Most of the comments have been addressed and the manuscript has been improved significantly. However, I believe a few areas still need further explanation and additional quantification to strengthen the paper. Please find my comments below, in response to the original and author comments.
1) "RC 2.1: One area I feel could use more discussion in particular is missed detections and false alarms. What is the probability of a false detection of wake impingement from the experiment, and the same for missed detections when wake impingement actually occurred? How were these probabilities accounted for when deciding which thresholds to use for the detection algorithm?"
AC: "Currently we cannot make any statements about the probability of a false detection. The purpose of the manuscript is to introduce the method to the community and show that it gives satisfactory results for the experiment considered here."
Although you might not be able to determine probabilities, please discuss whether there are any occurrences of missed detections and false alarms in the data. For example, in the wake sector, are there any periods not flagged as waked by the algorithm? And if so, how many? Same for the detection of waked periods outside of the wake sector.
2) RC 2.2 "The other area that I believe should be discussed more is the applicability of the algorithm to different wind turbines, sites, and wind conditions. This research demonstrates that the LOS Doppler spectrum can be used to detect waked conditions well for the site and conditions analyzed. Although briefly discussed in the conclusions, it is unclear what steps would need to be taken to implement the method at a different site with a different rotor size, turbine spacing, or atmospheric conditions. For example, simulations of the algorithm for different conditions using CFD would be a useful approach. Further analysis of the wind conditions during the experiment, such as turbulence intensity and atmospheric stability, would help show how applicable the algorithm is to a variety of wind conditions."
AC "A paragraph at the end of the conclusion section has been added that discusses the topic of different site parameters. We believe that more data is needed to make statements about the generality of the linear relationship found in this experiment."
The new paragraph explains that further experiments are needed to determine how general the wind direction correction algorithm is, but the generality of the wake detection algorithm should be discussed as well. Furthermore, some site condition information such as the distribution of wind speed and direction is provided in Fig. 3, but can you add information at least about the distribution of TI and ideally stability during the measurement period? You show that the algorithm works well for this period, but knowing what conditions occurred during this period will help readers understand the general applicability of the algorithm.
3) RC 2.9 "Pg. 7, ln. 11: "At the initialization the algorithm requires some observations to establish correct values of the running averages." Explain in more detail how the initialization of the algorithm is performed. Does the algorithm require that the wind conditions during operation be similar to the conditions during initialization? And how frequently does the algorithm need to be calibrated? Especially for detecting full wake conditions when the absolute TI is used to detect wakes, how do you account for the possibility of the freestream TI increasing after the algorithm is initialized, in which case higher freestream TI could be detected as a full wake?"
AC "More details to the initialization have been added. Yes, the conditions during operation need to be similar to conditions during operations. This fact has been added to the text.
From our experience no calibration is need with the data we have processed. The algorithm assumes that all changes in small-scale turbulence stem from upstream wakes."
In the new text you mention that running averages of \hat{\phi}, TI_LOS2, and TI_LOS1 are needed to initialize the algorithm. But the description of the algorithm for wake detection only mentions using DeltaTI_LOS and TI_LOS1 and TI_LOS2. Do you also use \hat{\phi} as part of the algorithm? If so, provide more details.
It would help greatly with understanding the algorithm if you explain how the various detection thresholds for partial wake and full wake situations are chosen based on the running averages.
4) RC 2.11 "Pg. 13, lns. 1-5: Does the empirical relationship used to correct wind direction measurements when wakes are detected need to be determined for every site where the algorithm is used? Or is the relationship found valid in general? Additionally, after correcting the wind directions, how does the RMS error between the corrected lidar wind direction and the sonic anemometer compare to the error during freestream conditions? Although the corrected directions look reasonable, some quantification of the error would strengthen the results."
AC "To validate the generality of the linear relationship more empirical data is needed. This is mentioned at the end of the conclusion section and was also mentioned by RC1 in comment RC 1.13 & 1.14. We currently have some indication that the relationship at different site is also well described by a linear fit. However, the offsets is close to zero (as found in this study), but the slope seems to vary."
How does the RMS error between the corrected lidar wind direction estimate and the sonic wind direction compare to the error during freestream conditions? Has the correction reduced the error to close to the freestream error? Some quantification of the results would be appreciated. |

Both referees aknowledged the quality of the revised manuscript but one of them, based on your answers, would like to have additional explanation and quantification of the some results (see referee 2's comments).

Consequently, I suggest you to proceed with a second round of revision to ensure that all new referee comments are answered.

Best regards

Sandrine Aubrun