Dear authors,

Thank you very much for all the effort made in this innovative work. I find the continuation and improvement that you have made in the ABL+wakes simulation in RANS very important, since high resolution LES is still very slow and expensive when you want to include the interaction of several wind farms. In my opinion, the structure of the work is very good, but it is necessary to add some case studies and results to be able to reinforce the statements that are arrived when comparing the different RANS methodologies. Below, I leave the revisions.

Mayor revisions

• Section 4.2 Single wake
  • The numerical issue on top of the wind turbine for the RANS-N case in stable conditions is the major limitation of this new method to be further used in ABL+wakes simulations. The author points that this is due to the low eddy viscosity near the top of the ABL height. Also, the eddy viscosity profile is one of the major differences between RANS-lmax and RANS-N. I think that this big issue should be clarified in this current work. For example by plotting the eddy viscosity profile from LES and deciding with RANS approach resolves better the eddy viscosity. If the LES data is not available, at least a small literature review paragraph on this topic should be made.
  • Figure 4 shows that the largest differences between the RANS methods are located at downstream distances larger than 7D (both for velocity deficit and eddy viscosity). Since there is no more LES data to compare with, the authors could propose another sub section where, for example, the power output of a small wind farm test is compared using RANS, LES and, if available, SCADA.
• Conclusions
  • The final conclusions that RANS-N is better for simulating low ABL+wakes is a rushed conclusion, especially since it triggers numerical error on top of the turbine. The comparison against LES up to 7D is not helping much in the decision. It is preferable to change that sentence, and highlight that this the beginning of the study of a new way of simulation ABL+wakes.

Minor revisions

• Abstract
  • Mention at the end that there is still work on how to simulate wakes in low ABL.
• Introduction
  • Better mention “state of the art N-S LES implemented in CPU”
  • It could be more complete if the authors mention papers where the temperature equation has been actively used in RANS to resolve the ABL+wakes.
• Section 2.3
  • Since this is the new proposed method, it is important to present first the literature review on how this equations and ideas have been previously used by other authors. If it is totally new, then the authors should also remark this as a novelty.
• Section 3.1
  • The use of a precursor domain height of 100km looks quite new (and then used for a 2.3km 3D domain height). How the authors arrived to that decision? Is it possible to present a sensitive study on the precursor domain height?
• Section 4.1
  • How is the turbulence intensity calculated from the resulting TKE in RANS? Specially for the stable case.
• Conclusions
  • It is important to mention if there is a proper way of simulating unstable conditions with any of the 3 ABL methods. Unstable conditions are the most frequently condition in the North Sea and is important to know how to correctly simulate wind farm wakes in this condition.
• Appendix B
  • Could you also plot the TKE for the different mesh resolutions? That one is even more sensitive to the mesh than the velocity.

The paper concerns the development of a RANS model correction of the k-epsilon model for ABLs in conventionally neutral and stable conditions.  The model consists of an added buoyancy turbulence production term, modifying the k and epsilon equations, based on an assumed constant temperature gradient in the ABL.  The model is sold as (a) having a simple form, (b) requiring exactly the correct number of non-dimensional numbers for specification, and (c) reproducing well LES simulations of identical flows.

The paper is clearly written and structured, and generally I can recommend for publication, with the following revisions (mostly concerning clarification of the work):

Major comments:

- The authors' starting point is their own RANS-Theta model, and the model proposed here (RANS-N) is quite a minor variation on that basic idea (differing only in the prescribed potential temperature profile).  My interpretation of the RANS-Theta profile is that is corresponds well to the physically common atmospheric condition of a distinct capping inversion layer, whereas the RANS-N model represents (at best) a condition found rarely in nature.  This leads to some questions:

  - The only argument the authors given against the RANS-Theta model is the fact that if "inconsistent" parameters are specified, then the flow profile is nonphysical.  Then I would say: don't specify inconsistent parameters!  This is true of almost any model (including the k-epsilon model itself).  Please explain in detail why you consider this a downside of the model.  Is it difficult to specify consistent parameters?  Have the authors made efforts in this direction, and what are the conclusions?

  - This reader would greatly appreciate details of the thought- and research-process that lead to the development of the RANS-Theta to RANS-N.  The authors hint at their reasoning, but in particular I'm curious what lead to the specification of the linear temperature profile.  I think it's not motivated by physics per se; is it just the simplest one-parameter curve that was chosen?

  - The RANS-Theta and -N models lead to different turbulence intensity profiles and (dramatically different) turbulence length-scale and direction profiles (Figure 2).  Which of these correspond better to the LES results (not plotted)?  Which of these correspond better to ABLs in nature?  Especially wind-turning should have a dramatic effect on wind-farm predictions, should it not?  Which model is better justified in this sense?

- In the comparison to LES (Section 4.1), it's not clear to this reader how the parameters in Table 2 have been estimated.  My concern is that since the LES is being used for paramater calibration, that subsequently assessing accuracy of the models against the same data is a statistical "inverse crime", and not really informative with respect to model accuracy.

Didactic improvements:

- Convective ABLs are not considered here, please explain why not.

- The Brunt Vaisala frequency is introduced without comment.  Explain what it is, and how it relates physically to the height of the ABL.

- A plot of the RANS-Theta profile vs the RANS-N profile (or its gradient) in the model discussion would be instructive.

Typos:

l108 - lowercase theta