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Numerical studies on typhoon surges in the Northern Taiwan
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Coastal Engineering 54 (2007) 883 – 894 www.elsevier.com/locate/coastaleng
Numerical studies on typhoon surges in the Northern Taiwan Wei-Po Huang a,⁎, Chiang-An Hsu b , Chen-Shan Kung c , John Z. Yim d a
Department of Hydraulic Engineering, Sinotech Engineering Consultants, 5F, No.19, Lane 71, Lin-Yi Street, 100 Taipei, Taiwan, ROC b Civil and Hydraulics and Informatics Research Center, Sinotech Engineering Consultants, Taiwan, ROC c Department of Hydraulic Engineering, Sinotech, Taiwan, ROC d Department of Harbour and River Engineering, National Taiwan Ocean University, Taiwan, ROC Received 8 November 2006; received in revised form 28 May 2007; accepted 31 May 2007 Available online 10 August 2007
Abstract A numerical model for the simulation of typhoon surge has been developed for the coastal areas of the northern Taiwan. Results from the model outputs are then used as a typhoon surge data bank for 7 main estuary areas in this region. The data bank consists of the historical typhoon events from 1980 to 2004. Both characteristic and frequency analyses of the typhoon surge in the coastal region have been studied. Using these data, a relation between the surge height and pressure distribution is obtained. It is shown that, either the numerical model, or the statistical equations presented in this paper, can be used to predict possible surge heights in the estuary areas with sufficient accuracy. © 2007 Elsevier B.V. All rights reserved. Keywords: Typhoon surge; Forecast; Finite volume method
1. Introduction Taiwan lies on the west side of the Pacific Ocean and is usually invaded by typhoons in summers and autumns. When typhoon approaches to the coast, a surge usually occurs. This is induced either by the strong onshore winds which pile the water up, or the low barometric pressure that causes the sea level to rise. If it occurs during high tides, the risks of coast flooding will be enhanced. A flood defense plan to minimize the economic and social damages caused by possible storm surges is of vital importance for an efficient coastal management strategy. In this respect, numerical simulation and/or statistical analysis are the two most important tools for the predictions of possible water level rise due to typhoon surge. This paper presents our recent efforts toward this purpose. Simulations of storm surges are usually carried out through the use of a two-dimensional shallow water equation. The Navier–Stokes equations are simplified by a depth averaging procedure (Benqué et al., 1982). Madsen and Jakobsen (2004) simulated storm surge and flood in the Bay of Bengal by using Mike 21 hydrodynamic model developed by DHI Water and ⁎ Corresponding author. Tel.: +886 9 1870 8135; fax: +886 2 8761 1595. E-mail address: [email protected] (W.-P. Huang). 0378-3839/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2007.05.015
Environment (DHI, 2002). The model allows the use of nested grids based on a dynamically consistent two-way nesting technique for the increasing of the computational grids in the concerned region. However, the model may have difficulties when applied to complex coastal lines, or long and narrow estuaries. Plüβ and Schödter (2001) studied the characteristics of storm surges in German estuaries. They used a so-called TELEMAC-2D hydrodynamic model based on a finite element method. Non-uniform triangular grids were used in this model so that efficient and flexible simulations can be obtained. FEMA used the SLOSH model (Sea Lake and Overland Surges from Hurricanes) to predict the maximum surge heights for most US coastlines (FEMA, 2006a,b). This model was developed by Jelesnianski et al. (1992). Actually, two types of analyses, i.e., the MEOW (Maximum Envelope of Water) and the MOM (Maximum of Maximum), are included in the SLOSH model. The former analysis derived the highest water level due to parallel tracks of hurricanes with the same direction, speed and intensity to retrieve the uncertainty of the hurricane movement forecast. The latter gives an estimate of the highest water level due to a composite of the MEOW. This is to say, the MOM analysis yields the worst-case scenario. The mesh of the model is built as sector grids that lead to the similar drawback as that of Mike 21.
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All these studies have shown satisfactory results. However, it is found that all these simulation procedures suffer from an inherent weakness. It can be argued that, all the predicted meteorological conditions, such as the typhoon travel route, the atmospheric pressure distribution, and the maximum wind speed, can have strong effect on storm surges. That is to say, all surge simulations can have favorable results only after typhoon passages. This is because only then, are the meteorological parameters used in the procedures correct. On the other hand, before the landfall of typhoon, the uncertainty of the typhoon forecast increases the difficulty for predicting surge height. At present, the accuracy for predicting these parameters is confined by our limited knowledge of the meteorology (Soares et al., 2002). This can be seen from the typhoon forecasts issued by the national and international weather bureaus. For example, the errors of tolerance of predicted tracks of typhoon propagation issued by the JTWC (Joint Typhoon Warning Center, 2005) or the JMA (Japan Meteorological Agency, 2002) are usually within 200 km. This is almost equal to half the length scale of Taiwan. This leads to uncertainties of predicting the surge height for relatively small regions such as Taiwan. An efficient numerical scheme or a statistical data bank may provide a better solution for the problem mentioned above. Efficient simulation scheme is needed once modifications of the predicted typhoon track or other parameters are available. In this way, the surge simulation can be kept ongoing. The statistical data bank, on the other hand, is used to evaluate the potential hazard. Generally speaking, the more factors are considered in the simulation, the more faithfully results can be obtained. However, this will force the numerical schema to be more timeconsuming. In a surge hazard warning system, both efficiency and accuracy are of primary concern. It seems that a statistical
Fig. 2. Schematic representation of the set up mesh for simulation.
database can resolve the problem. Through the use of the database, forecasted results can be adjusted by comparing with the results of similar typhoons. These procedures can be done rapidly. The database can also be used for various kinds of purposes, such as evaluation of flood hazard, coastal morphology, as well as for engineering design. If the measurements were well implemented, the database can be built by using historical data. A comparison of the results obtained for the Red River and Vistula Delta was given by Pruszak et al. (2005). The magnitudes of typhoon surge in different latitudes were estimated using measured data. However, not all the meteorological happenings in the littoral region can be well
Fig. 1. The geographic positions of the study region.
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Fig. 3. The track of typhoon Aere (CWB, 2006).
observed and recorded. The measurements could be destroyed by the severe weather sometimes and the data for extreme weather were unavailable. In this case, numerical simulation can be used to hindcast and reconstruct the typhoon events, and the results may be used for the database. Liu (1987) used a coupled meteorological-hydrodynamical 3-D numerical model to investigate water level variations during typhoon passage. Since the calculation is rather time-consuming, a number of modal typhoons were used to expand the database by Liu.
The objective of this study presented in this paper is to develop a surge simulation model and to build up a database of surge height for the northern coast of Taiwan since 1980. The area studied in this paper consists of 7 main estuaries and tidal observation points. A schema of the geographic locations is shown in Fig. 1. 2. Mathematical background 2.1. Hydrodynamic model The factors affect the fluid field, such as wind, Coriolis force, the bottom friction, fluid shear stress and topographical boundary conditions will be considered in the present model. The governing equations of the model consist of the two horizontal (x and y direction) components of momentum and an equation for the conservation of mass. The equation of continuity and momentum are shown in Eqs. (1), (2) and (3) respectively. Continuity equation Ah Ap Aq þ þ ¼ Sh At Ax Ay
ð1Þ
The momentum equation in the x-direction, which is from west to east, is expressed as: Ap A p2 gh2 A pq 1 þ þ ¼ ghS0X þ Xq þ ssx sbx þ At Ax h Ay h q 2 1 A A h APa hsexx þ hsexy þ Sp þ q Ax Ay q Ax Fig. 4. The simulated result of the surge height distributions.
ð2Þ
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Fig. 5. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Aere).
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The momentum equation in y direction (south to north) is expressed as: Aq A pq A q2 gh2 1 s þ sy sby þ þ ¼ ghS0Y þ Xp þ At Ax h Ay h q 2 1 A A h APa þ hsexy þ hseyy þ Sq: q Ax Ay q Ay ð3Þ where t x, y, z
time spatial coodinates which x and y are horizontal coordinates and z is vertical coordinate h water depth g gravity acceleration Pa atmosphere pressure ρ the density of water Ω the parameter of Coriolis force S0X, S0Y the bed slope in x and y directions, respectively; τxs, τys the wind stress terms in x and y directions τxb, τyb the bottom friction terms in x and y directions e e e τxx , τyy , τxy the depth-averaged Reynolds stresses h S the source term of the continuity equation Sp, Sq the source terms of the momentum equation in the x and y directions. The equations are discretized using the semi-discrete, cellcentered and finite-volume methods. Taking a semi-discrete approach has the advantages that the discretization schemes in
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spatial and temporal domain can be more easily and flexibly designed. 2.2. Wind and pressure field The wind field of a typhoon is usually very intense, and spatially inhomogeneous, as well as directionally varying. The large gradients of the wind speeds and the rapidly varying wind directions of the typhoon vortex can generate very complex ocean wave fields. However, for practical applications the wind fields are usually expressed in the form of parametric models. In this paper, the typhoon wind field is assumed to have a form which is nearly circular. The pressure distribution is assumed to have an exponential form and can be express by (Holland, 1980): B
Pr ¼ Pc þ ðPn Pc ÞeðRmax =rÞ
ð4Þ
where Pc is the pressure at the center, Pn is the ambient or environmental pressure, and has a value of 1016 hPa, r is the radius (the distance from the center), Rmax is the radius of the maximum wind, and B is a shape parameter. Usually, the shape parameter B has values ranging from 1 to 2.5. Huang et al. (2005) have used several theoretical distributions for typhoon pressure and its wind field to estimate possible typhoon surges for the coastal regions in northern Taiwan. It is found that, a shape parameter B with a value of 1 yields the most favorable results. The wind speed distribution is usually derived using a gradient wind model or simply by using an empirical expression.
Fig. 6. The track of typhoon Talim (CWB, 2006).
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The distribution used in this study was that proposed by (Hsu et al., 1999) which can be expressed as: " 2 #1=2 Pn Pc Rmax ðRmax =rÞ 1 1 Xr ð5Þ Vg ¼ e þ Xr 2 2 qa r where Vg ρa
gradient wind speed the density of the air.
The shear stress of the wind and the pressure field are the external forces in the present model.
2.3. Boundary condition formulations Various types of boundary conditions are needed for the model. These will be described shortly in the following. The four seaward boundaries are assumed to be non-reflective to minimize reflections of the outgoing waves. At present, information concerning astronomic tidal variation on the open sea is unavailable to us; we have, therefore, set the initial water level to zero in the present model. This means that, variations of the water surface elevations were induced by typhoon only. Close to the land, a moving boundary condition is used so that the process of wetting and drying of the surge flats can be taken into account.
Fig. 7. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Talim).
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2.4. Mesh construction for the area studied This study focuses on the development of a storm surge simulation model which has both high spatial resolution, as well as efficient computation ability. The region considered in the study lies within the longitudes from 117° E to 126° E and the latitudes from 18° N to 28° N. The DTM (Digital Terrain Model) bathymetric data were obtained from the NGDC (National Geophysical Data Center, 2004) and from the NCOR (National Center for Ocean Research, 2004). The length of the grid sides in the littoral region close to the coast was 300 m, and for those in the deep sea far away from Taiwan a length of 15,000 m was used. In this way, the efficiency of simulation can be increased substantially. A total of 29,266 triangular elements and 16,402 nodes are used for the simulation. The setups of the mesh for the simulation are shown in Fig. 2. 2.5. The computational rate When the potential of a typhoon invasion exists, the CWB (Central Weather Bureau, 2006) of the Republic of China carries out prediction every 3 h. In each forecast, the meteorological information will be updated, and calculated results are used as prediction for the next 3 h. In carrying out our surge simulation, the boundary conditions can be obtained from the forecast. These include, the predicted typhoon track, the pressure at the center, the radius of the maximum wind speed, typhoon radius, and the maximum wind speed of the depression. That is to say, the typhoon surge simulation of the present study start after the typhoon forecast issued by the CWB. On the other hand, for the purpose of “pre-warning”, the
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computation should be done within an hour or so. Each step of the simulation should simulate 6-h surge distribution including the past and the future 3 h. This means that, the ratio of the computational rate, i.e., real to computational time, should be higher than 6:1. The presented numerical scheme of surge simulation has a rate of 9.6:1, and is seen to be far higher than necessary. All the computations were carried out on an Intel Pentium IV personal computer with a 2.6 GHz CPU and 1 GB DRAM. 3. Results and discussion 3.1. Boundary conditions calibration Three typhoons are used to calibrate the hydraulic boundary conditions of the present model. These three typhoons are Typhoon Aere (2004), Typhoon LongWang (2005), and Typhoon Talim (2005). These three typhoons have made most severe impacts to the northern Taiwan within last 2 years (2004 and 2005). The atmospheric parameters issued by the typhoon forecast of the CWB were used as boundary conditions for the surge simulation. The CWB has 7 tidal observation stations operational along the coast. The stations have the name Zhu-Wei, Tam-Sui, Lin-Sah-Bue, Keelung, Long-Dong, Geng-Fang and Su-Ao. However, due probably to malfunctions of the tidal gauges, records of water surface fluctuations are sometimes missing. Whenever available, these were used for the calibration. Typhoon Aere was a Category 1 typhoon with winds estimated at the maximum intensity to be 65 knots. It approached to Taiwan from the southeast and turn around to the northwest coast on 20 Aug. 2004. The typhoon eye did not make landfall.
Fig. 8. The track of typhoon Longwang (CWB, 2006).
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However, the economic activities in the northern part of Taiwan have been halted for 2 days. The typhoon track is shown in Fig. 3 (CWB, 2006). Fig. 4 is the estimated surge heights when typhoon Aere is closest to Taiwan. Measured and simulated results on each tidal observation points along the northern coast of Taiwan are shown together in Fig. 5. The solid line with hollow square symbols is the simulated water surface elevation, which is the sum of simulated surge height plus that due to astronomic tides and the measured ones are represent in the solid lines with circular symbols. The astronomic tidal heights are estimated through harmonic analysis (CWB, 2006). Simulated and measured surge heights are shown as lines with crosses and triangular symbols respectively. The later one is
the difference between the measured sea water level and the predicted astronomic tide. It is noted that predicted astronomic tides have minor phase lags and different amplitudes as those of actual ones. That is due to the fact that only a limited number of harmonic functions are used in the estimate, and these are insufficient to express the variation of the astronomic tides. Nevertheless, it can be seen that, the differences of the phase lag and that of the amplitudes are less than 0.5 h and 0.5 m, respectively. It is thus concluded that the agreements between simulated and measured results are satisfactory. It can also be seen that, in the figure, simulated fore runners (08/23 12:00–08/24 12:00) are always smaller than those extracted from tidal records. The deviation was caused by two
Fig. 9. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Longwang).
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reasons. One of the reasons is that variation of the astronomic tides has not been exactly reproduced. The derived component of the measured surges can still contain harmonics of the tidal variation due to the small phase lags between recorded and simulated tidal variations. The other reason could be that, swells generated by typhoons were not considered in the model. Swells usually have heights ranging from 1 to 3 m (Dean and Darlymple, 2002), and they have speeds faster than those of typhoon waves (Munk, 1947). The incoming long waves pile up along the coast continuously may also cause the rise of sea water level measured nearshore. With typhoon approaching, the effect of the swell will be long gone. It can be seen that from 08/ 24 18:00 to 08/25 00:00, i.e., when typhoon Aere was close to Taiwan, the differences between simulated and measured results are smaller. This seems to indicate that, with typhoon approaching, the performance of the present model will be better. Talim was a storm of category 4 with maximum winds at 95 knots, and a low pressure of 925 hPa at the center (Fig. 6). At least 7 people were reported killed by the storm in Taiwan. The typhoon stayed in the east coast of Taiwan for 6 h then headed west over Taiwan in 3 h. In the meantime, the strength of
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Typhoon Talim decreased rapidly due to the obstruction of the Central Mountain located in the middle of Taiwan. The pressure increased from 925 hPa to 955 hPa and the wind speed in the center decreased from 95 knots to 78 knots. Comparisons of the results are shown in Fig. 7. It can be seen that the surges around the northern part of Taiwan are rather small. They were all less than 0.5 m. Typhoon Longwang was a super typhoon of Category 5 with winds over 90 knots (Fig. 8). It swept over the middle of Taiwan on 1 Oct. 2005. The radius of typhoon was small but it was very compactly structured. It advances with a speed of 18–20 km/ h while crossing Taiwan. Simulated and measured results are shown in Fig. 9. Su-Ao is the tidal station closest to the point that where typhoon made landfall. From Fig. 9, it can be seen that, simulated and measured surge heights are, respectively, 0.549 m and 0.542 m. This shows that the model has estimated the peak value of the surge almost exactly. It can also be seen that, the surge heights of other measuring stations decrease with the increasing distance away from the typhoon center. It can thus be concluded that, in general, simulated water surface heights agree well with those measured.
Table 1 The peak value of the simulated typhoon surge of each estuary Typhoon
1980 Norris 1981 Ike 1981 June 1981 Maury 1984 Alex 1984 Freda 1985 Nelson 1985 Brenda 1986 Nancy 1986 Wayne 1986 Abby 1987 Vernon 1987 Alex 1989 Sarah 1990 Marian 1990 Ofelia 1990 Yancy 1991 Ellie 1992 Polly 1992 Ted 1994 Doug 1994 Gladys 1996 Herb 1997 Amber 1998 Otto 1998 Yanni 1998 Zeb 2000 Kai-Tak 2000 Xangsane 2001 Toraji 2001 Nari 2002 Nakri 2003 Vamco 2004 Aere 2004 Haima 2004 Nockten
The peak value of the surge height (m) Lao-Jie
Nang-Kang
Tam-Sui
Huang
Shuang
De-Zi-Kou
Lan-Yang
0.61 0.11 0.39 0.29 0.32 0.42 0.23 0.92 0.22 0.47 0.29 0.46 0.13 0.30 0.02 0.31 0.83 0.43 0.43 0.34 0.84 0.35 1.42 0.13 0.07 0.03 0.23 0.35 0.16 0.77 0.37 0.27 0.04 0.86 0.08 1.03
0.59 0.11 0.41 0.31 0.31 0.41 0.24 0.91 0.19 0.49 0.28 0.49 0.15 0.32 0.02 0.26 0.81 0.42 0.37 0.36 0.88 0.34 1.39 0.14 0.07 0.04 0.24 0.34 0.17 0.80 0.29 0.27 0.04 0.85 0.09 1.01
0.43 0.14 0.51 0.34 0.22 0.40 0.31 0.99 0.17 0.60 0.25 0.56 0.21 0.40 0.03 0.21 0.80 0.43 0.14 0.41 1.14 0.21 1.33 0.09 0.06 0.04 0.28 0.47 0.21 0.85 0.12 0.25 0.05 0.90 0.14 0.99
0.53 0.14 0.41 0.30 0.15 0.37 0.29 0.77 0.14 0.50 0.24 0.48 0.25 0.37 0.03 0.12 0.72 0.37 0.20 0.32 0.88 0.34 1.20 0.17 0.04 0.04 0.27 0.45 0.20 0.63 0.16 0.23 0.06 0.66 0.13 0.81
0.63 0.22 0.38 0.28 0.11 0.35 0.38 0.57 0.14 0.44 0.34 0.44 0.27 0.35 0.04 0.10 0.65 0.34 0.15 0.17 0.83 0.38 1.04 0.17 0.03 0.07 0.41 0.42 0.31 0.58 0.14 0.30 0.09 0.49 0.18 0.74
0.66 0.17 0.43 0.15 0.22 0.31 0.23 0.29 0.26 0.53 0.41 0.47 0.21 0.41 0.06 0.19 0.59 0.20 0.29 0.28 0.73 0.55 0.94 0.32 0.06 0.07 0.33 0.44 0.25 0.51 0.27 0.29 0.06 0.28 0.10 0.74
0.68 0.19 0.46 0.12 0.19 0.27 0.26 0.21 0.27 0.51 0.44 0.47 0.19 0.44 0.06 0.19 0.55 0.15 0.28 0.24 0.70 0.53 0.94 0.32 0.06 0.08 0.40 0.42 0.30 0.51 0.26 0.27 0.06 0.19 0.13 0.74
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The differences between measured and simulated peak surge heights for all these 3 cases are less than 10%. In the calculations, the boundary conditions of the bottom frictions, eddy viscosity, and wind drag coefficients were fixed. It is thus concluded that, the present setups of the model are validated. 3.2. Building surge database It is rather often that the regions around estuary are urbanized to a substantial extent, and are inhabited by a relatively large population. In the mean time, these are also the regions which usually suffer from the storm surges and flooding. However, the tidal observation points are sparse along the littoral region of northern Taiwan. The 7 estuaries of the main tributaries in the research region are Lao-Jie, Nang-Kan, TamSui, Huang, Shuang, De-Zi-Kou and Lan-Yang estuary. TamSui is the only estuary which has set the tidal measurement. The tidal observation stations mentioned previously were unfortunately far away from these estuaries. Moreover, a control of the quality of measurements was not done before 1997. The data available are incomplete and are therefore not suitable to be used as a database. The feasibility of the present numerical model was assessed in the previous section. It is shown that, the estimated peak values of the surge heights can be considered as acceptable. Here in this section, we present simulated surges of these estuaries of the historical typhoon events for the
years from 1980 to 2004. Estimated peak values are shown in Table 1. Typhoons in these years are considered only when their tracks have distances less than 250 km away from Taiwan. It can be seen from Table 1 that, surges in the western side of Taiwan are usually larger then those of the eastern side. This is due to the fact that, the continental shelf is shallower in the western Taiwan, and that the bathymetry is flatter than that of eastern Taiwan. The largest surge event was due to typhoon Herb (1994), and occurred at Lao-Jie estuary. Simulated peak values of the surge alone the west coasts, which includes LaoJie, Nan-Kan, and Tam-Sui are, respectively, 1.42 m, 1.39 m and 1.33 m. The measured peak surge value in the Tam-Sui estuary was 1.31 m and is seen to be quite close to the simulated one. Frequency analysis is a vital component of coastal hazard assessment. Through the analysis, possible surge height can be estimated, and thus provides information for surge flood prevention and engineering design works. Here we used models of extreme value distributions to fit simulated annual peak values of typhoon surge. These statistical distributions include: the normal, the two- and three-parameter log-normal, the Pearson type Ш, the log-Pearson type Ш, and the type I extreme value distributions. Mathematical expressions for these distributions can be found in textbooks concerning frequency analysis (Shahin et al., 1993), and will not be repeated here. The analyses showed that, as far as the standard errors and the sum of residuals are concerned, the Pearson type Ш, and the three-
Fig. 10. The frequency analysis of the surge heights for the Tam-Sui estuary.
W.-P. Huang et al. / Coastal Engineering 54 (2007) 883–894 Table 2 The frequency analysis of surge height of each estuary Estuary
Lao-Jie
Nang-Kan
Tam-Sui
Huang
Shuang
De-Zi-Kao
Lan-Yang
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Table 3 The goodness-fit equations of each estuary
The surge height Return period (year)
Three parameters log-normal distribution
Pearson type III distribution
5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
0.78 0.99 1.20 1.47 0.78 0.98 1.18 1.45 0.84 1.04 1.23 1.47 0.72 0.86 1.03 1.24 0.65 0.78 0.91 1.08 0.61 0.73 0.84 0.98 0.61 0.73 0.84 0.97
0.79 1.00 1.21 1.49 0.78 0.99 1.19 1.46 0.84 1.05 1.24 1.47 0.72 0.87 1.04 1.24 0.65 0.79 0.92 1.08 0.61 0.73 0.84 0.98 0.61 0.73 0.84 0.97
parameter log-normal distributions yield most favorable results. Fig. 10 shows the results of fitting the Tam-Sui estuary. Table 2 summarized the possible surge heights of each estuary for the recurrence interval of 5, 10, 20, and 50 years for both the threeparameter log-normal and the Pearson type Ш distributions.
Estuary and coordinates
The goodness-fit equation
R-square
Lao-Jie E:121.1647° N:25.0891° Nang-Kan E:121.2388° N:25. 1215° Tam-Sui E:121.4094° N:25.1745° Huang E:121.6399° N:25.2348° Shuang E:121.9386° N:25.0225° De-Zi-Kao E:121.8207° N:24.8436° Lan-Yang E:121.8323° N:24.7143°
η = 0.017ΔP − 0.101 η = 0.016ΔP − 0.100 η = 0.016ΔP − 0.102 η = 0.014ΔP − 0.179 η = 0.012ΔP − 0.068 η = 0.011ΔP − 0.060 η = 0.011ΔP − 0.060
0.81 0.82 0.76 0.87 0.87 0.81 0.82
ΔP = (1016 − Pc)[1 − exp(− Rmax/r)].
It has been discussed previously that the decrease of the uncertainty of the surge simulation depends on the enhancement of the reliable forecast of the typhoon track and the pressure distribution. If the movement of typhoon deviated from the prediction, the surge simulation must be modified for the succeeding times. However surge simulation is a rather timeconsuming process and this could delay the executions of an emergency evacuation plan. Furthermore, it is probably that the simulation could only be carried out by a trained professional and is not easily operational. All these difficulties can be overcome through the use of appropriate statistical techniques. It is known that surge height is directly proportional to the difference between the central and the surrounding pressures of the cyclone Eq. (6). Here a regression equation is obtained from all the parameters considered to be important in determining the surge height. These are, the atmospheric pressure of typhoon (Pc), the distances between typhoon eye and each estuary (r), the radius of the maximum winds (Rmax), and the simulated surge heights (η) of each historical typhoon. The distances (r) between typhoon eye and each estuary are computed following the methodology proposed by Meeus (1998). Fig. 11 shows the goodness-of-fit results for the Shuang estuary. The result in the figure stands for the combined effects of the meteorological parameters and the simulated surges of the historical typhoons. These typhoon surges are outputs of the simulation every 30 min during the lifetime of the typhoon. The regression equations of each estuary and the correlation coefficients (R-square, Eq. (7)) are summarized in Table 3. It can be seen that the slopes of the equations are steeper for the western estuaries than for the eastern. This means that, for the same typhoon strength, the surges in the western estuaries are larger. The coordinates of each estuary are also presented in Table 3 for the reference to estimate the distance (r) from the center of typhoon to each estuary. Using these equations, an estimate of the surge height can be rapidly given without going through the complicated simulation process. In Taiwan, coastal protections are usually designed with a return period of 20 years for storm surges. Using the method proposed in this paper, evaluation of the potential hazard for each estuary can be easily carried out. h i g / DP ¼ ð1016 Pc Þ 1 exp ðRmax =rÞ
Fig. 11. Results of the goodness-fit for the Shuang river estuary.
RQsquare ¼
SSe SSe þ SSr
ð6Þ ð7Þ
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SSe
the sum of the squares of all the residual values. A residual is the difference between the fit y value and the actual y data value at any given x value. SSr the sum of squares of the difference between the average of all y values and the fit y values at each x location where a data point occurs. R-square shows how well the data are explained by the best-fit line. 4. Conclusions A high-resolution numerical model has been developed in this paper. This model has an acceptable computational time, and it is shown that, the model is capable of predicting the surge heights along the coastal areas of the northern Taiwan. The meshes used in the model consist of triangular unstructured grids, and this increases the flexibility for the cases of irregular coastlines and narrow estuaries. It also increases the efficiency of the simulation. For deep, open sea regions, larger meshes can be used. On the other hand, for simulations of the littoral zone, smaller meshes should be used. A computational rate up to 9.6:1 can be achieved by the present scheme. The accuracy of simulate results has been checked through comparison with records from tidal stations. It is shown that deviations between measured and simulated peak surge heights are less than 10%. Using the model proposed in this study, a data bank of the historical surge heights for the period of 1980 to 2004 was constructed. Using these, a data bank of historical typhoon events was constructed. The regression equations of the surge height and ΔP are obtained and these can be used for the prediction of the surge height of estuaries before the actual landfall of typhoon occurs. It is therefore concluded that, the numerical model and the statistical equations proposed in this study are all capable of predicting the surge hazard or northern Taiwan. References Benqué, J.P., Hauguel, A., Viollet, P.L., 1982. Engineering Applications of Computational Hydraulics, vol. 2. Pitman Publications. CWB, the Central Weather Bureau, 2006. Typhoon hazard messages. http:// 61.56.13.9/data.php.
Dean, R.G., Darlymple, R.A., 2002. Coastal Process with Engineering Application. Cambridge University Press, UK. DHI, 2002. Mike 21, Coastal Hydraulics and Oceanography, Hydrodynamic Module, Reference Manual, DHI Water and Environment, Hørsholm, Denmark. FEMA, Federal Emergency Management Agency, 2006a. Hurricane Katrina Rapid Response, High Water Mark Collection for Hurricane Katrina in Albama, Final Report, FEMA-0605-DR-AL. FEMA, Federal Emergency Management Agency, 2006b. Hurricane Rita Rapid Response, Coastal & Riverine High Water Mark Collection, Final Report, FEMA-1606-DR-TX. Holland, G.J., 1980. An Analytic Model of the Wind and Pressure Profiles in Hurricanes. Monthly Weather Review, vol. 108, pp. 1212–1218. Hsu, T.W., Liau, J.M., Lee, Z.S., 1999. Prediction of storm surge at northeastern coast of Taiwan by finite element method. Journal of the Chinese Institute of Civil and Hydraulic Engineering 11 (4), 849–857. Huang, W.P., Hsu, C.A., Lin, J.S., Kung, C.S., Huang, C.K., 2005. Numerical Studies on Typhoon surges in the northern part of Taiwan. Proceedings of the 27th Ocean Engineering Conference in Taiwan, Taichung, Taiwan, pp. 283–288 (in Chinese). Meeus, Jean, 1998. Astronomical Algorithms. Willimann-Bell Inc., pp. 223–241. Jelesnianski, C.P., Chen, J., Shaffer, W.A., 1992. SLOSH: Sea Lake and Overland Surges from Hurricane Phenomena, NOAA Technical Report NWS 48, National Weather Service, Silver Spring, MD. JMA, Japan Meteorological Agency, 2002. Warning and Advisories-Tropical Cyclone. http://www.jma.go.jp/en/typh/. JTWC, Jiont Typhoon Warning Center, 2005. Current Western Pacific/India Ocean Tropical System-TC Warning Graphic. http://www.npmoc.navy.mil/ jtwc.html. Liu, S.K., 1987. The project of building the typhoon surge and climate parameters forecast model. Report of the Central Weather Bureau, vol. 279. Munk, W.H., 1947. Tracking storms by forerunners of swell. Journal of the Atmospheric Science 4 (2), 45–57. Madsen, H., Jakobsen, F., 2004. Cyclone induced storm surge and flood forecasting in the north Bay of Bengal. Coastal Engineering 51, 277–296. National Geophysical Data Center, 2004. GEODAS Data. http://www.ngdc. noaa.gov/mgg/geodas/geodas.html. National Center for Ocean Research-Ocean Data Bank, 2004. Bathymetric Data. http://www.ncor.ntu.edu.tw/ODBS/depth/. Plüß, A.E., Schrödter, Ruodolph D., 2001. Characteristics of storm surges in German estuaries. Climate Research 18, 71–76. Pruszak, Z., Ninh, P.V., Szmytkiewics, M., Hung, N.M., Ostrowski, R., 2005. Hydrology and morphology of two river mouth regions (temperate Vistula Delta and subtropical Red River Delta). Oceanologia 47 (3), 365–385. Shahin, M., Oorschot, H.J.L.V., Delange, S.J., 1993. Statistical Analysis in Water Resources Engineering. Brookfield, USA. Soares, C.G., Weisse, R., Carretero, J.C., Alvarez, E., 2002. A 40 years hindcast of wind, sea level and waves in European waters. Proceedings of OMAE 2002: 21st International Conference on Offshore Mechanics and Arctic Engineering, Oslo, Norway, pp. 1–7.
Coastal Engineering 54 (2007) 883 – 894 www.elsevier.com/locate/coastaleng
Numerical studies on typhoon surges in the Northern Taiwan Wei-Po Huang a,⁎, Chiang-An Hsu b , Chen-Shan Kung c , John Z. Yim d a
Department of Hydraulic Engineering, Sinotech Engineering Consultants, 5F, No.19, Lane 71, Lin-Yi Street, 100 Taipei, Taiwan, ROC b Civil and Hydraulics and Informatics Research Center, Sinotech Engineering Consultants, Taiwan, ROC c Department of Hydraulic Engineering, Sinotech, Taiwan, ROC d Department of Harbour and River Engineering, National Taiwan Ocean University, Taiwan, ROC Received 8 November 2006; received in revised form 28 May 2007; accepted 31 May 2007 Available online 10 August 2007
Abstract A numerical model for the simulation of typhoon surge has been developed for the coastal areas of the northern Taiwan. Results from the model outputs are then used as a typhoon surge data bank for 7 main estuary areas in this region. The data bank consists of the historical typhoon events from 1980 to 2004. Both characteristic and frequency analyses of the typhoon surge in the coastal region have been studied. Using these data, a relation between the surge height and pressure distribution is obtained. It is shown that, either the numerical model, or the statistical equations presented in this paper, can be used to predict possible surge heights in the estuary areas with sufficient accuracy. © 2007 Elsevier B.V. All rights reserved. Keywords: Typhoon surge; Forecast; Finite volume method
1. Introduction Taiwan lies on the west side of the Pacific Ocean and is usually invaded by typhoons in summers and autumns. When typhoon approaches to the coast, a surge usually occurs. This is induced either by the strong onshore winds which pile the water up, or the low barometric pressure that causes the sea level to rise. If it occurs during high tides, the risks of coast flooding will be enhanced. A flood defense plan to minimize the economic and social damages caused by possible storm surges is of vital importance for an efficient coastal management strategy. In this respect, numerical simulation and/or statistical analysis are the two most important tools for the predictions of possible water level rise due to typhoon surge. This paper presents our recent efforts toward this purpose. Simulations of storm surges are usually carried out through the use of a two-dimensional shallow water equation. The Navier–Stokes equations are simplified by a depth averaging procedure (Benqué et al., 1982). Madsen and Jakobsen (2004) simulated storm surge and flood in the Bay of Bengal by using Mike 21 hydrodynamic model developed by DHI Water and ⁎ Corresponding author. Tel.: +886 9 1870 8135; fax: +886 2 8761 1595. E-mail address: [email protected] (W.-P. Huang). 0378-3839/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2007.05.015
Environment (DHI, 2002). The model allows the use of nested grids based on a dynamically consistent two-way nesting technique for the increasing of the computational grids in the concerned region. However, the model may have difficulties when applied to complex coastal lines, or long and narrow estuaries. Plüβ and Schödter (2001) studied the characteristics of storm surges in German estuaries. They used a so-called TELEMAC-2D hydrodynamic model based on a finite element method. Non-uniform triangular grids were used in this model so that efficient and flexible simulations can be obtained. FEMA used the SLOSH model (Sea Lake and Overland Surges from Hurricanes) to predict the maximum surge heights for most US coastlines (FEMA, 2006a,b). This model was developed by Jelesnianski et al. (1992). Actually, two types of analyses, i.e., the MEOW (Maximum Envelope of Water) and the MOM (Maximum of Maximum), are included in the SLOSH model. The former analysis derived the highest water level due to parallel tracks of hurricanes with the same direction, speed and intensity to retrieve the uncertainty of the hurricane movement forecast. The latter gives an estimate of the highest water level due to a composite of the MEOW. This is to say, the MOM analysis yields the worst-case scenario. The mesh of the model is built as sector grids that lead to the similar drawback as that of Mike 21.
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All these studies have shown satisfactory results. However, it is found that all these simulation procedures suffer from an inherent weakness. It can be argued that, all the predicted meteorological conditions, such as the typhoon travel route, the atmospheric pressure distribution, and the maximum wind speed, can have strong effect on storm surges. That is to say, all surge simulations can have favorable results only after typhoon passages. This is because only then, are the meteorological parameters used in the procedures correct. On the other hand, before the landfall of typhoon, the uncertainty of the typhoon forecast increases the difficulty for predicting surge height. At present, the accuracy for predicting these parameters is confined by our limited knowledge of the meteorology (Soares et al., 2002). This can be seen from the typhoon forecasts issued by the national and international weather bureaus. For example, the errors of tolerance of predicted tracks of typhoon propagation issued by the JTWC (Joint Typhoon Warning Center, 2005) or the JMA (Japan Meteorological Agency, 2002) are usually within 200 km. This is almost equal to half the length scale of Taiwan. This leads to uncertainties of predicting the surge height for relatively small regions such as Taiwan. An efficient numerical scheme or a statistical data bank may provide a better solution for the problem mentioned above. Efficient simulation scheme is needed once modifications of the predicted typhoon track or other parameters are available. In this way, the surge simulation can be kept ongoing. The statistical data bank, on the other hand, is used to evaluate the potential hazard. Generally speaking, the more factors are considered in the simulation, the more faithfully results can be obtained. However, this will force the numerical schema to be more timeconsuming. In a surge hazard warning system, both efficiency and accuracy are of primary concern. It seems that a statistical
Fig. 2. Schematic representation of the set up mesh for simulation.
database can resolve the problem. Through the use of the database, forecasted results can be adjusted by comparing with the results of similar typhoons. These procedures can be done rapidly. The database can also be used for various kinds of purposes, such as evaluation of flood hazard, coastal morphology, as well as for engineering design. If the measurements were well implemented, the database can be built by using historical data. A comparison of the results obtained for the Red River and Vistula Delta was given by Pruszak et al. (2005). The magnitudes of typhoon surge in different latitudes were estimated using measured data. However, not all the meteorological happenings in the littoral region can be well
Fig. 1. The geographic positions of the study region.
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Fig. 3. The track of typhoon Aere (CWB, 2006).
observed and recorded. The measurements could be destroyed by the severe weather sometimes and the data for extreme weather were unavailable. In this case, numerical simulation can be used to hindcast and reconstruct the typhoon events, and the results may be used for the database. Liu (1987) used a coupled meteorological-hydrodynamical 3-D numerical model to investigate water level variations during typhoon passage. Since the calculation is rather time-consuming, a number of modal typhoons were used to expand the database by Liu.
The objective of this study presented in this paper is to develop a surge simulation model and to build up a database of surge height for the northern coast of Taiwan since 1980. The area studied in this paper consists of 7 main estuaries and tidal observation points. A schema of the geographic locations is shown in Fig. 1. 2. Mathematical background 2.1. Hydrodynamic model The factors affect the fluid field, such as wind, Coriolis force, the bottom friction, fluid shear stress and topographical boundary conditions will be considered in the present model. The governing equations of the model consist of the two horizontal (x and y direction) components of momentum and an equation for the conservation of mass. The equation of continuity and momentum are shown in Eqs. (1), (2) and (3) respectively. Continuity equation Ah Ap Aq þ þ ¼ Sh At Ax Ay
ð1Þ
The momentum equation in the x-direction, which is from west to east, is expressed as: Ap A p2 gh2 A pq 1 þ þ ¼ ghS0X þ Xq þ ssx sbx þ At Ax h Ay h q 2 1 A A h APa hsexx þ hsexy þ Sp þ q Ax Ay q Ax Fig. 4. The simulated result of the surge height distributions.
ð2Þ
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Fig. 5. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Aere).
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The momentum equation in y direction (south to north) is expressed as: Aq A pq A q2 gh2 1 s þ sy sby þ þ ¼ ghS0Y þ Xp þ At Ax h Ay h q 2 1 A A h APa þ hsexy þ hseyy þ Sq: q Ax Ay q Ay ð3Þ where t x, y, z
time spatial coodinates which x and y are horizontal coordinates and z is vertical coordinate h water depth g gravity acceleration Pa atmosphere pressure ρ the density of water Ω the parameter of Coriolis force S0X, S0Y the bed slope in x and y directions, respectively; τxs, τys the wind stress terms in x and y directions τxb, τyb the bottom friction terms in x and y directions e e e τxx , τyy , τxy the depth-averaged Reynolds stresses h S the source term of the continuity equation Sp, Sq the source terms of the momentum equation in the x and y directions. The equations are discretized using the semi-discrete, cellcentered and finite-volume methods. Taking a semi-discrete approach has the advantages that the discretization schemes in
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spatial and temporal domain can be more easily and flexibly designed. 2.2. Wind and pressure field The wind field of a typhoon is usually very intense, and spatially inhomogeneous, as well as directionally varying. The large gradients of the wind speeds and the rapidly varying wind directions of the typhoon vortex can generate very complex ocean wave fields. However, for practical applications the wind fields are usually expressed in the form of parametric models. In this paper, the typhoon wind field is assumed to have a form which is nearly circular. The pressure distribution is assumed to have an exponential form and can be express by (Holland, 1980): B
Pr ¼ Pc þ ðPn Pc ÞeðRmax =rÞ
ð4Þ
where Pc is the pressure at the center, Pn is the ambient or environmental pressure, and has a value of 1016 hPa, r is the radius (the distance from the center), Rmax is the radius of the maximum wind, and B is a shape parameter. Usually, the shape parameter B has values ranging from 1 to 2.5. Huang et al. (2005) have used several theoretical distributions for typhoon pressure and its wind field to estimate possible typhoon surges for the coastal regions in northern Taiwan. It is found that, a shape parameter B with a value of 1 yields the most favorable results. The wind speed distribution is usually derived using a gradient wind model or simply by using an empirical expression.
Fig. 6. The track of typhoon Talim (CWB, 2006).
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The distribution used in this study was that proposed by (Hsu et al., 1999) which can be expressed as: " 2 #1=2 Pn Pc Rmax ðRmax =rÞ 1 1 Xr ð5Þ Vg ¼ e þ Xr 2 2 qa r where Vg ρa
gradient wind speed the density of the air.
The shear stress of the wind and the pressure field are the external forces in the present model.
2.3. Boundary condition formulations Various types of boundary conditions are needed for the model. These will be described shortly in the following. The four seaward boundaries are assumed to be non-reflective to minimize reflections of the outgoing waves. At present, information concerning astronomic tidal variation on the open sea is unavailable to us; we have, therefore, set the initial water level to zero in the present model. This means that, variations of the water surface elevations were induced by typhoon only. Close to the land, a moving boundary condition is used so that the process of wetting and drying of the surge flats can be taken into account.
Fig. 7. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Talim).
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2.4. Mesh construction for the area studied This study focuses on the development of a storm surge simulation model which has both high spatial resolution, as well as efficient computation ability. The region considered in the study lies within the longitudes from 117° E to 126° E and the latitudes from 18° N to 28° N. The DTM (Digital Terrain Model) bathymetric data were obtained from the NGDC (National Geophysical Data Center, 2004) and from the NCOR (National Center for Ocean Research, 2004). The length of the grid sides in the littoral region close to the coast was 300 m, and for those in the deep sea far away from Taiwan a length of 15,000 m was used. In this way, the efficiency of simulation can be increased substantially. A total of 29,266 triangular elements and 16,402 nodes are used for the simulation. The setups of the mesh for the simulation are shown in Fig. 2. 2.5. The computational rate When the potential of a typhoon invasion exists, the CWB (Central Weather Bureau, 2006) of the Republic of China carries out prediction every 3 h. In each forecast, the meteorological information will be updated, and calculated results are used as prediction for the next 3 h. In carrying out our surge simulation, the boundary conditions can be obtained from the forecast. These include, the predicted typhoon track, the pressure at the center, the radius of the maximum wind speed, typhoon radius, and the maximum wind speed of the depression. That is to say, the typhoon surge simulation of the present study start after the typhoon forecast issued by the CWB. On the other hand, for the purpose of “pre-warning”, the
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computation should be done within an hour or so. Each step of the simulation should simulate 6-h surge distribution including the past and the future 3 h. This means that, the ratio of the computational rate, i.e., real to computational time, should be higher than 6:1. The presented numerical scheme of surge simulation has a rate of 9.6:1, and is seen to be far higher than necessary. All the computations were carried out on an Intel Pentium IV personal computer with a 2.6 GHz CPU and 1 GB DRAM. 3. Results and discussion 3.1. Boundary conditions calibration Three typhoons are used to calibrate the hydraulic boundary conditions of the present model. These three typhoons are Typhoon Aere (2004), Typhoon LongWang (2005), and Typhoon Talim (2005). These three typhoons have made most severe impacts to the northern Taiwan within last 2 years (2004 and 2005). The atmospheric parameters issued by the typhoon forecast of the CWB were used as boundary conditions for the surge simulation. The CWB has 7 tidal observation stations operational along the coast. The stations have the name Zhu-Wei, Tam-Sui, Lin-Sah-Bue, Keelung, Long-Dong, Geng-Fang and Su-Ao. However, due probably to malfunctions of the tidal gauges, records of water surface fluctuations are sometimes missing. Whenever available, these were used for the calibration. Typhoon Aere was a Category 1 typhoon with winds estimated at the maximum intensity to be 65 knots. It approached to Taiwan from the southeast and turn around to the northwest coast on 20 Aug. 2004. The typhoon eye did not make landfall.
Fig. 8. The track of typhoon Longwang (CWB, 2006).
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However, the economic activities in the northern part of Taiwan have been halted for 2 days. The typhoon track is shown in Fig. 3 (CWB, 2006). Fig. 4 is the estimated surge heights when typhoon Aere is closest to Taiwan. Measured and simulated results on each tidal observation points along the northern coast of Taiwan are shown together in Fig. 5. The solid line with hollow square symbols is the simulated water surface elevation, which is the sum of simulated surge height plus that due to astronomic tides and the measured ones are represent in the solid lines with circular symbols. The astronomic tidal heights are estimated through harmonic analysis (CWB, 2006). Simulated and measured surge heights are shown as lines with crosses and triangular symbols respectively. The later one is
the difference between the measured sea water level and the predicted astronomic tide. It is noted that predicted astronomic tides have minor phase lags and different amplitudes as those of actual ones. That is due to the fact that only a limited number of harmonic functions are used in the estimate, and these are insufficient to express the variation of the astronomic tides. Nevertheless, it can be seen that, the differences of the phase lag and that of the amplitudes are less than 0.5 h and 0.5 m, respectively. It is thus concluded that the agreements between simulated and measured results are satisfactory. It can also be seen that, in the figure, simulated fore runners (08/23 12:00–08/24 12:00) are always smaller than those extracted from tidal records. The deviation was caused by two
Fig. 9. The comparison of the simulated and measured surge height and water surface elevation in each observation points (Typhoon Longwang).
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reasons. One of the reasons is that variation of the astronomic tides has not been exactly reproduced. The derived component of the measured surges can still contain harmonics of the tidal variation due to the small phase lags between recorded and simulated tidal variations. The other reason could be that, swells generated by typhoons were not considered in the model. Swells usually have heights ranging from 1 to 3 m (Dean and Darlymple, 2002), and they have speeds faster than those of typhoon waves (Munk, 1947). The incoming long waves pile up along the coast continuously may also cause the rise of sea water level measured nearshore. With typhoon approaching, the effect of the swell will be long gone. It can be seen that from 08/ 24 18:00 to 08/25 00:00, i.e., when typhoon Aere was close to Taiwan, the differences between simulated and measured results are smaller. This seems to indicate that, with typhoon approaching, the performance of the present model will be better. Talim was a storm of category 4 with maximum winds at 95 knots, and a low pressure of 925 hPa at the center (Fig. 6). At least 7 people were reported killed by the storm in Taiwan. The typhoon stayed in the east coast of Taiwan for 6 h then headed west over Taiwan in 3 h. In the meantime, the strength of
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Typhoon Talim decreased rapidly due to the obstruction of the Central Mountain located in the middle of Taiwan. The pressure increased from 925 hPa to 955 hPa and the wind speed in the center decreased from 95 knots to 78 knots. Comparisons of the results are shown in Fig. 7. It can be seen that the surges around the northern part of Taiwan are rather small. They were all less than 0.5 m. Typhoon Longwang was a super typhoon of Category 5 with winds over 90 knots (Fig. 8). It swept over the middle of Taiwan on 1 Oct. 2005. The radius of typhoon was small but it was very compactly structured. It advances with a speed of 18–20 km/ h while crossing Taiwan. Simulated and measured results are shown in Fig. 9. Su-Ao is the tidal station closest to the point that where typhoon made landfall. From Fig. 9, it can be seen that, simulated and measured surge heights are, respectively, 0.549 m and 0.542 m. This shows that the model has estimated the peak value of the surge almost exactly. It can also be seen that, the surge heights of other measuring stations decrease with the increasing distance away from the typhoon center. It can thus be concluded that, in general, simulated water surface heights agree well with those measured.
Table 1 The peak value of the simulated typhoon surge of each estuary Typhoon
1980 Norris 1981 Ike 1981 June 1981 Maury 1984 Alex 1984 Freda 1985 Nelson 1985 Brenda 1986 Nancy 1986 Wayne 1986 Abby 1987 Vernon 1987 Alex 1989 Sarah 1990 Marian 1990 Ofelia 1990 Yancy 1991 Ellie 1992 Polly 1992 Ted 1994 Doug 1994 Gladys 1996 Herb 1997 Amber 1998 Otto 1998 Yanni 1998 Zeb 2000 Kai-Tak 2000 Xangsane 2001 Toraji 2001 Nari 2002 Nakri 2003 Vamco 2004 Aere 2004 Haima 2004 Nockten
The peak value of the surge height (m) Lao-Jie
Nang-Kang
Tam-Sui
Huang
Shuang
De-Zi-Kou
Lan-Yang
0.61 0.11 0.39 0.29 0.32 0.42 0.23 0.92 0.22 0.47 0.29 0.46 0.13 0.30 0.02 0.31 0.83 0.43 0.43 0.34 0.84 0.35 1.42 0.13 0.07 0.03 0.23 0.35 0.16 0.77 0.37 0.27 0.04 0.86 0.08 1.03
0.59 0.11 0.41 0.31 0.31 0.41 0.24 0.91 0.19 0.49 0.28 0.49 0.15 0.32 0.02 0.26 0.81 0.42 0.37 0.36 0.88 0.34 1.39 0.14 0.07 0.04 0.24 0.34 0.17 0.80 0.29 0.27 0.04 0.85 0.09 1.01
0.43 0.14 0.51 0.34 0.22 0.40 0.31 0.99 0.17 0.60 0.25 0.56 0.21 0.40 0.03 0.21 0.80 0.43 0.14 0.41 1.14 0.21 1.33 0.09 0.06 0.04 0.28 0.47 0.21 0.85 0.12 0.25 0.05 0.90 0.14 0.99
0.53 0.14 0.41 0.30 0.15 0.37 0.29 0.77 0.14 0.50 0.24 0.48 0.25 0.37 0.03 0.12 0.72 0.37 0.20 0.32 0.88 0.34 1.20 0.17 0.04 0.04 0.27 0.45 0.20 0.63 0.16 0.23 0.06 0.66 0.13 0.81
0.63 0.22 0.38 0.28 0.11 0.35 0.38 0.57 0.14 0.44 0.34 0.44 0.27 0.35 0.04 0.10 0.65 0.34 0.15 0.17 0.83 0.38 1.04 0.17 0.03 0.07 0.41 0.42 0.31 0.58 0.14 0.30 0.09 0.49 0.18 0.74
0.66 0.17 0.43 0.15 0.22 0.31 0.23 0.29 0.26 0.53 0.41 0.47 0.21 0.41 0.06 0.19 0.59 0.20 0.29 0.28 0.73 0.55 0.94 0.32 0.06 0.07 0.33 0.44 0.25 0.51 0.27 0.29 0.06 0.28 0.10 0.74
0.68 0.19 0.46 0.12 0.19 0.27 0.26 0.21 0.27 0.51 0.44 0.47 0.19 0.44 0.06 0.19 0.55 0.15 0.28 0.24 0.70 0.53 0.94 0.32 0.06 0.08 0.40 0.42 0.30 0.51 0.26 0.27 0.06 0.19 0.13 0.74
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The differences between measured and simulated peak surge heights for all these 3 cases are less than 10%. In the calculations, the boundary conditions of the bottom frictions, eddy viscosity, and wind drag coefficients were fixed. It is thus concluded that, the present setups of the model are validated. 3.2. Building surge database It is rather often that the regions around estuary are urbanized to a substantial extent, and are inhabited by a relatively large population. In the mean time, these are also the regions which usually suffer from the storm surges and flooding. However, the tidal observation points are sparse along the littoral region of northern Taiwan. The 7 estuaries of the main tributaries in the research region are Lao-Jie, Nang-Kan, TamSui, Huang, Shuang, De-Zi-Kou and Lan-Yang estuary. TamSui is the only estuary which has set the tidal measurement. The tidal observation stations mentioned previously were unfortunately far away from these estuaries. Moreover, a control of the quality of measurements was not done before 1997. The data available are incomplete and are therefore not suitable to be used as a database. The feasibility of the present numerical model was assessed in the previous section. It is shown that, the estimated peak values of the surge heights can be considered as acceptable. Here in this section, we present simulated surges of these estuaries of the historical typhoon events for the
years from 1980 to 2004. Estimated peak values are shown in Table 1. Typhoons in these years are considered only when their tracks have distances less than 250 km away from Taiwan. It can be seen from Table 1 that, surges in the western side of Taiwan are usually larger then those of the eastern side. This is due to the fact that, the continental shelf is shallower in the western Taiwan, and that the bathymetry is flatter than that of eastern Taiwan. The largest surge event was due to typhoon Herb (1994), and occurred at Lao-Jie estuary. Simulated peak values of the surge alone the west coasts, which includes LaoJie, Nan-Kan, and Tam-Sui are, respectively, 1.42 m, 1.39 m and 1.33 m. The measured peak surge value in the Tam-Sui estuary was 1.31 m and is seen to be quite close to the simulated one. Frequency analysis is a vital component of coastal hazard assessment. Through the analysis, possible surge height can be estimated, and thus provides information for surge flood prevention and engineering design works. Here we used models of extreme value distributions to fit simulated annual peak values of typhoon surge. These statistical distributions include: the normal, the two- and three-parameter log-normal, the Pearson type Ш, the log-Pearson type Ш, and the type I extreme value distributions. Mathematical expressions for these distributions can be found in textbooks concerning frequency analysis (Shahin et al., 1993), and will not be repeated here. The analyses showed that, as far as the standard errors and the sum of residuals are concerned, the Pearson type Ш, and the three-
Fig. 10. The frequency analysis of the surge heights for the Tam-Sui estuary.
W.-P. Huang et al. / Coastal Engineering 54 (2007) 883–894 Table 2 The frequency analysis of surge height of each estuary Estuary
Lao-Jie
Nang-Kan
Tam-Sui
Huang
Shuang
De-Zi-Kao
Lan-Yang
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Table 3 The goodness-fit equations of each estuary
The surge height Return period (year)
Three parameters log-normal distribution
Pearson type III distribution
5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
0.78 0.99 1.20 1.47 0.78 0.98 1.18 1.45 0.84 1.04 1.23 1.47 0.72 0.86 1.03 1.24 0.65 0.78 0.91 1.08 0.61 0.73 0.84 0.98 0.61 0.73 0.84 0.97
0.79 1.00 1.21 1.49 0.78 0.99 1.19 1.46 0.84 1.05 1.24 1.47 0.72 0.87 1.04 1.24 0.65 0.79 0.92 1.08 0.61 0.73 0.84 0.98 0.61 0.73 0.84 0.97
parameter log-normal distributions yield most favorable results. Fig. 10 shows the results of fitting the Tam-Sui estuary. Table 2 summarized the possible surge heights of each estuary for the recurrence interval of 5, 10, 20, and 50 years for both the threeparameter log-normal and the Pearson type Ш distributions.
Estuary and coordinates
The goodness-fit equation
R-square
Lao-Jie E:121.1647° N:25.0891° Nang-Kan E:121.2388° N:25. 1215° Tam-Sui E:121.4094° N:25.1745° Huang E:121.6399° N:25.2348° Shuang E:121.9386° N:25.0225° De-Zi-Kao E:121.8207° N:24.8436° Lan-Yang E:121.8323° N:24.7143°
η = 0.017ΔP − 0.101 η = 0.016ΔP − 0.100 η = 0.016ΔP − 0.102 η = 0.014ΔP − 0.179 η = 0.012ΔP − 0.068 η = 0.011ΔP − 0.060 η = 0.011ΔP − 0.060
0.81 0.82 0.76 0.87 0.87 0.81 0.82
ΔP = (1016 − Pc)[1 − exp(− Rmax/r)].
It has been discussed previously that the decrease of the uncertainty of the surge simulation depends on the enhancement of the reliable forecast of the typhoon track and the pressure distribution. If the movement of typhoon deviated from the prediction, the surge simulation must be modified for the succeeding times. However surge simulation is a rather timeconsuming process and this could delay the executions of an emergency evacuation plan. Furthermore, it is probably that the simulation could only be carried out by a trained professional and is not easily operational. All these difficulties can be overcome through the use of appropriate statistical techniques. It is known that surge height is directly proportional to the difference between the central and the surrounding pressures of the cyclone Eq. (6). Here a regression equation is obtained from all the parameters considered to be important in determining the surge height. These are, the atmospheric pressure of typhoon (Pc), the distances between typhoon eye and each estuary (r), the radius of the maximum winds (Rmax), and the simulated surge heights (η) of each historical typhoon. The distances (r) between typhoon eye and each estuary are computed following the methodology proposed by Meeus (1998). Fig. 11 shows the goodness-of-fit results for the Shuang estuary. The result in the figure stands for the combined effects of the meteorological parameters and the simulated surges of the historical typhoons. These typhoon surges are outputs of the simulation every 30 min during the lifetime of the typhoon. The regression equations of each estuary and the correlation coefficients (R-square, Eq. (7)) are summarized in Table 3. It can be seen that the slopes of the equations are steeper for the western estuaries than for the eastern. This means that, for the same typhoon strength, the surges in the western estuaries are larger. The coordinates of each estuary are also presented in Table 3 for the reference to estimate the distance (r) from the center of typhoon to each estuary. Using these equations, an estimate of the surge height can be rapidly given without going through the complicated simulation process. In Taiwan, coastal protections are usually designed with a return period of 20 years for storm surges. Using the method proposed in this paper, evaluation of the potential hazard for each estuary can be easily carried out. h i g / DP ¼ ð1016 Pc Þ 1 exp ðRmax =rÞ
Fig. 11. Results of the goodness-fit for the Shuang river estuary.
RQsquare ¼
SSe SSe þ SSr
ð6Þ ð7Þ
894
W.-P. Huang et al. / Coastal Engineering 54 (2007) 883–894
SSe
the sum of the squares of all the residual values. A residual is the difference between the fit y value and the actual y data value at any given x value. SSr the sum of squares of the difference between the average of all y values and the fit y values at each x location where a data point occurs. R-square shows how well the data are explained by the best-fit line. 4. Conclusions A high-resolution numerical model has been developed in this paper. This model has an acceptable computational time, and it is shown that, the model is capable of predicting the surge heights along the coastal areas of the northern Taiwan. The meshes used in the model consist of triangular unstructured grids, and this increases the flexibility for the cases of irregular coastlines and narrow estuaries. It also increases the efficiency of the simulation. For deep, open sea regions, larger meshes can be used. On the other hand, for simulations of the littoral zone, smaller meshes should be used. A computational rate up to 9.6:1 can be achieved by the present scheme. The accuracy of simulate results has been checked through comparison with records from tidal stations. It is shown that deviations between measured and simulated peak surge heights are less than 10%. Using the model proposed in this study, a data bank of the historical surge heights for the period of 1980 to 2004 was constructed. Using these, a data bank of historical typhoon events was constructed. The regression equations of the surge height and ΔP are obtained and these can be used for the prediction of the surge height of estuaries before the actual landfall of typhoon occurs. It is therefore concluded that, the numerical model and the statistical equations proposed in this study are all capable of predicting the surge hazard or northern Taiwan. References Benqué, J.P., Hauguel, A., Viollet, P.L., 1982. Engineering Applications of Computational Hydraulics, vol. 2. Pitman Publications. CWB, the Central Weather Bureau, 2006. Typhoon hazard messages. http:// 61.56.13.9/data.php.
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