Overall Thoughts

The authors review control-oriented modeling of wind direction variability with the aim of improving controller design and performance in realistic wind farm flow scenarios. The physics behind wind direction variability and the main modeling methods are discussed—including challenges related to data quality and uncertainty—as well as methods for yaw control (i.e. maintaining yaw-alignment or intentional yaw-misalignment).

I have several comments to help clarify some points throughout the text (considering the increased length of a review paper). Regardless, I think this manuscript is a comprehensive review of its stated objectives and should be accepted for publication.

Comments

Line 73/103: There are several points throughout Section 2 where descriptions like “long term,” “small scale,” “low frequency,” etc., are used to describe certain regimes of physical processes. Section 2.1 ties the definition of some of these descriptors to specific length and time scales, but I’m not sure if those definitions are consistent throughout Section 2. I think it could be helpful to specify what these descriptions of scale mean when they come up, or clearly summarize them at the beginning.

Line 121: This clockwise rotation with height is only true in the Northern Hemisphere.

Line 132: This sentence suggests that time scales of ~10 minutes are significant for wind farm flow control. Can that be explicitly stated/summarized somewhere? The authors argue that a range of length and time scales are important for modeling wind direction variability, but the control problem itself is rooted in a specific range of length and time scales. I think that added context could be helpful to the reader.

Line 161: What is meant by “current developments in high-fidelity farm flow models” that are out of reach to the majority of the research community? Are the authors referring to direct numerical simulations? And then the argument is that large eddy simulations are more practical and within reach? I think this wording is slightly confusing because “high-fidelity” is linked to large eddy simulations at Line 171.

Eq. 1: Some parentheses could be added to clarify order of operations in this equation.

Fig. 2: This figure needs labels and more context to provide value to the reader; I personally didn’t understand much from these vector diagrams. Related: how is the vector defined in the complex plane (Line 290)?

Line 346: Yaw misalignment is mentioned before this point, but I’m not sure if it is clarified that is in reference to the hub height time-averaged wind direction. There is certainly instantaneous misalignment at any time, but the focus is on error relative to time-averaged (over the relevant time scale of the control problem) wind direction.

Line 393: Is there a reason why the Heck, Johlas, and Howland (2023) citation is not used here in addition to the Howland et al. (2020) citation? The 2023 paper also derives a physics-based model for the power ratio/power reduction factor from first principles, assuming that the thrust force characteristics as a function of yaw misalignment are known.

Line 421: Rotating the rotor to the “right” is unclear—does this refer to clockwise rotation?

Line 506: Why are the yaw signals “mostly wrong?” Based on the description of the Draxl paper in the next sentence, I would think it’s more appropriate to say that the signal is wrong at start-up?

Line 564: Could slightly more description be given for these measurement-free yaw control methods? Based on the text here, I can’t wrap my head around how these techniques could work.

The manuscript is a comprehensive review of the current state of research on understanding wind direction variability and its modelling for control applications. It is divided into an introduction, six sections in which different aspects and areas of application or areas strongly dependent on wind direction variability are discussed, a summarising discussion and a conclusion.

The thorough treatment of these many important areas justifies the increased length of the manuscript.

Overall, the manuscript gives a very good overview of many research questions and aspects and clearly shows that a good understanding of wind direction variability is crucial in many fields of wind energy application and that this understanding is still incomplete.

This also shows the need for further research and provides a good introduction to the topic, especially for new scientists.

Overall, I therefore consider this paper to be an important contribution. Nevertheless, in addition to RC1's comments, I have a few more comments, which I describe below:

1. line 25: "EC 61400-1" Here, the "I" for IEC is missing.

2. line 59: "as as" is a typo.

3. line 206: "the maximum horizontal resolution of these models is too large to allow them to accurately investigate intra-wind farm effects"; I assume you mean that the resolution of a mesoscale model like WRF is not high enough to resolve intra-wind farm effects, is that correct?

4. line 285 eq(1). The definition for the absolute minimum distance according to (Farrugia2009) is fine, although I agree with RC1 that additional parentheses can be helpful. As stated in the author's comment, this will be updated. 

However, the equation given in (Farrugia2009) is not complete, in my opinion. (Note that Farrugia substracts the second variable from the first, which is the opposite of eq1 of this paper). E.g. (in degrees for simplicity): Δ(190°, 0°). The result should be -170°. This case is not covered in Eq1 of Farrugia2009 in the "if cases".

To simplify things, I suggest the shift trick from Rott2018: Δ(A,B) = ((B-A+π) mod 2π)-π

The only difference is that with the shift trick per definition if the distance of A and B is precisely π, the result is Δ(A,B) = -π, which is equivalent to a rotation of π, but in opposition to the definition of the sign in Farrugia2009. But this allows us to define the Δ operator directly, without if cases. And from this, the absolute can be defined, and not vice versa. 

5. line 298: Eq3 calculates the "regular" variance (or variance "on the line", which is the term that Fisher uses), which is the expected quadratic difference of the individual samples to the "arithmetic" mean. The circular variance is defined in Fisher1995 (Statistical analysis of circular data) and also in (Cremers and Klugkist, 2018) (https://www.frontiersin.org/articles/10.3389/fpsyg.2018.02040/full) as v=1-\overline{R}, where \overline{R} is the mean resultant length (dashed line in Figure2 divided by n). The circular variance is a measure of the variability of the data, like the variance "on the line", but it is bounded between 0 and 1 and is mathematically different from the variance "on the line". Calculating the circular standard deviation is also more complicated than the standard deviation "on the line". The problem with the "on the line" statistics arises because distributions on the circle wrap around; therefore, the interpretation of the statistics is not the same (see Note 2 in Fisher1995).  

However, for the application of short-term wind data, the widths of wind direction distributions are comparatively very small, and the chances of wrapping around are basically 0. Therefore, it makes sense to use the common terminology like variance and standard deviation, although this is mathematically not 100 % correct. In this review paper, however, the difference should be emphasised very clearly. 

6. line 300: I would be careful with the interpretation from Hanna1983, as many questions remain unanswered here, and a lot has to be assumed. What exactly does lateral TI mean? Does it refer to a reference system, or is a mean (arithmetic or circular) of 0 assumed here? Does a weighted mean wind direction have to be used here? It might be that this relationship mentioned in Hanna1983 is a good approximation in stable stratification. Still, the mathematically correct way to calculate the lateral turbulence intensity should be from the wind vectors. The proper context should be explained in more detail here, or the formula should not be mentioned.  

7. line 494: "Wind vanes or sonic anemometers positioned atop the nacelle within the disturbed flow region behind the rotor are often used to measure the apparent hub height wind direction". This measurement error was confirmed, quantified and corrected in our latest investigation (https://wes.copernicus.org/preprints/wes-2023-53/). I feel bad for promoting my paper here, but you might consider adding the reference.

8. line 589: "Wind Direction Forecasting" is an essential topic for many applications that significantly differ in time scales. Long-term forecasts, short-term forecasts, and shortest-term forecasts (nowcasts). Since this is a paper about Control-oriented modelling, it should be clear that the forecasts are in the shortest-term range, but the reader could be reminded at the beginning of this section to avoid confusion.