This paper presents a lot of work and should be published.  However, there are so many potential sources of error that it seems that definitive conclusions are hard to make.  The paper recommends more study, but it is not clear whether further study will be able to unravel the problems.  Some primary ones are chaos in the climate system, impacts of unknown El Niño and La Niña at the time of the eruption, seasonal timing of the growth cycle of the tree rings vs. the volcanic forcing, the latitude of the eruption, and the subsequent latitudinal transport.  Some of the figures could be made clearer (see below).

The analysis focuses on the UKESM model and summer temperature response, presumably because of tree ring proxy data.  But why not all the other impacts, including El Niño, summer monsoon precipitation, and winter warming?  Still, it would be nice to evaluate the model for these impacts for the modern period, including for surface temperature, so that we can have confidence that the model does a good job in simulating the climate response to volcanic eruptions.

How do you account for the possible presence of La Niña or El Niño at the same time of the volcanic eruptions you are using to compare to the simulation, both in the real world and the model simulations?  For example, we know that the actual 1982 El Chichón response would have been much cooler without the simultaneous El Niño, and that for 1991 Pinatubo it would have been somewhat cooler.   (See Soden, Brian J., Richard T. Wetherald, Georgiy L. Stenchikov, and Alan Robock, 2002:  Global cooling following the eruption of Mt. Pinatubo: A test of climate feedback by water vapor.  Science, 296, 727-730.)  El Niño and La Niña are random in the observational record, but I don’t think you have data on them at the time of the volcanic eruptions.  In models, we have found that the probability of an El Niño the next winter is higher with a tropical eruption, but does the model you used respond this way?

I find the colors of the triangles in Fig. 1 hard to interpret.  Many look the same and the Southern Hemisphere colors are very similar.  I recommend a much wider range of distinct colors, or actually plotting the latitude on the figure using the scale on the right as the axis.  You could then use open circles for the eruptions so as not to hide the other lines.  And please give a scale for the size of circles or triangles.  “Size” is not defined.  Is it width of the symbol, or its area that represents the emissions?  Also the lines for the different data sets are hard to distinguish.  Why are some thinner and some dashed.  Make them thicker and use primary colors – red, green, and blue – to make them distinct.

Why is 1458 Undefined?  I thought it was the accepted date for Kuwae.  Or are you sure Kuwae was 1452? 

How do you know the latitude of the unidentified eruptions?  From the relative depositions in Greenland and Antarctica?  How do you account for varying transport strengths both from random climate variation or forced circulation from the eruptions?

The colors of the lines in Fig. 2 are hard to distinguish.  CESM and IPSL are very similar, and the UKESM colors are similar.  Make them distinct.  The color distinction of the eruption latitude is still a problem, like in Fig. 1.  Plot the latitudes as values in the vertical.

Again, in Fig. 9 all the lines have very similar colors.  Use bright red, green, and blue to distinguish them.

Are you concerned that additional diffuse radiation after volcanic eruptions would enhance tree growth, making what you interpret as pure radiative volcanic signal actually also a signal of diffuse radiation “fertilization?” (See Robock, Alan, 2005:  Cooling following large volcanic eruptions corrected for the effect of diffuse radiation on tree rings.  Geophys. Res. Lett., 32, L06702, doi:10.1029/ 2004GL022116.)  This would lower the tree ring response, making the tree rings an imperfect measure of the temperature.

You mention special treatment of the forcing from the Laki eruption, because we have some observations.  But what climate response did you get from it?  It is a great illustration, at least on a continental scale, that chaotic weather can cause warming over Europe the summer of 1783 rather than the expected cooling.  How do you address this in your interpretations of the responses to the other eruptions?  (See Zambri, Brian, Alan Robock, Michael J. Mills, and Anja Schmidt, 2019b:  Modeling the 1783–1784 Laki eruption in Iceland, Part II: Climate impacts.  J. Geophys. Res. Atmos., 124, 6770-6790, doi:10.1029/2018JD029554.)

Review by Alan Robock

This paper addresses both model-to-model uncertainty and volcanic forcing uncertainty in the last millennium. The paper is well written, presents interesting results regarding both large model and forcing uncertainty and is a nice contribution to the scientific literature. I suggest it is accepted subject to the suggestions below. 

Major comments:

Figure 1: eruption colorscale is hard to distinguish in the purple colours south of the equator, and are the triangles linearly related to the size of the eruption? 

As noted by the authors there is spread among different ensemble members of the same model (e.g. line 398-399). Can the 9 idealised UKESM members be used to estimate the internal variability in each model? Then it would be good to put the model differences in context of the internal variability. I.e. if we consider internal variability how different are the models from each other and from the observations? 

When referring to the differences between a,b, & c in Figure 3 those cited by the authors are really hard to see by eye in the Figure. Are the models really closer together in panel c compared to a? I don't see this by eye. 

It seems CESM is quite different to UKESM . Do you have the data to add CESM to Figure 5 for comparison? I think this would be very useful. 

Minor comments:

Line 62, 'However' does not make sense in this context

Line 110 should near 'now simulate'

Line 315 is this drift or something else? Why is CESM warming?

Line 333 - if CESM does does something different to the other models can you state what it is doing here?

Line 610 - can you put the not shown figure in Supp?

Line 658 - add references for the response of ENSO - there are quite a lot of papers that consider this please cite at least one

Papers to consider: 

https://www.nature.com/articles/s41586-023-06447-0

https://www.nature.com/articles/s41561-019-0400-0