3.1. Preliminary Comparison with a Sonic Anemometer on Land
Although there is no reference sensor available in the fjord allowing a direct assessment of the data recorded with the multi-lidar configuration, two meteorological masts were installed at the end of 2015 by the company Kjeller Vindteknikk AS (Kjeller, Norway), abbreviated KVT in the following, on the island of Ospøya. This island is located ca. 2.3 North of LW2. The southernmost mast is 50 high and installed at a height of ca. 35 above the mean sea level. This mast is equipped with one Gill WindMaster Pro 3-axis sonic anemometer (Lymington, Hampshire, UK) at a height of 67 and two others located at 83 above the mean sea level. The three sonic anemometers operate at a sampling frequency of 10 . The mast and the data gathered by the sonic anemometers are owned by KVT. Therefore, a detailed analysis of the mast instrumentation and its measurement data is out of the scope of the present study. Nonetheless, during the last four days of the measurement campaign, LW2 conducted a fixed LOS scan toward the mast, with an elevation angle of 1.85°. KVT provided velocity measurements from the sonic anemometers so that a comparison with the lidar data could be conducted in terms of mean value and standard deviation of the along-beam velocity component. To the authors’ knowledge, the sonic temperature measurement data were, however, not stored. For the sake of brevity, only data recorded by the sonic anemometer installed at the altitude of 83 are considered in the following. At the scanning distance of 2.3 , the range gate closest to the met mast is at a height of ca. 75 above the mean sea level.
To simplify the comparison between the velocity data recorded by the lidar and the sonic anemometer, the along-beam component is considered. For the sonic anemometer,
is estimated using:
where
is the azimuth angle;
is the elevation angle and
is the wind direction, as defined in Equation (
7).
Figure 5 shows that the 1
-averaged along-beam velocity component is remarkably well captured by LW2. A more detailed comparison of the two device performances is provided in
Figure 6. The best linear fit between the mean wind velocity of the along-beam component recorded by LW2 and the sonic anemometer shows a squared correlation coefficient of
and almost no bias. For the standard deviation, the squared correlation coefficient is also significantly large and equal to
, but a systematic discrepancy is observed between the lidar data and the sonic anemometer data, which is expected and attributed to the spatial averaging effect. The results presented in
Figure 5 and
Figure 6 are not surprising, as a similar comparison with sonic data has already been done in the past by Pauscher et al. [
7]. Nevertheless, the comparison given herein shows that the wind data recorded by the multi-lidar system in the Bjørnafjord and presented in the following are reliable.
3.2. Statistical Moments
The wind roses displayed in
Figure 7 for the E-W configuration (left) and the N-S one (right), represent the wind data recorded by the long-range WindScanners in the laser-beam intersection volume generated by LE and LW2. In both cases, the majority of wind records represents a wind direction from north-northwest, i.e., almost aligned with the scanning beam of LE, with wind velocities up to 17.7
s
for the N-S configuration and up to 13.8
s
for the E-W configuration. For wind velocities above 8
s
, the average values of
and
estimated using the N-S configuration are 0.056 and 0.042, respectively. For the the E-W configuration,
and
are in average equal to 0.043 and 0.030, respectively. The ratio
is, therefore, equal to
for the E-W configuration and
for the N-S configuration, which is in the range of expected values [
26]. The low turbulence intensity recorded here may not be explained by the ABSA influence alone, although that effect does result in an underestimation of the standard deviation of the wind velocity and thereby an underestimation of the turbulence intensity.
Following Equation (
9), which is defined for a neutral stratification, a roughness length of 0.003
and an altitude of 25
above sea level gives a turbulence intensity of 0.11. A roughness length as low as 0.0001
has been reported for flows over the sea at moderate wind speeds [
33,
34]. For
, the turbulence intensity calculated according to EN 1991-1-4 [
18] and corrected for the ABSA is
, which is much closer to the values recorded during the measurement period. For this reason, turbulence statistics assuming a roughness length
are investigated in the following. At low wind velocities, statistical measures defined primarily for shear generated turbulence are estimated with large uncertainties. This is mainly due to the increasing number of non-stationary samples, related to increased convective mixing and buoyancy effects, and to less extent, to increasing errors in the lidar measurements. In
Figure 8, one can see that the turbulence intensity estimates become steady for a mean wind velocity around 6 m
s
. In the following, the estimated turbulence intensity is therefore discussed for
m
s
, i.e., for wind velocities large enough to provide consistent wind statistics.
A rigorous estimation of the atmospheric stability relies on measurements of vertical fluxes of momentum and heat. This can be done using either a meteorological mast instrumented with cup anemometers, temperature and humidity sensors [
35] or a 3D sonic anemometer able to measure the sonic temperature [
36,
37]. In the present case, such an instrumentation was not available, and no measurement of the vertical profile of mean wind velocity above the sea surface could be conducted using the lidars, due to the low elevation angles used. Therefore, alternative methods are considered in the present study to discuss possible effects of a non-neutral atmosphere on the lidar measurement data.
The low turbulence intensity observed may be partly due to a stable atmospheric stratification, for which values lower than
were recorded at a height of 70
above the sea level and for
m
s
in an offshore environment by e.g., Hansen et al. [
38]. Previous studies conducted at bridge sites in coastal areas have also reported a turbulence intensity close to or below 0.06. Sacré and Delaunay [
39] measured
at
for moderate winds from the sea (11.6
s
to 15.7
s
) and a neutral stratification. For a seasonal wind, Toriumi et al. [
40] measured a turbulence intensity close to 0.04 at
for a mean wind velocity of about 23
s
, which is strong enough to assume that mechanically-generated turbulence was dominating over buoyancy effects.
For
m
s
, the standard deviation of the wind direction is lower than 3.75
(N-S configuration) and 2° (E-W configuration) for 80% of the wind samples. According to Sedefian and Bennett [
41], such a low standard deviation may correspond to a slightly stable atmospheric stratification. Nonetheless, the low standard deviation of the measured wind direction may also result from the ABSA effect.
Figure 8 indicates that a stable atmosphere may have been predominant during the monitoring with the E-W configuration since the turbulence intensity measured for
m
s
is systematically lower than for the N-S configuration, whereas the wind direction is almost the same (
Figure 7). For
m
s
, the turbulence intensity seems to be rather constant, whereas Equation (
23) leads in
Figure 8 to a clear increase of the turbulence intensity with the mean wind velocity. This suggests that the roughness of the sea in the Bjørnafjord is not clearly increasing with the mean wind velocity, as typically observed in an offshore environment.
The uncertainties regarding the atmospheric stability observed during the measurement campaign highlight the need to associate the lidar data to measurements from weather stations and sonic anemometers on land.
3.3. Wind Spectra Comparison
Each individual spectrum is estimated using the periodogram power spectral density (PSD) estimate with a Hamming window, which corresponds to the particular case of Welch’s algorithm with a single segment. We chose to use a single segment so that the wind spectrum can be described down to a frequency of 0.0017 . To reduce the large random error that results from the use of the periodogram PSD estimate, the different spectra are ensemble averaged. An additional smoothing of the PSD in the high-frequency range is done using non-overlapping block average with 60 blocks that are equally spaced on a log scale.
The PSD estimate of the along-wind component is displayed on the left panel of
Figure 9, whereas the right panel shows the PSD estimate of the along-beam component recorded by LE. In both panels, only samples characterized by a mean wind velocities between 11
s
and 18
s
are considered, but only the ensemble averaged PSD estimates are displayed for the sake of clarity. The relatively large velocity range selected justifies the use of the wavenumber
(left panel) or
(right panel) instead of the frequency. The wind spectra are pre-multiplied by the wavenumber and divided by the variance of the corresponding wind velocity component. For 11 m
s
m
s
, the wind direction is on average equal to 330° (
Figure 7), and the along-beam component is, therefore, almost equal to the along-wind component. Assuming the flow is uniform in the middle of the fjord,
was calculated using the data gathered at scanning distances ranging from 2
to 3.5
, i.e., 15 different range gates. This results in a slightly smoother wind spectrum at every frequency than for the PSD estimate of the along-wind component.
The wind spectra from the Handbook N400 and NORSOK standard are calculated for
and superimposed to the measured PSD. The normalization of the spectra by the variance of the wind velocity allows, in particular, a reduction of the uncertainty related to the estimation of the roughness length. For the NORSOK and N400 spectra,
is estimated using Equation (
28). However, the lidar data is known to be associated with underestimated values of
and
. Therefore,
and
were estimated directly from the time series, and a correcting coefficient was introduced, assuming an underestimation of ca. 30%, as suggested by
Figure 4.
In
Figure 9, the measured spectral peak and the one estimated using the NORSOK spectrum are well aligned. The spectral peak of the N400 spectrum is located at a slightly higher wave-number than the measured one. For
, the NORSOK spectrum gives higher spectral values than observed from the recorded data. This is not unreasonable, as other studies [
42,
43] have shown that wind spectra measured offshore often contain more energy at low frequencies compared to the wind spectra measured onshore. This is partly due to the fact that, in an offshore environment, the size of eddies is not limited by topographical changes. Although the flow from north-northwest recorded in the Bjørnafjord comes from the ocean, it is likely affected by the islands upstream of the monitored domain as well as the shoreline of the fjord. Consequently, an offshore wind spectrum model, such as the one used in the NORSOK standard may overestimate the spectral values at low wave-numbers. The discrepancies between the measured spectrum and the NORSOK spectrum may also be related to a slightly stable atmospheric stratification. For
m
s
, Andersen and Løvseth [
44] observed a negligible difference between the Frøya spectrum measured in stable and neutral stratification. On the other hand, Mann [
45] found strong effects of stability on spectra over the Great Belt, Denmark, up to over 16
s
, albeit at a height of 70
.
When the high-frequency range of the N400 wind spectrum is attenuated using the ABSA model presented in Equation (
26), the slope of the high-frequency part of the modified spectrum is sharper than measured, as seen in
Figure 9. Similar observations have been reported by e.g., Pauscher et al. [
7] with the long-range WindScanner system or e.g., Angelou et al. [
46] with the short-range WindScanner system. The discrepancies between the modelled ABSA and the measured one may be due to fluctuations of the wind direction and the use of multiple scanning beams to retrieve the horizontal wind components. For frequencies above 0.22
and
14 m
s
, i.e., wave-numbers above 0.10, the right panel of
Figure 9 shows that the PSD of the along-beam wind velocity component is considerably attenuated by the ABSA, viz. The high-frequency turbulent components are under-represented in the lidar data.
Figure 10 shows the
spectrum, estimated without normalization by
. Consequently, the wind spectra need to be split into several velocity bins, since a different mean wind velocity now has a significant effect on the magnitude of the PSD estimate. The study of
allows the assessment of an appropriate roughness length for the N400 spectrum. The spectra displayed in
Figure 10 are, therefore, complementing those displayed in
Figure 9. In
Figure 10, the N400 spectra is estimated with
, which is 30 times lower than proposed in the Handbook N400. Nevertheless, it leads to a fairly good agreement between with the measured wind spectra, especially for
m
s
. The NORSOK spectrum is found to systematically overestimate the PSD of the along-wind velocity component, which is likely due to the fact that this spectrum is site-specific.
3.6. Application of an Alternative Coherence Model
The more complex dependency of the measured co-coherence on the lateral separation may be modelled using Bowen’s coherence model [
55], which is derived from the Davenport coherence model, except that the decay parameter
has the following form:
where
and
are two coefficients to be determined and
z is the measurement height. The function is an idealized representation of the lateral coherence of the along-wind turbulence near the ground. Bowen et al. [
55] arrive, for example, at
and
. In the present case,
and
are determined using a least-square fit to the measured co-coherence. Minh et al. [
56] proposed a more complex three-parameter coherence model, which also depends on
and
, but is independent of the measurement height. For the sake of simplicity, only the Bowen model is investigated in the following.
Figure 15 shows that the Bowen coherence model seems to provide a much better fit to the measured coherence than the Davenport coherence model at both
and
.
Figure 16 shows, however, that the fitted coefficients display a large variability at
. This is likely due to the fact that the coherence seems to become independent of
for
and the majority of the cross-wind separations are larger than 50
for
. The low dependency of the estimated co-coherence on
at large crosswind separations is reflected in the negative value of
that counterbalances
, as shown in the right panel of
Figure 16.
The Bowen coherence model suggests that the coherence depends on the measurement height
z and
, which is not predicted by the Davenport coherence model. To estimate the wind load on a suspension bridge, the measurements should, therefore, be conducted at the deck height. Because the Bowen coherence model was designed at an altitude lower than 20
, it is uncertain beyond which height such a model ceases to be valid. Measurement in a narrower Norwegian fjord reported in ([
54], chapter 2), conducted at a height of 60
for a wind speed above 8
s
, showed, for example, that a coherence model that is simply scaled by
was sufficient to properly capture the lateral wind coherence of the along-wind component.