The two referees have looked again at the paper and agree that it has been improved significantly in revision. Referee 2 now recommends publish as and Referee 1 recommends further minor revisions. My view is that implementing Referee 1's recommendations would significantly improve the paper and I therefore ask you to provide a further revised version of the paper, plus responses to Referee 1. If the revision is adequate and the response clear my intention is then to accept the paper without further consulting Referee 1.

You have made some useful changes in this revision, but I still some some points (some raised by Referee 2, some not) that are problematic. Those points are listed below.

Please consider these further and make appropriate revisions or explain why revision is not appropriate. I then hope to be able to accept the paper for publication.

(1) You have generally followed the advice of Referee 2 and used the term ‘vertical wavenumber squared’ for the quantity signed in (1). But you consider to use the term ‘Mean Refractive Index Squared (MRIS)’, e.g. in referring to Figures 2 and 3, but also elsewhere.

I assume that this is a mistake? Please can you confirm that it is and make the necessary correction, or explain.

(2) Figure 8: You say ‘In contrast, planetary waves tend to propagate away
from regions of low values of this quantity.’. But this sounds like reasoning associated with an index of refraction and as Referee 2 has emphasised, what you are considering is not an index of refraction. So surely all that can be said is that planetary waves are likely to be trapped in the vertical when the value of this quantity is small.

(3) Re:

Referee's comment:
L146-149 – I don't see the statement in Hu and Tung (2007) that there should be a discontinuity
in the Rossby wave propagation at the tropopause between 20-40N. What are you referring to
here?
The Authors response:
We do not refer this to Hu and Tung (2002) paper. We only refer to this paper because in this paper the authors have discussed about the importance of subtropical tropopause as gateway
controlling vertical propagating of planetary waves.

But you continue to say “we expect
to see a discontinuity in the Rossby wave propagation as
discussed”. It is not clear to me what this means. Certainly Hu and Tung (2002) do not use the term ‘discontinuity’. In fact one thing that Hu and Tung (2002) do say is: “First, such increases of u_z and u occur only in the subtropics, which is not the main gateway for wave propagation into the stratosphere.” — i.e. they seem to be emphasising the important role of the vertical shear in the extra tropics rather than in the 20-40N region that you mention. So it is also not clear to me that there should be any simple association between the change in sign of the vertical shear in the 20-40N region and change in planetary wave behaviour. My advice is not to make statements unless they are vital to the focus of the paper — and it is not clear that a statement about a ‘discontinuity’ and its relation to change in sign of vertical shear is essential. But I leave you to decide what to do about this.

(4) l271-274: ‘’area’ would clearer as ‘range’, I think. The sentence ‘The upper and lower
limits are referring to the maximum and minimum values
of any variable that fuzzy logics tries to set various MVF
for them.’ — is confusing — there is a problem with the English, amongst other things. Perhaps you mean ‘The upper and lower
limits refer to the maximum and minimum values
of any variable. Within these limits fuzzy logic assigns a Membership Value Function (MVF).’?

(5) Figure 12: You have chosen to stay with the same height range (100-10 hPa) rather than to change to that of Figure 11 (1000-100hPa) - that is your choice. But the statement ‘As Figure 11’ in the caption is then confusing — I suggest you say something like ‘As Figure 11, but restricted to the 100-10hPa range,’

I think that the changes made in the latest revision of the paper are useful and I am pleased to accept the paper for publication in ACP.

The only remaining issue I can see regards comment (2) -- you changed some of the text in the paper but there seems to be a remaining inconsistency regarding
l517 (Section 7) — ‘Smaller values of Pr_Ro (y,z)
demonstrate the places where Rossby waves are absorbed or
reflected from these regions.’ — this still seems to be discussing a refractive index rather than a squared vertical wavenumber. My suggestion is that you make a small adjustment to address this, as a technical correction.