Modeling of tropical cyclone winds and waves for emergency management

Ocean Engineering 30 (2003) 553–578 www.elsevier.com/locate/oceaneng

Modeling of tropical cyclone winds and waves for emergency management Amal C. Phadke a,1, Christopher D. Martino a,2 Kwok Fai Cheung a,∗, Samuel H. Houston b,3 a

Department of Ocean and Resources Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA b Hurricane Research Division, NOAA National Weather Service, Miami, FL 33149, USA

Abstract This paper compares three commonly used parametric models of tropical cyclone winds and evaluates their application in the wave model WAM. The parametric models provide surface wind fields based on best tracks of tropical cyclones and WAM simulates wave growth based on the wind energy input. The model package is applied to hindcast the wind and wave conditions of Hurricane Iniki, which directly hit the Hawaiian Island of Kauai in 1992. The parametric wind fields are evaluated against buoy and aircraft measurements made during the storm. A sensitivity analysis determines the spatial and spectral resolution needed to model the wave field of Hurricane Iniki. Comparisons of the modeled waves with buoy measurements indicate good agreement within the core of the storm and demonstrate the capability of the model package as a forecasting tool for emergency management.  2002 Elsevier Science Ltd. All rights reserved. Keywords: Aircraft wind measurements; Buoy measurements; Hurricanes; Parametric wind models; Tropical cyclones; WAM; Wave model; Waves; Winds

Corresponding author. Tel.: +1-808-956-3485; fax: +1-808-956-3498. E-mail address: [email protected] (K.F. Cheung). 1 Presently at Sea Engineering Inc., Houston, TX 77084, USA 2 Presently at Pacific Missile Range Facility, Department of Defense, Kekaha, HI 96752, USA 3 Presently at Central Pacific Hurricane Center, NOAA National Weather Service, Honolulu, HI 96822, USA ∗

0029-8018/02/$ - see front matter  2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 9 - 8 0 1 8 ( 0 2 ) 0 0 0 3 3 - 1

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1. Introduction

The Hawaiian and many other Pacific islands are at risk of severe damage and life threatening conditions from large swells and coastal flooding produced by tropical cyclones. A simulation package is being developed at the University of Hawaii, in collaboration with the Pacific Disaster Center, to integrate the modeling of storm waves and surge generated by tropical cyclones as well as the subsequent coastal wave processes and run-up on dry land. The present paper deals specifically with the modeling of the wind and wave fields in the open ocean. The computed deepwater waves are used for coupling with a storm surge model and as boundary conditions for the modeling of coastal wave processes and runup. Advancements in wave theory have led to the development of a series of spectral wave models that can produce accurate representation of intricate sea-states when provided realistic surface wind input. WAM is a third generation spectral wave model that simulates wave growth based on wind energy input (Komen et al., 1994). The WAM Development and Implementation Group (WAMDIG, 1988) has done extensive verification analysis in the North Atlantic Ocean and the North Sea and briefly described modeled waves for three tropical cyclones in the Gulf of Mexico. Cavaleri et al. (1989) investigated the application of WAM in the shallow waters of the Adriatic Sea. Zambresky (1989) validated a global WAM model using buoy data taken from the Gulf of Alaska, the Hawaiian Island region, the east coast of the US, and the North Atlantic. Janssen et al. (1997) showed a global WAM model can produce up to 5 days of useful forecasts in the Northern Hemisphere. The existing WAM models are normally used to simulate waves due to weather systems much larger than tropical cyclones and their operational experience might not be directly applicable here. The wind field of a tropical cyclone is composed of a relatively small and intense core, in which wind speeds and directions change rapidly in space and time. This poses a problem for the existing global WAM models, which usually have spatial resolution of one degree and cannot fully depict the core of the wind or wave field. Furthermore, a wave model must have high spectral resolution to depict the rapidly changing and complex wave field. Most regional and global WAM models have directional resolution of 24 bins and might not adequately resolve the multi-directional wave field generated by a tropical cyclone. The application of WAM to tropical cyclone events requires surface wind input over the entire course of the storms. Mesoscale meteorological models can provide three-dimensional wind structures of tropical cyclones through lengthy computations. For emergency management, it is more practical to use a parametric model to specify the surface wind fields based on National Oceanic and Atmospheric Administration (NOAA), National Weather Service (NWS) Forecast/Advisories, which are issued every 6 h in the event of a tropical cyclone. This study compares the modified Rankine vortex model, the Holland model, and the Sea, Lake and Overland Surge from Hurricanes (SLOSH) wind model, and evaluates their application in WAM through a hindcast study of Hurricane Iniki, which directly hit the Hawaiian Island of Kauai in 1992. The compact wind structure and high intensity of Hurricane Iniki

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provide a demanding case study to examine the capability of the wind and wave models and to test the proposed modeling procedures for tropical cyclone events.

2. The wave model (WAM) WAM is a third generation ocean wave prediction model. Komen et al. (1994) provided a detailed description of the theoretical background and numerical procedures. The governing equation describes the energy balance for wave growth based on wind energy input. The evolution of a two-dimensional wave spectrum F in time and space is defined by the transport equation ∂ ∂ ∂ ∂F ⫹ (cosf)⫺1 (f˙ cosfF) ⫹ (l˙ F) ⫹ (q˙ F) ⫽ S ∂t ∂f ∂l ∂q

(1)

where t denotes time, q is the wave direction, f and l are coordinates in latitude and longitude respectively, f˙ and l˙ represent the group velocity components in the respective coordinates, q˙ represents the rate of change of wave direction, and S includes energy input due to wind stress, dissipation due to white capping, and nonlinear energy exchanges between wave components. A bottom friction term can be included in S, if wave shoaling is also considered. The Deutshes Klimarechenzentrum at Hamburg, Germany supplied the WAM Cycle-4 source code. Gu¨ nther et al. (1992) describes the input requirements and operations of WAM Cycle-4. The user needs to specify the modeled region in a Cartesian or spherical coordinate system, the spatial and spectral resolution, a series of wind fields, and the time-step sizes. If refraction is considered, the user needs to supply the bathymetry or background currents. The wave growth equation is solved using a second-order, central difference scheme. The time step for the integration of the transport equation must meet the Courant–Freidrich–Lewy (CFL) criterion and be equal to or a multiple of the time interval of the source function integration. The initial condition can either correspond to zero wave energy or a uniform wave height. Depending upon the fetch and wind field, a period of time in the beginning of the simulation is needed to attain a developed sea state. The model can output time series of computed wave parameters at specified locations or snapshots of the results over the entire region at specified times.

3. Modeling of tropical cyclone winds Tropical cyclones are one of the most difficult phenomena in the atmosphere to fully describe and predict even with the highly sophisticated mesoscale models. Wind measurements from surface platforms, satellites, and aircraft reconnaissance may be available during and prior to landfall, but are seldom sufficient to describe the threedimensional and constantly changing wind structures over the entire course of their existence. Engineers and scientists often resort to using parametric models to

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approximate the two-dimensional wind structure within a tropical cyclone in practical applications. 3.1. Parametric wind models There are several parametric wind models, each of which has been shown to be valid and useful for at least one tropical cyclone event in a particular region. Essential to a parametric model is the representation of the wind flow in an idealized stationary tropical cyclone by concentric circles. The wind speed is zero at the center and increases rapidly to its maximum at the radius of maximum wind and then decreases gradually to zero at large radii. Three commonly used parametric wind models: the modified Rankine vortex, SLOSH wind, and Holland models are summarized in this section. The modified Rankine vortex model uses a shape parameter X to adjust the wind speed distribution in the radial direction V ⫽ Vmax V ⫽ Vmax

冉 冊 冉 冊 r

X

Rmw Rmw r

X

for r ⬍ Rmw

(2)

for r ⱖ Rmw

(3)

where r is radial distance from the center of the storm, Rmw is the radius of maximum winds, and Vmax is the maximum wind speed. The value of X has been determined empirically from observed tropical cyclones to have a range of 0.4⬍X⬍0.6 (Hughes, 1952). Although the value of X can be used as a calibration parameter for hindcast calculation, an average value of 0.5 is used here to test the predictive capability of the model. The NWS currently uses the SLOSH model for storm surge computation for coastal locations and inland waters affected by tropical cyclones (Jelesnianski et al., 1992). It is driven by a parametric wind model, which has been tested against NOAA Hurricane Research Division’s observation-based surface wind fields and found to produce realistic values (Houston and Powell, 1994; and Houston et al., 1999). This SLOSH wind model gives the wind speed as V ⫽ Vmax

2Rmwr . R ⫹ r2 2 mw

(4)

This equation does not involve a tuning parameter and is applicable within and beyond Rmw. The SLOSH wind model produces a wind profile, which is smoother near Rmw compared to the modified Rankine vortex model. Both the modified Rankine vortex and SLOSH wind models require user specified Rmw and Vmax. For general applications, it is more convenient to calculate the wind fields based on the storm central pressure, which is commonly available for the life span of a tropical cyclone. Atkinson and Holliday (1977) studied numerous tropical cyclones in the northwest Pacific and constructed the empirical relationship for Vmax in terms of the storm central pressure pc

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Vmax ⫽ 3.44(1010⫺pc)0.644

557

(5)

where Vmax and pc have the units of m/s and mb respectively. Despite the region where the data was taken from, Eq. (5) has been shown to give accurate estimates of Vmax for tropical cyclones in various other basins (Powell and Houston, 1998). This relation is used to compute Vmax for the modified Rankine vortex and SLOSH wind models. The Holland model provides a wind field directly from input values of Rmw and pc (Holland, 1980). It is based on the exponential distribution of the atmospheric pressure field proposed by Schloemer (1954) with the addition of a peakedness parameter B

冋 冉 冊册

Rmw p⫺pc ⫽ exp ⫺ pn⫺pc r

B

(6)

where p is the pressure at r and pn is the ambient pressure. The wind speed distribution in the radial direction is determined from the equilibrium between the centrifugal force of a rotating air mass with the atmospheric pressure gradient and the Coriolis forces. The resulting wind speed is called the gradient wind speed and is given by V⫽

冪

冉 冊 冋 冉 冊册

B(pn⫺pc) Rmw B Rmw exp ⫺ r r r

B

⫹

r2f2 rf ⫺ 4 2

(7)

where f is the Coriolis parameter and r is air density. The Coriolis force is relatively small compared to the pressure gradient and centrifugal forces near Rmw and Eq. (7) becomes Vmax ⫽

B(pn⫺pc) . re

冪

(8)

Holland (1980) compared his model results and Atkinson and Holliday’s (1977) estimates to the measured data for the northwest Pacific tropical cyclones studied by Dvorak (1975), and obtained good agreement. Harper and Holland (1999) recently suggested an empirical relation for B pc⫺900 B ⫽ 2⫺ for 1.0 ⬍ B ⬍ 2.5. 160

(9)

A value of B=1 brings the equation back to Schloemer’s wind profile, which is characterized with a lower wind speed at Rmw and a more gradual decrease beyond Rmw. 3.2. Adjustments of modeled winds The axisymmetric horizontal wind fields generated by the parametric wind models correspond to mean boundary-layer or gradient winds above the surface. The computed wind speed is adjusted to the standard 10-m elevation using

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V10 ⫽ KmV

(10)

where Km is a correction factor. Harper and Holland (1999) suggested that Km = 0.7 for the Holland model, whereas Powell (1987) suggsted 0.75⬍Km⬍0.8 for the SLOSH wind model. Based on comparisons between collocated aircraft and surface buoy observations in the vicinity of hurricanes, Powell and Black (1990) later confirmed Km = 0.8 for SLOSH. Since the modified Rankine vortex model uses the same input Vmax as SLOSH, the same correction factor of 0.8 also applies. The resulting wind speed from Eq. (10) corresponds to the sustained winds, which are regarded as having an averaging time of 8 to 10 minutes. Krayer and Marshall (1992) provided gust factors applicable to tropical cyclone winds. A multiplication factor of 0.92 converts the sustained wind speed to hourly average for WAM input. The parametric wind models assume a circular wind flow pattern and do not adequately depict the actual surface wind directions, which point toward the center of the storm. For a stationary tropical cyclone, the NWS standard project hurricane approximates the inflow angle at the surface as a function of r as

冉

b ⫽ 10° 1 ⫹

r Rmw

b ⫽ 20° ⫹ 25°

冉

冊

for 0 ⱕ r ⬍ Rmw

r

Rmw

冊

⫺1 for Rmw ⱕ r ⬍ 1.2Rmw

b ⫽ 25° for ⱖ1.2 Rmw

(11a) (11b) (11c)

where b is measured inward from the isobars (Bretschneider, 1972). Based on Eq. (11a,b,c), b varies linearly from 10° at the center to 20° at Rmw, and then increases linearly to 25° at 1.2Rmw, and remains at 25° beyond 1.2Rmw. In the Northern Hemisphere, tropical cyclone winds spin in the counter-clockwise direction. The forward motion of a tropical cyclone increases the wind speed in the right quadrants and decreases the wind speed on the left. Jelesnianski (1966) suggested the following equation to account for the forward motion of a slow-moving tropical cyclone: U(r) ⫽

Rmwr V R2mw ⫹ r2 F

(12)

where VF is the forward velocity of the storm and U is the correction term, which is vectorially added to the axisymmetric wind velocity computed from a parametric model. This correction is equal to zero at the center of the storm and increases to a maximum of 0.5VF at Rmw, and then decreases radially outward to zero. Eq. (12) ensures that the forward velocity effects are limited within the storm. This approach is recommended by the Shore Protection Manual (1984) and used in SLOSH for storm surge calculation (Jelesnianski et al., 1992). The forward velocity correction, however, is not universally agreed upon. Some researchers have suggested that a constant value of 0.5VF or VF should be added throughout the entire storm system (e.g., Bretschneider, 1972; Harper and Holland,

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1999). Furthermore, Bretschneider’s (1972) correction has an additional term to account for the modification of the wind fields due to change in storm direction. These approaches create an unrealistic wind flow outside the storm, unless the corrections are abruptly cut off at a certain distance from the center creating a discontinuity in the wind field. Based on aircraft measured winds, Houston et al. (1999) showed that the SLOSH wind model along with the forward-velocity correction based on Eq. (12) can adequately depict the surface wind fields of a number of landfalling tropical cyclones in the Atlantic basin.

4. Hurricane Iniki There was an average of 3.2 tropical cyclones per year in the Central North Pacific basin during the period 1966–97 (Chu and Clark, 1999). Hurricane Iniki of 1992 is chosen for this case study, because it is the most recent landfall and has the best available atmospheric and oceanographic data record. The storm brought extreme winds and flooding to the Hawaiian Island of Kauai. The American Insurance Services Group and the Insurance Information Institute ranked the $1.6 billion in losses from Iniki as the fifth most costly insured catastrophe in US history (Storm Data, 1992). 4.1. Storm history Taken from the more detailed account by Storm Data (1992), the system that would later become Iniki was first declared to be a tropical depression 2690 km southwest of Baja California near 12°N 135°W at 2100 UTC 6 September, 1992. The system was upgraded to tropical storm status and named Iniki by the Central Pacific Hurricane Center (CPHC) at 0300 UTC 8 September. Fig. 1 shows the storm track after Iniki passed 140°W. With further intensification and an increase in forward speed to 6.5 m/s, Iniki developed into a hurricane at 0900 UTC 9 September, when it was 816 km south–southwest of Hilo, Hawaii and moving west–northwest. Later on 10 September, Iniki started to take a more northwestward track, and by 11 September, it continued to turn in a more northward direction, when it was about 640 km south of Lihue, Kauai. Hurricane Iniki made landfall on the south coast of Kauai at approximately 0120 UTC 12 September. Fig. 2 provides a satellite image of the hurricane at landfall. The maximum sustained wind speed was in excess of 60 m/s. Forty minutes after landfall, Iniki’s center departed the northern coast and continued on a northward track. The hurricane brought extensive inundation from wave runup superimposed on the storm surge. The maximum coastal flooding occurred along the southeast coast of Kauai, which was located in the right-forward quadrant of Iniki during landfall. The south coast of Kauai is particularly vulnerable to high surf because of the steep offshore slope. The tide gauges at Port Allen and Nawilwili recorded a storm-water level of about 2 m above Mean Lower Low Water (MLLW). Due to high surf, the storm water reached a maximum level of 9 m, with a typical range

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Fig. 1. Path of Hurricane Iniki.

of 2–5 m. Sea Engineering, Inc. (1993) and Fletcher et al. (1995) provided a survey of the coastal inundation on Kauai due to Iniki. Chiu et al. (1995) provided a detailed account of Iniki’s impact on Kauai. 4.2. Storm data The three parametric wind models are customized to use a common set of input parameters available through NWS Forecast/Advisory products, which are updated every 6 h during a tropical cyclone. Table 1 shows the best and enhanced tracks of Hurricane Iniki after 0000 UTC 09 September 92, when the storm passed 150°W and subsequently became a Saffir–Simpson scale Category 1 Hurricane. The best track was constructed by CPHC after the event and contains the location, minimum central pressure, as well as the maximum 1-min sustained wind speed at 6-h intervals. The enhanced track was produced by NOAA Hurricane Research Division (HRD) based on archived aircraft measured winds. It contains the location of the circulation center at 1-h intervals for 15 h prior to landfall. The two tracks are not identical, because the best track is based on additional sources of data including satellite images. These observations of the hurricane ‘center’ may not exactly match the circulation center found by aircraft flying inside the storm. In the hindcast calculation

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Fig. 2.

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Satellite image of Hurricane Iniki at landfall (Courtesy of NOAA/NWS).

here, the best track is augmented by the enhanced track to provide more detailed circulation center locations to calculate the wind fields prior to landfall. The most crucial parameter, and at the same time elusive to quantify, is the radius of maximum winds, Rmw. In reality, there is no defined circle where the maximum sustained winds circulate around the storm center. The maximum wind speed may be found in well-developed tropical cyclones within the intense rain-bands or even an outer eye-wall (Willoughby et al., 1982). The rain-bands do not wrap around the eye in a circular flow, but often are segmented around the storm in a spiral pattern as shown in Fig. 2. To add to the ambiguity, Rmw is not very well defined for a weak cyclone and varies throughout the life of the storm (e.g., Croxford and Barnes, 2002). Recreating the wind field of a tropical cyclone as it moves along a path is difficult when considering parameters such as Rmw. The common approach is to use one Rmw throughout the entire storm analysis. This is done to minimize the uncertainty associated with repeatedly changing Rmw during the storm. US Air Force Reserves (AFRC) reconnaissance aircraft measurements are avail-

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Table 1 Best and enhanced tracks of Hurricane Iniki 1992 UTC(H D/M)

0000 0600 1200 1800 0000 0600 1200 1800 0000 0600 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 0000 0010 0020 0600 1200

09/09 09/09 09/09 09/09 10/09 10/09 10/09 10/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 11/09 12/09 12/09 12/09 12/09 12/09

NWS best track Long (°W)

Lat (°N)

150.2 151.6 152.9 154.3 155.5 156.9 157.8 158.6 159.3 159.8 160.2 – – – – – 160.0 – – – – – 159.8 – – 159.4 159.0

12.4 12.7 13.0 13.4 13.8 14.3 14.7 15.2 15.9 16.8 18.2 – – – – – 19.5 – – – – – 21.9 – – 23.7 25.7

HRD enhanced track Long (°W) – – – – – – – – – – 159.967 159.957 159.934 159.911 159.888 159.871 159.891 159.869 159.848 159.830 159.832 159.784 159.708 159.684 159.666 – –

pc (mb)

Lat (°N) – – – – – – – – – – 18.058 18.246 18.447 18.708 18.939 19.172 19.467 19.803 20.140 20.474 20.798 21.301 21.906 22.230 22.523 – –

996 992 992 984 980 960 960 951 948 947 940 – – – – – 945 – – – – – 945 – – 959 980

able for nearly 18 h from 1000 UTC 11 September 1992 through the time of Iniki’s landfall on Kauai. The AFRC WC-130 aircraft passed through Iniki’s flight-level circulation center at approximately 3-km (700 mb) altitude. The method of Powell et al. (1996) provides adjustment of the flight-level winds to the surface. The resulting wind speeds are equivalent to 10-min means at 10-m elevation and are valid for marine exposure only. The wind speeds in the form of radial profiles across the storm provide useful data to verify the parametric wind models. Examination of the adjusted wind fields at the surface provides an average Rmw of 23 km, which is used in the three parametric wind models in this case study. Fig. 1 also shows the locations of four National Data Buoy Center (NDBC) moored buoys operating in the vicinity of the Hawaiian Islands during Hurricane Iniki. The storm passed within 250 and 73 km, respectively, of NDBC Buoys 51002 and 51003 (referred to as Buoys 2 and 3), providing surface wind and wave measurements on the left and right sides of the storm track. The other two buoys near Hawaii offer

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minimal comparison value, since they were located at much greater distances away from the storm. The NDBC buoys recorded wind speed and direction for 8.5 min at 1-h intervals. For comparison with the wind model output, the buoy winds were converted from the 5-m level, where they were recorded, to the standard 10-m level using the algorithm developed by Liu et al. (1979). The buoys recorded the significant wave height and peak period for 20 min at 1-h intervals. The significant wave height is based on the Rayleigh distribution, which is strictly applicable to a narrowbanded spectrum. Although this is not the case in tropical cyclone conditions, this is considered to be the most appropriate method of quantifying wave heights according to a sea state.

5. Results and discussion 5.1. Hurricane Iniki winds Both the maximum wind speed and the distribution are important for wave hindcast calculations. Fig. 3 compares the modeled wind profiles with the adjusted AFRC measurements across the center of the storm in the north-south and east-west directions around noon on 11 September 1992. The positive r axis in the figure points toward the east or north. The times for the wind profiles were recorded when the aircraft passed through Iniki’s flight-level center. The storm center was approximately at 18.1°N and 160.0°W and moving at a forward speed of 5.5 m/s in the northerly direction. The maximum winds occur at 23 km to the east of the storm center, where the storm forward motion effect is maximum and directly adds to the counterclockwise cyclonic flow. The modified Rankine vortex and SLOSH wind models use the same pressure–velocity relation of Atkinson and Holliday (1977) and give the same prediction of the maximum wind speed. Although the Holland model uses a different pressure–velocity relation, it gives a very similar peak wind speed compared to the other two models. Fig. 4 provides a comparison of the modeled wind profiles and the adjusted AFRC measurements approximately 10 h later, when the storm was at 20.9°N 159.8°W approximately 100 km south of Kauai. The storm was moving north at a high forward velocity of 12.7 m/s. The parametric models correctly simulate the wind speeds on the left and right sides of the storm and demonstrate the validity of the forward velocity correction of Jelesnianski (1966) even for a fast-moving hurricane. The modified Rankine vortex model, in comparison to the other two models, produces narrower peaks and more gradual attenuation of the wind speed from the center and gives the best overall agreement with the measured wind speed. However, the measured winds in both Figs. 3 and 4 show an anomaly starting at about 75 km east and north of the storm center. This might be due to the interaction between Iniki’s low central pressure and the high-pressure ridge northeast of the storm. The large pressure gradient likely increased the wind speed in the northeast quadrant of the storm. It is also possible that the higher wind speeds are due in part to rainbands or convective rings located beyond the Rmw as described by Croxford and Barnes (2002).

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Fig. 3. Modeled wind profiles and adjusted AFRC measurements around noon on 11 Sept. 1992. (a) North–south track through Iniki’s center at 1119 UTC. (b) East–west track through Iniki’s center at 1235. ——, modified Rankine vortex; ------, SLOSH wind model; ········, Holland model; 쐌, aircraft measurement.

The measured and modeled sustained wind speeds and directions at Buoy 2 are shown in Fig. 5. Buoy 2 was located on the right-hand side of Iniki’s track and was within 250 km at the time of the storm’s closest approach. The three parametric models give noticeably different predictions and underestimate the measured wind speeds at this buoy. The modified Rankine wind speed attenuates more gradually in the radial direction and is closest to the measurements. In contrast, the wind direc-

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Fig. 4. Modeled wind profiles and adjusted AFRC measurements on late 11 Sept. 1992. (a) North–south track through Iniki’s center at 2050 UTC. (b) East–west track through Iniki’s center at 2222 UTC. ——, modified Rankine vortex; ------, SLOSH wind model; ········, Holland model; 쐌, aircraft measurement.

tions associated with the three parametric models are very similar and match closely with those recorded by the buoy until 1200 UTC 11 September, when Buoy 2 was approximately 460 km away from the storm. The parametric models do not correctly simulate the wind field far away from the storm center, because other weather systems and their interaction with the storm are not modeled. In addition, the storm made a right turn after it passed Buoy 2. This might have produced complications in the wind field that are not reproduced by the parametric wind models used here.

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Fig. 5. Modeled and measured sustained winds at Buoy 2. (a) Wind speed. (b) Wind direction. ——, modified Rankine vortex model; ------, SLOSH wind model; ········, Holland model; 쐌, buoy measurement.

Fig. 6 shows a comparison of the measured and modeled sustained wind speeds and directions at Buoy 3, which was within 73 km to the west of the storm track near Iniki’s inner core. The modified Rankine vortex, SLOSH wind, and Holland models are in good agreement with the measured data near the maximum observed wind speeds. The modified Rankine vortex model gives higher predictions at low wind speeds and provides better overall agreement with the measured wind speeds for the entire time series. All model computations of wind direction compare well

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Fig. 6. Modeled and measured sustained winds at Buoy 3. (a) Wind speed. (b) Wind direction. ——, modified Rankine vortex model; ------, SLOSH wind model; ········, Holland model; 쐌, buoy measurement.

with the observations, especially when the storm was close to the buoy. Both the modeled and recorded wind directions change rapidly around the time of the peak wind speed, when the storm center passed near the buoy. The results show that all three parametric models are capable of reproducing the wind field near the core of the storm. The good agreement between the computed and measured wind speeds indicates that the parametric models along with their adjustments described in Section

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3.2 can accurately depict the wind condition within the inner core of a tropical cyclone. 5.2. WAM resolution Most global and regional wave models have spatial resolution ranging from 0.083° to 2° and spectral resolution of 25 frequency and 24 directional bins. The simulation of a rapidly changing and compact wave field requires high spatial and spectral resolution. The CPU time can be prohibitive, if a large domain is also required. It is, therefore, necessary to identify the resolution requirements for WAM to adequately simulate a tropical cyclone wave field. Iniki’s compact core provides a demanding test to determine the optimal resolution. In the sensitivity test, the modified Rankine vortex model provides the input wind field of an idealized stationary tropical cyclone corresponding to Iniki at its maximum strength (pc = 938 mb). The computation is performed for a 10°×10° domain with the storm at the center. Grid resolution varies between 0.05°, 0.1°, and 0.2° with time step sizes determined from the CFL criterion as 120, 300 and 600 s respectively. The directional bins considered are 24, 36, 48, and 60, and the frequency bins are 25. The input wind field generates a steady-state wave field after 36 h of simulation time. The computed maximum significant wave height for the various spatial and spectral resolution ranges from 9.0 to 9.2 m, which is typical for a stationary tropical cyclone of this size and intensity. Although the computed maximum significant wave height is not very sensitive to the resolution, the predicted wave field is. Fig. 7 shows the steady-state wave fields computed for the 0.05° grid with 24, 36, 48, and 60 direction bins. Since the simulated storm system is stationary, the computed wave fields are expected to resemble the wind field’s circular pattern. The results show that the waves are primarily generated in the core of the storm, in which the wave field exhibits a circular pattern with directions similar to the winds. The wave field in the core does not show dependence on the number of direction bins used in the computation. As the waves propagate away from the core, they follow an outward spiral pattern and cluster into the prescribed direction bins at large distance from the storm. The wave field in Fig. 7a shows that a WAM model with 24 directional bins might not be able to correctly predict the swell generated by tropical cyclones. Increasing the number of directional bins to 48 reduces the magnitude of the spikes and spreads the wave energy more evenly in all directions as shown in Fig. 7c. Because the wave propagation directions align with the rectangular grid system, a few spikes are still present in the north–south and east–west directions even with 60 direction bins. For the directional resolution of 48 bins, a grid size of 0.1° gives a reasonable depiction of the wave field as shown in Fig. 8a. However, obvious distortion of the circular wave field is observed in Fig. 8b, when the grid size is increased to 0.2°. The results presented in Figs. 7 and 8 are based on 25 frequency bins. Martino (2000) showed that almost identical wave fields can be obtained using 50 frequency bins and confirmed the validity of using 25 frequency bins for not only waves produced by large-scale weather phenomena, but also by tropical cyclones. The analysis has shown that the CPU time increases linearly with the number of

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Fig. 7. Steady-state wave fields for an idealized stationary tropical cyclone using 0.05° grid and 25 frequency bins. (a) 24 direction bins. (b) 36 direction bins. (c) 48 direction bins. (d) 60 direction bins.

frequency and direction bins. When the grid size is reduced from 0.1° to 0.05°, a smaller time step is also required and the resulting CPU time increases tenfold. Based on this parametric study and computing time consideration, the 0.1° grid resolution, 48 directional bins, and 25 frequency bins are recommended for the simulation of Hurricane Iniki. If only the maximum wave conditions are required, 24 directional bins would be sufficient to resolve the wave field near the core of the storm and this will reduce the CPU time by 50%. 5.3. Hurricane Iniki waves The WAM model for this case study extends from 150°W to 165°W and from 10°N to 25°N. The Hurricane Iniki waves are simulated for a 3.5-day period starting

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Fig. 8. Steady-state wave fields for an idealized stationary tropical cyclone using 60 direction and 25 frequency bins. (a) 0.1° grid. (b) 0.2° grid.

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at 0000 UTC 9 September, when the center of Hurricane Iniki crossed into the computational domain. Fig. 9 compares the computed wave conditions with the measurements at Buoy 2, which was located 250 km east of the storm center at its closest approach. The modified Rankine wind field, despite its closer agreement with the wind speed at this buoy, markedly underestimates the significant wave height. The SLOSH wind and Holland models, which produce much weaker winds in this region,

Fig. 9. Modeled and measured wave conditions at Buoy 2. (a) Significant wave height. (b) Mean wave period. ——, modified Rankine vortex model; ------, SLOSH wind model; ········, Holland model; 쐌, buoy measurement.

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result only in slightly smaller wave heights. This can be explained by the fact that the computed wave energy is primarily generated within the core of the storm, in which the three parametric models produce very similar wind fields. Given the large distance between the buoy and the storm, the recorded wave energy at this location was likely generated by weather systems not considered in the parametric models. The high local winds associated with the high pressure gradient northeast of the storm, as observed in Figs. 3 and 4, most likely increased the wave energy recorded at this buoy. The computed wave period based on the modified Rankine wind field shows reasonable agreement with the buoy measurements. The Holland and SLOSH wind models, which produce lower wind speeds and less local seas outside the core of the storm, give longer wave periods as expected. Fig. 10 compares the computed significant wave heights and average periods with the measurements at Buoy 3. The wave heights computed from all three parametric wind models show good agreement among themselves and with the measurements around the time when Iniki passed within 73 km from the buoy. In particular, the modified Rankine winds accurately reproduce the measured wave height for over 24 h around the peak. The wind field and subsequently the waves outside the hurricane, as well as the swell propagating into the computational domain, are not considered here. The computed wave heights deviate from the measurements, when the storm was far from the buoy and other weather patterns prevail. The computed wave period based on the modified Rankine wind input shows strong correlation with the wave height when the storm was near the buoy, and a period of 10.5 s is reasonable for the wave conditions near the core of a compact tropical cyclone. The wave periods computed by the Holland and SLOSH wind fields are longer due to the lack of local seas they generate outside the core of the storm. The recorded wave periods, however, are less than 8 s during the peak of the event and are probably evidence of seas generated locally within the strong winds to the left of the storm. Similar locally generated steep wave conditions were recently measured to the left of the 1998 Hurricane Bonnie in the Atlantic Basin (Wright et al., 2001). The storm forward velocity influences the wave field to a great extent. Fig. 11 shows the computed wave field based on the modified Rankine wind model, which gives the best overall agreement with the buoy measurements. The storm is located at 19.5°N 159.9°W, which is just northeast of Buoy 3, and is moving north at 9.7 m/s at its maximum strength. The computed maximum significant wave height is 13.0 m, compared to 9.0 m for the stationary tropical cyclone of the same size and intensity as shown Fig. 8a. The wave field is not axis-symmetric and does not exhibit the outward spiral pattern under a stationary tropical cyclone. The storm’s forward motion and wave propagation direction coincide in the right quadrants. This results in a nearly continuous transfer of energy from the winds to the waves despite the limited fetch under the hurricane. The waves are higher with longer periods and have similar directions as the winds in these quadrants. The computed wave field in the two left quadrants has lower wave heights and shorter wave periods due to time and fetch limitation as the storm moves out of the wave generation region. The waves in the left quadrants have directions perpendicular to the winds and appear to orig-

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Fig. 10. Modeled and measured wave conditions at Buoy 3. (a) Significant wave height. (b) Mean wave period. ——, modified Rankine vortex model; ------, SLOSH wind model; ········, Holland model; 쐌, buoy measurement.

inate from the right. The wave periods are longer in the two forward quadrants as the high energy waves from the right quadrants propagate away from the storm. Fig. 12 shows the simulated wave field for Hurricane Iniki as it makes landfall and is moving rapidly north at a speed of 14.3 m/s. This forward velocity exceeds the group velocity of the waves and the storm outruns the circulation center of the wave field. The model gives the highest waves on the southeast coast of Kauai near Poipu, where the waves approach the coastline normally causing the most significant flooding. Since refraction is not considered, the simulated waves do not wrap around the island coast. The wave energy propagates along the channels and diffuses behind

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Fig. 11. Modeled wave field at maximum pressure drop using modified Rankine vortex wind input. (a) Significant wave height. (b) Mean wave period. +, storm center; 쐌, buoy locations.

the individual islands. The waves behind the island chain are dominated by locally generated seas with shorter periods and the same general direction as the winds. One of the objectives of the WAM simulation is to provide boundary conditions for the next level of models to simulate coastal wave transformation and runup. Further verification of WAM’s capability to simulate hurricane waves can be made with the

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Fig. 12. Modeled wave field at landfall using modified Rankine vortex wind input. (a) Significant wave height. (b) Mean wave period. +, storm center; 쐌, buoy locations.

measured wind and wave fields of Hurricane Bonnie off the Florida coast as reported by Wright et al. (2001).

6. Conclusions The capability of the modified Rankine vortex, SLOSH, and Holland models to reproduce the buoy and aircraft measured wind data during Hurricane Iniki has been

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examined. All three parametric wind models give similar and reasonable representation of the measurements near the core of the storm. The modified Rankine vortex model gives the best overall agreement, while the SLOSH and Holland models underestimate the wind speed outside the core of the storm. The wind-level and averagingtime adjustments as well as the forward-velocity correction produce reasonable results here. These parametric models do not consider weather systems outside the storm and are not expected to reproduce the wind conditions far away from the center. The sensitivity of the WAM results with respect to the spectral and spatial resolution has been examined using an idealized stationary tropical cyclone corresponding to Iniki at its maximum strength. While the computed maximum wave height is not very sensitive to the model resolution, the resulting wave field is. The wave model requires a grid size of 0.1° and spectral resolution of 48 directions and 25 frequencies to provide adequate representation of Iniki’s entire wave field. If only the wave field in the core of the storm is needed, 24 direction bins would be sufficient to resolve the wave spectrum. Since Hurricane Iniki is considered to be a compact and very intensive tropical cyclone, the recommended spatial and spectral resolution should be sufficient for other storms. The wave fields of Iniki have been computed based on a constant radius of maximum winds of 23 km determined from aircraft measurements. The three parametric wind fields accurately produce the peak wave height measured around the time when the storm passed within 73 km from Buoy 3, but underestimate the measurements at Buoy 2 located 250 km from the storm’s closest approach. The computed wave heights deviate from the measurements, when the buoy was far from the highest winds within the inner core of the storm. The modified Rankine wind input produces a wave field most representative of the storm event. This study has shown that WAM can predict tropical cyclone waves if the wind field is properly modeled and that the parametric wind input can accurately predict the extreme wave conditions under a tropical cyclone for emergency management.

Acknowledgements This work is funded by National Aeronautics and Space Administration, Office of Earth Science, Grant No. NAG5-8748, in collaboration with the Pacific Disaster Center, Kihei, Hawaii. The authors are thankful to the NWS and WAM communities for their assistance with this project. SOEST Contribution No. 5883.

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