2.1 Chemistry–climate modelling

WACCM (the Whole Atmosphere Community Climate Model) is the atmospheric component of the NCAR Community Earth System Model version 1 (CESM1.2.2). WACCM has a horizontal resolution of 1.9^∘ in latitude and 2.5^∘ in longitude (Marsh et al., 2013) and is coupled to interactive ocean and sea ice components (Danabasoglu et al., 2012; Holland et al., 2012). Ozone concentrations are calculated interactively, including a total of 59 species  (Marsh et al., 2013). With its well-resolved stratosphere and high model top ($\mathrm{5.1}\times {\mathrm{10}}^{-\mathrm{6}}$ hPa) on 66 vertical levels (Marsh et al., 2013), WACCM has been documented to capture stratospheric trends and variability reasonably well (Haase and Matthes, 2019; Rieder et al., 2019; Oehrlein et al., 2020).

SOCOL (SOlar Climate Ozone Links) version 3 is based on the middle atmosphere configuration of the general circulation model ECHAM5 (MA-ECHAM5), which is interactively coupled to the chemistry transport model MEZON (Model for Evaluation of oZONe trends Egorova et al., 2003). The model version SOCOL-MPIOM is additionally coupled to the ocean–sea-ice model MPIOM (Stenke et al., 2013; Muthers et al., 2014). SOCOL-MPIOM has a model top at 0.01 hPa, 39 vertical levels, and a horizontal resolution of 3.75^∘ × 3.75^∘ (Stenke et al., 2013). Ozone is calculated interactively based on a set of 140 gas-phase reactions, 46 photolysis reactions, and 16 heterogeneous reactions involving 41 species. Like WACCM, SOCOL-MPIOM captures stratospheric variability reasonably well (Muthers et al., 2014).

To gain an understanding of the dependency of stratospheric ozone trends and variability in the Arctic on the GHG loading, we compare simulations of high- and low-emission scenarios throughout the 21st century (2005–2099). For the high-emission scenario, GHGs follow the RCP8.5 pathway, whereas the low-emission scenario is based on the RCP2.6 pathway (Meinshausen et al., 2011); hODSs follow the A1 scenario according to WMO (2014). In addition to the transient simulations, we perform time slice simulations of the early (year 2000) and late (year 2075) 21st century with the fixed, seasonally varying GHGs and hODSs of the respective year. For simulations of the year 2075, boundary conditions follow the RCP8.5 pathway. In these time slice simulations, each covering 200 years, trends in stratospheric ozone and climate are omitted, allowing us to robustly assess long-term changes in the variability due to changes in GHG and hODS levels.

2.2 CCMI simulations

We compare our model results with sensitivity simulations of high-emission (SEN-C2-RCP85) and low-emission (SEN-C2-RCP26) scenarios conducted for phase 1 of CCMI (CCMI-1). GHG emissions of those simulations follow the RCP8.5 and RCP2.6 pathways (Meinshausen et al., 2011), respectively, with hODSs following the A1 scenario (WMO, 2011) . The high- and low-emission pathways therefore only differ in their assumptions regarding future GHG emissions, while hODSs are equal for both scenarios. Model simulations usually cover the period 2000–2100. We analyse all models that performed the SEN-C2-RCP85 simulation, namely SOCOL CCMI, WACCM CCMI, CCSRNIES-MIROC3.2, CMAM, EMAC-L47MA, IPSL, ULAQ-CCM, and UMSLIMCAT, with a subset of them also performing the SEN-C2-RCP26 simulation. The models participating in CCMI-1 exhibit substantial differences in the implementation of stratospheric (heterogeneous) chemistry and PSC schemes. For example, the amount of halogen source gases treated in the models varies between 2 (UMSLIMCAT) and 14 (SOCOL). For PSCs, some models assume thermodynamic equilibrium, while other models account for deviations from thermodynamic equilibrium. Further, some models explicitly include supercooled ternary solutions (STSs), and implementations differ in terms of PSC sedimentation across models. A detailed description of the CCMI-1 models is presented by Morgenstern et al. (2017).

To investigate the robustness of the evolution of ozone minima in CCMI models, we perform out-of-sample testing with CCMI-2022 simulations (SPARC, 2021). The moderate-emission scenario of CCMI-2022 simulations (REF-D2) follows the SSP2–4.5 pathway (Meinshausen et al., 2020), and hODSs follow the WMO (2018) baseline scenario. We analyse all models that performed the REF-D2 scenario, namely CNRM-MOCAGE, NIWA-UKCA2, CCSRNIES-MIROC3.2, CMAM, and EMAC-CCMI2. Model simulations were generally conducted for the time period 1960–2100. Here, we analyse the period 2000–2100. In addition to the CCMI-2022 simulations, we perform simulations with SOCOLv4 (Sukhodolov et al., 2021) following the CCMI-2022 REF-D2 boundary conditions. SOCOLv4 is an updated version of SOCOL-MPIOM based on the Earth system model MPI-ESM1.2 (Mauritsen et al., 2019), and it is additionally coupled to the sulfate aerosol microphysical model AER (Weisenstein et al., 1997). An overview of all model simulations and available ensemble members that were analysed in this study can be found in Table 1. For all models, we use the model output for Arctic mean ozone; temperature; and, where available, active chlorine species (ClO_x = ClO + Cl + 2 Cl₂O₂) interpolated to pressure levels.

Table 1Model experiments analysed in this study.

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2.3 Reanalysis

Model results for the early 21st century are compared to the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA2) for the period 1980–2020 (Gelaro et al., 2017). MERRA2 has a horizontal resolution of 0.5^∘ × 0.625^∘ and 72 vertical levels with a model top at 0.01 hPa, and we use 6-hourly instantaneous data output, which is then converted into monthly and springtime averages. MERRA2 has been shown to agree well with satellite and ozone sonde data regarding stratospheric ozone variability (Wargan et al., 2017; Davis et al., 2017; Bahramvash Shams et al., 2022). Further, we compare MERRA2 to the Stratospheric Water and Ozone Satellite Homogenized (SWOOSH) database for the period 2004–2020 using a horizontal resolution of 2.5^∘ (Davis et al., 2016).

2.4 Analysis methods

Our analysis focuses on boreal spring, which we define as March–April averages, where ozone anomalies are maximized in the models. Unless stated otherwise, the results below show averages over the polar cap, defined as 60–90^∘ N, applying latitudinal weighting according to the cosine of latitude. Lower-stratospheric ozone is defined as a partial ozone column between 30 and 70 hPa in DU (Friedel et al., 2022a). The ozone distributions shown contain all ensemble members of a simulation (without averaging). The mean magnitude of the ozone minima is defined as the lowest 20th percentile of springtime ozone anomalies for both time slice and transient (scenario) simulations. For time slice simulations, we thus average over the 40 lowest springtime ozone anomalies to derive the mean ozone minima strength. For transient simulations, we calculate the mean magnitude of ozone minima in a 25-year running window. For each window, the anomaly in each spring is calculated relative to the springtime climatology of that window, and the mean ozone minima are then calculated by averaging over the lowest 20th percentile of ozone anomalies (i.e. the 5 lowest springtime ozone values out of 25 springs). Uncertainty in the magnitude of the ozone minima is defined as the sensitivity to the inclusion of one more (6 out of 25) and one less (4 out of 25) spring into the calculation. For ensemble simulations with multiple members, this analysis is conducted for each ensemble member individually before averaging. Similarly, the temperature of particularly cold winters is defined as the lowest 20th percentile of springtime temperature at 50 hPa in a 25-year running window, and the uncertainty of this variable is calculated by including one more or one less spring in the calculation. For climatologies, uncertainties are given as standard deviations from the mean. For simulations containing multiple ensemble members, climatologies are calculated as ensemble means, and uncertainties are given as the root mean square of the individual members' uncertainties. Trends are generally estimated by linear least-squares regressions of the respective ensemble mean, and the uncertainty in trends is given by the standard error of the slope. The significance of trends is estimated by p values calculated using a Wald test (Fahrmeir et al., 2013).

3.1 Evolution of Arctic ozone minima in CCMI models

To identify the spread in simulated Arctic ozone and the evolution thereof across CCMs, we start by analysing springtime Arctic ozone anomalies in the early (2005–2029) and late (2070–2094) 21st century. Anomalies are defined as deviations from the climatology of the respective time period. Figure 1 shows distributions of Arctic lower-stratospheric ozone anomalies for the high-emissions scenario (RCP8.5) simulated with WACCM, SOCOL-MPIOM, and CCMI-1 models. In the following, we will concentrate on negative ozone anomalies. For the early time period (Fig. 1a), differences in the magnitude of ozone anomalies across models are striking; while some models simulate negative ozone anomalies larger than −40 DU for the springtime mean lower-stratospheric ozone column, other models barely show anomalies exceeding −5 DU. In the reanalysis product MERRA2, which covers recent-past to present-day climate (1980–2020), negative ozone anomalies reach up to −40 DU. Thus, most of the CCMs (7 out of 10) do not reproduce the most extreme negative ozone anomalies under current climatic conditions compared to reanalysis. In comparison, by the end of the century, CCMs provide a more coherent picture; almost all models simulate negative ozone anomalies, with a maximum of −20 DU. Thus, according to CCM simulations, extreme ozone loss beyond −20 DU is unlikely past 2070 in the high-emission scenario. Large ozone variability and extreme ozone loss comparable to MERRA2 is not projected by any model at the end of the century.

Figure 1Probability density distributions calculated based on kernel density estimation of stratospheric partial ozone column (30–70 hPa) in spring (March–April) normalized by the mean partial column ozone of the respective time period in the early (2005–2029 – a and b) and late (2070–2094 – c and d) 21st century in CCMI-1 models for RCP8.5. Whiskers show the 20th and 80th percentiles of the distributions. The multi-model mean shows the distributions over all models (excluding MERRA2) containing each ensemble member with equal weight. Similar figures for RCP2.6 and CCMI-2022 can be found in the Appendix (Figs. A2 and A3).

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Further to changes in ozone anomalies, it is important to note that the mean ozone climatology is changing across the two time periods considered. Under the high-emission scenario, RCP8.5, Arctic stratospheric ozone is expected to increase from 136 to 153 DU in terms of the multimodel mean over the course of the 21st century (see Fig. A1) due to the combined impact of a range of processes: the decrease in hODSs, a strengthening of the Brewer–Dobson circulation (BDC) by GHGs (i.e. larger transport of ozone from the tropics to the poles) (Butchart, 2014), stratospheric cooling by GHGs in the tropical and mid-latitude regions (which slows down ozone depletion there), and increasing methane concentrations (Revell et al., 2012). This projection of an Arctic ozone recovery of 17 DU from 2000 until 2100 is consistent with what has been reported previously for the lower stratosphere in CCMI-1 models (Dhomse et al., 2018). The rise in mean ozone suggests that, even during the most severe projected negative anomalies of −20 DU by the end of the century, there will hardly be any less ozone than is the case with the current mean.

In the following, we will focus on the most extreme negative ozone anomalies, defined as the lower 20th percentile of springtime ozone anomalies and referred to as ozone minima. To examine changes in ozone minima over time, we calculate the ozone minima in a 25-year running window (i.e. average over the 5 most extreme negative ozone anomalies out of 25 springs). Ozone anomalies are thereby calculated with respect to the climatology in the corresponding window. Figure 2 shows the evolution of the ozone minima over time for all model simulations and different GHG emission pathways: RCP8.5 (Fig. 2a), RCP2.6 (Fig. 2c), and SSP2–4.5 (Fig. 2e). Again, there is a large scatter across the models in terms of the strength of the simulated ozone minima at the beginning of the century, ranging from −22.5 to −3 DU. Over time, the model spread decreases, and by the end of the century, it ranges from −10 and −3 DU. The uncertainty in the magnitude of ozone minima is therefore reduced over the course of the century. Models that simulate large ozone minima under current conditions (2005–2029) also show the largest ozone minima under future conditions (e.g. UMSLIMCAT), but the magnitude of these future minima is significantly smaller. In contrast, models with small ozone minima under present-day conditions (e.g. CMAM) show hardly any change in the magnitude of these minima under future conditions.

Figure 2Evolution of the strength of Arctic ozone minima in CCMI-1 models under RCP8.5 (a) and RCP2.6 (c), as well as for CCMI-2022 models under SSP2–4.5 (e). Correlation of the trend in ozone minima strength and the strength of the ozone minima in the first 25 years defined by the mean ozone anomaly of the 20th percentile (5 out of 25 strongest ozone minima in running window, normalized by the ozone climatology of running window) (b, d, f). The mean strength of ozone minima in MERRA2 from 1980 to 2020 is given by the solid black line. The grey shading shows the uncertainty of the MERRA2 ozone minima strength, as explained in the “Material and methods” section. The mean ozone minima strength in SWOOSH from 2004 to 2020 is shown by the stippled grey line. Circles in (a) show the ozone minima strength of the WACCM and SOCOL-MPIOM time slice simulations for the years 2000 and 2075, respectively.

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The future decline in the magnitude of ozone minima is related to the magnitude of the Arctic ozone depletion under current conditions (see negative correlations of −0.84 to −0.96 in Fig. 2b, d, f). The development of ozone minima is thereby strongly correlated with the initial strength of the ozone minima in the respective model. Consequently, models with large ozone minima at the beginning of the century generally show larger trends towards less-pronounced ozone minima in the future, whereas models with small ozone minima show no trends at all. Linear regression of the trend in ozone minima to their initial magnitude shows that this relationship is independent of the emission scenario; i.e. the regression slope is the same across all scenarios considered ($s=-\mathrm{0.1}$). The scenario independence suggests that greenhouse gases other than hODSs (such as carbon dioxide, methane, nitrous oxide, and water vapour), which differ among the scenarios, may not be critical to the development of ozone minima.

Given the strong correlation of the trend in ozone minima and their initial magnitude, the large inter-model spread can be used to constrain projections of future ozone minima by observations. To this end, we compare the simulated ozone minima in the present-day climate with ozone minima observed during the past 40 years (1980–2020) in MERRA2 (black line in Fig. 2 b, d, f) and find that the models that most realistically reproduce current ozone minima project a decrease in extreme negative ozone anomalies of about 1 DU per decade (see intersection of regression line and reanalysis). Hence, using past ozone minima in reanalyses as an emergent constraint suggests that extreme negative ozone anomalies will likely be  8–10 DU (and therefore around 50 %) less severe by the end of the 21st century. A similar result is found when using the SWOOSH database for the period 2004–2020 as an observational constraint, for which we define the ozone minima strength based on the three strongest ozone minima in that period (20th percentile – stippled grey line in Fig. 2b, d, f). It is to be noted that an emergent constraint analysis can only be a useful tool for reducing uncertainty in future projections if it (1) survives out-of-sample testing and (2) exhibits a physical mechanism underlying the strong statistical relationship (Hall et al., 2019; Simpson et al., 2021). While the former is fulfilled by the independence of the results from emission pathways and model sets, the latter will be discussed below.

A more precise method for estimating the likely evolution of ozone minima is weighted model means. Here, we calculate weights for each individual model based on their ability to reproduce the present-day ozone minima (performance) and their interdependence (i.e. the family relationship of some models) (Knutti et al., 2017; Amos et al., 2020; Morgenstern et al., 2017). The model weights are then used to calculate a weighted arithmetic mean of the trend in ozone minima. Resulting model weights and a more detailed description of the methodology can be found in the Appendix (Sect. A2). Weighted model means suggest a reduction of the magnitude of ozone minima of 1.0 (RCP8.5), 1.1 (RCP2.6), and 1.0 (SSP2–4.5) DU decade⁻¹. Thus, weighted model means are largely scenario independent and agree well with estimates of the emergent-constraint approach.

Since many models only simulated one single ensemble member for future projections (see Table 1) and because the sample used for calculating the ozone minima is small (five springs per running window width), we test the sensitivity of our results to sample size using 200-year time slice simulations performed with the CCMs WACCM and SOCOL-MPIOM. By using fixed boundary conditions for the years 2000 and 2075, we omit any trends in ozone or temperature due to changes in hODSs and GHGs. Consistently with the previous definition, we again select the 20th percentile of the most extreme negative ozone anomalies (40 out of 200) to define the magnitude of the mean ozone minima in the time slice simulations. The ozone minima in these simulations, shown as circles in Fig. 2a, agree very well with the transient simulations, suggesting that the smaller sample size in transient simulations is sufficient to derive robust results (see also Fig. A6).

3.2 The source of model differences in the current climate

We have shown that model dispersion in simulated ozone can be useful in constraining the evolution of ozone minima. However, the question arises as to why CCMs show large differences in the magnitude of ozone minima under current climatic conditions in the first place. Arctic ozone minima are caused by both chemical ozone depletion and dynamical variability (Tegtmeier et al., 2008); usually, ozone minima are preceded by reduced wave activity and, consequently, a strengthening and cooling of the polar vortex, as well as a weakening of the BDC. Dynamical resupply of ozone to the polar region is therefore reduced, and cold temperatures allow for the formation of PSCs and chlorine activation, consequently leading to ozone depletion. The amount of ozone depleted thereby depends on the amount of active chlorine species (ClO_x) in the stratosphere. In Fig. 3a, we show that the strength of ozone minima strongly correlates with the stratospheric Arctic mean ClO_x concentrations (at 50 hPa) across models in the beginning of the 21st century. Hence, the differences in the magnitude of ozone minima in different models are attributable to differences in chemical ozone destruction by ClO_x. The amount of activated chlorine in the stratosphere itself depends on the volume of the PSCs, which in turn is strongly temperature dependent. We find a large spread (around 10 K) in the mean Arctic stratospheric temperature across models in winter and spring (January–April). This model scatter is consistent with what has been reported previously by Morgenstern et al. (2022) for some CMIP6 and CCMI-2022 models. The reasons for such differences in the models' mean stratospheric springtime temperatures are likely linked to differences in the large-scale circulation, such as the BDC, or the lifetime and shape of the polar vortex. Here, we complement the analysis by Morgenstern et al. (2022) by connecting those temperature biases to ClO_x concentrations and finally the magnitude of ozone minima. When linking the mean polar cap temperature at 50 hPa to stratospheric ClO_x concentrations at the same altitude in the CCMs, we find a linear relationship, with a correlation coefficient of $R=-\mathrm{0.69}$ (see Fig. 3b). Thus, differences in ClO_x concentrations among models can largely be attributed to temperature biases. Models which show a warm temperature bias (e.g. CMAM – dark-blue markers) under present-day conditions compared to MERRA2 (vertical solid black line in Fig. 3b) generally have small ClO_x concentrations (Fig. 3a) and thus simulate only weak ozone depletion and consequently weak Arctic ozone minima. In turn, models with a cold-temperature bias (e.g. CCSRNIES-MIROC3.2 – red markers) simulate large ClO_x concentrations, strong ozone depletion, and large ozone minima. Models which best reproduce the Arctic mean temperature from MERRA2 generally also agree better with MERRA2 in terms of the magnitude of the simulated Arctic ozone minima. This behaviour compares well with previous results showing that temperature biases limit the models' ability to reproduce observed PSC coverage (Snels et al., 2019; Steiner et al., 2021).

Figure 3Relation between ClO_x concentration in late winter and spring (January–April) at 50 hPa and the strength of the ozone minima in the first 25 years (a), as well as the relation between ClO_x concentrations and mean temperature in January–April in the first 25 years of simulation (b). Colours indicate the different models as in Figs. 1 and 2. The dotted black lines show the linear regression. The Pearson correlation coefficient is denoted by R. The mean ozone minima strength and the mean temperature in MERRA2 are shown by the black lines. The shading and vertical error bars in (a) show the uncertainty of ozone minima strength, as explained in the methods section. The mean ozone minima strength in SWOOSH from 2004–2020 is shown by the stippled grey line in (a). Grey shading, as well as error bars in (b), shows the standard deviation.

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Besides temperature biases, differences in total inorganic chlorine (Cl_y) across models could partly be responsible for model differences in ClO_x. A large inter-model spread in Cl_y in CCM simulations has been reported previously by Eyring et al. (2006, 2007) and has been attributed to differences in the transport of chemical species within the stratosphere (Eyring et al., 2006). Moreover, differences in the number of chlorine source gases considered (Morgenstern et al., 2017) and in the overall treatment of photolysis in the models (Sukhodolov et al., 2016) could contribute to the biases in the ozone minima. However, for the Arctic region, the correlation between Cl_y and ClO_x concentrations is low across the models analysed here (see Fig. A7 in the Appendix).

3.3 The source of model differences in future projections

Now that we have established the reasons for differences in simulated ozone minima in the current climate across models, we investigate the reasons for the differences in future ozone minima trends. Trends in ozone loss are impacted by both the decline in hODS concentrations and the potential changes in stratospheric temperature due to GHG emissions, which might impact the formation of PSCs. In addition, dynamical changes might contribute to temperature trends, as discussed below. Besides, an increase in stratospheric water vapour might change the abundance of PSCs in the future (von der Gathen et al., 2021). In Fig. 4, we investigate both the relationship of declining ClO_x and the temperature trends with changes in ozone minima. Trends in ozone minima are strongly correlated with changes in ClO_x concentrations; models with large ClO_x concentrations under the current climate (e.g. CCSRNIES-MIROC3.2 – red markers) show a large decline in ClO_x over the next century and therefore a large decline in ozone loss. Models that have low ClO_x concentrations to start with (e.g. CMAM – dark-blue markers) show almost no changes in active chlorine species in the future and thus barely any changes in ozone loss. The development of ozone minima in individual CCMs is therefore strongly driven by changes in stratospheric ClO_x concentrations.

Figure 4Dependence of the trend in ozone minima on the trend in ClO_x concentrations (a) and on the 50 hPa temperature trend in cold springs (b). Colours indicate the different models as in Figs. 1 and 2. A positive trend in ozone minima strength means a decrease in the magnitude of ozone minima in the future. Negative temperature trends mean that cold winters and springs are getting colder, and positive temperature trends mean that cold winters and springs will be less extreme in the future. Dotted black lines show the linear regression. The Pearson correlation coefficient is denoted by R. Box plots show changes in the mean ozone minima strength (c), ClO_x changes (d), and temperature changes in cold springs (e) across models and scenarios. Triangles mark the median change, and black lines mark the mean change across models. The circle in (c) shows the weighted arithmetic model mean. Note that not all models used to calculate the weighted mean are shown in (a) and (b) due to lack of ClO_x data in some models.

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Next, we investigate the relation between long-term changes in Arctic stratospheric temperature and ozone minima. For ozone minima, the temperature evolution of the coldest winters and springs is most relevant as large amounts of PSCs and severe ozone loss are expected only under sufficiently cold conditions (< 196 K). Further, it has previously been shown that GHG cooling especially impacts the PSC formation in extremely cold Arctic winters (Rex et al., 2004; Tilmes et al., 2006; von der Gathen et al., 2021). We therefore focus on the temperature evolution of the coldest 20 % of the winter and spring seasons (January–April mean) in a 25-year running window, similarly to Morgenstern et al. (2022). Overall, CCMs do not agree on the sign of stratospheric temperature trends in late winter and spring in especially cold years (Fig. 4b). In addition, models also do not agree on the temperature response to additional GHG forcing (see temperature trends for RCP2.6 vs. RCP8.5 in the individual models). On average, models show a slightly positive temperature trend (consistent with the weak but significant Arctic warming projected in boreal spring reported in the WMO (2018) assessment; see their Figs. 5–8), but the spread ranges from −0.6 to +0.5 K decade⁻¹ (Fig. 4e). This inter-model spread is consistent with what has been reported previously for CCMVal2 models (Bohlinger et al., 2014). Overall, the correlation between stratospheric temperature trends and changes in ozone minima is moderate (0.59) and is mainly caused by the two most extreme negative (ULAQ-CCM) and positive (CCSRNIES-MIROC3.2) values. For the bulk of the models that show no or only minor temperature changes (within −0.2 and 0.2 K decade⁻¹), the temperature trends do not seem to be connected with trends in ozone minima (Fig. 4b). Thus, for this majority of models, different trends in ClO_x concentrations drive different trends in ozone minima, and temperature changes only play a secondary role. However, for models with large temperature trends, like ULAQ-CCM (−0.6 K decade⁻¹) and CCSRNIES-MIROC3.2 (+0.5 K decade⁻¹), changes in temperature seem to be reflected in ozone minima trends. For example, in the extreme example of ULAQ-CCM, cold winter and spring seasons become extensively colder in the future (see round turquoise marker in Fig. 3b), which results in a more efficient activation of ClO_x. The more efficient activation of ClO_x is in opposition to the decline in atmospheric CFC concentrations. As a result, the ClO_x concentration and the magnitude of ozone minima hardly change in this model (see Figs. 1 and 2b).

To highlight the uncertainty in Arctic stratospheric temperature trends in CCMs, we show temperature trends in extremely cold boreal winters (January–April mean) for the whole atmosphere for the high-emission scenario RCP8.5 in Fig. 5. Although the models agree on the sign of the temperature changes in the troposphere and most of the stratosphere, there are large inter-model differences for the Arctic lower stratosphere (marked by the grey square), with some models projecting a warming and others projecting cooling. This uncertainty is most likely due to several competing processes that contribute to stratospheric temperature trends over the Arctic; GHGs radiatively cool the stratosphere. This GHG cooling is responsible for the negative temperature trends in large parts of the stratosphere. At the same time, the forthcoming recovery of Arctic ozone (see Fig. A1) is expected to radiatively heat the stratosphere, offsetting a great part of the GHG cooling (Maycock, 2016; Kult-Herdin et al., 2023). In addition to changes in radiation, changes in large-scale dynamics are expected to impact stratospheric temperature. In particular, a projected strengthening of the Brewer–Dobson circulation (BDC) due to increasing GHGs will drive a stronger downwelling and associated adiabatic dynamical heating over the North Pole (Butchart, 2014). Since CCMs show different sensitivities to GHG and hODS forcings  (Morgenstern et al., 2018), the contribution of the individual processes to temperature trends might vary across models. For example, the evolution of stratospheric dynamics and dynamical variability in the Arctic is very uncertain and highly model dependent (Ayarzagüena et al., 2018, 2020; Abalos et al., 2021; Karpechko et al., 2022), which likely contributes to the uncertainty in Arctic stratospheric temperature trends. In this context, it has already been shown that both radiative and dynamical processes add to the projected temperature spread across CCMs in the lower stratosphere (Bohlinger et al., 2014).

In summary, changes in the magnitude of ozone minima are strongly correlated to the decrease in ClO_x across models. Changes in the temperature of cold winters, however, only correlate with changes in ozone minima in models with extreme temperature trends ($>\pm \mathrm{0.2}$ K decade⁻¹). Thus, we conclude that long-term changes in Arctic ozone minima are strongly driven by long-term changes in stratospheric ClO_x concentrations. Changes in temperature, on the other hand, seem to play a secondary role in the evolution of Arctic ozone minima for the majority of the models. The relation between changes in ClO_x and changes in ozone minima serves as an underlying physical mechanism for the emergent constraint analysis, as described above. Even if temperature trends are not decisive for the development of ozone minima, it should again be emphasized that temperature biases in the mean state are important to explain the large model scatter in the magnitude of ozone minima under present-day conditions.

Figure 5Temperature trend of the coldest 20 % of the winter and spring seasons (January–April mean) in a 25-year running window over the course of the 21st century in CCMI1 models for RCP8.5. Stippling marks regions which are not significant at the 5 % level. The grey square marks the region of interest (60–90^∘ N polar cap, 30–70 hPa).

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