The manuscript presents an analysis of archived model data that participated in the PMIP project.  The authors propose the Laurentide ice sheet  resutled in more stretching of the polar vortex (PV), which contributed to colder and more variable temperatures in eastern North America south of the ice sheet.

It is my impression that the authors are not that familiar enough with stratosphere-troposphere coupling and polar vortex variability to adequately interpret their model analysis of stratosphere-troposphere coupling.  Scientists well versed on stratosphere-troposphere coupling would not make the omission mentioned in my first minor comment.  A stretched polar vortex was first described in Cohen et al. 2021 and that paper and Kretschmer et al. 2018, at a minimum need to be read carefully and cited.  But there are many other recent papers that should be included.

I aso think the authors chose poorly when they analyzed CESM-FV2 and ignored CESM2-WACCM-FV2.  WACCM was designed with improved simulation of troposphere-stratosphere coupling.  Whether the goal was achieved is still an open question but if at all possible the authors should include analysis of CESM2-WACCM-FV2 in their study.

I found the paragraph describing polar vortex variability during Arctic amplification, LGM and PI starting on line 161 as conflating of different ideas.  The authors state contradicting ideas that the polar vortex strengthens both in LGM when the climate was colder and during the present period of Arctic warming when the climate is warmer.  Also the ideas presented in Thompson et al. 2000, I would argue have not aged well with time.  They argued that increasing GHGs would strengthen annular modes in both the troposphere and stratosphere, neither of which has been observed in the quarter of a century since that work was published.  Also strengthening planetary waves should weaken the polar vortex not strengthen it.

The paragraph starting on line 197 describes the Laurentide ice sheets amplifying wave energy that leads to PV stretching.  PV stretching over North Ameirca is mainly trigerred by upward wave energy over Asia that is reflected downward over North America not by local upward wave energy. So what the authors are presenting is a novel idea of PV stretching that has no support from the scientific literature.  In a future version of the manuscript the authors need to show three dimensional wave activity flux in the LGM experiments to understand changes in wave reflection and stretched PVs in the LGM compared to PI or even in the ERA5 reanalysis.

Colder temperatures in the atmospheric column will lower geopotential heights in the stratosphere.  Therefore much colder tropospheric air temperatures over the Laurentide ice sheet can lower geopotential heights in the polar stratosphere in the same region giving the appearance of a stretched PV over North America. However the cold temperatures over North America are not related to or caused by PV variability.  This is not what the authors in the manuscript are discussing but this scenario needs to be excluded for the reason for colder temperatures over North America in the analysis.

I have some more minor suggested edits below.  I cannot recommend that the manuscript be published in its current form.  The authors need to familiarize themselves better with the scientific literature on PV variability in general and stretched PVs in particular.  With a better understanding of stratosphere-troposphere coupling, their interpretation of the analysis will be consistent with up to date thinking on PV variability.

Minor comments:

1. Line 37 – there are two types of polar vortex (PV) disruptions or weakenings, one where it splits as described in this sentence but also where the PV can be displaced away from the North Pole while remaining intact or in one piece.
2. Line 66 – what is actually meant by “polar amplification?” Currently the term is most commonly used to describe amplified polar or Arctic warming which is contradicted by the beginning of the sentence that states “cooling at high latitudes.”
3. Table 1 – I couldn’t find Table 1? Did the authors mean Table S1?
4. Lines 90-91 – it is my understanding that WACCM has a better resolved stratosphere than other versions of CESM2 and it is not just a chemistry model. On the NCAR web page it states that CESM2-WACCM-FV2 has 70 vertical layers and not 32 levels as in CESM2-FV2 with a much higher lid than 2.25 hPa as in CESM2-FV2.  If I am correct then the authors should not have discarded WACMM in their analysis.
5. Figure 1 – I really had a hard time reading this figure. I had to greatly blow up the figure to see the contour lines. Also the caption says that the red, black and blue lines represent the ERA5, yet they vary from plot to plot, how is that?

References:

Kretschmer, J. Cohen, V. Matthias, J. Runge and D. Coumou,. 2018b: The different stratospheric influences on cold extremes in northern Eurasia and North America, npj Climate and Atmospheric Science, doi: 10.1038/s41612-018-0054-4.

Cohen, J., L. Agel, M. Barlow, C. I. Garfinkel, I. White. 2021: Linking Arctic variability and change with extreme winter weather in the US, Science, 373 (6559), 1116–1121, DOI: 10.1126/science.abi9167.

 General comments

The observation data and numerical modelling have suggested that the Arctic stratospheric polar vortex (SPV) is playing role in inter-seasonal variability and predictability of the winter climate over Eurasia and North America. By analysing PV changes in the PMIP paleo-simulations, the author explored the PV changes and its influences on climate variability during the glacial climate. The results show that under LGM conditions, the PV stretched toward the Laurentide ice sheet increased the possibility of cold air outbreaks into mid-latitudes. This finding provides an explanation to the observed extreme winter cooling and long-stand inter-model spreads. The paper is well-written. I recommended to published it with the following minor revision.

Comments to authors:

Line 10: The abbreviation of polar vortex PV could be confused with PV of potential vorticity, suggested change to SPV.

Line 18: should be “was beyond…”

Line 86: Table 1 was not included. Should be Table S1?

Line 102: Present AWI-ESM resolution in the form of grid numbers, like for the other models.

Lines 122-132: add unit of gpm to VSI? like -1000 gpm and 70 gpm

Line140: Further specify that ERA5 is shown in black line. For instance, “This overall pattern fits the ERA5 re-analysis data, as shown by the similar shape of 250 gpm contour (black line in Fig. 1).

Line 172-174: “…previous climate models results found that the stratospheric polar vortex itself can be either colder or stronger with increasing GHG depends on the strengthen amplitude of the troposphere originated planetary waves (Baldwin et al., 2003). The expression is not very clear, please clarify.

Line 211：“warm-cold-warm-cold pattern” sound weird, do you mean dipole between mid- and high latitudes?

Figure 3: add confident level to the figure.

Add a figure to illustrate how PV different between the LGM and PI affect the climate.

Calculating wave activity fluxes by focusing on the North American to Eurasian cross section to analyze stratosphere-troposphere interactions?