Extreme fluctuations of wind speed for a coastal / offshore climate : statistics and impact on wind turbine loads

For measurements taken over a decade at the coastal Danish site Høvsøre, we find the variance associated with wind speed events from the offshore direction to exceed the prescribed extreme turbulence model of the IEC 61400-1 Ed.3 standard for wind turbine safety. The variance of wind velocity fluctuations manifested during these events is not due to extreme turbulence; rather, it is primarily caused by ramp-like increases in wind speed associated with larger-scale meteorological processes. The measurements are both linearly detrended and high-pass filtered in order to investigate how these events—and 5 such commonly-used filtering—affect the estimated 50-year return period of turbulence levels. The impact of the observed events on a wind turbine are investigated using aeroelastic simulations, that are driven by constrained turbulence simulation fields. Relevant wind turbine component loads from the simulations are compared with the extreme turbulence load case prescribed by the IEC standard. The loads from the event simulations are generally lower for all considered load components, with one exception: ramp-like events where the wind speed rises to exceed rated wind speed can lead to extreme tower base 10 fore-aft loads that exceed DLC 1.3 of the IEC standard.

5.) Placement of figures tend to occur prior to the narration; 6.) Comment on process for figure 4 to go from raw measurements to high-pass filtered measurements more carefully; 7.) When discussing design load cases and simulations, consider non-Gaussian fields as it is known that realistic fields may differ from Gaussian; 8.) Include literature on works considering conditional pdfs in regards to turbulence fields/statistics/wind power; 9.) Content/results on p12 should be expanded -this is the case with most results that physics based observations are missing.
In this case, given that the simulations are based on a model, it is relevant to justify their physicality; 10.) §5 is difficult to follow and should be revisited as well as explaining the results in more detail; 11.) Figure quality may be improved; 12.) Conclusions can be presented in non-bullet form and at the present the discussion and conclusions sections may be combined; 13.)Is it possible to extend the analysis to further cases for sake of comparison?
Reply to reviewer 1: Thank you for very much for your constructive review and comments.We have considered your suggestions and made changes 9) As you say, we do not have physical observations of wind turbine loads during these extreme variance events.This is why we simulate them in HAWC2 which is a model.This model has been referenced in § 4.1, but we have included a more in-depth explanation of the HAWC2 model.10) Yes, § 5 has been polished for a hopefully easier flow.Figure 8 have been removed (moved to appendix B), as Figure 9 shows the binned and average values of Figure 8.The text is trimmed.The main points should now stand out more clearly, while they have also been expanded on.
12) Yes, we have considered a more conventional conclusion section, without bullets.The purpose of the bullets is to give the reader a quick overview and an easier focus on the main findings, and after trying both versions we have decided to keep the bullets.
13) Yes, it is definitely possible for future work, e.g including more measurement sites or by lowering the curve of the selection criteria for the present site.wind turbine.
"an illustrative diagram would be useful here" Answer: We believe that Figure 5 serves to show the dimensions of the turbulence boxes.

"rotor speeds seem very low"
Answer: It does, but this is the correct value.At 9.6 rpm the tip speed of the blade is 90 m/s for the DTU 10 MW.For comparison the NREL 5 MW has a rated rotor speed of 12.1 rpm and maximum tip speed of 80 m/s.
"are these corresponding to the six events as shown in Figure 2?" Answer: No, they are randomly synthesized seeds.The word synthesized has been added to the stance to clarify.
"source time series is perhaps a bit confusing -may be interpreted as measured time series?"Answer: We think you are right, and have changed the legend in Figure 6 to say instead: Synthesized time series.

Introduction
The IEC design standard for wind turbine safety (61400-1 edition 3, IEC, 2005) outlines requirements that, when followed, offer a specific reliability level which can be expected for a wind turbine.The standard prescribes various operational wind turbine load regimes and extreme wind conditions that the wind turbine must be able to withstand during its operational lifetime.So-called design-load cases (DLC's) are described, following these prescribed regimes and conditions.One of the IEC prescriptions is an extreme turbulence model (ETM), which gives the ten-minute standard deviation of wind speed, with a 50-year return period, as a function of ten-minute mean wind speed at hub height.The ETM takes into account the long-term mean wind speed at hub height and is scaled accordingly through the wind speed parameters of the IEC wind turbine classes.
The model is prescribed in a design load case (DLC 1.3) for ultimate load calculations on wind turbine components; this DLC is considered to be important in wind turbine design, particularly for the tower and blades (Bak et al., 2013).For the standard to be effective, it must reflect the expected atmospheric conditions and the extreme events that a wind turbine may be exposed to.Likewise, it is important that DLC 1.3 is representative of observed extreme turbulence conditions.
The IEC standard recommends the uniform-shear spectral turbulence model of Mann (1994Mann ( , 1998) ) for generation of threedimensional turbulent flow, to serve as input to turbine load calculations.Gaussian turbulent velocity component fluctuations are synthesized via the 'Mann-model' spectra, and assumed to be stationary and homogeneous (unless the model is modified, as in de Mare and Mann, 2016).The model requires three input parameters, which have values prescribed by the standard.
In Dimitrov et al. (2017) it is shown that the parameters of normal turbulence and extreme turbulence differ, and how these differences influence wind turbine loads.There it is also shown how numerous 10-minute turbulence measurements from the homogeneous land (eastern) sectors exceed the ETM model at the Danish Test Centre for Large Wind Turbines at Høvsøre, indicating that the ETM model is not necessarily conservative.
A further investigation of 10-minute turbulence measurements exceeding the ETM level is needed to identify what kind of flow causes these extreme events and how they influence the estimated turbulence level at a given site.Fluctuation :::::::::: Fluctuations associated with mesoscale meteorological motion can have periods in the range of a minute up to hours (Vincent, 2010).In the shorter end of this range the fluctuations have a big influence on the ::: are ::: the :::: main :::::::::: contribution :: to ::: the 10-minute variance estimate (turbulence level).Short-time mesoscale fluctuations have been reported in connection with e.g.open cellular convection (Vincent et al., 2012), convective rolls (Foster, 2005) and streaks (Foster et al., 2006).The fluctuations are seen in measurements as coherent structures with a ramp-like increase in wind speed (Fesquet et al., 2009).These studies have been made with respect to identification, modelling, forecasting and wind power generation, but they do not consider the impact on wind turbine loads.
In this paper we aim to find and examine events where the 10-minute variance exceeds the ETM level; however : .:::::::: However here we consider them as non-turbulent events, :: as :::: they :::: are :::::: caused ::: by :::::::: ramp-like :::::::: increase :: in ::::: wind ::::: speed ::::::::: associated ::::: with ::::::::: larger-scale ::::::::::::: meteorological :::::::: processes, : which may be observed offshore or high above the surface layer.We use measurements from the measurement site Høvsøre, focusing on the western (offshore) sectors.We demonstrate how these events influence the estimate of 10-minute turbulence levels with a 50-year return period.This is done for the raw-, linearly detrended-, and high-pass filtered measurements.The observed events are simulated by incorporating measured time series using a constrained simulation approach, in order to get a realistic representation of the flow involved.The generated wind field realizations are fed to an aero-elastic model (Larsen and Hansen, 2015) of the DTU 10MW reference wind turbine (Bak et al., 2013), to investigate how they affect wind turbine loads.Finally, the load simulations with the observed events are compared to simulations corresponding to DLC 1.3 from the IEC 61400-1 standard.

Site and measurements
The data analysis and load simulations are based on 10 Hz wind speed measurements over a 10-year period, from November 2004 to December 2014, taken at :::::::::::: measurements ::::: from the Høvsøre Test Centre for Large Wind Turbines in western Denmark (Peña Diaz et al., 2016).Located over flat terrain 1.7 km east of the coastline, the site offers low-turbulence, near-coastal wind conditions.The site consists of five wind turbines arranged in a single row along the north-south direction, and multiple measurement masts.site, ::::::::::::: instrumentation :::: and :::::::::: observations :::: may :::: also :: be :::::: found :: in ::::::::::::::::::: Peña Diaz et al. (2016).: We consider measurements only from the western sector, with 10-minute mean wind direction between 225º and 315º.This range of wind directions is chosen for two reasons: (i) to avoid measurements from the wakes of the wind turbines and flow distortion from the mast; (ii) data from this sector corresponds to coastal and offshore conditions.

Selection criteria of extreme events
The first step in ::: For the selection of the extreme variance events is to calculate the observed apparent turbulence intensity (TI) of :: the : 10-minute averages of horizontal wind speed from the westerly sector, I ⌘ /U .Here is the 10-minute standard deviation of the wind speed , and U is the 10-minute mean wind speed.Next, the data is :::::::::::: measurements :: is : compared to the extreme turbulence model in the IEC 61400-1 standard (IEC, 2005), where the horizontal turbulence standard deviation is 1 :: The :::: light ::: mast ::: has ::::: aircraft ::::: warning :::: lights :: on ::: the :: top.
given by Here c is a constant of 2 m/s, I ref is the reference turbulence intensity at 15 m/s, V ave is the annual average wind speed at hub height, and V hub is the 10-minute mean wind speed at hub height, of which the model is a function : ; ::: the ::::::: variable :: of :::::: which :: 1 :: is :: a ::::: linear ::::::: function :: of.For the 'offshore' westerly directions considered at Høvsøre the long-term (10-year) mean of 10minute average wind speeds at 100 m height is U =10.4 m/s, which corresponds well to class I turbines within the IEC 61400-1 framework with V ave =10 m/s.The IEC standard has three turbulence categories: A, B and C, with A being the highest reference turbulence intensity, and C the lowest.The corresponding reference TI for each class may be seen in Table 1.At Høvsøre, the (decade-long) average TI corresponding to the IEC reference wind speed, i.e. 10-minute mean wind speeds of U = 15 ± 0.5 m/s, is below 0.12.This indicates that the reference turbulence class C and I ref of 0.12 will equal or exceed in severity the actual conditions at the site.
However, for the selection of events to analyze, a criterion corresponding to the IEC ETM model with turbulence class B is used.This is done in order to limit the selection to a representative subset of the most extreme events, while also limiting computational demands.The selected events can be seen in Figure 2 as blue dots that fall above the blue curve, i.e. these are events that have a high horizontal wind speed variance.The events are selected from measurements at 100 m height.
Figure : 3 shows the horizontal wind speed at 100 m from the lighting :::: light : mast and meteorological mast during six of the selected events.The events typically include a sudden rise in wind speed, which gives the main contribution to the high variance.Notice the sudden wind speed increase occurs approximately simultaneously at the two masts although they are ⇠400 m apart (for mean wind direction roughly perpendicular to the line connecting the masts), indicating that the events are due to large coherent structures-rather than extreme stationary turbulence.Here we use the inverse first-order reliability method (IFORM) to estimate the 50-year return period contour corresponding to the joint description of turbulence ( u ) and 10-minute mean wind speed (U ).This method was developed by Winterstein et al. (1993) and provides a practical way to evaluate joint extreme environmental conditions at a site.The first step in the IFORM analysis is to find the joint probability distribution f (U, u ).According to the IEC standard the 10-minute mean wind speed is assumed to follow a Weibull distribution 2 , and the 'strength' (standard deviation) of turbulent stream-wise velocity 5 component fluctuations ( u ) is assumed to be log-normally distributed conditional on wind speed.In the standard, the mean of 2 Here we use a 3-parameter Weibull distribution.This is done because after filtering out measurements with errors and missing periods, the lowest mean wind speed is 2.2 m/s.One could also use a 2-parameter Weibull distribution and fit with weights in the tail to obtain the same result. 5

Data processing
The data set used for the data analysis and simulation is the 10 Hz measurements from cup anemometers and wind vanes on the light mast in Høvsøre.
3.1 Estimation of 50-year joint extremes of turbulence and wind speed: IFORM analysis The measurements shown earlier in Figures 2 and 3 are raw (not processed or filtered), though it is common procedure to detrend data before estimating turbulence or associated return periods for a given turbulence level.Not all the extreme variance events are expected to be influenced by linear detrending, nor is such detrending necessarily appropriate for non-turbulent events; note e.g. the event shown in Figure 3c.Therefore we want to compare the 50-year return period of turbulence with the data, detrended in two different ways: linear detrending and high-pass filtering.Detrending is performed by making a linear least-squares fit to the raw 10-minute wind speed time series, with the linear component subsequently subtracted from the raw data.
Here we use the inverse first-order reliability method (IFORM) to estimate the 50-year return period contour corresponding to the joint description of turbulence ( u ) and 10-minute mean wind speed (U ).This method was developed by Winterstein et al. (1993) and provides a practical way to evaluate joint extreme environmental conditions at a site.The ::::::: IFORM :::::: method :: is :::::: widely :::: used :: in :::: wind :::::: energy :: to :::::: predict ::::::: extreme :::::::::::: environmental ::::::::: conditions :: or ::::::::: long-term :::::: loading ::: on :::: wind :::::::: turbines, ::: for ::::::: ultimate ::::::: strength ::::::: analysis.::::: More ::::::::: information ::: on ::: this ::::::: method ::: may ::: be ::::: found :: in ::: e.g.The : first step in the IFORM analysis is to find the joint probability distribution f (U, u ).According to the IEC standard the 10-minute mean wind speed is assumed to follow a Weibull distribution 3 , and the 'strength' (standard deviation) of turbulent stream-wise velocity component fluctuations ( u ) is assumed to be log-normally distributed conditional on wind speed.In the standard, the mean of u is expressed as a function of U , and the standard deviation of u is defined as In Figure :: In ::::: Figure : 4, µ u and u are shown as functions of 10-minute mean wind speed, from Høvsøre :::::::::: unprocessed measurements at 100 m (grey dots) and the expressions from the IEC standard (blue lines) with I ref = 0.12.The green lines show a third-and a second order polynomial fit to the binned measurements of µ u and u respectively (bins of 1 m/s).The IEC expression for µ u is higher than that from the measurements, but has a similar slope for mean wind speeds above 15 m/s.The difference is larger between the data and IEC expression for u , where the assumption of no mean wind speed dependency does not fit well to the data.Comparing the raw data (left), linearly detrended data (middle) and high-pass filtered data (right) it is seen that the detrending, and high pass filtering slightly lowers the values of µ u , while the reduction of u is much greater, especially for the high-pass filtered measurements.
The next step in the IFORM analysis is to obtain a utility "reliability index" which translates the desired return period T r (here 50-years) into a normalized measure corresponding to number of standard deviations of a standard Gaussian distribution: Here 1 is the inverse Gaussian cumulative distribution function (cdf), T t is the duration of a turbulence measurement (here 10 minutes) and n m is the number of 10-minute measurements corresponding to a 10-year period (which equals the time span of the data).Thus the reliability index equals the radius of a circular contour in standard Gaussian space, so that Where ::::: where the standard normal variables u 1 and u 2 are derived from physical variables using an iso-probabilistic transformation, which takes correlations into account.We invoke the Rosenblatt transformation (Rosenblatt, 1952), which relies on the fact that a multivariate distribution may be expressed as a product of conditional distributions: In this analysis, only two variables are considered, and the transformation may be performed in the following way: where F U is the three-parameter Weibull cdf and F u|U is the conditional log-normal cdf.Figures :: 5a :: to ::: 5d that the variance of u is significantly reduced by the high-pass filteringcompared with the linear detrending.The 50-year return period contour estimated with the linearly detrended data :::::: (Figure ::: 5b) : exceeds the one estimated with IEC turbulence class C , as the :: in ::: the ::::: whole :::::::::: operational ::::: wind ::::: speed ::::: range.::::: This :: is ::::::: because ::: the linear detrending does not affect events like the one seen in Figure 3c, and these events influence the estimate of the contour.In Figure 5 (right) ::::: indicate that the extreme variance events are not necessarily associated with linear trends.Some events are associated with wind speed fluctuations in a frequency range that may have a substantial impact on wind turbine loads.Therefore we investigate this impact, with constrained turbulence simulations incorporating the raw measurements that have not been detrended in any way.

Time series for simulation
The peak and the corresponding location of each event is identified in the following way: A moving average is subtracted from the wind speed signal and the maximum value of the differences identified: where u is the horizontal wind speed signal and ū60s is the moving average over 60 s.The peaks are not necessarily the highest value of the signal, but rather the highest value within a sharp wind speed increase.
Applying the selection criteria described in section 2.1 results in 99 identified events.Of these, 30 events are discarded as they include periods of missing measurements.A lower threshold of 4 m/s is put on u peak to exclude events mostly consisting of a linear trend or relatively insignificant peaks.Finally, events where the corresponding directional data fluctuated below 180º are discarded, :: i.e. ::::::::: temporary ::::::::: directional :::: data :::: from :::::: South, to exclude measurements from the wake of the nearby wind turbine.
A remaining 44 events are chosen for load simulations.The measured time series including the extreme events are used to generate constrained turbulence simulations (explained in more detail in Section 4.4) of 600 s duration.The time series period is selected such that the sharp wind increase, or ramp, occurs approximately in the middle of the time series, i.e., approximately 300 s before and after the peak.All the load simulations are performed using the DTU 10 MW reference wind turbine (RWT), which is a virtual wind turbine model based on state-of-the-art wind turbine design methodology.The main characteristics of the RWT may be seen in Table 2 and a more detailed description may be found in Bak et al. (2013).The controller used for the RWT is the Basic DTU Wind Energy controller (Hansen and Henriksen, 2013).

Turbulence simulations in HAWC2
The Mann spectral turbulence model (Mann, 1994(Mann, , 1998) ) is fully integrated into HAWC2, where a turbulence 'box' may be generated for every wind turbine response simulation.The turbulence box is a three dimensional grid that contains a wind velocity vector at each grid point.The turbulence boxes in this study all have 8192 ⇥ 32 ⇥ 32 grid points, in the x-, y-, and z-directions, respectively.The y-z plane is parallel with the rotor, and the distance between the grid points is typically defined so that the domain extent in the y-and z-directions becomes a few percent larger than the rotor diameter.The length of the x-axis (L x ) is proportional to the mean wind speed at hub height, L x = U • T , where T is the simulation time.The turbulence box is transported with the average wind speed at hub height through the wind turbine rotor.
The Mann model is based on an isotropic von Kármán turbulence spectral tensor, which is distorted by vertical shear caused by surface friction.Assumptions of constant shear and neutral atmospheric conditions in the rapid-distortion limit are used to linearize the Navier-Stokes equations, which may then be solved as simple linear differential equations.The solution results in a spectral tensor that may be used in a Fourier simulation, to generate a random field with anisotropic turbulent flow.The Mann model contains three parameters: • is an anisotropy parameter, that when positive, 2 u > 2 v > 2 w , which are the variances of the u-, v-and w-components of the wind speed, respectively.When = 0, the generated turbulence is isotropic, is the product of the Kolmogorov spectral constant and the rate of turbulent kinetic energy dissipation to the power of 2/3.The Fourier amplitudes from the spectral tensor model are proportional to ↵" 2/3 , hence increasing ↵" 2/3 gives a proportional increase in the simulated turbulent variances, but no change in the shape of the spectrum.
• L is the length scale which is representative of the eddy size that contains the most energy.
The IEC-recommended values of the parameters are: = 3.9, L =29.4 m (for hub heights above 60 m), and that ↵" 2/3 is set to a positive value, to be scaled with 2 u .It has been shown in numerous studies that these parameters can change significantly, e.g. with turbulence level (Dimitrov et al., 2017;Kelly, 2018), atmospheric stability (Sathe et al., 2013;Chougule et al., 2017) and site conditions (Kelly, 2018;Chougule et al., 2015).As we do not want to investigate the effect of changing these parameters, all turbulence realizations are chosen to have the same parameters.In the present study, the anisotropy parameter is chosen according to the IEC standard, = 3.9.The turbulence length scale is chosen differently, because the DTU 10 MW RWT is a relatively large wind turbine, and the turbulence length scale is expected to be of the same order of magnitude as the hub height (Kristensen and Frandsen, 1982).Here the length scale is estimated via as derived by Kelly (2018).The final 200 s of simulation data, i.e. after the wind-speed ramps, are used to estimate the length scale of turbulence and thus exclude the large coherent structure.Here u from 100 m height is used, along with dU/dz estimated between z = 160 m and z = 60 m.Using (9) the length scale is found on average to be hLi ⇡ 120 m over all events analyzed.The value chosen is therefore L = 120 m.

Design load case 1.3
The DLC is simulated based on the setup described in Hansen et al. (2015), where mean wind speeds at hub height of 4-26 m/s in steps (bins) of 2 m/s are used, and each simulation has a duration of 600 s. 4 .: The Mann turbulence model is used to generate Gaussian turbulence boxes, with six different random ::::::::: synthesized : turbulence seeds per mean wind speed.The simulation time of the turbulence boxes is defined to be 700 s, where the first 100 s are used for initialization of the wind turbine response simulation, and are disregarded for the load analysis.

Constrained turbulence simulations
The aim here is to generate turbulence simulations resembling the measured wind field of the extreme variance events.This is done by constraining the synthesized turbulence fields.The constraining procedure involves modifying the time series to represent the most likely realization of a random Gaussian field which would satisfy the constraints, using an algorithm described in Hoffman and Ribak (1991) and demonstrated with applications to wind energy in Nielsen et al. (2004) and Dimitrov and Natarajan (2017).For the constraining procedure we define three different random Gaussian fields as a function of location, r = {x, y, z}: 1. the constrained field, f (r), which is the generated field of the procedure, modified to resemble the measurements; 2. the source field, f (r), which here is a random realization of the Mann turbulence model; 3. the residual field, which is the difference between the constrained field and the source field, g(r) = f (r) f (r).
The constraints are a set of M values at given locations, C = {c 1 (r 1 ), c 2 (r 2 ), ..., c M (r M )}, which the constrained field is subject to, and is defined to have the required values at the given locations, f (r i ) = c i .At the constraint points, the residual field is given by g(r i ) = c i f (r i ), and for all other locations the values are conditional on the constraints in C. The conditional probability distribution of the residual field is denoted by the multivariate Gaussian distribution function: The conditional probability function of the field may be described as a shifted Gaussian around the ensemble average of g(r)|C, where h...i is the ensemble average, R i (r) = hf (r)C i i are the cross-correlation terms between the field and the constraints,

Constrained turbulence simulations
The aim here is to generate turbulence simulations resembling the measured wind field of the extreme variance events.This is done by constraining the synthesized turbulence fields.The constraining procedure involves modifying the time series to rep- Every third measurement is applied at each width along the y-axis, giving applied constraints at each y-location with a 3.33 Hz frequency.7 shows two examples of the u-velocity time series at hub height with and without applied constraints, for the same turbulence seeds as shown in Figure 6.
For the purpose of load simulations, six different constrained turbulence seeds are generated from each extreme variance event time series.Although applying the constraints makes the turbulence boxes similar in general, there are differences in the parts of the boxes which are far from the constraint locations.As a result, there will be a seed-to-seed variation in loads 5 simulated with constrained turbulence boxes, albeit much smaller than what is seen in the unconstrained case.

Load simulation results
In this section we compare the design load levels of the two simulation sets: DLC 1.3 and the constrained simulations with the extreme variance.DLC 1.3 consists of 72 simulations (6 seeds per 12 wind speed bins) and the constrained simulations consist of 264 simulations (6 seeds per 44 extreme variance event).

Extreme loads
In Figure 8 the standard deviation of the simulated hub height u-component wind speed is shown as function of the mean hub height u-component wind speed.Each dot shows the standard deviation averaged over six turbulence seeds.As the variance is scaled to match the target both for DLC 1.3 and the constrained simulations, the scatter of the mean standard deviation over the six different seeds is small.The standard error of the mean standard deviation is in the range of 0.008 -0.013 m/s, and 15 the standard error of the mean hub-height u-component wind speed is equal to, or less than 0.015 m/s.The standard deviation from the constrained turbulence simulations (blue dots) is higher than that of DLC 1.3 with one exception.For this case, some variance was lost as a consequence of changing the time interval selection to span ±300 s around the wind speed peak, and data with a negative trend was cut off.
In Figure 9   For the purpose of load simulations, six different constrained turbulence seeds are generated from each extreme variance event time series.Although applying the constraints makes the turbulence boxes similar in general, there are differences in the parts of the boxes which are far from the constraint locations.As a result, there will be a seed-to-seed variation in loads simulated with constrained turbulence boxes, albeit much smaller than what is seen in the unconstrained case.

Load simulation results
In this section we compare the design load levels of the two simulation sets: DLC 1.3 and the constrained simulations with the extreme variance.DLC 1.3 consists of 72 simulations (6 seeds per 12 wind speed bins) and the constrained simulations consist of 264 simulations (6 seeds per 44 extreme variance event).

Extreme loads
In Figure : 8 the standard deviation of the simulated hub height u-component wind speed is shown as function of the mean hub height u-component wind speed.Each dot shows the standard deviation averaged over six turbulence seeds.As the variance is scaled to match the target both for DLC 1.3 and the constrained simulations, the scatter of the mean standard deviation over the six different seeds is small.The standard error of the mean standard deviation is in the range of 0.008 -0.013 m/s, and the standard error of the mean hub-height u-component wind speed is equal to, or less than 0.015 m/s.The standard deviation from the constrained turbulence simulations (blue dots) is higher than that of DLC 1.3 with one exception.For this case, some variance was lost as a consequence of changing the time interval selection to span ±300 s around the wind speed peak, and data with a negative trend was cut off.
The extreme tower ::: top :::: tilt-, :::: yaw-:::: and ::::: tower base side-side moments generally :::: show :: a :::::: general : increase with wind speed.The extreme blade root flap-and tower base fore-aft moments peak around rated wind speedand the differences in the magnitude between the two simulation sets are not as large as for the other load components.For the extreme blade root edge moment it is seen that the loads peak around rated wind speed for both simulation sets, but the main difference is that after 16 m/s the DLC 1.3 loads and the scatter increases with wind speed.
The mean extreme moments from IEC DLC 1.3 (grey dots).The mean extreme loads from the constrained simulations (blue dots).
In Figure 9 the characteristic extreme loads per mean wind speed bin are compared, i.e. the values from Figure B1, binned and averaged.For the comparison, we omit the wind speed bin at 26 m/s, as there are no extreme events within that wind speed bin.The error bars show the standard deviation of the extreme loads of each wind speed bin.It is seen that for all considered load components, the most extreme characteristic extreme loads are from DLC 1.3.However, the extreme tower-base fore-aft loads are higher from the constrained turbulence simulations for wind speed bins at 8 m/s and between 14-20 m/s.
Table 3 lists the overall characteristic loads from each simulation set (the extremes seen in Figure 9), together with their ratio.The difference of the overall extremes from the two simulation sets is largest for the tower-top yaw moment, where the extremes are lower from the constrained simulations.The overall extremes are of similar magnitude for the tower base fore aft moment and the blade root flap moment.turbine blades begin to pitch.Also, : at :::: the :::: time when the wind speed at hub height reaches rated wind speed, the wind speed over the upper half of the rotor :: at ::::: 179 m : is above rated wind speed, leading to higher loading there :: on ::: the :::::: upper ::: half ::: of ::: the :::: rotor.From the turbulence simulations, the most noticeable difference in the wind turbine response is that in the constrained turbulence simulation the time of the peak tower base fore-aft moment is very distinguishable at 390 s.While for the stationary turbulence the peak response occurs around 150 s, but numerous times it reaches above 200000 kNm during the simulation.
Note that the axes in the top panels are the sameand : , :: as ::: are the axes in the bottom panelsare the same.It is seen that although the standard deviation of the wind speed is lower in the stationary turbulence simulation, the wind speed extremes are greater, with instantaneous wind speed reaching below 2 m/s and above 22 m/s.
In Figure : 11 we compare some of the most extreme tower top moments from the two simulation sets.The stationary turbulence simulation in Figure 11, has U = 22 m/s, u = 3.4 m/s, with a peak tower top tilt moment of 36601 kNm and a peak tower top yaw moment of 28917 :::::: 28900 kNm; in contrast the constrained turbulence simulation has U = 21.3 m/s, u = 6.6 m/s, with a peak tower top tilt moment of 30777 ::::: 30800 kNm and a peak tower top yaw moment of 18560 :::::: 18600 kNm.As in the previous example, the time of peak loads is very clearly identified in the constrained turbulence simulation, and the peak value is significantly higher than the response for the remainder of the simulation.For the stationary turbulence simulation, the tower top yaw-and tilt moments often reach high values throughout the simulation.Extreme tower-top moments tend to be observed when there is high shear across the rotor.In stationary turbulent flow the variation in wind speed across the rotor arises as turbulent eddies sweep by, hitting only part of the rotor, leading to high wind shear.The extreme tower top loads from the constrained simulations are in connection with high vertical wind shear arising during the wind speed increase (ramp event).

Discussion
In the load time series comparison, the general differences in the wind turbine response of the two simulation sets are visualized; for the constrained simulations the peak loads are distinguishable and occur because of the velocity increase associated with the ramp-like event.The discrepancies between the two simulation sets for the extreme tower top loads indicate that the shortterm wind field variability across the rotor is generally higher in the stationary turbulence simulation than for the constrained simulations.As shown in the time series comparison of Figure 11, the short-term vertical wind shear can be high in connection with the extreme events, yet the tower top tilt moment does not exceed that prescribed via DLC 1.3.When non-uniformity in the stationary turbulence fields occurs around rated wind speed, it can also lead to high extreme tower base fore-aft moments that are connected to high thrust on the rotor.The extreme tower base fore-aft moments from the constrained simulations are highest for mean wind speed bins between 8 m/s and 16 m/s.In this wind speed range, the wind speed is typically below rated wind speed at the beginning of the simulation and later increases beyond rated wind speed.When the wind speed starts to rise, it does so coherently across the rotor plane, resulting in high thrust and tower base fore-aft moments, before the wind turbine controller starts to pitch the blades.The tower base fore-aft moments for the extreme turbulence case (IEC DLC 1.3) were expected to be lower than those of the extreme variance events; however, this was generally true only (on average) for certain wind speed bins.The overall characteristic tower base fore-aft moment of DLC 1.3 is 3% higher than for the extreme events.
The load simulation results show that the extreme turbulence case DLC1.3 indeed covers the load envelope caused by extreme variance events.However, the differences seen in the time series and in the load behavior indicates that extreme variance observations as events are entirely different from situations with stationary, homogeneous turbulence.This questions the basis for the definition of the IEC Extreme Turbulence Model (ETM) which is defined in terms of the statistics of the 10-minute standard deviation of wind speed.As most observations of the selected extreme variance events include a short term ramp event, it would perhaps be more relevant to compare these events with other extreme design load cases in the IEC standard, e.g. the extreme coherent gust with direction change, extreme wind shear or the extreme operating gust.Since these are the absolute highest variance events observed at Høvsøre during a ten year period, they would also appear in the site-specific definition of the ETM model.Therefore, it may be necessary to exclude or re-assign such events to the relevant load case type.
The design and cost of a wind turbine may depend on how this consideration is done.
It was seen in the IFORM analysis in section 3.1 that the estimated 50-year return period contour of the linearly detrended data exceeded the the 50-year return period contour of normal turbulence (corresponding to the ETM class C).This is consistent with the findings of Dimitrov et al. (2017), who performed similar analysis of linearly detrended measurements from Høvsøre, though from the easterly (homogeneous farmland) sector.For the high-pass filtered measurements, the turbulence level was reduced significantly as well as the estimated 50-year return period of turbulence.This is seen as the high-pass filtering effectively removes variance of low frequency fluctuations with time scales larges than 200 ::: 300 s, as the chosen cut-off frequency was 1/200 ::: 300 Hz.This finding suggests that for typical hub heights as considered (z ⇡ 100 m) at a coastal site like Høvsøre, extreme variance events are not representative of homogeneous, stationary turbulence and can be filtered out by high-pass filtering.It should be kept in mind though, that these events may be considered for extreme design load case purposes other than turbulence.In that case it is important not to use detrending of any kind on the measurements, as these extreme fluctuations will then not be identified and characterized correctly.

Conclusions
The main objective of this study is to investigate how extreme variance events influence wind turbine response and how it compares with DLC 1.3 of the IEC 61400-1 standard.The selected extreme events are measurements of the 10-minute standard deviation of horizontal wind speed that exceed the values prescribed by the ETM model and include a sudden velocity jump (ramp event, transients in the turbulent flow), which is the main cause of the high observed variance.The events were simulated with constrained turbulence simulations, where the measured time series were incorporated in turbulence boxes for load simulations in order to make a realistic representation of the events, including the short term ramps and the coherent flow in the lateral direction as was seen in the comparison of measurements between the two masts in Figure : 2. The constraints force the turbulent flow of the simulations to be non-stationary and non-homogeneous.
Load calculations of the simulated extreme events were made in HAWC2 and compared to load calculations with stationary homogeneous turbulence according to DLC 1.3.To summarize, we have found that: • The extreme variance events are large coherent structures, observed simultaneously at two different masts with a 400 m (lateral) separation.
• Most extreme variance events include a sharp wind speed increase (short-time ramp) which is the main source of the large observed variance.
Appendix A ::: The ::::::  Comparing the raw data in Figure 4, to the linearly detrended data and high-pass filtered data in Figure A1 it is seen that the detrending, and high pass filtering slightly lowers the values of µ u , while the reduction of u is much greater, especially for the high-pass filtered measurements.

"
The layout of the figure could be made clearer.e.g.mark underneath (a) DLC 1.3 (b) constrained top panels -wind speed bottom panels -moments" Answer: They layout of the figure has been changed to make clearer.

Figure 2 .
Figure 2. The dots correspond to 10-minute TI :::::: standard ::::::: deviation :: of ::: the :::: wind :::: speed as a function of U at 100 m height over a 10-year period.The black and blue curves show the IEC extreme turbulence model, class C and class B respectively.The selected events (blue dots) are TI :: u values exceeding the extreme turbulence model class B.

Figure 2 .
Figure 2. Comparison of horizontal wind speed measurements at the meteorological mast (green curve) and the light mast (blue curve).The measurement height is 100 m at both masts, which are separated by ⇡ 400 m.The 10-minute averaged wind direction ✓ is from the light mast.

Figure 3 .
Figure 3.Comparison of horizontal wind speed measurements at the meteorological mast (green curve) and the light mast (blue curve).The measurement height is 100 m at both masts, which are separated by ⇡ 400 m.The 10-minute averaged wind direction ✓ is from the light mast.

Figure 5 .
Figure 5.The 50-year return period contours based on the measurements (green curves) and the IEC expressions (blue curves).The grey dots show the measurements.a) Raw measurements.b) Linearly detrended measurements.c) High-pass filtered measurements with a cut-off frequency: 1/600 Hz. d) High-pass filtered measurements with a cut-off frequency: 1/300 Hz.The dark grey circles indicate the extreme variance events.

Figure 5 Figure 5 .
Figure5shows the joint distribution of mean wind speed and turbulence, with contours corresponding to the 50-year return period.The contours are calculated based on the measurements (green curves), and the IEC expressions (blue curves) of µ u and u respectively.The parameters of the marginal distribution of the 10-minute mean wind speed data were found with maximum likelihood estimation of the three-parameter Weibull distribution (scale parameter: 9.75 m/s, shape parameter: 2.02,

Figure 6 .
Figure 6.Comparison between u-velocity components from unconstrained turbulence simulations, and from turbulence simulations with velocity jumps included using constrained simulation.a) seed 1003 without constraints, b) seed 1005 without constraints, c) seed 1003 with constraints, d) seed 1005 with constraints.Constraint locations are shown with black dots.

Figure 6 .
Figure 6.Comparison between u-velocity components from unconstrained turbulence simulations, and from turbulence simulations with velocity jumps included using constrained simulation.a) Seed 1003 without constraints.b) Seed 1005 without constraints.c) Seed 1003 with constraints.d) Seed 1005 with constraints.Constraint locations are shown with black dots.

Figure 7 .
Figure 7.Comparison of unconstrained and constrained streamwise (u-) velocity component in the middle of the turbulence box, y=89.6 m, z=119 m.Left: Seed 1003.Right: Seed 1005.

Figure : 7
Figure : 7 shows two examples of the u-velocity time series at hub height with and without applied constraints, for the same turbulence seeds as shown in Figure 6.

Figure 8 .
Figure 8.The mean standard deviation of the u-component of the simulated wind speed at hub height as function of mean wind speed at hub height.DLC 1.3 (grey dots) and constrained simulations with extreme variance events (blue dots).

Figure A1 .
Figure A1.Notation same as Figure 4 but for a) linearly detrended data, b) high-pass filtered data with cut-off frequency of 1/600 Hz and c) high-pass filtered data with cut-off frequency of 1/300 Hz.

Figure
FigureB1shows extreme moments as function of the u-component of the mean hub-height wind speed.Each dot shows the maximum/minimum load value of each 10-minute HAWC2 simulation for the tower top (top panels), the tower base (middle panels) and blade root (bottom panels).The simulations based on a particular extreme variance event may be identified as a cluster of six dots, as they have been simulated with six different turbulence seeds.For DLC 1.3 a cluster of six dots may be 10

Table 1 .
The IEC turbulence classes and associated turbulence intensities.

Table 2 .
The main characteristics of the reference wind turbine.

Table 3 .
The highest mean extreme moments for different load components ::::