Investigation of Marine Wind Veer Characteristics Using Wind Lidar Measurements

: A proper understanding of marine wind characteristics is of essential importance across a wide range of engineering applications. While the o ﬀ shore wind speed and turbulence characteristics have been examined extensively, the knowledge of wind veer (i.e., turning of wind with height) is much less understood and discussed. This paper presents an investigation of marine wind ﬁeld with particular emphasis on wind veer characteristics. Extensive observations from a light detection and ranging (Lidar) system at an o ﬀ shore platform in Hong Kong were examined to characterize the wind veer proﬁles up to a height of 180 m. The results underscored the occurrence of marine wind veer, with a well-deﬁned two-fold vertical structure. The observed maximum wind veer angle exhibits a reverse correlation with mean wind speed, which decreases from 2.47 ◦ to 0.59 ◦ for open-sea terrain, and from 7.45 ◦ to 1.92 ◦ for hilly terrain. In addition, seasonal variability of wind veer is apparent, which is most pronounced during spring and winter due to the frequent occurrence of the low-level jet. The dependence of wind veer on atmospheric stability is evident, particularly during winter and spring. In general, neutral stratiﬁcation reveals larger values of wind veer angle as compared to those in stable and unstable stratiﬁcation conditions.


Introduction
Energy harvesting from renewable energy sources is one of the major strategies to effectively reduce carbon footprints and accelerate sustainable development. The share of renewable energy sources of global electricity generation reached 26.4% in 2018 [1,2]. Renewable energy contains a mix of various technologies, such as wind energy, solar energy, tidal power, etc., which are naturally replenished on different timescales. In particular, wind energy is one of the mainstream renewable energy sources, which has been seen to develop at a remarkable pace across the world due to the high availability of resources and the maturity of the technology in terms of cost efficiency [3]. In 2019, the global new wind power installations surpassed 60 GW, a growth of 19% compared to 2018, and the total installed capacity rose to 650 GW [4]. It is worth mentioning that, while onshore wind power is still dominating the market, accounting for more than 95% of the total installations, offshore wind power has become increasing prevalent, especially in China, the United Kingdom and Germany [4].
Due to the differences in the respective installation environments, offshore wind power tends to exhibit a number of advantages compared to traditional onshore wind power [3,5]: occurs, which is consistent with those predicted by simulation and wind tunnel tests. Churchfield and Sirnivas [46] also observed that the wake is noticeably skewed in the veered inflow condition as it moves downstream, which, however, is not a simple passive tracer-like process. Englberger and Lundquist [47] showed that the shape and magnitude of veer wind profile in the wake depend closely on the wind veer conditions in the inflow. Choukulkar et al. [48] highlighted that the wind veer (i.e., wind direction shear) exhibits significant impact on the wind power availability in addition to wind speed shear, which generally leads to a decline in power-producing capacity. Similar conclusions were also obtained by Bardal et al. [49], who found a reduced power output in the whole partial load regime under high veer conditions. In contrast, Eriksson et al. [50] examined the effect of wind veer and the Coriolis force on an idealized farm-to-farm interaction case, in which the estimated power production was found to increase with the inclusion of the wind veer effect. Murphy et al. [51] concluded that the influence of wind veer on turbine power production is strongly tied with wind speed, in which a large wind veer angle generally results in power gains at a wind speed exceeding 10 m/s. Below this threshold value, the impact of wind veer appears to be somewhat negligible.
Hong Kong is a developed city that depends heavily on sustainable energy supply. The local authorities and energy companies are actively exploring new ways to diversify the energy supply portfolio with a view to achieve a less carbon-intensive and more sustainable energy system, among which, notably, offshore wind power has been established as a promising and cost-competitive renewable energy source. In such a context, several precedent studies have been undertaken to examine the viability of offshore wind power development in Hong Kong [52][53][54][55]. In particular, the authors present a series of studies with relevance to the assessment of offshore wind characteristics for wind energy application [5,18,56].
Nevertheless, it is worth mentioning that the aforementioned studies were primarily focused on the statistical analysis of wind speed and wind energy potential, whereas the information of wind veer at offshore sites, particularly in Hong Kong, has rarely been discussed and documented. Current design codes and standards for wind turbines or other marine-based structures have not taken into account the wind veer, which is possibly due to the lack of systematic wind veer assessment. On the other hand, given the complexity of forcing agents governing marine wind veer, its characteristics are likely to be site dependent. On this account, the current study is a continuation and extension of our previous study, with particular emphasis on marine wind veer characteristics. Extensive wind observations from a light detection and ranging (Lidar) system equipped at an offshore platform in Hong Kong are included and analyzed. The rest of this paper is organized as follows: Section 2 presents detailed information related to data collection and processing. Analyzed results and a discussion are documented in Section 3, and the major conclusions are summarized in Section 4.

Site Description and Measurement Instrumentation
The marine wind observation platform is located in the southern waters of Lamma Island (see Figure 1), with a nearest distance of approximately 3.5 km. Cheung Chau Island and Lantau Island are located off the northwest of the platform, with a distance of, respectively, 9 km and 15 km. The platform is exposed to a fairly open-sea terrain within the range of 60-240 • [24]. Wind speed and wind direction data are recorded by a comprehensive measurement system, consisting of a meteorological mast and a wind Lidar system (see Figure 1). In this study, a marine wind observation campaign was undertaken during the period from March 2012 to November 2015.
The wind mast is of a lattice structure design with a total height of approximately 22 m, where a pair of side-mounted A100L2 cup anemometers (manufactured by Vector Instrument) are positioned at 21.3 m above mean sea level (MSL), orientating, respectively, towards the northwest (denoted as NW anemometer, hereafter) and the southeast (SE anemometer, hereafter). Wind direction data are recorded by a wind vane (manufactured by Vector Instrument) located 18.6 m above MSL, orientating Atmosphere 2020, 11, 1178 4 of 14 towards the southeast. In order to eliminate the potential interference effect from the physical structure of the mast, the paired anemometers and the wind vane are mounted on horizontal cylindrical booms with a distance of 2.3 m to the center of the mast. The cup anemometer and wind vane were configured to record instantaneous data at a sampling rate of 1 Hz, which were further averaged and output at a time interval of 10 min using a CR3000 micro-logger system (manufactured by Campbell Scientific). The wind mast records contained the 10 min mean and standard deviation of wind speed and wind direction. The wind mast is of a lattice structure design with a total height of approximately 22 m, where a pair of side-mounted A100L2 cup anemometers (manufactured by Vector Instrument) are positioned at 21.3 m above mean sea level (MSL), orientating, respectively, towards the northwest (denoted as NW anemometer, hereafter) and the southeast (SE anemometer, hereafter). Wind direction data are recorded by a wind vane (manufactured by Vector Instrument) located 18.6 m above MSL, orientating towards the southeast. In order to eliminate the potential interference effect from the physical structure of the mast, the paired anemometers and the wind vane are mounted on horizontal cylindrical booms with a distance of 2.3 m to the center of the mast. The cup anemometer and wind vane were configured to record instantaneous data at a sampling rate of 1 Hz, which were further averaged and output at a time interval of 10 min using a CR3000 micro-logger system (manufactured by Campbell Scientific). The wind mast records contained the 10 min mean and standard deviation of wind speed and wind direction.
It is noteworthy that, although a traditional wind mast has been predominantly used for measuring and collecting wind data, its measurement height is often limited up to 50 m to 100 m due to structural and cost constraints, which is unsuitable for the proper observation of wind characteristics for utility-scale turbines with typical hub heights of 100 m to 130 m and rotor diameters of 150 m to 200 m [7,57]. Remote sensing technologies, in particular Doppler Lidar, are becoming increasingly popular in the wind energy community because of their ability to measure wind data over larger regions and higher altitudes [9]. In addition, Doppler wind Lidar reveals more flexibility in terms of transportation and installation, which is particularly important for offshore sites, given that the installation of a wind mast with either a fixed or floating platform can be prohibitively costly [7]. Given its practical usefulness, Doppler wind Lidar has been widely adopted for the accurate monitoring and collection of wind data [10][11][12][13][14]18,[58][59][60][61]. The wind Lidar system equipped at the platform is a 2nd generation Galion G250 Lidar Unit (distributed by SgurrEnergy), with a standard measurement range of up to 250 m. The wind speed measurement range is about 0-70 m/s, with an accuracy of ±0.15 m/s. The Lidar system is fixed on the southwest corner of the platform, with a center-to-center distance of 2.3 m to the mast. Essentially, the Galion Lidar is a pulsed laser device, which provides wind speed and direction measurements at multiple programmable heights in a fully remote manner. The principle of wind Lidar measurements is that the Lidar system omits laser pulses into the atmosphere, which are reflected by the existing aerosols. The along beam velocity can be calculated from the frequency shift using the Doppler It is noteworthy that, although a traditional wind mast has been predominantly used for measuring and collecting wind data, its measurement height is often limited up to 50 m to 100 m due to structural and cost constraints, which is unsuitable for the proper observation of wind characteristics for utility-scale turbines with typical hub heights of 100 m to 130 m and rotor diameters of 150 m to 200 m [7,57]. Remote sensing technologies, in particular Doppler Lidar, are becoming increasingly popular in the wind energy community because of their ability to measure wind data over larger regions and higher altitudes [9]. In addition, Doppler wind Lidar reveals more flexibility in terms of transportation and installation, which is particularly important for offshore sites, given that the installation of a wind mast with either a fixed or floating platform can be prohibitively costly [7]. Given its practical usefulness, Doppler wind Lidar has been widely adopted for the accurate monitoring and collection of wind data [10][11][12][13][14]18,[58][59][60][61]. The wind Lidar system equipped at the platform is a 2nd generation Galion G250 Lidar Unit (distributed by SgurrEnergy), with a standard measurement range of up to 250 m. The wind speed measurement range is about 0-70 m/s, with an accuracy of ±0.15 m/s. The Lidar system is fixed on the southwest corner of the platform, with a center-to-center distance of 2.3 m to the mast. Essentially, the Galion Lidar is a pulsed laser device, which provides wind speed and direction measurements at multiple programmable heights in a fully remote manner. The principle of wind Lidar measurements is that the Lidar system omits laser pulses into the atmosphere, which are reflected by the existing aerosols. The along beam velocity can be calculated from the frequency shift using the Doppler equation [7,62]. Throughout the measurement campaign, the wind Lidar was configured to operate in velocity azimuth display (VAD) mode, in which the azimuth angle is varied over a circle with the elevation angle fixed.
The angular speed was about 30 • /s. Data filtering was applied to the original high-resolution Lidar data by means of wind field reconstruction and a carrier-to-noise (CNR) filter. Likewise to the wind mast data, the Lidar system was configured to output the mean and standard deviation of horizontal wind speed and mean horizontal wind direction at every 10 min, the record time of which was well aligned with the mast data. In addition to the data filtering, rigorous data quality control (QC) was Atmosphere 2020, 11, 1178 5 of 14 also performed to enhance the validity of the Lidar measurements. For example, the Lidar system has a built-in data quality flag indicating the amount of data used to compute the 10 min statistical values. The maximum value of the quality flag is 17. In this study, a threshold quality flag of 12 is used to identify Lidar measurements with reasonable reliability. It is of note that, unlike other wind Lidar observation studies where the increment of measurement height is often a constant, the measurement height in this study is programmed in a non-uniform manner. The measurement height in the lower region (21.3 m to 44.1 m) increases at a vertical increment of 2.5 m, while that in the upper region (44.1 m to 178.3 m) increases at an interval of 20 m.

Fidelity of Wind Mast and Lidar Measurements
Prior to the analysis, it is important to examine the fidelity of the data involved. Given that the reliability of wind Lidar measurements is often validated using the nearby wind mast data [57], Figure 2 demonstrates the comparison of the 10 min mean and standard deviation of wind speed recorded by the paired cup anemometers (i.e., NW and SE), in which the fidelity of wind mast data can be represented by a ratio close to the standard value of 1. It is shown that the consequent ratio in regard to both the mean and standard deviation of the wind speed deviates remarkably from the standard value when the wind approaches from the direction of 135 • and 300 • , implying that the recorded wind data are likely to be obstructed by the physical mast structure within these direction ranges. Hence, in light of the methodology by Svensson et al. [9], the distorted wind mast data, i.e., those located within the shaded area in Figure 2, are not included in the following comparison analysis.
Atmosphere 2020, 11, x FOR PEER REVIEW 5 of 14 Likewise to the wind mast data, the Lidar system was configured to output the mean and standard deviation of horizontal wind speed and mean horizontal wind direction at every 10 min, the record time of which was well aligned with the mast data. In addition to the data filtering, rigorous data quality control (QC) was also performed to enhance the validity of the Lidar measurements. For example, the Lidar system has a built-in data quality flag indicating the amount of data used to compute the 10 min statistical values. The maximum value of the quality flag is 17. In this study, a threshold quality flag of 12 is used to identify Lidar measurements with reasonable reliability. It is of note that, unlike other wind Lidar observation studies where the increment of measurement height is often a constant, the measurement height in this study is programmed in a non-uniform manner. The measurement height in the lower region (

Fidelity of Wind Mast and Lidar Measurements
Prior to the analysis, it is important to examine the fidelity of the data involved. Given that the reliability of wind Lidar measurements is often validated using the nearby wind mast data [57], Figure 2 demonstrates the comparison of the 10 min mean and standard deviation of wind speed recorded by the paired cup anemometers (i.e., NW and SE), in which the fidelity of wind mast data can be represented by a ratio close to the standard value of 1. It is shown that the consequent ratio in regard to both the mean and standard deviation of the wind speed deviates remarkably from the standard value when the wind approaches from the direction of 135° and 300°, implying that the recorded wind data are likely to be obstructed by the physical mast structure within these direction ranges. Hence, in light of the methodology by Svensson et al. [9], the distorted wind mast data, i.e., those located within the shaded area in Figure 2, are not included in the following comparison analysis. Once the reliable wind mast data are extracted, the fidelity of the wind Lidar measurement can be routinely examined by comparing the synchronized mast and Lidar data at equivalent heights (i.e., 21.3 m), as shown in Figure 3. The comparisons of mean wind speed and wind direction are overall above the satisfactory level, with correlation coefficients above 0.95 and regression slopes above 0.93. The root mean square error (RMSE) for mean wind speed is 0.80 m/s, and that for mean wind direction is 7.59°. However, the standard deviations of wind speed measured by Lidar are found to be attenuated as compared to their counterparts, resulting in a correlation coefficient of 0.73 and a regression slope of 0.76. This is mainly attributed to the fact that the conical scanning feature of Lidar does not effectively resolve the turbulence with a length scale smaller than the probe length, which can result in a 20% reduction of the standard deviation measurement [63]. Similar results are also found by Peña et al. [11] and Shu et al. [18]. Since this study is focused primarily on the wind direction data, the attenuation of the standard deviation of the wind speed in Lidar data is neglected. Once the reliable wind mast data are extracted, the fidelity of the wind Lidar measurement can be routinely examined by comparing the synchronized mast and Lidar data at equivalent heights (i.e., 21.3 m), as shown in Figure 3. The comparisons of mean wind speed and wind direction are overall above the satisfactory level, with correlation coefficients above 0.95 and regression slopes above 0.93. The root mean square error (RMSE) for mean wind speed is 0.80 m/s, and that for mean wind direction is 7.59 • . However, the standard deviations of wind speed measured by Lidar are found to be attenuated as compared to their counterparts, resulting in a correlation coefficient of 0.73 and a regression slope of 0.76. This is mainly attributed to the fact that the conical scanning feature of Lidar does not effectively resolve the turbulence with a length scale smaller than the probe length, which can result in a 20% reduction of the standard deviation measurement [63]. Similar results are also found by Peña et al. [11] and Shu et al. [18]. Since this study is focused primarily on the wind direction data, the attenuation of the standard deviation of the wind speed in Lidar data is neglected.

Definition of Wind Veer Angle and Composite Analysis
In the meteorological community, the wind veer is standardly defined as when the wind turns clockwise as a function of height, while the wind back indicates a counter-clockwise turning of the wind. Fundamentally, wind veer is mostly associated with warm air advection and dynamic lifting, while wind back, in contrast, is related to cold air advection and dynamic sinking. In this study, the wind veer angle is defined as the deficit of wind direction measurements between the lowest observation level and those at higher altitudes. It should be mentioned that, in order to minimize the uncertainties associated with the variability of mesoscale, convective and small turbulent scales, the original 10 min data are further averaged to provide the corresponding 1 h means.
Given the availability of wind data involved in the current study, analyses of wind speed and wind veer profiles are conducted in a composite sense. Composite analysis is a powerful technique to identify the most distinctive characteristics of a meteorological or climatological phenomenon that is difficult to observe in totality. Composite analysis usually involves collecting large numbers of cases of a given meteorological phenomenon, and these cases are composited into a collection. In this case, the composite mean and some other statistical measures (e.g., standard deviation and statistical significance) can be estimated, which would provide a definitive picture of how such a meteorological phenomenon is influenced by the factors used in the composite stratification. Composite analysis has been extensively employed in previous studies, e.g., [64][65][66][67][68][69][70][71][72][73].

Definition of Wind Veer Angle and Composite Analysis
In the meteorological community, the wind veer is standardly defined as when the wind turns clockwise as a function of height, while the wind back indicates a counter-clockwise turning of the wind. Fundamentally, wind veer is mostly associated with warm air advection and dynamic lifting, while wind back, in contrast, is related to cold air advection and dynamic sinking. In this study, the wind veer angle is defined as the deficit of wind direction measurements between the lowest observation level and those at higher altitudes. It should be mentioned that, in order to minimize the uncertainties associated with the variability of mesoscale, convective and small turbulent scales, the original 10 min data are further averaged to provide the corresponding 1 h means.
Given the availability of wind data involved in the current study, analyses of wind speed and wind veer profiles are conducted in a composite sense. Composite analysis is a powerful technique to identify the most distinctive characteristics of a meteorological or climatological phenomenon that is difficult to observe in totality. Composite analysis usually involves collecting large numbers of cases of a given meteorological phenomenon, and these cases are composited into a collection. In this case, the composite mean and some other statistical measures (e.g., standard deviation and statistical significance) can be estimated, which would provide a definitive picture of how such a meteorological phenomenon is influenced by the factors used in the composite stratification. Composite analysis has been extensively employed in previous studies, e.g., [64][65][66][67][68][69][70][71][72][73]. Figure 4 illustrates the wind rose plots based on hourly wind data at different heights, which show a reasonable agreement. The dominant wind direction sectors are E and ENE. In addition, the wind speed is shown to slightly increase with height, reflected by a larger proportion of high wind speed at elevated heights.

Results and Discussion
Atmosphere 2020, 11, x FOR PEER REVIEW 7 of 14 Figure 4 illustrates the wind rose plots based on hourly wind data at different heights, which show a reasonable agreement. The dominant wind direction sectors are E and ENE. In addition, the wind speed is shown to slightly increase with height, reflected by a larger proportion of high wind speed at elevated heights. It has been well recognized that wind Lidar observations at this offshore platform can be heavily affected by the change in inflow direction due to the variation of upstream terrain [24]. Accordingly, the wind speed profiles in this study are divided into two main groups based on the mean boundary layer wind direction (see Figure 5): those from 60° to 240° are representative of a homogeneous opensea terrain, while those from 0° to 50° and 290° to 360° are representative of a hilly terrain. As can be seen, the mean wind speed profiles under an open-sea terrain typically exhibit a monotonic-type increase with height, which coincides well with the general characteristics of atmospheric boundary layer flow. The mean wind speed up to a height of 120 m can be satisfactorily approximated by the logarithmic law model, resulting in a surface roughness length (z0) ranging from 0.951 mm to 0.983 mm. In contrast, the wind speed profiles associated with a hilly terrain appear to be more irregular in shape, which consistently exhibit a local maximum at a height of about 80 m. This can potentially be caused by the presence of pronounced mountains in the corresponding direction, which is likely to disturb the wind flow. The performance of the logarithmic law fit of mean wind speed is not as good as that of the open-sea terrain. Moreover, the consequent surface roughness length lies in the range from 0.992 mm to 1.000 mm, which is slightly larger that of the open-sea terrain. Likewise, the vertical distribution of wind veer angle associated with different upstream terrain conditions is found to be somewhat different, as shown in Figure 6. The wind veer profiles for both open-sea and hilly terrain exhibit a well-defined two-fold vertical structure. For open-sea terrain conditions, the wind veer angle is found to slightly decrease and possess negative values in the lower It has been well recognized that wind Lidar observations at this offshore platform can be heavily affected by the change in inflow direction due to the variation of upstream terrain [24]. Accordingly, the wind speed profiles in this study are divided into two main groups based on the mean boundary layer wind direction (see Figure 5): those from 60 • to 240 • are representative of a homogeneous open-sea terrain, while those from 0 • to 50 • and 290 • to 360 • are representative of a hilly terrain. As can be seen, the mean wind speed profiles under an open-sea terrain typically exhibit a monotonic-type increase with height, which coincides well with the general characteristics of atmospheric boundary layer flow. The mean wind speed up to a height of 120 m can be satisfactorily approximated by the logarithmic law model, resulting in a surface roughness length (z0) ranging from 0.951 mm to 0.983 mm. In contrast, the wind speed profiles associated with a hilly terrain appear to be more irregular in shape, which consistently exhibit a local maximum at a height of about 80 m. This can potentially be caused by the presence of pronounced mountains in the corresponding direction, which is likely to disturb the wind flow. The performance of the logarithmic law fit of mean wind speed is not as good as that of the open-sea terrain. Moreover, the consequent surface roughness length lies in the range from 0.992 mm to 1.000 mm, which is slightly larger that of the open-sea terrain.
Atmosphere 2020, 11, x FOR PEER REVIEW 7 of 14 Figure 4 illustrates the wind rose plots based on hourly wind data at different heights, which show a reasonable agreement. The dominant wind direction sectors are E and ENE. In addition, the wind speed is shown to slightly increase with height, reflected by a larger proportion of high wind speed at elevated heights. It has been well recognized that wind Lidar observations at this offshore platform can be heavily affected by the change in inflow direction due to the variation of upstream terrain [24]. Accordingly, the wind speed profiles in this study are divided into two main groups based on the mean boundary layer wind direction (see Figure 5): those from 60° to 240° are representative of a homogeneous opensea terrain, while those from 0° to 50° and 290° to 360° are representative of a hilly terrain. As can be seen, the mean wind speed profiles under an open-sea terrain typically exhibit a monotonic-type increase with height, which coincides well with the general characteristics of atmospheric boundary layer flow. The mean wind speed up to a height of 120 m can be satisfactorily approximated by the logarithmic law model, resulting in a surface roughness length (z0) ranging from 0.951 mm to 0.983 mm. In contrast, the wind speed profiles associated with a hilly terrain appear to be more irregular in shape, which consistently exhibit a local maximum at a height of about 80 m. This can potentially be caused by the presence of pronounced mountains in the corresponding direction, which is likely to disturb the wind flow. The performance of the logarithmic law fit of mean wind speed is not as good as that of the open-sea terrain. Moreover, the consequent surface roughness length lies in the range from 0.992 mm to 1.000 mm, which is slightly larger that of the open-sea terrain. Likewise, the vertical distribution of wind veer angle associated with different upstream terrain conditions is found to be somewhat different, as shown in Figure 6. The wind veer profiles for both open-sea and hilly terrain exhibit a well-defined two-fold vertical structure. For open-sea terrain conditions, the wind veer angle is found to slightly decrease and possess negative values in the lower Likewise, the vertical distribution of wind veer angle associated with different upstream terrain conditions is found to be somewhat different, as shown in Figure 6. The wind veer profiles for both open-sea and hilly terrain exhibit a well-defined two-fold vertical structure. For open-sea terrain conditions, the wind veer angle is found to slightly decrease and possess negative values in the lower observation region, indicating the possible occurrence of wind back. At heights above 60 m, the value of the wind veer angle tends to increase monotonically with increasing height, reaching a maximum wind veer angle at about 180 m (i.e., the highest observation height in this study). It is clear that both the maximum wind veer angle and wind back angle (i.e., negative wind veer angle) are speed dependent. To illustrate, the maximum negative wind veer angle is found at a mean wind speed of 14-17 m/s, with a value of −0.58 • , and the maximum wind veer angle indicates a reverse relationship with mean wind speed, the value of which decreasing from 2.47 • to 0.59 • as the mean wind speed increases. In contrast, the wind veer profiles associated with the hilly terrain condition remain more or less unchanged up to a height of 45 m. With a further increase in height, the wind veer angle also exhibits a steady increase. The maximum wind veer angle decreases from 7.45 • to 1.92 • as the mean wind speed increases. This is potentially caused by the change in atmospheric stability as mean wind speed changes. Overall, it is found that the wind veer angles for the hilly terrain condition are significantly larger than those for the open-sea terrain. In order to gain a more representative understanding of wind veer characteristics at offshore sites, only the data associated with the open-sea terrain are included in the following analysis, unless otherwise specified.
Atmosphere 2020, 11, x FOR PEER REVIEW 8 of 14 observation region, indicating the possible occurrence of wind back. At heights above 60 m, the value of the wind veer angle tends to increase monotonically with increasing height, reaching a maximum wind veer angle at about 180 m (i.e., the highest observation height in this study). It is clear that both the maximum wind veer angle and wind back angle (i.e., negative wind veer angle) are speed dependent. To illustrate, the maximum negative wind veer angle is found at a mean wind speed of 14-17 m/s, with a value of −0.58°, and the maximum wind veer angle indicates a reverse relationship with mean wind speed, the value of which decreasing from 2.47° to 0.59° as the mean wind speed increases. In contrast, the wind veer profiles associated with the hilly terrain condition remain more or less unchanged up to a height of 45 m. With a further increase in height, the wind veer angle also exhibits a steady increase. The maximum wind veer angle decreases from 7.45° to 1.92° as the mean wind speed increases. This is potentially caused by the change in atmospheric stability as mean wind speed changes. Overall, it is found that the wind veer angles for the hilly terrain condition are significantly larger than those for the open-sea terrain. In order to gain a more representative understanding of wind veer characteristics at offshore sites, only the data associated with the opensea terrain are included in the following analysis, unless otherwise specified. As shown in many previous studies, the wind characteristics in Hong Kong are subject to distinct seasonal variability [22,74,75]. On the other hand, atmospheric stability also plays an essential role in modulating the wind veer characteristics since it governs the vertical distribution of momentum and other thermodynamic components in the atmospheric boundary layer [12,29,31,34,76]. On this account, it is necessary to investigate the seasonal variability of wind veer characteristics with a consideration of the change in atmospheric stability.
Given the lack of temperature measurements, the atmospheric stability is determined based on the simplified method proposed by Basu [77,78], in which the Obukhov length (L) can be calculated using only the wind speed data: (1) R is calculated based on wind speed measured at three different heights (e.g., in this study, = 23.8 m, = 28.8 m, = 33.9 m): where is the stability correction term, ∆ is the wind speed difference measured at heights and and ∆ is the wind speed difference measured at heights and . It should be noted that the relatively lower measurement heights are used mainly because the adopted method for As shown in many previous studies, the wind characteristics in Hong Kong are subject to distinct seasonal variability [22,74,75]. On the other hand, atmospheric stability also plays an essential role in modulating the wind veer characteristics since it governs the vertical distribution of momentum and other thermodynamic components in the atmospheric boundary layer [12,29,31,34,76]. On this account, it is necessary to investigate the seasonal variability of wind veer characteristics with a consideration of the change in atmospheric stability.
Given the lack of temperature measurements, the atmospheric stability is determined based on the simplified method proposed by Basu [77,78], in which the Obukhov length (L) can be calculated using only the wind speed data: (1) R is calculated based on wind speed measured at three different heights (e.g., in this study, z 1 = 23.8 m, z 2 = 28.8 m, z 3 = 33.9 m): Atmosphere 2020, 11, 1178 where ψ M is the stability correction term, ∆U 31 is the wind speed difference measured at heights z 3 and z 1 and ∆U 21 is the wind speed difference measured at heights z 2 and z 1 . It should be noted that the relatively lower measurement heights are used mainly because the adopted method for determining atmospheric stability is deeply rooted in Monin-Obukhov similarity theory (MOST; [79]). Therefore, all the measurement heights used in this relation should be within the surface layer (i.e., constant flux layer), where MOST is valid [77,78]. (2) R N is calculated according to the given heights, assuming z 3 > z 2 > z 1 : (3) The Obukhov length (L) is determined using the empirical ψ M functions [80,81]. If R > R N , Equation (1) is used in conjunction with Equation (3). Conversely, if R < R N , then Equation (3) is replaced with Equation (4).
. Consequently, the classification of atmospheric stability in this study is tabulated in Table 1. As can be seen in Figure 7, the wind veer characteristics behave in response to the change in both seasonality and atmospheric stability. Seasonal variability is apparent with respect to the shape and magnitude of wind veer angle. Specifically, larger wind veer angles are mostly observed during winter (i.e., December, January and February) and spring (i.e., March, April and May) months, with a maximum value of about 5.5 • , whereas the wind veer during autumn (i.e., September, October and November) is much less significant, indicating a wind veer angle smaller than 0.8 • . The larger wind veer angles during spring and winter can be mainly attributed to the more frequent occurrence of a low-level jet during these months [67]. Peña et al. [12] and Brown et al. [29] both stated that the presence of low-level jets is advantageous for yielding more significant wind veer since the wind near the low-level maximum can be much larger than the geostrophic wind. Moreover, the height where the wind veer profile starts to increase is also found to be a function of seasonal variation, in which the value associated with winter and spring months is about 100 m, whereas that for summer (i.e., June, July and August) and autumn is about 80 m. On the other hand, the dependence of wind veer profile on atmospheric stability is also examined, which is most pronounced during spring and winter. Typically, a larger wind veer angle is often linked to neutral stratification conditions, whereas the smallest wind veer angle is associated with unstable stratification conditions. The effect of atmospheric stability on the wind veer profile can also be found during summer and autumn, but not to such a significant extent.

Summary and Conclusions
A proper understanding of marine wind characteristics is important, which provides great implications across a wide range of engineering applications, in particular offshore wind turbine design and wind power output. However, the majority of the existing literature has been focused on offshore wind speed and turbulence characteristics, whereas the knowledge of wind veer is much less understood and discussed. This study investigates the marine wind veer characteristics based on extensive Lidar observations at an offshore platform in Hong Kong. The major conclusions in this study can be summarized as follows:


The occurrence of wind veer in the marine wind field was well observed, which can be affected by the change of upstream terrain conditions. In general, the wind veer profiles tend to exhibit a two-fold structure, in which the wind veer angle in the lower observation altitudes is likely to remain unchanged or slightly decrease, whereas at higher observation altitudes, the wind veer angle usually increases monotonically with height. From a comparative analysis point of view, the wind veer angles for hilly terrain conditions are much larger than those for open-sea terrain.  The maximum wind veer angle tends to exhibit a reverse correlation with mean wind speed, i.e., the larger the mean wind speed, the smaller the veering angle. With an increase in mean wind speed, the value decreases from 2.47° to 0.59° for open-sea terrain, and from 7.45° to 1.92° for hilly terrain.

Summary and Conclusions
A proper understanding of marine wind characteristics is important, which provides great implications across a wide range of engineering applications, in particular offshore wind turbine design and wind power output. However, the majority of the existing literature has been focused on offshore wind speed and turbulence characteristics, whereas the knowledge of wind veer is much less understood and discussed. This study investigates the marine wind veer characteristics based on extensive Lidar observations at an offshore platform in Hong Kong. The major conclusions in this study can be summarized as follows: The occurrence of wind veer in the marine wind field was well observed, which can be affected by the change of upstream terrain conditions. In general, the wind veer profiles tend to exhibit a two-fold structure, in which the wind veer angle in the lower observation altitudes is likely to remain unchanged or slightly decrease, whereas at higher observation altitudes, the wind veer angle usually increases monotonically with height. From a comparative analysis point of view, the wind veer angles for hilly terrain conditions are much larger than those for open-sea terrain.
The maximum wind veer angle tends to exhibit a reverse correlation with mean wind speed, i.e., the larger the mean wind speed, the smaller the veering angle. With an increase in mean wind speed, the value decreases from 2.47 • to 0.59 • for open-sea terrain, and from 7.45 • to 1.92 • for hilly terrain. Seasonal variability of the wind veer profile is apparent, in which winter and spring often possess larger values of wind veer angle, whereas autumn usually possesses the smallest value. On the other hand, the height at which the wind veer profile starts to increase with height is also found to be a function of seasonality. The dependence of wind veer on atmospheric stability was examined, which is most pronounced during spring and winter. Typically, larger wind veer angles can be found under neutral stratification conditions. It, however, should be noted that the results given in the present paper are based on Lidar observations made at an offshore platform in Hong Kong, which could be more or less site specific. The inclusion of more extensive observations to a larger spatial extent is recommended in a view to provide a more general understanding of wind veer characteristics in the marine environment.