This work is one of the very few attempts to understand and characterize the sequence of events leading to circulation—manifested as the cooling or warming of very deep water—in thermobaric, deep freshwater lakes using a simplified 1D model. The philosophy behind using this simplified 1D approach is to isolate the effects of thermobaricity and cabbeling, rather than focusing on wind-driven energy input or the complex hydrodynamics associated with realistic 2D or 3D bathymetry. That being said, the model successfully identified how the variation of the temperature of maximum density (Tmd) with depth under significant pressure alone (thermobaricity) can drive mixing in a deep lake. The model was applied to a deep, cold Japanese caldera lake (Lake Shikotsu), where the hydrodynamics are believed to be predominantly vertical. It also demonstrates how using potential density at the surface may lead to completely different results compared to using stability criteria.

• The abstract would benefit from additional concluding sentences that elaborate on the key outcomes of the model, particularly the main physical features identified.

• A clear distinction between thermobaric instability, thermobaricity, and cabbeling is needed, as these concepts are often confused. This clarification should be addressed consistently throughout the manuscript, including the conclusion. It would also be valuable to highlight that, in this case, cabbeling appears to result from eddy diffusion across Tmd at different depths—a particularly novel observation that, to my knowledge, has not been previously reported. As I understand it, this process involves the diffusion between a parcel of water already at a warmer temperature of maximum density (Tmd) and colder water, ultimately producing water at a lower Tmd. This mechanism deserves emphasis given its potential implications for deep mixing processes and how is it compared with “thermobaric instability”.

• There has been brief but noteworthy scientific debates regarding the appropriate criteria for evaluating stability, which merit mention. For instance, Georg Wüst (1932) and V. W. Ekman (1934) discussed the use of potential density—specifically, surface-referenced potential density—as a means of assessing stability. However, it is important to clarify that potential density referenced to an intermediate depth has since been recognized as a more reliable indicator. This approach closely resembles what is being applied here, but at a common depth corresponding to the lower parcel, and is supported by studies including Peeters et al. (1996), which also deserves mention. Finally, when considering which density measure to adopt, it may be useful to briefly reference the concept of quasi-density and explain why it has been excluded from the present analysis to contribute to the ongoing knowledge on the topic! It is very satisfying to see a comparison done with potential density at the surface, which I also believe one of the novel parts of this work.

• Why is the stability criterion being expressed in terms of density rather than simply using potential temperature, especially since salinity is excluded? (Gill, 1982; Imboden and Wüest, 1995). This approach might avoid the complications of selecting an appropriate density reference. On that note, as mentioned in your manuscript (line 202), in-situ density is largely dominated by pressure, and there has been a brief scientific debate on the validity of using in-situ density for stability evaluation (A.H. Lee and G.K. Rodgers, 1972; Thomas Osborn and Paul LeBlond, 1974), ultimately ruling out its use. I believe what you are referring to in this publication is potential density at a common reference depth (at the lower parcel depth, not at the surface), which is conceptually like using an intermediate depth. It is not in-situ density, otherwise potential density at the surface is also in-situ density but the in-situ density at P2=0.  An important consideration is what happens when this comparison crosses the Tmd line, as this transition is critical in our case: the compensation depth, which is defined relative to Tmd, governs the overall flow structure. Also, I believe more justification is needed for the choice of evaluating density using the speed of sound (which is not measured, or maybe you have measurements not mentioned?), rather than the TEOS-10 approach utilizing potential temperature and salinity? As mentioned, it is mentioned that TEOS-10 “which includes the effect” compared to potential density, but still, potential density “at the surface”.

• I think it is worth defining the compensation depth. You later refer (line 71) to the intersection of the temperature profile with Tmd, which could be described as the compensation depth. It may help with clarity to introduce and use this term consistently throughout the manuscript.

• It is mentioned that the temperature profile remains isothermal throughout. Is this monitored using thermistors or a CTD, and what is the measurement accuracy of this isothermal profile? For example, is the variability within 0.1 °C or 0.5 °C? Clarifying this would help assess the significance of the observed isothermal conditions compared to the observed cooling/warming of the bottom water and also compare with other lakes. Additionally, where is the surface water temperature (model forcing) measured, and at what exact depth? In other lakes I believe it is usually at least 3-5 m deep in the surface mixed layer (I mean the shallowest thermistor).

• Can you provide a specific analysis or statistic isolating how much of the observed changes are driven by diffusion leading to “cabbeling” or “thermobaricity”? Additionally, how would changing the diffusion coefficient affect the overall process, since it seems like the main driver? It is also unclear how the surface layer remains stable while convection occurs just beneath it that is (I believe) driven by cabbeling induced through diffusion? Clarifying this mechanism would help improve the physical interpretation.

• Why are some profiles perfectly following Tmd, and are they considered stable according to the used stability criterion? Because I would think that maybe again turbulent diffusion perturbations might deem these profiles unstable. That would be interesting to think about.

• I think you need to clarify more the particular use of ±0.4 °C for different climate scenarios, the selection of a three-year spin-up period, and the chosen value for the diffusion coefficient. Also, the method of mixing during the 1hour time step, is it sweeping downwards? When does the algorithm stop?

• The discussion needs more comparison with previous studies especially with the closest model (Piccolroaz 1D model in 2013).

Specific notes:

Line 60: “Admittedly” I am confused from the structure of this sentence, what is being admitted?

Line 76: Potential density “at the surface “. I think it is worth stating this whenever mentioned.

Line 105: So, this is the oscillation frequency using potential density at a common depth, not using in-situ density as it appears. Because in-situ means in its place, but you are evaluating both at P2, so it is confusing. Using actual in-situ density gradient to evaluate N² would give a misleading sign as it is always dominated by pressure, hence again it is worth noting that this is not the in-situ density gradient, but the potential density or the density at a common reference that is the lower parcel depth.

Thermobaric circulation in deep freshwater lake by Marks et. al.

In this work, the authors undertake a numerical process study to demonstrate the effects of a thermobaric circulation in a cylindrical domain. This domain is inspired by Lake Shikoku, which has been previously observed to undergo thermobaric circulation. The authors employ a 1D column model to explore the vertical transport of heat over several simulated years. The main crux of the argument is that by considering the in-situ density (as opposed to the potential density which excludes thermobaric effects a priori), the authors identify the process by which thermobaric effects effectively mix the water column. Overall, I thought this article was put together well, and interesting. I have a few concerns, however, that should be addressed prior to publication.

Main points

• I am certainly empathetic to the process study approach utilized by the authors, and I’m happy to read work that uses an idealized approach to learn about different process in isolation. I am, however, wondering about the relative importance of thermobaric effects to other, potentially more vigorous, dynamical effects, especially those ignored in this study. I think a discussion on this topic by the authors would help the framing of the work.
• Related to the above point, on line 111, the authors comment “this kind of deep water renewal is suspected to have a significant influence in this lake”, and I’m wondering if they could clarify if they think this based on the observational data, or for some other reason, such as the depth.
• While I was reading this work, I kept asking myself “What is the specific thing that thermobaricity is doing that’s different”? It wasn’t until I read section 3.5 that things (sort of) cleared up for me, though I’m still not quite sure. 
  • In my opinion, the argument the authors try to make could be strengthened by first using section 3.5 as a straw man, and then discussing the new results (i.e. the results WITH thermobaricity). I think the authors even have their conclusions laid out this way already. Related to this, I encourage the authors to add a picture similar to figure 4, but for the “non-thermobaric” case. I think that would strengthen their argument for “what thermobaricity does”.
  • I sort of understand what the authors are getting at in the “Convective Mixing” section, but I think some sort of schematic explaining the convective cell detached from the surface looks like, or maybe an arrow placed on figure 4(b) describing what they mean. (This would certainly aid in my understanding).

Minor Points

There are typos in a few places (eg lines 73, 77, 112, 118, and a few more). Please carefully check the manuscript

Line 36: Can the authors clarify what they mean? This sentence beginning with “Ultimately…” is confusing and I’m not sure what the authors mean.

Can the authors provide a little more info on how they arrived at equation (6). It’s not so clear to me, but I think they’ve taken the derivative of rho_pot (rearranged from equation (3)), and then made the approximation that rho_pot \approximation rho_in-situ in the denominator of equation (6)?

The authors mention that p=0 corresponds to atmospheric pressure at the surface (line 140), but this convention is employed (equation (4)) before it is mentioned in (section 3). Please mention this convention upon first usage.

Lines 94-97: it's not clear to me what you're saying here. Is this maximal deviation the deviation that occurs over 360 m, or between 3 and 4 deg(C), or something else? The sentence in line 96 seems to imply it’s something else.



Line 133: Can the authors clarify what they mean by this sentence? I’m getting confused by the use of the words in the parentheses.

Line 203: “Stability frequency” is used. Is this standard? “Brunt-Väisälä frequency” is used in the abstract. I would standardize the usage throughout the paper.



In figure 1,  pressure on the vertical axis is positive, but on the subsequent figures, it’s negative. I would suggest that it be standardized to one or the other, or clarified in the text.

The authors model convection in a phenomenological way (i.e. all heat is exchanged between adjacent layers instantaneously). For the purposes of this work, I think it's probably fine, but I don't really know. Can the authors comment on whether they think that their approach is actually a good representation of the true convective processes going on in a lake? I.e. are the timescales appropriate? Is there evidence of a lake-wide circulation?