Power Law

The power law is an empirical model with a simple mathematical function describing the mean wind-speed profile as

Lidar Observations of the Typhoon Boundary Layer Within the…

where U(z_r) denotes the reference wind speed at a reference height z_r, andα denotes the power exponent. In neutral stratification, the power exponent depends only on the terrain roughness, which, for example, is 0.14 for flat terrain.

3 Typhoon Descriptions and the Observation Site

Typhoons Dujuan and Soudelor, which occurred in 2015, took analogous tracks when pass-ing the island of Taiwan, as shown in Fig.1a, and, according to reports from the Central Weather Bureau of Taiwan, had comparable storm intensities. Both typhoons developed into super typhoons before making landfall with maximum 10-min mean wind speeds of 51 and 48 m s⁻¹, respectively, and pressures of 925 and 930 hPa near the typhoon centres. The typhoon radii, defined according to the Beaufort Scale 7 wind force, were 220 km and 300 km for Typhoons Dujuan and Soudelor, respectively.

Typhoon Dujuan made landfall at 1700 local time (hereinafter referred to as Taipei time, UTC + 8 h) on 28 September in Nanao Township, Yilan County. Typhoon Soudelor landed at 0500 local time on 8 August in Sioulin Township, Hualien County. The Central Mountain Range, with an average height of 2000 m and 99 mountain peaks over 3000 m in height, is oriented longitudinally and covers two-thirds of the island of Taiwan. When a typhoon encounters the high part of the range, the typhoon–orography interaction splits the typhoon vortex into upper and lower layers, with a demarcation height observed at approximately 3.5 km due to the blockage effect, which reduces the strength of the typhoon (Pan et al.

2010). This mesoscale variability, affecting the three-dimensional structure of the flow at a scale the order of kilometres, is unlikely to influence the boundary-layer formation close to the surface, as illustrated in Sect.5.4. The shortest distances from the observation site to the typhoon centres were approximately 80–100 km, indicating that the typhoon wind speeds were measured primarily in the outer rainbands. Because Typhoon Soudelor caused severe destruction in the Northern Mariana Islands, Taiwan, and eastern China, the name “Soudelor”

was retired in 2017 (ESCAP2017).

Figure1a also shows the locations of the buoys Cimei (buoy C) and Siao-Liuqiu (buoy S) near the experimental site, whose observations are used to evaluate the atmospheric stability and power exponents over the sea, as explained in Sect.4.3. Buoy C was located approxi-mately 80 km to the west at an almost identical latitude as Hsingda Harbour, while buoy S was located approximately 70 km east-south-east of Hsingda Harbour.

A lidar wind profiler was installed in the southern port of Hsingda Harbour (22.8655°N, 120.2076°E) in the south-west region of Taiwan. Figure1b shows the local geography of the observational site, which is approximately 1.5 km to the east of Taiwan Strait, and within a radius of 2 km, the terrain is generally flat and surrounded by parks, farms, and fish farms.

A small town west of the site has low-rise houses and scattered middle-rise apartments of heights lower than 10 m. In the outer area, within a radius of 2–5 km, small villages and towns are distributed, with two dense residential areas to the north and south-west, while Tainan City is located to the north approximately 15 km away. The foothills of the Central Mountain Range are 12 km to the east, with the local highest mountain of height over 2000 m, and located 60 km to the east.

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Fig. 1 Google images (Google Earth V 7.3.0, Image © 2018) of the island of Taiwan with a tracks of the Typhoons Dujuan and Soudelor and the locations of the Cimei and Siao-Liuqiu buoys, and b the observational site in Hsingda Harbour. The yellow circles on the tracks in (a) represent a time interval of 6 h (Taipei time, UTC + 8)

4 Methods of Typhoon Observations 4.1 Doppler Lidar Wind Profiler

The Leosphere Windcube v2 is a pulsed lidar using the Doppler beam-swinging technique (Cariou 2011) composed of four laser beams emitted consecutively in the four cardinal directions at a half-opening angleφ  28° to the zenith, followed by a fifth vertical beam to directly measure the vertical velocity component. Figure2illustrates the Doppler beam-swinging scheme in the orthogonal frame. The standard metrological coordinate system is employed, in which u represents the east–west velocity component, with positive values to the east, v represents the north–south velocity component, with positive values to the north, and w is the vertical velocity component, with positive values upwards. The horizontal velocity components u and v are retrieved from the radial velocities of the beam position by

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Fig. 2 Schematic of the Doppler beam-swinging technique used by the Leosphere Windcube v2 lidar within the orthogonal frame used here

u Vr E− Vr W

2sinφ (7)

and

v  Vr N− Vr S

2sinφ , (8)

where VrN, VrE, VrS, and VrW represent the radial velocities observed from the beams pointing to the north, east, south, and west, respectively. The vertical velocity component is directly measured from the vertical beam,

w  Vr V, (9)

where VrVdenotes the radial velocity in the vertical direction.

The Windcube v2 lidar is designed to measure wind-speed profiles using a maximum of 12 altitudes, for which the observation heights are adjustable between 40 and 290 m.

The measurement in each radial direction takes approximately 0.77 s to accumulate the backscattering data from the moving aerosols, so that one scan cycle takes 3.86 s on average.

With a relatively short scan period, the Doppler beam-swinging technique is advantageous for unsteady-flow measurements (Drew et al.2013). The mean wind speed U and wind direction θ are obtained through U √

¯u²+¯v²andθ  tan⁻¹(¯v/ ¯u), where the overbar denotes the mean value of the horizontal velocity components for a certain time interval.

A previous calibration was made by comparing the measurements of the Windcube lidar with Vaisala WXT520 ultrasonic anemometers installed on a 70-m mast on booms at heights of 50 and 70 m. The test site was located at Changhua Coastal Industry Park (24.1072°N, 120.3928°E) inside a wind farm near the shore. A range of wind speeds up to 21 m s^–1were observed for one week per season for a total of four weeks, and for hourly mean wind speeds

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> 5 m s^–1, the discrepancies observed between the lidar and ultrasonic anemometers were approximately 3% at both 50- and 70-m heights. A more detailed description of the validation can be found in Tsai et al. (2017).