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Hurricane Bonnie wind flow characteristics as determined from WEMITE
Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 767–789
Hurricane Bonnie wind flow characteristics as determined from WEMITE John L. Schroeder*, Douglas A. Smith Wind Science and Engineering Research Center, Department of Geosciences, Texas Tech University, Box 41023, Lubbock, TX 79409-1023, USA Received 16 August 2001; received in revised form 28 August 2002; accepted 17 December 2002
Abstract The Wind Engineering Mobile Instrumented Tower Experiment (WEMITE) successfully gathered high-resolution wind speed data from within Hurricane Bonnie as it made landfall near Wilmington, North Carolina, on 27 August 1998, at 04:00 UTC. This data is used to inspect the variations in turbulent characteristics of the wind during the passage of the storm. Specifically, turbulence intensities, integral scales, gust factors and power spectral densities are evaluated. Results indicate there is general agreement with the Krayer/Marshall gust factor curve, additional low-frequency energy in the longitudinal power spectral density compared to various model spectra, and a wide variation in integral scales even within the same roughness regime. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Hurricanes; Wind speeds; Turbulence intensities; Integral scales; Gust factors; Power spectral densities
1. Introduction It has long been recognized that the database to evaluate turbulent characteristics of the wind within the hurricane planetary boundary layer (HPBL) is limited for several reasons [1]. Even when anemometers survive the storm and the data acquisition system continues to maintain electrical power, the wind speed is rarely sampled at rates which make it useful in determining its turbulent characteristics. *Corresponding author. Tel.: +1-806-742-3476; fax: +1-806-742-3446. E-mail address: [email protected] (J.L. Schroeder). 0167-6105/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0167-6105(02)00475-0
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Recognizing this void, engineers and atmospheric scientists at Texas Tech University (TTU) created a mobile apparatus, the Wind Engineering Mobile Instrumented Tower Experiment (WEMITE), to collect high-resolution wind speed data from within hurricanes. Other institutions, including Clemson University and the University of Florida, have also participated in similar mobile field operations. The WEMITE apparatus was deployed four times during the 1998 Atlantic Hurricane Season including Hurricane Bonnie (26–27 August) in Wilmington, North Carolina. This paper focuses on the initial findings, in terms of the traditionally calculated turbulent parameters, as determined from the data collected from the Hurricane Bonnie deployment.
2. WEMITE apparatus During the 1998 season, the WEMITE tower was 10.7 m (35 ft) tall and measured the horizontal wind speed and direction at 10.7, 6.1 and 3.1 m (35, 20, and 10 ft) above ground level. It also measured vertical wind speed at 10.7 and 3.1 m (35 and 10 ft), and temperature, barometric pressure and relative humidity at the 1 m (3.3 ft) level. All instruments were sampled at 5 Hz. Instrumentation was selected based on a compromise between the durability and sensitivity of the instrument; anemometer details are provided in Table 1. Data was collected on a laptop computer after multiplexing and conversion from analog to digital format. The tower was guyed from the 10.7 m level to provide resistance to the windinduced load and ensure minimal dynamic response, as any dynamic excitation of the tower would be reflected in the collected wind speed data. The trailer was stabilized using four-outrigger arms; each of which are 1.8 m (6 ft) long. Overall, there were eight points of contact from the tower and trailer to the ground, each made with modified trailer anchors. All of the WEMITE systems were powered via a wind generator and a bank of four-deep cycle batteries. The wind generator is rated to approximately 55 m/s, after which the battery bank will carry the systems for a minimum of another 48 h, which is much longer than the typical duration of a hurricane in one location. A schematic of the WEMITE apparatus is provided in Fig. 1. 2.1. WEMITE anemometry limitations The R.M Young Wind Monitor offers a durable instrument capable of surviving sustained wind speeds of 60 m/s and gusts of 100 m/s. According to its specifications, Table 1 Details of the WEMITE wind speed instrumentation employed during the 1998 Atlantic Hurricane Season Instrument
Range (m/s)
Dynamic response (distance constant)
R.M. young wind monitor Gill propeller anemometer (vertical)
0–60 0–35
Propeller 2.7 m, Vane 1.3 m 2.1 m
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Fig. 1. Schematic of WEMITE adapted from Conder et al. [5].
the instrumentation provides for a distance constant (63% recovery) of 2.7 and 1.3 m for the propeller and vane, respectively. The anemometer mechanically filters the amplitudes of short wavelength gusts. Assuming that the anemometer response can be modeled by a first-order linear differential equation with constant coefficients, the response ratio, R (recorded wind speed/actual wind speed), can be expressed as [2] 1 Ri ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi; 1 þ ð2pðl=li ÞÞ2
ð1Þ
where Ri is the response ratio for wavelength li ; l the anemometer distance constant and li the wavelength i: Thus, the amplitude of a gust with wavelength 17 m will be attenuated to a level of approximately 70.8% of its true value by the anemometer. Wavelengths longer than 17 m are attenuated less than the 17 m wavelength while wavelengths shorter than 17 m are attenuated more than the 17 m gust. One complication in employing a propeller–vane anemometer is the dynamic resonance of the vane. The vane used for the Hurricane Bonnie deployment has a damped natural wavelength of 7.4 m, along with a damping ratio of 0.3. The amplitude ratio (measured direction/actual direction) for wavelengths around 7.4 m is approximately 1.8 [2]. Directional changes are associated with the calculation of lateral wind speeds, whose instantaneous values will be over-estimated due to this resonance. Additionally, this inflation of the instantaneous lateral wind speeds tends to provide for an over-estimation of the lateral wind speed spectra and lateral turbulence intensities.
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Fig. 2. Hurricane Bonnie 6-h best-track (data from the Tropical Prediction Center website) position fixes and WEMITE deployment position.
3. Hurricane Bonnie deployment Hurricane Bonnie made landfall near Wilmington, North Carolina, at 04:00 UTC on 27 August 1998 (data from Tropical Predication Center website). The storm developed in the Atlantic about 675 miles east of the Leeward Islands [3]. Bonnie continued west-northwest across the Atlantic reaching its maximum intensity with a central pressure of 954 mb on 24 August. After this point, Hurricane Bonnie slowed in forward motion and the storm began to weaken. Upon making landfall, Bonnie had weakened to a minimal category 3 hurricane with maximum sustained (1-min) wind speeds in a marine exposure estimated to be near 45 m/s [4]. Bonnie continued to slowly meander north along the coastline with the northwest portion of the eye passing over the Wilmington area. The WEMITE tower was deployed at the New Hanover County Airport near Wilmington, NC by a group of TTU graduate and undergraduate students. The deployment location and storm track are shown in Fig. 2. The tower was erected from 4:15 to 5:15 AM EDT with data collection starting at 5:15 AM EDT (9:15 UTC). The approximate location of the WEMITE tower was 34 160 3000 N and 77 540 3000 W. Also located at the airport was the National Weather Service (NWS) ASOS station located at 34 160 0600 N and 77 540 2200 W. The aerial photograph in Fig. 3 depicts the locations of both the WEMITE and ASOS platforms. 4. Analysis 4.1. Wind speed summary statistics and validation The complete wind speed and wind direction records from the 10.7 m anemometer on WEMITE are shown in Figs. 4 and 5, respectively. Luckily, the ASOS station
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Fig. 3. Aerial photograph of the deployment site (Castle Hayne, NC Quadrangle, US Geological Survey, 1980) identifying the locations of the WEMITE and ASOS platforms. The figure has been reproduced from Conder et al. [5].
remained operational during the entire event, providing an opportunity for comparison with the WEMITE collected data. Comparison of the wind speed data collected at both sites, as shown in Fig. 6, is excellent, as the separation between the two locations is less than 1 km. Other comparisons [5] between the data acquired from the WEMITE and ASOS platform indicate similar results. Maximum sustained and gust wind speeds as recorded by the different platforms are shown in Table 2 for comparison. Hurricane Bonnie did not generate 1-min sustained hurricane force winds at the WEMITE location; however, it did provide for gusts (5-s) over hurricane force as recorded by ASOS and WEMITE and a peak
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Fig. 4. WEMITE wind speed record collected from the 10.7 m anemometer during the passage of Hurricane Bonnie.
Fig. 5. WEMITE wind direction record collected from the 10.7 m anemometer during the passage of Hurricane Bonnie.
gust (0.2-s) of almost 38.2 m/s as recorded by the WEMITE tower. Only minimal damage was noted in and around the Wilmington vicinity by TTU personnel following the storm. A histogram (Fig. 7) of the deviations of 2-s wind speeds about the 5-min means indicates the wind speed distribution is approximately Gaussian. Other histograms,
773
30 25
ASOS 20 15 10
WEMITE 5
0
0
0
0
0 50
40
30
20
10
00
00
23
22
00
00 21
00
20
00
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00 17
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0 12
Mean (2-Minute) Wind Speed (m/s)
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Time (UTC) Fig. 6. Comparison of ASOS and WEMITE wind speed data collected during the passage of Hurricane Bonnie.
Table 2 Comparison of wind speeds obtained via WEMITE and ASOS platforms for Hurricane Bonnie
0.2-s gust (m/s) 3-s gust (m/s) 5-s gust (m/s) 1-min sustained (m/s) 2-min sustained (m/s)
ASOS station
WEMITE
NA NA 32.9 NA 25.2
38.2 33.6 33.5 25.0 24.4
such as one categorizing the deviations of 1-min wind speeds about 1-h means (not shown for brevity), indicate similar results. Hurricane Bonnie was certainly moving slowly at the time it made landfall, and except for the sharp changes in wind speeds, associated with the collapsing eyewalls, the wind speed record appears visually to be fairly quasi-stationary (especially over 5-min durations). This may not be the case in other hurricanes, especially those with a more robust mesoscale structure moving at a rapid translational speed. 4.2. Surrounding roughness lengths The WEMITE apparatus was deployed in an open field, but a dense forest was located approximately 300 m to the west and northwest. During the first portion of the storm, the wind approached from an upstream roughness that can be classified as airport exposure with an average roughness length of 0.038 m (based on turbulence). As the wind direction changed with the passage of the eye, a second rougher regime was encountered towards the end of the record. Fig. 6 reflects this change in
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774 1400
1200
Frequency
1000
800
600
400
200
0 -20
-15
-10
-5
0
5
10
15
20
Deviation of 2-Second Wind Speeds from 5-Minute Means (m/s) Fig. 7. Histogram of the deviations of the 2-s wind speeds about 5-min means as recorded by WEMITE during the passage of Hurricane Bonnie. Only data with an airport exposure is used to construct this figure. An equivalent Gaussian distribution is overlaid on the histogram for comparison.
roughness as the ASOS and WEMITE collected wind speeds start to depart after approximately 02:30 UTC. This northwest approach direction allowed for a transitional flow regime to form at the WEMITE deployment site [1,6,7]. Thus, the boundary layer profile and turbulence characteristics were not in equilibrium with either the upstream densely forested roughness or the open grassy roughness immediately surrounding the WEMITE deployment location. Letchford et al. [8] has completed a detailed examination of the surrounding terrain conditions and roughness regimes. Fig. 8 provides a time history of the WEMITE roughness lengths calculated using the wind speed profile and turbulence intensity methods. The profile method assumes a logarithmic wind profile through the three WEMITE anemometer heights and applies a least-squares best-fit technique to the mean wind speeds. The resulting best-fit parameters include the intercept which corresponds to the estimated roughness length. The turbulence method not only assumes a simplified log-law which can be applied to the data, but also that the ratio between the standard deviation of the wind speed record and the friction velocity is equal to 2.5. Under these assumptions, the roughness length can be directly related to the turbulence intensity and instrument height. In the process of using each method, the original wind speed time series was segmented into 5-min sub-segments
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Roughness Length (m)
1 Airport
10.7 m Turbulence Intensity Ratio 0.1 0.01 0.001
Profile
Transitional
30
30
30 6: 07 :
4: 02 :
1: 57 :
23
:5
2: 30
7: 30 :4
21
42 :3 0
7: 30
19 :
:3 17
:3
2: 30
7: 30 15
:2
2: 30 13
:2 11
9: 17 :
30
0.0001
Time (UTC) Fig. 8. Time history of estimated roughness lengths occurring at the WEMITE deployment site during the passage of Hurricane Bonnie. Roughness estimates were produced using wind speed profile and turbulence intensity methods.
(with 50% offset assuming independence) for which roughness estimates were made. The 5-min estimates were then assembled into a time history represented by Fig. 8. For a more comprehensive review of the various methods to estimate roughness lengths, the reader is directed to Barthelmie et al. [9]. 4.3. Turbulence intensities Turbulence intensities are determined by taking the ratio between the standard deviation found in a given wind speed record and normalizing it with the mean wind speed into a dimensionless quantity. Traditionally, wind engineers have determined the longitudinal (along-wind) and lateral (cross-wind) turbulence intensities; vertical turbulence intensity is also calculated, given the record for the vertical wind speed exists. Historically, little work has been completed in even the basic understanding and determination of turbulence intensities as generated within the HPBL, largely due to a lack of data. Some attempts have been made [10–14] with some deviation noted between hurricane and extratropical or monsoon-generated winds. Turbulence intensity is one of the parameters ‘‘matched’’ in the wind tunnel and present in building codes and standards. The intensity of the turbulence in the upstream wind affects the overall static load on a building, and the dynamic excitation present on flexible buildings and components. The turbulence intensity varies in different terrain and stability conditions, increasing for rougher and increasingly unstable conditions. The turbulence intensity will also vary when calculated using different averaging times, as shown in Fig. 9. Fig. 9 was compiled by randomly selecting a portion of the WEMITE data several hours in duration, segmenting the record using various window lengths (1, 5, 10 min, etc.), determining the turbulence intensity for each window, and collecting the summary statistics (maximum, minimum and mean
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Total Turbulence Intensity
0.4 0.35 0.3
Maximum
0.25 0.2
Mean
0.15 0.1
Minimum 0.05 0 0
100
200
300
400
500
600
Averaging Time (seconds) Fig. 9. Time dependency of the turbulence intensity statistic.
value) based on each window length employed. For purposes of this paper, a 5-min averaging time with a 50% offset between data segments (assuming independence) was employed to determine the turbulence intensities. It can be seen in Fig. 9 that the mean turbulence intensity as determined by using the Hurricane Bonnie data becomes fairly stable at approximately 3-min with only a modest increase of 2.7% indicated between 5 and 10-min. Hence, the mean calculated turbulence intensity indicates only minimal dependence on averaging time once above 5-min. Turbulence intensity will also be affected by nonstationarities which exist in the record. However, the nonstationary effects are usually minimal without the presence of an abrupt change in wind speed and direction as found in Schroeder et al. [10]. The classification of the data as stationarity or nonstationary was defined in a weak sense [15] through examination of the first and second moments. Each data segment was examined with the nonparametric run test using a 0.95 significance level. This examination revealed that approximately 33% of the 5-min data segments were nonstationary with respect to the mean longitudinal wind speed, while only 2.2% of the data records were nonstationary with respect to the variance in the longitudinal wind speed records. These results are indicative of a hurricane environment where the wind speed record is expected to ramp up prior to the arrival of the storm center, and decrease following its departure. 4.3.1. Turbulence intensity statistics As shown in Fig. 10, the longitudinal turbulence intensities from the 10.7 m WEMITE anemometer range from 12% to 35% for the airport exposure and increase to 17–41% for the remaining (transitional) portion of the storm. Except for one sharp peak near 22:00 UTC, only subtle changes with time are noted in the record. The lateral turbulence intensities have the same pattern with one sharp peak at approximately 22:00 UTC and variations from 12% to 42% for the airport exposure and 16–35% for the transitional roughness regime. Vertical turbulence intensities range from 7% to 11% for the airport exposure and 7–22% for the
25
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Wind Speed
20
0.35 15
0.3 0.25
10
0.2 5
0.15
30
23
7: :4
21
:5 2: 30 1: 57 :3 0 4: 02 :3 0 6: 07 :3 0
0
2: 30
0
:4
:3 19
:3 7
2:
17
:3 15
:2
2: 13
:2 11
17 9:
7: 30
30
0.1
30
Long. Turbulence Intensity
777
Mean Wind Speed (m/s)
0.45
:3 0
Long. Turbulence Intensity
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Time (UTC) Fig. 10. Time history of longitudinal turbulence intensity as determined from the 10.7 m WEMITE data during the passage of Hurricane Bonnie.
Table 3 Longitudinal turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the longitudinal mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
269 17.6 24.4 12.2 2.0
74 28.0 40.7 17.3 4.8
133 19.4 34.6 13.0 2.8
27 29.9 41.0 17.8 5.3
transitional exposure; however, there is no peak in the time history. Examination of the 5-min time segment containing the peaks in lateral and longitudinal turbulence intensities indicates a sharp and temporary wind direction change as can be seen in Fig. 5. This change induces an intense ‘‘artificial’’ peak in the turbulence intensities due to the nonstationarity of the record. This sharp direction change occurs over a time period of approximately 15-s and only occurs at the 10.7 m (35-feet) level. Its physical meaning is unknown, but interaction of the anemometer with debris (paper, plastic, etc.) may have caused the abrupt change. The authors cannot prove or disprove the temporary change in direction. The determined turbulence intensities are summarized in Tables 3–5 where stationarity is determined with respect to the first moment (mean) of the longitudinal, lateral, and vertical wind speed records. Additionally, Tables 6–8 document the turbulence intensities where stationarity is determined with respect to the variance (second moment) of the longitudinal, lateral, and vertical mean wind speeds. Only a minimal increase in the mean turbulence intensity is noted between the stationary and nonstationary data segments.
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Table 4 Lateral turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the lateral mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
355 16.4 41.8 12.3 3.6
95 26.2 34.7 16.0 3.6
47 16.6 20.1 13.7 1.6
6 25.0 26.7 23.9 1.2
Table 5 Vertical turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the vertical mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 8.5 10.5 6.5 0.7
101 15.4 22.3 6.5 2.6
9 8.1 8.9 7.3 0.6
0 N/A N/A N/A N/A
Table 6 Longitudinal turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the longitudinal wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 18.2 34.6 12.2 2.5
97 28.3 41.0 17.3 5.0
9 18.7 22.2 14.7 2.8
4 32.6 39.9 28.7 5.2
4.3.2. Turbulence intensity ratios Combining these different turbulence intensity components by constructing ratios, one can make a comparison to values which are thought to exist in neutrally stratified surface layers [16]. Given a neutral surface layer (constant flux layer) with homogeneous roughness, the momentum flux becomes independent of height and only depends on the friction velocity. Employing this similarity hypothesis, the following ratios between the turbulence intensities can be derived, where Iu ; Iv ; and Iw represent the longitudinal, lateral and vertical turbulence intensities, respectively;
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Table 7 Lateral turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the lateral wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
381 16.4 41.8 12.3 3.6
93 26.2 34.7 16.0 3.6
21 15.7 17.3 14.3 0.9
8 25.5 27.2 23.9 1.2
Table 8 Vertical turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the vertical wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 8.5 10.5 6.5 0.7
96 15.4 22.3 6.5 2.6
9 8.8 10.1 7.0 1.0
0 N/A N/A N/A N/A
and su ; sv ; and sw represent the standard deviation of the longitudinal, lateral and vertical wind speed records s w Iw ¼ ¼ 0:52; su Iu
ð2Þ
sv Iv ¼ ¼ 0:76: s u Iu
ð3Þ
The turbulence intensity ratios determined from the 10.7 m WEMITE wind speed data are shown in Fig. 11. For the airport exposure, during the first portion of the hurricane record, the mean ratios between the lateral and longitudinal turbulence intensities and the vertical and longitudinal turbulence intensities are 0.92 and 0.47, respectively, representing a deviation of 21% and 11% from the expected values. The cause for these departures is not completely understood; however, some of the observed difference in the lateral turbulence intensity ratio is attributable to resonance effects in the wind direction measurements as discussed previously. 4.4. Gust factors Gust factors are a ratio between a peak wind speed of some duration within a given data segment and the mean wind speed of the same segment. Historically, there
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1.4 1.2
Lat/Lon Turbulence Intensity Ratio
1 0.8 0.6 0.4 0.2
Vert/Lon Turbulence Intensity Ratio
9: 17 :3 0 11 :2 2: 30 13 :2 7: 30 15 :3 2: 30 17 :3 7: 30 19 :4 2: 30 21 :4 7: 30 23 :5 2: 30 1: 57 :3 0 4: 02 :3 0 6: 07 :3 0
Turbulence Intensity Ratio
780
Time (UTC) Fig. 11. Turbulence intensity ratios as determined from 10.7 m WEMITE wind speed data collected during Hurricane Bonnie. Solid lines are drawn at the expected values of 0.92 and 0.47.
has been some disagreement as to the applicability of the Durst curve [17] to hurricanes, as other studies [18] have indicated ‘‘gustier’’ winds within hurricanes. From the 10.7 m Hurricane Bonnie wind speed data collected with WEMITE, 2-s/ 10-min gust factors were calculated using 10-min data segments (and a 50% offset assuming independence). An average gust factor of 1.55 was determined for the airport exposure from 201 individual values with a maximum value of 2.16. These values fall more in line with the 1.55 mean value determined by Krayer and Marshall [18]. Their results were determined using wind speed strip chart records collected from four different hurricanes; each record was collected from a location with a surface roughness length representing an airport exposure (Z0 ¼ 0:03 m). Beyond the airport exposure, the second, rougher (transitional) regime at the end of the WEMITE data record had gust factors as high as 2.46 with an average value of approximately 1.85. These values cannot be directly compared to Krayer and Marshall’s results due to the accompanying change in surface roughness length. Another comparison can be made if we generate a curve of gust factors based on a mean hourly wind speed and peak gusts of variable duration. This curve, shown in Fig. 12, was constructed by employing a 20-min offset between the 1-h data segments (assuming independence) and using only data from the first portion of the record (airport exposure). Comparison to the Krayer/Marshall curve indicates a similar result with only a minimal amount of deviation at small gust durations. Considering the sensitivity of the determined gust factors statistics to the surrounding terrain conditions, and given the ‘‘lumped’’ classifications employed for airport and transitional exposure based on roughness lengths, further examination was completed. Constructing a plot (Fig. 13) of the 2-s/10-min gust factors versus roughness lengths (as determined using the turbulence intensity estimating method) for the data classified as airport exposure reveals a linear relationship. Employing the slope and intercept, as determined from a least-squares
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2 1.9 1.8
Gust Factor
1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 1
10
100
1000
Duration of Gust (seconds) Fig. 12. Gust factor curve based on mean hourly wind speeds determined by using Hurricane Bonnie data with airport exposure (connected with open data points) compared to Krayer/Marshall (unconnected with closed data points).
Gust Factor (2-sec/10-min)
2.4 2.2 2 1.8 1.6 1.4
y = 2.4597x + 1.4244 2
R = 0.3862
1.2 1 0
0.05
0.1
0.15
0.2
Roughness Length (m) Fig. 13. Scatter plot of 2-s to 10-min gust factors determined from the 10.7 m Hurricane Bonnie wind speed data (airport exposure only) along with a best-fit linear regression line overlaid.
best-fit, with a roughness length of 0.03 m yields an expected gust factor of 1.50 which is still closer to the mean value determined by Krayer and Marshall. 4.5. Integral scales The longitudinal integral scale simply represents the average along-wind dimension of the wind gusts in a given data segment. Thus, integral scales (longitudinal, lateral, and vertical) are related to the total static load on a structure. As the integral scale increases, the gust size increases, along with its total influence on a structure. Therefore, integral scales are inherent in building standards and are ‘‘matched’’ by wind tunnel operators in order to properly model the wind and collect
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realistic building pressure data. Only a limited amount of analysis [10,14] has been completed on the integral scales present within the HPBL due to a lack of highresolution wind speed data. Longitudinal integral scales can be calculated using several methods which stem from the determination of the power spectrum and autocorrelation function (ACF). The results presented in this paper are determined using Eqs. (4)–(6). First, the ACF (ruu ) was calculated for 5-min data (using a 50% offset assuming independence) segments of instantaneous (5 Hz) longitudinal wind speed (u) from the 10.7 m WEMITE data using Eq. (4). The ACF curve was then fitted with an exponential curve (ruuf ) up to the lag duration (t) where the derivative of the ACF curve is zero (i.e. the slope is zero). Once the exponential curve was fit, it was integrated from 0 to infinity to obtain the time integral scale (Tuu ) using Eq. (5). The time integral scale is then multiplied by the mean longitudinal wind speed (U) over the same 5-min data segment to obtain the longitudinal integral scale (Luu ) using Eq. (6). As with the determination of turbulence intensities, the time period used to calculate the ACF curve will affect the calculation of the integral scales. Fig. 14 graphically identifies this effect as the ACF curve shifts rightward (indicating higher correlations) at a given lag with increasing window length. Larger window lengths (averaging times) will also reduce the value of mean wind speed determined from the record, but this reduction does not fully compensate for the increased area under the ACF curve. Therefore, the determined value of the integral scale tends to increase with increasing window length. This increase is at least partially the result of trends in the mean wind speed which become more evident with larger window lengths. Therefore, if one evaluates the integral scale values from a wind speed record without some segregation of stationary/nonstationary data segments (defined as those without/ with resolvable trends), the broad results may be biased towards slightly larger values due to these effects ruu ¼
E½fuðtÞ Ug fuðt þ tÞ Ug ; s2u
ð4Þ
Autocorrelation Coefficient
1.2 1 0.8
2-minute data segment
0.6
5-minute data segment
0.4
15-minute data segment
0.2 0 0
100
200
300
Lags Fig. 14. Mean ACFs determined from Hurricane Bonnie using various data segment lengths.
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Tuu ¼
Z
783
N
ruuf ðtÞ dt;
ð5Þ
0
Luu ¼ UTuu :
ð6Þ
The results from Hurricane Bonnie, shown in Table 9, indicate a mean longitudinal integral scale of 100 m for stationary data segments within the airport exposure with a maximum of 255 m noted. Results from the nonstationary data segments indicate an increase in mean longitudinal integral scale to 145 m with a maximum value of 376 m found. This increase represents an increase of 46% in the average longitudinal gust size for the nonstationary data (based on the first moment only) relative to the stationary data. Examination of the longitudinal integral scales determined from data within the transitional flow regime indicate an average longitudinal gust size of 68 and 90 m for stationary and nonstationary data segments, respectively. This decrease in integral scale is expected given the increase in surface roughness values corresponding to the transitional regime relative to the airport exposure. Upon further examination of the longitudinal integral scale time history (Fig. 15), two different integral scale regimes can be observed which are not associated with changes in surface roughness. The first regime, evident from 11:15 to 13:15 UTC (among other times), exhibits a lower-average integral scale and few, if any, peak values above 150 m. The second regime, event from 13:15 to 15:15 UTC (among other times), maintains a larger mean integral scale and numerous peaks between 200 and 250 m. These two regimes seem to alternate intermittently and are especially evident from the start of the record through approximately 20:00 UTC. Although the cause of these two regimes is unknown, convective downdrafts occurring at various locations within the storm may lead to larger scaled turbulence being active in certain regions of the storm relative to others. 4.6. Power spectral density (PSD) estimates A PSD estimate of the longitudinal wind speed record was made for a 2-h data segment near the peak of the storm. For this 2-h time period from 17:50 to
Table 9 Longitudinal integral scales determined from WEMITE data during the passage of Hurricane Bonnie Stationary
No. 5-min segments Mean (m) Maximum (m) Minimum (m) Standard deviation (m)
Nonstationary
Airport
Transitional
Airport
Transitional
269 99.9 254.6 37.6 37.3
74 68.4 179.5 31.3 24.5
133 144.9 376.3 36.9 64.4
27 90.2 175.8 32.4 34.4
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Wind Speed
350 20
300 250
15
200 10
150 100
5
50
Long. Integral Scale 0
0
0
:3 07 6:
02
:3
0 4:
57 1:
2: :5 23
:3
30
30 7:
30 2:
:4 21
:4
7:
30 19
:3
2:
30 17
:3
7: :2
15
30 2: :2
13
:3 11
17 9:
30
0
Mean Wind Speed (m/s)
400
0
Longitudinal Integral Scale (m)
784
Time (UTC) Fig. 15. Time history of longitudinal integral scales as recorded from the 10.7 m WEMITE data collected during the passage of Hurricane Bonnie.
Fig. 16. Wind speed time history obtained from the 10.7 m WEMITE anemometer from 17:50 to 19:50 UTC. The vertical axis represents the instantaneous wind speed minus the mean wind speed.
19:50 UTC, the wind speed averaged approximately 21.3 m/s, and remained relatively consistent as shown in Fig. 16. The longitudinal PSD estimate is shown in Fig. 17. Reduced frequency is employed as the horizontal axis and normalized power (power spectrum divided by the variance) multiplied by the frequency is used for the vertical axis. The Nyquist frequency is 2.5 Hz, given the sampling rate of 5 Hz. The original 2-h segment of wind speed data was segmented into 10-min data sub-segments (with a 50% offset assuming independence). Each of these
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785
Normalized PSD * Freqeuncy (n*S uu/Var(u))
0.45
Hurricane Bonnie FSU Terrain Perturbed Terrain Kaimal
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0.0001
0.001
0.01
0.1
1
10
Reduced Frequency (n*z/U) Fig. 17. Longitudinal wind speed PSD estimate from the 10.7 m WEMITE data (17:50–19:50 UTC) compared to several model spectra.
Table 10 Model spectral shape factors (adapted from Geurts [22])
Suu
FSU Terrain: C ¼ 1; a ¼ 5=3; b ¼ 5=3; g ¼ 1
Perturbed Terrain: C ¼ 1; a ¼ 1; b ¼ 5=3; g ¼ 1
Kaimal: C ¼ 1; a ¼ 1; b ¼ 5=3; g ¼ 1
A
B
A
B
A
B
20.53
475.1
40.42
60.62
21.66
33
sub-segments was then used to calculate individual nonparametric PSDs. The final presented PSD (Fig. 17) was the average of these 23 individual PSDs. Comparisons, as provided in Fig. 17, between the acquired data and several spectra models such as the perturbed terrain or flat-smooth-uniform models [19] or neutral Kansas model [20,21], indicate the longitudinal wind speed data lacks highfrequency energy and contains more low-frequency energy than expected. The model spectra used for comparison are detailed by Eq. (6) and Table 10, where n is the frequency, f the reduced frequency, Suu the longitudinal spectral density function, and the coefficients A; B; C; a; b; and g determine the shape and position of the model spectra. In general, the peak frequencies are in reasonable agreement, and the lack of high-frequency energy is at least in part due to the minimal response characteristics of the Wind Monitor anemometer used for the WEMITE application. Given the anemometer specifications previously discussed, one would expect an under-estimation (based on a response ratio of 0.99) of the longitudinal spectra at reduced frequencies at and beyond approximately 0.09. The additional lowfrequency energy in the estimate is most likely from the ‘‘storm’’ environment and is in agreement with previous research completed by Powell et al. [1] which indicates more low-frequency energy in the spectrum. An additional source of low-frequency
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energy would result from trends and other nonstationarities in the record, and in many extreme wind records this source is not trivial. However, the record in question was strategically chosen because it is very well behaved. For instance, removing subtle trends across the first and second half of the record only reduces the total variance by 0.43% nSuu Af g ¼ : 2 su ðC þ Bf a Þb
ð7Þ
4.7. Spectragram A spectragram is a more useful tool for trying to evaluate changes in energy content throughout the storm, as temporal changes in time are not lost through averaging over the entire event or even a segment of several hours in length. So if one is searching for an event which occurs over a period of minutes, then the spectragram offers a more valuable tool to highlight such changes. Spectragrams of the wind record collected by the 10.7 m anemometer of WEMITE during Hurricane Bonnie are shown in Figs. 18a and b. In these figures, the vertical axis is the logarithm (base 10) of the frequency, the horizontal axis is time, and the brighter colors indicate higher amounts of normalized power (power divided by variance) multiplied by frequency. These figures were calculated by separating the record into 10-min data segments that were subsequently divided into 2.5-min subsegments. Each sub-segment of data was used to calculate a local PSD using both autoregressive AR(50) and nonparametric methods. Once the PSDs from each local 2.5-min sub-segment were determined, they were averaged together within each 10-min block. The resulting 10-min averaged PSDs were then assembled into a time history of PSDs (spectragram) for display. From these figures it can be seen that the nonparametric method yields a much noisier solution, but one can resolve that the peak frequency and peak amplitudes change with time. Changes in peak frequency can result from increasing wind speed or actual changes in the process. Using a normalized peak frequency can neutralize the effects of increasing winds speeds, and given the most active scale of the process remains constant with time, the normalized peak frequency would not change. The variability in normalized peak frequency (period) for the Hurricane Bonnie data with airport exposure ranges from 0.06 (period, T; of 17 s) to less than 0.01 Hz (T ¼ 100 s) representing a 600% variation from one location in the storm to another. One can also note the change in normalized peak frequency associated with the change in exposure found at the end of the record. Higher-frequency energy (smaller scales) becomes more active with the rougher transitional exposure. Energy at the low-frequency end of the PSDs was found to be higher than expected during certain time frames. Time periods with excesses of low-frequency energy correlate to larger integral scales due to the relationship between the ACF and the PSD. In general, the variability of energy is large, and the storm cannot be well represented by using one averaged PSD for the entire event. The peak of the
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Fig. 18. (a) Nonparametric spectragram of Hurricane Bonnie as recorded by the 10.7 m WEMITE anemometer. (b) Autoregressive spectragram of Hurricane Bonnie as recorded by the 10.7 m WEMITE anemometer.
energy content is usually related to time scales on the order 100 s, but concentrations in energy exist periodically at 15–30 s time scales.
5. Conclusions and results This paper provides the results of the evaluation of turbulence intensities, gust factors, longitudinal integral scales and power spectral densities recorded in
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Hurricane Bonnie (1998) by the Wind Engineering Mobile Instrumented Tower Experiment. The results indicate: 1. There are mainly subtle changes in the turbulence intensity values throughout the passage of Hurricane Bonnie. One sharp peak in the lateral and longitudinal turbulence intensities does exist near the peak of the storm. These extreme values are associated with a temporary change in wind speed and direction (a highly nonstationary data segment); 2. There is general agreement between the gust factor statistics derived with the Hurricane Bonnie WEMITE data and results provided by Krayer and Marshall [18]; 3. Longitudinal integral scales are shown to increase by an average of 46% for stationary versus nonstationary data segments. This increase is at least in part due to the incorporation of trends in the wind speed record (as expected in a hurricane) contaminating the determination of the ACF. Integral scales vary widely throughout the storm. The time history suggests that there are two separate regimes of longitudinal integral scales that are not correlated with changes in exposure (roughness). One of these regimes produced integral scales that are substantially larger than the other. The reason for these two regimes is not currently understood, but the presence of convective scale influences is a possible reason; 4. The longitudinal PSD indicates there is more low-frequency energy in the wind record than expected by various model spectra; and 5. The spectragram indicates there are large variations in the energy content of the record throughout the passage of the storm. Normalized peak frequencies vary by as much as 600%.
Acknowledgements The authors would like to acknowledge the support of INEEL for the construction and deployment of the WEMITE tower during the 1998 Atlantic Hurricane Season, as well as NIST (Department of Commerce NIST/TTU Cooperative Agreement Award 70NANB8H0059) and the Insurance Friends of NHC for supporting the analysis efforts. The authors also acknowledge the time spent by two anonymous reviewers whose comments added great value to this paper.
References [1] M.D. Powell, S.H. Houston, T.A. Reinhold, Hurricane Andrew’s landfall in south Florida Part I: standardizing measurements for documentation of surface wind fields, Weather and Forecast 11 (1996) 304–328. [2] F.V. Brock, S.J. Richardson, Meteorological Measurement Systems, Oxford University Press, New York, 2001.
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[3] L.A. Avila, Highlights of the 1998 Atlantic hurricane season: year of landfalls, in: Proceedings of the 23rd Conference on Hurricanes and Tropical Meteorology, Dallas, TX, 1999, pp. 1282–1285. [4] M.D. Powell, Hurricanes at landfall, in: Proceedings of the 23rd Conference on Hurricanes and Tropical Meteorology, Dallas, TX, 1999, pp. 107–108. [5] M.R. Conder, R.E. Peterson, J.L. Schroeder, D.A. Smith, Comparison of hurricane wind data during Hurricane Bonnie: The Texas Tech Wind Engineering Mobile Instrumented Tower Experiment (WEMITE) and the NWS Wilmington ASOS, in: Proceedings of the 13rd Symposium on Boundary Layers and Turbulence, Dallas. TX, 1999, pp. 484–487. [6] S.P. Arya, Introduction to Micrometeorology, Academic Press, San Diego, 1988. [7] E. Simiu, R.H. Scanlan, Wind Effects on Structures: An Introduction to Wind Engineering, Wiley, New York, 1986. [8] C. Letchford, A. Gardner, J.R. Howard, J.L. Schroeder, A comparison of wind prediction models for transitional flow regimes using full-scale hurricane data, J. Wind Eng. Ind. Aerodyn. 10 (2001) 925–945. [9] R.J. Barthelmie, J.P. Palutikof, T.D. Davies, Estimation of sector roughness lengths and the effect on prediction of the vertical wind speed profile, Boundary-Layer Meteorol. 66 (1993) 19–47. [10] J.L. Schroeder, D.A. Smith, R.E. Peterson, Variation of turbulence intensities and integral scales during the passage of a hurricane, J. Wind Eng. Ind. Aerodyn. 77/78 (1998) 65–72. [11] C.C. Wu, A.N.L. Chiu, Comparison of some ambient and typhoon instantaneous wind speed characteristics, J. Wind Eng. Ind. Aerodyn. 13 (1983) 43–53. [12] H. Ishizaki, Wind profiles, turbulence intensities, and gust factors for design in typhoon-prone regions, J. Wind Eng. Ind. Aerodyn. 13 (1983) 55–66. [13] E.C. Choi, Characteristics of typhoons over the South China Sea, J. Ind. Aerodyn. 3 (1978) 353–365. [14] C.C. Chuen, Correlation and spectral functions of atmospheric turbulence, in: Proceedings of the Third International Conference Wind Effects on Buildings and Structures, Tokyo, Japan, 1971, pp. 45–55. [15] J.S. Bendat, A.G. Piersol, Random Data Analysis and Measurement Procedures, Wiley, New York, 1986. [16] J.E. Cermak, A.G. Davenport, E.J. Plate, D.X. Vieges, Wind climate in the city, in: Proceedings of the NATO Advanced Study Institute on Wind Climate in Cities, Waldbronn, Germany, 1983. [17] C.S. Durst, Wind speeds over short periods of time, Meteorol. Mag. 89 (1960) 181–186. [18] W.R. Krayer, R.D. Marshall, Gust factors applied to hurricane winds, Bull. Am. Meteorol. Soc. 73 (1992) 613–617. [19] H. Tieleman, Universality of velocity spectra, J. Wind Eng. Ind. Aerodyn. 56 (1995) 55–69. [20] J.C. Kaimal, J.C. Wyngaard, Y. Izumi, O.R. Cote, Spectral characteristics of surface layer turbulence, J. R. Meteorol. Soc. 98 (1972) 563–589. [21] J.C. Kaimal, J.J. Finnigan, Atmospheric Boundary Layer Flows, Their Structure and Measurement, Oxford University Press, New York, 1995. [22] C.P.W. Geurts, Wind-induced pressure fluctuations on building facades, Technische Universiteit Eindhoven, Faculteit Boouwkunde, Vakgroep Constructief Ontwerpen, 1997.
Hurricane Bonnie wind flow characteristics as determined from WEMITE John L. Schroeder*, Douglas A. Smith Wind Science and Engineering Research Center, Department of Geosciences, Texas Tech University, Box 41023, Lubbock, TX 79409-1023, USA Received 16 August 2001; received in revised form 28 August 2002; accepted 17 December 2002
Abstract The Wind Engineering Mobile Instrumented Tower Experiment (WEMITE) successfully gathered high-resolution wind speed data from within Hurricane Bonnie as it made landfall near Wilmington, North Carolina, on 27 August 1998, at 04:00 UTC. This data is used to inspect the variations in turbulent characteristics of the wind during the passage of the storm. Specifically, turbulence intensities, integral scales, gust factors and power spectral densities are evaluated. Results indicate there is general agreement with the Krayer/Marshall gust factor curve, additional low-frequency energy in the longitudinal power spectral density compared to various model spectra, and a wide variation in integral scales even within the same roughness regime. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Hurricanes; Wind speeds; Turbulence intensities; Integral scales; Gust factors; Power spectral densities
1. Introduction It has long been recognized that the database to evaluate turbulent characteristics of the wind within the hurricane planetary boundary layer (HPBL) is limited for several reasons [1]. Even when anemometers survive the storm and the data acquisition system continues to maintain electrical power, the wind speed is rarely sampled at rates which make it useful in determining its turbulent characteristics. *Corresponding author. Tel.: +1-806-742-3476; fax: +1-806-742-3446. E-mail address: [email protected] (J.L. Schroeder). 0167-6105/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0167-6105(02)00475-0
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Recognizing this void, engineers and atmospheric scientists at Texas Tech University (TTU) created a mobile apparatus, the Wind Engineering Mobile Instrumented Tower Experiment (WEMITE), to collect high-resolution wind speed data from within hurricanes. Other institutions, including Clemson University and the University of Florida, have also participated in similar mobile field operations. The WEMITE apparatus was deployed four times during the 1998 Atlantic Hurricane Season including Hurricane Bonnie (26–27 August) in Wilmington, North Carolina. This paper focuses on the initial findings, in terms of the traditionally calculated turbulent parameters, as determined from the data collected from the Hurricane Bonnie deployment.
2. WEMITE apparatus During the 1998 season, the WEMITE tower was 10.7 m (35 ft) tall and measured the horizontal wind speed and direction at 10.7, 6.1 and 3.1 m (35, 20, and 10 ft) above ground level. It also measured vertical wind speed at 10.7 and 3.1 m (35 and 10 ft), and temperature, barometric pressure and relative humidity at the 1 m (3.3 ft) level. All instruments were sampled at 5 Hz. Instrumentation was selected based on a compromise between the durability and sensitivity of the instrument; anemometer details are provided in Table 1. Data was collected on a laptop computer after multiplexing and conversion from analog to digital format. The tower was guyed from the 10.7 m level to provide resistance to the windinduced load and ensure minimal dynamic response, as any dynamic excitation of the tower would be reflected in the collected wind speed data. The trailer was stabilized using four-outrigger arms; each of which are 1.8 m (6 ft) long. Overall, there were eight points of contact from the tower and trailer to the ground, each made with modified trailer anchors. All of the WEMITE systems were powered via a wind generator and a bank of four-deep cycle batteries. The wind generator is rated to approximately 55 m/s, after which the battery bank will carry the systems for a minimum of another 48 h, which is much longer than the typical duration of a hurricane in one location. A schematic of the WEMITE apparatus is provided in Fig. 1. 2.1. WEMITE anemometry limitations The R.M Young Wind Monitor offers a durable instrument capable of surviving sustained wind speeds of 60 m/s and gusts of 100 m/s. According to its specifications, Table 1 Details of the WEMITE wind speed instrumentation employed during the 1998 Atlantic Hurricane Season Instrument
Range (m/s)
Dynamic response (distance constant)
R.M. young wind monitor Gill propeller anemometer (vertical)
0–60 0–35
Propeller 2.7 m, Vane 1.3 m 2.1 m
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Fig. 1. Schematic of WEMITE adapted from Conder et al. [5].
the instrumentation provides for a distance constant (63% recovery) of 2.7 and 1.3 m for the propeller and vane, respectively. The anemometer mechanically filters the amplitudes of short wavelength gusts. Assuming that the anemometer response can be modeled by a first-order linear differential equation with constant coefficients, the response ratio, R (recorded wind speed/actual wind speed), can be expressed as [2] 1 Ri ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi; 1 þ ð2pðl=li ÞÞ2
ð1Þ
where Ri is the response ratio for wavelength li ; l the anemometer distance constant and li the wavelength i: Thus, the amplitude of a gust with wavelength 17 m will be attenuated to a level of approximately 70.8% of its true value by the anemometer. Wavelengths longer than 17 m are attenuated less than the 17 m wavelength while wavelengths shorter than 17 m are attenuated more than the 17 m gust. One complication in employing a propeller–vane anemometer is the dynamic resonance of the vane. The vane used for the Hurricane Bonnie deployment has a damped natural wavelength of 7.4 m, along with a damping ratio of 0.3. The amplitude ratio (measured direction/actual direction) for wavelengths around 7.4 m is approximately 1.8 [2]. Directional changes are associated with the calculation of lateral wind speeds, whose instantaneous values will be over-estimated due to this resonance. Additionally, this inflation of the instantaneous lateral wind speeds tends to provide for an over-estimation of the lateral wind speed spectra and lateral turbulence intensities.
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Fig. 2. Hurricane Bonnie 6-h best-track (data from the Tropical Prediction Center website) position fixes and WEMITE deployment position.
3. Hurricane Bonnie deployment Hurricane Bonnie made landfall near Wilmington, North Carolina, at 04:00 UTC on 27 August 1998 (data from Tropical Predication Center website). The storm developed in the Atlantic about 675 miles east of the Leeward Islands [3]. Bonnie continued west-northwest across the Atlantic reaching its maximum intensity with a central pressure of 954 mb on 24 August. After this point, Hurricane Bonnie slowed in forward motion and the storm began to weaken. Upon making landfall, Bonnie had weakened to a minimal category 3 hurricane with maximum sustained (1-min) wind speeds in a marine exposure estimated to be near 45 m/s [4]. Bonnie continued to slowly meander north along the coastline with the northwest portion of the eye passing over the Wilmington area. The WEMITE tower was deployed at the New Hanover County Airport near Wilmington, NC by a group of TTU graduate and undergraduate students. The deployment location and storm track are shown in Fig. 2. The tower was erected from 4:15 to 5:15 AM EDT with data collection starting at 5:15 AM EDT (9:15 UTC). The approximate location of the WEMITE tower was 34 160 3000 N and 77 540 3000 W. Also located at the airport was the National Weather Service (NWS) ASOS station located at 34 160 0600 N and 77 540 2200 W. The aerial photograph in Fig. 3 depicts the locations of both the WEMITE and ASOS platforms. 4. Analysis 4.1. Wind speed summary statistics and validation The complete wind speed and wind direction records from the 10.7 m anemometer on WEMITE are shown in Figs. 4 and 5, respectively. Luckily, the ASOS station
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Fig. 3. Aerial photograph of the deployment site (Castle Hayne, NC Quadrangle, US Geological Survey, 1980) identifying the locations of the WEMITE and ASOS platforms. The figure has been reproduced from Conder et al. [5].
remained operational during the entire event, providing an opportunity for comparison with the WEMITE collected data. Comparison of the wind speed data collected at both sites, as shown in Fig. 6, is excellent, as the separation between the two locations is less than 1 km. Other comparisons [5] between the data acquired from the WEMITE and ASOS platform indicate similar results. Maximum sustained and gust wind speeds as recorded by the different platforms are shown in Table 2 for comparison. Hurricane Bonnie did not generate 1-min sustained hurricane force winds at the WEMITE location; however, it did provide for gusts (5-s) over hurricane force as recorded by ASOS and WEMITE and a peak
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Fig. 4. WEMITE wind speed record collected from the 10.7 m anemometer during the passage of Hurricane Bonnie.
Fig. 5. WEMITE wind direction record collected from the 10.7 m anemometer during the passage of Hurricane Bonnie.
gust (0.2-s) of almost 38.2 m/s as recorded by the WEMITE tower. Only minimal damage was noted in and around the Wilmington vicinity by TTU personnel following the storm. A histogram (Fig. 7) of the deviations of 2-s wind speeds about the 5-min means indicates the wind speed distribution is approximately Gaussian. Other histograms,
773
30 25
ASOS 20 15 10
WEMITE 5
0
0
0
0
0 50
40
30
20
10
00
00
23
22
00
00 21
00
20
00
19
18
00
00
00
00 17
16
15
00
14
13
00
0
0 12
Mean (2-Minute) Wind Speed (m/s)
J.L. Schroeder, D.A. Smith / J. Wind Eng. Ind. Aerodyn. 91 (2003) 767–789
Time (UTC) Fig. 6. Comparison of ASOS and WEMITE wind speed data collected during the passage of Hurricane Bonnie.
Table 2 Comparison of wind speeds obtained via WEMITE and ASOS platforms for Hurricane Bonnie
0.2-s gust (m/s) 3-s gust (m/s) 5-s gust (m/s) 1-min sustained (m/s) 2-min sustained (m/s)
ASOS station
WEMITE
NA NA 32.9 NA 25.2
38.2 33.6 33.5 25.0 24.4
such as one categorizing the deviations of 1-min wind speeds about 1-h means (not shown for brevity), indicate similar results. Hurricane Bonnie was certainly moving slowly at the time it made landfall, and except for the sharp changes in wind speeds, associated with the collapsing eyewalls, the wind speed record appears visually to be fairly quasi-stationary (especially over 5-min durations). This may not be the case in other hurricanes, especially those with a more robust mesoscale structure moving at a rapid translational speed. 4.2. Surrounding roughness lengths The WEMITE apparatus was deployed in an open field, but a dense forest was located approximately 300 m to the west and northwest. During the first portion of the storm, the wind approached from an upstream roughness that can be classified as airport exposure with an average roughness length of 0.038 m (based on turbulence). As the wind direction changed with the passage of the eye, a second rougher regime was encountered towards the end of the record. Fig. 6 reflects this change in
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774 1400
1200
Frequency
1000
800
600
400
200
0 -20
-15
-10
-5
0
5
10
15
20
Deviation of 2-Second Wind Speeds from 5-Minute Means (m/s) Fig. 7. Histogram of the deviations of the 2-s wind speeds about 5-min means as recorded by WEMITE during the passage of Hurricane Bonnie. Only data with an airport exposure is used to construct this figure. An equivalent Gaussian distribution is overlaid on the histogram for comparison.
roughness as the ASOS and WEMITE collected wind speeds start to depart after approximately 02:30 UTC. This northwest approach direction allowed for a transitional flow regime to form at the WEMITE deployment site [1,6,7]. Thus, the boundary layer profile and turbulence characteristics were not in equilibrium with either the upstream densely forested roughness or the open grassy roughness immediately surrounding the WEMITE deployment location. Letchford et al. [8] has completed a detailed examination of the surrounding terrain conditions and roughness regimes. Fig. 8 provides a time history of the WEMITE roughness lengths calculated using the wind speed profile and turbulence intensity methods. The profile method assumes a logarithmic wind profile through the three WEMITE anemometer heights and applies a least-squares best-fit technique to the mean wind speeds. The resulting best-fit parameters include the intercept which corresponds to the estimated roughness length. The turbulence method not only assumes a simplified log-law which can be applied to the data, but also that the ratio between the standard deviation of the wind speed record and the friction velocity is equal to 2.5. Under these assumptions, the roughness length can be directly related to the turbulence intensity and instrument height. In the process of using each method, the original wind speed time series was segmented into 5-min sub-segments
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775
Roughness Length (m)
1 Airport
10.7 m Turbulence Intensity Ratio 0.1 0.01 0.001
Profile
Transitional
30
30
30 6: 07 :
4: 02 :
1: 57 :
23
:5
2: 30
7: 30 :4
21
42 :3 0
7: 30
19 :
:3 17
:3
2: 30
7: 30 15
:2
2: 30 13
:2 11
9: 17 :
30
0.0001
Time (UTC) Fig. 8. Time history of estimated roughness lengths occurring at the WEMITE deployment site during the passage of Hurricane Bonnie. Roughness estimates were produced using wind speed profile and turbulence intensity methods.
(with 50% offset assuming independence) for which roughness estimates were made. The 5-min estimates were then assembled into a time history represented by Fig. 8. For a more comprehensive review of the various methods to estimate roughness lengths, the reader is directed to Barthelmie et al. [9]. 4.3. Turbulence intensities Turbulence intensities are determined by taking the ratio between the standard deviation found in a given wind speed record and normalizing it with the mean wind speed into a dimensionless quantity. Traditionally, wind engineers have determined the longitudinal (along-wind) and lateral (cross-wind) turbulence intensities; vertical turbulence intensity is also calculated, given the record for the vertical wind speed exists. Historically, little work has been completed in even the basic understanding and determination of turbulence intensities as generated within the HPBL, largely due to a lack of data. Some attempts have been made [10–14] with some deviation noted between hurricane and extratropical or monsoon-generated winds. Turbulence intensity is one of the parameters ‘‘matched’’ in the wind tunnel and present in building codes and standards. The intensity of the turbulence in the upstream wind affects the overall static load on a building, and the dynamic excitation present on flexible buildings and components. The turbulence intensity varies in different terrain and stability conditions, increasing for rougher and increasingly unstable conditions. The turbulence intensity will also vary when calculated using different averaging times, as shown in Fig. 9. Fig. 9 was compiled by randomly selecting a portion of the WEMITE data several hours in duration, segmenting the record using various window lengths (1, 5, 10 min, etc.), determining the turbulence intensity for each window, and collecting the summary statistics (maximum, minimum and mean
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Total Turbulence Intensity
0.4 0.35 0.3
Maximum
0.25 0.2
Mean
0.15 0.1
Minimum 0.05 0 0
100
200
300
400
500
600
Averaging Time (seconds) Fig. 9. Time dependency of the turbulence intensity statistic.
value) based on each window length employed. For purposes of this paper, a 5-min averaging time with a 50% offset between data segments (assuming independence) was employed to determine the turbulence intensities. It can be seen in Fig. 9 that the mean turbulence intensity as determined by using the Hurricane Bonnie data becomes fairly stable at approximately 3-min with only a modest increase of 2.7% indicated between 5 and 10-min. Hence, the mean calculated turbulence intensity indicates only minimal dependence on averaging time once above 5-min. Turbulence intensity will also be affected by nonstationarities which exist in the record. However, the nonstationary effects are usually minimal without the presence of an abrupt change in wind speed and direction as found in Schroeder et al. [10]. The classification of the data as stationarity or nonstationary was defined in a weak sense [15] through examination of the first and second moments. Each data segment was examined with the nonparametric run test using a 0.95 significance level. This examination revealed that approximately 33% of the 5-min data segments were nonstationary with respect to the mean longitudinal wind speed, while only 2.2% of the data records were nonstationary with respect to the variance in the longitudinal wind speed records. These results are indicative of a hurricane environment where the wind speed record is expected to ramp up prior to the arrival of the storm center, and decrease following its departure. 4.3.1. Turbulence intensity statistics As shown in Fig. 10, the longitudinal turbulence intensities from the 10.7 m WEMITE anemometer range from 12% to 35% for the airport exposure and increase to 17–41% for the remaining (transitional) portion of the storm. Except for one sharp peak near 22:00 UTC, only subtle changes with time are noted in the record. The lateral turbulence intensities have the same pattern with one sharp peak at approximately 22:00 UTC and variations from 12% to 42% for the airport exposure and 16–35% for the transitional roughness regime. Vertical turbulence intensities range from 7% to 11% for the airport exposure and 7–22% for the
25
0.4
Wind Speed
20
0.35 15
0.3 0.25
10
0.2 5
0.15
30
23
7: :4
21
:5 2: 30 1: 57 :3 0 4: 02 :3 0 6: 07 :3 0
0
2: 30
0
:4
:3 19
:3 7
2:
17
:3 15
:2
2: 13
:2 11
17 9:
7: 30
30
0.1
30
Long. Turbulence Intensity
777
Mean Wind Speed (m/s)
0.45
:3 0
Long. Turbulence Intensity
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Time (UTC) Fig. 10. Time history of longitudinal turbulence intensity as determined from the 10.7 m WEMITE data during the passage of Hurricane Bonnie.
Table 3 Longitudinal turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the longitudinal mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
269 17.6 24.4 12.2 2.0
74 28.0 40.7 17.3 4.8
133 19.4 34.6 13.0 2.8
27 29.9 41.0 17.8 5.3
transitional exposure; however, there is no peak in the time history. Examination of the 5-min time segment containing the peaks in lateral and longitudinal turbulence intensities indicates a sharp and temporary wind direction change as can be seen in Fig. 5. This change induces an intense ‘‘artificial’’ peak in the turbulence intensities due to the nonstationarity of the record. This sharp direction change occurs over a time period of approximately 15-s and only occurs at the 10.7 m (35-feet) level. Its physical meaning is unknown, but interaction of the anemometer with debris (paper, plastic, etc.) may have caused the abrupt change. The authors cannot prove or disprove the temporary change in direction. The determined turbulence intensities are summarized in Tables 3–5 where stationarity is determined with respect to the first moment (mean) of the longitudinal, lateral, and vertical wind speed records. Additionally, Tables 6–8 document the turbulence intensities where stationarity is determined with respect to the variance (second moment) of the longitudinal, lateral, and vertical mean wind speeds. Only a minimal increase in the mean turbulence intensity is noted between the stationary and nonstationary data segments.
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Table 4 Lateral turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the lateral mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
355 16.4 41.8 12.3 3.6
95 26.2 34.7 16.0 3.6
47 16.6 20.1 13.7 1.6
6 25.0 26.7 23.9 1.2
Table 5 Vertical turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the vertical mean wind speed Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 8.5 10.5 6.5 0.7
101 15.4 22.3 6.5 2.6
9 8.1 8.9 7.3 0.6
0 N/A N/A N/A N/A
Table 6 Longitudinal turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the longitudinal wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 18.2 34.6 12.2 2.5
97 28.3 41.0 17.3 5.0
9 18.7 22.2 14.7 2.8
4 32.6 39.9 28.7 5.2
4.3.2. Turbulence intensity ratios Combining these different turbulence intensity components by constructing ratios, one can make a comparison to values which are thought to exist in neutrally stratified surface layers [16]. Given a neutral surface layer (constant flux layer) with homogeneous roughness, the momentum flux becomes independent of height and only depends on the friction velocity. Employing this similarity hypothesis, the following ratios between the turbulence intensities can be derived, where Iu ; Iv ; and Iw represent the longitudinal, lateral and vertical turbulence intensities, respectively;
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Table 7 Lateral turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the lateral wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
381 16.4 41.8 12.3 3.6
93 26.2 34.7 16.0 3.6
21 15.7 17.3 14.3 0.9
8 25.5 27.2 23.9 1.2
Table 8 Vertical turbulence intensity statistics for Hurricane Bonnie classified in terms of stationarity with respect to the variance in the vertical wind speed record Stationary
No. 5-min segments Mean (%) Maximum (%) Minimum (%) Standard deviation (%)
Nonstationary
Airport
Transitional
Airport
Transitional
393 8.5 10.5 6.5 0.7
96 15.4 22.3 6.5 2.6
9 8.8 10.1 7.0 1.0
0 N/A N/A N/A N/A
and su ; sv ; and sw represent the standard deviation of the longitudinal, lateral and vertical wind speed records s w Iw ¼ ¼ 0:52; su Iu
ð2Þ
sv Iv ¼ ¼ 0:76: s u Iu
ð3Þ
The turbulence intensity ratios determined from the 10.7 m WEMITE wind speed data are shown in Fig. 11. For the airport exposure, during the first portion of the hurricane record, the mean ratios between the lateral and longitudinal turbulence intensities and the vertical and longitudinal turbulence intensities are 0.92 and 0.47, respectively, representing a deviation of 21% and 11% from the expected values. The cause for these departures is not completely understood; however, some of the observed difference in the lateral turbulence intensity ratio is attributable to resonance effects in the wind direction measurements as discussed previously. 4.4. Gust factors Gust factors are a ratio between a peak wind speed of some duration within a given data segment and the mean wind speed of the same segment. Historically, there
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1.4 1.2
Lat/Lon Turbulence Intensity Ratio
1 0.8 0.6 0.4 0.2
Vert/Lon Turbulence Intensity Ratio
9: 17 :3 0 11 :2 2: 30 13 :2 7: 30 15 :3 2: 30 17 :3 7: 30 19 :4 2: 30 21 :4 7: 30 23 :5 2: 30 1: 57 :3 0 4: 02 :3 0 6: 07 :3 0
Turbulence Intensity Ratio
780
Time (UTC) Fig. 11. Turbulence intensity ratios as determined from 10.7 m WEMITE wind speed data collected during Hurricane Bonnie. Solid lines are drawn at the expected values of 0.92 and 0.47.
has been some disagreement as to the applicability of the Durst curve [17] to hurricanes, as other studies [18] have indicated ‘‘gustier’’ winds within hurricanes. From the 10.7 m Hurricane Bonnie wind speed data collected with WEMITE, 2-s/ 10-min gust factors were calculated using 10-min data segments (and a 50% offset assuming independence). An average gust factor of 1.55 was determined for the airport exposure from 201 individual values with a maximum value of 2.16. These values fall more in line with the 1.55 mean value determined by Krayer and Marshall [18]. Their results were determined using wind speed strip chart records collected from four different hurricanes; each record was collected from a location with a surface roughness length representing an airport exposure (Z0 ¼ 0:03 m). Beyond the airport exposure, the second, rougher (transitional) regime at the end of the WEMITE data record had gust factors as high as 2.46 with an average value of approximately 1.85. These values cannot be directly compared to Krayer and Marshall’s results due to the accompanying change in surface roughness length. Another comparison can be made if we generate a curve of gust factors based on a mean hourly wind speed and peak gusts of variable duration. This curve, shown in Fig. 12, was constructed by employing a 20-min offset between the 1-h data segments (assuming independence) and using only data from the first portion of the record (airport exposure). Comparison to the Krayer/Marshall curve indicates a similar result with only a minimal amount of deviation at small gust durations. Considering the sensitivity of the determined gust factors statistics to the surrounding terrain conditions, and given the ‘‘lumped’’ classifications employed for airport and transitional exposure based on roughness lengths, further examination was completed. Constructing a plot (Fig. 13) of the 2-s/10-min gust factors versus roughness lengths (as determined using the turbulence intensity estimating method) for the data classified as airport exposure reveals a linear relationship. Employing the slope and intercept, as determined from a least-squares
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2 1.9 1.8
Gust Factor
1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 1
10
100
1000
Duration of Gust (seconds) Fig. 12. Gust factor curve based on mean hourly wind speeds determined by using Hurricane Bonnie data with airport exposure (connected with open data points) compared to Krayer/Marshall (unconnected with closed data points).
Gust Factor (2-sec/10-min)
2.4 2.2 2 1.8 1.6 1.4
y = 2.4597x + 1.4244 2
R = 0.3862
1.2 1 0
0.05
0.1
0.15
0.2
Roughness Length (m) Fig. 13. Scatter plot of 2-s to 10-min gust factors determined from the 10.7 m Hurricane Bonnie wind speed data (airport exposure only) along with a best-fit linear regression line overlaid.
best-fit, with a roughness length of 0.03 m yields an expected gust factor of 1.50 which is still closer to the mean value determined by Krayer and Marshall. 4.5. Integral scales The longitudinal integral scale simply represents the average along-wind dimension of the wind gusts in a given data segment. Thus, integral scales (longitudinal, lateral, and vertical) are related to the total static load on a structure. As the integral scale increases, the gust size increases, along with its total influence on a structure. Therefore, integral scales are inherent in building standards and are ‘‘matched’’ by wind tunnel operators in order to properly model the wind and collect
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realistic building pressure data. Only a limited amount of analysis [10,14] has been completed on the integral scales present within the HPBL due to a lack of highresolution wind speed data. Longitudinal integral scales can be calculated using several methods which stem from the determination of the power spectrum and autocorrelation function (ACF). The results presented in this paper are determined using Eqs. (4)–(6). First, the ACF (ruu ) was calculated for 5-min data (using a 50% offset assuming independence) segments of instantaneous (5 Hz) longitudinal wind speed (u) from the 10.7 m WEMITE data using Eq. (4). The ACF curve was then fitted with an exponential curve (ruuf ) up to the lag duration (t) where the derivative of the ACF curve is zero (i.e. the slope is zero). Once the exponential curve was fit, it was integrated from 0 to infinity to obtain the time integral scale (Tuu ) using Eq. (5). The time integral scale is then multiplied by the mean longitudinal wind speed (U) over the same 5-min data segment to obtain the longitudinal integral scale (Luu ) using Eq. (6). As with the determination of turbulence intensities, the time period used to calculate the ACF curve will affect the calculation of the integral scales. Fig. 14 graphically identifies this effect as the ACF curve shifts rightward (indicating higher correlations) at a given lag with increasing window length. Larger window lengths (averaging times) will also reduce the value of mean wind speed determined from the record, but this reduction does not fully compensate for the increased area under the ACF curve. Therefore, the determined value of the integral scale tends to increase with increasing window length. This increase is at least partially the result of trends in the mean wind speed which become more evident with larger window lengths. Therefore, if one evaluates the integral scale values from a wind speed record without some segregation of stationary/nonstationary data segments (defined as those without/ with resolvable trends), the broad results may be biased towards slightly larger values due to these effects ruu ¼
E½fuðtÞ Ug fuðt þ tÞ Ug ; s2u
ð4Þ
Autocorrelation Coefficient
1.2 1 0.8
2-minute data segment
0.6
5-minute data segment
0.4
15-minute data segment
0.2 0 0
100
200
300
Lags Fig. 14. Mean ACFs determined from Hurricane Bonnie using various data segment lengths.
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Tuu ¼
Z
783
N
ruuf ðtÞ dt;
ð5Þ
0
Luu ¼ UTuu :
ð6Þ
The results from Hurricane Bonnie, shown in Table 9, indicate a mean longitudinal integral scale of 100 m for stationary data segments within the airport exposure with a maximum of 255 m noted. Results from the nonstationary data segments indicate an increase in mean longitudinal integral scale to 145 m with a maximum value of 376 m found. This increase represents an increase of 46% in the average longitudinal gust size for the nonstationary data (based on the first moment only) relative to the stationary data. Examination of the longitudinal integral scales determined from data within the transitional flow regime indicate an average longitudinal gust size of 68 and 90 m for stationary and nonstationary data segments, respectively. This decrease in integral scale is expected given the increase in surface roughness values corresponding to the transitional regime relative to the airport exposure. Upon further examination of the longitudinal integral scale time history (Fig. 15), two different integral scale regimes can be observed which are not associated with changes in surface roughness. The first regime, evident from 11:15 to 13:15 UTC (among other times), exhibits a lower-average integral scale and few, if any, peak values above 150 m. The second regime, event from 13:15 to 15:15 UTC (among other times), maintains a larger mean integral scale and numerous peaks between 200 and 250 m. These two regimes seem to alternate intermittently and are especially evident from the start of the record through approximately 20:00 UTC. Although the cause of these two regimes is unknown, convective downdrafts occurring at various locations within the storm may lead to larger scaled turbulence being active in certain regions of the storm relative to others. 4.6. Power spectral density (PSD) estimates A PSD estimate of the longitudinal wind speed record was made for a 2-h data segment near the peak of the storm. For this 2-h time period from 17:50 to
Table 9 Longitudinal integral scales determined from WEMITE data during the passage of Hurricane Bonnie Stationary
No. 5-min segments Mean (m) Maximum (m) Minimum (m) Standard deviation (m)
Nonstationary
Airport
Transitional
Airport
Transitional
269 99.9 254.6 37.6 37.3
74 68.4 179.5 31.3 24.5
133 144.9 376.3 36.9 64.4
27 90.2 175.8 32.4 34.4
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Wind Speed
350 20
300 250
15
200 10
150 100
5
50
Long. Integral Scale 0
0
0
:3 07 6:
02
:3
0 4:
57 1:
2: :5 23
:3
30
30 7:
30 2:
:4 21
:4
7:
30 19
:3
2:
30 17
:3
7: :2
15
30 2: :2
13
:3 11
17 9:
30
0
Mean Wind Speed (m/s)
400
0
Longitudinal Integral Scale (m)
784
Time (UTC) Fig. 15. Time history of longitudinal integral scales as recorded from the 10.7 m WEMITE data collected during the passage of Hurricane Bonnie.
Fig. 16. Wind speed time history obtained from the 10.7 m WEMITE anemometer from 17:50 to 19:50 UTC. The vertical axis represents the instantaneous wind speed minus the mean wind speed.
19:50 UTC, the wind speed averaged approximately 21.3 m/s, and remained relatively consistent as shown in Fig. 16. The longitudinal PSD estimate is shown in Fig. 17. Reduced frequency is employed as the horizontal axis and normalized power (power spectrum divided by the variance) multiplied by the frequency is used for the vertical axis. The Nyquist frequency is 2.5 Hz, given the sampling rate of 5 Hz. The original 2-h segment of wind speed data was segmented into 10-min data sub-segments (with a 50% offset assuming independence). Each of these
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785
Normalized PSD * Freqeuncy (n*S uu/Var(u))
0.45
Hurricane Bonnie FSU Terrain Perturbed Terrain Kaimal
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0.0001
0.001
0.01
0.1
1
10
Reduced Frequency (n*z/U) Fig. 17. Longitudinal wind speed PSD estimate from the 10.7 m WEMITE data (17:50–19:50 UTC) compared to several model spectra.
Table 10 Model spectral shape factors (adapted from Geurts [22])
Suu
FSU Terrain: C ¼ 1; a ¼ 5=3; b ¼ 5=3; g ¼ 1
Perturbed Terrain: C ¼ 1; a ¼ 1; b ¼ 5=3; g ¼ 1
Kaimal: C ¼ 1; a ¼ 1; b ¼ 5=3; g ¼ 1
A
B
A
B
A
B
20.53
475.1
40.42
60.62
21.66
33
sub-segments was then used to calculate individual nonparametric PSDs. The final presented PSD (Fig. 17) was the average of these 23 individual PSDs. Comparisons, as provided in Fig. 17, between the acquired data and several spectra models such as the perturbed terrain or flat-smooth-uniform models [19] or neutral Kansas model [20,21], indicate the longitudinal wind speed data lacks highfrequency energy and contains more low-frequency energy than expected. The model spectra used for comparison are detailed by Eq. (6) and Table 10, where n is the frequency, f the reduced frequency, Suu the longitudinal spectral density function, and the coefficients A; B; C; a; b; and g determine the shape and position of the model spectra. In general, the peak frequencies are in reasonable agreement, and the lack of high-frequency energy is at least in part due to the minimal response characteristics of the Wind Monitor anemometer used for the WEMITE application. Given the anemometer specifications previously discussed, one would expect an under-estimation (based on a response ratio of 0.99) of the longitudinal spectra at reduced frequencies at and beyond approximately 0.09. The additional lowfrequency energy in the estimate is most likely from the ‘‘storm’’ environment and is in agreement with previous research completed by Powell et al. [1] which indicates more low-frequency energy in the spectrum. An additional source of low-frequency
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energy would result from trends and other nonstationarities in the record, and in many extreme wind records this source is not trivial. However, the record in question was strategically chosen because it is very well behaved. For instance, removing subtle trends across the first and second half of the record only reduces the total variance by 0.43% nSuu Af g ¼ : 2 su ðC þ Bf a Þb
ð7Þ
4.7. Spectragram A spectragram is a more useful tool for trying to evaluate changes in energy content throughout the storm, as temporal changes in time are not lost through averaging over the entire event or even a segment of several hours in length. So if one is searching for an event which occurs over a period of minutes, then the spectragram offers a more valuable tool to highlight such changes. Spectragrams of the wind record collected by the 10.7 m anemometer of WEMITE during Hurricane Bonnie are shown in Figs. 18a and b. In these figures, the vertical axis is the logarithm (base 10) of the frequency, the horizontal axis is time, and the brighter colors indicate higher amounts of normalized power (power divided by variance) multiplied by frequency. These figures were calculated by separating the record into 10-min data segments that were subsequently divided into 2.5-min subsegments. Each sub-segment of data was used to calculate a local PSD using both autoregressive AR(50) and nonparametric methods. Once the PSDs from each local 2.5-min sub-segment were determined, they were averaged together within each 10-min block. The resulting 10-min averaged PSDs were then assembled into a time history of PSDs (spectragram) for display. From these figures it can be seen that the nonparametric method yields a much noisier solution, but one can resolve that the peak frequency and peak amplitudes change with time. Changes in peak frequency can result from increasing wind speed or actual changes in the process. Using a normalized peak frequency can neutralize the effects of increasing winds speeds, and given the most active scale of the process remains constant with time, the normalized peak frequency would not change. The variability in normalized peak frequency (period) for the Hurricane Bonnie data with airport exposure ranges from 0.06 (period, T; of 17 s) to less than 0.01 Hz (T ¼ 100 s) representing a 600% variation from one location in the storm to another. One can also note the change in normalized peak frequency associated with the change in exposure found at the end of the record. Higher-frequency energy (smaller scales) becomes more active with the rougher transitional exposure. Energy at the low-frequency end of the PSDs was found to be higher than expected during certain time frames. Time periods with excesses of low-frequency energy correlate to larger integral scales due to the relationship between the ACF and the PSD. In general, the variability of energy is large, and the storm cannot be well represented by using one averaged PSD for the entire event. The peak of the
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Fig. 18. (a) Nonparametric spectragram of Hurricane Bonnie as recorded by the 10.7 m WEMITE anemometer. (b) Autoregressive spectragram of Hurricane Bonnie as recorded by the 10.7 m WEMITE anemometer.
energy content is usually related to time scales on the order 100 s, but concentrations in energy exist periodically at 15–30 s time scales.
5. Conclusions and results This paper provides the results of the evaluation of turbulence intensities, gust factors, longitudinal integral scales and power spectral densities recorded in
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Hurricane Bonnie (1998) by the Wind Engineering Mobile Instrumented Tower Experiment. The results indicate: 1. There are mainly subtle changes in the turbulence intensity values throughout the passage of Hurricane Bonnie. One sharp peak in the lateral and longitudinal turbulence intensities does exist near the peak of the storm. These extreme values are associated with a temporary change in wind speed and direction (a highly nonstationary data segment); 2. There is general agreement between the gust factor statistics derived with the Hurricane Bonnie WEMITE data and results provided by Krayer and Marshall [18]; 3. Longitudinal integral scales are shown to increase by an average of 46% for stationary versus nonstationary data segments. This increase is at least in part due to the incorporation of trends in the wind speed record (as expected in a hurricane) contaminating the determination of the ACF. Integral scales vary widely throughout the storm. The time history suggests that there are two separate regimes of longitudinal integral scales that are not correlated with changes in exposure (roughness). One of these regimes produced integral scales that are substantially larger than the other. The reason for these two regimes is not currently understood, but the presence of convective scale influences is a possible reason; 4. The longitudinal PSD indicates there is more low-frequency energy in the wind record than expected by various model spectra; and 5. The spectragram indicates there are large variations in the energy content of the record throughout the passage of the storm. Normalized peak frequencies vary by as much as 600%.
Acknowledgements The authors would like to acknowledge the support of INEEL for the construction and deployment of the WEMITE tower during the 1998 Atlantic Hurricane Season, as well as NIST (Department of Commerce NIST/TTU Cooperative Agreement Award 70NANB8H0059) and the Insurance Friends of NHC for supporting the analysis efforts. The authors also acknowledge the time spent by two anonymous reviewers whose comments added great value to this paper.
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[3] L.A. Avila, Highlights of the 1998 Atlantic hurricane season: year of landfalls, in: Proceedings of the 23rd Conference on Hurricanes and Tropical Meteorology, Dallas, TX, 1999, pp. 1282–1285. [4] M.D. Powell, Hurricanes at landfall, in: Proceedings of the 23rd Conference on Hurricanes and Tropical Meteorology, Dallas, TX, 1999, pp. 107–108. [5] M.R. Conder, R.E. Peterson, J.L. Schroeder, D.A. Smith, Comparison of hurricane wind data during Hurricane Bonnie: The Texas Tech Wind Engineering Mobile Instrumented Tower Experiment (WEMITE) and the NWS Wilmington ASOS, in: Proceedings of the 13rd Symposium on Boundary Layers and Turbulence, Dallas. TX, 1999, pp. 484–487. [6] S.P. Arya, Introduction to Micrometeorology, Academic Press, San Diego, 1988. [7] E. Simiu, R.H. Scanlan, Wind Effects on Structures: An Introduction to Wind Engineering, Wiley, New York, 1986. [8] C. Letchford, A. Gardner, J.R. Howard, J.L. Schroeder, A comparison of wind prediction models for transitional flow regimes using full-scale hurricane data, J. Wind Eng. Ind. Aerodyn. 10 (2001) 925–945. [9] R.J. Barthelmie, J.P. Palutikof, T.D. Davies, Estimation of sector roughness lengths and the effect on prediction of the vertical wind speed profile, Boundary-Layer Meteorol. 66 (1993) 19–47. [10] J.L. Schroeder, D.A. Smith, R.E. Peterson, Variation of turbulence intensities and integral scales during the passage of a hurricane, J. Wind Eng. Ind. Aerodyn. 77/78 (1998) 65–72. [11] C.C. Wu, A.N.L. Chiu, Comparison of some ambient and typhoon instantaneous wind speed characteristics, J. Wind Eng. Ind. Aerodyn. 13 (1983) 43–53. [12] H. Ishizaki, Wind profiles, turbulence intensities, and gust factors for design in typhoon-prone regions, J. Wind Eng. Ind. Aerodyn. 13 (1983) 55–66. [13] E.C. Choi, Characteristics of typhoons over the South China Sea, J. Ind. Aerodyn. 3 (1978) 353–365. [14] C.C. Chuen, Correlation and spectral functions of atmospheric turbulence, in: Proceedings of the Third International Conference Wind Effects on Buildings and Structures, Tokyo, Japan, 1971, pp. 45–55. [15] J.S. Bendat, A.G. Piersol, Random Data Analysis and Measurement Procedures, Wiley, New York, 1986. [16] J.E. Cermak, A.G. Davenport, E.J. Plate, D.X. Vieges, Wind climate in the city, in: Proceedings of the NATO Advanced Study Institute on Wind Climate in Cities, Waldbronn, Germany, 1983. [17] C.S. Durst, Wind speeds over short periods of time, Meteorol. Mag. 89 (1960) 181–186. [18] W.R. Krayer, R.D. Marshall, Gust factors applied to hurricane winds, Bull. Am. Meteorol. Soc. 73 (1992) 613–617. [19] H. Tieleman, Universality of velocity spectra, J. Wind Eng. Ind. Aerodyn. 56 (1995) 55–69. [20] J.C. Kaimal, J.C. Wyngaard, Y. Izumi, O.R. Cote, Spectral characteristics of surface layer turbulence, J. R. Meteorol. Soc. 98 (1972) 563–589. [21] J.C. Kaimal, J.J. Finnigan, Atmospheric Boundary Layer Flows, Their Structure and Measurement, Oxford University Press, New York, 1995. [22] C.P.W. Geurts, Wind-induced pressure fluctuations on building facades, Technische Universiteit Eindhoven, Faculteit Boouwkunde, Vakgroep Constructief Ontwerpen, 1997.