Our set of SOCOLv4  simulations comprises an ensemble of transient simulations with and without the HT forcing, i.e. 150 Tg of WV and 0.5 Tg of SO₂ have been distributed over the emission region (22–14° S, 182–186° E and 25–30 km) within 15 January similarly to the community recommendation . We perform a 5-year spin-up before the HT eruption. Both ensembles comprise 10 ensemble members. We stress that the Quasi-Biennial Oscillation (QBO) is nudged in both simulations with and without the HT forcing. We use equatorial zonal wind at 10 hPa as a proxy for Quasi-biennial Oscillation (QBO) to demonstrate a link between QBO and the polar vortex in SOCOLv4, i.e. the so-called Holton-Tan mechanism . For a detailed description of our SOCOLv4 simulations, we refer to Appendix A1 in .

As indicated in , the anomalous WV following HT decays and propagates vertically too rapidly in SOCOLv4 compared with MLS/SWOOSH (cf. globally averaged WV anomaly in SOCOLv4, MLSv6 and SWOOSH in Fig. ) or some of the other models . Note that the contour at 0.5 ppmv does not reach the year 2024 in SOCOLv4, unlike in SWOOSH. This limitation is well documented for the SOCOL model family: SOCOLv4 retains, as in previous SOCOL versions, a too-fast residual circulation and excessive mixing in the surf zone, and its tropical water-vapour tape-recorder signal propagates upward too rapidly . Related stratospheric transport biases are also common in many CCMs, as indicated by too-young age of air (AoA) and overly rapid tropical ascent in CCM intercomparisons , although their magnitude and vertical/latitudinal structure vary across models.

Overall, SOCOLv4 is adequate for broad NO_x/HO_x/ClO_x driven ozone depletion/recovery studies . The main remaining weaknesses are transport and mixing, and photolysis at large solar zenith angles over the high latitudes of the Southern Hemisphere e.g..

We prescribed WV and ozone anomalies from MLS for the extended winter 2024/2025 (OW3) and calculated longwave and shortwave radiative heating rates using konrad's  interface to the Rapid Radiative Transfer (RT) Model for General circulation models RRTMG;. We state that these radiative calculations are robust for various solar zenith angles. We accompany these calculations using a precise line-by-line RT simulations see details in

Throughout our analysis, we evaluate significance fields using the minimum local p-values from Student's t-test with global test statistics. Most of the illustrations in Sect.  show differences between simulations with and without the HT forcing. For the MLSv6 observation, we compute local p-values as empirical two-sided rank p-values for each target month-pressure bin. We confirm this approach using local Monte Carlo p-values with 1000 samples.

We investigate the response of resolved planetary waves (PWs) using the Eliassen-Palm flux diagnostics EPF; applied to the SOCOLv4 6-hourly outputs. EP fluxes are computed and scaled following . The EPF convergence serves as an indicator of wave dissipation, and the EPF divergence (EPFD) indicates sourcing. We illustrate all EPF diagnostics from 1 October 2023 to 30 March 2024 in the Supplement.

We calculate the Southern Oscillation Index (SOI) using sea level pressure (SLP) standardised difference between Tahiti (17.65° S, 149.45° W) and Darwin (12.46° S, 130.84° E) as a proxy for the El Niño Southern Oscillation (ENSO). Negative and positive SOI values coincide with abnormally warm and cold ocean waters across the eastern tropical Pacific typical of El Niño and La Niña episodes, respectively.

We set the scene by illustrating the daily evolution of stratospheric dynamics in the extended winter 2024/2025 (the third observed winter after the HT eruption; thus, marked as OW3) using the MERRA2 reanalysis in Fig. . Here, the zonal-mean winds diagnosed at 60° N at 10 hPa illustrate that the SPV strength exceeds the average strength during DJF 2024/2025. Next, we turn the focus to anomalies of WV, temperature, and ozone (derived from the MLS observations in Fig. ), to put the exceptionally strong SPV in the context of the lingering HT perturbation in polar latitudes. The WV anomalies (see Fig. A) are characterized by “tongues” with concentrations of up to 2 ppmv. The first tongue appears in the mesosphere during September 2024 and continuously propagates downward with time to ∼ 10 hPa, where it gradually weakens and dissipates by March 2025, when it merges with the stratospheric background. A second tongue forms in the mesosphere in January 2025 and also propagates downward (not shown for the chosen time frame of Fig. ). The WV anomaly is statistically significant (at respective p-values for given figure) over much of the descending tongue. In contrast, the negative ozone and temperature anomalies are statistically significant only locally, mainly along the upper flank of the WV tongue starting around 0.1 hPa in September and ending below 10 hPa in February (see Fig. B, C), reflecting the large daily and interannual variability of polar wintertime conditions. We therefore do not interpret the 2024/2025 anomalies as uniquely attributable to HT; rather, the observations indicate a plausible HT contribution superimposed on internal dynamical variability. The temperature anomalies are followed by their positive counterparts. By October, an enhanced ozone anomaly (∼0.5 ppmv) emerged around 10 hPa, leading to effective warming due to ozone absorption of solar radiation and increased mixing and thereby masking the WV-induced cooling propagating downward. In March, we observe a significant increase and decrease in stratospheric and mesospheric polar temperatures, respectively. However, the stratospheric ozone anomalies have both alternating positive and negative bands. This corresponds to the stratospheric final warming during which the SPV does not recover and transitions to summer conditions, with easterly winds across the stratosphere (see Fig. A). The observed stratospheric and lower-mesospheric longwave cooling rates are dominated by CO₂ together with ozone and WV . The close correspondence between the WV and ozone anomalies and the diagnosed temperature response suggests the radiative cooling observed in OW3. However, a comparison with OW2 (see Fig. ) implies that slowly descending WV, i.e. dynamical preconditioning (see EHF in Fig. B), positively feeds back on radiative cooling and strengthens the vortex. We examine this mechanism explicitly in the model simulations below.

The downward propagating tongue of WV during winter is captured in our SOCOLv4 ensemble. The feature emerges in the extended winter 2023/2024 (marked as the second model winter after the HT eruption, MW2; see Fig. A) and winter of 2024/2025 (MW3; see Fig.  A). The WV enhancement is, however, underestimated compared to observations in Fig. A, especially in MW3. Given the well-documented model deficiency of accelerated transport of SOCOLv4 (discussed in detail in Sect. ), we argue that the winter MW2 in our simulations is comparable to OW3 in observations (see Sect. and Fig. ). For the MW2 SOCOLv4 yields a similar strengthening of the vortex with a less pronounced weakening than observed at the end of OW3 (cf. Fig. D at 10 hPa and Fig. A). In analogy, we assume MW3 matches with the upcoming OW4, as we detail further below.

For MW2 (equaling OW3) we attribute the initial ozone destruction in the upper stratosphere and lower mesosphere to increased OH concentrations induced by the excess WV from the HT eruption (HO_x cycle) and the ClO_x activation from chlorine reservoirs (see Fig.  ). These coincide with a negative anomaly in NO_x mainly attributable to cooling at these levels . In contrast, as reported in , the positive ozone anomaly limited to September–November and rather in the lower to mid stratosphere, similar to MLS, emerges due to increased conversion of NO_x to the HNO₃ reservoir given an overall higher abundance of OH. While negative ozone and negative temperature anomalies are not statistically significant (at respective p-values for given figure) along the entire WV tongue similarly as in observations (see Fig. ), they are associated with a stronger SPV and correspondingly weaker poleward transport of ozone from lower latitudes reflected by the EHF (red line in Fig. D) and AoA (Fig. ). Thus, the paired SOCOLv4 simulations indicate that HT forcing shifts the ensemble-mean circulation response toward stronger polar westerlies. However, this ensemble-mean response does not imply that individual ozone, temperature, or wind anomalies, or the full observed evolution of OW3, can be uniquely attributed to the HT forcing.

Next, we investigate the radiative effect of the observed changes in WV and O₃ on temperature via offline radiative transfer (RT) calculations (see Sect. ). These RT calculations presented in Fig.  reveal that perturbations in both WV and ozone abundances are capable of inducing cooling rates in the order of -0.5 to -1 K d⁻¹, with WV and ozone dominating the change in the longwave and shortwave heating rates throughout the stratosphere and in the upper layers, respectively. These heating rate anomalies are collocated with those observed (see Fig. C) and simulated (see Fig. C). SOCOLv4, however, does yield a weaker temperature response initially, attributable to weaker changes in shortwave heating rates following the weaker ozone anomaly than seen in the MLS observations.

We confirm these calculations using the line-by-line RT simulations (see Sect. ). The resulting longwave heating rates from prescribed time-evolving WV and ozone from SOCOLv4 are shown in Fig. .

As detailed in , the radiative-cooling recovery of SSW-induced temperature anomalies in the absence of dynamical heating is dominated by longwave radiative cooling, and is characterized by increasing e-folding times from the upper to middle stratosphere. If we invert the e-folding times (4–7.5 d in the upper stratosphere) of , we obtain an equivalent heating-rate effect of roughly 0.13–0.25 K d⁻¹ K⁻¹. Given that the e-folding time increases in the lower stratosphere and decreases towards the mesosphere, we expect that temperature perturbations translate into weaker and stronger heating-rate effects at lower and upper levels, respectively. In the lower stratosphere, the air cools more slowly because there is a deeper layer of atmosphere above it that absorbs the radiation, re-emits it upwards but also downwards, and thereby effectively reduces the amount of energy that can escape into space. Closer to the tropopause, the cooling effect reduces as the radiation emitted depends strongly on the background temperature itself . This asymmetry may explain the different persistence of the heating rate anomalies at different heights that appear in Fig. B. Furthermore, the pronounced positive heating rate anomaly around 1 hPa spanning from December 2024 to March 2025, consistent with enhanced longwave heating related to decreased ozone, aids in explaining the rapid change from negative to positive temperature anomalies (see Figs. C and C).

The negative temperature anomalies throughout the upper stratosphere and lower mesosphere result in an enhanced meridional temperature gradient (see Fig. ), which strengthens SPV via the thermal wind balance. The SPV strengthening may initially enhance vertical wave propagation during October, a time when ZW are usually weak and thus allow more PWs to propagate upwards into the stratosphere . In this respect, we understand the simultaneously observed anomalously high EHF at 100 hPa (see Fig. B) as a proxy for upward propagation of PWs e.g.. This way we associate the anomalously weak ZW below in the stratosphere to anomalously breaking PWs (see visualization of EPF in the Supplement, Sect. ). As the cooling progresses downward, it aids the strengthening of the winds, which tend to be too strong for wave propagation . This may confirm the nonlinearity of SPV for generally large wave forcing during the NH winter conditions . The stronger SPV is associated with pronounced negative and positive temperature anomalies below and above, respectively. A similar dipole structure has been discussed in studies diagnosing SH high-latitude temperature trends as a consequence of ozone depletion (e.g. ; ). attributed the positive temperature anomaly at upper levels to increased downwelling, and thus, consequently, adiabatic warming due to enhanced gravity wave propagation. Correspondingly, stronger westerlies in the stratosphere filter eastward gravity waves while westward gravity waves propagate freely upward and deposit their momentum above.