Surface Drag Coefficient Behavior During Hurricane Ike
Brian C. Zachry1, Chris W. Letchford2, Delong Zuo3, John L. Schroeder4, and Andrew B.
Kennedy5
1
Doctoral Student Wind Science and Engineering Research Center, Texas Tech University,
Lubbock, Texas, USA, [email protected]
2
Department Head of School of Engineering, University of Tasmania, Hobart, Tasmania,
Australia, [email protected]
3
Assistant Professor of Civil Engineering, Texas Tech University, Lubbock, Texas, USA,
4
5
[email protected]
Associate Professor of Atmospheric Science, Texas Tech University, Lubbock, Texas, USA,
[email protected]
Assistant Professor of Coastal Engineering and Geological Sciences, University of Notre Dame,
Notre Dame, Indiana, USA, [email protected]
ABSTRACT
As a result of increasing wealth, infrastructure, and population along the hurricane prone coast,
there is a growing need for observations of surface layer quantities to improve hurricane and
wave/surge forecasting. Results are presented from a field campaign coordinated among Texas
Tech University (TTU), the University of Florida (UF), and the University of Notre Dame (UND)
during the 2008 Atlantic Hurricane Season. Research teams successfully collected valuable wind
and wave data during the passage of Hurricane Ike. A TTU StickNet platform obtained wind
measurements in true marine exposure with a fetch across the Houston ship channel, and three
UF/UND wave gauges collected shoaling wave data adjacent to landfall. Findings indicated that
the drag coefficient reached a limiting value at wind speeds near hurricane force; in relative
agreement with deep water measurements reported in [1]. At slower wind speeds the drag
coefficient was higher than over deep water. This suggests that storm surge models may require
separate forcing parameterizations in such complex wave/bathymetric conditions. Coastal
roughness lengths provide evidence that Exposure D should be prescribed by ASCE along the
hurricane prone coastline.
INTRODUCTION
Over 35 million people are currently living in hurricane prone coastal regions stretching from
Texas to North Carolina [2]. With an increase in population inevitable, it is necessary to
formulate rigorous mitigation procedures against potential hurricane damage. Field
measurements provide valuable data needed to generate more accurate ocean wave models,
hurricane storm surge-, track-, and intensity forecasts, as well as define conservative wind
loading provisions in the ASCE Standard for new structures being built along the coast. As deep
water datasets of important surface layer quantities continue to grow, it becomes obvious that
there is a significant data gap in shallow water and at the coast. This void is primarily due to the
episodic and uncertain nature of hurricanes and the profound difficultly in conducting in situ
measurements in extreme environments.
Hence, the majority of previous research studies have been conducted in weak to moderate wind
regimes of 5 < U 10 < 28 m/s (where U 10 is the standard 10 m reference height mean wind speed)
and are limited to: (1) field measurements made in deep water [3-5], (2) field measurements in
1
lakes [6,7], (3) laboratory measurements [8-10], and (4) theoretical studies valid over deep water
[11]. Recently, [1,12,13] made deep water, open ocean measurements of air-sea momentum flux
in hurricanes, and [14] performed laboratory measurements in simulated extreme winds. Surface
momentum exchange τo is typically described in terms of a 10 m drag coefficient CD, defined as:
CD 
o
u*2

U 102 U 102
(1)
where u* is the friction (shear) velocity and ρ is air density. These deep water findings indicate
that CD increases with wind speed, but reaches a limiting value: with [1,14] suggesting CD ≈
0.0025 at winds of 33 m/s and [12] suggesting CD ≈ 0.0018 at 22-23 m/s. Saturation of the drag
coefficient in hurricanes has been attributed to the effects of spray droplets acting to limit
turbulent mixing [1,15-17]. In laboratory or short-fetch situations, CD saturation is likely a result
of air-flow separation from the dominant waves. The separated flow skips from crest to crest
(bypassing the troughs), and thus sheltering the wave surface [17].
It is well known that wave interaction with the bottom topography (i.e., bathymetry) causes wave
conditions in shallow water to be markedly different than in deep water. This region is
characterized by a rapidly changing water surface profile due to wave shoaling and breaking
transformation processes [18-21]. Although yet to be determined, the drag coefficient in this
region is hypothesized to be significantly larger than in deep water due to: (1) decrease in the
wave phase speed, defined as the speed at which an individual wave propagates, (2) increase in
wave steepness, (3) rapidly varying surface wave field, and (4) the fact that waves may not align
with the mean wind near the shore. Waves that propagate into a region of variable depth will
undergo refraction. This may lead to increased roughness along the coast [22]. In one laboratory
study [23], it was found that there was up to a 100% increase in total wind stress over actively
breaking waves compared to waves of similar steepness just prior to breaking (‘incipient’
breaking waves). Other laboratory experiments have also suggested increased surface stress
above breaking waves [24,25]. Based on the wave transformation processes listed above, the
deep water surface drag coefficient is likely to underestimate wind stress and thus storm surge
near the coast.
Storm surge models currently employ parameterizations that have been developed in deep water
[26]. If drag coefficient behavior is different in shallow water, then separate parameterizations
need to be employed in this region. The drag coefficient in Lake Ontario, Canada was examined
[27] as waves transformed from deep water, to shoaling, and finally breaking in wind speeds of
around 14 m/s. The findings support the hypothesis that shallow water drag is higher than that
observed in deep water. The highest drag coefficients were found over shoaling waves and the
smallest over deep water waves. Measurements are also needed to clarify the debate on the
ASCE wind load standard along the hurricane prone coast. Using a limited dataset, it was
successfully argued [28] that the drag coefficient over shoaling waves in hurricanes conditions is
significantly higher than well offshore, equivalent to Exposure C. Prior to the work of [28], the
roughness length in hurricane prone regions was set at zo = 0.003 m (Exposure D). However, it is
anticipated that the upcoming version ASCE 7-10 will defer back to Exposure D in the hurricane
prone coastal region [29]. Regardless, a comprehensive dataset is needed to verify this standard.
2
Work presented here aims to advance our understanding of momentum exchange at the coast.
Rare measurements of hurricane winds in marine exposure and nearshore waves were obtained
during the passage of Hurricane Ike in 2008. Drag coefficient behavior is determined for 2-min
mean winds (referenced to 10 m) ranging from 5 < U 10 < 33 m/s.
FIELD INSTRUMENTATION
Hurricane wave and surge measurements were obtained using gauges developed by Andrew
Kennedy at UND (formerly UF). Wave gauges are self-recording pressure transducers housed
inside a water-tight PVC pipe enclosure anchored to the sea floor using a steel base weighing 25
kg (Figure 1). Similar bottom mounted pressure transducers have been effectively used as field
wave gauges since 1947 [30]. A full deployment consists of over 30 gauges deployed aerially via
helicopter and released to the sea bed in depths of 10-15 m. They are limited to shallow water
due to attenuation of the wave-induced pressure with depth. Sea bed pressures were obtained
using a 100 PSI absolute (689 kPa) Measurement Specialties Model 85 Ultrastable piezoelectric
silicon pressure sensor connected to a TattleTale TFX-11v2 data logger sampling at 1 Hz. Each
instrument was calibrated in the laboratory against a Paroscientific quartz oscillation transducer.
Based on the sensor range and a 12 bit A/D converter, measurement resolution is equivalent to
1.7 cm of seawater (sensor resolution via noise in the circuitry is ~0.8 cm). The gauges are
powered by four 3.6 volt lithium batteries, yielding a battery life on order of 11 days.
Figure 1: Photos of (a) UF/UND wave gauge and (b) TTU StickNet 110A taken by the Galveston County
Office of Emergency Management during retrieval (looking south-southwest toward the ship channel).
In situ measurements of kinematic and thermodynamic variables were obtained using rapidlydeployable surface weather observing stations (termed StickNet) developed by wind
engineering/atmospheric science students and faculty at TTU. The StickNet model deployed for
this work was equipped with an RM Young Wind Monitor model 05103V (Figure 1). Wind
speed and direction were measured at a height of 2.25 m and the sensors were sampled at 5 Hz.
This propeller-vane anemometer is capable of measuring wind speeds of 0-100 m/s. Wind speeds
and direction have an accuracy of ± 0.3 m/s and ± 3º, respectively. Owing to an external LGM
battery, measurements can be collected for up to seven days. The platforms can be deployed in
approximately two minutes and have been designed to withstand 3-second peak wind gusts of 63
m/s (not including the external battery dead weight or bottom (center) anchor). Currently, a full
deployment consists of 24 platforms. For additional information on SitckNet, consult [31].
3
HURRICANE IKE DEPLOYMENT
Nine bottom mounted wave/surge gauges were deployed in advance of Hurricane Ike along 360
km of Texas coastline stretching from Corpus Christi to near the Louisiana border. More than 5
million data points were collectively recorded from the eight recovered pressure transducers.
Three gauges (W-Y) were located adjacent to landfall, and provided valuable datasets (Figure 2).
Gauge location, distance from the immediate coast, and mean depth are provided in Table 1. The
gauges were deployed in the shoaling region at an average depth of 10.4 m and mean distance of
5.6 km from the shoreline. Because the continental shelf is relatively wide in this region, gauge
depths were still relatively shallow.
Figure 2: StickNet and UF/UND wave gauge deployment locations during Hurricane Ike.
A total of 24 StickNet probes were deployed by the TTU Hurricane Research Team (TTUHRT)
throughout Hurricane Ike’s landfall region. To fulfill the research objective, StickNet 110A was
deployed in Old Fort Travis Park on the Bolivar Peninsula near 29º 12.834’N and 94º 45.558’ W
(approximately 10 km from wave gauge X) at 0120 UTC on 12 September 2008 (Figure 2).
StickNet 110A was strategically placed as close to the water as possible (instruments must avoid
the immediate storm surge threat) and away from the affects of coastal structures or objects that
cause air flow interference. Wind flow at probe 110A was unobstructed in all directions with an
onshore (fetch off the water) component, except from 90º-110º (standard meteorological
convention with a 360 degree compass oriented clockwise from north) due to air flow
interference with Fort Travis (~150 m from the probe). Ike had a relatively large eye at landfall
which was estimated to be 74 km in diameter. The official center passed < 15 km to the west of
probe 110A, allowing for ‘classic’ hurricane eye passage time histories. Wind measurements in
marine exposure were collected during the southern eyewall passage as the winds shifted from
30º-60º to around 190º-230º (Figure 2). The fetch was from the Gulf of Mexico, along Galveston
4
Island, and finally across the Houston and Galveston Bay ship channel (approximately 3 km
wide). At its closest point, StickNet 110A was located about 90 m from the water at an elevation
of approximately 5.2-5.8 m above mean sea level (MSL). Figure 1 is a photo taken during
retrieval, showing its close proximity to the channel. A seawall located at the land/water
interface was estimated to be 4.6-5.2 m tall and the deployment site elevation was about (not
surveyed) 0.6 m above that. Based on water markings present on the tripod during retrieval, it
was estimated that the probe experienced a high water mark of 0.6 m, suggesting a peak surge of
5.8-6.4 m (USGS surge gauges were not located near 110A). This rise in water level ultimately
acted to ‘place’ the probe directly at the land/water interface during the storm by removing most
(or all) of the land surface between the probe and the channel.
Table 1: Wave/surge gauge characteristics and measured wave properties obtained during Hurricane Ike.
The distance column is an approximate linear distance from the gauge to the shoreline.
Gauge
Latitude
Longitude
W
X
Y
29° 04.284’N
29° 16.876’N
29° 29.786’N
95° 02.375’W
94° 42.537’W
94° 23.304’W
Mean Depth
(m)
13
9.5
8.7
Max Hs
(m)
4.5
4.5
4.0
Distance
(km)
13
9.5
8.7
METHODOLOGY
WAVE/SURGE MEASUREMENTS
Time series of analog voltage output from the transducers were converted to absolute pressure
(Pa), and subsequently water pressure measurements by subtracting out time records of
atmospheric pressure from nearby sources (e.g., NDBC records). Adjusted time series were
analyzed using standard wave spectral analysis techniques [20] to determine wave and sea
properties using 30-min data segments. Sequential segments of the fluctuating pressure were
linearly detrended prior to spectral analysis. Fast Fourier Transforms were calculated with a
Hanning window with no overlap of the neighboring data blocks. To limit amplification of high
frequency noise in the signal when converting bottom pressure spectra to surface elevation
spectra, spectral values for frequencies with sea bed pressure response factors of Kp < 0.11 were
cut from the record. For gauge depth provided in Table 1, cutoff frequencies ranged from 0.240.3 Hz. Wave heights determined from a bottom-mounted pressure gauge in the presence of
strong currents can contain significant error due to the Doppler shifting of wavenumber caused
by changes in wave phase speed. Because of the lack of good current measurements, these
corrections were not attempted here. As high quality surge hindcasts of the storm become
available, we will include Doppler corrections using computed velocities.
STICKNET WIND MEASUREMENTS
Quality data analysis requires the use of pristine wind speed and direction time series. Figure 3
shows the raw 1-min mean wind speed and direction time series obtained form StickNet 110A.
The following quality assurance measures were employed. First, a visual check revealed no
obvious instrument malfunction. Second, there were no observable spikes or erroneous data
points in the wind speed record. For the selected 22-hour time record (located between the
vertical lines in Figure 3), 110A measured a maximum instantaneous wind speed of 39.4 m/s (in
the eyewall), a minimum of 2.7 m/s (measured near the end of the time series), and a mean of
5
11.7 m/s. On the contrary, the wind direction record contained some obvious spiking (abrupt
change in wind direction) during passage of some of the strongest winds in the southern eyewall
(not apparent in Figure 3 as these points were ‘smoothed’ by averaging). These spikes were
likely due to instrument noise. Spikes in wind direction greater than 260º (roughly > 5 standard
deviations) were removed from the time series (a total of 34 data points), along with the
corresponding wind speed data points. Because the majority of the removed data points had
directions > 280º, they would have been discarded regardless as there were flow obstructions
west-northwest of the probe. Data were not smoothed (averaged) with adjacent points for the
reason above and also since nearby points often contained ‘spiked’ data as well. Although the
record is no longer continuous, error associated with removing such a few number of data points
is insignificant.
Figure 3: Raw wind speed and direction time records (averaging time of one minute) obtained from StickNet
110A during the passage of Hurricane Ike. Data located between the vertical lines are used in the analysis.
Turbulence intensity (TI) is a measure of the fluctuating component of the wind. Generally
speaking, TI characterizes the intensity of gusts in the flow. It is defined as the ratio of the
standard deviation of fluctuating wind to the mean wind speed. Since StickNets collect singlelevel wind data, the turbulence intensity method [32] was utilized to estimate the roughness
length and the drag coefficient as follows:
 z
 1
z o  z a exp   ; C D  k 2 ln a
 TI 
  zo



2
(2)
where za = 2.25 m is the anemometer height and k = 0.4 is the von Kármán constant. This
method assumes a logarithmic wind profile and that the ratio of the standard deviation to the
friction velocity is 2.5, which is valid in smooth terrain for zo < 0.1 m [33]. The inherent
6
variation in TI with height is accounted for in the assumptions used in its derivation. Along with
other wind statistics, TI varies based on averaging time. To determine where TI stabilizes, the
wind speed record was windowed into various averaging times and mean, maximum, and
minimum values of TI were computed (Figure 4). This work utilizes a 2-min averaging time.
Figure 4 shows that TI becomes fairly stable by 2-min with only a slight increase of 6.0% from
2- to 10-min. This window length captures variations in the smaller scales of motion, which are
driven by surface roughness.
Figure 4: Dependency of the total turbulence intensity (TI) on averaging time. A 2-min averaging time is
denoted by the vertical dashed line.
TI is sensitive to nonstationarities (in mean or variance) present in the wind speed record, as
these moments are used to calculate TI [34]. Nonstationarities lead to anomalous TI values,
which directly affect the estimation of zo and ultimately CD.
Stationarity of the wind speed record was examined using the modified reverse arrangement test
at a significance level of α = 0.01 [35]. The rationale is to test for the presence of a trend (i.e., a
changing mean or variance value) due to a source of nonstationarity in the signal. The number of
stationary wind speed data segments with respect to mean, variance, and mean and variance are
provided in Table 2. The majority of nonstationary segments were due to trends in the first
moment. This paper only uses weakly stationary segments (i.e., segments with mean and
variance being stationary). Stationarity statistics for TI and zo are reported in
Table 2: Number of stationary and nonstationary 2-min wind speed data segments evaluated with respect to
mean, variance, and both the mean and variance (a total of 666 data segments).
Variable
Wind Speed
Statistic
Stationary
Nonstationary
Mean
598
68
Variance
646
20
Mean & Variance
583
83
7
Table 3: Turbulence intensity and roughness length statistics after wind speed stationarity was evaluated with
respect to mean and variance.
Statistic
Mean
Minimum
Maximum
Standard Deviation
Turbulence Intensity (%)
Stationary
Nonstationary
13.4
14.4
9.59
10.3
18.4
19.7
1.62
1.99
Roughness Length (mm)
Stationary
Nonstationary
1.67
2.94
0.0665
0.133
9.66
14.1
1.50
2.84
ANALYSIS AND DISCUSSION
NEARSHORE WAVES AND WAVE ESTIMATES IN THE HOUSTON SHIP CHANNEL
StickNet 110A measured marine exposure with the upwind roughness associated with the local
wave conditions in the ship channel. Placement of the probe near the ship channel makes
analysis difficult as the bathymetry is not representative of a typical beach shoreline, where
waves propagate towards shore from oceanic deep water. In the vicinity of Probe 110A (termed
inner bar channel by the US Army Corps of Engineers) the channel is approximately 14 m deep.
Near the edges the channel is shallow (similar to any coast), but drops off quickly with a slope of
2.5:1. The situation was made even more complicated by the complex wave conditions that
likely existed in the channel. Below is a discussion of wave interaction in the waterway.
There were two wave fields interacting in the channel: swell and wind-driven waves, both drive
the drag coefficient in this complex environment. During the storm, a primary wave field
propagated from the ocean into the channel with highly complex interaction with local changes
in bathymetry and breakwaters (e.g., refraction, diffraction, wave breaking). Although gauge X
measured maximum significant wave heights of 4.5 m, the waves that made it into the channel
were undoubtedly smaller. The size of the waves in the channel, were, in part, a function of wave
alignment with the channel entrance. If the wave field was aligned with the channel, the waves
were relatively larger; however, if the waves were not aligned, interaction with the local
bathymetry and jetties results in smaller waves. Slight differences in wave heights are irrelevant
and would not affect the situation markedly. Probe 110A was located 9.2 km north of gauge X
and they were separated by a linear distance of 10.3 km. Regardless of wave-channel alignment,
energy dissipation over the 9.2 km distance is significant. A secondary, fetch limited wave field
was generated by the local wind flow across the channel. Simple fetch and duration limited
calculations [20] indicate a significant wave height of about Hs = 1.5 m and a peak period on the
order of Tp = 4 s. These waves are extremely steep – white-capping is likely ubiquitous for such
steep waves in strong winds. This likely created a situation where flow separation (or even
skimming flow) occurred. These waves also interacted with the primary waves coming into the
channel. Wave shapes were also affected by the presence of strong currents. Unfortunately, this
overall situation is far too complex to estimate, and current theory is inadequate.
DRAG COEFFICIENT
It is customary to report the drag coefficient (and other parameters) to the standard 10 m height
velocity. Estimating the 10 m drag coefficient provides a way to compare values obtained for
Hurricane Ike to other observational and laboratory studies (discussed below). Mean wind speed
data obtained at 2.25 m (denoted U 2.25 ) were referenced to 10 m using the neutral stability loglaw. In the surface layer shear stress is assumed to be constant with height [36]. Therefore, the
8
2.25 m drag coefficient can be translated to the standard 10 m height using the following
equation:
C D (10 )
U 
 C D ( 2.25)  2.25 
 U 10 
2
(2)
Hereafter, CD refers to the drag coefficient referenced to the standard 10 m height unless
otherwise noted. Stationarity statistics for CD are provided in Table 4. Nonstationary segments
have higher mean and standard deviations values than the stationary segments.
Table 4: Drag coefficient statistics (measured at 2.25 m) referenced to 10 m after stationarity in the wind
speed record was evaluated with respect to mean and variance.
3
Statistic
Mean
Minimum
Maximum
Standard Deviation
CD(10) × 10
Stationary
Nonstationary
2.00
2.27
1.13
1.27
3.32
3.71
0.404
0.517
It was mentioned above that approximately 0.6 m of surge occurred at the probe based on water
markings upon retrieval. Therefore, local storm surge inundation at probe 110A requires an
additional scaling factor. This is because water rise acts to change the theoretical height of the
anemometer relative to the ground/water surface. Height changes affect zo estimates via the TI
method and the wind speed translation up to 10 m. Any depth of water lowers the anemometer
height, resulting in lower zo, faster 10 m wind speeds, and thus lower 10 m drags. To properly
take this into account, time series of local water level are required; however, no storm surge
sensors were located near 110A. When high quality storm surge hindcasts become available,
analyses will take the computed water levels at probe 110A into account. Since these data are
currently not available, the conservative approach (results in lower CD) is to assume that 0.6 m of
surge lasted throughout the backside of the storm (za = 2.25-0.6 = 1.65 m). Since this assumption
is unlikely (and based on an estimate of 0.6 m of surge), the authors chose to neglect any local
rise in water level.
The primary interest of this work was to determine drag coefficient behavior with wind speed.
The standard way to assess CD versus U 10 is to partition the wind speed data (and corresponding
CD values) into bins with equal ranges. Six wind speed bins were chosen (5-10,…,30-35).
Although the number of bins employed is somewhat arbitrary, there must be a sufficient number
of data points in each bin to be a representative sample. With a limited number of 2-min onshore
wind regime data segments acquired during Hurricane Ike (especially for the strongest winds), it
is assumed that if the number of data points in each bin is N larger than 15, a representative
sample has been achieved. Binning is advantageous here, as the trend in CD with wind speed can
be determined.
Statistics for the six wind speed bins are shown in Table 5. Mean 2-min wind speeds are nearly
centered in each of their respective bins, except for the 20-25 and 25-30 m/s bins. Ideally, one
would want the wind speeds in each bin to be centered; however, due to the relatively few
9
number of data points in these bins, this is rather difficult to achieve. Wind directions are very
similar for the strongest wind speeds. For slower speeds the winds have a greater southerly
component. This is a result of the winds backing as the hurricane moved north of the region late
in the record (where the weaker winds were observed). Regardless, mean wind directions for
each bin are within 20º (with relatively small standard deviations), showing that a very similar
fetch existed throughout the record.
Table 5: The drag coefficient referenced to 10 m for different wind speed bins (and other
statistics/parameters). 2-min mean wind speed data segments were partitioned into six wind speed bins (along
with the corresponding 2-min mean wind direction and drag coefficient). Observed wind speeds at 2.25 m
were translated to 10 m using the neutral stability log-law.
U 10 Bins (m/s)
Number of 2-min Segments
Mean Wind Speed
St. Dev. Wind Speed
Mean Wind Direction
St. Dev. Wind Direction
3
Mean Roughness Length × 10
3
St. Dev. Roughness Length × 10
3
Mean Drag Coefficient × 10
3
St. Dev. Drag Coefficient × 10
5-10
197
8.47
1.16
200
4.95
1.32
1.25
1.90
0.386
10-15
196
12.1
1.50
210
4.64
1.68
1.66
1.99
0.431
15-20
90
17.4
1.50
219
4.70
1.77
1.25
2.07
0.343
20-25
33
21.8
1.33
214
2.06
2.14
1.62
2.16
0.365
25-30
49
27.9
1.41
217
5.56
2.37
1.86
2.22
0.370
30-35
18
31.0
0.812
220
6.67
2.11
1.37
2.16
0.353
A scatter plot of CD versus U 10 (not shown) determines that these quantities are not correlated (R2
< 0.3). Therefore, ‘binning’ becomes helpful. Binned drag coefficient are plotted against wind
speed in Figure 5. It can be seen that CD varies little within this wind speed range, where the
difference between the maximum and minimum values is 0.32×10-3. The drag coefficient
increases with wind speed initially, reaches a limiting value of 0.0022 at a wind speed near 28
m/s, and decreases for wind speeds above 28 m/s. Although there are only 18 data points in the
maximum wind speed bin, this decreasing trend (or plateau) is clearly evident.
A caveat to the results presented above is that the data that make up the lowest wind speed bin
(5-10 m/s) generally occurred well after the eye passed. It is estimated that the surge likely
receded from this portion of the Bolivar Peninsula after about 12 hours; exposing the land
surface between the channel and the probe. The latter portion of the time record analyzed above
(22 hours) was truncated so that only 12 hours of data remained. Since the strongest winds
occurred early in the record, only the two lowest wind speed bins were affected by the truncation
(Figure 5). The lowest wind speed bin showed a significant decrease in CD to a mean of 0.00168.
It should be noted that only 15 data segments were in the 5-10 m/s bin (over 100 in the 10-15 m/s
bin). This suggests that the long record could potentially ‘contaminate’ data in the lowest wind
speed bins. Further analysis will be conducted when computed surge levels become available.
COMPARISON TO OTHER STUDIES
It is useful to compare drag measurements in this complex environment with other studies
(Figure 5). Three well-known deep water studies were utilized [1,12,14]. The data were also
compared to shallow water drag coefficients reported in [37]. The first comprehensive set of
deep water drag coefficient measurements in hurricane conditions were obtained by [1]. They
10
estimated CD by fitting the logarithmic law wind profile to four different vertical depths: 10-100,
20-100, 10-150, and 20-150 m. Their drag coefficient values in Figure 5 are an average of the
four layers. Both the present study and [1] indicate that CD reaches a limiting value and decreases
for higher wind speeds. Hurricane Ike and deep water limiting values are similar, but the former
occurred at wind speeds below hurricane force. In [1], mean drags reached a limiting value of
0.0022 at a wind speed near 33 m/s. Laboratory simulation of deep water drag in extreme winds
(reported by [14] for the momentum budget method) are consistent with a leveling off around 33
m/s, but with a marginally higher limiting value of 0.0026. Drag coefficient data collected during
CBLAST experiment [12] for Hurricanes Fabien and Isabel (2003) indicate a leveling off around
0.002 at markedly lower wind speeds near 22-23 m/s. Based on the presented studies, coastal
drag coefficient behavior is in accord with deep water, where a limiting value is reached and CD
decreases for higher wind speeds.
Examination of Figure 5 also reveals that coastal drags are significantly higher for low to
moderate wind speeds of < 25 m/s (regardless of record length). [1,37] shoaling and deep water
data decreased rapidly for wind speeds below hurricane force. Crudely extrapolating their results
to slower winds (e.g., 10 m/s) the drag coefficient would be considerably less than those obtained
here during Ike. Laboratory observations also indicate lower drags for lighter winds and that the
trend in CD with increasing wind speed is much steeper than the present study. This result is
likely a consequence of the complex wave conditions in the Houston ship channel generating a
‘rough’ (wave) surface even under light winds.
Figure 5: Comparison of mean 10 m drag coefficient in hurricane conditions for this study (coastal), shallow
water [37], open ocean measurements from [1] (mean of the four layers) and [12], and in simulated extreme
wind in the laboratory from [14] (using the momentum budget method).
11
SUMMARY AND CONCLUDING REMARKS
Field observations of nearshore wave conditions and coastal wind measurements were obtained
during the passage of Hurricane Ike. Three wave gauges were deployed adjacent to landfall in
the shoaling wave region at a mean depth of 10.4 m. They were closely collocated with StickNet
110A placed on the Bolivar Peninsula. The probe measured wind data at 2.25 m with the mean
flow coming across the Houston ship channel; not directly from the Gulf of Mexico. Wave
conditions in the channel were extremely complex. Strong cross-channel winds generated fetch
limited waves across the 3 km wide channel. Waves coming into the ship channel from the ocean
and strong currents complicated the situation. Due to this interaction, wave gauges deployed
offshore Port Bolivar were not representative of the waves in the channel. High quality hindcasts
(when available) will arguably provide the best characterization of waves in the channel. The
surface layer quantities presented are representative of the wave roughness in the waterway.
Results obtained in the study provide the following conclusions.
Observed drag coefficient behavior is similar to that found in deep water [1,14], where CD
increased with wind speed, reaches a limiting value, and decreases thereafter. Aerodynamic drag
increased with wind speed until around 28 m/s where a limiting value of 0.0022 was reached.
This provides evidence that the limiting CD value at this location is on the order of deep water
values. This may also be the case in regions with complex bathymetry and coastal formations
that interfere with the local waves, fetch limited conditions, or in regions with a wide shallow
continental shelf (where the largest waves are well offshore). Saturation of CD is likely a result of
sea spray and skimming flow as the waves are fetch-limited and very steep. Although higher
wind speed data are needed, the drag coefficient tends to decrease with wind speeds greater than
28 m/s. A major difference between deep and shallow water drag exists at lower wind speeds.
Drag coefficient at lower wind speeds are much greater than deep water values [1] or those found
in the laboratory [14]. This result could be a consequence of the complex wave conditions in the
channel creating a ‘rougher than normal’ surface under light to moderate winds. Based on this
analysis, storm surge models using a deep water wind speed dependent drag coefficient may be
slightly underestimating hurricane storm surge, and additional forcing parameterizations are
needed in such complex roughness situations.
Structures built on the hurricane prone coast are currently being designed to withstand wind
loads specified by Exposure C. Data obtained in complex seas during Hurricane Ike suggest that
this region is smoother than that prescribed by ASCE 7-05. Surface roughness values (Table 4)
are an order of magnitude smaller than open terrain (zo = 30 mm), and are within the range of
Exposure D (1 < zo < 5 mm). An average of the six wind speed bins yields a mean roughness
length of 1.90 mm (Table 5). ASCE Exposure C corresponds to a CD = 4.75×10-3, which is more
than twice the maximum value obtained here. These findings suggest that nearshore roughness is
less than that prescribed by ASCE in hurricane regions, indicating that current design wind
speeds may be underestimated.
ACKNOWLEDGEMENTS
Funding support for the lead author was provided by the National Science Foundation
Interdisciplinary Graduate Research and Training (IGERT) program under Grant No. 0221688
and Texas Tech University. We want to acknowledge and thank the UF/UND wave/surge
12
deployment team and the TTU Hurricane Research Team (TTUHRT) for collecting invaluable
data during Hurricane Ike.
REFERENCES
[1] M.D. Powell, P.J. Vickery, T.A. Reinhold. Reduced drag coefficient for high wind speeds in tropical
cyclones, Nature. 422 (2003) 279-283.
[2] U.S. Census Bureau. Facts for features: 2009 hurricane season begins. Retrieved April 19, 2009,
from http://www.census.gov/PressRelease/www/releases/archives/facts_for_features_special_editions/013534.html.
[3] S.D. Smith. Wind stress and heat flux over the ocean in gale force winds, J. Phys. Oceanogr. 10
(1980) 709-726.
[4] W.G. Large and S. Pond. Open ocean momentum flux measurements in moderate to strong winds, J.
Phys. Oceanogr. 11 (1981) 324–336.
[5] M.J. Yelland and P.K. Taylor. Wind stress measurements from the open ocean, J. Phys. Oceanogr. 26
(1996) 541-558.
[6] M.A. Donelan. The dependence of the aerodynamic drag coefficient on wave parameters, in:
Proceedings of the first International Conference on Meteorology and Air–Sea Interaction of the Coastal
Zone (Netherlands, 1982), American Meteorological Society, Boston, 1982. pp. 381-387
[7] S.S. Ataktürk and B.B. Katsaros. Wind Stress and Surface Waves Observed on Lake Washington, J.
Phys. Oceanogr. 29 (1999) 633-650.
[8] J.J. Buckles, T.J. Hanratty, R.J. Adrian. Turbulent flow over large-amplitude wavy surfaces, J. Fluid
Mech. 140 (1984) 27-44.
[9] M.L. Banner and W.L. Peirson, Tangential stress beneath wind-driven air water interfaces, J. Fluid
Mech. 364 (1998) 115-145.
[10] W. Gong, P.A. Taylor, A. Dörnbrack. Turbulent boundary-layer flow over fixed aerodynamically
rough two-dimensional sinusoid waves, J. Fluid Mech. 312 (1999) 1-37.
[11] J.A.T. Bye and A.D. Jenkins. Drag coefficient reduction at very high wind speeds, J. Geophys. Res.
111 (2006) C03024.
[12] P.G. Black, E.A. D’Asaro, W.M. Drennan, J.R. French, P.P. Niiler, T.B. Sanford, E.J. Terrill, E.J.
Walsh, J.A. Zhang. Air-sea exchange in hurricanes: synthesis of observations from the coupled boundary
layer air-sea transfer experiment, Bull. Amer. Meteor. Soc. 88 (2007) 357-384.
[13] E. Jarosz, D.A. Mitchell, D.W. Wang, W.J. Teague. Bottom-up determination of air-sea momentum
exchange under a major tropical cyclone, Science 315 (2007) 1707-1709.
[14] M.A. Donelan, B.K. Haus, N. Ruel, W.J. Stianssnie, H.C. Graber, O. B. Brown, E.S. Saltzman. On
the limiting aerodynamic roughness of the ocean in very strong winds, J. Geophys. Res. 31 (2004)
L18306.
[15] V.K. Makin. A note on the drag of the of the sea surface at hurricane winds, Boundary-Layer
Meteorol. 115 (2005) 169-176.
13
[16] V.N Kudryavtsev. On the effect of sea drops on the atmospheric boundary layer, J. Geophys. Res.
111(2006) C07020.
[17] V.N Kudryavtsev and V.K. Makin. Aerodynamic roughness of the sea surface at high winds,
Boundary-Layer Meteorol. (2007) 289–303.
[18] E.B. Thornton and R.T. Guza. Energy Saturation and Phase Speeds Measured on a Natural Beach,
J. Geophys. Res. 8 (1982) 9499-9508.
[19] R.A Holman and A.H. Sallenger. Setup and swash on a natural beach, J. Geophys. Res. 90 (1985)
945–953.
[20] R.G. Dean and R.A. Dalrymple. Water wave mechanics for engineers and scientists, World
Scientific, Singapore, 1991.
[21] K.T. Holland, B. Raubenheimer, R.T. Guza, R.A. Holman. Runup kinematics on a natural beach, J.
Geophys. Res.100 (1995) 4985-4993.
[22] W.H. Munk and M.A. Traylor. Refraction of ocean waves: a process linking underwater topography
to beach erosion, J. of Geology. 55 (1947) 1-26.
[23] M.L. Banner and W.K. Melville. On the separation of air flow over water waves, J. Fluid Mech. 77
(1976) 825–842.
[24] H. Kawamura and Y. Toba. Ordered motion in the turbulent boundary layer over wind waves, J.
Fluid Mech. 197 (1988) 105-138.
[25] N. Reul. Etude expe’rimentale de la structure de l'e´coulement d'air au-dessus de vagues
courtesde´ferlantes, Université de la Mediterranee, France, 1998.
[26] J.J. Westerink, J.C. Feyen, J. H. Atkinson, R.A. Luettich, C.N. Dawson, M.D. Powell, J.P. Dunion,
H. J. Roberts, E.J. Kubatko, H. Pourtaheri. A new generation hurricane storm surge model for Southern
Louisiana, in review (2005).
[27] F. Anctil and M.A. Donelan. Air-water momentum flux observations over shoaling waves, J. Phys.
Oceanogr. 26 (1996) 1344-1353.
[28] P.J. Vickery and P.F. Skerlj. Elimination of exposure D along the hurricane coastline in ASCE 7, J.
Struct. Eng. 26 (2000) 545-549.
[29] D.A. Smith. Personal Communication. September 2008.
[30] S.R. Massel. Ocean surface waves: their physics and prediction. World Scientific, River Edge, New
Jersey, 1996.
[31] P Skinner. Observations of the surface boundary structure within supercell thunderstorms. Masters
Thesis, Texas Tech University, Lubbock, TX.
[32] 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.
[33] J. Counihan. Adiabatic atmospheric boundary layers – review and analysis of data from period
1880-1972, Atmospheric Environment. 9 (1975) 871-905.
14
[34] J.L. Schroeder and D.A. Smith. Hurricane Bonnie wind flow characteristics as determined from
WEMITE, J. Wind Eng. Ind. Aerodyn. 91 (2003) 767–789.
[35] J.S. Bendat and A.G. Piersol. Random data: analysis and measurement procedures, John Wiley &
Sons, New York, 1986.
[36] R.B. Stull. An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers,
Dordrecht/Boston/London, 1988.
[37] M.D. Powell. High Wind Drag Coefficient and Sea Surface Roughness in Shallow Water, in: Final
Report to the Joint Hurricane Testbed, JHT, 2008. pp. 1-24.
15