Please see the attached PDF file.

Dear Authors,

First of all, I would like to congratulate you on this very nice manuscript. The results are very impressive and important! Accurate and precise TI measurements with lidar will be very helpful for the wind community. Especially, the comparison of numeric simulations to real measurements is great!

Further, the paper is very nicely written and very well organized.

Please find below two important issues and some minor issues which hopefully help to further improve the manuscript.

1. Probe Volume in simulations: It makes a lot of sense to me that in 4.1 and 4.2 the measurement volume is not considered, since the analysis with the measurement also uses the “unfiltered” radial velocities. Of course, the method from 3.1 could be also applied to simulated data, but this would add more complexity to the simulation and paper. However, in 4.3, volume averaging is applied. This then causes issues with the bias (first paragraph of Section 5) and also is a bit inconsistent. Therefore, I would propose the authors to consider following ideas (or any other which could solve the issue):
   
   a) Add some lines in the discussion and in the beginning of Section 4 about that issue.
   
   b) Apply the method from 3.1 also to the simulated measurements (if possible) from Section 4.3.
   
   c) Ignore volume averaging in Section 4.3 as well, focus only on cw lidar.
   
   For idea a and b, Section 4.3 could be renamed to “… lidar opening angle, focus distances, and lidar type”. For idea c, you would need to remove the “lidar type dependency investigation” from abstract etc. Personally, I tend to Option c, if not too much work, since the paper already provides a lot of information and the lidar type dependency investigation is maybe not so interesting as the rest.
2. The discussion section could be improved: The impact on the matrix from Equation 15 on the opening angle could be discussed in more detail. This might also help to give a more precise conclusion e.g. in the abstract, only a “large opening angle” is mentioned, but there should be an optimum, since e.g. for very large angles closer to 90 deg, the uncertainty for the u component should increase a lot. The first paragraph is also focusing on Figure 12 only and some discussion on the results from Section 4.1 and 4.2 could be added. Further, the second paragraph mentions the assumed frozen turbulence and homogeneity as well as the induction zone. Here a discussion of the impact of these effects could be added. The impact of other assumption/limitation of this study could be added, e.g. the limitation to small yaw misalignment angles.

Some minor details:

• l82: you could introduce U.
• 2.: A simple sketch for the angles would be helpful. You could also explain about the coordinate system, which might be helpful to understand, why e.g. the opening angle is between the beam and the NEGATIVE x-axis.
• Figure 2, 3, 6: the z label (“z [m]”) is mirrored.
• Equation 6: The error function usually uses \sqrt(\pi) in the denominator instead of \pi. And you could also mention that Erf is the error function.
• L112: “frequencies … inside the volume are not considered except the dominant frequency detected by the centroid method”: this is a bit inaccurate, since the range weighting function acts as a filter and damps high frequencies in the wind much more than lower frequencies, but is not perfect (i.e. considering only some frequencies).
• Equation (13): The partial derivative from Equation (12) “(…) ^2” should be “2* (…)*n_i*n_j”. Maybe I miss something. But if not, you could add the 2. It does not make any difference, Equation (13) is correct without it, but it might be easier to reproduce.
• Equation (14) and (15): Similar to the previous comment, couldn’t you simplify these equations by removing n_i and n_j, which is present on both sides? This would help with the discussion on the impact of this matrix. But maybe I totally misunderstood the complexity.
• l155: is a simple mean over all radial velocity components already providing already the variance in u, v, and w? There should be still some weighting with the cos^2, right? If so, this might be a bit misleading.
• Section 3.3: The scan rate of the lidar systems is not mentioned here. Did you use the time resolution of the wind field or did you use a certain scan rate (e.g. 200 Hz for the SpinnerLidar or 4 Hz for a typical pulsed lidar)?
• L183: here it is not clear to me, what do you mean with velocity bin. One would expect a discretization of the distance from -M to M. Also, the “bin^{-1}” for the unit of the resolution might not be necessary, since I think it is clear that the resolution is per bin.
• Table 1: the typical CW lidar has a beam radius of 28 mm, which would be 2.8 x 10^-2 m, not -4. I assume this is a typo, since for the 2.44 m mentioned in Section 3.4 one need 28 mm and 0.28 mm would be very small.

And here some very minor details, which might be helpful. If not, please simply ignore them.

• Table 1 and 2: I am not sure about the WES style, but in general it is a bit more common to use the caption on top rather below the table. Please check.
• Figure 7, caption: you could avoid the line break between “62” and its unit “m”, e.g., using the latex package siunitx.
• l77: “Section 5” might be more consistent compared to “Sect. 5.”
• When you have a list of numbers, e.g. l173 or l186, you could use white spaces after the comma.