General comments

The paper is strong in the technical aspects with well selected analyses to possibly support the hypothesis that the distribution of the CWS event durations can be described with an exponent.

While it is an interesting topic to address, and important to highlight that the standard turbulence model is inadequate, the paper lacks proper motivation. More information would be needed to determine how these events may increase the WT loads. Are they coherent, i.e. do they occur throughout the heights enveloping the rotor area? Which design case of the IEC WT design standard do they fit into, or is a new design case needed (Introduction, L31)? How can the knowledge of these events help the WT and wind plant controller? Can an event be predicted from past few seconds of data?

A major shortcoming is that the period of the observation used for the analysis is too short. Much more data must be analyzed for a meaningful publication. One could for example object against using the statement "conclusive", not once but twice: in the Abstract, and in the section 4.2, page 11. When the period of data collection is extended, the data could then also be separated by wind direction, surface heat flux, and possibly expose additional properties.

The curvature of the spectrum (figures 5, 6, 7) indicates imperfect power law. There is curvature present even at the long durations, which does not help the results being conclusive. One would need to propose a theory at least trying to explain the power-law with physical characteristics of the boundary layer (stability, surface roughness, ...) and then blame the disagreement on incomplete data or another possible cause.

Specific comments

Abstract

L3: please elaborate on "particular dynanmic responses"

L6: what is meant by "the challenging power law behaviour" and why is this introduced with a reference to extreme events? Extreme events are not mentioned anywhere in the paper, other than extremely long CWS duration. Speaking of extreme events ... please verify if they perhaps follow any of the typical extreme event distributions

Section 2.1

L109: It is hard to imagine how would a WT know that a CWS event is imminent and switch into the appropriate control mode in practice.

Section 3.4

L158: Good that the effect of the threshold amplitude is analyzed. Would it not be appropriate to add the resulting alpha exponent as another row in Table 3 and so enable easy comparison of different alphas?

Review of "Periods of constant wind speed: How long do they last in the

turbulent atmospheric boundary layer?"  (WES-2024-32)

This work addresses an academically interesting subject, but in its current form the draft unfortunately has some serious deficiencies. This includes speculation about extreme winds and turbine loads; the manuscript does not connect (directly) to extremes nor give a solid basis for loads. 

More importantly perhaps, its analysis of only 4.6 days of measurements cannot be used to justify statistics for loads accruing over the multi-decadal lifetime of a turbine, especially for extremes (see e.g. Dimitrov et al., 2018).  The large variations in "critical" exponent for calm-durations may be a affected by this, but it is not clear.

The lack of citation (or even use) of previous mathematical developments for persistence statistics is also an issue, especially given the conclusions about T_c(epsilon); e.g., Hurst exponents (or even fractal dimension) for such have been explored by numerous authors.

The fitting of a power-law over ranges where log-log plots show significant curvature, as well as the subsequent neglect of both the range of application or functionally different form of PDF -- and implied lack of convergence for the power-law given the resultant exponents -- are serious issues to be rectified, requiring more analysis. 

Overall the work on systematically quantifying the duration of 'persistent' periods offshore (and possibly capturing their statistics via a CTRW or other model) is interesting, and could merit publication; but to connect this with extremes would likely require significantly more work, which would be the subject of another separate publication(s). 

Specific line-by-line comments:

l.1: this is not a "non-investigated" topic; see e.g. Majumdar's "Persistence in nonequilibrium systems" (1999), or in the ABL, e.g. Chowdhuri, et al. (2020), https://doi.org/10.1063/5.0013911 .

l.3: jets are not shown here to be "characteristic wind field structures" responsible for or related to constant wind speed periods, nor has this been referenced (shown elsewhere).

l.5: how have the constant-wind speed periods been related to extreme events? This should be removed unless such connection has been shown.

l.6-7: extreme events are known to follow "fat-tail" or power-law behavior, this is not new; "show" should be "confirm".

l.45: wasn't the event-measurement approach developed in 2022, or how is this different?

l.65: "Such strong periods are expected to have a stronger influence on a WT" does not seem correct, given that the periods with weakest fluctuations will have _less_ effect on wind turbine loads.

l.81-82: note that this (and Fig.1) is essentially the (reverse of) the generalized gust description of L.Kristensen et al (1991) following from Rice (1945). 

l.132 (also eq.2, l.107-109): which averaging interval is used for the sigma_u here?  Is it for each 10-minute period, or over the entire 5-day dataset?  

l.133: do you mean that taking A=0.3 means here that Iu<=0.02 due to the mean wind speed value (presumably ~15 m/s)? This is not clear.  (Or why not pick A based on Iu?)

l.134: The values of ε are not provided in Table 2.

l.161: There is not a simple 'clear power-law decay' for all values of A; in Fig.5 one sees a curved line which becomes straighter for rarer longer T_c. 

l.162: the finding 2<alpha<3 also means that the PDF can't integrate to 1 (its normalization constant is undefined), consistent with the fact that the lines are curved particularly at more common (shorter) T_c.  The distribution is more like a stretched exponential or some other extreme value PDF.  You cite Clauset/Shalizi/Newmann2009, but are still fitting a straight line on log-log (which they advised against) despite evidence that the power-law has a limited range of application for T_c. 

Fig.5: the horizontal axis has 1/3 empty space, and should be reduced; one can also then see more clearly where the curves become flat or not.

Fig.9: there is no scale on the p(Tc) axis, spanning (apparently) 8 orders of magnitude; please include scaling factors and reduce empty space (extra 3-4 orders of magnitude on vertical axis and 50% horizontally).

Fig.9b caption: mention dotted red horizontal line here also.

l.49: the mean and variance constraints demand that alpha<2 and alpha<3 respectively, but these are weaker constraints than that on the PDF itself (alpha<1); thus I recommend removing this phrase.

l.245: "very long" needs to be quantified, especially because you have used only a few days of data.

l.246-7: you state "offshore conditions maintain a more unperturbed ABL", but compared to what?  What (normalized) metric are you invoking to state this?  

l.255: "proved the turbulent nature of the wind speed" does not make sense as a statement alone, and without saying how. What does this mean, is this statement necessary?

l.261-2: the spectral gap is an effect, it does not cause effects; maybe state "phenomena related to the spectral gap"

l.268-270: how do weak-turbulence periods cause "critical loads"?  I suggest removing this phrase, unless you can explain and justify.  Similar for "resonance".  The justification on l.281 and later is ok (though it is a weaker effect than anti-correlated coherent turbulence across the rotor).

l.298, eq.(A1): there needs to be some minimum x and/or alpha<1, otherwise C is undefined, i.e., the integral of p(x) from 0 to infinity does not converge.  You state simply "alpha>1" later in Appendix B, but this constraint should be mentioned here.  In App.B you do assume an x_min, without explanation.

l.319: "≲" should be "≳" here; i.e., the mean and variance constraints demand that alpha<2 and alpha<3 respectively, but these are weaker constraints than that on the PDF itself (alpha<1).  Given the latter, I would suggest removing the statement about mean and variance, unless you wish to move it to App.B add conditions on it with the use of x_min.

l.322-3 is the sentence about seismic events relevant here?

l.370: should there be a comma between 0.9 and 1 for alpha_L?

An annotated PDF is also included to aid.