Hourly Mean Wind-Speed Profiles

Despite the weak influence of the outer circulation of Typhoon Dujuan in stage I, not only is the wind speed considerably increased, but the surface friction velocity increases from values less than 0.1 to 0.3 m s⁻¹. The increase of the wind shear reduces the thermal effect and, hence, the wind direction is more uniform with height. Figure5displays the measured wind-speed profiles in stage I with respect to the corresponding neutral logarithmic profiles.

With the relatively higher wind speeds of 8 < U_R< 12 m s⁻¹during the day in Fig.5a, the wind-speed profiles are composed of two layers, with the lower layer in good agreement with the logarithmic profile, and the upper layer demonstrating a nearly uniform mixed layer over the height range of 140–160 m. This feature resembles the typhoon boundary layers observed in Amano et al. (1999) using sodar observations, in which a constant wind-speed layer above the so-called gradient height was shown as low as 100 m. However, the atmospheric conditions represented in stage I is a mixed state induced by the interaction of the typhoon’s outer circulation and the local mesoscale convection in the coastal zone. In fact, this physical process generates different types of boundary layers during the evening and night, as shown in Fig.5b. Although the buoy data suggest neutral stratification, it is anticipated that the wind-speed profiles are the result of weak stable stratification over land, but observations of thermal stratification are not available.

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Fig. 5 Wind-speed profiles weakly influenced by Typhoon Dujuan during stage I showing a a uniformly-mixed layer above the surface layer during the day and b weakly stable conditions in the early morning (left two panels) and in the evening (right two panels). The upper left corner of each panel shows the timestamp in Taipei time (UTC + 8)

In stages II and III corresponding to relatively high wind speeds, the vertical variation of the wind direction is insignificant, with the maximum difference of 9° between the heights of 40 and 240 m, implying the validity of the mixing-length model for the observed wind-speed profiles. Figure6displays the hourly mean wind-speed profiles for every 2 h in stages II and III in comparison with the theoretical models. Because the wind speed consistently increases in stage II and decreases in stage III, the reverse-arrangement test introduced by Bendat and Piersol (1982) enables examination of the stationarity, with non-stationarity found at 0600 local time on 28 September, and at 0000, 0600, 1800, and 2000 local time on 29 September.

However, differences in wind-speed profiles between the stationary and non-stationary cases are insignificant. Inside the boundary layer, the wind speed monotonically increases with height, and exceeds the values of the logarithmic profile over a certain altitude depending on the scaling parameter u_∗o/f_c. In stage II, for example, with relatively small values of u_∗o giving u_∗o/fc< 10⁴from 0400 to 1000 local time on 28 September, the Coriolis parameter is important, which modifies the wind-speed profiles above a height of 100 m where the Gryning, Blackadar, and Deaves and Harris models show better agreement with the observations than the logarithmic profile. Apart from the case at 0400 local time on 28 September, the profile demonstrates substantial inconsistency with the theoretical predictions. With the increase of the surface friction velocity corresponding to the values 10⁴< u_∗o/fc < 2.2×10⁴ between 1200 and 1600 local time on 28 September, the top of the logarithmic layer slightly increases to a height of 100–120 m, and the deviations from the logarithmic law are generally reduced in the mixed layer. For values u_∗o/f_c> 2.2×10⁴associated with the largest friction velocities

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Lidar Observations of the Typhoon Boundary Layer Within the…

of 1.9 and 2.1 m s⁻¹at 2000 and 2200 local time on 28 September in stage II, and a friction velocity of 1.3 m s⁻¹at 0000 local time on 29 September in stage III, Prandtl’s mixing-length theory successfully describes the profiles up to a height of 240 m.

Due to the influence of rainfall, wind-speed profiles deviate significantly from the theo-retical predictions in the upper layers at both 0200 and 0400 local time on 29 September in stage III, as shown in Fig.6b; however, ABL development under rainfall is unlikely to be explained theoretically. Nonetheless, as the loading from strong wind shear together with heavy rain particles may cause devastating damage to turbine blades and structures (Chou et al.2013), further study is needed regarding the rainfall effect on the ABL development.

The wind-speed profiles in stage III between 0600 local time on 29 September and 0400 local time on 30 September demonstrate consistent patterns, with agreement with the Blackadar, Gryning, and Deaves and Harris profiles in the mixed layer for values 10⁴< u_∗o/f_c< 2.2× 10⁴ over the height ranges of 100–160 m, representing the thickness of the surface layer caused by variations in friction velocity.

The lidar measurements clearly demonstrate that the formation of the typhoon boundary layer is governed by the scaling ratio u_∗o/fcin the finite mixing-length model as introduced in Peña et al. (2010). With a large value of u_∗o/f_c, the logarithmic layer significantly extends above the conventionally-accepted neutral surface-layer height of 100 m, and reaches a height of 300 m as reported by Tse et al. (2013) under the strong wind shear caused by typhoons.

The physical interpretation is that the mechanical turbulent mixing induced by the extreme wind speed generates the large vertical momentum flux, which maintains the constant shear layer at a considerably higher altitude. In contrast, for a small value of the parameter u_∗o/f_c, the decrease in the momentum flux reduces the depth of the surface layer to, for example, approximately 80 m, as shown in Fig.6a at 0800 local time on 28 September.

The phenomenon of the uniform mixed layer in stage I of Typhoon Soudelor during the day was not frequently observed, as shown in Fig.5a for Typhoon Dujuan, only occurring at 1600 local time on 7 August. In contrast, the development of neutral wind-speed profiles in the mixed layer in stage II is consistent with those of Typhoon Dujuan, showing agreement with the Gryning, Blackadar, and Deaves and Harris profiles for values 10⁴< u_∗o/f_c< 2.2×10⁴, and following the logarithmic profile for values u_∗o/f_c > 2.2×10⁴. Figure7demonstrates that the wind-speed discrepancies between the observed and logarithmic profiles are u_∗o/fc

dependent, with the theoretical curves simulated using the logarithmic, Gryning, Blackadar, and Deaves and Harris profiles. The Gryning profile used z_o 0.2 m, which is approximately the average value of the roughness length in stages II and III. At 100 m in the surface layer shown in Fig.7a, the discrepancies are negligible, except for very small friction velocities, while at 200 m in the mixed layer shown in Fig.7b, the discrepancies are considerable. The increase in the value of u_∗o/fcreduces these discrepancies, implying that the observations are tending to agree with the logarithmic model.

After the typhoon passes southern Taiwan and moves further away (stage IV), the flow is accelerated towards the mesoscale low pressure over the Taiwan Strait, inducing flow from south-west-south, which transports unstable warm and moist air to the island, and occasionally produces torrential rainfall (Chien et al.2008). The heavy rainfall is observed for Typhoon Soudelor, but not for Typhoon Dujuan, as shown in Fig3. In this stage, which occurred from 1000 to 1400 local time on 30 September, jet-like wind-speed profiles were observed (see Fig.8), with the peak wind speeds as low as 180 m at 1100 local time on 30 September, corresponding to the rapid increase in the wind speed (see Fig.3a). For airflow accelerated by the mesoscale-low-induced pressure gradient, a frontal system is initiated, driving the flow near the surface, resulting in the formation of a jet-like boundary layer. The jet then develops with respect to time and downstream distance, and the height of the

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Fig. 6 Typhoon wind-speed profiles in the outer rainbands displayed for every 2 h in comparison with the theoretical profiles in a stage II with the typhoon approach and increase of the mean wind speed, and b stage III with the typhoon departure and decrease of the mean wind speed. The upper left corner in each panel contains the timestamp in Taipei time (UTC + 8)

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Fig. 7 Discrepancies between the measured wind-speed profiles and the logarithmic profile during Typhoons Dujuan and Soudelor depending on the surface parameter u_∗o/fcat heights of a 100 m, and b 200 m, in comparison with the differences calculated from the Blackadar, Gryning, and Deaves and Harris profiles using zo 0.2 m for the Gryning profile

Fig. 8 Wind-speed profiles of the induced south-west-south flow in stage IV showing the wind-speed reduction in the upper layer after the typhoon passed southern Taiwan. The upper left corner of each panel shows the timestamp in Taipei time

speed maximum increases. After 1400 local time on 30 September, as the flow acceleration diminishes, the wind-speed profiles are comparable to those displayed in Fig.5b. While the Blackadar, Gryning, and Deaves and Harris models cannot explain the jet-like profile, they do predict a thinner ABL with a reduced height of the wind-speed maximum for small friction velocities. For example, given u_∗o 0.1 m s⁻¹and z_o 0.1 m, the wind-speed maximum is located at approximately 300 m in height. However, the models fail to describe the profiles shown in Fig.8corresponding to a relatively large surface friction velocity between 0.6 and 0.7 m s⁻¹.