The paper reports on a case study of Borneo vortex that affected Vietnam and Thailand. Simulations of the vortex with the UM are analysed conventionally and with a semi-geotriptic code. This code is used to partition the vertical motion into that forced by latent heating, geostrophic forcing and friction. The study concludes that the case examined comprised a mid-level diabatic Rossby wave and presumably a Rossby edge wave on the lower boundary, part of which developed into the Borneo vortex. These counter-propagating Rossby waves temporarily affected each other, but did not phase lock. The conclusions are supported very nicely with some idealised theory for diabatic Rossby waves.

I enjoyed reading the paper and recommend that it is accepted. The paper makes a strong contribution to the field. In my view, the insights from the semi-geotriptic code and the application of some diabatic Rossby wave theory are the most novel and important contributions. I have only one major comment, but quite a few minor comments.

Major comment

The semi-geotriptic tools is an important part of the study and appears to be very effective. Although the basic idea of making a semi-geostophic and Ekman balance approximation is qualitatively easy to imagine the details are not. Given the theory is not well known, the code not widely used, and the semi-geotriptic tool of central importance to the paper, I feel the paper requires a clearer, expanded summary of the semi-geotriptic tool. 

Minor comments

Line 8. “comprised of” should be “comprises”.

Line 13. Should be “… is in quadrature …”.

Line 121. “… with reduced air-sea drag at high wind speeds.” What’s the point you’re making here? It sounds like this is change would be of real significance to tropical vortices. Expand.

Line 128. Perhaps spell out explicitly what the geostrophic momentum approximation is (advection by the full wind but the advected momentum approximated by its geostrophic value.) This approximation is familiar to those working in the midlatitudes, but possibly not so familiar to tropical researchers.

Line 135. This sentence is a bit cryptic. Explain exactly what you mean by “… can be deduced from the pressure field using the notion of “balanced dynamics”. The details matter.

Line 145. Sentence structure problem. “… , with geostrophic and diabatic forcing.” What about the geostrophic and diabatic forcing?

Line 149. What’s the “convexity condition”? Is the condition that the equation is elliptic? Is it related to the sign of the PV as in midlatitude semigeostrophic theory? Spell out what you mean.

Line 149-150. “This discrepancy is particularly the case near the equator. Therefore, the data passed to the SGT tool has reduced horizontal resolution.” Why “therefore”? How does the second sentence follow from the first?

Line 159. What’s the difference between the “full meridional wind” and the “total meridional wind”? How are they defined? This is an example of where the SGT tool is not sufficiently well explained for the reader to comfortably follow the arguments in the paper.

Line 165. “… the SGT tool mostly captures the large-scale flow …”. “Mostly” is a bit subjective. Could you make this statement more quantitative? Perhaps calculate the pattern correlation or something similar.

Line 171. What is the “unbalanced residual”? It isn’t defined. I can probably guess, but it needs to be clearly defined. This is another example of the SGT tool not being properly explained. I don’t think the reader should have to shift though the original paper to find these definitions.

Line 172. True, the SGT tool partitions the flow into a diabatic part and a geostrophic forcing, but there’s no assessment of how accurate or meaningful the association with diabatic and geostrophic forcing is. So, I’m unconvinced by the statement “Figure 2 demonstrates the ability of the SGT tool to partition the 3D ageostrophic flow …”.

Figure 3. Define the white circle in the figure caption.

Figure 3. It appears to me the only one panel is needed. What do the other two panels really add to the story?

Figures 4 and 5. Mark the vortex center on these plots.

Figures 4 and 5. There are 8 panels in total, which seems too many to me given we don’t learn much from them. We learn only that the vortex propagates to the west (which we learn again in Figs. 7-9) and that the N768 MetUM accumulated rain field is too smooth. I’d delete one of these figures.

Lines 233-234. Either expand on these recent developments or delete the sentence. As it is now the sentence doesn’t convey much.

Figures 7 – 9, panel b. Why plot potential temperature? It isn’t referenced anywhere in the text.

Line 254. Grammatical error: “comprised of”.

Line 276. Why is it important that the “moist stability gradient occurs with the region of large-scale vertical shear”?

Line 279 – 28 . Panels 11a (diabatic heating in the global MetUM) and 11b (w from the MetUM diagnosed with the SGT tool) are similar. Then the paper says that this “shows that the region of ascent identified by the SGT tool are representative of the flow in the MetUM”. I don’t understand what’s meant here by “are representative of the flow”. Wouldn’t this claim require you to compare w from the MetUM against that diagnosed with the SGT tool, which is Fig. 11b?

Lines 291 – 292. “The wave is large amplitude in the sense that it is obvious in the velocity vectors of the full flow”. I don’t think you can simply claim that it’s obvious – it needs some quantification. What makes it obviously large amplitude?

Figure 12. Point out that panels c and d are the same as Figs. 1a and 1b.

Lines 295 – 296. The shift is very slight. Is it more than a grid space or two? Some how significant is this shift really?

Line 304. “Also” and “too” mean the same thing. Delete one.

Line 307. Expression problem: “… this choice … is chosen …”.

Line 328. “oth” should presumably be “both”.

Lines 336 – 338. Punctuation problems that affect the meaning. Insert comma after first “that”. Insert comma after “precisely”. Delete second “that”. Insert comma after “flow”.

Lines 364 and 485. What does “home-base” mean exactly? Don’t make the reader wade through the references.

Lines 416 – 417. The effects of gradients in the basic state PV have been omitted in the calculation of the phase speeds. I think there needs to be some assessment of the plausible size of these terms and how their omission affects the calculation. These are potentially large terms.

Line 458. ‘… varies more quickly in the vertical than vertical velocity does at some “moist stability interface” … ‘. What exactly does this mean? What is the mathematical expression? And why is the moist stability interface in quotes? What additional idea are you trying to convey?

Line 462. “ … where G … schematically represents …”. What does “schematically represents” mean, especially in the context of a mathematical expression?

Lines 483 and 484. The notation c_1^2 is a bit misleading as the 2 doesn’t mean the phase speed is squared. Perhaps c_12 would be better. Likewise, c_21 might be better than c_2^1.

The paper performed case studies of Borneo Vortices (BV) using multiple sources of data, including satellite imagery and the MetUM experiments combined with an SGT scheme. The paper is interesting to read and is valuable for understanding the dynamical mechanism behind the extreme BV as such a high-impact system is not well understood and not adequately studied. However, I suggest the authors carefully check whether the key information of the experiment designs has been provided. Particularly, information on the experiment types of the used MetUM experiments is missing and should be supplemented. Major Revision is suggested. Specific comments are as follows:

1. Section 2.2: The authors state that the SGT scheme is coupled with the MetUM model to simulate the geostrophic wind components. Could you clarify whether the SGT scheme applied in this paper is run offline or online and why? Also, please specify what variables the SGT scheme produces and which the paper has used. Does it just extract the geostrophic components from the winds? Why can't it be driven by any existent numerical products like reanalysis data? This information needs more clarity as the readers may doubt why the MetUM is necessary for such a study. 
2. The reasons for the use of the MetUM are not clear in the abstract and the methodology section. Please clarify.
3. Lines 10-16: The description of the physical processes needs more information, i.e. what are the dominant/secondary factors?
4. Figure 11: One of the critical perspectives of the decomposition of the geostrophic/ageostrophic winds is to examine the role of atmosphere-topography interaction while this is not sufficiently discussed in the paper.
5. Figure 1a, c, e: Seems there is a pronounced southward extension of the mid-latitude high-pressure surge across the upstream of BV. Many studies have discussed the importance of such a synoptic signal to the occurrences of BVs, while such signals are not well discussed in this paper. The authors are suggested to show more information about the upstream, particularly the location of the southward extending Siberian High (or Mongolian High in mainland China) that has been considered an essential source of wave-propagation. Analyses of the geostrophic/geostrophic components of the high-pressure will also be interesting.
6. Figure 1, 7-10: For the vertical profile of BVs, it is suggested to use storm-relative coordinates instead of geographical coordinates.
7. All figures: I suggest the authors show and discuss the full lifetime track of the selected BV case and the central point (eye) corresponding to the time step focused. 
8. All figures: Analyses of flows at different time steps are and it is difficult to find which time step corresponds to the developing/mature/weakening stage of BV. I suggest the authors supplement why these time steps are selected in the figure captions and the corresponding descriptions. 
9. Line 187: Please clarify why the TRACK-based dataset based on ERA5 is not used.
10. Section 2.1 and Figure 6: The purpose of comparing the global simulation with the limited-area simulation is not clear. Please clarify in the methodology section. Please also clarify whether the global simulation provides LBCs to the limited-area simulation.
11. Section 2.1: Please clarify the types of the used MetUM simulations. Are they historical analyses or forecast experiments?

Recommended reference:

Liang, J., J. L. Catto, M. K. Hawcroft, M. L. Tan, K. I. Hodges, and J. M. Haywood, 2023: Borneo Vortices in a warmer climate. npj Clim. Atmos. Sci., 6, 1–8, https://doi.org/10.1038/s41612-023-00326-1.

Pang, B., and R. Lu, 2017: The identification of Borneo vortex and its synoptic features in boreal winter. 19th EGU General Assembly, EGU2017, Vol. 19 of, Vienna, 2457–2457 https://ui.adsabs.harvard.edu/abs/2017EGUGA..19.2457P/abstract.