We use a suite of experiments described in depth in , which includes also a detailed descriptions of the models under analyses. The first set of experiments is a 2-year experiment over 2022–2023 with nudged temperature and meteorology as well as observed sea surface temperatures (SSTs) and sea ice (Exp2a in , here denoted “Nudged”; note this is distinct from Exp2b, not included in this study, which does not require prognostic aerosols). The second set of experiments is a 10-year long experiment over 2022–2031 with free running meteorology, using either imposed climatological SSTs and sea ice (Exp1_fixedSST in , here “Fixed-SST”) or with the atmosphere model coupled with the ocean (Exp1_coupled, here “Coupled”). Each experiment includes at least one simulation that involves the combined injection of 0.5 Tg of SO2 and 150 Tg of H2O (“SO2andH2O”), alongside a control simulation without any injections (“NoVolc”). The Nudged experiment also includes single-forcing simulations that inject only SO2 (“SO2only”) or only H2O (“H2Oonly”). The location, altitude, and amount injected are different between models in order to better match the observed plume in the first couple of days, but they remain consistent across experiments between models. Models account for the interactive coupling between aerosol, water vapor, radiation, and dynamics, allowing the fast descent due to water vapor longwave cooling to be simulated through this coupling. A summary of the experiments is provided in Table , and detailed model-specific injection settings are listed in Table .

Nudged was conducted by 5 models: the Whole Atmosphere Community Climate Model version 6 WACCM6; coupled with the four-mode modal aerosol module MAM4, and the Community Aerosol and Radiation Model for Atmospheres CARMA; , WACCM6-MAM and WACCM6-CARMA, respectively; the Model for Interdisciplinary Research On Climate – CHemical Atmospheric general circulation model for Study of atmospheric Environment and Radiative forcing version 6 MIROC-CHASER; ; the atmospheric component of CESM1, the Community Atmosphere Model version 5 CAM5; using the sectional aerosol microphysics model CARMA CAM5-CARMA; , and the UK Earth System Model version 1.1 UKESM; . Fixed-SST was carried out with two models, WACCM6-MAM and MIROC-CHASER, while only WACCM6-MAM participated in Coupled. WACCM6-MAM ran 30-member ensembles for both Fixed-SST and Coupled, whereas MIROC-CHASER ran 10-member ensembles for Fixed-SST. Further information about the participating models can be found in the references above, as well as in .

We use two observational datasets in this study: the Global Space-based Stratospheric Aerosol Climatology version 2.22 GloSSAC, for zonal monthly-mean stratospheric aerosol optical depth (AOD), and the Stratospheric Water and Ozone Satellite Homogenized dataset version 2.6 SWOOSH, for water vapor.

GloSSAC provides a long-term and global record of stratospheric aerosol properties, including the stratospheric AOD at 525 nm used here. It is primarily based on Stratospheric Aerosol Gas Experiment (SAGE) measurements up to mid-2005, with Optical Spectrograph and Infrared Imaging System and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations used thereafter, and SAGE III/ISS extending the climatology to the present. Additional data from other satellites, as well as ground-based, airborne, and balloon-borne instruments, are included to fill observational gaps . Although SAGE III/ISS data have limited spatial and temporal coverage, particularly during the first weeks following the Hunga eruption, they are considered robust because they rely on solar occultation and do not require assumptions about aerosol type or particle size distribution. In contrast, limb-scatter datasets such as Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP), used for comparison in , depend on additional assumptions about aerosol properties . For these reasons, GloSSAC is adopted as the primary observational reference, providing a consistent and reliable basis for evaluating modeled stratospheric aerosol evolution over longer timescales.

SWOOSH is a long-term and global record of stratospheric ozone and water vapor measurements from multiple satellite instruments (SAGE II, Meteor-3M SAGE III, Halogen Occultation Experiment, Upper Atmosphere Research Satellite Microwave Limb Sounder, and Earth Observing System Aura Microwave Limb Sounder) spanning 1984 to the present.

There are important differences among the radiative forcing estimates of volcanic eruptions derived from nudged simulations, which provide the instantaneous radiative forcing (IRF); free-running atmosphere-only simulations, which yield the effective radiative forcing (ERF), following the definition of ; and fully coupled simulations with an interactive ocean, which are generally referred to as radiative forcing (RF).

IRF represents the combined effect of direct interactions between the forcing agent and radiation, as well as interactions between the forcing agent and clouds . ERF, defined by as “change in the net TOA downward radiative flux after allowing for atmospheric temperatures, water vapour and clouds to adjust, but with surface temperature or a portion of surface conditions unchanged”, is the sum of IRF and rapid adjustments. These rapid adjustments which occur over weeks to months, before global-mean surface temperatures can respond, are due to changes in tropospheric and stratospheric temperature, water vapor, surface albedo, and clouds, and are distinct from slower feedbacks that are driven by surface temperature changes . In coupled model simulations, RF includes IRF, rapid adjustments to that forcing, and slower climate feedbacks resulting from the coupled ocean–atmosphere response .

The radiative forcings are calculated under both Clear-Sky (CS, without clouds) and All-Sky (AS, including the effects of clouds) conditions. Unless otherwise specified, all values are assumed to be calculated under Clear-Sky conditions.

IRF is calculated in climate models using a double radiation call that excludes aerosols from online radiative calculations (“Clean-Sky”) following the method proposed in in order to separate the contribution of aerosols from that of other components. Since nudging reduces variability in meteorological fields, it typically limits any stratospheric temperature adjustments, as radiative forcing is calculated as the difference between the perturbed and unperturbed case (Eq. ). As a result, the IRF from aerosols and water vapor, either combined or individually, can be approximated using the corresponding Nudged experiments (Eqs.  and , respectively). 1IRF=FSO2andH2O, Nudged-FNoVolc, Nudged2IRFaerosol=FSO2only, Nudged-FNoVolc, Nudged3IRFgas=FH2Oonly, Nudged-FNoVolc, Nudged

In the case of WACCM6-MAM simulations, both methodologies have been applied. Notably, in contrast to previous studies, all forcing estimates presented here treat stratospheric water vapor as a forcing rather than a feedback, due to its direct injection. The second estimate of IRF in WACCM6-MAM for aerosols (sulfate, black carbon, primary organic matter, secondary organic aerosols, sea salt, and dust) and gases (water vapor, dioxygen, carbon dioxide, ozone, nitrous, methane, chlorofluorocarbons) is derived through a double radiation call (Eqs.  and , respectively). Within this approach, Fclean denotes the Clean-Sky calculation, which excludes aerosols. 4IRFaerosol=(FSO2andH2O, Nudged-FNoVolc, Nudged)-FSO2andH2O, Nudgedclean-FNoVolc, Nudgedclean5IRFgas=FSO2andH2O, Nudgedclean-FNoVolc, Nudgedclean

ERF and RF are calculated as the difference between the perturbed and unperturbed case (Eqs.  and , respectively). 6ERF=FSO2andH2O, Fixed-SST-FNoVolc, Fixed-SST7RF=FSO2andH2O, Coupled-FNoVolc, Coupled

We calculate the different radiative forcings at three key atmospheric levels – top of the atmosphere (TOA), tropopause (TROP), and surface (SURF), as the sign and magnitude of RF can differ by altitude and carry distinct physical implications. The radiative forcing at the three levels is presented for each model according to data availability. Radiative forcing at TOA reflects the overall perturbation to the Earth's energy budget and is commonly used to estimate the potential influence on global average temperature. At the tropopause, RF captures the net energy change affecting the coupled troposphere–surface system, and is considered less affected by upper stratospheric processes and better represents tropospheric heating. In contrast, RF at the surface does not directly correspond to surface temperature responses but is more relevant for understanding impacts on the hydrological cycle, particularly changes in precipitation patterns .

The IRF includes all optically active components, such as stratospheric aerosols, water vapor, ozone, and polar stratospheric clouds (PSCs). For model intercomparison, we use clear-sky forcing to minimize uncertainties associated with aerosol–cloud interactions that arise from differences in cloud parameterizations among models.

All models show qualitative agreement in the spatial distribution of the IRF under clear-sky conditions at TOA (Fig. ), at TROP (Fig. ), and at SURF (Fig. ). At each level, the response is primarily located in the Southern Hemisphere (SH); therefore, most of the following analyses will focus on the SH only.

A consistent pattern of negative forcing appears across models in both the SO2andH2O and SO2only experiments (first and second columns in Figs. , , and ). This forcing peaks in the tropics during the first few months following the eruption and then moves to mid- to high-southern latitudes by 2023, with substantial negative forcing persisting through the end of 2023 in the SH. Likewise, all models simulate a negligible IRF from the H2Oonly experiment (third column of the same figures). Therefore, the models consistently attribute nearly all of the radiative forcing to the aerosol perturbations rather than to the injected water vapor.

Global means (Fig. a–c) and hemispheric means (60° S-EQ in Fig. d–f; 60–90° S in Fig. g-i) show the multi-model average and inter-model spread, and highlight the magnitude of the IRF in each injection experiment. These means further clarify that the IRF from H2Oonly is negligible: it is slightly negative at TOA (first column) and slightly positive at TROP and SURF (second and third columns). This behavior results from the vertical distribution of water vapor in the stratosphere and the lack of stratospheric temperature adjustment, which together increase outgoing longwave radiation while enhancing downward longwave re-emission. Especially at the surface, the IRF remains positive but very small, as the radiative forcing is dominated by sensible and latent heat fluxes, which are controlled by the prescribed surface temperature in these simulations.

For the aerosol forcing, which constitutes essentially the entirety of the Hunga radiative forcing, the models generally agree on its temporal evolution but exhibit substantial differences in its magnitude. The multi-model mean TOA IRF from SO2andH2O is -0.35 ± 0.12 Wm-2 over 60° S-EQ (2022–2023 average; Fig. d–f), where the inter-model spread is roughly one third of the mean magnitude. The global mean forcing is approximately half of the 60° S-EQ values, reflecting the strong SH dominance of the perturbation. Over the high southern latitudes (60–90° S; Fig. g–i), the mean TOA IRF is -0.26 ± 0.23 Wm-2, indicating large uncertainty, with the standard deviation nearly matching the mean (September 2022–December 2023 average). Comparing the injection experiments, the IRF from SO2andH2O is generally comparable to SO2only at TOA, but less negative at TROP and SURF: over the 60° S-EQ, TROP IRF is -0.32 ± 0.13 for SO2andH2O versus -0.43 ± 0.12 Wm-2 for SO2only; at the surface, these values are -0.29 ± 0.12 versus -0.36 ± 0.11 Wm-2.

The shortwave (SW) component of the IRF follows the evolution of stratospheric AOD (Fig. ) but is additionally modulated by the strong seasonality of solar insolation, producing relative minima during the Austral winter. This is particularly evident at high southern latitudes (Fig. g–i), where the small negative SW IRF is partially offset by a positive longwave (LW) contribution. Generally, the LW signal coincides with the peak in stratospheric AOD, which, over the high southern latitudes, occurs during the Austral winter of 2023.

The SW IRF is similar between TOA and TROP but smaller in magnitude at SURF in both SO2andH2O and SO2only experiments. However, at all levels, the SW IRF is more negative in SO2andH2O during the first few months after the eruption and then becomes less negative compared to SO2only, consistent with the evolution of stratospheric AOD in the two experiments (Fig. j and k). The differences in the net IRF between the two experiments decrease at TOA but increase at TROP due to the different LW responses to water vapor, which is slightly negative at TOA and positive at TROP.

Figure  provides further insight into the TOA IRF contributions from aerosols (IRFaerosol) and water vapor (IRFgas), based on analyses from WACCM6-MAM using both methods described in Sect. 2.2. Among the models, WACCM6-MAM shows the strongest aerosol response (first and second columns of Fig. ). Multiple interesting features emerge from an analysis of Fig. , which also includes a comparison of clear-sky and all-sky IRF.

The IRF from the SO2andH2O and SO2only simulations (black and orange lines in Fig. a) show similar behavior from late 2022 onward. However, substantial differences are evident during the first 6 months (on the order of 20 % in WACCM6-MAM, Fig. c), with the exact duration being model dependent (Fig. ). This is in agreement with previous studies indicating that the co-injection of stratospheric water vapor promotes faster particle growth to optically efficient scattering sizes, reaching an effective radius of about 0.4 µm over less than a month (Fig. a–c for SO2andH2O versus Fig. d–f for SO2only). Further details on the microphysical aspects, using the same protocol and model simulations, are provided in (comparison of the particle size with observation in Fig. 3.18). As a result, SO2andH2O produces a larger initial stratospheric AOD (Fig. j and k) and corresponding negative radiative forcing. Later on, the forcing becomes similar due to a compensating effect: SO2only shows a larger stratospheric AOD, while SO2andH2O shows a stronger gas contribution (negative at TOA). The SO2andH2O forcing becomes slightly weaker only in the last few months of 2023, when the gas IRF in the two simulations becomes comparable (Fig. c).

Figure  shows the longer-term evolutions of the moving average forcing, calculated as: 81Nt∑i=1NtRFi where Nt represents the number of months elapsed, and RFi is the radiative forcing at month i. We use the moving average forcing instead of the instantaneous forcing to highlight the time-averaged impact of the eruption over time, which provides a better measure of its overall climatic effects. This is shown for the free-running simulations with fixed climatological SSTs and sea ice (Fixed-SST). For this experiment, only two models, WACCM6-MAM and MIROC-CHASER, performed the simulations. The TOA ERF estimates show a very good agreement between the two models, both in terms of the overall magnitude and the rate of dissipation of the forcing, which is partly true also for the ERF estimates at the surface (see Tables  and ). Larger differences between the models are present for the ERF estimates at the tropopause, whereby WACCM6-MAM shows a more negative average forcing (by 0.1 Wm-2) in the first year (Table ) and a different overall trend throughout the simulations.

Although the ERF response is broadly consistent between the two models, notable differences emerge in their simulated stratospheric AOD (Fig. d and g). In particular, we observed significant discrepancies in the timing of aerosol formation and the onset of its decline. In MIROC-CHASER, stratospheric AOD starts to decline 2 months after the eruption, right after reaching its peak. In contrast, WACCM6-MAM shows a peak in stratospheric AOD 3 months post-eruption, which remains at peak levels for 6 months before beginning to decrease. However, the models generally agree on the volcanic cloud's southward transport, with the volcanic cloud moving towards 60° S after 4 to 5 months and reaching the pole by December 2023. The persistence of the aerosol cloud at low-to-mid latitudes in the SH is different between the two models, with WACCM6-MAM showing some persistence all the way to the end of 2023, whereas MIROC-CHASER show a full dissipation by late 2023.

Contrary to the stratospheric AOD, the water vapor upward diffusion (Fig. e and h) shows more persistence in MIROC-CHASER than WACCM6-MAM, with the latter showing no residual water vapor anomaly below 1 hPa by late 2026, whereas MIROC-CHASER shows at least 0.5 ppm more in the upper stratosphere remaining all the way to 2028. MIROC-CHASER also shows a stronger positive tropical ozone anomaly between 10 and 20 hPa compared to WACCM6-MAM, and a negative ozone anomaly higher up between 1 and 2 hPa, with the negative anomaly more persistent over time in both models (Fig. f and i), explained by a potential enhancement of the HO_x-driven loss cycle due to the water vapor anomaly .

As with the instantaneous radiative forcing, the gas response varies depending on the atmospheric level at which it is calculated and the vertical distribution of the gases. Additionally, temperature adjustments are included here. We speculate that the stronger stratospheric AOD anomaly in WACCM6-MAM, along with the stronger water vapor and ozone anomalies in MIROC-CHASER, may either offset the radiative forcing at the top of the atmosphere (TOA) or amplify it at the tropopause (TROP). This could explain the similar forcing observed in Fig. a and the larger differences seen in Fig. b. This aspect is only further explored in Sect. 3.3 for WACCM6-MAM, where the availability of separate aerosol and gas radiative contributions allows for a clearer disentangling of each factor.

In Fig.  we also provide a comparison with available observations, with more in depth comparisons presented in . In general, both models show good qualitative agreement with the observations. While GloSSAC does not capture the pronounced peak immediately following the eruption, which is evident in other observational datasets discussed in , this mainly reflects the limited spatiotemporal coverage of the SAGE III/ISS observations on which GloSSAC is based during the earliest post-eruption phase. Despite this limitation, transport toward the Southern Hemisphere occurs on similar timescales in both the observations and the simulations, with WACCM6-MAM showing a better match in terms of the residual aerosol cloud around 60° S. In terms of H2O, models generally reproduce the upward transport pattern; however, SWOOSH consistently reports higher values. As also noted in , the comparison between models and observations is primarily aimed at assessing transport patterns, since anomalies are derived differently in each case, requiring careful consideration for a meaningful quantitative comparisons. In the following section, we will discuss how the results for WACCM6-MAM compare between fully coupled and nudged simulations.

In this section we show a comparison of radiative forcing in the three different experiments, which only WACCM6-MAM conducted in full. This comparison provides useful insights to the different ways to define the radiative impacts of the volcanic cloud between RF, ERF and IRF.

Figure  shows that, across all experiments and at the three atmospheric levels, the simulated clear-sky radiative forcing is negative and locally statistically significant in the Southern Hemisphere during the first two years following the eruption. The sign, as well as the spatial and temporal evolution, is consistent across the different model configurations and atmospheric levels considered. However, when including the atmospheric temperature adjustments in Fixed-SST and the ocean response in Coupled, the radiative forcing from aerosols and water vapor is substantially smaller than in the nudged simulation, particularly at TOA. This difference is more evident when averaging over the Southern Hemisphere (60° S to the equator), as shown in Fig. .

In Fig. a, the clear-sky IRF at TOA during the first 2 years after the eruption is -0.43 Wm-2 in the nudged simulations, whereas in the free running experiments it is -0.27 Wm-2 in both the coupled ocean and atmosphere-only cases. Although smaller than in the nudged simulations, these responses remain outside the range of natural variability, which is estimated in Fig.  as one standard deviation from the control ensemble (NoVolc). In general, while most of the results presented here are for the SH only, when considering global mean the values are reduced by approximately half, reaching a value of -0.09 Wm-2 at the TOA for the Coupled experiment in 2022–2023, which falls within the range of natural variability (see Fig.  and Table ).

The reduced net radiative forcing relative to the nudged case arises from the inclusion of temperature and ozone adjustments. Indeed, differences in the simulated stratospheric AOD changes among the experiments are negligible (Fig. a–c), consistent with previous studies showing that atmospheric nudging does not necessarily improve the representation of the residual stratospheric circulation . Instead, the response is largely dominated by gas-driven variability, which is strongest in the Coupled experiment and includes a late-period negative radiative forcing in 2025 that is not present in the other simulations (Fig. a and b).

The separation of aerosol–radiation and gas–radiation contributions to the total radiative forcing (Fig. ) shows that the negative TOA forcing during the first two years following the eruption is primarily driven by the aerosol contribution from Hunga, partially offset by a positive contribution from changes in gases. This behavior contrasts with the nudged simulations, where the gas–radiation interaction produces a negative forcing (Fig. ). In the free-running simulations, the gas contribution is strongly influenced by natural variability (red line in Fig. ), particularly for all-sky radiative forcing, which limits the detectability of the forced response without large ensemble sizes (Fig. ).

In the second half of 2025, as the tropical stratospheric AOD returns to background levels (Fig. a–c), only the Coupled experiment exhibits a significant negative radiative forcing in the tropics at both TOA and TROP, with magnitudes comparable to those observed during the first post-eruption year (Fig. a and b), while the forcing at SURF becomes positive. This late-period forcing in the Coupled experiment is primarily driven by gas–radiation interactions, with significant negative clear-sky values emerging in 2025 (Fig. a, red lines).

The gas radiative forcing results not only from Hunga-induced changes in stratospheric water vapor (which are similar across the three experiments; Fig. d–f) but also from changes in stratospheric temperature and ozone (Fig. g–i), as well as associated dynamical adjustments that modulate both, particularly in the lower stratosphere. These contributions are further explored in Fig. . The gas–radiation interaction is dominated by the LW component (Fig. a–c), with differences among the atmospheric configurations driven primarily by temperature and dynamical responses: has shown an upper-level cooling due to the water vapor and a lower stratospheric level warming from LW absorption from the sulfate aerosols in the free-running simulations.

During the first two years following the eruption, the TOA gas radiative forcing is positive in the Coupled simulation, more variable in Fixed-SST, and negative in the Nudged case (Fig. a–c). This behavior reflects the combined effects of increased water vapor in the middle stratosphere and reduced ozone in the lower stratosphere. When temperature and dynamical changes are excluded, as in the Nudged simulation, the water vapor increase and ozone decrease (black curves in Fig. f and i) enhance outgoing LW radiation at TOA, resulting in a negative forcing. In contrast, when temperature adjustments are included, as in the Coupled and Fixed-SST simulations, the cooling at higher altitudes where water vapor anomalies peak (black curves for water vapor and red curves for temperature in Fig. d and e) reduces outgoing LW radiation, yielding a positive TOA forcing during the first two post-eruption years. Furthermore, the Coupled shows a distinct evolution in the tropical lower stratosphere, characterized by increased ozone and warming during 2022–2023, followed by decreased ozone and cooling in 2025 (Fig. g). Because ozone in the lower stratosphere acts as a greenhouse gas, these changes contribute to an additional positive radiative forcing during the first two years and a negative forcing in 2025, when water vapor anomalies have largely returned to background levels. The close correlation of changes in ozone and temperatures in this region, not seen in Fixed-SST (Fig. h), is strongly indicative of their dynamical origin, suggesting an associated decrease in tropical upwelling in 2022–2023 and increase in 2025.

As discussed in , the coupled ocean WACCM6-MAM simulations shows a significant modulation of the El Niño–Southern Oscillation (ENSO) variability by the eruption, with La Nina like response in 2022–2023 and an El Nino like response in 2025. In general, ENSO is an important driver of interannual variability in tropical upwelling, which in turn modulates lower-stratospheric temperatures and ozone , and can therefore exert a substantial influence on the overall radiative forcing.