The paper is a numerical case study of a real extratropical cyclone. It investigates the role of individual microphysical processes in warm conveyor belt (WCB) heating and their impact on the circulation through modification of the potential vorticity. This problem has been only tackled by few studies before and needs to be deeper investigated in models with km-scale grid spacing and using state-of-the-art microphysical schemes like the two-moment scheme used in the paper. One original aspect of the study is to separate the heating and PV budgets between fast, intermediate and slow ascent trajectories. Such a decomposition is relevant since coarser resolution models do not represent fast ascent trajectories and it is important to check if such trajectories have an important effect on the whole heating budget. According to the present paper, the relative contribution of such trajectories in the heating budget is small because the number of such trajectories is small but is worth detailing the underlying processes because their proportion may vary from case to case.

The paper is well organized and very cleanly written. The choice and quality of the figures are very good. The cited literature is comprehensive. The heating budget along WCB trajectories is shown to be dominated by condensation of cloud droplets and vapor deposition on ice which confirm previous studies. The potential vorticity tendencies are positive in the lower troposphere due to condensation and vapor deposition but also due to melting and evaporation of rain. in the upper troposphere, PV is reduced via condensation, vapor deposition and long wave radiation. As previously said, the most original parts of the results come from the separated budgets of the fast, intermediate and slow ascents. An important effort is made by the authors to explain the CCN activation and the modification of the CCN activation scheme based on airborne measurements of aerosols. I am not expert on this latter aspect but it was not clear to me how the measurements were used to fit parameters of equation (1) determining the CCN number concentrations. My second concern is that the authors make an emphasis on this section fixing the right CCN number concentrations (section 2.3) but Fig.B1d clearly shows that this calibration of the scheme has almost no effect on the heating budget. So I am wondering if it is really necessary to put such a strong emphasis on this modification of the CCN activation scheme. Also in the conclusions (line 706), the authors mention CCN concentration modifies averaged heating rate profiles but it seems to be negligible looking at Fig.B1d. To conclude, I really enjoyed reading the paper, the results are well presented, some of them are original, some of them confirm previous studies, but the articulation of the CCN activation section with the rest of the paper is not clear to me. Therefore I recommend publication of the paper once the authors clarify the relevance of the CCN activation section within the whole paper and the conclusions related to the sensitivity of the heating and PV budgets to the CCN distribution. I have also added specific comments below.

General comments:

1) The reason of choosing NAWDEX IOP7 is never said. Is it because some aerosols measurements are available from FAAM flights ? I am not expert on aerosols variability. But it is not clear to me if the calibration made of the CCN activation scheme duing weeks that are not overlapping with IOP7 case is relevant.

2) In the beginning of section 2.3, it would be good to present the objectives of that subsection and the different steps needed to tune the CCN activation scheme. It is difficult for a non specialist to undestand the different steps. Since this section is quite long and the paper includes 3 figures on that aspect (Fig.2, A1, B1), the authors need to think which results listed in the abstract really depend on the modified CCN activation scheme. Would the results be the same with the original CCN activation scheme?

Minor comments:

1) Introduction: you may want to cite the recent paper of Mazoyer et al (2023, MWR) showing the sensitivity of the WCB heating rate and upper-tropospheric PV to the mixed-phase clouds representation using the one-moment scheme of Meso-NH.

2) Line 106: Which WCB case study ? So far, the case study was not introduced.

3) line 135: I do not see a separation between (i) and (ii). (ii) is included in (i) isn't it ?

4) Figure 2: too small / dotted and dashed lines not really visible.

5) line 230: this is logical since the weather regime is zonal until late September and blocked between early October and late October.

6) Line 238: maybe one sentence to understand the purpose of using the cloud parcel model. to initilize which variable ? How are used the observations ? This might be straightforward for some readers but not for all of them.

7) EQ (1) what are the constant parameters that are modified ?

8) Lines 260-263. According to Eq (1), CCN concentrations varies with w and p. So please be more precise when the word "varioability" is used.

9) Figure 3, the yellow and green boxes are difficult to see

10) Figure 5c, total is in shadings, isn't it ? where is the light blue contour ? the blue contour does not seem to be rain since it goes well above the 273K isotherm.

11) Is Figure 5 done with composites at different longitudes / latitudes but same time ? or different times ?

12) Line 410: where is it shown?

13) It is not so clear that turbulence-related heating is larger for fast ascent. Maybe give the other values for comparison

14) Line 498, why is there a cooling and not a heating ? We expect growth of ice crystals at the expense of liquid droplets in WBF process. 

15) line 491 Does the evaporative cooling of cloud droplets only included in SATADII ?

16) Line 506: why is evaporative cooling term prior to ascent positive in Fig.8d-f ? I think this is due to the fact that accumulative diabatic heating is plotted from t=0 and that there is a decrease of accumulative heating from t=-10 to t=0 and in fact it represents cooling. Am I correct ?

17) Line 508: why is Fig.8b here referred ?

18) Line 525: is the moisture content of the different categories of trajectories before their ascent shown somewhere ?

19) Line 529: please refer to figures. Fig. 9b?

20) Line 531: do you mean summing QGDEP and QXRIM ?

21) Line 558: The total vapor deposition seems to me the same between the various categories of trajectories but the relative contribution of vapor deposition is smaller (Fig. 9b). I would change the sentence by replacing "vapor deposition" by "relative contribution of vapor deposition".

22) I am surprised to see that the slight increase of PV after t=20h-30h (solid black curves in Fig.12a-c)is not captured by the sum of all diabatic heating processes (dashed black curves) which are negative at those times. Since the trajectories are in the upper troposphere at that time I do not expect PV tendency due to momentum non conservative processes to be important there. Do you have an idea of why such an increase in PV ? Could it be related to trajectories near the tropopause where PV gradients are strong and the Lagrangian trajectories are artificially crossing iso PV values ?

23) Lines 609-614: there are some redundancies with lines 599-601. 

24) Line 616: do you mean that integration of QXDEP along WCB trajectories is near zero ? Looking at QXDEP in Figs.12d-f gives me the feeling that the integration should be positive. Even though the saturation adjustment leads to stronger positive peaks in DPV/Dt than QXDEP, the integrated values over the whole time of the saturation adjustment term seems to be small because after t=20h it is negative.

25) "PV rates FOR the second adjustment"

26) Lines 625-30 and also lines 495: I did not get why there is a counteracting effect of the second adjustment with respect to the turbulence ?

27) Surprisingly, the turbulence term is more negative than the radiative term in Fig.12 and is mainly responsible for reducing PV after t=10h (Fig.12 e-f). Comparing Fig. 10c (TURB) with 11d (RAD) does not provide the same picture as in Fig.12. Why ?

28) Lines 660-665: I agree with most of the conclusions. But the sum of TURB and SATADII in Fig.12 seems to me to be the major source of PV reduction. This is in contrast with the cross sections of Fig.10 and 12 where we do not see any major negative PV tendency in TURB (Fig.10c). IN other words, I struggle interpreting the green dashed curve associated with TURB in Figs.12d-f

29) Since the original and modified versions CCN activation scheme lead to almost the same heating budget (Fig.B1d) and I imagine the same PV budget why is it so important in the paper to show the whole approach of CCN activation and its calibration with FAAM flights observations ?

30) Line 687: according to Fig.12, turbulence is important for PV reduction (see above)

31) Line 696: I would expect heating from WBF process ?! Why am I wrong ?

32) Line 706: I do not agree with this statement, the heating budgets are very similar between the two runs.

33) Line 707: Mazoyer et al (2021) used the same type of resolution as in the present paper and found a very small impact of aerosols (see their remark page 3965)

34) Line 718 "will result"

35) line 728: The compensation between second adjustment and turbulence is only partial in Fig.12 and the net effect seems to be a large PV reduction (same question as above)

Reviewed by Gwendal Riviere

Dear Authors,

This is a very good manuscript. See attached my comments and suggestions (mainly on how to highlight the key results in it)

Apologies for the delay and best wishes