Taking the Motion out of Floating Lidar: Turbulence Intensity Estimates with a Continuous-Wave Wind Lidar

Round 1

Reviewer 1 Report

Major comments:
1. The introduction and importance of the study is correctly presented. Nevertheless, some of the critical methodologies presented in the manuscript are not properly explained.

2. The length of the document seems excesive, which makes it less understandable. I suggest to combine/rearrange some formulae/figures or reduce the extend of some sections.

3. Results of the methodology look promising but merge different data: Figure 7 and 8 average differenet conditions per height, Fig 9 and 10, per HWS or angle. It would be interesting to see, for example, Figure 11 or 12 for a specific height.

Some lesser comments:

Line 29. After acronym is defined, it should be applied along the text, e.g., line 57.

Lines 63-65 "Since turbulence intensity is the most widely-used parameter of turbulence and we will limit our analysis to it after briefly presenting the horizontal mean wind speeds" Poorly written, rewrite please.

Line 111. "heading has an offset" or "heading is shifted/rotated". It is ambiguous to say a rotation "from the x-direction". I'd rather say clockwise or counter-clockwise of z-axis.

Figure 2. Is not clear in caption that a) and b) have translational and rotational motion (if I understood correctly), and c) and d), only rotational. f_v is the period of translational or rotational motion? I can't see the explanation of the difference between lines on each subplot (I count 8 in figure a,Heave,Yaw). It's confusion to use the same symbol for azimuth and wind direction (also in line 168). X-axis symbol not present in third row.

Line 253-256. What do you mean with these sentences?

Line 265. Subsection title suggests that also veer is corrected.

Line 271. Change "Sheer" for "Shear". Review full text.

Line 272. Cannot be inferred by integration of the vertical velocity MRU or tidal data?

Line 287. Is not clear from where it comes equation (19).

Line 292. Ii is not clear where 5,8% value comes. A wind sheer profile is used? Power-law, log-law, with which exponent? Are there some (alpha, z) combination for which this value would be not acceptable?

Line 374. Remove "also".

Line 382. It is also considered the wind veer in the correction?

Line 388. Section 3.2 doesn't specify the lateral motion compensation of each LoS. Is it considered in the results of section 4? It would be interesting to see an estimation of the contribution of each, rotational and translational motion, to the total motion-induced turbulence.

Figure 4 caption doesn't specify that represents the motion compensated Standard Deviation.

Lines 422-436. First says "The ideal motion compensation algorithm can reduce the measured turbulence down to exactly the level of a fixed lidar if the timing between motion and lidar data is correct" but then you look for the minimum of the "motion-corrected standard deviation". It is not clear from the text why both points are the same.

Line 476. The std. dev. of the turbulence intensity is 3.7 m/s, this is a about 75% of the mean value. How consistent is the hypothesis of constant correction factor? How dependent is this factor on the measurement height?

Line 479. "This is the only information we use the correction factor for in this study. All results in this paper are presented without applying the correction factor." These two sentences look contradictory. Is the correction applied or not?

Line 498. Both or any? If only one of the files has less than 75% of the raw data available is considered correct?

Line 503. Is not clear what availability means here.

Line 580. Without further information about particular contribution of each term I'd say "suggest" instead "indicates"

Line 591. Slightly.

Line 592 Substitute "height" for "measurement level"

Line 595. Sentence "would explain why the measured motion-induced TI is erroneously low compared to the value our algorithm calculates" as written suggests that error is not on the algorithm or methodology.

Line 598. Shorter focus length and cone diameter shouldn't lead to a reduction in the reference lidar TI?

Line 633. This could be checked by looking at some complementary sensors such as sonic anemometer of the lidar.

Line 645. Why 0.04% is unrealistically low?

Line 651. I understand "lidar's internal data processing"

Line 655 Bin 3.5-5 [deg] also has high emulation error but there is no overestimation on the compensated TI.

Line 661. The figure depicts the DIFFERENCE BETWEEN THE TI of the floating lidar with regard to the fixed reference lidar

Line 665. Difficult to see gray line.

Line 694. Have you looked at other lidar parameters as: Points in Fit, Spatial Variation, Backscatter, ...?

Lines 701-709. Very speculative or poorly explained: Interval of tilt <1 [deg] is representative of the whole dataset? What is the 96% of the remaining error?

Line 756. Efficacy of the proposed methodology is clearly justified in the paper for the interval between 4 and 10 m/s bins. Without further information about the contents of the lower (0-4) and higher (10-Inf) bins, this conclusions is not proved in the paper.

Line 757. Same comments as previous for angles

Author Response

We thank Reviewer 1 a lot for a very thorough review. The revised version of the manuscript has a significantly higher quality than the original version thanks to many useful comments that we are happy to respond to in the following:

Major comments:
1. The introduction and importance of the study is correctly presented. Nevertheless, some of the critical methodologies presented in the manuscript are not properly explained.

We agree and added a proper description of the critical methodologies presented in the manuscript: "The aim of the work presented here was to develop and validate a method that corrects TI estimates from a floating continuous-wave wind lidar aboard a buoy being deployed offshore. For our approach, we measure the motion of the buoy in all six degrees of freedom and record the line-of-sight velocity spectra of the lidar. We then compensate for the motion of the lidar before we reconstruct the wind vectors under consideration of the rotation of the buoy. A method to synchronize the lidar and motion data is an integral feature of our approach."

2. The length of the document seems excesive, which makes it less understandable. I suggest to combine/rearrange some formulae/figures or reduce the extend of some sections.

The document is relatively long. We therefore added a hint to skip reading the sections about theory and how the motion compensation algorithm is implemented for readers who are not interested in reproducing or understanding the motion induced error in detail. We also removed several passages of the text to shorten the manuscript. See also response to lesser comment regarding Line 253-256.

3. Results of the methodology look promising but merge different data: Figure 7 and 8 average differenet conditions per height, Fig 9 and 10, per HWS or angle. It would be interesting to see, for example, Figure 11 or 12 for a specific height.

We understand the reviewer's interest in seeing Figure 11 or 12 for a specific height and modified both figures accordingly. The transparency of the markers does now represent the height level at which the corresponding values were measured. We also added an explanation to the text. The individual analysis of single heights does not reveal any systematic effects. We therefore decided to not add separate figures which show only one specific height.

Some lesser comments:

Line 29. After acronym is defined, it should be applied along the text, e.g., line 57.

We checked all occurences of "turbulence intensity" and replaced them by the acronym "TI".

Lines 63-65 "Since turbulence intensity is the most widely-used parameter of turbulence and we will limit our analysis to it after briefly presenting the horizontal mean wind speeds" Poorly written, rewrite please.

We rewrote the passage to: "TI is the most widely-used parameter of turbulence. We will therefore limit our analysis to it after briefly presenting the horizontal mean wind speeds."

Line 111. "heading has an offset" or "heading is shifted/rotated". It is ambiguous to say a rotation "from the x-direction". I'd rather say clockwise or counter-clockwise of z-axis.

In order to make the statement unambiguous, we changed the sentence to: "...its heading is rotated around the z-axis by theta_0=30deg from the x-direction towards the y-direction"

Figure 2. Is not clear in caption that a) and b) have translational and rotational motion (if I understood correctly), and c) and d), only rotational. f_v is the period of translational or rotational motion? I can't see the explanation of the difference between lines on each subplot (I count 8 in figure a,Heave,Yaw). It's confusion to use the same symbol for azimuth and wind direction (also in line 168). X-axis symbol not present in third row.

a) and b) have purely translational motion. We added this information to the first reference to a).

f_v is the frequency of motion, both translational or rotational. We added this information to the caption and to the first occurrence in the text.

In order to explain the meaning of the eight different lines we now write that "Color shades represent different phases of the oscillatory motion.".

We introduced the wind direction Theta in the caption of the figure and the referring text. We also recreated the figure so that it includes the x-axis symbols also in the third row.

Line 253-256. What do you mean with these sentences?

The intention was to explain that it is not necessary to worry about the fact that the measurement "circle" of a moving lidar is no longer a round circle. We removed these sentences to shorten the text.

Line 265. Subsection title suggests that also veer is corrected.

Yes, the effect of veer is described in this subsection and our motion compensation does compensate for it.

Line 271. Change "Sheer" for "Shear". Review full text.

We replaced all occurrences of "sheer" to "shear".

Line 272. Cannot be inferred by integration of the vertical velocity MRU or tidal data?

It can be estimated like suggested but we ignore it because elevation changes caused by heave motion are negligibly small compared to elevation changes caused by buoy tilting. To make this clear we write that "We ignore the elevation variations caused by heave motion because they are small...".

Line 287. Is not clear from where it comes equation (19).

We added a description to clarify the origin of (19).

Line 292. Ii is not clear where 5,8% value comes. A wind sheer profile is used? Power-law, log-law, with which exponent? Are there some (alpha, z) combination for which this value would be not acceptable?

Yes, the lidar measured wind profile is used and linearly inter- and extrapolated. A wind shear model could be used if not enough elevations would be available. Presenting the calculations behind k=5.8% would unfortunately require a lot of text and figures and the manuscript is already long. We therefore decided to give only the most important results here. We added information that the value given is based on the measurement data used in this study.

Line 374. Remove "also".

Deleted

Line 382. It is also considered the wind veer in the correction?

Yes, wind veer is considered in the correction because we interpolate the mean wind vectors between the height levels and not only the horizontal mean wind speed. We added a remark to section 2.3.3. "However, we consider wind veer in the motion compensation algorithm that we present in section 3.2."

Line 388. Section 3.2 doesn't specify the lateral motion compensation of each LoS. Is it considered in the results of section 4? It would be interesting to see an estimation of the contribution of each, rotational and translational motion, to the total motion-induced turbulence.

It is unclear what the reviewer means by "lateral motion compensation". If they mean compensation of the three translatory degrees of freedom, we refer to lines: 377-382 (revised). Section 4 shows the results with compensation of all effects described in section 2.3.

We agree that an analysis of the individual contributions of translation and rotation would be very interesting. It is possible to run the computations with only rotational or only translational motion compensation being enabled. Also wind shear and veer can be enabled or disabled. We did not include this analysis in our study.

Figure 4 caption doesn't specify that represents the motion compensated Standard Deviation.

We added this information.

Lines 422-436. First says "The ideal motion compensation algorithm can reduce the measured turbulence down to exactly the level of a fixed lidar if the timing between motion and lidar data is correct" but then you look for the minimum of the "motion-corrected standard deviation". It is not clear from the text why both points are the same.

Line 476. The std. dev. of the turbulence intensity is 3.7 m/s, this is a about 75% of the mean value. How consistent is the hypothesis of constant correction factor? How dependent is this factor on the measurement height?

We do not make use of the ZX correction factor in our results but present TI=sigma_U/U. If the correction factor would be applied it would be determined for every single 10-min interval. The correction factor is a function of measurement height and measured TI.

Line 479. "This is the only information we use the correction factor for in this study. All results in this paper are presented without applying the correction factor." These two sentences look contradictory. Is the correction applied or not?

See above. We added that "We do not apply this correction factor to our TI estimates but we can use it to get an approximate idea of the impact of the reduced line-of-sight averaging and reduced diameter of the measurement cone of the fixed reference lidar."

Line 498. Both or any? If only one of the files has less than 75% of the raw data available is considered correct?

We "filter out files for which less than 75% of raw data is available."

Line 503. Is not clear what availability means here.

We rewrote the sentence to: "This keeps all intervals for which data is available from all height levels from both lidar units."

Line 580. Without further information about particular contribution of each term I'd say "suggest" instead "indicates"

Changed to "suggests"

Line 591. Slightly.

Thanks.

Line 592 Substitute "height" for "measurement level"

Yes, measurement level reads better here. Changed.

Line 595. Sentence "would explain why the measured motion-induced TI is erroneously low compared to the value our algorithm calculates" as written suggests that error is not on the algorithm or methodology.

That is what we would like to say here.

Line 598. Shorter focus length and cone diameter shouldn't lead to a reduction in the reference lidar TI?

Shorter focus length and cone diameter should lead to an increase in the reference lidar TI "as shown with the help of the correction factor in section 3.5.".

Line 633. This could be checked by looking at some complementary sensors such as sonic anemometer of the lidar.

The met station of the lidar cannot measure vertical wind speeds and its update frequency is less than 1Hz. It is therefore not possible to check the sign of the radial velocities with it. An additional 3d sonic anemometer could be used but was unfortunately not available. We added: "Further investigation, e.g., with in-situ anemometry is required to test this explanation."

Line 645. Why 0.04% is unrealistically low?

The value seems unrealistically low "in comparison to the value of 0.63% measured for 1deg<\overline{\alpha}<1.5deg".

Line 651. I understand "lidar's internal data processing"

That is indeed the better expression.

Line 655 Bin 3.5-5 [deg] also has high emulation error but there is no overestimation on the compensated TI.

Yes, but bin 3.5-5 [deg] is not as high as bin 5-10 [deg].  Bin 3.5-5 [deg] is an intermediate between bin 3-3.5 [deg] and bin 5-10 [deg] with regard to both, the emulation error and the resulting over-/underestimation. It could be overseen that the right y-axis for the emulation error is offset from the primary left y-axis. We added a thin black line for y=0 in figure 10.

Line 661. The figure depicts the DIFFERENCE BETWEEN THE TI of the floating lidar with regard to the fixed reference lidar

We use the suggestion of the reviewer and write now: "The figure depicts the difference between the TI values of the floating lidar and the fixed reference lidar. These differences are the measurement error of the floating lidar with regard to the fixed reference lidar."

Line 665. Difficult to see gray line.

We replaced the gray line in figure 11 by one in a darker tone that assures better visibility.

Line 694. Have you looked at other lidar parameters as: Points in Fit, Spatial Variation, Backscatter, ...?

No. Points in Fit, Spatial variation (binary), and Backscatter are only available in the Modbus output files that we did not use for our data processing.

Lines 701-709. Very speculative or poorly explained: Interval of tilt <1 [deg] is representative of the whole dataset? What is the 96% of the remaining error?

We agree with the reviewer and rewrote the passage.

Line 756. Efficacy of the proposed methodology is clearly justified in the paper for the interval between 4 and 10 m/s bins. Without further information about the contents of the lower (0-4) and higher (10-Inf) bins, this conclusions is not proved in the paper.

We removed the intervals of mean wind speeds.

Line 757. Same comments as previous for angles

We removed the intervals of buoy tilt angles.

Reviewer 2 Report

General Comments:

Overall this paper is well written and is , by far, the best treatment of the TI issues relevant to wind retrievals from buoy mounted DWLs.

While the compensation for platform induced motion on scales of MBL turbulence is presented a rigorous manner, the experimental set up had two primary weaknesses: 1. Assuming the land (fixed) DWL had the same exposure to the winds and locally generated turbulence as did the floating DWL nearly 400 m away over water; 2. Having to reconstruct the LOS DWL retrievals outside the data processing routines optimized (supposedly) by the DWL developers. This later point raises questions as to how to make the proper compensations for data collected by other users who do not reconstruct the LOS data. However, the utility of the findings presented in this paper remains very high in terms of providing significantly better estimates of TI for wind energy predictions.

It would be useful for the authors to give an example of how critical the 50% overestimation of TI would be to determining the wind energy potential for a potential offshore site.

Specific Comments:

Line 56 and following: What GPS/INS (or MRU) was used in this study? What was its update frequency?

Line 266 and following: While the authors nearly convinced me that sheer and veer were not as significant players in the rotation impacts, they clarified the anticipated impact issue in the paragraph starting line 300.

Line 294: check spelling (extend) and explain why you are not “able” to measure.

Line 355: while this assumption appears risky, it appears to work…. Please explain how the wind vectors are derived by the ZX300 processor.

Lines 546-548: This offsetting of speed and surface roughness effects is fortunate in your case. Can it be generalized? This point is consistent with my more general concern about the experimental setup. Again, this is not a fatal flaw in an otherwise very useful motion compensation approach.

Line 660: What is meant by “absolute” error? Square root of the square?

Figure 11 b, and c: hard to see the tilt and emulation error lines.

Author Response

We thank Reviewer 2 for their work and the encouraging feedback on our manuscript. It helped to improve the quality of our manuscript. In the following we reply to all points they raise:

General Comments:

Overall this paper is well written and is , by far, the best treatment of the TI issues relevant to wind retrievals from buoy mounted DWLs.

While the compensation for platform induced motion on scales of MBL turbulence is presented a rigorous manner, the experimental set up had two primary weaknesses: 1. Assuming the land (fixed) DWL had the same exposure to the winds and locally generated turbulence as did the floating DWL nearly 400 m away over water;

Yes, a comparison with two closely colocated lidar units of which one is floating and the other one is fixed would have been ideal for our purpose. Such a setup requires an offshore platform which we did not have access to for this study. We still believe that the turbulence at both measurement locations is comparable because, first, the stretch of undisturbed inflow is long compared to the separation distance and, second, the influence of changing surface roughness on turbulence develops vertically upwards with increasing distance from the location of roughness change. A rule of thumb says that changes in surface roughness influence the turbulence at heights up to 1/10 of the distance. In our case the sea to land transition is approx. 150m away from the reference lidar. That means we would expect increased turbulence values up to a measurement elevation of only 15m. Because the lowest elevation that we compare is 40m above sea level we expect our measurements to be independent of the roughness change.

2. Having to reconstruct the LOS DWL retrievals outside the data processing routines optimized (supposedly) by the DWL developers. This later point raises questions as to how to make the proper compensations for data collected by other users who do not reconstruct the LOS data. However, the utility of the findings presented in this paper remains very high in terms of providing significantly better estimates of TI for wind energy predictions.

Exactly. Making the line-of-sight data from the ZX300 available is cumbersome and not having them makes it impossible to use our approach. We show the potential inherent in the method and hope that the manufacturer ZX lidars will support working with the radial wind speed data in future.

It would be useful for the authors to give an example of how critical the 50% overestimation of TI would be to determining the wind energy potential for a potential offshore site.

Such an estimation would be useful but lies outside the scope of this study. Regarding the influence of turbulence on aerodynamic loads on wind turbines we add that "Trusting in such erroneously high TI values could for example result in extra costs caused by choosing overdesigned wind turbines."

Specific Comments:

Line 56 and following: What GPS/INS (or MRU) was used in this study? What was its update frequency?

We added the information that the MRU 6000 motion reference unit by Norwegian Subsea is used in this study. The update frequency of 50 Hz is now added to section 3.5. (Instrumentation and measurement setup)

Line 266 and following: While the authors nearly convinced me that sheer and veer were not as significant players in the rotation impacts, they clarified the anticipated impact issue in the paragraph starting line 300.

Here, it is unclear what the reviewers intention is. Section 2.3.3. explains the influence of wind shear and veer. We agree that the influence is very low but believe it should not be forgotten.

Line 294: check spelling (extend) and explain why you are not “able” to measure.

We corrected the spelling mistake and changed "extend" to "extent". Regarding our inability to model the effect of wind veer we changed our statement to the following: "The effect of wind veer might increase the measured turbulence again to some unknown extent. The effect is difficult to quantify because wind veer involves dynamic changes in wind direction which lead to significant deviations from the figures-of-eight as explained in section 2.3.2."

Line 355: while this assumption appears risky, it appears to work…. Please explain how the wind vectors are derived by the ZX300 processor.
Yes, we are lucky that this simple method turns out to be widely successful. The ZX300 processor reconstructs the wind vectors from unsigned radial velocities and overcomes the resulting sign ambiguity with the help of wind direction measurements at ground level. Hence, no sign is assigned to the line-of-sight measurements. We now write in section 3.1: "The sign ambiguity of the wind direction results from the use of unsigned line-of-sight velocities. It is resolved with the help of wind direction measurements of a local weather station. Though, flipping the sign of the wind vector does neither influence the mean wind speed nor the turbulence intensity."

Lines 546-548: This offsetting of speed and surface roughness effects is fortunate in your case. Can it be generalized? This point is consistent with my more general concern about the experimental setup. Again, this is not a fatal flaw in an otherwise very useful motion compensation approach.

We do better not try to generalize any findings regarding the differences in mean wind speed. The differences we find between floating at fixed lidar lie well within the measurement accuracy of 0.1m/s given by the manufacturer ZX lidars.

Line 660: What is meant by “absolute” error? Square root of the square?

The word "absolute" was wrong here. We removed it.

Figure 11 b, and c: hard to see the tilt and emulation error lines.

Thanks for this last hint. We agree and darkened the tilt angle line. We would like to stick to the current line style and color for the emulation error because it is of secondary importance here. Making the line more apparent would distract from the primary content in the figures.