GENERAL COMMENTS

The topic of the article, which is the optimization of wind farm operation in presence of noise constraint, is meaningful for the research community and within the scope of WES. The ideas it conveys are useful to address the problem of noise emission; the article is also an application of an optimization for a discrete variable problem, and the approach can be used in other studies not related to the noise emission topic. The objectives and hypothesis of the research are clear and clearly outlined. The discussion of the methodology and the results is backed up with sufficient detail. The article is generally well structured.

For these reasons, I think the article deserves to be published in the WES journal. Prior to publication, I would like to ask the authors to address the comments below. I included in “specific comments” some suggestions that I think can make the article more effective. In “technical corrections” you can find a list of typing errors, the request to improve clarity of some sentences, or suggestions to improve the presentation quality.

SPECIFIC COMMENTS

• I would modify the title to cover the use of two sound propagation models of different fidelity. For example: “Optimization of wind farm operation with a noise constraint and two sound propagation models of different complexity”.
• The abstract conveys the meaning of the article, but it doesn’t give key results. The abstract should present in brief the main results of the article and offer a short description of their interpretation.
• 56-60: “the aim of this paper is … in the specific flow case”. I think this does not cover the true aim of this paper. I would say the aim of this paper is to present a computational framework to optimize the operational mode of turbines in a wind farm in presence of a noise constraint. This is the main goal. Then, there is a second one, which is to show the eventual advantages of using a more complex and computationally expensive sound propagation model in place of a simpler one. The sentence “but could be transferred to layout optimization with noise constraints by considering the Annual Energy Production (AEP) of the wind farm instead of the power production in the specific flow case” is not clear. Instead of this sentence, I suggest you summarize the main elements of novelty of this article and explain its expected impact.
• Section 2. I think it would be benificial to add a couple of sentences at the beginning of the section (below the main title) to introduce the structure of the computational framework; you should briefly explain how Topfarm and PyWake are combined and how the sound propagation model come into play. I would anticipate here the sentence at lines 186-187: "the modeling in the problem is divided into two parts: the wind farm wake modeling and the sound propagation modeling" and add some details to it.
• Section 4.2. I think you should add some details about the vertical wind profile used for these simulations, consistently with what is done in the next subsection.
• Section 5.3. In my opinion this section does not bring any new result, so it can be shortened, removing parts already covered before, and merged with conclusions.

TECHNICAL CORRECTIONS

• 6-7: the sentence “Thus, as the WindSTAR model introduces a higher complexity of the sound propagation computations, it likewise introduces a higher computational time” is redundant and can be removed.
• 21-23: “A method for effectively choosing at which operational mode each of the wind turbines should operate during varying atmospheric conditions is therefore needed”. The link between operational mode and the atmospheric conditions is not clear. What do you mean with atmospheric conditions? You should name the parameters you are considering, like temperature, air density, …
• 41: what do you mean with “meteorological conditions”? You should be more specific.
• 44-45: “Thus, the attenuation of the sound has further been shown to change with the stability of the atmosphere (Barlas et al. , 2018)”. The link between this sentence and the text before it is not clear.
• 47: remove “immense”.
• 51: “is along with the ISO 9613-2 model used for optimization in this study.” Change with “is used along with the ISO 9613-2 model for optimization in this study.”
• 55: replace “the model” with “it”.
• 85: Frequency (f) is used in the equations above and should be introduced after eq 1.
• 108: “in the r-direction”. Is it “radial direction”?
• 108: “ a grid resolution of …”. I think you should define the coordinates system (what are the r and z directions?).
• 113 and 126: “too excessive” remove “too”.
• 128: “to be uncorrelated and the average” is it “average pressure”?
• 132: “From which the attenuation of the sound will henceforth be referred to as the transmission loss, TL”. This sentence is not clear and should be rephrased.
• 143-144: “While the ISO 9613-2 model can be evaluated on a laptop, the amount of physics included in the WindSTAR model require a cluster for the computations”. Can you support this sentence with quantitative information (i.e., execution time for the same simulation with the two models)?
• 149: “which estimates i.e. the Levelized Cost of Energy (LCoE)” remove “i.e.”.
• 149-150: “Topfarm has among others previously been used” replace with “Topfarm has been previously used”.
• 163: “presented” change with “presented here”.
• 168: “PyWake is loosely coupled to WindSTAR and wrapped with the Topfarm optimization framework”. This sentence is unclear and must be rephrased.
• 168: “Furthermore, the” replace with “The”.
• 169: “Ct curve” replace with “Ct (thrust coefficient) curve”.
• 169: “wind turbine type” replace with “wind turbine under consideration”.
• 170: “an iterative downstream manner” unclear, try to use different words.
• 171: “(Bastankah et al. , 2014)” remove brakets.
• 172-176: “WindSTAR has previously been coupled … in the presented work”. I think these sentences do not add much to the discussion and can be removed. In case you want to keep them, you must explain more clearly the meaning of the sentence “However, the source strength is provided through the operational modes and the Qian wake model is further not yet available in the PyWake framework, but only loosely coupled with WindSTAR through an implemented Fortran version” and why this is important for the rest of the analysis.
• 193: remove “both model parts (red.” and “)”.
• Figure 1: Can you modify this chart to highlight differences between the approach based on WindSTAR and on the ISO standard?
• 220: I would reword the title, for example “Test cases for the optimization framework”.
• 224: replace “has a size” with “consists of”.
• 227: I think you can remove “In order to have dwellings in a near distance of the wind farm at which the noise constraints should be fulfilled”.
• 229: add the sentence “Here, the noise constraints must be fulfilled” at the end of the paragraph.
• 230: remove “original”.
• 235: “the sensitivity of the Lp” change with “the sensitivity of the Lp in a greater number of turbine operating conditions;”
• 235: “while the higher LW values of the larger turbine type introduce a larger need for optimization”. Change with “moreover the higher LW values of the larger turbine introduce a larger need for optimization”.
• 243: replace “These distances” with “These nondimensional distances”.
• Figure 2 and Figure 3: I think it would be best to use the same limits for the x-axis in the two figures.
• 250: “considered outside of” replace with “not influenced by”.
• Caption of Figure 4: “in the wake of (a) wind turbine”.
• 260: “The wind turbine type” replace with “This”.
• Caption of Figure 5: “CT sensitivity of WindSTAR obtained transmission loss” not clear.
• 287: “are used” is “is used”.
• 294: “in the wake” add here “of an upstream unit”.
• 302: “are representative to a hard” is “are representative of a hard”.
• Figure 7, figure 12, figure 15: there are no units in the x and y axes labels.
• Figure 8, figure 10, figure 13, figure 14, figure 16: the two subplots on the left are not clear. I suggest plotting the lines in a 2D plot. The color (or line style) is enough to distinguish the 7 turbines.
• 343: “In general, it should for all optimization cases be kept in mind” change with “In general, it should be kept in mind for all optimization cases”.
• Figure 9, figure 11, figure 17: the colormap should use a discrete number of colors equal to the number of operational modes.
• 358: replace “this is” with “this occurs”.
• 404-405: “Hence, the CT curves … the wind farm”. Not clear.

General comments

In this paper, the authors propose a method to optimize the power production of a wind farm while setting noise constraints at specific receivers by changing the operational modes of the individual wind turbines. Two sound propagation models are considered: one simple engineering model (ISO 9613-2) and one physical model based on the parabolic approximation (WindStar). The optimization takes into account the effect of the wind turbine wake with a simple analytical model. The approach is tested on various configurations and quite convincing results are obtained. One interesting result is obtained in the specific case where the wind speed direction is aligned with a row of 7 wind turbines. In this case the optimal power production is not achieved when all wind turbines are in the least noise reducing mode (m=0). This result was surprising (to me), and could be more highlighted by the author if they believe it can be exploited in practical operations.

Some of the choices made by the authors are questionable (source directivity neglected, only 1 frequency per octave band in the propagation calculation, quite rigid ground chosen, ...). The choices are not clearly justified, and it is difficult to assess their impact on the optimization results.

In summary, the approach seems original and of practical use to adapt the curtailment plan to a given wind farm and to specific atmospheric conditions. However the assumptions used and the choice of the input parameters deserve to be better justified and discussed. Thus, I recommend that the authors revise their work according to the major corrections detailed below.

Specific comments

1. Propagation model assumptions and implementation

- Directivity: you assume line 80 that the wind turbine has a uniform directivity with Dc = 0. This is quite surprising because the wind turbine has a marked horizontal directivity, with a difference of typically 6dB between downwind and crosswind directions (see Oerlemans and Schepers 2009 for instance). Why don’t you account for it?

- Turbulence influence: you explain lines 136-141 that you neglect the scattering effect due to turbulence. But turbulence has also a strong effect on the sound power level.  As shown by Buck and Oerlemans (AIAA J. 2018), the sound power spectrum can vary by at least 5dB at low frequencies depending on the atmospheric turbulence level. As you consider the source strength of wind turbines a given by the manufacturer, this can be a limitation. Could you comment on this issue? 

- Number of frequency calculations: you consider only one frequency per octave band in your calculations. This is sufficient for the sound power spectra because it is broadband, but it is not sufficient for propagation effects because of ground interference phenomena. Indeed the octave band center frequency can as well be at the interference minimum or maximum which completely changes the result. Usually several frequencies per octave band (or 1/3 octave band) are considered to correctly calculate the relative SPL spectrum to avoid this problem. 

- I don’t understand your definition of the SPL in Equations (4) and (5): you need to replace p_free by p_ref = 20 microPa if you want to obtain SPL, or you need to add a Delta if you want to define the SPL relative to free field! Also, if this is a ratio of squared amplitudes there is no factor of 2. See for instance Equation (3.6) of Salomon’s book Computational Atmospheric Acoustics.

- Source modeling: you write line 128-129 “the use of the 3 distributed point sources has previously shown good comparison with field measurements (Nyborg et al. , 2022).” In this conference paper the comparison is not that convincing, with many 1/3 octave bands in Figures 5, 8 and 10 with more than 5dB difference between WindStar and measurements. To validate this approach, it would be interesting to compare the results with the WindStar model in Cao et al. (2022) including 36 point sources. Have you done it?

- You explain Lines 110-111 that there are numerical issues at 4 and 8kHz with the WindStar model: could you explain why? There is no reason why the parabolic equation should not work at these frequencies!

2. Input and output parameters

- Ground model and parameters: you use in WindStar the ground impedance model of Attenborough (1985) that has 4 parameters: flow resistivity (sigma), porosity, tortuosity and grain shape factor. Thus it is not sufficient to give the values of sigma. Also you consider in Section 4.3 a value of 2x10^4 kPa.s.m−2. This seems quite high, usually the value of flow resistivity for grass ground is below 1000 kPa.s.m−2. In your previous study by Cao et al. (2022) you used 250 and 500kPa.s.m−2. Can you justify the use of such a high value?

The same question can be asked regarding the ISO9613-2 model, as the ground factor is 0 in this study, while it was 0.5 in Cao et al. (2022).

Follow-up question: what is the influence of a change in the ground impedance on the optimization results?

- Atmospheric conditions: you consider in Section 4.3 a logarithmic profile. You justify it line 447-448 where you write that “the logarithmic inflow profile is deemed acceptable for the flat terrain in the studied wind farm cases”. However this profile is only valid for neutral conditions. For stable conditions that typically occur at night, more significant wind shear is present and other profiles such as the power law profile need to be used (see for instance van den Berg, Wind Energy 2008). Could you justify the choice of neutral conditions? Also, you seem to neglect the effect of the temperature profile on the results. Is it a valid assumption?

- Transmission loss: you introduce it line 131 but you haven’t given its definition.

3. Discussion on the results

- The axis of Figures 7, 12 and 15 are difficult to read: are these distances in meters? It would be clearer to use the distances in kilometers or in terms of rotor diameter D. Also add the receiver number 1 to 4 as used in the following tables and figures. Finally, it would also be useful to give the distance of each receiver to the closest wind turbine.

 - You write line 342 “Thus, a higher L p,j could be expected at these positions due to scattering of sound into the shadow zone.” This is not granted as the levels are quite small in the shadow zone, even if scattering due to turbulence is taken into account. Thus the overall SPL will be dominated by the low frequencies that are not in the shadow zone yet (see Figure 13 of Barlas et al. (2017) at 1386m for instance). Note also that at moderate distances the levels can be higher upwind than downwind (Figure 13 of Barlas et al. (2017) at 252m, 630m and even at 1008m), thus the fact that the receiver is upwind does not necessarily imply that the level should be lower, as you do sometimes (see lines 418-420).

- Sensitivity of the results on input parameters: in Table 2 you show that a variation in wind direction can have a significant effect on the results. Wouldn’t it be better to optimize the operational modes for a range of wind direction (and maybe wind speed) values? Also could you comment (in the discussion section?) on the sensitivity of the results on other input parameters such as ground impedance, wind speed profile, temperature profile, turbulence level? (see previous paragraph on input parameters).

- Scatter plot of Figure 11: the results for ISO9613-2 are quite surprising because all wind turbines are highly curtailed (mode 5 or 6), except one that is close to one of the receiver. Isn’t there a problem with this solution?

- You mention in Section 5.3 the use of a gradient-based approach that requires continuous function in the optimization process: is it possible to use such an approach with WindStar? Is it compatible with the use of discrete variables? (operational modes)

- You write line 449-451: “In addition, the turbulence effects in the atmosphere are neglected due to the high computational costs. This will in some scenarios, i.e. when considering receptors in the upwind position of a wind turbine, lead to higher uncertainties due to the omitted scattering of sound”: As mentioned previously, atmospheric turbulence plays also a role on the noise emission, and would change the low-frequency part of the spectrum. This may need to be added in the discussion section.

4. Organisation of the paper

Abstract:

• the abstract usually includes the main results/conclusions of the paper. This is missing here.
• the sentence “The optimization is performed by use of the TopFarm framework and the PyWake wind farm modeling” is difficult to understand for someone who hasn’t read the paper. It needs to be clarified that TopFarm is used for the optimisation algorithm and that PyWake is used for flow modeling.

Section 3 Optimisation flow:

• I think it would be easier to understand this part if you present the optimization problem given by Equation (7) before the flow chart of Figure 1 that is quite complex
• You mention line 204 that the flow chart reduces when using the ISO9613-2 model. Wouldn’t it be interesting to add another flowchart for this simpler case?
• Equation (7): I think the constraint is not on the sum of the SPL L_p_ij! Correct this equation
• Line 194, you introduce the power of a wind turbine P_i as a function of U0, theta and m_i. Is this power calculated in Topfarm or in PyWake? Please add a sentence in the corresponding section to precise how the power is calculated as a function of U0, theta and m_i.

Section 4.2: it is not clear what are the ground impedance, temperature and wind speed profiles that are used in the WindStar calculations. Are they the same as those described in Section 4.3 for the test cases? If so you should consider reorganising Section 4.

Appendix A: I am not sure this appendix is necessary, as the results seem quite similar to U=10m/s. If you decide to keep it, add a brief description of the content of the Appendix at the beginning.

Technical corrections:

• You use “receptor” throughout the paper, where I think you should use “receiver” According to Oxford dictionnary a receptor is “a sense organ or nerve ending in the body that reacts to changes such as heat or cold and makes the body react in a particular way”. Usually the term “receiver” is preferred in the context of environmental acoustics.
• lines 41-44: quite long sentence. Consider splitting it into two sentences to make it clearer.
• Line 64: I suppose C_T is thrust coefficient, but you need to define it! Throughout the paper you use C_T a lot, you could sometimes replace C_T by thrust coefficient.
• You write line 104 that “the GTPE model is approximated to a 2D model by assuming independence of the direction of propagation from the source”: independence of what? Do you mean that wind speed and temperature are supposed to be independent on range or independent on the azimuthal angle? Please rephrase and clarify.
• Line 149: you write “which estimates i.e. the Levelized Cost of Energy (LCoE) and the AEP of the wind farm in question”. Rephrase and define AEP.
• Line 156: extend => extent
• Line 282: “it is considered negligible compared to the high transmission losses expected”. Not very clear please rephrase.
• Line 292: “The hub height wind speed is kept at U0 = 10 m/s,...” Not true as Uhub is 9.3m/s for the SWT-2.3-93 turbine. Correct this.
• Line 358 page 18: rephrase the sentence “This is even though the...”