the impact of ozone feedbacks been quantitatively assessed. Moreover, past studies focused on monthly averaged climate variables and chose fixed reference months (March/April) to define springtime ozone extremes, ignoring interannual variations in the timing of those events.

Many operational forecast and reanalysis systems as well as climate models neglect possible impacts of stratospheric ozone on surface climate by prescribing a diagnostic ozone forcing^22,23,24, thus ignoring ozone feedbacks. Furthermore, they typically use a zonally averaged ozone climatology, whereas a longitudinally resolved ozone forcing may better represent the climatology and trends of the Arctic polar vortex and surface climate, as idealized model experiments show^25,26,27. However, the importance of the spatial structure during Arctic ozone depletion is still unclear. A three-dimensional representation of stratospheric ozone in prediction models could therefore help to improve predictability at the surface.

In this Article, we shed new light on the surface impacts of Arctic ozone depletion (1) by improving the detection of ozone depletion events and their surface signature through consideration of their relative timing and (2) by disentangling effects of ozone feedbacks, zonal ozone asymmetries and dynamical contributions in model simulations.

Ozone–surface climate connection in observations

We revisit springtime ozone depletion and associated surface patterns from 1980 to 2020 in the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA2) reanalysis dataset²⁸. We define springtime ozone minima on the basis of partial stratospheric ozone column (30–70 hPa) over the polar cap (60–90° N) and identify and rank for each year the minima in daily ozone values within March and April, and the day exhibiting the lowest ozone value is termed as ‘ozone minimum date’. In the following, we use the terms ‘ozone minima’ and ‘ozone depletion’ interchangeably (Supplementary Information section 5). For further analysis, the ten years—25% of the 41-year-long period—with the lowest springtime ozone values are considered. This detection method allows for a better alignment of stratospheric ozone depletion and associated surface effects compared with previous studies^13,14.

In the 30 days following the ozone minimum date, we find predominantly a positive phase of the AO (Fig. 2, mean AO index of 0.52) with negative sea-level pressure (SLP) anomalies in the polar region and positive SLP anomalies in mid-latitudes, especially over northwestern Europe (Fig. 1a). This pattern is consistent with previous studies¹³. The positive AO is associated with regional temperature anomalies: warming over Siberia and large parts of Eurasia (up to 2 K) as well as over western Europe (up to 1 K) and cooling over southeastern Europe (Fig. 1b). Furthermore, we find reduced precipitation over large parts of Europe and central Asia and increased precipitation over the Arctic (Fig. 1c).

Fig. 1: Surface climate following springtime Arctic ozone depletion.

a–l, Composites of SLP (a,d,g,j), surface temperature (b,e,h,k) and precipitation (c,f,i,l) anomalies in observations (MERRA2; N = 10) (a–c), WACCM INT-O3 (N = 50) (d–f), CLIM-3D (N = 50) (g–i) and CLIM-2D (N = 50) (j–l) after ozone minima in the 25% of winters with most extreme ozone loss (average over the 30 days after the ozone minimum date). Stippling shows significance on a 4.6% level (2σ) following a bootstrapping test. The following springs are included in the observations (a–c): 2020, 2011, 2005, 2002, 2000, 1997, 1996, 1995, 1993, 1990.

Although MERRA2 shows a strong connection between stratospheric ozone depletion and a positive AO at the surface, the spread in the mean AO index averaged over the month after the ozone minimum date between individual events is large, and for two out of the ten events the AO is negative (Fig. 2). This spread is similar to the uncertainty in the tropospheric response after sudden stratospheric warmings^29,30. Nevertheless, there is a clear shift towards a predominantly positive phase of the AO in the aftermath of stratospheric ozone depletion. Our new detection method used here not only confirms the robust statistical connection between springtime stratospheric ozone values and surface climate reported previously, but also reveals an even larger surface signal following strong stratospheric ozone depletion than reported by past studies^13,14 (Supplementary Fig. 9).

Fig. 2: The AO index following winters with extreme ozone loss.

The box plot shows the distribution of the mean AO index (20–90° N) at 1,000 hPa in the 30 days following the ozone minimum for MERRA2 (red) and WACCM (grey) INT-O3, CLIM-O3 and CLIM-2D. Triangles and numbers indicate the mean AO index in the 30 days after the ozone minimum date averaged over the 25% most extreme winters. The upper and lower edges of the boxes show the upper and lower quartile; the whiskers represent the maximum and minimum values of the respective distribution. For MERRA2, individual data points for each ozone minimum are shown. For a discussion of the robustness of the AO response, refer to section 2 of the Supplementary Information.

Isolating the influence of ozone on surface climate

To establish the causality of the ozone–surface coupling, we perform targeted model experiments designed to isolate the ozone impact on stratospheric dynamics and surface climate, known as ozone feedbacks. We use two chemistry–climate models, Whole Atmosphere Community Climate Model version 4 (WACCM4)³¹ and Solar Climate Ozone Links- (SOCOL-) MPIOM³². These models have different dynamical cores and chemistry modules, offering independent responses. With both models, we perform three simulations employing present-day boundary conditions: one with fully interactive ozone chemistry (INT-3D), one with prescribed daily three-dimensional climatological ozone (CLIM-3D) and one with a prescribed zonally averaged ozone climatology (CLIM-2D) from the same underlying model to avoid introducing any systematic biases. Unlike other studies using a similar set-up^27,33, experiments with prescribed ozone climatologies (CLIM-3D and CLIM-2D) still employ the chemistry scheme. However, in these experiments, the calculated ozone field is radiatively inactive; instead, the respective ozone climatology is used by the radiation module. Thus, the calculated ozone acts purely as a passive tracer in CLIM-3D and CLIM-2D, and ozone feedbacks on the atmospheric circulation are disabled (Fig. 3a).

Fig. 3: Simulation set-up and ozone feedback mechanism.

a, Set-up of INT-3D, CLIM-3D and CLIM-2D. INT-3D treats ozone chemistry fully interactively; that is, the calculated ozone field has a direct feedback on the atmosphere via the model radiation schemes. By contrast, the CLIM experiments do not use interactively calculated ozone in the radiation module. Instead, the radiation module uses an ozone climatology, which has been derived from INT-3D runs with interactive ozone of the same model. b, Ozone feedback mechanism in the aftermath of strong springtime Arctic ozone loss. Shown are impacts of ozone depletion on short-wave heating, temperature (T) and wind speed (U) in the lower stratosphere and subsequent impacts on surface AO and upper stratospheric temperature.

Simulations with WACCM CLIM-2D show significant negative SLP anomalies over the polar cap, positive temperature anomalies over large parts of Eurasia and increased precipitation close to the pole following the 25% strongest springtime ozone minima (Fig. 1j-l). Surface anomalies in CLIM-2D following Arctic ozone depletion are thus comparable to observations in their sign and pattern for large parts of the NH, but are substantially weaker (compare with Fig. 1a–c). Simulations employing CLIM-3D show slightly improved results compared with the observations, especially over Europe. The CLIM-3D experiment captures the observed high SLP and temperature anomalies as well as dry anomalies over northwestern Europe; this pattern is absent in CLIM-2D (Fig. 1g–l). However, neither CLIM-2D nor CLIM-3D captures the full magnitude of the surface signal (they capture only up to 40% of the AO signal in WACCM). Since ozone anomalies do not exert any radiative–dynamical feedback in the CLIM setting, springtime surface anomalies in these runs are due solely to dynamical variability and are linked to an exceptionally strong polar vortex and a cold stratosphere. This suggests that the magnitude of surface patterns found in the observations cannot be explained by dynamical variability alone.

Simulations with INT-3D, which additionally include ozone feedbacks, show significantly enhanced surface anomalies compared with CLIM-2D and CLIM-3D in the 30 days after springtime Arctic ozone depletion. More specifically, negative SLP anomalies over the pole are up to 4 hPa larger (Fig. 1d), temperature anomalies in Eurasia are enhanced by more than 1 K (Fig. 1e) and precipitation anomalies over the Arctic are increased (Fig. 1f). Most notably, the distribution of the AO index and its mean (0.50) in the month after the ozone minimum date in INT-3D is comparable to the AO index in reanalysis with a mean of 0.52, while the mean is smaller in CLIM-3D (0.21) and close to zero in CLIM-2D (0.01) (Fig. 2). Since differences in surface anomalies between INT-3D and CLIM show the direct impact of ozone feedbacks, we conclude that stratospheric ozone actively forces NH surface climate in the aftermath of springtime ozone depletion.

Model experiments with SOCOL-MPIOM corroborate these results, albeit with a slightly smaller ozone impact. In SOCOL-MPIOM, anomalies in surface temperature are weaker in CLIM-2D compared with INT-3D, while in simulations with CLIM-3D, the anomalies are well captured for some parts of the Northern Hemisphere, especially over Europe and Siberia (Extended Data Fig. 1). However, zonal asymmetries both in the ozone distribution and in the polar vortex are overestimated by this model (Supplementary Figs. 3–5), which might lead to an overestimation of the surface impact of ozone asymmetries (CLIM-3D versus CLIM-2D). The impact of zonal asymmetries of a climatological ozone forcing is thus model dependent (Supplementary Information). In addition, the magnitude of the AO response is to some extent model dependent. Whereas there is a strong (60%) and significant enhancement of the AO induced by ozone anomalies in WACCM, the signal in SOCOL-MPIOM is smaller (30%) and less significant (Supplementary Fig. 2). However, the AO index in SOCOL-MPIOM is less congruent with the SLP anomalies around the ozone minima than in WACCM (Extended Data Fig. 2 and Supplementary Fig. 1). Hence, the AO index does not reflect the full extent of the ozone-induced surface patterns in SOCOL-MPIOM. Despite these caveats, the contribution of ozone depletion to regional surface anomalies is consistent across models; in both models, ozone feedbacks substantially contribute to certain features of the surface signal, such as the low pressure anomaly over the North Pole and the high-pressure anomaly and decreased precipitation over Northern Europe (Extended Data Figs. 5 and 6). The robustness of these results in both models emphasizes the importance of interactive ozone chemistry to capture the full magnitude of the surface signal following Arctic ozone depletion.

Ozone feedback mechanism

Comparison of stratospheric conditions in CLIM and INT-3D experiments around the ozone minima provides insights into the mechanism through which ozone affects surface climate. Impacts of ozone asymmetries on the polar vortex shape are discussed in Supplementary Figs. 3–5. Ozone depletion is closely tied to a strong stratospheric vortex with a cold lower stratosphere³⁴. This strong polar vortex is generally accompanied by positive temperature anomalies in the upper stratosphere^35,36 due to increased wave guiding towards and increased dissipation within the upper stratosphere. These upper-stratosphere temperature anomalies descend to the lower stratosphere once sunlight returns to the polar cap in spring and the vortex starts to dissipate; this is reproduced by all model experiments (see Fig. 5a for WACCM (contour lines) and Extended Data Fig. 4c,d for SOCOL-MPIOM). In the lower stratosphere, a stronger polar vortex is associated with reduced transport of ozone-rich air into the polar regions³³, which contributes dynamically to the reduced Arctic ozone abundance.

Ozone depletion by anthropogenic halogens initiated by these background conditions exerts an additional forcing on stratospheric temperature and dynamics: due to the loss of ozone, there is less solar absorption in the stratosphere between 50 and 100 hPa in model simulations that include ozone feedbacks (Fig. 5c), leading to larger and more persistent cold anomalies in the lower stratosphere (Fig. 5a). As a result, the depletion event prolongs the lifetime of the polar vortex. In model experiments including ozone feedbacks, the spring polar vortex break-up (‘final stratospheric warming’) is significantly delayed compared with experiments with climatological ozone (by up to ten days; Supplementary Table 1). Hence, Arctic ozone anomalies actively extend stratospheric winter conditions, which is expressed by a more persistent positive Northern Annular Mode (NAM) index in the lower stratosphere in INT-3D compared with CLIM (Fig. 4). Prolonged stratospheric anomalies are expected to induce anomalous states in the troposphere and a shift in the surface AO²⁹, which is evident in WACCM (Fig. 2). In SOCOL-MPIOM, the lower stratospheric anomalies (NAM at 100 hPa) are sustained, and coupling to the troposphere is enhanced (Extended Data Figs. 3 and 4), although less than in WACCM. Since the lifetime of stratospheric anomalies is critically related to the magnitude of their surface response³⁷, the less persistent polar vortex in SOCOL-MPIOM might reduce the AO response in this model compared with WACCM.

Fig. 4: Influence of ozone depletion on stratosphere–troposphere coupling.

a–c, Composites of NAM indices (20–90° N) around the ozone minima in WACCM INT-3D (a), CLIM-3D (b) and CLIM-2D (c). Day zero indicates the date with the largest extent of the ozone minima (ozone minimum date’). Stippling shows significance on a 4.6% (2σ) level following a bootstrapping test (Methods).

Moreover, positive temperature anomalies in the upper and middle stratosphere are stronger in simulations including ozone feedbacks (Fig. 5a, days 30–60). This is due to an increase in planetary wave dissipation following the strengthening of the polar vortex through ozone feedbacks, similar to what has been reported previously for spring conditions with an already weakened polar vortex^27,38,39. An increase in planetary wave breaking in the upper stratosphere leads to a strengthening of the Brewer–Dobson circulation, which implies increased downwelling over the pole, resulting in adiabatic heating³⁸ (Fig. 5d, days 30–60).

Fig. 5: Impact of ozone feedbacks on short-wave and dynamical heating.

a–d, Differences of polar cap (60–90° N) temperature (a), ozone (b), short-wave heating (c) and dynamical heating (d) anomalies between INT-3D and CLIM-3D around the ozone minima in WACCM. Day zero indicates the date with the largest extent of the ozone minima (‘ozone minimum date’). Contour lines in the temperature plot show temperature anomalies in CLIM-2D around the ozone minima with a contour interval of 1.5 K. Stippling shows significance on a 4.6% (2σ) level following a bootstrapping test.

A schematic illustration of the ozone feedback mechanism is shown in Fig. 3b. The ozone feedback mechanism presented here is a description of the downward impact of springtime ozone depletion in the NH in a mechanistic way and is consistent with our understanding of the dynamical impacts of the ozone hole in the SH. Although ozone depletion is much less frequent in the Arctic than in the Antarctic, we conclude that the large contribution of ozone depletion to springtime surface climate as well as the mechanism by which ozone affects the stratospheric circulation is analogous in both hemispheres.

Implications for predictability

Dynamical variability in the stratosphere has previously been shown to provide skill for subseasonal to seasonal prediction for the Northern Hemisphere, both for winter (for example, refs. ^40,41,42) and for spring⁴³. Such stratospheric predictability bears a broad societal relevance, for example, in the context of wind electricity generation⁴⁴ and human health⁴⁵. Forecast systems with an enhanced stratospheric resolution have been shown to provide improved skill for tropospheric predictions⁴⁶. Forecast errors for the North Atlantic region can be traced back to the initial state of the polar stratospheric vortex and uncertainties in stratosphere–troposphere coupling in a subseasonal prediction system⁴⁷. One potential reason for such errors is that most state-of-the-art prediction systems lack interactive stratospheric ozone chemistry⁴⁸. Indeed, stratospheric ozone information could further enhance subseasonal to seasonal predictions, and experiments with a simplified ozone scheme that mimics interactions between dynamics and chemistry show promising results¹⁶.

The results presented here contribute to this discussion in two ways. First, they shed new light on the nature of the ozone–surface climate connection in the NH—a relationship controversially discussed. Our modelling experiments show in a robust manner that the substantial fraction of the springtime NH surface pattern in the aftermath of strong stratospheric ozone depletion cannot be explained by dynamical variability alone. Rather, ozone feedbacks represent an important contribution to the surface response. We therefore conclude that interactive ozone chemistry is essential for weather and climate models to realistically reproduce NH spring conditions. Where interactive ozone chemistry is not feasible, our results suggest that a spatially resolved ozone forcing can lead to improvements compared with the method still widely used in weather and climate prediction, namely, a zonally averaged ozone representation^22,23,24. However, impacts of ozone asymmetries are model dependent, and stratosphere–troposphere coupling is highly underestimated when interactive ozone chemistry is absent (Fig. 4 and Extended Data Fig. 3). A second contribution is that these new findings create new incentives to explore the value of stratospheric ozone for subseasonal to seasonal prediction. Our results should thus serve as a motivation to explore ways to include a more realistic representation of stratospheric ozone in forecast models and to further investigate the prediction skill arising from stratospheric ozone depletion in current and future climate for both hemispheres. Despite the projected Arctic ozone recovery, large dynamical variability will ensue in the future, leading to large episodic springtime depletion⁴⁹. Hence, Arctic ozone will continue playing an important role in future climate variability.

Methods

Models

We investigate ozone feedbacks in two chemistry–climate models, WACCM version 4 and SOCOL-MPIOM. WACCM is the atmospheric component of the National Center for Atmospheric Research Community Earth System Model version 1. It is a fully interactive high-top chemistry–climate model³¹ coupled to an active ocean⁵⁰ and sea-ice components⁵¹. Extending to the lower thermosphere (5.1 × 10⁻⁶ hPa) in altitude with 66 vertical levels and a well-resolved stratosphere³¹, WACCM has been documented to capture stratospheric trends and variability reasonably well and has been used in many recent studies analysing interannual stratospheric variability (for example, refs. ^9,27,33,52). WACCM has a horizontal resolution of 1.9° latitude and 2.5° longitude³¹ while the ocean has a nominal latitude–longitude resolution of 1°. Being coupled to an interactive chemistry scheme⁵³, WACCM calculates ozone concentrations over a set of chemical equations between a total of 59 species³¹ and therefore actively simulates feedbacks between ozone and dynamics. In addition, WACCM can be run in a ‘specified chemistry’ mode, where ozone concentrations and other radiative species are prescribed in the form of zonal mean or three-dimensional monthly or daily mean climatologies⁵⁴.

SOCOL version 3 is a chemistry–climate model based on the general circulation model MA-ECHAM5 and the chemistry-transport Model for Evaluation of Ozone Trends⁵⁵, which are interactively coupled via three-dimensional temperature and wind fields and through radiative forcing induced by several greenhouse gases (GHGs: water vapour, ozone, methane, nitrous oxide and CFCs)⁵⁶. The Model for Evaluation of Ozone Trends includes a set of 140 gas-phase, 46 photolysis and 16 heterogeneous reactions between 41 species. SOCOL in its default configuration therefore incorporates feedbacks between ozone and dynamics. Like WACCM, SOCOL can be run in a specified-chemistry mode through decoupling of chemistry and general circulation model, in which case ozone concentrations are prescribed as zonal mean, monthly mean climatologies or three-dimensional, daily mean climatologies³². The model version SOCOL-MPIOM used in this study is additionally coupled to the ocean-sea-ice model MPIOM³². SOCOL-MPIOM has a model top of 0.01 hPa with a well-resolved stratosphere and 39 vertical levels and a horizontal resolution of T31 (3.75° × 3.75°) (ref. ⁵⁶). Despite exhibiting a cold pole bias in the stratosphere during winter⁵⁶, SOCOL has been documented to capture the annual ozone cycle and ozone trends⁵⁶ as well as stratospheric variability³² reasonably well.

Boundary conditions

Since both WACCM and SOCOL-MPIOM are models with fully coupled radiation, chemistry and dynamics, both models incorporate ozone–circulation feedbacks. For the study at hand, we run both models under invariant year-2000 boundary conditions with fixed, seasonally varying atmospheric GHG concentrations including ozone-depleting substances (ODSs) and a nudged quasi-biennial oscillation (QBO). Therefore, the model simulations show only very small trends (Supplementary Fig. 6 and Supplementary Discussion). For SOCOL, GHG concentrations and ozone ODSs have been prescribed following the approach in ref. ⁵⁶, and the QBO has been nudged according to ref. ⁵⁷. In WACCM, a perpetual 28-month QBO cycle was forced on the basis of the set-up described in ref. ³¹. Boundary conditions were prescribed following the Coupled Model Intercomparison Project phase 5 (CMIP5) forcing datasets⁵⁸. With concentrations of ODSs being set to year-2000 levels, this set-up yields a high polar stratospheric ozone variability in spring and thus maximized ozone feedbacks. It also removes the effects of climate change, thereby aiding the statistical analysis.

Experiment design

To assess the impact of ozone feedbacks, we contrast runs with fully interactive and specified ozone chemistry in both models. Within the fully interactive ozone runs (INT-3D), the free-running models interactively calculate ozone concentrations, therefore allowing the simulation of ozone feedbacks into the general circulation. Averaging over all 200 simulated years of INT-3D SOCOL and INT-3D WACCM, ozone climatologies are derived and used as prescribed forcings in simulations without interactive ozone (CLIM-2D and CLIM-3D). We perform two different simulations with specified ozone chemistry, one using a zonal mean, monthly mean ozone climatology derived from INT-3D (CLIM-2D) and another one using a three-dimensional, daily mean ozone climatology from INT-3D (CLIM-3D).

For both runs with specified ozone chemistry (CLIM-3D and CLIM-2D), we use a hybrid model set-up: while interactive ozone is still being calculated and saved as output, it is decoupled from the models’ radiation schemes and replaced by ozone climatology from INT-3D. In this set-up without interannually varying radiative ozone forcing, ozone feedbacks are not simulated; ozone thus acts as a passive tracer of dynamical variability in the stratosphere. The advantage of this set-up compared with a more standard approach without any chemistry scheme is the better comparability between INT and CLIM experiments, as the oxidation of other radiatively active gases, such as CH₄, N₂O and CFCs, by ozone via O(¹D), is still considered in the CLIM setting. Comparisons of CLIM experiments with runs with interactive ozone chemistry therefore allow us to draw robust conclusions about the role of ozone feedbacks in the climate system. In addition, the hybrid approach allows us in to apply the same definition for detecting the 25% most extreme ozone minima as for reanalysis (50 events out of 200 simulated years) in all CLIM and INT experiments. A similar set-up has already been used in the context of SH ozone depletion⁵⁹. To account for the high interannual stratospheric variability within the system, we simulate a total of 200 model years for each of the four runs. The model set-up is illustrated in Fig. 3a.

Sampling of ozone minima

Springtime ozone minima are defined on the basis of daily zonally averaged ozone mixing ratios. To exclude outliers from being counted as ozone minimum, a five-day running mean of ozone mixing ratios is derived from the daily data. To detect the impact of ozone feedbacks, it is desirable to select the springtime ozone minima on the basis of the altitude exhibiting the largest interannual ozone variability. Since the year-to-year ozone variance maximizes at different altitudes in WACCM, SOCOL-MPIOM and MERRA2 (Supplementary Fig. 7), we select years with springtime ozone minima on the basis of partial ozone column from 30 to 70 hPa rather than on the basis of a specific altitude to standardize treatment of different datasets. The partial ozone column was calculated on the basis of the five-day running mean daily ozone mixing ratios in Dobson units (DU) according to

$${{\mathrm{O}}}_{3,{{{\rm{pcol}}}}}=\frac{1{{{\rm{DU}}}}}{2.687\times 1{0}^{16}{{{{\rm{molecules}}}}}\,{{{{{\rm{cm}}}}}^{2}}}\mathop{\sum }\nolimits_{p = 30{{{\rm{hPa}}}}}^{70{{{\rm{hPa}}}}}\frac{{\chi }_{{{\mathrm{O}}}_{3}}(p)\times 10\times {{\Delta }}p}{g\times {m}_{{{{\rm{air,d}}}}}}$$

(1)

where ${\chi }_{{{\mathrm{O}}}_{3}}(p)$ denotes the ozone mixing ratio at pressure level p, Δp describes the distance to the next pressure level in Pa, g is the gravitational constant (cm s^–2) and m_air,d is the mass of dry air (g molecule^–1). For each year within a dataset, the minimum polar cap mean (60–90°N) partial ozone column value within March and April is selected. For each dataset, the 25% of years with the lowest minimum partial ozone column in March and April are considered ‘low-ozone years’ (10 events in MERRA2 and 50 events for each model simulation). The day at which the minimum ozone value occurs is considered the ozone minimum date. If not stated otherwise, the data is weighted with the cosine of latitude for latitudinal averaging.

Calculation of anomalies

To calculate anomalies of a variable, a climatology for the respective variable is derived for each day of the year by averaging each calendar day over all years available in the dataset. This daily climatology is subtracted from the daily variable values to obtain daily anomalies. For MERRA2, a daily climatology is derived by averaging over the years 1980–2019. Since the spring in 2020 exhibited particular strong anomalies in both stratospheric and surface climate and the MERRA2 record is comparably short, the year 2020 is excluded in the calculation of the daily climatology¹¹.

Bootstrapping significance test

A one-sample bootstrapping significance test is performed to estimate the significance of mean anomalies composited around the ozone minimum (for example, refs. ^27,33). For a composite including the 25% most extreme springtime ozone minima, 500 random composites are created by sampling data around the respective ozone minimum dates in random years to create a normal distribution of random composites. The actual composite is considered significantly different from zero if it differs more than two standard deviations from the mean of the randomly created distribution, which is equivalent to a significance at the 95.4% level. The procedure for a two-sample bootstrapping significance test is conducted accordingly: to compare two composites, random composites are created as described in the preceding in both datasets and the difference of both random composites is calculated. Repeating this procedure 500 times, we create a distribution of 500 random samples. The difference between the samples is considered significant if it differs more than two standard deviations from the mean value of the random distribution.

Calculation of AO and NAM indices

While the AO and NAM in general describe the same phenomenon of simultaneous fluctuations in geopotential height of opposite sign over the polar cap and lower latitudes²⁹, we refer to the NAM as the pattern on all vertical levels, whereas the AO is used to describe the near-surface profile at 1,000 hPa (ref. ²⁹). Empirical orthogonal functions (EOFs) are used to calculate the AO and NAM indices following method 3 in ref. ⁶⁰. For each pressure level, we calculate the leading EOF spatial pattern of year-round daily zonal mean geopotential height anomalies north of 20° N while applying latitudinal weights as the square root of the cosine of latitude (ref. ²⁹). Daily geopotential height anomalies are then projected onto the EOF loading pattern to find the principal component (PC) time series. Principal components are normalized to unit variance to derive the respective AO and NAM indices.

Calculation of dynamical heating rate

We calculate the vertical (${\bar{w}}^{* }$) and meridional (${\bar{v}}^{* }$) component of the residual circulation according to the transformed Eulerian mean framework described by equations 3.5.1 and 3.5.2 in ref. ⁶¹. To examine changes in temperature induced by ozone-related changes in the Brewer–Dobson Circulation, we calculate the adiabatic dynamical heating in the Arctic stratosphere on the basis of the quasi-geostrophic theory according to

$$\frac{\updelta \bar{T}}{\updelta t}=S\times {\bar{w}}^{* }$$

(2)

where $\bar{T}$ is the zonal mean temperature and S is the atmospheric stability parameter⁶², which can be calculated according to ref. ⁶³ as follows:

$$S=\frac{H\times {N}^{2}}{{R}^{* }}.$$

(3)

Here, N² denotes the Brunt–Väisälä frequency, H the atmospheric scale height and ${{R}^{* }}$ the specific gas constant for mixed gases.

Calculation of final warming date

Final warmings are defined as the first date when the zonal mean wind at 60° N and 10 hPa turns easterly and does not return to westerlies for more than ten consecutive days until the next winter⁶⁴. Uncertainty in the final warming date is estimated on the basis of the standard deviation.