We sincerely thank the reviewer for these positive and useful comments.

'I thought that the analysis was well done, and I found compelling. However, I am somewhat confused about the goal of the study..'

The reviewer expressed some uncertainty over the goal of the study. A similar point was also raised by RC2. As such, we propose to add a new discussion in the opening paragraph of our revised manuscript addressing this point and highlighting the value we see in quantifying the impact of Arctic amplification on the timing of breaches in the Paris goals. While we agree that the direction of the impact on timing is a straightforward result, since faster warming in the arctic must cause an earlier breach of temperature limits in our framing, we argue that there is value in quantifying the magnitude of this impact. In part, this is because the traditional framing of Arctic amplification in terms of a ratio of warming rates can be difficult to interpret, especially for those from a climate policy perspective, where the more important question is how Arctic amplification contributes to total global warming.

'I wonder if a more relevant use of the analysis is to argue how the accelerated Arctic warming leads to more rapid changes in the Arctic and even better how this leads to more rapid changes across the population centers of the Northern Hemisphere’

The assessment of the local consequences in the Arctic of it’s rapid warming and links to changes in mid-latitude Northern Hemisphere climate, are both important and large research areas. Although not in the scope of this piece, we propose to add additional reference to these impacts in our discussion. 

'In summary, I thought that this was a well-executed study and that the results are correct.  What I struggle with is the importance of highlighting that Arctic amplification will accelerate crossing the Paris Agreement temperature thresholds that is an obvious and therefore maybe trivial result and conclusion.  And I wonder making a different point with the same analysis..'

The reviewer also raises the question of whether additional analyses might further highlight the implications of our results. Two examples are offered but we feel a third option is more amenable to our methods. We will add a new component to our results in our revised manuscript assessing how the uncertainty in Arctic warming over coming decades impacts the uncertainty in the timing of crossing temperature thresholds. As expected given the faster warming in the Arctic, our calculations show that the region accounts for a larger proportion of the inter-model variability in the timing of crossing temperature thresholds than would be expected based on its size. Using a partial correlation analysis, we estimate that around 15% of the uncertainty in 1.5°C crossing year across the multi-model ensemble under SSP2-4.5 can be attributed to the uncertainty in near-term Arctic warming. 

We thank the reviewer for these detailed and thoughtful comments which have been helpful in improving our manuscript.

The reviewer makes 4 specific recommendations which we now reply to in turn, after which we then respond to several other comments made in the made body of the review.

(1) 'I would like to see the perceived problem better articulated..'

We will rework our opening paragraph in our revised manuscript to highlight the value we see in quantifying the impact of Arctic amplification on the timing of breaches in the Paris goals. This text will also explain that we aim to produce a useful statistic for those interested in Arctic change from a broad range of backgrounds, including those in the climate policy community, for whom the traditional framing of Arctic amplification in terms of a ratio of warming rates can be difficult to interpret. We argue that framing Arctic amplification in terms of its contribution to global warming, and the timing of Paris breaches, provides a more intuitive and therefore impactful quantification of the phenomenon.  

(2) 'The phrasing “X years earlier” could be misleading..'

We agree that the “years earlier” phrasing had the potential to be misleading. As such, we have edited this throughout the paper for our revised version, and in Figure 1, so that we will now refer to the real world (with Arctic amplification) as our base case and then refer to the number of years ‘later’ when crossing occurs under the hypothetical case without Arctic amplification.

For example, our abstract previously read: “Here we reframe this amplified Arctic warming in terms of global climate ambition to show that it causes a breach of the Paris Agreement’s 1.5 °C and 2 °C limits 5 and 8 years earlier, respectively.”

It will now read: “Here we reframe this amplified Arctic warming in terms of global climate ambition to show that without Arctic amplification, the world would breach the Paris Agreement’s 1.5°C and 2°C limits 5 and 8 years later, respectively.”

(3) 'Relatedly, be explicit that the Paris targets refer to (and only to) global mean temperature..'

This is an important point, and will now add an explicit note to this effect at the end of our introduction. We propose to add the following sentence after line 31:

“We also note that our analysis does not imply any change from current estimates in the expected timing of breaching Paris limits, which refer explicitly and only to global mean temperature (UNFCCC. Conference of the Parties (COP), 2015).”

(4) 'Consider reframing the piece (or at least adding some calculations) on the effect of model uncertainty in AA to the projected timing of breaching the Paris targets, as a way to better connect to the call for better modelling of the Arctic.'

This is a useful suggestion, and we have performed the suggested extra analysis and will add it to our results section. As expected given the faster warming in the Arctic, our calculations show that the region accounts for a larger proportion of the inter-model variability in the timing of crossing temperature thresholds than would be expected based on its size. Using a partial correlation analysis to control for the fact that Arctic warming is strongly correlated to warming outside of the Arctic (across the multi-model ensemble), we estimate that around 15% of the uncertainty in 1.5°C crossing year across the multi-model ensemble under SSP2-4.5 can be attributed to the inter-model variation in near-term Arctic warming.

Responses to other comments:

'As soon as you start considering averages excluding the Arctic, it ceases to be a global mean and therefore, has no real bearing on the Paris targets. By excluding the Arctic, you are, in essence, redefining the Paris targets.'

Our analysis does exclude the Arctic, but only so as to model what the global warming would be in a world where the Arctic warms at the global mean rate. As such, our interpretation is that we are always comparing global mean warming in our analysis, it’s just that the method to estimate the ‘global mean warming’ in our hypothetical (and unphysical) world without Arctic amplification uses an average excluding the Arctic.

Although the rationale for the new framing is not well articulated, it appears one motivation is to call for better monitoring and modelling of the Arctic. Whilst I support this goal, it’s not at clear to me that the (arguably small) difference in the timing of reaching 1.5/2 attributed to AA provides the best justification for this.

This is a fair point, and one we will take into account in reworking our discussion. We propose to include a revised version of our final paragraph as below:

“While we have focused here only on the direct impact of Arctic warming on global temperature change, the local impacts should not be overlooked. Under 2°C of global warming, Arctic temperatures are expected to rise by 4°C in the annual mean, and 7°C in winter, with profound consequences for local people and ecosystems (Post et al., 2019). Additionally, amplified Arctic warming contributes to the global challenges that motivated the 1.5°C target, such as sea level rise and permafrost thaw. These local and global impacts are a primary motivation for improving the representation of the Arctic in Earth System Models and for accurate observational monitoring in the region. Our findings offer one additional motivation for such work — that Arctic warming has an outsized influence on both the timing of and uncertainty in projected breaches of the Paris agreement’s temperature limits.”

'Perhaps a clearer way to demonstrate the potential benefits of improved Arctic modelling is to show that uncertainty in AA is related to that in the timing of breaching the Paris goals.  You could attempt to put some numbers on this. Rather than compare cases with and without Arctic amplification, you could compare how the upper and lower bounds of modelled AA translate into differences in the projected timing of breaching the Paris targets.'

The suggested uncertainty analysis will be included in our revised manuscript. In addition to the analysis discussed above, to answer the question posed here we we can also use a multiple linear regression model for crossing year of the 1.5°C threshold under SSP2-4.5 predicted by the (1) near-term Arctic warming rate and (2) near-term warming rate outside the Arctic. Such a model suggests that controlling for warming outside the Arctic, the difference in Arctic warming rate between the 10^th and 90^th percentile models causes a 3 year difference in crossing year. This is larger than difference in crossing years between our low and high emissions scenarios.

Thank you for taking the time to post these insightful and constructive comments, which have been very useful in improving our work. We respond to indivdual apsects of the comment in turn below:

'As you say in the paper, the counter-factual isn't really a world without the feedback mechanisms that drive AA, it's just a weird world where for some reason the Arctic warms at exactly the same rate as the rest of the globe. That's all fine in my head now but I share the feelings of the other reviewers that this result isn't really all that remarkable and I'm finding it a little tough to understand how best to interpret the 'delayed years' concept in light of the very unnatural counterfactual.' 

While we agree that the sign of the effect we present is unsurprising, we think that it would be useful for the community both within polar science and more broadly to have a peer-reviewed estimate of it’s magnitude. Part of the motivation for conducting this analysis was that the traditional framing of Arctic amplification in terms of a ratio of warming rates can have little cut-through with those used to thinking about the climate problem in terms of global mean temperature change and targets. Our framing aims to provide a more readily interpretable quantification of the phenomenon. We will spell out this motivation more clearly in our updated introduction.  

'I think as the reviewers have alluded to, the Paris targets are really focussed around policy responses to prevent certain GMST targets being reached, so the framing around Paris in this paper almost makes it sound like AA is something we could potentially turn off or on, which obviosuly we can't. I think the papers closest to this are the ones that try and isolate the role of say sea ice changes in driving AA/GMST changes, but I dont think i've seen those expressed in terms of delayed years for temp breaches, but the motiovation behind this study is a bit different perhaps.'

Our motivation in linking AA to the Paris targets was simply to find a quantification for the size of AA with which readers will be most familiar. We agree though, that it is important to be absolutley clear that our results do not have any impact on when we expect to cross thresholds, since as you say, we can't control AA. We propose to add a sentence highlighting this at the end of our introduction (see response to RC2). 

'I'm also doubtful of the idea that the analysis shown here presents a compelling case to study the Arctic more beyond what we already knew about the fact it's warming much more than other parts of the world (a concept us polar scientists regularly use in proposals already!).'

This is a fair point and we will make several changes to our discussion to better put in context the implications of our findings for motivative Arctic science. Our proposed updated final paragraph is as follows:

“While we have focused here only on the direct impact of Arctic warming on global temperature change, the local impacts should not be overlooked. Under 2°C of global warming, Arctic temperatures are expected to rise by 4°C in the annual mean, and 7°C in winter, with profound consequences for local people and ecosystems (Post et al., 2019). Additionally, amplified Arctic warming contributes to the global challenges that motivated the 1.5°C target, such as sea level rise and permafrost thaw. These local and global impacts are a primary motivation for improving the representation of the Arctic in Earth System Models and for accurate observational monitoring in the region. Our findings offer one additional motivation for such work — that Arctic warming has an outsized influence on both the timing of and uncertainty in projected breaches of the Paris agreement’s temperature limits.”

'perhaps a clearer demonstration would be assessing how the AA factor changes over time, and the degree to which fixing the current AA factor in future runs would change the expected timing of breaches. Then the question becomes - how does a low or high end AA scenario impact Paris breaches? If that spread is meaningful then i think you could say 'look, we need to study the Arctic more to know what type of AA we are in for and how this might impact Paris breach timings!' '

The suggestion to focus more on how uncertainty in Arctic warming influences uncertainty in crossing of temperature thresholds was also made by RC2, and we agree makes a good addition. As such, we have conducted analysis on this point which we will add to our revised results section. As expected given the faster warming in the Arctic, our calculations show that the region accounts for a larger proportion of the inter-model variability in the timing of crossing temperature thresholds than would be expected based on its size. Using a partial correlation analysis to control for the fact that Arctic warming is strongly correlated to warming outside of the Arctic (across the multi-model ensemble), we estimate that around 15% of the uncertainty in 1.5°C crossing year across the multi-model ensemble under SSP2-4.5 can be attributed to the uncertainty in near-term Arctic warming. We can assess the specificquestion posed, of how different near-term rates of Arctic warming influence the crossing year using multiple linear regression model for crossing year of the 1.5°C threshold. This model suggests that controlling for warming outside the Arctic, the difference in Arctic warming rate between the 10^th and 90^th percentile models causes a 3 year difference in 1.5°C crossing year. This is larger than difference in crossing years between our low and high emissions scenarios. The reason to construct this analysis in terms of Arctic warming rate, rather than the AA, is that decreased warming outside the arctic increases the warming ratio and thus the value of AA. As a result, the AA variable itself doesn’t allow for separating the influence of local Arctic warming versus (correlated) warming outside the Arctic on crossing year in the multi-model ensemble.

'A final little comment, most papers I've seen studying AA use temperatures in the tropics (-30 to 30) as the baseline. I see why you didn't do that but I think it might be worth a comment?'

Thanks for this point. We will add a note that our definition is different to that used in some of the key literature, such as Pithan & Mauritsen (2014), which takes AA to be the ratio of warming North of 60°N to warming 30° S–30° N.

References:

Pithan, F., & Mauritsen, T. (2014). Arctic amplification dominated by temperature feedbacks in contemporary climate models. Nature Geoscience, 7(3), 181–184. https://doi.org/10.1038/ngeo2071

Post, E., Alley, R. B., Christensen, T. R., Macias-Fauria, M., Forbes, B. C., Gooseff, M. N., et al. (2019). The polar regions in a 2°C warmer world. Science Advances, 5(12), eaaw9883. https://doi.org/10.1126/sciadv.aaw9883