It is an interesting research work to evaluated the lidar-assisted wind turbine control under various turbulence characteristics using a four-beam liar and the NREL 5.0 MW reference turbine, which could be beneficial to the Lidar-assisted wind turbine control community. The paper is well organized and written. I recommend to accept the paper after considering and modifications are made according the following comments:

Grammar and typos:

Line 24: missing whitespace between control ... (CPFF), please also cross-check in the whole content of the paper, this appears in many places.

LIne 37: averaging -> average

Line 55: ... (Schlipf, 2015) uses ... change to ... Schlipf uses ...

LIne 81: "... designing ..." -> design

Line 82: present -> presents

LIne 90: structure -> structures

line 106 a -> an

line 129: yz plane -> yz-plane

line 175: "... Simley and Pao Simley and Pao (2015) ..." I guess the bracket around the cited reference is missing

line 176: what is Ih? it should be "In" right?

line 190: Never use a symbol, e.g., "L" to start a sentence.

line 276: propagates -> propagate

line 277: try to replace semi-column with comma when seperating the cited references. This applies to all the context of your paper. Please cross check all of them.

line 305: is -> are

line 308: is -> are,

line 326: frequency -> frequencies, are -> is. cutoff -> cut-off

line 327: that -> those

line 340: delete "alone"

line 395: contributed -> affected?

line 400: are -> is

line 477: by -> in?

line 517: "Introduction the FF pitch ..." -> "Introducing the FF pitch ..." or "Introduction of the FF pitch ..."

line 557: "... two turbulence ..." -> "... two turbulence model ..."

line 558: "... provided ..." -> "... suggested ..."

line 570 - 571: " ... We further analyzed the transfer function, which is important for designing a filter, which removes uncorrelated content in the signal for lidar-assisted control." Please consider to rewrite this sentence.

line 593: "Overall, with this work ..." -> "... with this work ..."

General comments:

1. line 43 to 45: the author states: "... two turbulence models are commonly used ...," But later 3 models are mentioned in the following sentence "... they are the Mann uniform shear model Mann (1994) and the Kaimal spectra Kaimal et al. (1972) and exponential coherence model (hereafter referred as to Mann model and Kaimal model respectively) ..."
2. line 68 to 69: "... The length scale can have an impact on the power spectrum and turbulence spatial coherence." could you show an example to demonstrate this?
3. LIne 91: suggest to use vector notation for 'x', e.g., $\vec{x}$
4. line 100: what is $\Phi_ij(k)$ in Equation 3?
5. Line 162: Please double check the equation 15, the symbol $F_11(k_1)$ is wrongly typed in Latex.
6. Sometimes, "evoturb" is used in the context, sometimes "evoTurb" is used, please unify them
7. line 190 - 194: This description is redundate, because this has been mentioned in the introduction section
8. line 210 - 211: "... Except for a relatively larger error for the v component auto-spectrum under very unstable stability, the rest fittings show very good agreements. ...", I don't see this conclusion in Figure 2, Please double check this statement.
9. line 234 - 236: "... we summarize the lidar wind preview quality for the investigated four-beam lidar and the NREL 5.0MW reference turbine under different atmospheric stability classes. ..." what do you want to express? Maybe the author wants to express "the lidar wind preview quality for the NREL 5MW reference turbine under different atmospheric stability classes"?
10. line 237: section 3.1, the procedure of calculating the "Turbine-estimated rotor effective wind speed" is missing. How do you get "$u_1(x)$"? by EKF estimator or other method?
11. line 309 - 310: "... The coherence in the unstable case is especially lower using the Kaimal model, which can be caused by the direct product method ...". Do you have any reference to support this statement?
12. line 315: Please consider to re-formulate this sentence. "... If a filter with the gain GRL(f) turns out to be an optimal Wiener filter (Simley and Pao, 2013; Wiener et al., 1964), which results in minimal output variance for a multi-inputs multi-outputs system. ...". This sentence does mean anything.
13. line 330 - 334: what about the cut-off frequency for different mean wind speed other than 16 m/s? The author needs to specify this.
14. line 374: equation 36, why the derivative of steady-state pitch angle is calculated with respect to Turbine estimated Rotor Effective Wind Speed ($u_RR$)? and multiplied with ($u_LLf$)) makes the equation mathmatically not exactly correct. What about using the Lidar estimated REWS when evaluating the derivative of steady-state pitch angle?
15. line 408: "... 4096×11×64×64 grid points, corresponding to the time, and the x, y and z directions ...". This means to me only 11 grid points in the x direction? (I suppose x-direction is the u-component direction). This seems to me too less grid points
16. In Figure 7, the time series of generator power should not have such kind of relative large oscillation because the author has mentioned that the constant Power mode (see line 367) is used in the simulation for above rated wind speed and 16 m/s mean wind speed should well above rated and has less probability to be at below rated wind. Could you please explain this in your paper?
17. The followed up comments is as the follows: line 450 - 452: "... Lastly, the generator power is shown in panel (g) where much less power fluctuation is observed in FFFB control. Because the power fluctuation is highly coupled with the rotor speed fluctuation, the less fluctuating power can be expected from the less rotor speed fluctuation in FFFB control." This statement is not correct. As it was mentioned before, the constant power mode is used, what fluctatuated should be the generator torque and coupled to the rotor speed variations.
18. line 505 - 509: The statement is fair. It could be better to add some suggestions on how to solve this issue.
19. line 512 - 513: "... In the stable stability, the reduction is better at 14 ms−1, where the value is close to 4%, and it drops to 2% by higher wind speeds.". Does this mean for the stable atmosphere case, the probability of the wind speed lying in the transition range betweem below rated and above rate is lower than that of the unstable atmosphere case? Adding a probability exceedance plot should help the discussion better.
20. The discussion between line 522 and line 524 should be explained. Please see the comments number 16 and 17.
21. line 569 - 570: "... The coherence using the Mann model is generally higher in all atmospheric stability classes than the coherence using the Kaimal model. ...". For larger turbine, e.g., DTU10MW turbine, the coherence using the Mann model is generally much lower than the one using Kaimal model. The author needs to justify this in the context of his paper.

This is an interesting manuscript that uses stochastic wind fields and aeroelastic simulations to examine the effectiveness of lidar-assisted control in reducing loads, as well as the lidar measurement coherence, for three different stability classes using both the Mann and Kaimal turbulence models. This is an important topic because lidar-assisted control is typically only evaluated using the default Mann and Kaimal turbulence conditions, based on neutral stability. Evaluating lidar-assisted control in different conditions more accurately indicates how well the control strategy will work in the variety of conditions encountered by turbines during their lifetime. The authors provide a detailed overview of the turbulence models and simulation process and show relevant metrics when presenting the results. However, I have one major technical comment on the manuscript as well as many smaller comments that I believe should be addressed.   

When simulating wind fields for all three stability classes, the same turbulence intensity is used for all cases (IEC class 1A). But in reality, stable atmospheric conditions will typically have much lower turbulence levels than unstable conditions, with neutral being somewhere in between. Therefore, the conditions being simulated likely don’t represent stable, neutral, and unstable conditions very well. Would you be able to include more realistic TI values for each stability? Or can you discuss why you are using the same TI for each stability class? Further, how accurate is the wind evolution model in the extended Mann model when using the unrealistic TI values for some stability classes? I assume it was developed using field measurements, but how well do these field measurements represent the class 1A turbulence simulated here for each stability class?

Another non-technical general comment is that there are many places in the manuscript where sentences are broken into two sentence fragments. For example, line 192: "It is clear that a larger coherent eddy structure… While the eddy structure is much smaller…", line 211: "It can be seen that the turbulence… While the variation in the anisotropy…", line 402: "To include the turbulence evolution… Four-dimensional stochastic turbulence…" I would suggest reviewing the manuscript and combining sentence fragments like these into single sentences.

Specific comments

1. Introduction: Much of the paper compares lidar measurement coherence between the Mann and Kaimal models. Since there has been some previous work in this area (e.g., Dong et al. (2021)), it would be helpful to discuss how this research compares to the previous work. 
2. Line 34: "The lidar measurements can be contaminated by lateral and vertical wind speed components": to understand why lateral and vertical wind speed components "contaminate" the lidar measurements, it would be helpful to explain what you are trying to estimate (i.e., how do you define the REWS you are trying to estimate. The rotor average of the longitudinal component?)
3. Line 54: Can you provided a reference for ROSCO?
4. Fig. 1 caption: Can you provide a reference for how the length scales were chosen for each stability class?
5. Line 70: "Because the turbulence spectrum peaks…" This is an incomplete sentence.
6. Section 2.2: Are you assuming zero spatial coherence for the lateral and vertical velocity components? It would be helpful to discuss this here.
7. Section 2.3.1: The extended Mann model with evolution clearly shows a dependence on length scale (e.g., Eq. 14). Can you discuss how other wind conditions, such as turbulence intensity, affect the coherence? For example, in Simley and Pao (2015) there is a strong relationship between TI and coherence, but it isn’t clear how this is captured in the extended Mann model.
8. Line 186: "impact on filter design for LAC": I would suggest explaining what filter you are referring to here.
9. Eq. 20: Why is the real number operator needed here? By definition, won't the coherence be a positive real number? Otherwise, can you explain how coh_{11} can contain imaginary components?
10. Line 212: "while the variation in the anisotropy Gamma does not show a clear trend towards the atmospherically." Based on Table 1, there is a clear trend between Gamma and stability. Are the values for Gamma and length scale in Table 1 switched perhaps?
11. Line 219: "we use three sets of gamma = 200, 400, and 600 s" Why did you choose these three values?
12. Line 222: "which is the median separation for a commercial lidar measuring in front of the turbine" Can you provide a reference or list some examples of commercial lidars and their measurement ranges?
13. Line 229-231: It is unclear what you mean by "rarely large a_x" and why this suggests you should use gamma = 600 s for the unstable case. More generally, can you discuss in more detail why you chose 600 s to represent the unstable condition (e.g., why not 500 s or 800 s)? Further, can you discuss how accurate the selected gamma values are for the class 1A turbulence intensity used in the simulations? And how would gamma change for different TI values? (e.g., Simley and Pao (2015) observed a strong relationship between TI and coherence).
14. Line 257: "azimuth angle phi and elevation angle beta" The math is hard to follow in this section without understanding how the azimuth and elevation angles are defined. Can you define these angles or show them in a figure? 
15. Eq. 27-32: Shouldn't the angles phi and beta be a function of the lidar beam and therefore depend on the index "i"?
16. Eq. 31: I think there should be the imaginary number "i" in front of "k_1 Deltax_i". Also, as written, because Deltax_i equals x_i, it seems that S_RL(k_1) won't contain the phase delays between the measurement points and the rotor because the k_1 dependence of the exponent simplifies to exp(i(k1*x1 - k1*x_1)) = 1. Should Deltax_i in the equation simply be replaced by x_R to model the correct phase delay?
17. Line 288: "the ith lidar measurement position" Can you clarify whether the index "i" refers to the lidar measurement position (e.g., combination of beam and range gate) or just the lidar beam? Earlier on line 267, the index "i" was described as representing the beam number.
18. Line 302: "typical four-beam pulse lidar trajectory": Can you discuss why this is "typical"? Are there commercial examples you could reference?
19. Table 3: As mentioned in an earlier comment, the azimuth and elevation angles haven’t been defined. Can you define these or show them in a figure?
20. Line 330: What are the units of the cutoff frequency 10^-3?
21. Line 330: "This also indicates that the filter design is not sensitive to the change in turbulence parameters… and a constant filter design is robust." How does the filter design depend on the wind speed? Do the cutoff frequencies change?
22. Table 4: Please specify the units of the frequencies
23. Line 340: "to make each controller module as standard alone as possible," This sentence is a little confusing. What do you mean by "standard alone"?
24. Section 4.2: Do you model the time delay between measurement points due to the sequential scanning of the lidar in the simulations or assume that each point is measured at the same time?
25. Line 354: "the blockage effect" usually refers to the reduction in wind speeds upstream of a wind farm. Is this what you are referring to here? If not, I would suggest clarifying or using a different term.
26. Line 367: "we have chosen the option of constant power mode": Can you explain this control mode for readers unfamiliar with the term?
27. Eq. 36: This equation is hard to understand. Wouldn’t the feedforward pitch command simply be theta_{ss}(u_{RR}) (i.e., the steady-state pitch angle as a function of wind speed)? Otherwise, please discuss why this equation is used and how it is derived.
28. Line 385: What is the value of the actuator delay that is used?
29. Eq. 39: This equation is also hard to understand. It seems like it is missing the actual time delay that you are trying to solve for. Also, should the 1-second lidar averaging delay be included here too? Further, is there enough lead time to account for the filter, pitch, and lidar averaging times for all cases analyzed?
30. Line 411: What is the mean flow field used for the Kaimal model-based wind fields? Is it the same as the power law shear mean flow field used for the Mann wind field?
31. Line 414: "The lengths in the y and z directions are both 150 m": It would be good to discuss why these lengths are smaller than for the Mann wind fields.
32. Line 416: "hub height wind speed from 14 m/s to 24 m/s with a step of 2 m/s are considered." It would be helpful to include simulation results for 12 m/s because this is above rated for the NREL 5 MW turbine and lidar-assisted pitch control would be active. Additionally, Table 4 lists the cutoff frequencies of the lidar filter for 16 m/s. How do the cutoff frequencies change for the different wind speeds simulated?
33. Fig. 7: Since you are using the constant power control mode (where typically torque is controlled to maintain constant power regardless of generator speed), it is surprising to see such high power fluctuations. Can you discuss why this is the case?
34. Line 454: "The spectra are averaged by different samples corresponding to the simulated results by different random seed numbers." This sentence is hard to understand.
35. Line 461: "In the unstable case, the RWES spectrum does not reduce a lot compared to a single point u spectrum…" To illustrate this point, it would be helpful to include the single point spectra in Fig. 8.
36. Line 474: "…which can be summarized as higher spectra in the rotor motion by the Kaimal model than the Mann model." It would be easier to see this if you used the same y axis limits in Figs. 9 and 10.
37. Line 481: "The reduction in the blade root out-of-plane motion is not very observable from the plots…" But significant reduction between 0.02 and 0.2 Hz can also be observed.
38. Section 5.2.3: It would be nice to add some more discussion to this section, for example, providing some reasons why the load reduction from lidar-assisted control might be different for the different stability classes.
39. Line 491: Can you provide a reference for "rain flow counting"?
40. Line 495: "For rotor speed, pitch rate… the standard deviation… is calculated". What is the significance of the std. dev. of pitch rate? Is this a common metric for pitch actuator damage? Why would this be used instead of the std. dev. of pitch angle, or the average pitch rate, etc.?
41. Line 522: "As for the electric power STD…": Again, why is there any significant power fluctuation, since the constant power control model is used?
42. Line 524: Why is there a significant reduction in mean power at 14 m/s?
43. Line 546: "the electricity productions are similar either using LAC or not…" Again, there is a significant drop in power at 14 m/s with LAC. What causes this?

Minor comments:

1. In many places throughout the manuscript, there are citations without parentheses, for example line 44: "Mann (1994)." If the reference is actively used as part of the sentence, it is ok to leave the parentheses out, such as lines 46-48. Otherwise, I suggest using parentheses, for example, as is done in line 25.
2. Eq. 15: Should the second "1" in F_11 be a written as a subscript as well?
3. Eq. 23: Can dk_2dk_3 be replaced by the symbol used in Eq. 8?
4. Line 315: "If a filter with the gain…" This sentence is hard to understand and appears to be incomplete.
5. Line 321: "natural" -> "neutral
6. Line 436: "Karmann"-> "Kalman"
7. Line 512: "14 m/s" -> "16 m/s"?
8. Line 541: "16 m/s" -> "18 m/s"?
9. Line 627: The paper "Dong et al. 2021" has been published as a full paper, so the reference should be updated.