The paper extends the recent wake superposition model proposed in Bastankhah et al. 2021 by using a super-Gaussian distribution to express wake velocity deficit profiles, instead of a Gaussian distribution. The former is expected to improve results in the near-wake region. As discussed in the manuscript, the integral form of the conservation of momentum deficit for a waked turbine cannot be solved analytically for a super-Gaussian profile. However, the author used a numerical method as well as two approximate analytical methods to compute the integral. Results are compared with the LES data for two wind farm layout configurations. Overall, the paper is well-written with clear figures and interesting and critical discussion of results. So I recommend the publication provided that my below comments (in no particular order of importance) are addressed:

- Equation 6: I think "n" should be replaced with "k". Please check!

- Equation 9: It is not clear how this equation is obtained. Please provide more clarification about how model coefficients (shown in Equation 9 and Table 1) are tuned.

- Line 93: "... are estimated using a local rotor element area ponderated average". Please clarify what this means and how it affects obtained results.

Line 100: "... lead to superimposed velocity deficit". I am not sure if I understood what this sentence means. Please paraphrase it and elaborate what you mean here.

Figure 2: It is shown that MC methods underpredicts the velocity deficit for the second turbine. Line 107 states that this is a consequence of the application of the "modified" momentum conservation. So please add the results for the "original" momentum conservation as I think this would strengthen your argument and also would be interesting for the reader to see how they are compared with each other.

- The main contribution of this work is the inclusion of super-Gaussian profile. To more clearly show how significant this affects the results, please include original model predictions (using Gaussian profile) in both figures 2 and 3. 

The proposed manuscript extends previous superposition-based wake models to super-Gaussian profiles. While such approach results in an integral with no analytical solution, the author proposes different approximations (numerical and analytical) that are evaluated against the LES results from Bastankhah et al. (2021). It is found that both approximations have a satisfactory agreement with the numerical data.

I consider the proposed model of interest for the community and the results sound. In consequence, I think the paper is suitable for publication on WES. Nevertheless, I have several remarks that should be addressed prior to publication:

• As also proposed by another anonymous reviewer, figure 3 should also show the Gaussian and numerical models. This would support the conclusions drawn by the author.
• Also, both in figures 2 and 3 the agreement between different models and the LES should be quantified to show the overall performance of them.
• Which is the influence of the rotor disk discretization (line 93) in the results? The author states a 12x12 polar grid has been used but this number is not discussed.
• I am not convinced about the relevance of figure 1. It is not expected that an approximated super-Gaussian profile will perform better than a Gaussian one? Also, the maximal relative error for the kEquiv model still seems to be high. I propose the author gives such value in the main text. Furthermore, on the same topic, which are the values of kEq used in figures 2 and 3?
• I find section 3 too short. For instance, the parameter a_f is not defined and its relevance never explained. Also, can the author be more specific about the poor performance previously exhibited by the super-Gaussian model?
• This is just a suggestion, but it would help the reader to add a diagram, maybe as an inset in a figure, where the layout of the farm and the parameters n and i are shown.
• The caption of figure 2 should give more details. For instance, where are the turbines placed? Also, before the streamwise distance 5x/d_0 all models collapse? And why the velocity deficit increases after x/d_0=2?
• The manuscript has some typos and problems with definitions. In line 43 should say ‘interestingly’ instead of interesting. In line 45 and equation 4 the velocity U is not defined and shown alternatively with and without capital letters. In line 65 it is not clear if the characteristic widths are or not normalized.