The manuscript presents a quantitative and mechanistic analysis of mean-sea-level-pressure precursor patterns observed before sudden stratospheric warmings, comparing results between ERA5 and ICON model simulations. One important contribution of the study is therefore to demonstrate the potential of ICON for studying stratosphere-troposphere coupling and for seasonal forecasting in general. It is noteworthy that the results indicate anomalous surface weather to be present for up to three months after the precursor patterns first occur.  Additionally, the relatively large sample size obtained from the model simulations allows the authors to resolve the results for different months, indicating the need for careful interpretation when composites are based on events from an entire winter season.

However, parts of the mechanistic explanations were unconvincing to me in the current form. A discussion of how the applied localized wave activity analyses relate to planetary wave diagnostics would be beneficial (please see my comments below).

Overall, I found the paper well-written and interesting to read. Therefore, I recommend that the paper be published once the major concerns are addressed.

Major comment 1:

You have demonstrated that a strong positive difference of MSLP over the Ural region and the Pacific region, which is defined as the "precursor index", is followed by "significant tropospheric NAM signals for up to 3 months after the original anomaly in the precursor index" (ll. 184f). I agree that this is remarkable and that it can likely represent an important source of predictability for seasonal forecasting.

However, it would be beneficial to address or discuss the potential role of any confounding processes. Specifically, it would be worthwhile to explore whether ENSO teleconnections could project on both the identified precursor regions, particularly over the Pacific, and anomalies of the polar vortex.

Major comment 2:

I have some concerns about the Plumb flux analysis in the second part of the study. It would be helpful if the authors provided more information on the formulation used for the vertical Plumb flux and referenced previous successful applications.

Unlike the Eliassen-Palm flux (divergence), I am unaware of how localized Plumb flux theoretically relates to changes in the zonal mean flow, which could be discussed more in detail (e.g., see ll. 234f: "The connection between wave activity in 100 hPa and the stratospheric polar vortex is not as straightforward as one might expect, as increased Plumb flux does not necessarily imply a weakening of the stratospheric polar vortex.").



I wonder if the presented precursor geopotential anomalies in Figure 1 might reflect anomalous planetary wave activity, given their projection on the climatological wave-1. An intensified wave-2 pattern could possibly explain why anomalies are larger over the Ural region than over the Pacific, potentially questioning if it were in fact two distinct mechanisms that relate the observed precursor signals over the Ural and over the Pacific to the stratospheric anomalies.



In addition, I have two suggestions regarding the Plumb flux analyses. First, providing typical orders of magnitude for the Plumb flux and its variability in Figure 5 would be helpful in interpreting the observed anomalies of up to 0.02 m^2/s^2. Second, providing typical correlation coefficients associated with the plotted regression coefficients in Fig. 6 may aid in interpreting the amount of co-variability.

Minor comments:

• ll. 39-41: maybe you could be a bit more clear about what you mean by "not predictable beyond deterministic timescales"; (e.g., in the provided reference, Karpechko 2018 concludes that "[...] days 8–12 before the events, the SSWs can be considered predictable in a probabilistic sense. After day 7 the predictability can be considered to be close to deterministic.")
• ll. 77: Have you tested using only winters where you have both ICON simulations and ERA5 data available (1979/80 to 2016/17)? Alternatively, you may want to add a small comment why you think this is not necessary.
• ll 86-89: You may want to consider stating which spatial domain was used to calculate the EOFs, if the data was area-weighted for the calculation of the EOFs and how ERA5 and ICON data was deseasonalized.
• Fig. 1: I'm unsure about what you mean by "Composites  of [...] MSLP [...] for the same January weak vortex events in ERA5 and ICON". If I'm correct then events in ERA5 and ICON are basically independent (sorry for my ignorance if not)?
• Fig. 2: The presented composites are based on a strongly negative January-mean NAM. Given the relatively long timescales in the stratosphere, I would imagine that in some cases, the negative NAM in January results from a SSW that happened already in December. In that case, part of the surface signal observed in December could in principle correspond already to a surface response of the SSW. In case you agree, you could consider adding a comment. However, I see that it is not strictly necessary as you will address the time lag between tropospheric precursor and stratospheric anomaly more in detail in Fig. 2.
• ll. 130: A two-sample significance test could provide additional confirmation that the observed differences between ERA5 and ICON are explainable by sampling.
• Fig. 2: I expect "@ 100hPa" to be wrong.
• Fig. 2: Is it surprising that ICON shows significant regression coefficients even after 60 days and longer? (How much longer?)
• Fig. 4: How many events are shown in each composite?
• ll. 181-182: Is this because the precursor pattern directly projects onto the NAM or is it because the precursor pattern connects with a polar vortex anomaly which then leads to an altered NAM  index?
• Fig. 6: Maybe you want to add "at 100 hPa" after meridional mean Plumb flux.
• Fig. 7: Only the 10% largest absolute correlation coefficients are shown. What is the obtained threshold for the correlation coefficient?
• l. 287: "and/or": this might be beyond the scope of your study, but I imagine it would be indeed interesting to understand whether the combined pattern emerges from the composite averaging or really occurs combined during individual events
• l. 307: "Vertical planetary wave fluxes do not explain the link between extended Aleutian MSLP and the stratospheric NAM. Here it is a pattern that resembles the two main centers of action of the PNA which directly penetrates into the stratosphere.": Fig. 8c does show a clear displacement, i.e., a wave 1 signal in the stratosphere and to my understanding, Fig. 8b does not exclude the possibility that anomalous wave 1 activity is also present in the troposphere, even if strongly induced via the PNA. It would be useful if you could clarify/ discuss this when considering my major comment 2.
• General comment: To my understanding, (quasi-)observed SSTs are prescribed in the simulations. To what extent do you think does this need to be considered when interpreting the good agreement between ERA5 and ICON results?

review of "How do different pathways connect the stratospheric polar vortex to

its tropospheric precursors?"

This paper revisits the role of a strengthened  Ural high and Aleutian low for variability of the NH polar vortex. In agreement with previous work, the authors find that a Ural high and an Aleutian low leads to a weaker vortex. The more novel aspects of this paper are: 1) inclusion of ICON results; 2) a focus on daily timescales to better isolate the relevant timescales; 3) a discussion of which calendar month the response peaks. Finally, the authors include a discussion of mechanisms, but as discussed below I find this discussion to be limited and problematic. Major revisions are needed before I can give a final assessment of the quality of this paper/

Major comments:

1. As discussed above, I don't find the mechanism part of this paper convincing. The authors use Plumb 1985 fluxes which were derived explicitly for stationary waves, and apply this method for time varying waves! There are better fluxes available (Plumb 1986, or even better Takaya and Nakamura 2001) that are more appropriate for the application. Hence any conclusions reached using a unsuitable formulation should be treated with caution.

Further, they appear to ignore the previously proposed mechanism. As discussed in Garfinkel et al 2010 (already cited) and Smith and Kushner 2012 (not cited) among many others, transients that are in phase with the climatological wave-1 or wave-2 field enhance it, and via constructive interference lead to an overall increase in wave-driving. It just so happens that a transient Ural high and Aleutian low are in phase with the stationary waves, and hence enhance it. The importance of wave-1 and wave-2 arises specifially because higher wavenumbers cannot propagate vertically in the presence of strong zonal wind (Charney and Drazin 1961). Do the authors think this mechanism is wrong? unimportant? They cite Garfinkel et al 2010 and Bao et al 2017, and so I assume they are aware of it. This mechanism was found to be important for the stratospheric polar vortex response to a range of external forcings, as discussed in detail in Smith and Kushner (see references therein) and dozens since that have cited Garfinkel et al 2010 and Smith and Kushner.

That the authors appear to ignore the previous proposed mechanism is particularly grating due to statements along the likes of "there is only a very vague understanding of the localised coupling mechanisms and involved timescales, in particular when it comes to connecting tropospheric precursor patterns to the strength of the stratospheric polar vortex. " (line 3)  or "pressure anomalies in the North Pacific region, has received less attention in literature focusing on precursor patterns of SSWs" (line 53). These two statements are just plain incorrect.

2. Why should the trop->strat coupling differ from early winter to late winter? Why would ICON have too weak coupling? These questions should be answered in the revised paper (assuming these differences across months and between data sources are statistically signififcant). 

It is not clear to this reviewer how Plumb fluxes would help answer this question. In contrast, the stationary waves in the different calendar months or different data sources will differ, and hence the heat flux anomaly for a given strengthed height or MSLP anomaly will differ (Watt-Meyer and Kushner 2015).

minor comments:

line 38 the most recent multi-model and multi-SSW assessment of SSW predictability is by Chwat et al 2022 

xlabel of figure 2: MSLP is not at 100hPa.

line 145 "conceptual" seems an odd word to choose here

line 260: you would need to look at the zonal component of the Plumb flux to better relate the zonal position of anomalies in the troposphere with that in the stratosphere, though as discussed above I don't find Plumb fluxes useful. An alternate plot would be something similar to figure 2 of Ineson and Scaife 2009, but created for a range of lags.

Smith, K.L. and Kushner, P.J., 2012. Linear interference and the initiation of extratropical stratosphere‐troposphere interactions. Journal of Geophysical Research: Atmospheres, 117(D13).

Watt-Meyer, Oliver, and Paul J. Kushner. "The role of standing waves in driving persistent anomalies of upward wave activity flux." Journal of Climate 28, no. 24 (2015): 9941-9954.

Chwat, Dvir, Chaim I. Garfinkel, Wen Chen, and Jian Rao. "Which Sudden Stratospheric Warming Events Are Most Predictable?." Journal of Geophysical Research: Atmospheres 127, no. 18 (2022): e2022JD037521.

Plumb, R.A., 1986. Three-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of the time—mean flow. Journal of Atmospheric Sciences, 43(16), pp.1657-1678.

Plumb, R.A., 1986. Three-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of the time—mean flow. Journal of Atmospheric Sciences, 43(16), pp.1657-1678.

Ineson, S, and A. A. Scaife. "The role of the stratosphere in the European climate response to El Niño." Nature Geoscience 2, no. 1 (2009): 32-36.

Takaya, K., & Nakamura, H. (2001). A formulation of a phase-independent wave-activity flux for stationary and migratory quasigeostrophic eddies on a zonally varying basic flow. Journal of the Atmospheric Sciences, 58(6), 608-627.