The study presents numerical simulation runs by the WRF model to investigate recovery processes from an hypothetical 50x50 km2 offshore wind farm. The WRF is driven by real weather data. The experiments quantify the recovery processes under different wind speeds and wind turbine spacing. 

The study is well structured and written, although the language can be improved at some parts. The results are presented clearly, but some figures need be improved to be more accessible to the reader. The discussion picks up on the novel results but also remains very superficial at some points. My main criticism of the study is the neglection of the stability, which is a main control parameter for wake recovery. This is further explained in the comment sections. With the consideration of this aspect and further improvement, the study can be a very valuable contribution to the offshore wind energy community. 

General comments

The abstract gives a detailed description of the study, but remains very vague on the results. The results need to be presented more precisely and concretely, (e.g how is high inter turbine spacing defined, densely packed etc…).  For more details please see the specific comments. 

My main criticism is that the study does not take into account the stability and boundary-layer height regarding wake recovery. For the description of offshore wind farm impacts on the atmosphere (such as far wake effects/blockage effect or the influence of the farm on vertical turbulent moment flux, as mentioned on p.13 l.24), a consideration of the stability and ABL top (as mentioned in p.10 l.25) as major parameter, along with the park layout and wind speed, have been identified in several recent studies (e.g. Djath et al . 2018, Siedesleben et al . 2018, Cañadillas et al. 2019, Platis et al. 2020 etc…). However, this study only takes turbine spacing and the wind speed into account. 

In addition, the results from these mentioned studies and further recent studies about the ongoing investigation of the far field effects of offshore wind farms are not addressed in the study. 

Also on p.13 l.24: Turbulent vertical mixing depends on the thermal and dynamic stability.  Also for strong horizontal wind speed during strong convective conditions vertical recovery may remain the main contributor. Therefore, I highly suggest at least to take the stability (e.g. lapse rate or Richardson bulk number) for the investigated cases into account and include them in the discussion. 

Figures have to be re-worked including units to the scales. For some figures I also recommend to enlarge them to make them more readable. Also the range of the scale hat to be rearranged as e.g in figure 6 a) the variation is seen hardly. 

To make things easier for the reader, I suggest to define the mean wind direction as positive x. This will help the reader to compare easier cases A with B and C. This will also help to better distinguished between flow effect parallel and perpendicular to the flow e.g., the interpretation of Figures 3 b) , 4,  5 and 6. 

Why is the recovery only presented for the wind farm domain (Fig. 6). I expect also far field effects similar to the wake effects to be seen in the vicinity of the wind farm. Also this will give a broader picture of the upwind and downwind effects. 

Specific comments

p.1 l.14. How is high defined? Narrow spacing? Please be more precise.

p.1 l.16: What is meant by can be quantified using low-order empirical equations? Please be more more concrete.

p. l.17. What is meant by high wind speed. Which range are you referring to?

p.2. l.15: What version of the WRF model? Which wind turbine parameterization ? Please rephrase the sentence in the abstract or in the introduction as they are identical. 

p.4. l14ff: I suggest to add a figure showing the relation between grid cell and turbine spacing in order to makes things more clear for the reader

p. 5 l.15: This is still a simulation, so the term ‘realistic’ is not appropriate. 

p.6. l.5: Please introduce here what k,i,j is referring to. 

p.6. l.18:Over which domain are the horizontally averaged? Over the wind farm domain?

Eq. 8 Please describe what is defined by î and ĵ ?

p.9. l15: Please give a broader description about the  statistical analysis. 

Eq. 15: The denominator on the right-hand side of Eq. 9 should contain the unit. I also suggest to write 140m – 28m 

p.7 l.25 Why small v ?

Fig. 3. The figure is hard to read, especially 3c). Please enlarge the plots and the labels. Please add a unit to the scales. For case A the resolution is way to small to be able to follow the analysis on page. 9. l. 15-16. 

p.10. l.5: Not true several other studies such as Platis et al. 2018, 2020, Siedersleben et al. 2018 reported a deceleration of up to 40 % in the wake of offshore wind farms. 

p.10 l.25. What is the height of the ABL top? 

Fig. 4. I recommend to mark the area where the wind farm is located. 

Fig. 4: Case A III. Why is there a deceleration and then an acceleration of the flow between 0-1000 m and  at x= 780-850 km?

Fig. 4 The upwind deceleration seem very impressive. I am wondering whether a too small simulation domain is causing an intensification by boundary reflections? Is there a way to assess this influence ?

Fig. 4 b. Why is a streak pattern visible? Can this be also attributed to artifacts caused by the simulation? 

p.11.9 ff. I do not understand how this argument contributes to case C-I. Please describe more clearly.

Fig. 5 I don ot understand the meaning of the legend at the second left figure in the first row.

Fig .5.  The description and argumentation of the results is at some points not very precise. 

p.11. l.17.  It would be helpful for the reader just to mention again very briefly the difference between synoptic and micro scale. 

p.11 l.8-10. “It is possible that this meso-scale momentum transport aids in the wind farm recovery

by making more momentum available for downward mixing by turbulence.” This is very speculative. Is there a way to justify it ? Can the variations at different heights be explained?

Fig. 6: Why does the plots in case of III look much coarser then for I and II  ?

Fig. 7a) Why is there such a sharp boundary (jump) at about x= 4x10-3 ? Because of the different cases? This could be mentioned in the text. 

p. 17 l. 11. Please refer to the equation or describe the integration by an seperate equation. 

p.18 l. 31. What do you mean exactly by synoptic scale effects?

Technical corrections

p.2. l.1 ff: Please put the citations in chronological order. 

p.4 l.9: Please correct: boundary-layer scheme

p.4 l.10: Please correct: second-order moments

p.6 l.22 typo error ‘that’

Fig. 7 b)-d) Please title the figures with its specific cases. 

References:

Djath, B., Schulz-Stellenfleth, J., and Cañadillas, B.: Impact of atmospheric stability on X-band and C-band synthetic aperture radar imageryof offshore windpark wakes, Journal of Renewable and Sustainable Energy, 10, 043 301, 2018

Cañadillas, B., Foreman, R., Barth, V., Platis, A., Siedersleben, S. K., Bange, J., Lampert, A., Bärfuss, K., Hankers, R., Schulz-Stellenfleth, J.,Djath, B., Emeis, S., and Neumann, T.: Offshore wind farm wake recovery: Airborne measurements and its representation in engineeringmodels, Wind Energy, https://doi.org/10.1002/we.2484, 2019.

Platis, A., Hundhausen, M., Siedersleben, S. K., Lampert, A., Bärfuss, K., Schulz-Stellenfleth, J., Djath, B., Emeis, S., Neumann, T., Cañadil-385las, B., and Bange, J.: Long-range modifications of the wind field by offshore wind parks - results of the project WIPAFF, MetZet, 2020b

Siedersleben, S. K., Lundquist, J. K., Platis, A., Bange, J., Bärfuss, K., Lampert, A., Cañadillas, B., Neumann, T., and Emeis, S.: Micrometeorological impacts of offshore wind farms as seen in observations and simulations, Environmental Research Letters, 2018

This study explores different recovery processes in a large hypothetical offshore wind farm in the Arabian Sea for 3 different meteorological conditions using the mesoscale model WRF and the Fitch WFP. The manuscript is well written in general. Some figures could be improved to faciliate the undestanding of the reader. I think it is an interesting study that should potentially be published in WES, after carefully addressing the comments below.

General comments

My main criticism of this study is that, while the three different cases certainly consider different wind speed ranges, they might also have different stability ranges. However, the stability for the cases is not discussed (see specific comments below), although various studies have shown an impact of stability on wakes (Lee and Lundquist 2017, Cañadillas et al. (2020) to mention just a few).

My second concern is the sensitivity of the model results with respect to the vertical resolution. The vertical resolution is rather coarse (>20 m) compared to the resolution, which is suggested to be necessary to capture wind farm effects (e.g. Siedersleben et al 2020, Tomaszewski and Lundquist (2020) or Pryor et al. (2020)). In addition Pryor et al. (2020) also pointed out that the TKE magnitude depends on the vertical resolution. One of your conclusions concerns the effect of TKE advection on the recovery process. This conclusions could be faulty, if the resolution is too coarse. Please elaborate.

Specific comments

p 1, line 27ff: Is the citation of so many studies necessary here?

P 2, line 8: “… also confirmed by LES…”, in line 5 you write that the recovery process was previously investigated by LES simulations. Why is the study by Calaf et al. (2010) listed separately from the others?

P 2, line 27: Here you write that TKE advection is deactivated in your study, while later on Page 5, line 14-17 you write that both activated and deactivated scenarios are used. Please make these statements consistent.

P 3, line 3: Please provide the version number of the WRF version that you have used. The bug found by Archer et al. (2020) showed, how important it is to document clearly, which version number has been used.

P3, line 19: How transferable are your results to other regions? This farm is quite far offshore. Existing offshore farms are closer to the coast. How could coastal effects change your results?

P3, line 24: A vertical resolution of > 20 m is at the upper limit of the necessary resolution to capture wind farm effects correctly as studies by Siedersleben et al 2020, Tomaszewski and Lundquist (2020) or Pryor et al. (2020) have indicated. In addition Pryor et al. (2020) also pointed out that the TKE magnitude depends on the vertical resolution. How sensitive are your results to vertical resolution?

P4, line 4: Was the Sea Surface Temperature also taken from that source?

P4, line 4-11: A tabular overview could provide a better overview on the set-up

P4, line 14: This is a rather small turbine compared to turbines that are currently being installed offshore. Why have you used such a small turbine and how representative are your results for more modern turbines?

P5, line 7: Atmospheric stability is another relevant parameter for wind energy. Is the stability similar in all three cases? Otherwise this will affect the conclusions as well.

P 6, Eq 6: Define what hat^i and hat^j mean. Consider to add subindex “h” to indicate that hub-height winds are used here

P 8, line 18: How do these values compare with Volker et al. (2017)

Figure 3, 4, 6: Please add variables and units to the colorbar.

Figure 3: Are averages over the entire two or three day period shown in that figure? Or is it a snapshot? Please clarify. Consider to add the “plots depict the wind farm only, that is the black square in (c), if appropriate“. In figure (c), please add: every xth vector is shown

P 9, line 13: here it says averaged over the rotor depth, while in the caption of figure 3 “hub-height wind” is mentioned. Please clarify.

P 9, line 17: The wake length depends also strongly on stability. Again, have you checked that the stability is the same in all simulations?

P 10, line 3: Wake lengths can be defined in many ways. You mention a wake length of 521 km, which is very long. Please add your definition of a wake length

P 10, line 13 – 15 and Figure 4: The figure could be easier understandable, if Case A would be turned into the mean wind direction and thus the colours would be the same in all cases. Please consider doing so.

Figure 7 (a): Most points follow the linear trend. However there are also quite some points with relatively high momentum loss rate but small vertical recovery (especially around 10*10⁻³ ms⁻²). During which situations does this behaviour occur? Also there is a sharp drop at about 3*10⁻³ ms⁻², where does this come from?

Figure 8: Why is only the U-momentum flux considered here, even though the wind direction is south-west / north-east?

Section 3.7: I think this section deserves a bit more elaboration and possibly a figure. As you mention in your introduction on page 2, there has been a debate, whether TKE advection needs to be activated or not. With that in mind, it would be good to give more evidence for your conclusion on TKE advection.

Technical corrections

P5, line 21: Consider to add “the method by” in using Avissar and Chen (1993).

P6, line 22: “that” is used before and after the citation

P8, line 7: “As” should not be capitalized

P8, line 23-24: Fig. 3b is referenced twice within one sentence

Figure 3: sub-figures are usually referenced only with (b) not with Fig. 3 (b). Please check with the journal guidelines

P 13, line 22: consider to add “side” or the like after “at the upwind”

P 18, line 28: “till” is rather colloquial. Consider to use “until” instead of “till”

P 19, line 24 – 28: I agree with the authors that it is an interesting study, but how significant a contribution is cannot be known before publishing. I would suggest to advertise it a bit less.

P 19, line 31: Code availability: Please add the URL to the WRF github repository (or where ever you downloaded WRF)

P 19, line 32: Code availability: Please also add namelist.wps to the the repository. Why are only the example files for 0.5 km included in the repository, even if they are modified within the code it would be good to have them all. Please also add a descrption of model changes in the 5 files that you mention in the README.

P 20, line 1-2: Please add a link to the NCEP data.

P 21, line 10: Chou et al: How can this publication be accessed? Please provide a doi / url

P 21, line 30-31: Hong et al: How can this publication be accessed? Please provide a doi / url

P 22, line 22: line 1-2: IRENA: How can this publication be accessed? Please add a url.

P. 22, line 7: Li et al: How can this publication be accessed? Please provide a doi / url

P. 22, line 16: Noppel et al: How can this publication be accessed? Please provide a doi / url

P 22, line 26: Skamarock et al: How can this publication be accessed? Please provide a doi / url. In addition: your zenodo repository indicates that you have been using WRF 4.2.1, why do you cite version 3 here?

P. 23 line 5: Zeng et al: How can this publication be accessed? Please provide a doi / url

References

Cañadillas B, Foreman R, Barth V, Siedersleben S, Lampert A, Platis A, Djath B, Schulz-Stellenfleth J, Bange J, Emeis S, Neumann T (2020) Offshore wind farm wake recovery: Airborne measurements and its representation in engineering models. Wind Energy 23(5):1249–1265, DOI 10.1002/we.2484

Lee JCY, Lundquist JK (2017b) Observing and Simulating Wind-Turbine Wakes During the Evening Transition. Boundary-Layer Meteorology 164(3):449–474, DOI 10.1007/s10546-017-0257-y

Siedersleben, S.K., Platis, A., Lundquist, J.K., Djath, B., Lampert, A., Bärfuss, K., Cañadillas, B., Schulz-Stellenfleth, J., Bange, J., Neumann, T. and Emeis, S.: Turbulent kinetic energy over large offshore wind farms observed and simulated by the mesoscale model WRF (3.8.1), Geosci. Model Dev. (Online), 13(NREL-JA-5000-75874), https://doi.org/10.5194/gmd-13-249-2020, 2020.

Tomaszewski JM, Lundquist JK (2019) Simulated wind farm wake sensitivity to configuration choices in the Weather Research and Forecasting model version 3.8.1. Geoscientific Model Development Discussions, Final version published after completion of this study at DOI 105194/gmd-13-2645-2020 DOI 10.5194/gmd-2019-302

Pryor SC, Shepherd TJ, Volker PJH, Hahmann AN, Barthelmie RJ (2020) ”Wind Theft” from Onshore Wind Turbine Arrays: Sensitivity to Wind Farm Parameterization and Resolution. Journal of Applied Meteorology and Climatology 59(1):153–174, DOI 10.1175/jamc-d-19-0235.1

Volker PJH, Hahmann AN, Badger J, Jørgensen HE (2017) Prospects for generating electricity by large onshore and offshore wind farms. Environmental Research Letters 12(3), DOI 10.1088/1748-9326/aa5d86