General comments

The discussion paper "Correction of motion influence for nacelle[-]based lidar systems on floating wind turbines" submitted by Gräfe et al. introduces two models for analyzing the motion-induced measurement error on wind speed estimates from nacelle-based wind lidars on floating offshore wind turbines. Both models are used to quantify measuerement bias and uncertainty caused by a variety of motion parameters and wind conditions. The paper also describes the results achieved by applying two methods for separate removal of the motion-induced measurement bias and uncertainty. The title of the manuscript clearly reflects the content of the work with regard to motion correction, but it understates the significant amount of work done towards quantification of the measurement error.

The addressed topic is of high relevance to the Wind Energy Science journal because accurate nacelle-based lidar measurements are relevant for power curve measurements and wind turbine pitch control. With its focus on floating offshore wind turbines the paper is of international interest and in particular relevant for regions where wind resources over shallow water are scarce. The paper combines existing methods of lidar simulation with new ideas for how they can be used for nacelle-based wind lidars on floating offshore wind turbines. The conclusions of the work are of high relevance to the scientific and industrial community, in particular the recommendation to not use uncompensated data from pitching nacelle-based wind lidar is important. 

The objectives and methods of the study are clearly outlined in the introduction and described in enough detail to make the study reproducible. All assumptions that are made for modelling the lidar measurements are stated explicitely. Though, several of the assumptions made are not or not sufficiently reasoned. They are also not well discussed in terms of their implications to the results. This should be improved in a revised version of the paper.

Many simulation results are presented and briefly discussed. The paper would benefit from a more concise presentation of the most important results and a more in-depth discussion that focuses on the results that are of practical relevance. 

Overall, the presentation of the work has a clear structure and is well written. The overall good readability is interrupted by very many minor mistakes regarding missing dashes, commas, and prepositions.

I recommend that publication of the manuscript should be reconsidered after major revisions.

Specific comments

1 Introduction

In general, relevant literature has been cited and described. The authors should also include the main findings and limitations of the cited references, so that existing knowledge gaps become clear that motivate the paper. Please explain explicitly why your study extends the existing body of literature.

l 11: The abstract should be improved by making it more concise and result oriented. For example "Further, we discuss the need for motion compensation..." should be replaced by for example "We find that motion compensation is needed if...".

l 71-75: This analysis of an error cause should better be moved to section 3 where it can be put into context that is still missing in the introduction.

l 91: Better include the objectives to be the conclusion of your literature research instead of a short separate subsection. 

l 95: A third objective is probably the assessment of the introduced correction methods.

2 Methodology

The methodology separated into analytical and numerical modelling is well described. Subsection 2.1 is missing information about time and duration of the campaign, also relevant information about environmental conditions during the campaign are missing (calm or rough sea states...). Some of the notation introduced in 2.2 and 2.3 is incoherent or unclear. Please revise.

l 129: Give a reference to where in the manuscript the lidar is fully described (beam timing, range gates...) 

l 145f: This is probably a reasonable simplification but the authors must explain why surge and sway can and should be omitted. Are they small compared to the rigid body motion due to tilt of the floater?

l 148: Variable "a" must be introduced.

l 155: Refer to Figure 2 and introduce x_trans and z_heave

l 165: Please describe: What are the implications of these simplifications on the measurements? Why are they acceptable?

l 167: The "u-component" of the wind vector is often referred to in the manuscript but it is never introduced. The authors should define it in the methods section.

l 172: Mention the specific beam geometry here or refer to where in the manuscript it is given.

l 175: Please include the rotation matrix Rx,y,z (or R(ψ,β,γ)), instead of just mentioning it.

l 180: Briefly describe why volume averaging is omitted (or refer to 2.3 where it is mentioned). Also why is turbulence not needed in the analytical model?

l 208: "surge", "sway" and "heave" have been introduced and should be used for consistency with the rotational DoF.

Eq. 11: What is the index I referring to?

Eq. 12: Index "P" or "p" (Figure 3)

Fig. 3: This figure needs improvements: By definition [xI,yI,zI] are the current positions of the lidar focus points. And [xp,yp,zp] are the positions of focus points after translation. What is the dashed blue vector? If it shall be the translation vector, why does it not connect [xI, yI, zI] and [xp,yp,zp]? Things stay a bit unclear to me.

l 220: Stick to the x,y,z order: "surge, sway and heave".

3 Motion influence in nacelle based lidar measurements

Both 3.3 and 3.4 would benefit from a concise summary of findings like it is given at the end of 3.2. Which parameters are the most critical for uncertainty and bias? What are the ranges of error caused by the different analysed parameters?

l 230: Use subplot labels, e.g., "(a)" to refer to parts of a figure. This accounts for several instances througout the manuscript (e.g., l 341).

l 238: For the frequently occurring wind speed range around 10 m/s, the pitch standard deviation (approx. 0.5deg) is lower than the mean pitch angle (approx. 0.6deg). From this, it is not intuitive that there will be "significant fluctuations in the lidar measurements" while "no large errors in the mean wind speed estimates due to the mean pitch angles are expected". Please explain why you assume stronger influence from the dynamic motion. The authors can do so for example by adding to the plot the translational velocity of the lidar caused by tilt.

Fig. 4 caption: Left: Describe error bars in left plot. What do they show? Right: Which LOS velocity? (Is it arbitrary?). In general, give more information in the captions (here: Data from measurements or simulation?), so that readers who first don't read the text get a better impression.

l 246: Second peak is not visible in the spectrum which ends at 0.5 Hz. Instead, second peak is visible at 0.33 Hz?

l 253: How are uncertainty and bias defined? Maybe refer to the definitions in the appendix.

l 263: The authors should mention that the first analysis presented here is valid only for steady displacement (or very slowly fluctuating motion << 1Hz)

l 263: "of [displacement] in individual DOF"

Fig. 5: Use differentiating text for the subplots in one column (e.g., "Yaw, α=0.0", "Yaw, α=0.1"...). All plots with zero motion but shear show mean reconstructed u velocities < reference wind speed. I understand that this is due to averaging over the rotor plane but it is not intuitive and makes interpretation of the entire figure difficult. Consider normalizing the y-axis to wind speed at zero motion. Or at least add the recontructed wind speed at zero motion to the plots as horizontal lines.

l 270: "stays nearly constant" (roll leads to slightly reduced vertical measurement positions)

l 275: This could be better described with the help of the chosen vertical shear model (Eq. 4): The effect of heave leads to identical sinusoidal variations of the measurement elevation for all four beams. As a result the reconstructed wind speeds in u-direction will show a minor negative bias, i.e, lidar-measured wind speeds will be lower than reference wind speed. This is because the horizontal wind speeds increase slower with increasing height than they decrease with decreasing height. The authors could also give an example to prove the insignificance of this bias in comparison to other biases. Without such a prove the reader might not believe that "no significant bias is introduced by the heave displacement".

l 277 f: It must be clarified that this is true for slow motion relative to the 1Hz scanning pattern of the lidar.

Fig. 6 caption: Describe the value of α. 

l 301: Figure 7 shows uncertainties "up to 15%", not "up to 20%" 

Fig. 8: Use a),b),c), and d) as titles above the subplots and refer to Table 2 in the caption. Otherwise, it is difficult to get all relevant information and interpret the Figure. 

l 324: Isn't it straightforward to show that this relationship is reciprocal: Half the period-> double the translational velocity -> double the uncertainty? The authors can consider using Pitch frequency instead of Pitch period for the horizontal axes in Fig. 8 to show a linear relationship.

l 354: This is 0.5% of the measurement value and would be very significant. In this case the deviations between analytical and numerical solution would need to be explained. From the Figure, it looks like the deviations are actuallz below 0.02m/s. 

4 Correction Approaches

l 358-364: Good to summarize but as an improvement, consider to describe the three effects in terms of uncertainty and bias separately. Maybe use a table with DOFs (vertical) and uncertainty and bias (horizontal). Then fill the cells with strong (++,--), low (+,-) and no effect (0). 

l 370: "nacelle-based lidar"

l 396: How small are "small time scales"?

l 408: The authors should explain their motivation for not "correcting lidar measurement time series based on the instantaneous turbine tilt angles". Although this would offer a chance correcting for bias and uncertainty at once. What is advantageous about the look-up table plus frequency filtering? What are the drawbacks?

Eq. 13, l 413: "v_correction" is later called "v_corr".

Table 7 caption: Introduce "Hs" and "Tp" here.

5 Results

l 465-475: Consider removing these three short paragraphs including Figs. 11 and 12. Another parameter study does not add new knowledge and the efficacy of the model-based correction will be shown in Fig. 15. If the authors decide to keep the figures, they should be combined into one

l 482 & 489: Give ME in % here. Relative error is less dependent on WS.

Fig. 13:  Adjust both y axes to use the same grid lines: For example:

y left: [-0.4 0.2]

y right: [-6 6]

I recommend showing the relative error.

l 498ff: Consider deleting this paragraph and Fig. 15. It does not contain new ideas or knowledge.

l 505: I agree. Please add: How do the authors assess the remaining motion-induced error? (Why) Is it acceptable?

l 509: Put this into a wider context also considering lidar-specific effects: line-of-sight averaging and cross contamination caused by combining spatially-separated measurement volumes.

Fig. 16 caption: Is wave case 1,2 or 3 shown?

l 512: Which is the natural pitch frequency? Please add the value, if known.

l 516: Why is the MAE of the filtered lidar wind speed estimates slightly higher than the uncorrected value? Also, how do you explain that the remaining error after correction is approximately the same for all cases?

6 Discussion

l 541: The authors should discuss what is the effect of including turbulence, volume averaging and the real scanning pattern.

l 561: I agree. Many practical issues like time-synchronization and measurement accuracy are not considered here. Please explain the possible consequences for the application of your method.

7 Conclusion

l 588: In my opinion the wind shear coefficient should be added to the list of parameters determining the bias.

Appendix

l 618: At least pitch deflection and velocity in x direction are correlated. Who could this influence the results?

l 633f: What are the implications of this assumption for reconstructed wind vectors in a turbulence wind field?

l 643: What is the measurement plane (the lidar measures along four lines)? Also, it depends on the spatial structure of the turbulent wind field if the samples taken along four beams are representative of the entire measurement plane.

Technical corrections

l 4: Words like "well" should be avoided. They usually don't add value to the manuscript. (also "much", l 539)

l 4: The manuscript is missing commas in many instances. For example: "In this work, we investigate..."

l 5: The manuscript is missing dashes in many instances. For example: "...forward-looking nacelle-based lidar systems..." or "...motion-induced effects..."

l 11: The abstract should be written as one paragraph.

l 84: "are calculated"

l 104: "Second," "on an analytical"

l 112: "simulation"

l 119: "Figure" should be capitalized throughout the manuscript. Same for "Equation", "Eq.", and "Table".

l 125: "Ideol's"

l 146: "DOF" instead of "DoF" or vice versa for consistency througout the manuscript.

l 184: "given"

l 194f: "quantify the bias", "as a function"

l 209: "positions are obtained" (plural)

l 212: [xI xI xI]?

l 240f: "as well [as!]" should be replaced by "and" wherever possible.

l 255: "follow[s]" or better "is the same as..."

l 317: "MAE" instead of "MEA"

l 378: "the use [of] nacelle[-]based lidar"

l 393: "maintain the [the] rotor..."

l 396: "measurement[s]"

l 405: "section [3?]"

Table 7: Units [m] and [s] are not written in italics (also l 670).

l 463: "over a[n] averaging"

l 505: "floater[']s"

l 525: "measur[e]ments"

l 536: "measure[me]nts"

l 551: "model [to] calculate"

l 583: "results [uncertainties] derived"

l 611: Rewrite this sentence, or remove "a output".

l 654: "[A]ppe[nd]ix"

l 655: "a[n] parameter"

l 665: "[b]ias" 

l 677: "the [the]"

l 683: "minim[a]"

General comments

A generally well-constructed and timely article dedicated to the quantification of motion induced uncertainties of wind speed derived from measurement of nacelle based lidar systems mounted on floating offshore wind turbines. The methodology is clear and explicit and given with enough details in such a way comparative investigation can be performed in an efficient way. There are, however, some assumptions that should be more elaborated.

The major result of the manuscript is that the uncertainty and bias in the 10 min wind speed are mainly driven by the pitch angle of the floater and the pitch amplitude. Thus, this paper presents a valuable contribution to the international wind energy community, since nacelle-based lidar measurements can be used to improve the speed regulation of wind turbines by a look-ahead update to the collective pitch control, thus reducing the loads applying on tower and blades and optimizing power output.  

Globally the manuscript is easy to read, however, the authors should put some efforts on punctuation throughout the entire document, the missing of many commas make difficult to follow the authors’ ideas. Also, the manuscript contains many typographical errors. I recommend a quick proofread. I’ve noticed that one reviewer makes the effort to provide an almost exhaustive list of the errors. It will help. Moreover, the manuscript will benefit from being rewritten in a more concise format. For these reasons, I cannot suggest the paper for submission in WES before some major revisions.

Specific comments

Abstract

The abstract should be written in a more concise format and in a single paragraph.

Introduction

The literature is up to date. However, the main findings and weaknesses should be mentioned. What is lacking in these studies? What the authors couldn’t or haven’t done is their paper that you think it would worth being investigated? The objectives of your paper should be built to tackle what’s missing in the cited papers.

Moreover, it is not clear, and not only in the introduction, on which metric the quantification of the uncertainties, the bias and the correction of motion is going to be applied. I finally figured it out that the wind speed is investigated after reading one third of the paper. It is often said that the analysis will be focus on “lidar measurement”. It is not clear what’s behind this expression. I had sometimes the feeling that turbulence, for example the turbulence intensity, would also be the topics of the paper. Expressions such as “probe volume averaging effect” (p. 7, line 180) have confused me. Please clarify.

p.4, line 99. It seems that surge and sway effects won’t be addressed in the manuscript. It is then specifically written in page 5, line145 that both DOFs are not considered. Low-frequency fluctuations in surge and sway impact the LOS velocity fluctuations for floating lidar measurement. I agree that this low-frequency fluctuations are not governing the main dynamics of a nacelle, so both surge and sway can be put aside. However, it should be clarified in the text.

Methodology

The rotation matrix (Eq .7) should be written for the uninformed reader.

P11, line 243. Which method did you apply to compute the power spectral density? Welsh? Periodogram? Both methods are quite sensitive to the input parameters such as the “window”. It should be clarified (method used and relevant input parameters). Hopefully, for your study the choice of the method wouldn’t have a significant impact since you seek at identifying the spike induced by the motion. So please clarify briefly.

Results

Since I’ve recommended to write a more concise version of the manuscript I’m wondering if figures 11, 12 and 15 and the associated text are really relevant. I think these parts could be removed or at least shorten without affecting the content of the paper.

Discussion

I understand that the benefit of your analytical model is a gain in computational time but I’m wondering if it sufficient to chose this approach over more sophisticated approaches, i.e., model employing the generation of synthetic turbulent wind fields, to assess the uncertainty and bias in wind speed due to the movement? What would be your recommendations in term of model choice to a uniformed reader who would like to perform a similar study to yours? Specially what would be the impact of using a model with or without representation of turbulence?

General comment

This paper presents a study of the measuring accuracy of a wind lidar mounted on the nacelle of a floating wind turbine. The authors perform an estimation of the expected uncertainties and biases on the wind lidar measurements that are introduced due to the motion of the floating wind turbine. I think that it is an overall well-written study and its topic is interesting for the readers of the Wind Energy Science journal.  Please find below a list of minor comments and suggestions for improvements of the manuscript.

Specific comments

1. Line 157, Equation (3). I suggest using a different symbol for the translation velocities

2. Line 214: What is the function that describes f(a)? and is “a” the measurement distance or the distance from the measuring location?

3. Line 215: What is the length of range gate and how many points along the beam were used for the discretization?

4. Line 245: Do the authors refer to Figure 4 (right) when they write: “the second peak is the tower natural bending frequency at around 1 Hz”? The plot presents the power spectral density down to 0.5 Hz.  A second peak can be found around 0.3 Hz. Do the author mean that one?           

5. Line 247: Is it the lidar pitch signal or the IMU pitch signal? If it is the former, on which basis this conclusion is drawn? If it the latter, isn’t already stated in the sentences 241-242.

6. Line 265: Can you add which equation is used here to estimate the u- component?

7. Line 269: Figure 5. Can you clarify in the manuscript which are the top and the which are the bottom beams? I guess that the VLos1 and VLos2 correspond to the top beams.

8. Line 284: The authors present in Figure 6 the impact that the translational velocities of the lidar device on the measured LOS velocities. The values of these velocities seem high. Have they been calculated based on the motion of the FLOATGEN demonstrator floating wind turbine?

9. Line 345: The “lidar wind speed estimate” is the u-component estimate?

10. Lines 376-377: Why are biases up to 0.1 m/s (which are presented in Figure 9) characterized as significant?

11. Line 385: The authors write that the “dynamics induced fluctuations in lidar wind speed measurements which are indicated by high measurements uncertainties”. Why are these uncertainties considered high for a load evaluation?

12. Line 494: it is written “u-component wind speed of the original wind field averaged over the rotor plane”. However, in line 496 it is written “the lidar measured u-component is observed”. I guess that it is the same quantity in both cases. I think that this is confusing. Therefore, I suggest that a different symbol is used to denote the longitudinal component of the wind vector from the rotor averaged wind speed throughout the manuscript.

13. Line 502: In Figure 14 the power spectral density of the original wind field is presented along with uncorrected and filtered wind lidar lidar estimations. First, why is the maximum frequency 0.3 Hz? Shouldn’t it be 0.5 Hz if the sampling rate of the lidar is 1 Hz? Also, the PSD of both the uncorrected and filtered lidar signals are higher than the original wind field in the frequency bandwidth from 0.075 Hz to 0.3 Hz. In line 509 it is stated that “the reference PSD of the original wind field represents an average over all points in the rotor plane. Therefore, the spectrum lies below the lidar estimated spectra”. Why do the authors did not choose to plot the PSD of the reference u-component? The same question applies also to the results presented in Figure 16.

Technical corrections

1. Line 51: Replace “imprtant” with “important”

2. Lines 119-120: Please reformulate the sentence “a … space, defining… is defined”

3. Line 184: “given” not “give”

4. Line 199: Please change the “chapter” with the “section”

5. Line 247: Please change the “velocities” with “velocity”

6. Line 347, Figure 9: There is an inconsistency between the a) and c) ploys. In (a) the shear exponent symbol is included, but not in (c).

7. Line 381: What does WFC stand for?

8. Line 406: The section 5 has not been presented yet.

9. Line 413 and Line 421: I guess the u_correction and u_corr. represent the same quantity. I suggest using one way to denote it.

10. Line 463: Change the “figure” with “figures”

11. Figures 11 and 12: In the y-axis it is written “absolut” instead of “absolute”.

12. Line 508: Caption of Figure 16: Replace the word “simualated” with “simulated”

13. Line 525: replace “measurments” with “measurements”

14. Line 537: Replace the word “chapter” with the word “section”

15. Line 611: Replace “uncertainty a output” with “uncertainty of an output”

16. Line 613: The sum shouldn’t be over “n”?

17. Line 621: Add the subscript “i” to “a” in the equation A3

18. Line 626: Add “in the reconstructed”

19. Line 646, Equation A6: Shouln’t be “n” instead of “4”

20. Line 661: introduced in Section 2.2

21. Line 670: The units “m” should not be in italic

22. Line 673: Delete one of the “the” from the “the the reference”

23. Line 677: Correct the “the the estimation”

24. Equations A9 and A10, please correct typos.