I asked the two referees to comment on the revised version of your paper. One referee required more than the standard amount of time, and I agreed to this in view of the fact that the revisions you made were significant and also that a large amount of time had elapsed since the original contribution to the paper.

When I requested comments from the referees I emphasised that a paper containing negative results could be valuable -- if the work was clearly presented.

One referee has responded that the paper that the paper should now be accepted, but gave no reasoning at all to support that. The other takes the view that the paper is clearer, but that it is still difficult to find the important points and to find any connection between the scientific questions posed and the results obtained and recommends rejection.

I have looked carefully at the paper myself and I have listed several detailed comments below. My inclination is to agree with the critical referee that there continue to be many aspects of the paper that are unclear and, notwithstanding the principle that a paper can be a valuable contribution even if it contains only 'negative' results, it still seems to me that the paper falls short of providing a clear presentation of a set of interesting numerical simulations that will be a genuine help to others who are planning this sort of work.

Therefore my overall conclusion is that the paper is not yet suitable for publication. I am willing to consider a further revised version, but I do ask you to consider carefully the comments of the referee and my own comments which are set out below.
To be honest, I think that the paper would be much clearer if you focused much more on a clear description of the simulations and what exactly could be deduced from them -- perhaps with some discussion of how the simulations might be modified further to resolve some of the questions that are currently unresolved.

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I have covered several points in my detailed comments below, but I have highlighted two that are of particular concern.

One is that the paper does not seem to take account of important contributions to the recent literature. I have highlighted a couple of very recent review articles, but another seeming omission concerns your comments in l411-420 about the difficulty of maintaining a relevant basic state when certain physical processes are omitted. The paper by Ma and Kuang (2016) also discusses this point and my impression from that paper is that investigation of the MJO via omission of selected physical processes has been used previously in several cases. So whilst you may have good reason to believe that your approach is a significant advance on previous work, you need to explain why.

A second is the reliance on detailed comparison between time-longitude or time-latitude plots. Your point that comparison on the basis of gross measures such as the RMM index may be valid, but if the reader is to have confidence in the sort of comparison you make and the conclusions then you draw then the presentation needs to be as clear as possible -- for one thing, if patterns are to be compared then it is far better it they appear as individual panels of the same Figure -- I would say that it better even if it requires some repetition. (Though I am not convinced that it does require repetition in your case.) You might also consider whether it is absolutely essential to present all cases -- e.g. in Figure 6 is it really essential to present 8 cases, particularly given that these are all individual realisations and therefore it must always be uncertain whether effects of different perturbations to physics are robust.

DETAILED COMMENTS

Abstract

l3: You give the motivation here as seeking support for the 'free wave' theory -- but you don't say directly that no support is found.

l4-5: 'The reduction in friction tends to improve the MJO forecasts, but hardly in any additive manner.' -- actually it is quite difficult to see any systematic improvement -- you see improvement by some measure in one or two cases. It would be more honest to say something like -- 'no systematic improvement is found'. -- something like what you have said in l75-76.

Main text

l15: 'a pre-existing MJO' -- I think that you mean that an early stage MJO event is in the initial conditions and that a successful forecast captures the subsequent development and propagation of that MJO.

l16: 'especially in' (no comma)

l21: "or 'physics' for short"

l24: 'Plant and Yano' according to your reference list.

l24-25: It seems very surprising that you do not refer to recent review articles here such as Zhang et al (2020) who provide a critical survey of theories for the MJO. Of course you may think that the Zhang et al (2020) survey is inadequate, but potentially such a review is far more helpful for a reader who wants to understand this than a long list of historical references -- some of which, I believe, are not now regarded as providing viable theories. Another recent review is that of Xiang et al (2020) -- again in looking at those aspects of the MJO that are not yet understood it seems important to exploit these reviews as far as possible (and to note their specific shortcomings if that is appropriate) rather than keep on regenerating a selected of historical references.

l39: 'dissipations' > 'dissipation'

l40: 'A classical work by Chang (1977) makes this point by invoking surface friction as a mechanism to slow down the propagation speed ...' -- this may be important as an early paper but is this really now seen as a viable mechanism given much greater understanding of convectively coupled waves in general and the active role of moisture in the MJO in particular?.


l45: 'When physical forcings are switched off from a model, an alternative mechanism for generating MJOs must also be considered.' I found this a puzzling sentence. Are you saying that the 'free Rossby wave dynamics' theory REQUIRES extratropical forcing to initiate events -- i.e. this is an important part of the theory? In which case it would be clearer to explain this along with the theory -- e.g. l30-35 -- rather than adding it later as a detail of the implementation of the perturbed physics.

l49: Note that there is a paper by Hall et al (2016) that may go rather further than some of these other papers in testing the idea that extratropical forcing

l57: It wasn't clear to me how you addressed Q2. None of your experiments seem specifically designed to address Q2 and you don't seem to provide any compelling evidence for the relevance, or irrelevance, of an incident Rossby wave train. (See also Comment 6 of the Referee.)

Table 1: 2 should be 'OFF selected for total physical tendency', I think.

l67: As noted previously, this seems a very indirect approach to question 2 as you have defined it -- because it may affect the dynamics/physics of the MJO as a tropical phenomena as well as affecting possible extratropical interactions which are the subject of Q2. Perhaps Q2 needs reformulating.

l90: 'and it is likely also model specific' -- it is difficult to see this as a finding of your investigation -- which is what this sentence appears to be about -- it might be true, but you haven't found it.

l103: My understanding is that the purpose of the revised paper is to set out the results of some sensitivity studies, so that other researchers may benefit from your experience. Your original motivation in starting this work was to provide support for the 'free Rossby wave' but that was not successful. I think readers will be confused by your regular reference to this idea -- e.g. here it is being used to justify why a particular field -- the 150hPa stream function -- is being confused. It would be better to described the 'free Rossby wave theory' clearly early in the paper, explaining why particular fields such as the stream function might be relevant to it, and then to avoid using it as justification for the approach being taken until the discussion/conclusions section of the paper. Note that many other authors, not motivated by a 'free Rossby wave theory' have chosen the upper tropospheric stream function, or something similar, as a useful diagnostics -- e.g. Virts and Wallace (2014 JAS and references therein).

l119: You are now introducing the idea of nonlinear modons into what you have previously described as a 'free Rossby wave theory'. Again, as noted above, it would be much clearer to explain this theory carefully early in the paper and avoid making continued reference to it (in ways that evolve as the paper proceeds).

l122: 'These propagating structures' means the OLR on the one hand and the streamfunction on the other. 'not quite in phase' is a bit misleading -- the structures look very different (which is not to say that they are not both useful indicators of the MJO) and it is difficult to see that the differences are described simply by a phase difference. It doesn't seem very helpful to know a numerical value for a pattern correlation -- particular given that all the other pattern correlations that you show are between the same fields (but comparing e.g. observations and forecast).

l130: 'evincing' -- means indicating, 'equivalent to' might be better -- but one could also ask 'higher effective resolution that what'.

l134: for water substance' -- omit 'the'.

l136: 'the MJO event of concern'? 'the MJO event to be considered'.

l140-141: 'how can we improve them', 'in the introduction'

l144-147: There are two key questions mentioned here -- explain how they relate to each other.

l175-180: It is rather confusing to have a section titled 'Vorticity field' when in fact you never show the vorticity field. The point about lower tropospheric rotational flow being more difficult to interpret has already been made at the beginning of 2.1 -- the presentation seems disorganised.

l185: You emphasise here that very specific descriptions of the forecast behaviour will be presented -- but that basically means that you make comparisons on the basis of time-longitude plots and -- typically -- you focus on some features of these plots as significant and ignore others. Anything you can do to help the reader to follow all this would be valuable. For example. why not include the relevant observations plot in each figure where it is to be compared to forecasts. (You have done that in one or two cases.) It is probably more valuable to show panels (c)-(f) of Figure 1 in Figures where they can be used for comparison -- in Figure 1 you are essentially showing some information three times.


l195-205: Each of the parts of Figure 2 contains several lines -- they are thin and difficult to make out (even when magnified). The reader needs to be given more help in order to assess this Figures -- lines could be thicker, there could be labelling on the Figure relating colour of lines to particular experiment etc. You say that Figure 2(a) contains results from high-resolution runs and that these are not considered further in the paper -- so why not omit them -- that would help the reader focus on what is important.

l206-213: Notwithstanding your stated intention to discuss detailed evolution, the RMM analyses and figures are potentially very valuable in helping the reader to obtain a clear picture. You note here that the phase space trajectories for the analysis for the two forecast periods are not consistent because the anomalies are being defined with respect to different periods -- I suppose that is also the reason why the starting point for the different forecasts -- which are all started with the same initial conditions presumably -- is not the same. This makes it very difficult to interpret these plots as a measure of forecast skill. For example later (l258-260) you say that the forecast skill recovers towards the end of the forecast period -- that is certainly not obvious from the trajectory in the RMM plot. Would there not be advantages to making the RMM plots consistent -- i.e. choose fixed patterns defined by the observations to define the RMM coordinates -- then use those consistently for all forecast? This would potentially clarify statements such as l271-272 where it is claimed that the Ma forecast is better than the control cased.


l224: 'the model simulates those interactions features rather well' -- the significance of this statement is difficult to assess given that the purpose of the paper is surely not to assess the quality of the forecast per se but to assess how the quality of the forecast depends on including or excluding different physics.

l269: 'apparently in support of a free nonlinear-wave theory' -- my opinion is that statements like this potentially confuse the reader. There are other examples later but I won't list them all.

l402: 'failure of emulating the free dynamics ... maintaining a realistic mean state as detailed further below' -- this does not seem to be a new conclusion -- e.g. see Ma and Kuang (2016), which you have not cited.

l421: These conclusions regarding initial conditions -- longer forecasts from an earlier phase may not be harder than a shorter one from a later phase, etc, are interesting but these conclusions are based on a single limited period. Therefore can any useful conclusion really be drawn from your work?

l441: 'The present study has also elucidated active interactions of MJOs with higher-latitude Rossby wave activities.' The results you show in Figure 9 are of course interesting but it seems difficult to make any systematic conclusions from this limited set of experiments. It wasn't clear to me what evidence was being used for some of your statements -- for example is the 'westward dispersion of the original dipole' visible in this Figure? Is the statement 'Overall, forecasts of these interactions are found to be rather robust and less sensitive ...' based on evidence presented here, or is it based on more general experience?

Nicholas M. J. Hall, Séverin Thibaut, Patrick Marchesiello, Impact of the observed extratropics on climatological simulations of the MJO in a tropical channel model, Climate Dynamics, 10.1007/s00382-016-3221-5, 48, 7-8, (2541-2555), (2016)

Ma, D., and Z. Kuang (2016), A mechanism-denial study
on the Madden-Julian Oscillation with reduced interference
from mean state changes, Geophys. Res. Lett., 43, 2989–2997,
doi:10.1002/2016GL067702.

Jiang, X., Adames, Á. F., Kim, D.,Maloney, E. D., Lin, H., Ki m, H., et al.(2020). Fifty years of research on theMaddenJulian Oscillation: Recentprogress, challenges, and perspectives.Journal of Geophysical Research:Atmospheres, 125, e2019JD030911.https://doi.org/10.1029/2019JD030911

Zhang, C., Adames, Á. F., Khouider, B., Wang, B., & Yang, D. (2020). Four theories of the Madden‐Julian Oscillation. Reviews of Geophysics, 58, e2019RG000685. https://doi.org/ 10.1029/2019RG000685

The authors have made useful revision to the previous version of the paper and I feel that further iterations are unlikely to be productive. It is over to researchers in the field to read the paper and decide for themselves whether or not it is making a useful contribution.

I am therefore pleased to accept the paper subject to further minor revisions as specified below. Please provide very brief responses to those that you prefer not to address.

l53: 'modellings' > 'modelling'

l58: 'tail off poleward of ca. 20 deg'

l67: 'ascend' > 'ascent'

l88-93: Personally I felt this point ('unique in modelling studies') was overstated. It might make the present study different from that of the two studies cited, but there have certainly been other studies where selective parts of a process have been eliminated -- e.g. Crueger and Stevens (2015, JAMES) have eliminated cloud-radiation effects, but not all radiative effects.

l106: Most papers include at this point a very brief outline of the structure. Certainly when I was reading the introduction -- which is quite long and covers several different topics -- I was thinking 'when are sufficient details of the model going to hbe given so that the work is reproducible'. So being told in advance that details of the model are going to be given in Section 2.2 would be helpful. Other readers might have been wondering about other points. My suggestion is to re-order material in Sections 1 and 2 to give three sections, one introduction and rationale, one on model (including details of sensitivity experiments -- i.e. Table 2) and one on choice of forecast cases. But at the very least please include a brief outline of structure somewhere in Section 1.

l113-116: 'according to the theory' > 'according to the free Rossby wave theory' (so that readers don't get the impression that all MJO theories require penetration of the vortex structure through the whole troposphere).

l118-125: It would be clearer if in identifying these events you added some kind of explicit indication of them to Fig 1. You could also note explicitly that active convection is indicated by blue in the OLR Figures and that white is simply saturation of the (negative) colour scale.

Figure 1: One disadvantage of this and many other Figures is that about half of the area shown (e.g. 200E to 40E) is completely irrelevant to the discussion. Please give information on units, also repeat explicitly that for the streamfunction is the latitudinal average of the NH value and minus the SH value.

l125: 'over December-January' > 'during December-January'

l128: 'as expected from the nonlinear free-Rossby wave theory' -- but the anticyclonic vortex pair surely appears in many MJO theories -- as an upper-level 'Matsuno-Gill' pattern resulting from an eastward propagating heating. The difference between theories (in my understanding) is the role of this upper level vortex pair -- vital part of the MJO mechanism or a passive consequence of an MJO arising from other processes.

l144: 'The MJO events ...' -- confusing because you have previously said 'cover one of the two most prominent events'.

Table 2: Again it would be helpful to give a little more explicit information in the caption -- i.e. 'standard [DATES], extended [DATES]'

l355: 3.5 title -- I suggest 'intrusion of an extratropical Rossby wave train' -- because you have at some point in the previous text referred to a possible equatorial Rossby wave.

l440-448: This idea that the forecast in the extended case might be better than in the standard case -- i.e. the forecast with the earlier initial condition is better is a bit confusing when you also point out that the westward-propagating cloud cluster than re-excites the MJO in the extended forecast appeared to die out in the observations -- so we seem to be in a 'better forecast for the wrong reasons' situation.

General comment [not essential to give response to this]: You mention initial condition sensitivities at various points -- doesn't such sensitivity that drawing conclusions on the systematic role of different physical processes from study of a single case with specified initial conditions is rather difficult?

I accept the paper in its current form for publication in ACP.