Numerical simulation of sea surface directional wave spectra under typhoon wind forcing

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2008,20(6):776-783

NUMERICAL SIMULATION OF SEA SURFACE DIRECTIONAL WAVE SPECTRA UNDER TYPHOON WIND FORCING* ZHOU Liang-ming Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China, E-mail: [email protected] WANG Ai-fang Engineering Reconnaissance and Design Institute, Ocean University of China, Qingdao 266071, China GUO Pei-fang Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China

(Received December 3, 2007, Revised January 7, 2008)

Abstract: Numercial simulation of sea surface directional wave spectra under typhoon wind forcing in the South China Sea (SCS) was carreid out using the WAVEWATCH-III wave model. The simulation was run for 210 h until the Typhoon Damrey (2005) approached Vietnam. The simulated data were compared with buoy observations, which were obtained in the northwest sea area of Hainan Island. The results show that the significant wave height, wave direction, wave length and frequency spetra agree well with buoy observations. The spatial characteristics of the signifciant wave height, mean wave period, mean wave length, wave age and directional spectra depend on the relative position from the typhoon center. Also, the misalignment between local wind and wave directions were investigated. Key words: typhoon, directional spectra, significant wave height, South China Sea (SCS)

1. Introduction  Typhoon-generated wave fields are of interest both scientifically for understanding wind-wave interaction physics and operationally for predicting potential hazardous. A typhoon with intense and fast-varying wind forms a complex ocean waves field which can propagate thousands of kilometers away from the storm center, resulting in dramatic variation of the wave field in space and time. Considerable efforts have been made to measure the directional spectra of storm-generated surface waves to investigate their spectral characteristics. Wyatt[1] described measurements of the directional spectra of storm wave using high-frequency radar to explain the effect of fetch on the directional spectrum of the Celtic Sea storm waves. Wright et al.[2] and Walsh et 

* Biography: ZHOU Liang-ming (1976-), Male, Ph. D., Associate Professor

al.[3] studied the spatial variation of hurricane directional wave spectra for both open ocean and landfall cases using the NASA Scanning Radar Altimeter for the first time. Holt et al.[4] examined the capability of synthetic aperture radar imagery from ERS-1 satellite to track the wave fields induced by an intense storm. Ocean wave modeling is a very useful and convenient way to obtain the spatial and temporal distribution of directional spectra without the limitations associated with measurements, although the simulation may be different from the actual situations because of wind input, model etc.. Zhong et al.[5] simulation the tropical cyclone Winnie (1997) using a triply-nested 3-D nonhydrostatic mesoscale model MM5. Based on WAVEWTCH I and WAVEWATCH II, a full-spectral third-generation wind-wave model, WAVEWATCH III (henceforth denoted as WW3) was developed at the National Oceanic and Atmospheric Administration-National Centers for Environmental Prediction (NOAA-NCEP).

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It has been used in many research programs to study surface wave dynamics, and as the operational wave model of the NCEP for global and regional wave forecast [6]. The WW3 has been validated over a globel-scale wave forecast and a regional wave forecast [7-9]. By the performance of this model, the sea surface directional wave spectra under hurricane conditions was evaluated from a hindcast of hurricane Bonnie in 1998 [10]. Moon et al.[11] constructed the complete wave spectrum with the Coupled Wave Model (CWW) by merging the WW3 wave model spectrum in the vicinity of the spectral peak with the spectral tail parameterization based on the equilibrium spectrum model of Hara and Belcher[12], and did numerical approach to account for misalignment between wind and wave directions. In this study, the WW3 is implemented in the SCS to investigate the directional wave spectrum under typhoon wind forcing. During the typhoon passage, availible buoy data including wind and wave are used to compare the simulated results with the observed data. Brief descriptions of the SCS, typhoon Damrey, wind fields, buoy observed data and WW3 wave model are given in Section II. Comparisons of the simulated typhoon-generated wave characteristics with observations are also given in this section. The wave field characteristics under typhoon wind forcing were discussed in Section ċ. The summary and conclusions are given in the final section. 2. Numerical simulation 2.1 The South China Sea (SCS) As the biggest margin sea of the western Pacific, the SCS is a semi-enclosed tropical sea located between the Asian land mass to the north and west, the Philippine Islands to the east, Borneo to the southeast, and Indonesia to the east, with a total area of 3.5×106 km2. Its southern border is 3oS between the South Sumatra and Karimantan Straits, and its northern border is the Strait of Taiwan from the northern tip of Taiwan to the southeast coast of China. The SCS is occupied by east Asian monsoon. In winter (between December and February), the northeast winter monsoon prevails, and cold fronts often influence the SCS. In summer, from June to August, the southwest monsoon trough and subtropical ridge exist alternatively over the South China Sea, with anticyclones, along with enhanced convection, migrating northward from the equator to the mid-latitudes. In addition, Tropical Cyclone (TC) is a very important weather factor influencing the SCS in summer and autumn. The propagating direction of SCS TCs is mianly west-forward. In the SCS, about more than 25 passages of TCs occur every year, which mainly occur in July and October.

2.2 Typhoon Damrey The Typhoon Damrey formed as a tropical storm east of Philippines on 21 September 21, 2005 and turned to northwest until September 23. During the turn to west the storm was developed into a severe tropical storm at 20:00 on September 23. It further intensified with the direction of southwest, and became a typhoon at 00:00 on September 25 with the maximum wind speed (10 min averaged) of 42 m/s. It propagated to west with the translation speed of 10 km/h -15 km/h and stroke Hainan Island on 26. The Typhoon Damrey made a landfall in the northern part of Vietnam at around 14:00 on September 27 and then weakened into a severe tropical storm. Figure 1 gives the track of the Typhoon Damrey, and Fig.2 gives a satellite image of Typhoon Damrey at 14:44 on September 25, 2005.

Fig.1

Track of Typhoon Damrey. Circles represent the position of typhoon center at 08:00 daily, and the square represents the location of buoy measuring wave and wind

Fig.2 Satellite image of Typhoon Damrey at 14:44 on September 25, 2005 when the typhoon center was located about 180 km east of Hainan Island and tracked westward (provided by Hainan Province Observatory). At this time, the position of typhoon center was at 19.0oN, 112.3oE, and the maximum wind speed (10 min averaged) reached 42 m/s

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2.3 Wind fields Directional spectra associated with a typhoon are very complicated and have quickly varying characteristics in time and space. Therefore, numerical modeling of sea surface directional wave spectra requires input wind data with high resolution. The surface wind fields for the Typhoon Damrey used as input data to the wave model are objective reanalysis wind field dataset, which are assimilated by many sources (including historical weather charts, synoptic maps, NASA QuickSCAT data with a 0.25o resolution, Typhoon Annual and Tropical Cyclone Yearbooks) and provided every six hours with the resolution of 0.2 o×0.2 o. Comparisons were carried out between this wind field data and the observations (given in Section 2.5), and the results show that wind fields produced from the assimilation method are in good agreement with the actual wind fields. 2.4 The wave model The WAVEWATCH-III is designed with more general governing transport equations that permit full coupling with ocean models, improved numerical and physical approaches, such as physics integration scheme, improved propagation schemes (of third order), and improved physics of wave growth and decay. It explicitly accounts for wind input, wave-wave interaction, and dissipation due to white-capping and wave-bottom interaction. The source terms of the WW3 use wind-wave interaction according to Chalikov and Belevich[13], as modified by Tolman[14] Discrete Interaction Approximation (DIA)[15] for nonlinear interactions (as in the WAM), and bottom friction as in the Joint North Sea Wave Project (JONSWAP). The model uses semi-implicit scheme for the source terms and a special treatment on the high frequency tail of the spectrum so that large time integration step can be employed to enhance computational efficiency. It is used to solve the spectral action density balance equation for directional wave-number spectra, and directly compute the non-linear energy interaction among waves at different frequencies to avoid the imposition of restriction on the spectral shape of the predicted spectra. Wave propagation is described by

dN ( k , T ) S ( k , T ) = dt V

(1)

where N (k ,T ) { F (k ,T ) / V is the wave action density spectrum, and F (k ,T ) is the wavenumberdirectional spectrum, V is the relative or intrinsic (radian) frequency, S represents the net effect of source and sink term for the spectrum F (k ,T ) , k and T are the wave-number and direction. The net source term S is generally considered to consist of

three parts, a wind-wave interaction term Sin , a nonlinear wave-wave interaction term S nl and dissipation (‘white-capping’) term S ds . In shallow water additional processes have to be considered, most notably, wave-bottom interactions Sbot . This defines S as

S = Sin + S nl + S ds + Sbot (2) The input source term is given as

Sin (V ,T ) = VE N (V ,T )

(3)

where E is a nondimensional wind-wave interaction parameter. The nonlinear wave-wave interaction term S nl can be modeled using the DIA. The dissipation term S ds is presented as a simple linear combination of

low-frequency

constituent

Sds ,l

and

high-

frequency constituent Sds , h

S ds = AS ds ,l + (1  A) S ds ,h

(4)

where A is a parameter which can be approximated by the frequency. And the bottom friction source term can be written as

Sbot (k ,T ) = 2*

n  0.5 N (k , T ) gd

(5)

where * is an empirical constant, which is estimated to be 0.038 m2s-3 for swell and 0.067 m2s-3 for wind seas, and n is the ratio of phase velocity to group velocity. The balance equation of Eulerian form for spectrum N is given as

wN w  w S + ’ x < x N + kN + T N = wt wk wT V x = c g + U

(6) (7)

wV wd wU  k< k =  wd ws ws

(8)

1 ª wV wd wU º T =  «  k< k ¬ wd wm wm »¼

(9)

where the vector c g is the group velocity and given

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by wave group velocity cg and wave drection T , s is a coordinate in the direction T , and m is a coordinate perpendicular to s . The grid in this study is regularly spaced by longitude-latitude grid, extending from 0oN to 26.0oN, 99.0oE to 125.0oE, and the spatial grid is 0.25o×0.25o. The interval of wind input is 6 h (at 0:00, 6:00, 12:00 and 18:00 h every day), and the wave model calculated from September19 to 29, 2005. Two time steps (600 s and 300 s) are used to reach computational efficiency: global time step (600 s) for the propagation of the entire solution, spatial time step (600 s) for the spatial propagation, spectral time step (600 s) for intra-spectral propagation, and source time step (300 s) for the source term integration. The initial field type is fetch-limited JONSWAP with no parameters. That is, the local spectrum is calculated using the local wind speed and direction, with the spatial grid size as fetch, to assure that the spectrum is within the discrete frequency range. The model provides the output of wave parameters such as wave spectra, significant wave ____

heights ( 4 E ), mean wavelength ( 2S k 1 ), mean ____

wave period ( 2S V 1 ), mean wave direction, peak frequency and peak direction. Here, E is spectrum energy, k is wave-number, V is radian frequency. The peak (dominant) frequency is calculated from the one-dimensional frequency spectrum. The peak (dominant) wave-number (wavelength) is calculated from the peak frequency using the dispersion relation. The basic spectrum given by the model is the wave-number-direction spectrum F  k ,T , and the traditional frequency-direction spectrum

F ( f ,T )

can be calculated from F  k ,T

F ( f ,T ) =

cg =

2SF (k ,T ) cg

nV kd ,n = 0.5 + k sinh(2kd )

(10)

(11)

where f is the frequency, cg is the group velocity, and d is the water depth. 2.5 Buoy data and validation During the Typhoon Damrey, a buoy named SZF2-1 was located in the northwest sea area of Hainan Island (see Fig.1) to measure the winds and waves, at the location of 19o46ƍ48.00ƎN, 109o07ƍ24.00ƎE (here after, we call this Point as “C”). The observed data included the wave height, wind speed and wind direction at 10 m height above

Fig.3 Comparisons (06:00 on 26 September 2005) between buoy observations and model input or results during Tyhoon Damrey passing through Point C

the sea surface, which were used to compare the model input and results. Figure 3(a) compares the input wind speed with the observed data at Point C from September 26 to 28. The root mean square (rms) errors between input and observed winds for this point are 3.8 m/s in speed and 28o in direction. Generally, the wind data for input are in good agreement with

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observations. Figures 3(b) and 3(c) compare significant wave heights and mean wave periods between observations and model simulation at Point C. The maximum of significant wave height and mean wave period reach 5.5 m and 8.4 s at 6:00 on September 26 respectively, while the simulation data are smaller than observations. However the model and the observation are still very similar. The estimated rms errors for significant wave height and mean wave period are 0.8 m and 1.1 s respectively. Figure 3(d) compares measured and hindcast one-dimensional frequency spectra at 06:00 on September 26, 2005. The spectral shape and peak frequency agree well, except that the second peak frequency obtained from simulation is smaller than that of observation. 3. Results and discussion 3.1 Wave fields characteristics Figure 4 shows distributions of significant wave height (Fig.4(a)), mean wave period (Fig.4(b)), wave age (Fig.4(c)), mean wave length (Fig.4(d), contours) and mean wave direction (Fig.4(d), thick arrows) at 00:00 on September 25, 2005 simulated with the presented model. Typhoon winds are typically asymmetric due to the typhoon movement. Winds are generally strnger (weaker) to the right (left) of the typhoon because the forward velocity of the storm adds to the wind velocity around its eye. In addition, the effective fetch and duration of the wave growth process are affected by the motion of the storm. The curvature of the wind field limits the fetch, but waves propagating in the direction of the storm motion remain under the influence of aligned wind for longer time and distance. The maximum significant wave height reaches 11 m in the right forward quadrant of the typhoon center and it propagates in the same direction as the typhoon. Waves to the right and front of the hurricane track become trapped and waves are exposed to prolong forcing from the wind. As a result, higher and longer waves are formed to the right and front of the track, while lower and shorter waves to the rear and left (Figs.4(a) and 4(b)), which is in agreement with the observations of Wright et al.[16]. Figure 4(c) shows that the wave age is also not symmetric about the center of the vortex. The youngest ocean waves are located in the upper-right half of the eye-wall. It is note-worth that, inconsistent with the significant wave height, the wave age is a minimum near the eye-wall structure coincident with the highest wind speeds and a little larger within the eye. The dominant waves propagate at significant angles to the low-level wind direction. In the rear half of the typhoon center, the dominant wavelength is considerably shorter relative to the long wavelength located in the front half (see

Fig.4(d)).

Fig.4 The wind fields (vector) and spatial distributions (contours) at 00:00 on September 25, 2005 during Typhoon Damrey. The direction of arrow represents the wind direction, and the arrow length is proportional to the wind speed. The maximum wind speed reaches 45 m/s in the open sea at this time. The mean wave direction was given in Fig.4(d) (thick arrows), where the direction of thick arrow represents the mean wave direction and the length of thick arrow is proportional to the mean wave length

3.2 Misalighnment of wind and wave A common characteristic in the model spectra is

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Table 1 Locations and distances from typhoon eye for nine points Point

Longitude (o)

Latitude (o)

Quadrant

Distance from eye

P0

113.00

18.80

Typhoon eye

0

P11

113.35

19.15

ĉ

R

P12

113.71

19.51

ĉ

2R

P21

113.35

18.45

Ċ

R

P22

113.71

18.09

Ċ

2R

P31

112.65

18.45

ċ

R

P32

112.29

18.09

ċ

2R

P41

112.65

19.15

Č

R

P42

112.29

19.51

Č

2R

the misalignment of local wind and waves due to the curvature in the typhoon wind fields. Except near the typhoon center, dominant waves are consistently found to the right of the wind direction (see Fig.4(d)), and the angle difference increasing with the distance form typhoon eye can be expressed by an exponential formula(see Fig.5).

Y = mX n

(12)

where Y is the angle difference, X is the distance from typhoon eye, and m and n are constant (0.52 and 0.89).

Fig.6

Fig.5 Scatter plot of angle difference between local wind and wave direction

Figure 7 gives the directional wave spectra for Points P11, P21, P31, and P41, at 00:00 on September 25, 2005. From the figure we may find the following characteristics: (1) Wider directional spread is to the left of the typhoon (see Figs.7(b), and 7(c)) and narrower spread is to the right of the typhoon (see Figs.7(a), and 7(d)). (2) The wave spectra to the right of the typhoon show a uni-modal swell system propagating in the direction of the typhoon translation (see Figs.7(a) and 7(d)), whereas the spectra in the rear and left of the typhoon display a more comlex structure with both swell and wind wave peaks (see Figs.7(b), and 7(c)). The peak wave direction in four quadrants are about 270o, 120o, 30o and 300o respectively, which shows that there exists a westward propagating swell with its peak wavelength near 160 m in Quadrant , (Point 11 and Point 12). In Quadrant ,,, spectra for

3.3 Spatial variation of directional wave spectra Typhoon produces complex and quickly varying wave spectra in space and time. In this section, wave spectra of nine points at 00:00 on September 25, 2005 when the Typhoon Damrey arrived at 113.00oE, 18.80oN were given for discussion. These points were located in different quadrant with different distances from the typhoon eye (see Fig.6 and Table 1).

Locations of nine points relative to typhoon center, where point P0 is located at the typhoon eye, and R is the maximum wind speed radius. The arrow represents the direction of typhoon translation (westward)

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Point 21 and Point 22 contain a similar feature with eastward and double peaks propagating wave, and the peak wavelength is about 140 m, which is shorter than the value of Quadrant ,. In the southwest quadrant at location Point 31 and Point 32, the simulated spectra indicate a double-peak wave field with a southward propagating wave and a longer peak wavelength of 200 m. However, at locations of Point 41 and Point 42, the wave state is characterized by the longest wavelengths (about 230 m) in the westward propagating swell. Fig.8

The wind fields (vector) and spatial distribution of wave energy E (contours) at 00:00 on September 25, 2005 during the passage of Typhoon Damrey. The arrow represents the wind direction, and the arrow length is proportional to the wind speed. The maximum wind speed reaches 45 m/s in the open sea at this time

In all quadrants, the wave energy in Quardrant Č is the highest, then in Quadrant ċ and Quadrant ĉ, where the value of wave energy in Quadrant Ċ is the least. It is noticeable that in Quadrants I and Č, wave energy at 2R locations is significantly higher than that of at R distance, while in Quadrants Ċ and ċ, but the difference is small. Figure 8 gives the spatial distribution of wave energy, which shows a consistent characteristic with significant wave height distribution. Spatial variations of the typhoon directional spectra are strongly dependent on the relative position from the typhoon eye. Figure 9 gives the variety of peak wave direction with the distance from the typhoon eye. For peak wave direction, it is found that in Quadrants Ċand ċ, it increases with the distance from the typhoon eye, and decreases with the distance in Quadrants ĉand Č. Whereas, when the distance is greater than 150 km, the peak wave direction levels off to constants, which are about 200o, 150o, 50o and 250o respectively.

Fig.9 Peak wave dircetion varies with the distance from typhoon eye in four quadrants

Fig.7

Directional wave spectra for Points P11, P21, P31 and P41 (Figs.7(a) to 7(d)) at 00:00 on September 25, 2005

4. Summary and conclusions In this study, wave field forced by the Typhoon Damrey has been simulated using the WAVEWATCH-III model, which shows that using

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realistic wind forcing and a high-resolution wave model may lead to successful simulations of surface wave fields in typhoon conditions. This allows more complete analysis of the typhoon-generated wave field than do observations at limited time and space. From the results of simulation modeling, it is found that the typhoon-generated wave field is mainly determined by the radius of maximum wind speed and the distance from the typhoon center. Wave fields under typhoon forcing can be described as follows: (1) higher and longer waves are formed to the right and front of the typhoon track, while lower and shorter waves to the rear and left, (2) angle difference between local wind and wave direction increases with the distance form the typhoon eye, which can be expressed by a exponential formula, (3) for directional spectra, wider directional spread is to the left of the typhoon and narrower spread is to the right of the typhoon, (4) the wave spectra to the right of the typhoon show a uni-modal swell system propagating in the direction of the typhoon translation, whereas the spectra in the rear and left of the typhoon display a more complex structure with both swell and wind wave peaks. Acknowledgement The authors wish to thank the South China Sea Institute of Oceanology, Chinese Academy of Sciences for providing the wind fields data under the Typhoon Damrey.

[4]

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