Thank you for your comment. It was very helpful for the revision of the article structure and clarify the parts that are not very common in wind energy studies.

RC1: It seems that there are only one or two examples shown for output from the ATS method using LES. I understand the LES simulation is used to test the method on an idealized case but unless you’re working with a larger subset of LES scans it doesn’t seem relevant to put LES in the title of the manuscript? I also wonder if you even really need the LES simulation for this study since it just seems to be used to explain the methodology.

The LES simulation serves as a simplified example to demonstrate the core methodology. We admit that the title can be misleading. The title is changed, and LES-related examples are moved into a stand-alone section ‘Proof of concept’ to separate them from the results. The LES examples now focus on the instantaneous wake instead of the averaged case.

RC1: The LES scan case highlights an interesting example – the ATS algorithm results in many wake shapes (noise) in the far wake; when comparing the ATS v. threshold deficit methods, are you considering these far wake shapes in the confusion matrices? It’s hard to tell if you completely ignored the far wake in the analysis or if it’s included but acknowledged as a source of uncertainty? Because it seems like these shapes would affect calculation of the wake centerline when comparing ATS centerline to Gaussian centerlines?

The far wake was always considered in the threshold verification. However, the current centerline detection algorithm processes only the first continuous wake shape, so the centerline detection from the ATS-detected wakes stops for some scans while the Gaussian method can continue (that does not indicate that it will succeed, though). We acknowledge the current limitation of the ATS centerline search, but plan to improve it further. 

RC1: The manuscript could benefit from better figure organization (some of the figures appear before they are called or are shown in incorrect sections, more on this in 8.). It seems the equations in section 4.1 might be somewhat out of order; it’s unclear where WP is actually used in the process of the ATS method?

The figure and table positions are mainly caused by the LaTeX formatting. Since the corrections affecting the paragraph length could change a figure position, we left it for the final editing.

WP matrix is now included in the algorithm description as a value.

RC1: It would be interesting (and likely important) to know how the radial velocity values are transformed from radial to cartesian components.

This could be a confusion caused by wording. The lidar data used in the thresholding are always stored in the rectangular matrix defined by the polar coordinate system (beam range, azimuth). This matrix is processed both by the thresholding and centerline algorithms. However, if plotted as it is, the polar matrix distorts the scanning filed in the far and near lidar range. Hence, we converted the coordinate field from (beam range, azimuth) to (x,y) to plot a scanned sector in a more human-readable way.

The thresholding method always used the radial velocity, because this method does not strongly depend on the actual wind speed values, but mostly their relative value.

RC1: The word “threshold” is used many times throughout the manuscript (i.e. in the introduction) before it’s completely clear what type of threshold is really being applied; it would help to clarify this for a broader scope of readers.

The threshold is now explained in the introduction when it is first mentioned:

In a simplest case, a threshold is a value that splits the range into two parts: all values below the threshold fall into one group, while the values higher than the threshold form the second group. When applied to the wind field for the wake identification, a threshold would split the data into the wake and free-flow points.

RC1: It might be helpful at the end (or beginning) of the methodology to have a table outlining and summarizing all of the techniques you’ve used, the amount of data (and what type of data) you’ve used for each technique, and to also clearly show which techniques you are comparing. You’re using two common techniques for comparison, comparing manually detected shapes and ceterlines, and also switching up the datasets for some of them (i.e. the inclusion of the LES case study) so it is rather hard to follow. In the first paragraph of the Results section you broadly summarize your process but I don’t think it’s enough to help with the organization. Maybe even call these comparisons Experiment A, B, etc. and label that in the table and section headers? Just for ease of organization.

Thank you for the suggestion. A summary table is added to the end of the Methodology section listing the method names, properties and the input data.

RC1: Do you have ensemble statistics for comparing Gaussian and ATS methods for centerline detection? As I understand it, Figures 16-19 are interesting case studies but the overall success of ATS v Gaussian is still ambiguous. Maybe you could have only one figure showing the R^2s for each wake (because it’s helpful for visualization) and then have a table for ensemble statistics (so you would reduce your figure count by about 3).

The direct comparison between Gaussian and ATS method is rather complicated, because the Gaussian method does not perform well enough on the noisy scans and merged wakes to be considered a good reference. R² statistics worked when the manual centerline was presented as a ‘true’ value. We planned a comparison based on visual inspection: score the success rate of the Gaussian and ATS methods in the near and far wake. This comparison was scrapped in favor of the verification against manual detection, but we will consider to include it back.

RC1: Figures, figure labels and captions should be clarified:

RC1: Figure 4 could use a label for the intensity colorbar below, and the caption states a “valid wind speed range” but this range isn’t clear numerically.

RC1: Figure 5 could use a label for the intensity colorbar below and labels for the entropy figures (a) and (c). It might also be helpful to put the location of turbines in this image as you did in other figures farther below.

RC1: Figures 7 and 8 and Table 1 should be in the previous section.

RC1: Table 2 should be in the previous section

All corrected

RC1: Labels for Figure 10c are ambiguous – what are helper lines?

This was an error in the plotting script, the ‘intersection’ labels should refer to the black dots. ‘Helper lines’ are labelled correctly and refer to the concentric circles described in the centerline detection algorithm.

RC1: Figure 11 is quite hard to follow in general, and it’s the first time the colorbar has been used to distinguish different wake shapes. This is another instance where discussing the output of the ATS (in terms of producing multiple wake shapes) would be helpful. Do you need the black dotted centerline in (d)? It might be helpful to switch (c) and (d) and remove the black centerline in d, also maintain a red color outline for the wake in (c) and (d) so readers don’t think you are using different methods to get the red and black wake outlines.

The figure is changed to show different methods in two different subplots + overlaid wake contours and centerlines in the third subplot. This allowed to keep the same legend without color conflict. The color-coded wake shape are now moved to Fig. 10.

RC1: Figure 15 – I’m not sure why the corrupted scans are included in this figure since they were difficult to inspect manually?

Some of the corrupted scans allowed to perform a manual detection. We agree, that it adds unnecessary complexity to the plot. Due to the corrections in methodology for the deficit-based threshold, the thresholds cannot be compared directly anymore. This plot became obsolete and is replaced with a box plot summarizing the percentage of true positives and true negatives for different methods against manual thresholding.

Figures 9-11 and 15 had experienced the most changes, so they are attached as a supplement.

RC1: Figure 19 – is the “missing” gray color referring to the non-filled gaps?

The ‘missing’ label is replaced with ‘no data’ in all relevant plots to improve clarity.

RC1: Figure 20 – not sure what invalid/valid and WIND and WAKE=WIND mean? Could you clarify?

The labels were dictated by the brevity to leave more space for the actual plot. The label for the scatter plot are changed as following:

‘invalid’ → ‘corrupted’

‘valid’ → ‘data’

WIND and WAKE refer to the respective directions and are labelled near the respective axes.

RC1: The conclusion feels rushed and some of the statements in the conclusion about success rates of the Gaussian v. ATS in the near wake seem confusing / misleading – are you using ATS to identify centerline for far wake objects? Again it’d be helpful to have ensemble statistics for Gaussian v. ATS and better clarification as to whether or not far wake objects are included in success rate analysis.

The far wake centerline is detected by the ATS method, when the detected wake shape is long enough. If the detected shape ends at, e.g., 4D, the ATS method cannot proceed, while the Gaussian method can – although it does not guarantee valid results for the Gaussian method. See the comment about ATS to Gaussian comparison.

The conclusion is now re-written to be more detailed on the methods used, their level of automation, advantages and disadvantages.

Minor Comments

Line 174 The word “significant” shouldn’t be used unless significance testing has been done

Removed

Line 125 The reference wind direction is mentioned several times and is an important part of the manuscript but it’s unclear whether this is wind direction as given by the met mast?

The reference wind and direction were mentioned in lines 98-99. We agree, that the mention was too brief and had to be more emphasized. Section 2 is now rearranged to describe the site, reference data and lidar scans in enough details.

Line 141 Why did you choose the wind speed of 7 ms-1 as appropriate?

The line should be read as ‘wind speed difference’. The value is chosen empirically for this particular data set.

Line 105 It’s a bit hard to follow when the reader has to scroll many pages down to Table 1; is it worth not mentioning table 1 and the scan subsets in this sentence instead mentioning them later, possibly in the data quality section.

Mention is removed

Line 163 Directional entropy is a bit of a misleading term. I was thinking it would be entropy in wind direction measurements of some sort; is there a better term to use for this?

We chose this term to have a short reference to the Shannon entropy calculated across the beam range or azimuth. Apparently, it matched a pre-existing term, which definition is different from what we had implied. The ‘directional entropy’ is now replaced by the ‘row and column entropy’ to avoid confusion.

Lines 163-185 This discussion would benefit from including numerical entropy values for the scans discussed, i.e. “The entropy calculated across the beam range highlights several lidar scans with an entropy decrease compared to other cases (insert mean entropy values for these cases)” – as is, the point of this paragraph is somewhat hard to follow although the figure is helpful; could we have a succinct sentence summarizing these results at the end of the paragraph marked by line 187? It would be helpful to include numerical values to further contextualize Table 1 as well. Also it would be important to clarify what constitutes “corrupted” measurements – is this based on SNR/CNR filtering? Or is it based on the number of data points that exceed the wind speed limit as you discuss later? Either way, it would be helpful to clarify what this means the first time it’s mentioned.

The entropy values are added.

The corrupted measurements refer to the non-physical values of the wind speed (100-1000 m/s) appearing in the scans due to the crosswind effects mentioned earlier in lines 115-130. The mention of the corrupted scans is now added to the line 130. The entropy criteria are now described in more detail.

Line 189 Can you be clearer about the numerical value of the percentage of data points that exceed the wind speed limit? Since this is an important criterion for identifying “corrupted scans”?

Added the following lines:

The corrupted scans in the data set consistently have at least 1% of points exceeding [30 m/s] limit. The percentage drops to 0-0.05% for the rest scans and corresponds to the occasional spikes.

Line 190 Why are the corrupted scans split into 5 subsets / why is that relevant?

The data set was initially split into subsets. The corrupted scans cover exactly five subsets and do not appear in other subsets. The total number of the corrupted scans is more relevant, indeed, so we will remove the mention of the subsets. Their count would be still seen from the overview table.

Lines 195-214 These should refer to Figure 8, not Figure 7, right?

Corrected

Lines 220-221 Can we have more detail about the phrase “shown to reproduce the wake shape rather accurately”?

Details about PALM reproducing double wake and polynomial kernel of the model are added.

Line 261 I think it’s worth stating in the previous paragraph that the output of the thresholding will result in multiple different shapes (particularly in the far wake), since this isn’t visible for the initial LES case (since it’s continuous). It’s an important result of the thresholding algorithm so I think it’s important to discuss it thoroughly and to discuss it well before you show it in Figure 11, for example.

The LES section is now re-organized to demonstrate the wake detection on an instantaneous wake.

Lines 324-326 You could probably remove this paragraph.

Removed

Lines 143-144 How many points constitute a “larger cluster” or high wind speed values? So if gap filling is not performed, are there just missing data values within the scan? And these are thus visible in the scan image?

We performed gap filling only for 1-3 adjacent spikes removed, as they left enough points around to perform a simple interpolation without introducing uncertainty to the data. The whole preprocessing procedure was aiming to clean the lidar scans from the obvious outliers, but not alter the original data too much.

The gap filling was not performed for the deleted points (values above 30 m/s). The thresholded images would show those points as ‘missing’ (‘no data’ in new notation). No distinction is made between originally missing data and values removed during the preprocessing.

Line 330 I’m not sure what “The deficit-based threshold is presented as the wind-speed threshold” means – can you clarify?

This is the threshold calculated as 95% of the free flow wind speed (Uref). It does not require for the wind field to be scaled to [0,1] range, like ATS method, but is applied to the velocity values. Since we had found an error in the method implementation to the radial velocity, the paragraph is removed and the whole subsection on the deficit-based thresholding is re-written.

Line 347 How many scans do you choose to demonstrate the methods’ performance? Why do you choose them? Again might be helpful to put this in a table.

We chose an example from each of the most represented non-corrupted subsets (parallel, aligned, bimodal) to demonstrate the method performance in each case and highlight the potential problems. Where possible, we tried to stick to ensemble statistics, since the scan selection could be highly subjective. A supplementary video was provided to present results of the wake identification for the whole data set.

Section 5.2 title should include a mention of the wake deficit method since you’re also comparing that with manual detection and ATS

The subsection title is changed to ‘Comparison of the ATS wake identification against the manual identification and deficit-based thresholding’.

Section 5.2 Would it be helpful to refer to manual detection as “ground truth” – so we know that you are comparing the performance of ATS and wake deficit to that of the manual detection and producing the confusion matrices as such? This just goes back to ease of organization; maybe a table as mentioned previously would make this clearer.

The manual detection is now emphasized as a ‘true’ detection.

Table 2 To understand the results better, could you explain why the manual-deficit exhibits such a comparatively high rate of false positives?

Due to the improved implementation of the deficit-based threshold, the table will be different now. The remark is still relevant for the selected subset, although the difference is not so dramatic. Since the deficit-based wake identification defines a threshold through a fixed relationship 0.95Uref, the method does not perform self-adjustments depending on the data quality. It appeared, that the deficit-based threshold is underestimated compared to the manual thresholding and identifies more points as wakes while they actually belong to the background flow (false positives).

Thank you for your comment and very detailed review of the methods used. Because of one of the questions we were able to identify an error in the deficit-based threshold. I will answer it in the beginning, since it had most affected the revision.

L329: How is the "free flow" wind speed calculated? Is this automatic or manual?

The free-flow wind speed is taken from the reference wind speed series since the lidar scan is quite noisy to rely on the specific value near a wind turbine. However, as explained in Sec. 3.2, the lidar measures radial velocity, but not the actual wind speed. Thus, the threshold calculated as 0.95Uref would not match well the free-flow radial velocity when the wind direction is too different from the scanned azimuths. This explains better performance of the deficit-based threshold on the bimodal case (wind blows along the scanned azimuths; the radial velocity is rather close to the actual wind speed) compared to aligned and parallel wakes (the direction difference is higher there).

This was not relevant for the ATS method, as it scales all information to the range of [0,1] regardless of the specific wind speed values. On the contrary, the deficit-based method has to work with the wind speed data and wind speed threshold defined in the same frame. Normally, a retrieval procedure should be carried out to reconstruct the wind field. Since we were not interested in the local flow direction, estimating a wind speed would be enough. The radial wind speed is a projection of the actual wind speed vector to the line of sight and can be approximated as:

u = U/cos(ref_WindDir – azimuth)

The estimation is added to the subsection on the deficit-based threshold (adding it to the Data section would make confusion, whether the same procedure is applied during the ATS method). The derivation of the expression will be provided in appendix.

This estimation, although being very crude, improved the performance of the deficit-based threshold for the parallel wakes, but not for the aligned subset – the threshold from the wind speed is still largely underestimated. The correction affected the results for the confusion matrices (Fig. 12-14) and Table 2. The deficit-based threshold cannot be compared to the manual threshold anymore, so we will replace Fig. 15 with a box plot.

The affected plots are provided in the supplement.

Major Comments

This study is not replicable in its current state

The manually segmented wakes are not uploaded to a publicly accessible database. This is problematic, as two scientists would manually segment the scans differently, and as such, the results here are not immediately reproducable.

That is the valid remark. We prepare the manual data set for the upload as well as the manual thresholds. The supplementary video will be re-recorded to include manual wake identification and deficit-based thresholding results.

L364-366: Additionally, parts of the novel algorithm are not presented in the paper.

We will add the crucial parts of the algorithm (thresholding and centerline detection) as pseudocode to the article. The full code is not quite optimized yet and lacks a function to allow centerline detection in the far wake, so it would be available upon request for now.

In its current state, the motivation for the study is somewhat weak

The new methodology seeks to improve the thresholding approach to wake identification. The authors state that "the most common wake detection method is… Gaussian". Is the thresholding approach common and important? When would this approach be used instead of the more popular Gaussian approach? The authors provide only one citation in the paragraph where the this technique is first discussed (L65), so it would appear that this approach is not commonly used.

The thresholding approach was also used as a step in the analysis in Bastine, D.; Witha, B.; Wächter, M.; Peinke, J. Towards a Simplified DynamicWake Model Using POD Analysis. Energies 2015, 8, 895-920. We did not include that reference, as their method required subtracting LES flow without wind turbine from the wake field, which is impossible to perform for lidar data. We will add this reference to the introduction to show different thresholding approach applications.

We believe that the thresholding approach had limited use due to its low flexibility. The automatic algorithm allows to overcome this disadvantage. Moreover, the algorithm is constructed in a way to require as little supplementary data as possible.

The validation methodology could be stronger

Wakes are manually segmented by hand-selecting a threshold between 0 and 1. I expected that wakes would have been segmented differently. I thought that a bounding countour was going to be manually drawn around every wake. This means that the validation study very specifically tests the question of "can we automatically pick the best threshold between 0 and 1" instead of "is our new idenfitication/characterization algorithm the best algorithm for the task". This is still presumably an important question, but we wish the authors to more clearly state that the primary goal of the text is to automatically pick the best threshold for wake identification

Yes, the comparison against manual detection describes, whether the automated method can perform better than the fixed threshold and whether the ATS method can be a replacement for the manual thresholding. We chose this approach because it allowed to perform a comparison for the whole data set in a relatively short period. Drawing a bounding contour requires time similar to manual centerline detection, performing it for the data set even without the corrupted scans (~475 valid scans) would be too time-consuming. We will consider to include few examples with manually drawn contour for some complicated cases.

The terminology regarding different wake identification algorithms was ambiguous, which made it difficult to assess what technique was being used at a given time

"Image processing" is a massive field of study, and as such, it is ambiguous to refer to one wake identification algorithm as simply an "impage processing" technique. Please be more specific about this terminology, and if this technique is coming from the image processing field, provide a citation as such.

The wake identification uses thresholding methods – this will be more emphasized in the text whenever the image processing is mentioned. In the centerline detection algorithm, the image processing is used only in a form of the connectivity analysis and contour extraction. After the contour is extracted, the centerline detection mainly relies on the geometrical properties of the curves.

Throughout the manuscript, please make a stronger distinction when "wake identification" is being carried out vs. when "wake characterization" is being carried out, in accordance with the cited Quon et al. (2020). Unless its meaning is exceedingly obvious in the context, please refrain from using "wake detection"

 e.g. Sec 4.2: The title of this section says "Wake detection". However, this subsection appears to be describing wake *characterization* moreso than wake *identification* (and "detection" implies "identification").

Since we have only introduced a centerline detection algorithm, but did not perform throughout analysis of the wake behavior, it felt too much to call it wake characterization. Your point is valid, nevertheless; the descriptions are corrected to refer to the thresholding method as ‘wake identification’ and centerline detection as ‘wake characterization’.

The structure of the different sections and subsections was unexpected, and as such, it made the narrative of the document more difficult to follow.

I recommend that wake identification methodology subsections should be placed next to eachother in Section 4, and similarly, wake characterization metholody subsections should be grouped together

This is rather hard to fulfil, because the Gaussian method perform boths actions simultaneously. Splitting the manual detection would produce two short disconnected descriptions. As suggested by RC1, we summarized the methods in a table closing the Methodology section: name the method is referred to further, input data, basic principles and level of the automatization.

I recommend that Section 2 be made into a subsection of the contents Section 3

Section 3 already includes several different topics, so we do not feel it would benefit from including technical information on the measurement site. We will regard the possibility to move all data description to Section 2 and leave Section 3 with just lidar data quality and prepocessing.

Is this truly an automatic algorithm that avoids the need to manually preprocess and manually segment?

Yes. All the corrections mentioned can be implemented and parametrized to run as a part of the main algorithm. This includes:

- Despiking and outlier removal, both depend on the parameters (see next comment). This procedure is not unique to the method and can be performed with any other tool convenient for user.

- Selection of the wake shape to perform centerline detection: the algorithm either selects a shape that contains a wind turbine or, if the wind turbine happens to lie in the free-flow, the largest wake shape in a prescribed radius (1-2D).

- Adjust the wake shape for the centerline detection: if the wake shape contains more than one turbine, increase the threshold until wind turbines belong to different shapes. This is a common case for the aligned wakes subset and some scans from the bimodal subset. Right now, we ran the thresholding algorithm with the same parameters for all scans. It could be that subset-specific processing and parameters can lead to a higher threshold, thus removing the necessity for the correction.

- Determine wind direction for the wake search to avoid ambiguity during the centerline detection: if available, take the wind direction from measurements, or run the centerline search method with a large step and approximate the wake direction from the found points.

The only non-automated part is the definition of the subset types which was performed after the manual inspection of the data set and entropy characteristics. However, it was only used to structure the results of the wake detection. No subset-specific corrections were yet applied during the preprocessing and wake detection.

L139-144: Is the despiking process manual or automatic? If it is manual, that potentially hinders the ability to apply the ATS algorithm on larger datasets.

- It is automatic but uses two parameters: maximum allowed wind speed (here – radial wind speed magnitude) – values above are considered non-physical; and removed and wind speed difference – if the wind speed falls into allowed range but differs from the local mean of the nearby points by the specified value, it is considered a spike.

Sec 4.1: This section has statements like "A similar point in the first derivative graph *can* be used" and "only a second derivative inflection point *can* be used". *Are* they used in your algorithm? Please be precise.

Yes, we use both, since the threshold based only on the second derivative may appear too strict. The paragraph is re-written as follows:

A similar point in the first derivative graph T1 is used as a control value. We select the threshold as an average value between first and second derivative inflection points to smooth the threshold detection outcome. If the points initially laid close to each other, the averaged threshold T=(T1+T2)/2 would not deviate too far from T2. If the difference between T1 and T2 is high, the smoothing prevents the threshold from being too strict -- a strict threshold may leave weak wakes undetected.

L265-266: The use of "preferably" makes me think that this algorithm is not automatic

Knowing the wind direction prior to the centerline detection allows to skip few conditional steps in the centerline search algorithms. Suppose, there is no information on the wind direction. According to the algorithm, we first draw a circle of a radius D centered at the wind turbine position.

(Note: the algorithm was updated and improved to cover more exceptions, so its current description may differ in details compared to the original article)

If there are only two intersections, the algorithm calculates a middle point of the arc. Two intersections split a circle into two arcs, hence, two midpoints: ‘upstream’ and ‘downstream’ of the wind turbine. Having only two intersections guarantees, that one point will lie inside the wake shape – the algorithm can take it as a wake point and proceed to the next step by increasing the circle radius.

However, if the very first circle finds more intersections and the wind direction is unknown, the algorithm does not get enough information to select a centerline point. To allow it continue, we first discard all midpoints in the free flow – that leaves only the points inside the wake shape. Then the algorithm draws few more circles with a step of 0.25-0.5D (the step is larger than used for the centerline detection) and searches for new midpoints. At this stage all points are accepted, since the actual wake direction is unknown. The wake direction is estimated by fitting a linear regression to the found points. While the wake direction estimated in a such way may strongly differ from the reference wind direction, it was generally enough to narrow the search for the actual centerline detection.

This complex algorithm is used solely to obtain an approximation of the wake direction to resolve ambiguity in the centerline detection if no other information about wind or wake direction is provided. The information on the wind direction allows to skip to the centerline detection and reduce errors caused by an erroneous estimation.

The centerline detection algorithm restarts from the beginning with a smaller step (~0.1D). Now, if two or more centerline point candidates are found, they are compared against the estimated direction (which midpoint inside a wake shape gives the lowest deviation from the estimated direction?) or local wake direction (which midpoint turns the wake by the lowest angle?). These checks attempt to prevent the centerline point identification upstream or on a side of an irregular wake.

The conclusion does not sufficiently summarize the manuscript

Please summarize the strengths and weaknesses of the novel algorithm, especially relative to the other wake identification/characterization techniques

The conclusion is now re-written to summarize the main features of the ATS method and areas for the improvement. The uncommon preprocessing procedures such as entropy criteria are also detailed.

Minor Comments

L3: What is the difference between a "wake pattern" and a "wake shape"?

The terms were supposed to make a distinction between a data set of dynamically changing wakes and an instantaneous wake. Since we are further referring to ‘wake shapes’ as cluster of points detected by the thresholding method, the mention in the abstract is changed to ‘the wake edges and centerline’ to avoid confusion.

L18: It is a drastic oversimplification to state that the velocity deifict at 5D decreases to 20%. Consider citing review articles such as Stevens and Meneveua (2017) and Prote-Agel et al. (2020) in the introduction

L20: Please provide a citation for "The typical turbine spacing in the wind farms is usually 8D", as I believe onshore and offshore spacing differ

L38: Is it correct to say that lidar measurements are in situ? I think of lidars as remote sensing instruments

L63: This sentence implies that thresholding algorithms are always applied 6–8D downwind of a turbine

These suggestions are considered and necessary corrections were implemented.

L69: What is the difference between an "image" and "processed wind speed data"? Is an "image" a raw version of the wind speed data?

The ‘image’ implies that the data did not originally have information about the wind speed at all. It could be a photo or a figure from the publication. We do not focus on images in the study, but remark few specifics in the Appendix.

The ‘processed data’ refers to the data after despiking and normalization by scaling to the range of [0,1]. While the value distribution resembles a respective grayscale image (as shown in Fig. A1), the data can be reverted back to the original wind speed as long as the minimum and maximum wind speed values used in scaling are preserved.

L116-117: I am surprised to hear that you only encounter two types of noise. I imagine there are more variables that confound your signal (e.g. solid objects). Perhaps it is more appropriate to say "two primary challenges that obfuscate the wake signal" rather than "noise". Also, please clarify what is meant by "high wind speed due to the measurement error"

Those types of noise were the types we had encountered in the particular data set and considered an obstacle for the accurate wake detection. This will be emphasized stronger to avoid misinterpretation. The measurement errors due to crosswind effects and beam reflection from rotor blades were described further in this subsection. The paragraph is slightly re-written to point out at the description.

L125: Where does the reference wind direction come from? A sonic on the mast? Wake angles?

L150: What does "reference data" refer to?

The reference wind and direction were mentioned in lines 98-99. We agree, that the mention was too brief and had to be more emphasized. Section 2 is now rearranged to describe the reference data prior to the more detailed description of lidar data.

L163: What is "directional entropy"? How does it differ from Shannon entropy?

We chose this term to have a short reference to the Shannon entropy calculated across the beam range or azimuth. Apparently, it matched a pre-existing term, which definition is different from what we had implied. The ‘directional entropy’ is now replaced by the ‘row and column entropy’ to avoid confusion.

L174-177: Are all the low entropy scans indicative of strong crosswind effects? The "also" on L175 makes it seem like this is only true sometimes.

Also to clarify, are "cross wind corrupted" scans and "spiked data" scans the same? Also, what is the difference between mostly blue scans (e.g. index 310) vs paritually blue scans (e.g. 405)?

The entropy plot was presented for the data scaled to [0,1] – higher values are closer to zero, lower values are closer to one. The difference between ‘mostly blue’ and ‘partially blue’ is caused by the maximum radial velocity in a lidar scan. The corrupted scans tend to have clear non-physical values 100-1000 m/s, while spikes show more realistic values within 15-50 m/s. Scaling a range [0,1000] to [0,1] smooths low velocities stronger than when the same procedure is applied to a range [0,50].

We now consider adding or replacing the existing plot by the entropy calculated for the data before scaling to the range of [0,1]. It renders the same patterns at wind turbine positions, but processes spiked and corrupted data differently from the entropy calculated for the scaled data. The corrupted scans can be still identified from the entropy across the beam range (similar to Fig. 6a), but the spiked scans blend with other non-corrupted scans.

L182: Scans 1-50 and 301-375 show substantial decreases. Why are smaller ranges stated?

The range for Fig. 6 was restricted to preserve the features for the non-corrupted scans. If the figure is plotted for the full range, the non-corrupted scans shift to red tones making the entropy fluctuations less distinguishable. At the same time, no interesting patterns are revealed for the corrupted scans except for the aforementioned gradual decrease of entropy. We decided to limit the color range to preserve more valuable information in the lidar scans suitable for analysis.

The figure with and without colorbar limits is provided in the supplement for the comparison.

Figure 5: Label the AV7 and AV10 wake

Labels were added

L210: Could you please clarify why the "bimodal subset" sees a bimodal distribution of wind speeds but the "parallel wakes" subset does not see a bimodal distribution? I don't understand why the "parallel wakes" subset also wouldn't see one large peak that represents the free flow and a second peak that represents the wakessds. Does this happen because the "bimodal" wakes largely stay within the field of view of the lidar whereas the "parallel" wakes leave?

The bimodal case has two wakes corresponding to the larger percentage of data points than in other cases. This happens because wakes form in the lidar near range. While the near range occupies rather small area in m², it has the same amount of data points as the far range, which in turn was not subjected to the wakes in our data set. When the scan data are presented as a histogram, the far wake and free flow points are encountered nearly equally often in the bimodal subset – those are the points forming two clearly separated peaks or merging into a flat one. Since the two wakes do not form on a regular basis, it limits the application of the thresholding methods that are working with a distinctive bimodal histogram.

Appendix touches this property of the bimodal subset and shows how the far wake peak disappears when the histogram is plotted for the image of a lidar scan sector and not the original polar coordinates matrix. The reference to the appendix is now added to the bimodal subset description.

Figure 2 is replaced with an example from the bimodal subset to show the difference between the lidar scan presented as a polar coordinate matrix and as a scanned sector plotted in the Cartesian coordinates. 

Considering the other subsets: A hint on a double peak can be seen in some aligned subset scans, mostly because of a good contrast between wakes and free flow, and large wake area in general. Parallel wakes subset has shorter wakes visible. AV7 wake leaves the scanning area before transition to the far wake. AV10 far wake is scanned at the heigher height than AV7 (158 m vs. 97m, see Fig. 1c), so it is weaker and easier merges with the noise.

Sec 3.4: What is the wind speed forcing of the LES?

The description of LES input parameters is expanded.

L232: You deal with at least two types of velocity distributions: unimodal (Fig 8a) and bimodal (Fig 8c). I am confused why you say you tend to only see one peak. As a reader at this point, I am wondering how the ATS algorithm performs on unimodal vs. bimodal data.

The bimodal cases have either two peaks of a different height, or a flat single peak. This results in strong fluctuations for the second derivative of the intensity distribution. The first derivative still shows one distinctive peak.

Section 5.6 deals with the specifics of the bimodal histogram and thresholding. The reference to the results from this section is also added to the methodology section.

L248-257: You say "We detect the threshold at the point where… the curvature approaches zero". But when you also say that "the curvature graph tail may fluctuate and complicate the detection of zero curvature". I am confused - do you use curvature, the second derivative, or the first derivative to select your threshold. Are you doing this on polynomial-fit curves or on the raw curves? Please clarify. This is one of the most important sections of the paper, but it is difficult to understand your algorithm.

We use first and second derivative curves, fit the polynomial to them to find the concave point and estimate two thresholds. The final value as their average.We do not use curvature plot because it can provide only one value for the threshold, which could be erroneous. The reasoning behind this is directly connected to the bimodal subset.

Usually, the second derivative in the bimodal subset has monotonically decreasing local minimums. If the ATS algorithm choses the local minimum and fitting range incorrectly, the threshold would be overestimated and could cut down most of the far wake. Calculating a supplementary threshold from the first derivative allows to compensate overestimation and preserve larger part of the far wake.

L264: What does "shape" mean?

The term is now clarified at the end of the ATS method description as follows:

Because of the wake irregularity, especially in the lidar scan, the method usually detects several clusters of the high intensity points. Any cluster may be a part of the wake as well as falsely detected noise. We do not yet make a distinction between wake and noise, and refer to the detected points as 'wake shapes'.

The mentions of ‘wake shape’ as a general shape of the wake are now removed to avoid confusion.

L269: Please demonstrate centerline detection on an instantaneous wake so we could get a sense of how this behaves on observational data

The figures related to LES wake detection were reworked. Figure 9 now demonstrates wake identification on the instantaneous LES data. Figure 10 shows the grayscale plot, thresholded image and color-coded wake shapes. Figure 11 shows the wake characterization via Gaussian method and centerline detection from the ATS method results. The contours and centerlines are plotted in a way to keep uniform legend. An additional figure shows a complex case of centerline detection for the irregular wake from a lidar scan to support the explanation of the centerline detection algorithm.

The corrected figures are provided in the supplement.

L276: Remove the word "presumably"

done

Fig 10c: "helper lines" and "intersections" have the same legend elements

This was caused by an error in the plotting script; the ‘intersection’ labels should refer to the black dots. ‘Helper lines’ are labelled correctly and refer to the concentric circles described in the centerline detection algorithm.

L283-284: Why is the wake direction ambiguous under these conditions? I would think that the wake direction is especially obvious in the "aligned" scenario

The ATS algorithm often identifies AV7 and AV10 wake as a single shape in the sligned subset. While it is obvious to a human eye, the algorithm running on the identified shape would detect a centerline point upstream and downstream for AV7 – both points looking equally valid for the algorithm because they lie inside a merged wake. If the wind or wake direction is known, the algorithm can search for the centerline points only along that direction. If no particular search direction is prescribed, the algorithm cannot choose a centerline point of two (or more) unless special routines are run to approximate the wake direction before the thresholding.

L285: I asked this earlier, but where does the reference wind direction come from?

See earlier comment on the reference wind direction.

L287-288: This seems like a major limitation. In the conclusion, please note that your algorithm does not work on weak wakes.

In this particular case, we did not regard AV11, because it is was scanned at the far lidar range near the scan border. The AV11 wake is not seen in the 'parallel' subset due to the flow direction leading it outside the scan and is often obstructed by the low speed formations (Fig. 14a). However, it becomes more clear in the aligned and bimodal case (can bee seen in Fig. 12e and 13e). Still, the part of the wake captured is rather small compared to the wakes presented in the same scan. Overall, the weakness of the wake was not a big problem for the identification, but very little information could be used from it compared to other wakes.

The point on weak wakes is rather vali for the parallel subset, we will see if we can include it some where in the description.

L295: "This feature" implies that the important feature is the transition from a single Gaussian to a double Gaussian. I believe you would like to say that the Gaussian distribution of wake deficit speeds is the important feature

The line changed to

The wake deficit distribution is similar to the Gaussian distribution in the far wake (Ainslie, 1988) and often shows a doubleGaussian peak in the near wake (Magnusson, 1999). The similarity to the Gaussian distribution makes a base for a widely used method to detect wake boundaries and centerline (Vollmer et al., 2016; Krishnamurthy et al., 2017).

L297: Can you roughly quantify "small plane inclination"?

About the same where we can use approximation sin A ~ A. If a wind turbine is scanned at the hub height, the plane elevation of 0.1 rad (5.7 degrees) would capture the wake until 5D. Considering the wake expansion, the wake could be also captured at further downstream distances of ~10D.

L319: Do reference wind directions and actual wake directions often significantly differ? If so, could you quantify a large discrepancy from either literature or this analysis?

We will cite Gaumond et al. (2014) in this section, but leave the details for the discussion in Section 5.5., where this problem is covered. Gaumond et al. (2014) observed a normal distribution of cup anemometer measurements taken within 10 minutes with a standard deviation of 2.67 degree. We got roughly five degree offset for the wake direction, which was enough to divert the automatic extraction of the wake profiles for the Gaussian method.

L343: Is the centerline assumed to be a straight line (as is assumed with the Gaussian calculations) or it is allowed to turn?

Both Gaussian and manual centerlines can turn. Probably, some wording in the Gaussian section implied that we regard a straight line, while this is not the case. The Gaussian method returns one center point per wake profile. However, we need to extract the wake profile to get the data for fitting. This was done by extracting data along the line perpendicular to the wind direction. The Gaussian distribution peak may shift from the middle of the extracted profile depending on the wake movement.

The manual centerline does not require intermediate lines, so we can draw it as a curve immediatelly.

L356: Do additional errors occur or do they not occur?

The wording is changed to avoid confusion:

Overall, the Gaussian method performs well in the range of 2<x/D<10. Further downstream (x/D>10) the wake recovers to the free flow and the wake deficit function becomes too weak to fit accurately; the fitting result may contain errors.

L371: Does "wake deficit" refer to the Gaussian method?

No, this is a method that uses 5% wake deficit or 95% of the free flow wind speed as a threshold.

L387: What does "it" refer to?

The manual threshold criteria. The line is changed to:

The aligned wakes subset utilizes the same manual threshold criteria for the wake splitting as bimodal subset (Fig. 13), although the condition may be harder to fulfill.

Figure 15: Why is the Corrupted data included here but excluded in Table 2?

The original intention was to show data for the scans that allowed manual identification despite strong crosswind effects. The figure became obsolete after we had to correct the implementation of the deficit-based method.

L430: Could you please remind me - does the ATS centerline detection only work for the closest wake shape? Is that why the algorithm doesn't detect the centerlines in the far wake?

Yes, we detect the centerline only for the first continuous shape near the wind turbine as of the current moment. Searching for the centerline in the far wake requires to determine which of the disconnected shapes downstream are identified correctly as a wake and the order in which they should be connected. We tested an algorithm for the LES case, which used the scheme: search for the next large shape in the downstream wake direction – extract he centerline – recalculate the wake direction – repeat until the end of the domain is reached. This algorithm is not applicable well to the lidar data due to the higher amount of false positives and a different way to store data. The LES data are simulated so that the wake is aligned with one of the Cartesian axes which gradually simplifies the centerline search. The lidar data are stored in the matrix defined by the polar coordinate system, i.e., the geometrical approach requires coordinate transformation back and forth. Right now, we are looking for the alternative solution for the centerline algorithm and see it as a good topic for a follow-up study.

L450: The previous section also compared Gauss and the ATS. Please be more specific with this header.

The subsection titles are now changed to

Comparison of the ATS wake identification against the manual identification and deficit-based thresholding

Comparison of the wake characterization using Gaussian and ATS methods

L465-466: I am surprised that the estimated wake direction deviates so strongly from the reference wind direction. You cite a few studies in the following paragraphs. How large are the deviations in those studies?

The deviations are not always mentioned explicitly. Gaumond et al. (2014) provides 2.67 degree standard deviation for the measurements. From the plots provided in publications on LES simulations and lidar measurements, we see that the Coriolis effects become noticeable at ~6D. That could a partial explanation for the difference between wind and wake direction, because the distance between met mast and closest wind turbine is ~8D. However, that explanation might not be enough. We had observed an offset of an order of 5⁰. If the same effect was observed for the wake, it would imply a deviation of the wake center 8D*tan(5⁰) = 0.7D. The cited articles show weaker effects for about the same distance. Besides, we could expect a normal distribution of the deviations from a number of effects (measurement error, yaw deflection, atmospheric conditions), yet we see a nearly constant offset.

Apart from the Coriolis effect, we are leaning towards the imperfection of the lidar orientation as the main cause for the deviation between wind and wake. We have performed a quick comparison to SCADA data for the same period and noticed a similar offset for the wind direction measured at the mast by the anemometer and at the wind turbine by SCADA system – this supports the assumption, that the wind-wake deviation is present and is not caused by the limitations of the centerline search algorithm or yaw deflection. Since the SCADA data deals with its own uncertainties and was not a focus of the original study, we are yet unsure whether to include it into the revised article, although it could make a good reference data set for the next study.

L490: See my comment about L210. Also, does your quantification of "near wake" agree with standard definitions of "near wake"? Also, please state why someone would want to distinguish between "near wake" and "far wake" within a lidar scan.

This section mainly served to show the capability of the ATS method for the particular condition, Based on your comment about ATS method performance for unimodal vs. bimodal histogram we will correct this part to focus more on the bimodal case specifics.

L505-506: As written, a reader would not understand that you developed a new preprocessing methodology. Please make that clearer.

The main novelty includes only entropy criteria. The despiking part is not specific to the method and can be performed in any other way convenient for the user. This will be emphasized more clearly.