Triple-lidar measurements of wind across a virtual rotor plane over a sea surface

An improved understanding of the spatiotemporal characteristics of the wind velocity field above the sea surface will benefit the design of modern offshore wind turbines. This study examines wind velocity data recorded on a bow-tie-like measurement pattern, approximately covering a rotor area diameter of about 70 m. The measurement data are obtained by triple continuous-wave Doppler lidars (short-range WindScanners). Two of the instruments are installed on a stable platform in the form of a suspension bridge deck, whereas the third is stationed on the ground nearby. Data from sonic anemometers installed above the bridge deck are used to validate the wind characteristics observed by the lidars. The lidar measurement data are explored in terms of wind flow mapping, mean flow characteristics and co-coherences. The results demonstrate the difference between the co-coherence at lateral and vertical separations and also differences from the coherence model in the IEC standard. The results further show the potential of lidar measurements to provide new insight into mean wind flow and turbulence characteristics applicable for offshore wind turbine design.


Introduction
Knowledge of the spatiotemporal characteristics of the wind field above the sea surface is of key importance for the design of offshore wind turbines [1].Remote wind sensing using wind lidars provides attractive possibilities to acquire this for the safe design of offshore wind turbines with respect to their response to wind loadings.
In the recent decade, remote wind sensing by lidars has found a wide range of applications in the wind energy industry, both using continuous-wave and pulsed lidars.For wind resource assessment and wind turbine wake studies, ground-based lidars are commonly adopted, as discussed in e.g.[2,3].Measurements in complex terrain are often supported by numerical flow modelling [4].For optimized power production and wind turbine control, lidars are installed on a wind turbine nacelle, [5,6].Offshore lidar wind measurements have been carried out from fixed platforms [7] or bottom-fixed wind turbines [8], as well as from floating platforms, such as buoys or ships [9].Both a single [10] and multiple [11] lidars have been adopted to access the lateral wind coherence offshore.However, most previous offshore studies have been focused on 2D measurements, usually ignoring the vertical component, which is considered in the present work.The objectives of the study are to verify the capability of lidar measurements to monitor the three wind velocity components, evaluate the wind field characteristics along an arbitrary radial direction in a "rotor plane", investigate the uniformity of the inflow as well as the first and second-order wind statistics including the turbulence spectra for all three turbulence components.In particular, the frequency-dependent correlation of wind fluctuations across a rotor plane (coherence) is estimated for vertical, radial, and lateral cross-wind separations.This remote sensing approach provides a unique advantage since the lateral coherence has not been properly observed from offshore measurement masts, where the anemometers are mainly aligned in the vertical direction.
The paper is organized as follows: Section 2 describes the measurement platform and the lidar measurement setup.Section 3 discusses the methods used to retrieve wind velocities from lidar recordings and the associated error propagation.Section 4 presents the mapping of the wind flow, a comparison of sonic and lidar observations, and the wind and turbulence characteristics.Finally, the main findings and conclusions of the measurement campaign are summarised in section 5.

Measurement Platform and the Monitoring System
In this study, a methodology for remote sensing of wind turbulence above the sea surface is tested by deploying a WindScanner measurement system from a transparent but stable platform, in the form of a suspension bridge deck (Figure 1a), 54 m above the sea surface, in a measurement domain spanned by a virtual wind turbine rotor.The platform is located in a fjord where the wind from the southwestern direction is favorable for inflow studies, as indicated by the arrows in Figure 1b.The flow was successfully monitored by lidars in an undisturbed region away from the bridge deck in a previous measurement campaign with a dual lidar system [12,13].
The wind field is examined using three synchronized continuous-wave lidars.Two of the lidars are deployed on the bridge deck 36 m apart.The third lidar is installed 38 m below the bridge deck, next to the tower foundation at the North end of the bridge and is positioned 10.5 m from the vertical plane defined by the two lidars on the bridge girder (Figure 2 and Figure 3a-c).All    1. Also, more details about the instrumentation can be found in [15].

Wind velocity formulation
With the three LOS velocities derived from Doppler spectra by the median frequency estimator, a geometric transformation can be applied to extract the 3D wind components: In the above equation, the wind components normal and parallel to the deck are denoted by v x and v y , and the vertical component is denoted by v z and M is defined as In equation 2, the azimuth and elevation angles are α and β, respectively.The angle between the main wind direction and the bridge axis, also called the yaw angle, is defined as: where v x and v y are the average of the across-deck and along-deck wind components.The wind-based coordinate system is illustrated in Figure 3d.Finally, the inclination angle, which is the angle of the wind direction and the horizontal plane, is defined by δ as: where, v z is the average of the vertical wind component.The calculated wind components v x , v y , and v z are rotated onto the main wind direction to obtain the along-wind (U + u) as well as across-wind (v) and vertical wind (w) fluctuations where the mean values of u, v, and w are approximatively 0 m s −1 .The vertical wind is thereby assumed as the summation of vertical mean wind velocity and zero-mean component i.e. v z = v z + w and along wind includes a vertical component.

The lidar data resolution
A Doppler wind lidar measures the radial velocity in a volume that is stretched along the beam and represented by the full width at half maximum (FWHM) [16].The FWHM increases quadratically with the distance from the lidar to the observation point, as shown in equation (5).
Here λ = 1.565 µm is the wavelength of the laser source; r is the measurement distance and r 0 ≈ 28 mm is the beam radius.Accordingly, ground lidar (R2D3) measures the along-beam velocity within larger volumes due to its larger distance to the measurement domain; the FWHMs vary between 4.73 m and 17.25 m.The two deck lidars capture the LOS velocity with FWHMs, ranging between 2.36 m and 5.37 m.

Error propagation in the measurement
The accuracy of the results partly depends on the condition number of the matrix M, which reflects to what degree the vectors formed by the three lidar beams are linearly independent, i.e. to what degree the three light beams are not coplanar [17].In this study, the condition number is at its largest value for the measurement location at the southern end of the horizontal line.However, in the whole domain it is below 10, which is a relatively small value and consequently, the wind velocity components can be reliably estimated using the designated measurement configuration.

Results
An 11-minute-long event, observed on 24 th September 2021, is chosen for the study presented in this paper.The wind direction was perpendicular to the measurement plane and there was no precipitation.For this wind event the sonic anemometer mounted 6 m above the bridge deck at hanger 8 (H08Wb), recorded a mean along-wind velocity of U =5.91 m s −1 , with the along-wind turbulence intensity of I u =0.22 and vertical turbulence intensity of I w =0.10.As the mean wind velocity is rather low, the turbulence intensity levels can be expected to be higher than is typical for offshore conditions [18, 19].

Wind flow based on WindScanner data
Figure 4 shows the fluctuating part of the incoming wind velocity and its variability along the horizontal line and vertical line of the scanning pattern.As can be seen, the velocity fluctuations along the two lines are consistent.The data illustrate the natural flow velocity variations, including occasional arrivals of large gusts, well correlated in the measurement domain.The along-wind turbulence intensity at the center of the bow-tie-like pattern is I u =0.215.The associated mean wind speed is U =6.0 m s −1 , and the mean wind direction, with reference to bridge axis, is γ=267 • for the point mentioned.

Comparison of the sonic anemometer and lidar observations
The recorded lidar data at the center of the bow-tie-like pattern are compared to data from sonic anemometers installed 6 and 10 m above the bridge deck on hanger 8 (H08Wb and H08Wt), respectively.The sonic anemometers are located 36 m away from the pattern's center in deck-wise direction, close to the southern end of the horizontal scanning line, and 40 m downwind of the scanning line.Figure 5 displays the comparison of the along-wind and vertical components.A good agreement is seen between lidars and sonic data, except for somewhat larger variabilities in the vertical component obtained from lidar data, mainly because of measurement noise.A slight shift in phase is also observed in Figure 5, as a result of around 40 m distance between the scanning pattern and the sonic anemometers in the wind direction.

Mean flow characteristics
The distribution of mean flow characteristics in space, along both the vertical and the horizontal line of the scanning pattern, is illustrated in Figure 6 and Figure 7, respectively.The mean wind speed in Figure 6 shows little variation at the top, and then it gradually reduces following the standard logarithmic profile.A logarithmic profile fitted to the values from ca. z=-26 m to z=+18 m is associated with roughness length and surface roughness coefficient of z 0 =0.034 m and κ=0.003, respectively, which represents an open flat terrain category, rather than a sea surface [20].This is likely because the wind passes over land before coming over the sea towards the lidars from the southwest.Also, a slight change in wind direction with height is observed with a direction becoming perpendicular to the measurement plane at the top of the scanning pattern.In Figure 7, a slight increase in the mean vertical wind speed towards the center of the fjord (positive y values), combined with a slight decrease in the mean wind speed, is associated with a modest increase in the inclination angle along the line, up to 4 • .

Co-coherence
The spatiotemporal characteristics of natural turbulence above the sea surface are further studied in terms of the frequency-dependent correlation of wind velocity fluctuations across the measurement domain.The so-called co-coherence, which captures the in-phase variation of the velocity components at different frequencies, is estimated using the real part of the normalised cross-spectral density of wind components S ij , simultaneously measured in two points, i and j: Here S i and S j are the auto-spectral densities of wind components in points i and j with a spatial separation d = l i − l j .In this study, the co-coherence of the along-wind component is estimated using the Welch method by 50% overlapping [21] of five-minute segments.To acquire synchronized time series, the measurement domain is discretized into grid cells (also called clusters) of 1-meter length in z and y directions and then a linear interpolation in time is applied to the time-series for each spatial cluster containing data samples.The sampling frequency of interpolation is set to be 1 Hz for all data clusters which is close to the actual sampling frequency of the data within all clusters except at the center, where the sampling frequency is close to 2 Hz.This leads to a frequency range of 3 mHz to 0.5 Hz for the spectral density.
The resulting co-coherence estimates are displayed in Figure 8, for a selected separation of 10 m.The co-coherence is slightly weaker along the vertical line, compared to the horizontal line.As expected, the flow synchronisation for an arbitrary, "inclined" radial orientation, falls between that for the vertical and the horizontal direction.The samples used to establish the co-coherence for the inclined separation were defined in such a way that one end of the separation is positioned on the vertical line while the other end is on the horizontal line.This led to two inclined separations of 10 m for each quarter of the circular domain being observed, and eight samples for the entire domain in total, corresponding to ca. ±53 • or ±37 • with respect to the horizontal plane.The estimated co-coherence for horizontal separations indicates a positive smooth underlying function, expected for a limited separation of 10 m in a cross-flow.The vertical and the inclined coherence display some minor negative values, likely related to the wind shear.
For the studied separation, all three co-coherences are, in the following, compared to the exponentially decaying coherence function provided in the IEC standard [18]: where U hub is the wind speed at a hub height equal to 6.0 m s −1 and r is the across-flow separation.In the present study, the hub height (z hub ) is 56 m.The velocity component integral scale parameter, L u , is taken as the integral length scale of the along-wind at hub height, which is found to be 202 m, for the data series used.C 1 and C 2 are here fitted to the estimated coherence data while the corresponding values given by IEC standard are included in the (last row of) Table 2.
The C 1 values are smaller than the value C 1 = 12 provided in the standard, indicating a higher level of turbulence synchronisation at the measurement site, which could excite a higher surge response of a floater compared to that associated with the standard coherence.The coherence for the vertical separations is slightly weaker than the one for the horizontal separations.As expected, the C 1 and C 2 values for inclined separations lie between the values for the vertical and horizontal separations.The estimated C2 coefficient, which defines the coherence at f ≃ 0, is considerably lower than the value in the IEC standard.It is associated with a high level of uncertainty, following a limited duration of the studied event.It should be noted that the lidar measures the radial velocity in a volume that is stretched along the lidar beams.This volume sampling of the velocity may in principle result in a higher correlation between individual

Figure 1 .
Figure 1.The Lysefjord Bridge.(a) View from the East, with lidar locations marked by red points.(b) Overview and position on a map, from [14].

Figure 3 .
Figure 3.The triple-lidar system and the reference coordinate system.(a-c) Two deck lidars and one ground lidar.(d) Wind-based coordinate system.

Figure 4 .
Figure 4. Mapping of the along-wind turbulence component, u, along the vertical and horizontal line of the scanning pattern.

Figure 5 .
Figure 5. Along-wind and vertical wind components recorded by WindScanners at the center of the scanning pattern and anemometers located 40 m downwind.

Figure 6 .
Figure 6.Profiles of across-plane, along-plane and vertical mean wind velocities, wind direction, inclination angle, and along-wind (from left to right), measured by the WindScanners along the vertical line of the scanning pattern compared to simultaneous measurements by anemometers.z=0 corresponds to 55.6 m above the sea surface.

Figure 7 .
Figure 7. WindScanner observations along the horizontal scanning line and the corresponding anemometer data.The mean wind components shown and the location of origo (y=0 at hanger 5) is defined in Figure 3.

Figure 8 .
Figure 8. Co-Coherence measured (dashed line) by lidars, fitted (dotted line), and provided by standard (solid line) for separation of 10 m. z hub and U hub are equal to 56 m and 6.0 m s −1 .

Table 1 .
Properties of the Doppler wind lidar short-range WindScanner system installation.