the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Periods of constant wind speed: How long do they last in the turbulent atmospheric boundary layer?
Abstract. A noninvestigated feature of the atmospheric turbulent wind, named periods of constant wind speed, is introduced and investigated. We hypothesize that such periods of constant wind speed are related to characteristic wind field structures (e.g., ramps or jets), which when interacting with a wind turbine may induce particular dynamical responses. Therefore, this study focuses on the characterization of the constant wind speed periods in terms of their lengths, probability of occurrence, and extreme events. Atmospheric offshore wind data are analyzed. Our findings reveal that the statistics of long constant wind speed periods are an intrinsic feature of the atmospheric boundary layer and show the challenging power law behaviour of extreme events, which depends on the local conditions and the precise definition of wind speed thresholds. A comparison to wind time series generated with standard synthetic wind models and to time series from ideal stationary turbulence suggests that these structures are not characteristics of smallscale turbulence but seem to be consequences of largerscale structures of the atmospheric boundary layer, and thus are a typical multiscale effect. Given the conclusive results, we show that the Continuous Time Random Walk model, as a nonstandard wind model, can be adapted to generate the statistics of those periods of constant wind speed measured from the atmospheric turbulent wind.
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CC1: 'Comment on wes202432', Subharthi Chowdhuri, 23 May 2024
Dear Authors,
Nice work! The authors may like to see the following papers, where a similar analysis has been proposed.
1. https://pubs.aip.org/aip/pof/article/32/7/076601/1065485
2. https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.014601
Thanks for your kind attention.
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes202432CC1 
AC5: 'Reply on CC1', Daniela Moreno, 16 Aug 2024
Dear Dr Subharthi Chowdhuri,
Thank you for the reference to your very interesting work, which we have been following for the last few years.
In fact, your study on the persistence of velocity fluctuations in atmospheric flows was cited in the introduction of our paper.
We would like to point out that our periods of constant wind speed (CWS) differ from the definition of persistence (i.e. the time between zero crossings) used in the papers you mentioned. A comparison between CWS periods and such persistence events is now included in the appendix of the revised manuscript.
Yours sincerely.
Citation: https://doi.org/10.5194/wes202432AC5

AC5: 'Reply on CC1', Daniela Moreno, 16 Aug 2024

RC1: 'Comment on wes202432', Anonymous Referee #1, 18 Jun 2024
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 powerlaw 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 distributionsSection 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?Citation: https://doi.org/10.5194/wes202432RC1 
AC1: 'Reply on RC1', Daniela Moreno, 16 Aug 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes202432/wes202432AC1supplement.pdf

AC2: 'Reply on RC1', Daniela Moreno, 16 Aug 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes202432/wes202432AC2supplement.pdf

AC1: 'Reply on RC1', Daniela Moreno, 16 Aug 2024

RC2: 'Reviewer Comment on wes202432, "Periods of constant wind speed"', Anonymous Referee #2, 08 Jul 2024
Review of "Periods of constant wind speed: How long do they last in the
turbulent atmospheric boundary layer?" (WES202432)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 multidecadal lifetime of a turbine, especially for extremes (see e.g. Dimitrov et al., 2018). The large variations in "critical" exponent for calmdurations 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 powerlaw over ranges where loglog 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 powerlaw 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 linebyline comments:
l.1: this is not a "noninvestigated" 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 constantwind speed periods been related to extreme events? This should be removed unless such connection has been shown.
l.67: extreme events are known to follow "fattail" or powerlaw behavior, this is not new; "show" should be "confirm".
l.45: wasn't the eventmeasurement 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.8182: 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.107109): which averaging interval is used for the sigma_u here? Is it for each 10minute period, or over the entire 5day 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 powerlaw 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 loglog (which they advised against) despite evidence that the powerlaw 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 34 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.2467: 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.2612: the spectral gap is an effect, it does not cause effects; maybe state "phenomena related to the spectral gap"
l.268270: how do weakturbulence 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 anticorrelated 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.3223 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.

AC3: 'Reply on RC2', Daniela Moreno, 16 Aug 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes202432/wes202432AC3supplement.pdf

AC4: 'Reply on RC2', Daniela Moreno, 16 Aug 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes202432/wes202432AC4supplement.pdf

AC3: 'Reply on RC2', Daniela Moreno, 16 Aug 2024
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