The discussion and presentation of the manuscript have been greatly improved and most of my comments have been addressed. I recommend that the following minor changes be made prior to publication.
Comments on author responses:
1) RC 1.2 Eqs. 16, 18, 19: Some derivation details (like Eqs. 6-8) or references to sources where these equations are derived would be appreciated.
"AC References to the a paper where details of the derivation of the formulas can be found have been added below the formulas. The reference is also found at the beginning of the section."
Where the new Eq. 22 is discussed, some reference should be pointed out where the derivation details can be found. Otherwise it is not until the next section where a reference is provided.
Pg. 9, ln. 1: "Details of the derivation of the previous two equations can be found in Mirzaei and Mann." The previous two equations are 23 and 24, but I don't see why Eq. 23 needs a reference, as it is quite simple given Eq. 21.
2) RC 1.4 Pg. 7, ln. 12: For the yaw misalignment correction, can you explain if you are trying to estimate the total horizontal wind speed, or the component perpendicular to the rotor? Additionally, comment on differences between measurements with the corrected velocities and the spectral model. For example, with yaw misalignment the measured wind will travel toward the rotor at an angle and reach the rotor at a different position than the model assumes. This could cause some differences between the measurements and model that the correction doesn’t account for.
"AC Here we trying to estimate the component perpendicular to the rotor. A clarification has been added below eq. 21. Also differences to the model have been pointed out. But in case of small yaw alignment the expected differences are assumed to be small."
It seems that you are removing the proposed correction for yaw misalignment and instead saying that the effects can be ignored for small yaw misalignments. I think this is a fair simplification, but the paragraph needs some work, as it is confusing. The sentence "For example, a turbulent structure will traveling along the mean wind direction…" What is this an example of? Of modeling errors that can exist when ignoring yaw misalignment? I feel that a 2nd sentence in this paragraph is needed, explaining that some modeling errors will exist because of effects of yaw misalignment. Then you can list examples before stating that the errors are expected to be small and are ignored.
3) RC 1.5 Table 2: Do you notice differences in length scales and other parameters if you bin by stability in addition to by sector, and would this be worth considering in the analysis?
"AC We have considered binning by stability as the Mann turbulence model is a representation of turbulence in the neutral atmosphere. However, we saw no deviations of the measured point spectra to the fitted Mann turbulence model for different stability classes, see appendix C. Thus, we did not divide the data into stability classes."
Interesting observation. However, I feel that it should be mentioned in the text briefly that binning by stability did not change the spectra significantly, but that binning by sector showed a large difference. Otherwise, readers might wonder if an opportunity was missed by not binning by stability.
4) RC 1.10 Pg. 15, ln. 7: "When comparing the experimental data to the Kaimal model, a larger mismatch is observed compared to region 1." It appears that the coherence for the Kaimal model does not change much between Figs. 9 and 10, and that the Mann model changes similar to the field measurements. Can you comment on this?
"AC The coherence changes are bigger for the Mann turbulence model because changes in the three dimensional structure of turbulence are better represented by the Mann turbulence model. The Kaimal model is less flexible at representing changes in the three-dimensional structure of the turbulence and thus smaller changes are seen between the two regions for this model."
"The coherence changes are bigger for the Mann turbulence model because changes in the three dimensional structure of turbulence are better represented by the Mann turbulence model." This is a good explanation that clearly states the advantages of the Mann model. I feel that this sentence, or something like it should be added to the text to supplement the existing discussion on pg. 16, lns. 11-15.
5) RC 1.12 Pg. 15, ln. 20: "the information theoretical delay estimator" This sounds like a great way to estimate the time delay. Could you briefly clarify how the two input signals are split into past and future? Are you comparing the past part of one signal to the future part of the other?
"AC The signal is split in the middle. Then both past values of the signal are compared to the both future values. This has been clarified in the manuscript. More details can be found in the reference."
I agree that details should be left for the reference. But the explanation in the text still needs improvement. Consider changing "…into two parts: the past and the future and calculating the mutual information of two signals." to something like: "…into two parts: the past and the future and calculating the mutual information between the past signals and the future signals."
Additional comments:
Pg. 7, ln. 23: "The implied sum… could also be written in vector and matrix notation as…" It seems strange to include this since the format of the vector and matrix equation referenced doesn't show up like this in Eq. 20.
Pg. 9, ln. 3: "the lidar systems probes focus points…" -> "the lidar system probes focus points…"?
Pg. 18, ln. 20: "Still, the results for both lidar systems show great overlap between the measured delay and the delay expected from advection speed and lidar geometry." Especially for the 2-beam lidar, the binned mean values are ~1 second lower than the predictions from the advection speed and lidar geometry for low wind speeds. This should be discussed briefly.
Fig. 12: Check the legend for the 4-beam plot. |

thank you for your revised manuscript. Your work is accepted, subject to the implementation of the modifications suggested by the reviewers.

Thank you for publishing your work in Wind Energy Science

Carlo Bottasso