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This is an interesting work addressing a new type of long-lived coherent vortices recently discovered in the stratosphere following the injection of large amount of smoke by pyro-convection resulting from wildfires.

It happens that these vortices are maintained by a localized heating source produced by the absorption of incoming solar radiation and are dissipated by the longwave radiative relaxation of the accompanying thermal anomaly. The study of response to localized heating in the atmosphere is not new in the context of convection and tropical cyclones but here the context is of a resulting stable ascending vortex which was not considered before.

This study is based on the reasonable approach of the maximum simplification. It considers an axisymmetric system where heating is proportional to the mixing ratio of an idealized tracer and a Newtonian relaxation modelling the longwave radiative damping of the temperature anomaly.

A very similar approach was adopted by another study, Podglajen et al. (2023) (hereafter P2023), currently under review for QJRMS and of which I am a co-author. . Most of my comments will be based on a comparison with this study and the previous works of Lestrelin et al. (2021) (hereafter L2021) and Khaykin et al. (2020) (hereafter K2020).

General comment

The manuscript seems to take as granted that the ERA5 reanalysis provide “observations” of the ascending vortices and in particular of the potential vorticity (PV) distribution. It is indeed remarkable that the smoke clouds as detected by the lidar CALIOP correspond very closely to the anomalies of PV in ERA5 (K2020 & L2021), even when two vortices are crossing at different altitudes (P2023). However, the ERA5 does not assimilate aerosol data and therefore the anomalous heating is absent. It is only informed by the assimilation of IASI infrared radiances and GPS radio-occultations which constrain the temperature (K2020). In principle the exact knowledge of the temperature distribution implies the knowledge of the equilibrated wind field but assimilation only provide a limited knowledge and vey different PV distributions can produce a fairly similar temperature distributions.

 Introducing an active tracer in a manner similar to that used in the present study, P2023 show that the PV distribution produced by fully resolved 3D simulations of the primitive equations is very different from that “observed” by ERA5. The main reason is that the tracer tends to form a front at its top, followed by a tail (a pattern visible on figures 4 and 5 of the manuscript) and that this has a determining impact on the PV field generated and maintained by the heating. This  important point has been, in my view, totally missed in the manuscript , and deserves some further examination by the authors, in particular regarding the scaling laws. P2023 also argue that the heating tracer dynamics is associated with a zero-PV, an aspect which is misrepresented here in part due to the restriction to the quasi-geostrophic framework.

Specific comments

L150: If one uses a log-pressure coordinate, the height scale in the continuity equation should not be different from that of the hydrostatic equation. This is presented as a “non-standard” feature but I would like to see some justification. Pretending to decouple the variation of density and the  stratification looks a bit weird in my view.

The prediction shown in Fig1a is first discussed as contradicting the observed pattern in Fig1b. There is obviously no contradiction if the pattern is a vertically moving vortex as indicated on L268. I find this presentation more confusing than illuminating. This is also discussed in L2021.

The initial conditions chosen in 3.2 are a tracer blob without initial PV anomaly. P2023 argue that the mass uplift due to pyro-convection means PV dilution at the top and therefore an initial PV anomaly accompanying the tracer anomaly, which is ignored here. The importance of the initial PV anomaly for the subsequent development is discussed in P2023.

a,b,c labels of panels are missing on Figure 2 and other figures.  The fonts on the small panels (axis, colorbar, legends) are too small and should be increased for readability. Take into account that the figures will be smaller in the final publication than in the manuscript.

L330: The rise of a shallow region of tracer depends on the distribution of tracer as a function of radius. A disk of uniform tracer will rise uniformly as least in the initial stage. The ascent depends on the heating which depends on the tracer.

The numerical simulations and the theoretical discussion in P2023 show that the PV decreases exponentially with time  to zero in the frontal region with a time scale that does not exceed a few days for realistic parameters, so that the validity of a QG model might be actually very short.  It should be noted that the “observations” of PV from ERA5 also show zero and even slightly positive PV at the center of the main vortex of the 2020 event (L2021).

Actually, the tracer problem with no temperature relaxation and neglecting lateral diffusion can be solved exactly as a Burgers’ equation in the transformed momentum coordinate system as shown in P2023. Then the PV can also be obtained as the corresponding hyperbolic equation can be solved by characteristic method.

L356-363: Another effect, which cannot be seen here, is to accelerate the ascent. The main reason is that the radiative damping reduces the decay of the tracer. See P2023.

L393-404: A main limitation of the QG model is that the PV is not advected by the vertical velocity. There is implicitly advection of the temperature but not of the vorticity, so one may expect that the PV anomaly will lag behind its true location and be deformed.It is likely that all the discussion contained in this paragraph is strongly affected by this limitation.

L415: Although this question was investigated, the cyclonic PV has not been seen so far in the tail of the vortices in the ERA5. However, it should be noted again that PV is forced in the model by the assimilation of temperature information and that this process does not need to satisfy the integral properties of PV conservation. It is also possible that the cyclonic PV is continuously washed out and dispersed by the vertical shear and cannot be detected.

Section 3.4: What is seen in this section is essentially what has been implemented in the model and so the results, which  display a cropped version of the patterns seen in previous section, are not really surprising. It should also be noted that there are two types of stripping involved her. One is the horizontal stripping studied by Mariotti et al., 1994 and the other one is the vertical stripping due to the vertical shear. In the case of the main vortex of the 2020 event, the two effects played a role at different stages of the evolution.

Section 3.6: The failure of the numerical solution of the inversion problem is not totally surprising. Although in principle the PV never reaches exactly zero, it can be so close that the numerical procedure breaks down. It is a bit surprising that the trend to zero is linear meaning a catastrophe at finite time as it is expected to be exponential.

Section 4: This is an interesting development which seems to bear some similarity with the radiative instability at the top of a cirrus cloud as studied, e.g., by Dinh et al., 2010.  I am however wondering of the relevance to the present problem as the scale of the instability is not at all that of the observed vortices which is in the mesoscale range, 500 to 1000 km. This approach neglects the role of the initial injection of mass as stated above.

L694: This is just not true when all effects are accounted as explained above.

There are many other points to be reworked in the conclusion in the lights of the comments made here.  

Minor comments

l.30: The co-location with other species is also shown clearly in K2020.

L45: It should be referred to Manney et al., 2006 for “frozen in” anticyclones

L159: T_b should be T_B

L172: Perhaps quote here the condition that PV should be non zero and of the sign of f to solve the Sawyer-Elliassen equation

L195: Add “anomaly” to temperature.

L235: Quote also Davies, 2015

L351-354: This is repeating L317-319

L525: Remove one the

L545: s should be h in the formula

References

Davies, H. C.: The Quasigeostrophic Omega Equation: Reappraisal, Refinements, and Relevance, Monthly Weather Review, 143, 3–25, https://doi.org/10.1175/MWR-D-14-00098.1, 2015.

Dinh, T. P., Durran, D. R., and Ackerman, T. P.: Maintenance of tropical tropopause layer cirrus, Journal of Geophysical Research, 115, D021014, https://doi.org/10.1029/2009JD012735, 2010.

Khaykin, S., Legras, B., Bucci, S., Sellitto, P., Isaksen, L., Tencé, F., Bekki, S., Bourassa, A., Rieger, L., Zawada, D., Jumelet, J., and Godin-Beekmann, S.: The 2019/20 Australian wildfires generated a persistent smoke-charged vortex rising up to 35 km altitude, Commun Earth Environ, 1, 22, https://doi.org/10.1038/s43247-020-00022-5, 2020.

Lestrelin, H., Legras, B., Podglajen, A., and Salihoglu, M.: Smoke-charged vortices in the stratosphere generated by wildfires and their behaviour in both hemispheres: comparing Australia 2020 to Canada 2017, Atmos. Chem. Phys., 21, 7113–7134, https://doi.org/10.5194/acp-21-7113-2021, 2021.

Mariotti, A., Legras, B., and Dritschel, D. G.: Vortex stripping and the erosion of coherent structures in two-dimensional flows, Physics of Fluids, 6, 3954–3962, https://doi.org/10.1063/1.868385, 1994.

Podglajen, A., Legras, B., Lapeyre, G., Plougonven, R., Zeitlin, V., Brémaud, V., and Sellitto, P.: Dynamics of diabatically-forced anticyclonic plumes in the stratosphere, https://doi.org/10.22541/essoar.169603596.62706666/v1, 30 September 2023, revised, sub judice in Quart. J. Roy. Met. Soc.