第 38 屆海洋工程研討會暨科技部計畫成果發表會 論文集 國立臺灣大學 2016 年 12 月 Proceedings of the 38th Ocean Engineering Conference in Taiwan National Taiwan University, December 2016
The Study on Hydrodynamics during Typhoon Tembin (2012) around Green Island Coast 1 2 3 2 Kai-Cheng Hu Wen-Shiun Lu Wen-Son Chiang Jin-Li Yu 1Assistant Research Fellow, Tainan Hydraulics Laboratory, National Cheng Kung University 2Research Fellow, Tainan Hydraulics Laboratory, National Cheng Kung University 3Research Assistant, Tainan Hydraulics Laboratory and Ph.D student, Dept. of Hydraulic and Ocean Engineering, National Cheng Kung University ABSTRACT
The storm surge and waves around Green Island during typhoon Tembin (2012) were calculated by employing a depth-integrated, wave-current coupled model developed by Dietrich et al. (2011). The Rankin vortex wind model with typhoon track parameters was used to generate the wind forcing. It is pointed out that typhoon Tembin was effected strongly by typhoon Bolaven. The Fujiwhara effect between typhoon Tembin and Bolaven should be considered further. To improve the wind forcing, the Fujiwhara effect was successfully treated as the superposition with two wind forcings. Overall, the comparisons between simulated results and measured data show a reasonable agreement. Finally, the difference of comparisons at the early stage was discussed. Keywords: adcirc, swan, storm surge, Fujiwhara effect
綠島地區颱風期間水動力探究 胡凱程 1 盧韋勳 2 江文山 3 余進利 3 1 成功大學水工試驗所助理研究員 2 成功大學水利系暨海洋工程學系博士班學生、水工試驗所研究助理員 3 成功大學水工試驗所研究員 摘要
本文以 Dietrich et al. (2011)所發展水深積分波流耦合模式針對 2012 年天秤颱風期間綠島 海域進行計算。模式所需風場以袁金窩動模式(Rankin-Vortex Model) 配合颱風軌跡參數計算而 得。所得模擬結果經與觀測數據及氣象觀測圖相比，說明布拉萬颱風對天秤颱風的影響顯著， 需額外考慮 2012 天秤與布拉萬颱風間的藤原效應(Fujiwhara effect)影響。為改善風場，以線性 疊加方式結合兩颱風風場做為風場輸入。模擬成果與觀測數據相符合，說明兩颱風間的藤原效 應可以線性疊加方式合理描述。最後，本文亦對於颱風模擬期間早期誤差提出合理說明。
關鍵詞：adcirc, swan, 暴潮, 藤原效應
Island during typhoons Tembin (2012) while the wave 1. Introdcution height is not the extreme one. General speaking, the Over the past decade, the largest storm surge is correlation between the storm surge and wave height 50.4 cm by analyzing the tide gauge station at Green is a strong relationship because these two variables are
95 always dominated by the strength of the typhoon. ∂∂NcN∂cN ∂ cNcNS ∂ ++++=x y σθ (1) Therefore, the finding is motivated this paper to ∂∂tx ∂ y ∂σ ∂ θσ further study. In Eq. (1), t is time, ()xy, Cartesian coordinates, To figure out the reason for the inconsistency, the θ the wave direction, σ wave frequency, N storm surge and wave during typhoons are necessary action density and ()ccxy, the wave energy to build. The employment of a proper numerical model propagation velocities. S denotes the source term might be a good choose to build the hydrodynamics. including wave energy input (wave growth by the Since the scales of current and wave are quite different, wind), energy loss and energy transfer. the whole simulations usually are separately The ADCIRC model developed by Luettich Jr et performed. Most researches use tidal current model to al. (1992) and Westerink et al. (1994) describes water describe the surface evolutions and current motions. surface evolution and current motion. For The wave fields are calculated by wave model (Ou et SWAN+ADCIRC model, the two-dimensional al., 2002). In recent years, the model coupled with depth-integrated equations of ADCIRC (2DDI) were wave and current was fully developed and more coupled with SWAN model. The ADCIRC-2DDI gives advanced. Many studies on the East Cost of US were as, 2 ∂ successfully done with the aid of wave-current ∂ζζ ∂∂J x J y ∂τ00 ∂ τ +τ 0 ++−QQxy − =0 (2) coupled model (Dietrich et al., 2011, 2012; Hope et al., ∂t2 ∂∂ txy ∂ ∂ x ∂ y ∂∂ ∂ζ 2 2013). UU g Jxx=−− Q Q y +− fQ y The main objective of this paper is to simulation ∂∂xy2 ∂ x the hydrodynamics during typhoon Tembin (2012) ∂−Ps ττsx bx −gH ζ +−+ αη (3) ∂ ρρ which the maximum of storm surge was reported xg00 ∂ζ around Green Island. This paper is organized as +()MD −+ U +τ Q xx ∂t 0 x follows. The methods will be first mentioned. The ∂∂ ∂ζ 2 VV g numerical setup will then be given. The observations Jyx=−− Q Q y −− fQ x ∂∂xy2 ∂ y will be described. Next, the numerical simulations will ∂ P −ζ +−s αη be discussed. Finally, the concluding remarks will be gH (4) ∂ygρ0 made. ττsy− by ∂ζ + +()MDyy −+ V +τ 0 Qy ρ ∂t 0 2. Methods ∂∂∂UUU ∂ P +UV + =−+− gζs αη ∂∂∂t x y ∂ xgρ0 To simulate the storm surge and wave during (5) ττ−−MD typhoons around Green Island, the SWAN+ADCIRC ++sx bx x x +fV ρ HH model coupled with the simulating waves nearshore 0 ∂∂∂VVV ∂ P (SWAN) and the advanced circulation (ADCIRC) is +UV + =−+− gζs αη ∂∂∂t x y ∂ ygρ0 used (Dietrich et al., 2011). The Rankin vortex (6) ττsy−− byMD y y formula is used to generate wind field to drive the ++ −fU ρ0HH storm surge and wave. ∂S ∂S τ =−−xx xy (7) 2.1 Model equation sx ∂∂xy ∂∂SS The Cartesian equations of SWAN model τ =−−xy yy (8) sy ∂∂xy describes wave motions with the spectral wave action balance equation and source/sinks (Booij et al., 1999) In Eq. (2), H is the water depth including reads, bathymetric depth h and surface elevation ζ ,
96 ()UV, the depth integrated currents, When several Rankin vortices are considered
()Qxy,, Q= H() UV the fluxes per unit width, and τ 0 such as the binary typhoon, the total pressure can be a numerical parameter which may be variable in space. treated as the superposition of ∆P reads, =+∆ In Eqs. (3-8), f is the Coriolis coefficient, g the PP0 ∑ P (14) gravitational acceleration, P the pressure at the s 2.3 Numerical setup surface, ρ the water density, η the potential, α 0 The version 51.52.05 of ADCIRC is empolyed the elasticity factor, τ the surface stresses due to s and is capbility to couple with SWAN. The winds and waves and τ the bottom stress. M , b unstructured mesh which is easy to locally increase the D are lateral stress gradients and momentum resolution where the solution gradients are large is dispersion terms. It remarks that h does not allow to adopted in SWAN+ADCIRC (Dietrich et al., 2011). change with t in ADCIRC-2DDI. The computational domain is from 10°N~50°N 2.2 Wind forcing and 110°E~150°E. The computational bathymetry are The wind forcing to drive wave and current was composed of the 200m resolution bathymetric data generated by using the Rankin vortex wind method (TAIDP 200m) released by Ministry of Science and (RVM). The RVM (Graham, 1959; Young and Sobey, Technology of Taiwan and the ETOPO1. 1981) reads, The insensitivity mesh grids are composed of 7 V ()RRmmmexp− 7() 1 RR , R < R 50,821 nodes and 98,964 triangular elements as shown r = (9) V + − ≥ in Fig. 1. The smallest mesh placed along the coast m exp( 0.0025Rm 0.05)() 1 RR mm , R R line is about 900m, while the largest mesh set the edge In Eq. (9), Vr is the rotational speed at distance r at western North Pacific ocean is about 80 km. For from center of typhoon, Vm the maximum wind wind forcing, typhoon tracks information given by speed and Rm the radius to maximum winds. In this Taiwan Central Weather Bureau (CWB) or Japan paper, the radius to maximum winds proposed by Meteorological Agency (JMA) are collected to input Graham (1959) was used, R = 28.52tanh[0.0873(ϕ − 28)] the RVM wind model. m (10) In this paper, the time step was commonly set to +12.22exp ()PPcf −0 33.86 + 0.2 V + 37.22 2 sec. To shorten the computational time, the parallel In Eq. (10), ϕ is latitude, V f the forward speed, computations are performed with 8~16 cores. P0 the neutral pressure which was commonly set to
1013.3 hPa and Pc the central pressure of typhoon. The total wind speed can be expressed as follows by considering the translation of typhoon,
VV=rf + 0.5 V cosφ (11)
In Eq. (11), φ is the angle between the radial arm and the line of maximum winds. Particularly, the deflection is caused by the friction between water and air and is given as follows Fig. 1. The sketch of mesh grids. (The 200m 10° , 0 <≤RRm resolution bathymetric data filled within the grey Φ=10 °+ 75 °()RRmm − 1 , R < R ≤ 1.2 R m (12) rectangle) 25°<,1.2RRm The pressure difference due to the presence of the 3. Observation typhoon can be given as The typhoon tracks of Tembin and Bolaven are ∆=P P − P = P − Pexp − RR (13) cc()0 () m illustrated as Fig. 2. Typhoon Tembin were active
97 during 0600 UTC 19 Aug to 1200 UTC 30 Aug. At 1800 UTC 23 Aug, Tembin passed through Green Island and made landfall over Southern Taiwan about one hour later. At 2300 UTC 23 Aug, it arrived the Taiwan Strait. Early on Aug 24, Tembin was expected to accelerate east-northeastward and gradually interacted with nearby typhoon Bolaven which actived during 0600 UTC 20 Aug to 0600 UTC 29 Aug. It is remarked that the Fujiwhara effect between Tembin and Bolaven was observationally reported. One evidence is that Tembin was initially moved westward, while Bolaven caused Tembin to turn eastward and moved along a counter-clockwise loop as shown in Fig. Fig. 4. Wind field and pressure distribution at 0000 2. Also, the pattern of the isobar contour nearby 1000 UTC 26 Aug 2012. (blue arrow: wind forcing by Tembin; red arrow: ERA data) hPa (see Fig. 3) could be recognized as the other evidence. At 1800 UTC 27 Aug, it made a second landfall on Southern Taiwan and passed through Green 4. Numerical Simulations Island again around 2100 UTC 27 Aug. 4.1 Wind forcing improvement The wind forcing to drive wave and current is key point to typhoon simulations. The typhoon track information including the central location, central pressure and maximum wind speed is the common recorded data, while wind field within a large domain with high resolution is limited to measure and to record. Therefore, to apply RVM wind model with typhoon tracks information to generate the wind forcing is still useful to many works. Figure 4 shows the wind field and pressure Fig. 2. The sketch of typhoon tracks of Tembin and distribution at 0000 UTC 26 Aug 2012 are generated Bolaven (2012). by RVM with the typhoon track information of Tembin. To check the wind forcing, the u10 (10 metre U wind component), v10 (10 metre V wind component) and msl (mean sea level pressure) of ERA interim reanalysis data with highest 0.125°×0.125° resolution from the European Centre for Medium-Range Weather Forecasts, hereafter names ERA data, are also plotted in Fig. 4. Clearly, the RVM wind field is inconsistent with ERA data. In addition, the wind directions around middle east coast of Taiwan are opposite. It is implied that the wave height might be overdetermined to Fig. 3. The weather chart at 0000 UTC 26 Aug 2012 by JMA. measured data since the region is shielded by the
98 topography of Taiwan land. of both Tembin and Bolaven are applied. The To improve above-mentioned shortcomings, the simulations begin at 0700 UTC 21 Aug 2012 and end presence of the influence caused by typhoon Bolaven at 1400 UTC 28 Aug 2012. should be further considered. In other words, the For comparison purpose, the Cases 1-2, the Fujiwhara effect contributed by typhoon Tembin and measured data and ERA data at CWB buoy station Bolaven should be considered. C6S62 (see Fig. 1) are plotted in Fig. 6. As seen in Fig. In fact, Fujiwhara effect had been proved from a 6, the differences among those data at C6S62 show series experiments on the interactions between pairs of that the ERA data which including more complete vortices in a water tank by (Fujiwhara, 1921, 1931). atmospheric motions are closer to the measured data at Mathematically, the experiments could be treated as C6S62 than to the computational results. While the the superposition of vortex pairs. For this reason, the wave height of ERA data during Aug 21 to Aug 24 is typhoon track information of both Tembin and still underestimated due to the underestimation of Bolaven is also involved to RVM to generate the wind wind speed. The difference might cause by the forcing. The upgrade version of Fig. 4 with deviation of winds which are shielded by terrain of considering the influence by Bolaven is illustrated as Taiwan in real situation (see Fig. 7). However, the Fig. 5. As shown in Fig. 5, the wind field and pressure shielding effect of wind is omitted in RVM wind distribution are obviously improved and could be the model. Therefore, the wind speed generated from reasonable wind forcing. RVM wind is much bigger than measured data at C6S62 and resulting computational wave height is also overdetermined. The slight differences on wind speed, storm surge and wave height could be found between Case 1 and Case 2. However, the wind direction during Aug 24 to Aug 28 is obviously improved by considering the Fujiwhara effect. The overall comparisons with measured data are reasonably good, suggesting that the present model applied wind forcing including Fujiwhara effect due to the interaction between typhoon Tembin and Bolaven can be used to accurately simulate storm surge and waves during the typhoon Tembin.
Fig. 5. Wind field and pressure distribution at 0000 UTC 26 Aug 2012. (blue arrow: wind forcing by 5. Concluding Remarks Tembin & Bolaven; red arrow: ERA data) In this paper, a tightly-coupled SWAN+ADCIRC 4.2 Numerical validation and result model developed by Dietrich et al. (2011) is employed to simulate the hydrodynamics around Green Island With the aid of reasonable wind forcing, the during typhoon Tembin and Bolaven. The Fujiwhara simulations are performed by two cases to emphasize effect is pointed as a key point to simulate typhoon the importance of the Fujiwhara effect which usually Tembin. The Fujiwhara effect due to typhoons Tembin be omitted when some return periods of storm surge and Bolaven is mathematically and successfully were calculated. Specifically, the wind forcing treated by using RVM wind model with both the generated by RVM with Tembin track parameters is typhoon tracks of typhoons Tembin and Bolaven. By applied in Case 1. For the Case 2, the track parameters
99 doing so, the computational result was thus improved. 105-2911-I-006-301/105-3113-E-006-016-CC2. More simulations around Green Island with high References resolution mesh grids will be tested in the future. 1. Booij, N. et al., (1999) “A third-generation wave model for coastal regions: 1. Model description and validation”, Journal of geophysical research: Oceans, 104, 7649-7666. 2. Dietrich, J. et al., (2011) “Modeling hurricane waves and storm surge using integrally-coupled, scalable computations”, Coastal Engineering, 58, 45-65. 3. Dietrich, J.C. et al., (2012) “Performance of the unstructured-mesh, swan+adcirc model in computing hurricane waves and surge”, Journal of Scientific Computing, 52, 468-497. 4. Fujiwhara, S., (1921) “The natural tendency towards symmetry of motion and its application as Fig. 6. The comparisons between computational results, observed data and ERA data. (blue line: wind a principle in meteorology”, Quarterly Journal of forcing by Tembin; red line: wind forcing by Tembin the Royal Meteorological Society, 47, 287-292. & Bolaven; green line: ERA data; block dot: observed 5. Fujiwhara, S., (1931) “Short note on the behavior data at C6S62 station) of two vortices”, Proceedings of the Physico-Mathematical Society of Japan, 13, 106-110. 6. Hope, M.E. et al., (2013) “Hindcast and validation of hurricane ike (2008) waves, forerunner, and storm surge”, Journal of Geophysical Research: Oceans, 118, 4424-4460. 7. Luettich Jr, R. et al., (1992) Adcirc: An advanced three-dimensional circulation model for shelves, coasts, and estuaries. Report 1. Theory and methodology of adcirc-2ddi and adcirc-3dl, DTIC Document. 8. Ou, S.-H. et al., (2002) “Simulating typhoon waves by swan wave model in coastal waters of Taiwan”, Fig. 7. Wind field and pressure distribution at 0000 Ocean Engineering, 29, 947-971. UTC 22 August 2012. (blue arrow: two RVM; red 9. Westerink, J. et al., (1994) Adcirc: An advanced arrow: ERA data) three-dimensional circulation model for shelves, Acknowledgments coasts, and estuaries. Report 2. User's manual for adcirc-2ddi, DTIC Document. The authors would like to acknowledge Prof. J.C. 10. Young, I. and Sobey, R., (1981) The numerical Dietrich at the North Carolina State University for prediction of tropical cyclone wind-waves, technical support of SWAN+ADCIRC model, Department of Civil & Systems Engineering, James development group of ADCIRC for the model Cook University of North Queensland. provision and the Ministry of Science and Technology of Taiwan for their support under grant MOST
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