Ayarzagüena et al. investigate how the stratospheric background state influences upward wave activity preceding Sudden Stratospheric Warmings (SSWs). Using ensembles of different models from the Stratospheric Nudging And Predictable Surface Impacts (SNAPSI) project, the study compares free-running, stratosphere-nudged and control simulations to ERA5 for three events: the February 2018 boreal SSW, the January 2019 boreal SSW, and the September 2019 austral minor SSW. The study aims to isolate the effect of the stratospheric state on the triggers of SSWs. Overall the paper provides a detailed study of the processes and wave fluxes that go into contributing to the different SSWs and attempts to separate tropospheric and stratospheric influences. The paper itself is rather long but the analysis is thorough and the authors walk the reader through the plots and their interpretation.  I would recommend publication after addressing the points below.

1) Figure 1 and Table 3. I have difficulty reconciling the fact that the ensemble mean line for CNRM in Fig 1(a) doesn’t show an SSW but 62% of the ensemble members do. Do you have a suitable plot to illustrate the spread please?

2) Figure 5 to 7: I think all the subplots should use the same colorbar within each figure. For ERA5, am I right in thinking that this is a difference from climatology whilst for the models it is a difference between the strongest and weakest ensemble members? As such I would expect that the model composite differences shown are larger than if you were able to do a comparison to the free running climatology of each model (like for ERA5). I would like to see a more careful discussion of what is being shown in these figures around line 320. Whilst there are similarities between the patterns in some models and ERA5, the strength is much weaker in all cases.

3) Figure 9: would it be helpful to add the multimodal mean?

4) Refractive index. The authors acknowledge around line 715 that the resonant growth is likely non-linear. It is my view that since the refractive index is derived from linear theory, it has serious limitations in how it can be applied and I would prefer if Fig 12 and 13 and associated discussion were omitted. 

5) The authors mention gravity wave drag as a source of uncertainty in models and as being important for triggering wave resonance. Have you looked at this in the SNAPSI models?

6) Line 745: I do not think interactive chemistry plays a role in the onset of SSWs but does later in the year. All the time periods analysed are in polar night.

Minor comments:

A general comment here is that the typesetting of the maths could be improved. For example, subscripts are used for both the z and \phi components of F and for partial derivatives.

Equation (1): Bold F for vector here and across manuscript.

Equations (1.1) and (1.2): \overline{\theta}_z rather than \overline{\theta_z}

Line 190: Define z. Also de-italicize ‘and \theta’.

Equation (2) actually comes from Kushner and Polvani (2004) Eq (7). The way they present it is much easier to read. 

Equation (4): Definition of q. Which PV? Quasi-geostrophic?

Table 3

- First column. Consider using the event names introduced in Table 2.

- Second row: 2018 should be 2019. 

- Third row. Maybe round 47.5% to 48% for consistency.

Supplementary figures S2 to S4 are far too small. 

References:

Kushner, P. J., and L. M. Polvani, 2004: Stratosphere–Troposphere Coupling in a Relatively Simple AGCM: The Role of Eddies. J. Climate, 17, 629–639, https://doi.org/10.1175/1520-0442(2004)017<0629:SCIARS>2.0.CO;2.

Please see the comment attached.

This study investigates the perfomance of 7 subseasonal-to-seaonal (S2S) forecast models in simulating 3 distint SSW events (2 in the NH and one in the SH). Moreover, it investigates the role of the stratosphere in triggering the Sudden Stratospheric Warmings (SSWs) in free-running simulations and two nudging setups where the stratosphere is either nudged to observations or climatology. The authors find that for some SSWs, the stratosphere plays a major role in modifying the stratospheric wave flux, but results seem to be very event-dependent. The paper is well written and results are presented clearly. The question posed is novel, since previous research has mainly focused on tropospheric drivers of SSWs. The paper is, however, very technical and I have some minor suggestions that migth improve readabilty.  I recommend publication after the comments below have been addressed.

General comments:

• Given that the main motiviation of the study is the improvement of predictability of SSWs, I think there is insufficient discussion on if and how the results presented help towards improving S2S forecasts, especially given that the mechanism/role of the stratopshere seems to be very event-dependent

• Especially section 5 is very technical and would benefit from a clear summary of the most important pints at the end of the section. It might even be shortened a bit to bring the main points across more clearly.

Detailed comments:

• It is unclear to me how the boxes in Figs. 5-7 are derived. Please add a more detailed explanation of this. I think it would help to add the box also to the ERA5 panel.

• Lines 375 ff.: I am not sure whether I understand how the Z500 anomalies are combined. In the text, it says “… by computing the sum of averaged anomalies for centers with positive anomalies or positive-minus-negative…”. In the latter case, are you substracting the absolute mean value of the negative anomaly?

• Figure 8: Two models have almost same color (CESM2-CAM6 and NAVGEM). I suggest changing colors for better visibility.

• Lines 446 ff.: In CNRM, not only an INCREASE in eddy heat flux at 100 hPa (Fig. 9a) is seen in NUDGED in the SSW 2018, but also a DECREASE in HF100 in this model in the SSW 2019 (Fig, 9b). Why? This should be discussed. The same tendencies can be seen in GLOBO and UKMO in the SSW 2019.

• Figure 10: Although the multi-model mean shows no difference between nudged and control, in many models there seem to be significant changes, but they do not agree on the sign (especially in the SSW2019 SH). I think it would be worth investigating/discussing this in more detail, as 5 out of 7 models show clear differences between nudged and control in Z500 impact for the SSW2019 SH.

• Lines 538 ff: I suggest changing the y-label in Fig. 12 to hPa instead of Pa to be consistent with the text. I also suggest marking the areas discussed in the text in Fig. 12 (e.g. 10-3 hPS). Otherwise the discussion surrounding this figure is hard to follow.

• Lines 549 ff.: Again, it is difficult to follow the discussion here. Which “shift towards the pole”? Again, marking the corresponding areas in Fig. 12 would improve readability of this part.

• Line 601: what is meant by “misrepresentation of the zonally symmetric stratospheric state in models”?