General Comments

In this study, various factors that might explain the underestimation of multidecadal NAO variability in CMIP6 models are examined. The authors find that the representation of NAO-AMV coupling may explain some proportion of intermodel spread in multidecadal NAO variability, but that more of the spread is explained by the spread in multidecadal stratospheric polar vortex variability and stratosphere-troposphere coupling strength.

One overarching comment is that while some figures include a comparison to observed values (Figure 1-3, 5), particularly after the section on the AMV less is included about the observed relationships in relation to NAO-IPV and NAO-SPV. It’s mentioned that the observed relationships are difficult to constrain, and in some cases it’s clear that the value would fall well off the figure, but I think it might be worth including mention of the values in the text or captions (even if it’s for a shorter period of time as in the case of the SPV), just to give some context for whether the models are even in the right ballpark. Or could you use the interannual values of the coupling for at least the NAO-SPV part to at least suggest what the relationship values might be for multidecadal timescales, as alluded to in the text and Figure S5?

Overall though this manuscript is well-written and the conclusions are well supported. The methods were explained clearly. The manuscript will be of interest to WCD readers.  I only have minor suggestions.

Specific Comments

Line 53: By poor observational constraints, do you mean that the record is too short, or that the observations are poor in quality/high in uncertainty? I would specify here, even though it’s explained more later in the paper.

Line 85: It makes sense why the data were regridded for consistency; however was there any sensitivity testing done to ensure this does not significantly affect the results? It may be worth looking at one of the models with higher resolution and comparing how much the metrics change for the original vs regridded data.

Line 119-120: Is this method preferable to say a linear fit of the data or some higher order fit? Did you test the sensitivity to other methods of trend removal?

Line 130, line 139: Here do you mean “20-year running mean”? (is there a sliding window as described for the NAO in the caption of Figure 1?). Otherwise it sounds like one 20-year period but it’s unclear whether they are overlapping or not.

Line 136-139: Here you could just say “To identify SSWs, we use the index of […] between the months of December through March

Line 222: Some of the models though seem like they could be overestimating AMV variability like EC-Earth3 (maybe a box and whiskers could be a way to identify where the obs value falls outside of the ~10^th percentile of each model’s ensemble distribution?).

Line 225: Were the relationships between the NAO variance and some measure of the periodicity of the AMV (Fig S2) considered, in a similar manner to Figure 4?

Line 234: For coupling metrics like the NAO-AMV coupling parameter and later the stratosphere-troposphere coupling parameter, I wonder how sensitive these results are to using correlations instead of regression coefficients? They should be similar of course, but the regression is also related to the spread of the AMV variance (in this case) so the correlation might be simpler to interpret in some ways.

Line 292-293: The sensitivity of the results could also be true though for other results, such as Figure 7b where the removal of the MIROC models (or the two “worst” models in each case) might result in better/worse relationships. I guess I’m not sure it’s “fair” to point that out here only for this part of the paper?

Figure 8b: I didn’t find where this panel is described in the text other than line 295, however that just refers to the stratosphere-troposphere coupling parameter, not the relationship between this parameter and the NAO variance.

Line 334-335: This result is a little counterintuitive, given what is said on line 229. Could you explain more? Does it have to do with these relationships not necessarily explaining the spread across models even though they may explain physical relationships within a single model?

Line 336-337: Alternatively, what about the climatological background wind speeds in the subtropics, as proposed by e.g., Sigmond and Scinocca 2010?

Technical Corrections

Lines 143-144: There were some issues in my pdf rendering at least with symbols in these sentences (there are weird missing “obj” symbols appearing around the references). Also there are no units after “500”

Line 188: add “multidecadal” in front of “NAO”

Line 190: change “seems to be” to “is”

Figure S1: x-axis labels are shifted off the tick marks

Figure 2: Two comments. The first is that the x-axis labels are shifted oddly here and don’t line up with the tick marks. The second is that at least by eye, the lines for 20CRv3 and ERA20C seem to lie higher than the halfway point between 1.0-1.5 tickmarks on the y-axis, but according to Figure 1c they should both lie at 1.15.

Figure S2: here the time period of 1900-2014 is mentioned though most of the other figures use 1900-2010. Is it possible to include the spectra for the observed datasets here? Or not really since these are ensemble-mean estimates of the forced response?

Line 206: change to “simulated AMV variance.”

Line 237: change “is toward the lower end” to “on the more negative end”

Line 333: remove url link

Figure 9a: typo in x-axis label

Line 368: remove “do”

The manuscript assesses multidecadal variability of the winter North Atlantic Oscillation (NAO) using historical simulations from 15 different climate models, each with at least 10 members. It is found that NAO variance is underestimated by models and potential causes are investigated. It is shown that NAO variance correlates significantly across the models with both the variance of the stratospheric polar vortex (SPV) and the coupling between the SPV and the NAO. Though causality cannot be identified, together these two factors explain 70% of the inter model spread in NAO variance. Furthermore, the coupling between the SPV and the NAO appears to be related to a measure of atmospheric eddy feedback. The authors also investigate other relationships finding no link to the Pacific, and a weaker though significant link to Atlantic Multidecadal Variability but only by processing in a way that precludes comparison with observations.

The manuscript is well written and the results are interesting. I recommend publication after addressing the minor comments below.

Table 1: A minor point but I believe there are 50 ensemble members for MIROC6, or are the data you need not available?

Lines 143-144 Eddy feedback parameter: looks like something is missing here?

Lines 158-159: please explain how serial correlation in the timeseries is accounted for

Fig 2: the model labels don't seem to match up with the dots - at least in my version

Fig S2: looks like not all of the models are included here?

Fig 5a: is the ensemble mean the average of the regressions for the individual ensemble members, or is it the regression between the ensemble means of the NAO and AMV? I think it is the former (this needs clarifying) but the latter would be highlight forced responses and might also be interesting (though not so easy to compare with observations).

Fig 5b: if I am reading it correctly it looks like the strongest observed regressions occur with AMV leading NAO? If so, I wonder how that relates to previous work suggesting AMV can be explained by the integrated NAO e.g. https://journals.ametsoc.org/view/journals/clim/32/22/jcli-d-19-0177.1.xml

Fig S3: the caption is a bit confusing. Presumably this is the average of the values for each ensemble member, since the ensemble mean has been removed?

Line 359: the values given in fig 9b appear to be different, r=0.52 p=0.05

Discussion: I presume that constraining the NAO variance (lines 393-394) is beyond the scope of this study, though it would enhance it if it could be done.

Discussion: Fig 5b appears to show further evidence of errors in all models. Perhaps a brief discussion of potential causes and implications could be included.