Large, low-latitude eruptions, such as the 1815 eruption of Mount Tambora in the Lesser Sunda Islands, can inject considerable amounts of sulfate into the lower stratosphere. Since the Brewer–Dobson circulation advects tracers upwards and polewards in the tropics , the volcanic aerosols from such eruptions have long residence times (from many months to years), making them capable of impacting surface climate in a substantial way. That impact is primarily a reduction in surface temperature, as the aerosols shield the surface from incoming solar radiation and cause cooling. It is thus not immediately obvious how such large eruptions would produce any surface warming.

Nonetheless, a series of observational and modeling studies, starting in the early 1990s and continuing to this day, have argued that low-latitude eruptions comparable to the one of Krakatau in 1883, or Pinatubo in 1991, do in fact cause surface warming over the Northern Hemisphere (NH) continents in the winters following the eruption. This surprising result was first reported in observational studies and initially supported by modeling studies . However, those observational results suffered from serious methodological flaws: to cite one example, the early claim of was based on a mere 12 eruptions, half of which did not actually occur in the tropics, averaged together irrespective of amplitude, commingling first and second post-eruption winters. In addition, the early low-resolution modeling results have not been replicated by the vast majority of later studies of those same eruptions – roughly all the major events since pre-industrial times – with stratosphere-resolving models at much higher horizontal and vertical resolution (e.g., ).

In spite of these later results, the idea that low-latitude eruptions might cause winter warming at Northern Hemisphere high latitudes has remained compelling, mostly because the original claims were predicated on a sound physical mechanism. As originally proposed by and , that mechanism consists of three steps: (1) the sulfate aerosols of volcanic origin in the tropical lower stratosphere absorb longwave radiation (LW) and cause anomalous warming in that region, and (2) this yields an enhanced Equator-to-pole temperature gradient which results in an anomalously strong stratospheric polar vortex during the winter months (via simple thermal wind balance) which, in turn, (3) induces a more positive phase of the Northern Annular Mode (NAM) at tropospheric mid-latitudes, accompanied by warmer Eurasian surface temperatures. We refer to this sequence of events as the “stratospheric pathway” mechanism.

Starting from the first link in the causality chain, it is widely documented that recent-generation climate models are able to simulate tropical lower-stratospheric warming in response to low-latitude volcanic eruptions. Figure 3 of , for instance, clearly shows that such post-eruption warming (typically of several ∘C) is simulated in models for all large eruptions since 1870. Furthermore, as demonstrated by , those same models are able to capture the weak acceleration of the polar vortex (typically of the order of a few meters per second) for the two largest events, the 1883 Krakatau and the 1991 Pinatubo eruptions. Why, then, are those models unable to produce a statistically significant forced post-eruption Eurasian surface winter warming?

An answer to this conundrum was proposed by who, focusing specifically on the 1991 Pinatubo eruption alone to avoid averaging large and small eruptions together, analyzed three large ensembles of model runs and showed that a polar vortex acceleration of a few meters per second is too small to impact the tropospheric NAM in a statistically significant way. Simply put, the large natural variability of the mid-latitude winter circulation completely overwhelms any forced signal coming from the stratosphere for that eruption. This result was recently – and independently – confirmed by with a much larger ensemble of runs of a stratosphere-resolving model (100 members). As in , that more recent study demonstrates that while a statistically significant volcanically forced acceleration of the polar vortex can be detected (in a model) with a sufficiently large ensemble of runs, for the 1991 Pinatubo eruption that forced acceleration is just too small to cause a statistically significant shift in the winter North Atlantic Oscillation (NAO) and, consequently, of Eurasian surface temperatures.

One may argue that the 1991 Pinatubo eruption was peculiar in some way and may not be representative of other eruptions. To address that question examined the other large, low-latitude event of the industrial era: the 1883 eruption of Mount Krakatau. That event not only falls within the instrumental period of many temperature reconstructions (so that we have a robust estimate of the surface temperature anomalies), but literally hundreds of model simulations of that eruption are available from the Coupled Model Intercomparison Project (CMIP). Examining several temperature reconstructions, highlighted that the weak Eurasian surface warming observed in the winter following that eruption falls well within the natural variability of Eurasian surface temperatures. Furthermore, examining CMIP model output, they confirmed the absence of a volcanically forced response in the surface temperatures at Northern Hemisphere mid-latitudes in the first winter following the Krakatau eruption.

At this point, then, one is inevitably led to ask: if Pinatubo and Krakatau are not large enough, how large does an eruption need to be to cause winter surface warming at Northern Hemisphere mid-latitudes? At the upper boundary, in a geoengineering context, it has recently been shown that large and sustained stratospheric sulfate injections do indeed produce winter warming over Eurasia (, see their Fig. 8, bottom right panel), and this surface warming (which is absent in the summer months) has been linked to stratosphere–troposphere dynamical coupling affecting the NAO . also found a robust impact of sustained lower stratospheric tropical warming on the NAO, using an idealized model. While these studies suggest that the stratospheric pathway to a winter Eurasian surface warming can indeed be operative, the sulfate injection in is equivalent to several Pinatubo-size eruptions each year, and sustained for many decades: such forcing is not comparable to any realistic eruption. One would like to examine stratospheric injections typical to actual eruptions and, starting from eruptions comparable to those of Pinatubo or Krakatau, methodically increase the amplitude of the injection until a clear winter warming over Eurasia appears.

A first step in that direction was recently taken by . Using a state-of-the-art model they performed and analyzed large-ensembles of idealized low-latitude eruptions with stratospheric sulfur injections ranging from 2.5 to 20 Tg(S), using the Easy Volcanic Aerosol (EVA) protocol of to generate the aerosol distributions. They report that for injections of 10 Tg(S) or larger, a statistically significant forced warming pattern is seen in their model, at latitudes northward of 55∘ N over a reduced set of longitudes (10–90∘ E). While this is an interesting result, the actual value of the forced warming produced by a 10 Tg(S) eruption is at most 0.75 ∘C (depending on specific regions selected). Such a value, it is important to note, is smaller than the natural year-to-year variability in surface temperature over Eurasia, as computed by from three temperature datasets spanning the 1850-to-present period (see their Fig. 3; variability is computed therein over the region 40–70∘ N, 0–150∘ E). Also, even for a 20 Tg(S) eruption, the largest amplitude explored in , the largest Eurasian warming in their model is 1.5 ∘C, which falls within the 2σ range of natural variability. Hence, while that study has demonstrated the existence of a statistically significant warming signal in a model by using a sufficiently large ensemble and a sufficiently large injection, the signal they report would hardly be exceptional: the winter following a 20 Tg(S) eruption would not be distinguishable from many other anomalously warm winters which are not preceded by a large, low-latitude eruption.

In this paper, building on the findings of , we perform a similar exercise but with a different goal. Rather than ask: How large does an eruption need to be to produce a statistically significant surface winter warming over Eurasia? We ask: How large does an eruption need to be to produce a forced winter warming over Eurasia that is substantially larger than the natural variability? The key idea is that one can always produce a statistically significant result by enlarging the ensemble size, thus reducing the noise and capturing the forced signal. But, in practice, what really matters is how large that forced signal is in comparison with the unforced variability. As we will show, our findings indicate that eruptions as large as 160 Tg(S) are unable to produce a forced winter Eurasian warming that exceeds natural variability in a significant way.

Our paper is structured as follows: in the next section we describe the model used, the protocol to generate a progressively larger sequence of idealized volcanic aerosol forcings, the simulations performed, and the analysis techniques employed herein. We specifically limit our study to eruptions occurring during neutral phases of the El Niño Southern Oscillation (ENSO), to characterize the volcanic impact without the (potentially) confounding influence of anomalous conditions in the tropical Pacific. In Sect. 3 we examine the impact of our idealized volcanic eruptions on the atmospheric circulation, in the stratosphere and in the troposphere, with particular attention on the response of the NAM which underlies the surface warming. We turn our attention to the latter in Sect. 4, and examine the Eurasian temperature response to our idealized eruptions, comparing it with the one from Pinatubo and Krakatau in the same model. We conclude the paper with a brief summary and a discussion of our model results in light of the observed eruptions of the past 2500 years.

Before discussing any Eurasian surface warming, we need to start by examining stratospheric temperature and circulation responses, to determine whether the volcanic aerosols in the lower tropical stratosphere are able to accelerate the polar vortex, with an accompanying positive phase of the NAM in the first DJF following the eruptions. The difference-from-control-run response of the atmospheric temperature T, as a function of latitude and height, for the first winter (DJF) followed each eruption is shown in the left column of Fig. . It is very clear that as the sulfur mass injection is increased from 5 to 160 Tg(S), the volcanic aerosols in the tropical lower stratosphere cause a progressively larger warming response, which reaches into the mid-latitudes for the larger amplitudes.

As expected from thermal wind balance, a similar response is seen in the zonal mean zonal wind u (Fig. , right column), with a progressively stronger polar vortex acceleration in the NH with stronger eruptions. Note that, in these idealized calculations, 20 Tg(S) are required to obtain a statistically significant vortex acceleration. At 10 Tg(S), an amplitude comparable to that of the 1991 Pinatubo eruption, 20 members are not sufficient to establish statistical significance. However, with a larger ensemble, size significance can be established for a 10 Tg(S) eruption, as documented originally by . In fact, report a significant polar vortex acceleration for even smaller EVA injections, down to 5 Tg(S) in their model, using 100-member ensembles. However, the very fact than 20 eruptions are not sufficient to establish significance speaks to the fact that the signal is small for injections smaller than 10 Tg(S), even in the stratosphere.

But let us now turn to the tropospheric circulation. In the right column in Fig.  one can see a clear dipole in the NH tropospheric mid-latitudes, which is statistically significant for injections of 20 Tg(S) and above, in our model. This dipole, which is most prominent over the North Atlantic (not shown), represents a poleward shift in the eddy-driven jet. It is customary to quantify such jet shifts in terms of the NAM, also known as the Arctic Oscillation, which has become a standard metric for stratosphere–troposphere coupling (e.g., see ). To illustrate the NAM in our model, the zonal mean zonal winds associated with 1 standard deviation of the NAM index are shown in Fig. a: notice how the NAM regressed winds resemble the Δu response in Fig. . This suggests that the NAM is likely to be a key tool in understanding the wind response. It is also worth emphasizing that the NAM explains a large fraction of unforced variability in u, as seen in Fig. b: over 50 % in the troposphere and over 75 % in the stratosphere.

To express the zonal wind response to the eruptions in NAM terms, we project Δu onto the NAM index, at each level, and plot this in units of the NAM standard deviation (σ) in Fig. c. Notice that the tropospheric response below 250 hPa is considerably smaller than the stratospheric response: except for the two most extreme cases, the tropospheric wind response is comparable to, or smaller than, the natural variability of the NAM, i.e., the signal-to-noise ratio is less than one. If indeed the Eurasian surface temperature anomalies following the eruption are driven by the stratospheric pathway mechanism via the NAM, they are also unlikely to exceed natural variability, except possibly for the largest injections. This will be carefully analyzed and discussed in the next section.

An alternative way of quantifying the zonal wind response in the context of natural variability is to ask: how many ensemble members are required to establish statistical significance? The answer to this is illustrated in Fig. e and f, where the Nmin values, computed as detailed in Sect. , are shown for winter post-eruption NAM and Δu, respectively. For both quantities, for injections smaller than 20 Tg(S) more than 20 eruptions are typically needed to establish a statistically significant response of the circulation in the troposphere. Thus, an individual event, such as the 1991 Pinatubo eruption, would be unremarkable in terms of its wind response: we remind the reader that, in fact, the polar vortex was anomalously weak – not strong – in winter 1991–1992, in spite of the volcanic aerosols present in the tropical lower stratosphere (see , and the discussion therein). Furthermore, assuming our idealized eruptions are representative of actual eruptions, even a 40 Tg(S) injection – which is more than 30 % larger than the 1815 Tambora injection – would require between 5 and 10 eruptions before a statistically significant signal in the tropospheric circulation at mid-latitudes could be ascertained. It is sobering to realize that there is only one eruption with a stratospheric sulfur injection larger than 40 Tg(S) in the past 2000 years (Samalas, in 1257), and possibly a second one if one reaches back to the past 2500 years (see Table 2 of ).

Lastly, before turning to surface temperatures, we wish to briefly discuss the response of the atmospheric circulation in the second winter after the eruption. There is some confusion on this matter in the literature: earlier studies suggested the presence of a considerable response in the second winter (e.g., ), whereas later studies have agreed that only the first winter should be considered (e.g., ), since there is essentially no memory in the stratosphere to carry the response 18 months after the eruptions, when the bulk of the aerosols are no longer in the stratosphere. To provide further evidence in support of the more recent consensus, we show the time series of the NAM response in our model for 3 whole years after the eruption, at three different levels (10, 100, and 850 hPa) and for all stratospheric injections from 5 to 160 Tg(S). As one can see in Fig. c, at 850 hPa there is no statistically significant NAM response in the second winter after the eruption (except, possibly, for the very largest injection mass) and thus no reason to expect a response in Eurasian surface temperatures, to which we now turn our attention.

The starting point of this discussion is the quantity ΔTs, the surface temperature anomaly, computed using the difference-from-control-run method, in the first post-eruption winter. Its ensemble mean ΔTs‾ , shown in the left column of Fig. , represents the forced response caused by the eruption for each injection amplitude. It is readily seen that for our idealized EVA eruptions, a statistically significant warming response starts to emerge for 20 Tg(S) injections over parts of eastern Eurasia, and covers most of Eurasia for 40 Tg(S) and above. To quantify this more carefully over Eurasia, we start by considering the region 40–70∘ N and 0–150∘ E, for consistency

Due to an unfortunate typographical oversight in both and , the Eurasian region in those studies was stated to comprise the longitudes 0–150∘ W, instead of the obvious 0–150∘ E. We have double-checked the code used in those studies and can confirm that the proper longitudes – i.e., those to the east of the prime meridian – were used in the actual calculations; thus, the results in those studies stand as reported. Unfortunately, also state analyzing a Eurasian region covering longitudes 0–150∘ W in their Fig. 10.

In a nutshell, we have explored the winter response to progressively larger, low-latitude eruptions using a stratosphere-resolving climate model with idealized prescribed volcanic aerosols, and two key results have emerged from our exploration. First, we have confirmed that with a sufficiently large stratospheric injection and with a sufficiently large ensemble size, statistically significant surface warming over Eurasia in the first post-eruption winter can be seen in a climate model, as reported in . Second, and most importantly, we have shown that for injections up to 160 Tg(S), the first post-eruption Eurasian winter warming forced by the volcanic aerosols is sufficiently small as to be indistinguishable from internal variability. With these key findings in mind, we are now ready to address several important issues, and also to place our results in the context of earlier studies and of the observational record.

First, regarding the emergence of a statistically significant post-eruption Eurasian winter warming: the threshold for this – for the idealized EVA aerosols – is 20 Tg(S) in our model, using 20-member ensembles. report the threshold to be at 10 Tg(S) using 100-member ensembles, for the same EVA aerosols. The difference largely resides in the fact that our ensemble size is considerably smaller but, in part, may also be due to model differences. From our model, we estimate that over 64 eruptions are needed for a 10 Tg(S) injection to produce significant warming. While do not report the values of Nmin, the mere fact that more than 60 events are needed speaks to how small the forced volcanic warming signal actually is in these models.

In fact, over the past 2500 years, there are only 33 eruptions with stratospheric injections estimated to be in excess of 10 Tg(S), according to the latest compilation by . Thus, assuming that EVA aerosols are representative of typical eruptions (which may not be the case; see below), and assuming that current-generation models are not lacking in significant aspects relevant to this problem, it is currently impossible to observationally validate this modeling evidence of a weak post-eruption winter warming over Eurasia given the limited eruption record. Focusing on larger eruptions would improve the signal-to-noise ratio, but that effort is similarly futile: for a 40 Tg(S) injection, our model suggests that eight events are needed to establish statistical significance, but only two such events are known to have occurred in the past 2500 years. One could look further back in time, but temperature reconstructions become even more problematic given that we are seeking a winter signal, and most tree-ring-based reconstructions are based largely on summer data (when trees actually grow).

Second, it must be kept in mind that the results in Table 1 apply only to the EVA aerosols, and some evidence suggests that these idealized aerosols at 10 Tg(S) produce more warming than the aerosols used for Pinatubo in the CMIP5 and CMIP6 model runs. For instance, found no statistically significant warming – even with 100 members – for Pinatubo when forced with an earlier aerosol reconstruction , although their model shows significant warming with EVA aerosols at 10 Tg(S). found no significant warming for Pinatubo with a 50-member ensemble of the CanESM2 model forced with CMIP5 volcanic aerosols, and found no surface warming for Krakatau with the 100-member Grand Ensemble . Also, Figs. 3 and 7 of indicate that the optical depth of EVA aerosols for a 9 Tg(S) injection is considerably larger than the one produced for Pinatubo by the Chemistry-Climate Model Initiative (CCMI; ), which formed the basis for the CMIP6 forcing. It is possible, therefore, that the EVA aerosol forcing might be unrealistically large and thus overly favorable to cause Eurasian winter warming, further underscoring our key conclusion.

Third, the reader may wonder if and how our findings might be altered if the eruptions coincided with El Niño or La Niña events. The extant literature is confounding: one study has claimed that El Niño is necessary to produce winter warming over Eurasia , but two earlier studies have reported that the winter warming signal is insensitive to the ENSO phase . Similarly, while some modeling studies have claimed that volcanic eruptions cause El Niño (e.g., ), others have argued that there is little evidence to support that claim (e.g., ; note: one of the referees of this paper insisted that we also cite his own critical views of that study, which can be found in ). The very existence of such contradictory claims in the peer-reviewed literature is a strong indication of a very small signal, at best. In fact, preliminary results from our model show no significant ENSO impacts on winter warming in the Northern Hemisphere, and we plan to report on that in a future paper.

Fourth, we wish to emphasize that modeled winter surface warming reported here, and in , does not validate the early modeling studies that claimed a forced winter warming following the Pinatubo eruption, but actually demonstrates how that warming was spuriously generated by those studies' inadequacies. Just to cite one example: , with an early GISS ModelE version at 4∘ × 5∘ horizontal resolution and with a mere 20 vertical levels, running with prescribed SST, reported a statistically significant winter warming over Eurasia after Pinatubo with a 5-member ensemble. This contrasts with the model used here, with over 100 vertical levels and finer horizontal resolution, which shows no forced Eurasian winter warming from Pinatubo aerosols, nor from the stronger EVA aerosols with 10 Tg(S) injection with a much larger ensemble. One might rebut that 10 years from now we will have even better models and that the conclusions reached here may again be revised. We agree that such a possibility is very real.

In fact, there is little doubt that, beyond model resolution, several aspects of our simulations are ready for improvement. Perhaps the most unrealistic aspect of the modeling setup employed here – which is common to nearly every study on the question of Eurasian post-eruption winter warming – is the fact that our volcanic aerosols are prescribed from an external file and thus inconsistent with the atmospheric circulation and composition. However, we note the existence of major uncertainties in interactive aerosol modeling, which the VolMIP community has labeled “drastic” . Also, whether the dependency of the aerosol optical depth on injection mass as parameterized in the EVA is truly representative of large eruptions remains an unanswered question, owing to the lack of observations. In any event, what emerges from our study, which independently confirms the findings of , is that the early claims of robust Eurasian winter warming for eruptions such as Pinatubo – and even smaller ones, such as the 1982 El Chichón or the 1962 Agung eruptions – simply cannot be reproduced with current-generation climate models: they have consistently failed to show any warming for such historical eruptions, because the signal-to-noise ratio is simply too small.

Fifth, and most importantly, our simulations clearly demonstrate that the signal-to-noise ratio is not only small for eruptions with sulfur injections comparable to those of Pinatubo and Krakatau, roughly 10 Tg(S): the signal-to-noise ratio remains small all the way up to 160 Tg(S). Even with that gigantic forcing, we have found that only 3 out of 20 members produce winter warming anomalies that exceed the 2σ range of the unforced variability in the control run (see the bottom left panel of Fig. ). In addition, if one nonetheless wanted to establish a statistically significant warming signal over Eurasia for 160 Tg(S) eruptions, at least four such events would be needed (see Table 1). Yet, not a single such eruption has occurred in the past 2500 years .

An alternative way to appreciate how the post-eruption response is overwhelmed by the internal variability is the following: let us look again at the 80 Tg(S) case, which is considerably larger than the 1257 Samalas eruption, the largest of the past 2500 years. For such an eruption ΔTs‾​​​​​​​∼1.8 ∘C over Eurasia (see Table 1), and this is very close to 1 standard deviation of the interannual variability, as seen in Fig.  (left column, second to last panel). So, using the 68–95–99.7​​​​​​​ rule for a standard Gaussian, we deduce that 16 % of the time, the winter anomalies in the absence of an eruption, are larger than the mean anomaly following an 80 Tg(S) eruption in our model. This means that over a period of 2500 years we expect 400 winters with an anomalous warming larger than the mean post-eruption warming. This is what we mean when we say that the post-eruption warming – even for eruptions larger than any of the ones known to have occurred over the last 2500 years – would be unremarkable and indistinguishable from internal variability.

Finally, we remind the reader that the new evidence we have presented here for the possible existence of post-eruption Eurasian winter warming comes from climate models. The observational evidence, at this point, is what is clearly lacking, especially when one considers that the models are telling us that many events are needed to separate the forced response from internal variability. As already noted, most of the early observational studies reached unsubstantiated conclusions, and the evidence for a winter warming provided by the most recent, and most comprehensive, observational study is also questionable. First, only 15 eruptions were examined in that study, of which only a handful are larger than Pinatubo or Krakatau. Second, their conclusions were reached by averaging together large and small eruptions, which confounds signal and noise. Third, and most importantly, the largest warming signal was found to occur in the second post-eruption winter, a fact that we find difficult to believe given the evidence presented above (see Fig. ). Fourth, that study was conducted with a single temperature reconstruction and, to date, it has not been independently confirmed with a different reconstruction. Since the models are now in good agreement in showing that the Eurasian warming signal – if it exists at all – is very small at best, more work is needed on the observational side to provide at least some plausible evidence (if not a statistically convincing demonstration) that the post-eruption winter surface warming is not a mere modeling artifact.