This work addresses an important problem in atmospheric dynamics, namely the dynamical processes underlying the formation of the baroclinic zone, as diagnosed by the slope of isentropic surfaces. A new pespective is introduced by looking at the slope evolution in phase space. It is found that the upper and the lower troposphere exhibit very distinct (in some sense opposite) dynamics for the slope evolution.

My own work also looks at phase space dynamics of the storm track and it will be no surprise that I find this approach of great interest. However, the manuscript left me wondering in the end, what the real conclusion was regarding the role of diabatic effects in slope dynamics. The writing is somewhat evasive and vague at many points so it is hard to interpret what the authors are actually saying.

I would imagine that a more clearer layout of the arguments at those points should clarify sufficiently what was specifically meant. Below I comment on the manuscript in order of line number, not in order of importance.

l.12: "... rendering the phasing ..."; did you mean something like "... suggesting that this phasing is ..."; I also assume that "phasing" actually means the order in which processes occur; perhaps that would be a clearer and simpler way of putting it?

l.88 Presumably you meant "d\theta/\dz < 10^{-4}..." not "> 10^{-4}"

l.92:"... does not affect our analysis as we exclude land grid points." Given that the cold air for the all-important cold air outbreaks is sourced on the land, it seems to me that it is strange to exclude land points: as a local tendency it is perhaps not important, but as a source of required air masses it is. How is that reflected in your equations or your analysis? It seems to me that the anomalously high diabatic cooling over land is absolutely crucial in providing a source of the gradient in the baroclinic zone.

Fig 1: Perhaps label the figures which are free troposphere and which are lower troposphere?

Also: you use the word "hatching" in this figure and figure 9, but you actually show a stippling. (I thought I'd check the dictionary on my computer, just to be sure. This is the entry: "hatching | ˈhatʃɪŋ | noun [mass noun] (in fine art and technical drawing) shading with closely drawn parallel lines: the miniaturist's use of hatching and stippling.")

l.132: "... mainly due to orographic effects advected ..." I do not know what the process is that you are describing. Please be specific what you actually mean. How does orography swap the sign of these effects, and how does this advection work?

Fig.2: Looking at the lower panel, it would be of interest to add a third line indicating "DIAB + TILT"; it is after all the lack of compensation between those two terms that provides the tendency for the slope. In that respect, could you please comment, perhaps somewhere around l. 135, whether the IADV term is smaller than the DIAB + TILT combination? If DIAB and TILT are largely compensating each other then their individual magnitudes do not matter that much. It seems to me that the mismatch between DIAB and TILT is the crucial variable. (Of course, the phase space analysis is diagnosing that mismatch in detail.)

Fig.3: This is a crucial figure, but it is also very dense and hard to read. Some separate comments:

• It feels more natural to me to put the free troposphere images at the top. I do not see any problem with describing the bottom plots first, Sn. 5.1, then the top plots, Sn 5.2.

   

• Could you add a couple of arrows, perhaps to Figs 3a and 3e, to indicate the direction of flow?
• Could you add a 1-1 line (or rather a line with slope -1) to indicate the line in phase space where TILT and DIAB exactly compensate and will not contribute to slope tendency. In this sense, phases (i) and (iii) are defined by the maximum distance from this line, and perhaps phases (ii) and (iv) need to be defined as lying exactly on this line.

l.176-179: I found this a very confusing bit. Are you describing your phase space portraits or are you actually speculating on mechanisms? What do you mean by “driving”: a description of what happens in the figures, or some causal mechanism? If a physical mechanism, you would need to be more specific: what processes are actually happening? If describing the figure, perhaps use a different word to "driving". Perhaps "leading"?

l.182: "...driving storm development": DIAB is a tendency for isentropic slopes, not for storm development.

l.200: Just a personal comment regarding style which, obviously, you may completely ignore. This paper is not easy to follow because of all the shorthand notation: TILT DIAB IADV KOE GSE ENP ENA TCWV CAO, …Please consider writing this stuff out in the text: there is no gain in shortening it, and it is a real pain to follow the text when using all this shorthand. I know it is a device used by many authors, but I believe that a paper should be as easy as possible to follow; Mike Mcintyre would agree with me on that. Do you really want readers to be trying to decipher what a CAO over the KOE is?

l.204: "TILT follows the advancing cold air front, while DIAB intensifies further upstream.":  It really would help if you explained these things a bit more specifically: why/how does TILT "follow" the advancing cold air? It is often not clear whether you are trying to describe the plots or to explain the plots. Could a schematic help?

And I remain somewhat puzzled: if "TILT follows the advancing cold air front" would this then not be manifested in the IADV term? I probably misinterpret the physical processes underlying these two terms, but it surely is an indication that it is not obvious what you are actually saying here.

l.218: "... the suppression of cyclonic activity, consistent with a weaker slope.": I am not sure what you are saying here: a weaker slope corresponds to reduced baroclinic growth. This is not obviously the same as saying that a suppressed cyclonic activity is consistent with a weaker slope. What do you mean with “suppression” anyway? Perhaps you simply meant “represent the anomalously low cyclonic activity…”?

l.245: What is the purpose of the hyphens around "phases" Are they the opposing phases of the Rossby wave or not? (I think they are.)

l.246: "... constitute a defining feature ..." : I do not know what this means. Can you be more specific? In what sense is it a “defining” feature? With this phrase it certainly doesn't sound like you managed to add physical understanding to the role of diabatic effects in the evolution of the strom track, which is probably underselling the results presented.

l.262: "... of moisture availability":  Moisture availability seems to imply that DIAB is a moisture limited process. Do you have evidence for that, or do you mean something else?

l.272: "neither": Double negative; it needs to be "either".

l.273: "... actually condition DIAB and TILT": what do you mean with the verb "condition"?

l.275: " driving": “Driving” or “leading” (as in “leading in time”)? Driving seems to imply a causal effect; if so, you need to explain how this causality works. The rest of the sentence seems to just describe the figure, but I think you developed a much clearer physical picture of why DIAB leads TILT in this case.

l.279-281 "...  suggesting that DIAB in the free troposphere is a distinctive aspect of the evolution of storm tracks, while the development and progression of anomalies in the composites for the near-surface are more contingent to the specific spatial domain considered.":  There are many words here, but it is not obvious what is actually said. Most people would agree, without any hesitation, that diabatic effects play an important part in the evolution of storm tracks (I am not sure what a “distinct aspect” is --distinct from what?). I also do not understand the final part of this very long sentence. What are you trying to say?

To conclude, after reading this, it is not obvious what the main take-home message is of the paper. I think it is the distinct dynamics between the two altitudes. My take on it is that TILT and DIAB mostly compensate on average, but at lower levels TILT leads DIAB due to the low level cold air advection being followed by sensible heat fluxes, while at higher levels DIAB leads TILT because the forced latent heat release produces some counteracting secondary circulation. Perhaps I misread the gist of the paper, but I think that it should be more clearly laid out what this take-home message is.

This study combines a quantitative assessment of the main contributors in the tendency equation of isentropic slopes with a phase space analysis that is able to shed light on the joint temporal evolution of these factors. While both methods have been applied before, there combination yields novel insights into the temporal behavior of storm tracks, making this paper a valuable contribution to the literature that also fits well in the scope of Weather and Climate Dynamics. However, I think that there are still some weaknesses in the presentation of the results that I'd ask the authors to address before I can recommend the paper for publication. On the one hand, these are related to a somewhat superficial description of details in the figures, leading to a few unclear points listed below. On the other hand, at some places (in my view in particular in section 5), the general conclusions obtained from the analyses are not articulated clearly enough, as also noted by the other reviewer.

Specific comments (in the order they appear in the manuscript):

- Line 58: Is there a reason why you still use the old ERA-Interim reanalysis instead of ERA5, which has been out for a few years now?

- Equation 2, line 85: This is more a conceptual (and also minor) point, but is it really the material derivative of S that you're aiming at, or rather the local tendency at a specific grid point (e.g., in your composite analysis)? Of course, this would not change your analysis at all, but it would rather mean that you neglect the ADV term in equation 16 of Papritz and Spengler (2015) than the IADV term in your equation 2, right?

- L 90: "over the western boundary currents": This is true for the Pacific, but not for the Atlantic

- L 105-106: As the regions of strong surface heat fluxes and high occurrence of CAOs are almost identical, it seems a bit arbitrary/suggestive to associate one with DIAB and the other one with TILT. I'd suggest to change the wording a bit to leave this more open.

- L 118: "despite weaker slope": Is it really weaker in the Atlantic?

- L 145: I'd suggest to use a different symbol for the velocity in phase space, as u already denotes the wind velocity in equation 2, which confused me in the first place.

- L 167: "slightly shorter cycles": This is only true for the western boxes; for the eastern ones, cycles are actually longer in the free troposphere.

- L 172: "increases both with DIAB and TILT": As it is larger for more negative TILT, this statement is technically not correct.

- L 174: "peaks in the lower-left quadrant": I can see this only for ENP.

- L 189-190: I find this sentence quite unclear. If the time reference does not correspond to the typical duration, what does it measure at all?

- L 201: "dominated by TILT": This is not really clear from the figure; the red regions (corresponding to DIAB) are even larger.

- L 205: "intensifies further upstream": Again, not really obvious to me. There is a lot of overlap and no clear spatial shift.

- L 208-209: Now I'm totally confused. There are more blue regions (corresponding to TILT) downstream, hence I'd write this sentence the other way around.

- L 213-214: TILT also prevails in the regions of the boundary currents.

- L 215: "anticyclonic geopotential anomalies start building up": not so much in the Pacific, at least at this stage

- Section 5.1: The more general conclusions from this section are not clear to me. I got a bit lost in the details, which, in addition, are not always consistent between text and figures (as noted above).

- L 225: "particularly in correspondence with the upper-level anomalies": Again not that obvious; e.g., in 7a DIAB is clearly shifted towards the lower-level anomaly.

- Section 5.2: Again, the general conclusions could come out more clearly. Most of the corresponding statements are quite generic (diabatic processes are important for midlatitude waves, L 246; primary importance of latent heat release in the diabatic restoration, L 256; role of moist diabatic processes in the evolution of cyclones, L 263) and already quite well known from previous studies (also from your own group...). What are really the new aspects from this analysis?

- L 277: "DIAB takes place ahead of storm activity, both in time and space": I'm not sure that this conclusion is justified. For instance, over the North Atlantic (Figs. 7a,c; 8a,c), both cyclonic anomalies and DIAB develop in parallel, and spatially quite well aligned.

- Figure 5: Should the caption read "below -15... for TILT"? Also, 15 seems to be quite high for DIAB when compared to Fig. 3; is this really correct? Indicate in the caption what the numbers on the sides of the plots indicate (mean DIAB/TILT).