2. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China;
3. Key Laboratory of Technology for Safeguarding of Maritime Rights and Interests and Application, SOA, Guangzhou 510310, China;
4. Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province, Changsha 410004, China
A tsunami is a series of destructive sea waves generated by earth activities and meteorological changes such as underwater earthquakes, volcanic eruption, underwater collapse and landslides. Among them, tsunamis generated by underwater earthquakes are relatively common, which manifest as strong disturbances of bodies of water caused by the sudden rising and falling of the sea floor terrain. Depending on the length of time it takes for a tsunami to reach shore, tsunamis can be divided into offshore earthquake tsunamis and distant sea earthquake tsunamis. Although the frequency of a tsunami is low, once it happens, the damage is huge. On December 26, 2004, a strong M_{W}9.1 earthquake occurred off the northwestern coast of Sumatra, Indonesia. The earthquake triggered a rare earthquake tsunami which spread across the world's oceans (Yeh H. et al., 2007). On March 11, 2011, a strong M_{W}9.0 earthquake struck off the northeast coast of Japan, a powerful earthquake in the Japanese waters, which triggered a Pacific-wide tsunami (Wang Peitao et al., 2012). According to statistics, there is one locally destructive tsunami globally every two years, and one trans-oceanic tsunami every 10 years (Yu Fujiang et al., 2011). Jing H.H. et al., (2013) found that there is a very high possibility that an earthquake will cause a tsunami, and in the past about 100 years, earthquakes with M≥8.8 all caused tsunamis.
China is located on the west of the Pacific Ocean, with a vast sea area and a coastline of 18, 000km, whose offshore waters are mostly located along the circum-Pacific seismic belt, where earthquake tsunamis occur occationally. China is the first country in the world which record earthquake tsunamis. According to an incomplete survey, 29 earthquake tsunamis occurred along the coastal areas of China from 47 A.D. to 2004, among which, 8-9 times were destructive tsunamis. Although there have been no destructive tsunamis in China since the founding of the People's Republic of China in 1949, earthquakes have recently been occurring frequently in the South China Sea, which will cause huge losses to the developed cities in the south and southeast of China if a tsunami induced (Bao Chenglan et al., 2005; Yang Maling et al., 2005; Liu Yingchun et al., 2007). China was hit by many tsunamis in histony, which occurred most frequently in Taiwan and its adjacent areas, followed by the continental shelf, Bohai Sea belongs to the low-incidence area. According to analysis of recorded tsunamis, among all provinces in China, Zhejiang logs the highest number of tsunamis, up to 45 times, followed by Jiangsu, Shandong, Shanghai, Fujian, Taiwan and Guangdong. Based on identified records of tsunamis, Taiwan has the highest number of occurrences, with eight, followed by Shandong, Guangdong and Zhejiang. All data shows that China is a tsunami risk zone, and the South China Sea is the most threatened area in China because the west of Luzon and the Manila Trench are seismically active (Pan Wenliang et al., 2009). Li Linlin et al. (2016) believes that the commonly used sliding model obviously underestimated tsunamis. Therefore, it is necessary to establish a coastal tsunami warning system in Guangdong to rapidly predict arrival times and the maximum wave height of tsunamis after its occurrence, which can provide great support for tsunami disaster prevention and mitigation so as to minimize the loss caused by tsunamis.
Tidal modules are generally not included in existing tsunami computing models. This is because the nonlinear interaction between tides and tsunamis are usually not considered, and the calculated tsunami wave height and tidal level are superimposed linearly to obtain water level at stations concerned. However, for shallow coastal waters, the nonlinear interaction between tides and tsunamis increases significantly, which affects the amplitude and arrival time of tsunami waves. In this study, the COMCOT model and global tidal model TPXO7.2 are used to establish a coupled mathematical model for astronomical tides and tsunamis in the coastal areas of Guangdong and for tsunamis along the Manila seismic belt. The risk of tsunamis in the coastal areas of Guangdong Province is analyzed by calculating simulated tsunami sources.
1 NUMERICAL MODELThe COMCOT model (Cornell Multi-grid Coupled Tsunami model), developed by Philip Liu's research group of the department of civil and environmental engineering, Cornell University, has been used to simulate historical tsunami events a number of times, including the 1992 Flores Islands tsunami in Indonesia (Liu P.L.F. et al., 1995), the 2003 Algeria tsunami(Wang Xiaoming et al., 2005), the 2004 Indian Ocean tsunami (Wang Xiaoming et al., 2006) and the 2011 Japan tsunami (Ying Chao et al., 2015; Jing Huimin et al., 2012). The entire process of tsunami generation, propagation, run-up and draw-down is effectively simulated. Linear and nonlinear shallow water equations in spherical and rectangular coordinate systems can be selected flexibly according to research scope, and all equations are discretized with the explicit leapfrog finite difference method.
1.1 Fundamental EquationsIn the spherical coordinate system, considering Coriolis force and ignoring seabed friction, the linear shallow water equations are as below:
$ \frac{{\partial \eta }}{{\partial t}} + \frac{1}{{R\cos \phi }}\left[ {\frac{{\partial P}}{{\partial \psi }} + \frac{\partial }{{\partial \phi }}\left( {\cos \varphi Q} \right)} \right] = 0 $ | (1) |
$ \frac{{\partial P}}{{\partial t}} + \frac{{gH}}{{R\cos \phi }}\frac{{\partial \eta }}{{\partial \psi }} - fQ = 0 $ | (2) |
where, η is the free surface displacement relative to the mean sea level, R is the radius of the Earth, H=η+h is the total depth of water, h is depth of still water, P is flux per unit width along the latitude, Q is flux per unit width along the longitude, ϕ and ψ are longitude and latitude respectively, f is coefficient of Coriolis force, g is gravity acceleration. When the tsunami propagates to the shore, nonlinear shallow water equations in Cartesian coordinates are adopted, and the bottom friction effect is taken into account. Its continuity equation and momentum equation are as below:
$ \frac{{\partial \eta }}{{\partial t}} + \frac{{\partial P}}{{\partial x}} + \frac{{\partial Q}}{{\partial y}} = 0 $ | (3) |
$ \frac{{\partial P}}{{\partial t}} + \frac{\partial }{{\partial x}}\left( {\frac{{{P^2}}}{H}} \right) + \frac{\partial }{{\partial y}}\left( {\frac{{PQ}}{H}} \right) + gH\frac{{\partial \eta }}{{\partial x}} + \frac{{g{n^2}}}{{{H^{7/3}}}}P{\left( {{P^2} + {Q^2}} \right)^{1/2}} = 0 $ | (4) |
$ \frac{{\partial Q}}{{\partial t}} + \frac{\partial }{{\partial y}}\left( {\frac{{{Q^2}}}{H}} \right) + \frac{\partial }{{\partial x}}\left( {\frac{{PQ}}{H}} \right) + gH\frac{{\partial \eta }}{{\partial x}} + \frac{{g{n^2}}}{{{H^{7/3}}}}Q{\left( {{P^2} + {Q^2}} \right)^{1/2}} = 0 $ | (5) |
where, P and Q are the volumetric fluxes in x and y direction, n is the Manning roughness coefficient.
1.2 Numerical SchemesEquations (1)-(5) are discretized with the leapfrog finite difference scheme, and nonlinear convection terms are discretized with the upwind scheme. Fig. 1 is a diagram of interlaced schemes. As can be seen from Fig. 1, wave height and volumetric flux are interlaced in space and time, wave height and water depth are located in the center of grids, and volumetric flux is located on grid lines. The truncation error of the numerical scheme is o(Δx^{2}, Δy^{2}, Δt^{2}), with second order accuracy in both space and time. COMCOT is a relatively mature tsunami numerical model, and the specific algorithm is detailed in the literature (Wang Xiaoming, 2009).
Initial conditions for a tsunami are determined by inputting seismic fault parameters and calculated using the elastic fault model. Mansinha and Smylie's elastic half-space dislocation model and Okada's theoretical model can be selected, which are also two commonly used elastic fault models at this stage. The elastic fault model is established based on the elastic dislocation theory, using fault dislocation data to calculate displacement at a specific point. For example, a fault dislocated in j direction by Δu_{i}, the integral of the entire rectangular fault range is obtained as below:
$ {u_i}\int\limits_\Sigma {\Delta {u_j}\left\{ {\lambda {\delta _{jk}}\frac{{\partial u_i^l}}{{\partial {\zeta _l}}} + \mu \left[ {\frac{{\partial u_i^j}}{{\partial {\zeta _k}}} + \frac{{\partial u_i^k}}{{\partial {\zeta _j}}}} \right]} \right\}} {v_k}{\rm{d}}\Sigma $ | (6) |
where, δ_{jk} is kronecker delta variable v_{k} is the outward vector perpendicular to the face of Σ, μ and λ are Lame constants, u_{i}^{j} is the displacement generated in i direction on the earth's surface under the action of unit stress of fracture surface in j direction.
A total of 9 parameters are input into the fault model of COMCOT, incorporating the longitude and latitude of the epicenter, focal depth, fracture length, fracture width, slippage, strike angle, dip angle and rake angle. The schematic diagram of the fault model is shown in Fig. 2.
In setting the boundary conditions, the water boundary is set as an open boundary. When the linear shallow water wave equation is selected, sea-land boundary is set as the vertical reflection boundary, and when the nonlinear shallow water wave equation is selected, the moving-boundary scheme is adopted, that is, dry and wet changes of the beach are taken into account. In this study, tidal forced boundary conditions are added into the model through source code modification (Li Linyan et al., 2012; Zhao Xin et al., 2016), the boundary of the open sea tidal level is obtained by the global tide model (TPXO7.2). This model calculates astronomical tide levels using 10 partial tides, incorporating 8 main partial tides, M_{2}, S_{2}, K_{1}, O_{1}, N_{2}, P_{1}, K_{2} and Q_{1}, and 2 long-period partial tides, M_{f} and M_{n}, which can basically construct the real astronomical tide process in deep water of open seas.
$ {\zeta _0}\left( x \right) = {\zeta _p}\left( x \right) + \sum\limits_{i = 1}^{10} {{A_i}\left( x \right)} \cdot \sin \left( {{\omega _i}t + {\alpha _i}\left( x \right)} \right) $ | (7) |
where, ζ_{0} is the tidal level at the boundary, ζ_{p} the static water level at the boundary. i takes the value of 1-10, corresponding to the above partial tide respectively, A_{i} and α_{i} denote respectively, amplitude and epoch of partial tide at 3 boundaries, ω_{i} is the angular frequency of the partial tide.
2 VERIFICATION OF THE TSUNAMI MODEL 2.1 Computational Domain and Grid LayoutThe COMCOT model is verified by the "3·11" tsunami in Japan. The model uses 2-layer nested grids. The first layer is within a range of 5°S-62°N, 105°E-179.5°E and grid size of 4′, the computational domain covers the East China Sea, Taiwan Straits in China, the South China Sea, Japan and part of western Pacific Ocean, linear shallow water long-wave equation in spherical coordinates is chosen as governing equation, and frictional effect is ignored. The second layer is within a range of 14.5°-28°N, 110°-126°E and grid size of 0.8′ (Fig. 3).
After the "3·11" earthquake tsunami in Japan, Tang et al.(2012) obtained that the initial sea surface displacement was uplifted by 10m and subsided by 3m using the monitoring data of the buoys D21418 and D21401 during the period of 0.42-0.58 hour and 0.8-1.23 hour respectively after the earthquake and the seismic source can be composed of 6 units of 100km×50km seismic sources along the Japan Trench, the run-up and draw-down of tsunami waves in more than 30 cities along the U.S. coastline can be and calculated 5 hours before the arrival of the tsunami, and the simulated values are in good agreement with the observed values. Wei Yong et al. (2013) also used the same fault setting to simulate the run-up and draw-down of the tsunami in the coastal areas of Japan, and the results showed that the accuracy of the simulated inundated ranges in Ibarakiken and Aomoriken reached 85.5%. The above fault settings of the National Oceanic and Atmospheric Administration is used as input conditions for the tsunami model to simulate the generation and propagation and the tsunami waves and output wave height series of DART buoy points in the coastal areas of Japan and tide stations in the coastal waters of China. The design of the seismic fault parameters is shown in Table 1.
Water level data of tsunami buoy stations 21401# (42.617°N, 152.583°E), 21413# (30.515°N, 152.117°E), 21418# (38.688°N, 148.769°E) and 21419# (44.455°N, 155.736°E) in eastern Japan after the tsunami are collected in this study for verification, buoy distribution is shown in Fig. 4 and model verification is shown in Fig. 5. At the four buoy points, the differences between the simulated values and the observed values of the first wave arrival time are less than 2 minutes. At buoy stations 21401# and 21419#, the differences between the simulated and observed wave heights are less than 2cm, and the simulated value at the buoy points are relatively consistent with the measured value. At stations 21418# and 21413#, the differences between the simulated and observed wave heights are 36cm and 21cm respectively, with relatively larger errors, which is related to the seabed topography errors and the accumulated errors of local initial wave value at tide stations.
Near the waters of the South China Sea, three subduction zones are considered to have the potential risk of earthquake induced tsunamis, which are the Manila subduction zone, subduction zone of the Ryukyu Islands and north Sulawesi subduction zone. The Manila Trench, located at the junction of the Eurasian plate and the Philippine Sea plate, starts from the north end of Palawan Island in the Philippines, develops along the western edge of Luzon in the Philippines to the north and reaches Taiwan island in the north, with a total length of about 1, 000km. The Eurasian plate subducts under the Philippines sea plate at a rate of 70mm/a, and the convergence and compression between the subduction plate and the overlying plate have lasted for quite a long time, and when the accumulated stress is released, an undersea earthquake will occur, triggering tsunami waves that will expose coastal areas such as Taiwan, Fujian, Guangdong and Hainan to the threat of tsunamis.
In this study, the COMCOT model is used to simulate the impact of the tsunami generated after the Manila Trench earthquake on coastal waters of Guangdong Province. The model adopts 2-layer nested grids, and the range of grids is shown in Fig. 5. According to trench azimuth and fault geometry, the United States Geological Survey divided Manila Trench into 6 fault zones, the distribution of hypocenters is shown in Fig. 6 with a magnitude of M_{W}9.3(Phuong et al., 2013), and source fault parameters are shown in Table 2.
Fig. 7 shows tsunami wave propagation and lead wave arrival time charts after the Manila trench earthquake. Tsunami waves generated from the earthquake in the Manila Trench spread to coastal waters of Guangdong Province 3 hours later. COMCOT can get more detailed simulation results of the sea area around open-sea islands, and based on the results of the second layer of COMCOT model, the maximum surge of water caused by tsunami near Guangdong Province can be obtained.
Fig. 8 shows the maximum surge of water affected by the tsunami generated by the Manila Trench earthquake in coastal waters around Guangdong Province. It can be seen from Fig. 8 that after the tsunami triggered by the earthquake at the Manila Trench is introduced into shallow water areas from deep sea areas, under the effect of shallow water, tsunami waves near Dongsha Islands will increase significantly, with the maximum surge of water reaching 11.95m and the maximum surge reaching about 4.87m after the tsunami waves reaches the coast of Guangdong Province. The velocity of tsunami waves is approximately (gH)^{1/2}, when tsunami waves coincide with high tide levels, coupling calculation shows that the total water depth H increases, the tsunami propagation velocity increases and the propagation time becomes shorter. If the calculation results of tide and tsunami are not taken into account, there will be a delay in time, about 15min, which may vary slightly depending on topography of coastal areas. Table 3 shows the surge and reduction of water and corresponding time at each oceanographic station of Guangdong Province under the influence of the Manila Trench earthquake.
To get a more detailed picture of the tsunami waves' impact on the coastal areas of Guangdong Province, places such as Haimen, Jiazi, Shanwei, Huizhou Port, Hong Kong, Guishan Island, Guangzhou, Dawanshan, Zhuhai Port, Hailingshan Island (Zhapo), Zhanjiang and Xiabo etc. along the coast of Guangdong are selected to obtain the change of water level with time, so as to analyze the effects of tsunami waves on coastal waters of Guangdong Province. Locations of sensitive points are shown in Fig. 9, and the affected time series is shown in Fig. 10. In the statistics of each oceanographic station, the maximum surge of water on Dongshan Island and Dawanshan is relatively significant, which is 11.95m and 4.87m respectively, the second is near Zhuhai Port and Jiazi, with the maximum surge of water reaching about 4m. The maximum surge of water reaches 3.76m near Huizhu port, 2.0m-2.5m in Haimen, Shanwei, Jing'an and Hong Kong, 1.5m-2.0m on Hailingshan Island (Zhapo), Shantou, Maoshihua (Shuidong Port), Dong'ao Island, Guishan Island, Xige and Chaozhou Port (Sanbaimen), and 1.0m-1.5m in Dapeng Bay (Yantian port), Daya Bay, Zhanjiang, Namoa (Yunao Bay), Mabianzhou (GPC Wharf), Hengshan, Sanzao Island, Denglong Island and Liusha, followed by Wushi, Xiabo, Xiagang, Bohe, Dianbai, Luzhou Island (North Port), Beijin and Hai'an, with the maximum surge of water reaching 0.5m-1.0m, and the maximum surge of water is 0.19m-0.50m in Macao, Zhuhai (Jiuzhou Port), Noi Ling Ding Island, Huangpu, Hengmen, Zhuhai (Xiangzhou), Beijie, Nansha (Shuiniutou), Guangzhou, Haiqin, Shenzhen Airport (Oil Wharf), Shangchuan Island (Sanzhou Bay), Shanbanzhou and Shekou (Chiwan), which is minimal. As can be seen from Fig. 10, the tsunami triggered by the Manila Trench earthquake reaches the coast of Guangdong about 2.5 hours later, and after tsunami waves reach the vicinity of sensitive points, the impact reaches the maximum within 1 hour and then gradually decreases. Noi Ling Ding Sea is less affected by tsunami waves due to the obstructions of islands dotted by the sea and its shallow topography, and the wave height is relatively small. The surge of water covers most parts of coastal areas of Guangdong in less than 5 hours, while the effect is relatively weaker on the areas west of Guangzhou and Zhanjiang.
Based on the COMCOT model, the coupled mathematical model of astronomical tides and tsunamis in the coastal areas of Guangdong is established in this paper, which is well verified by the "3·11" tsunami in Japan. Meanwhile, the effects of the tsunami generated by the Manila Trench earthquake on the coastal waters of Guangdong are simulated, data from oceanographic stations from east to west (from Haimen to Xiabo, etc.) along the coast of Guangdong are analyzed, and the main results are as follows:
(1) The tsunami coupling mathematical model established in this paper can well simulate the "3·11" tsunami in Japan, the difference between the simulated value and the observed value of the first wave arrival time is less than 2 min, the calculated results of wave height are compared with the measured value, and the difference is related to the seabed topography error and the accumulated error of local initial wave value at tide stations. This model provides a basis for the accurate assessment of the effects of tsunamis generated by the Manila Trench earthquake on the coastal areas of Guangdong Province.
(2) The tsunami triggered by the Manila Trench earthquake reaches the coast of Guangdong about 2.5 hours later, and after the tsunami waves reach the vicinity of sensitive points, the impact reaches the maximum within 1 hour and then gradually decreases. Noi Ling Ding Sea is less affected by tsunami waves due to the obstructions of islands dotted by the sea and its shallow topography, and the wave height is relatively small.
(3) Within 5 hours, the maximum surge of water covers most parts of the coastal areas of Guangdong, which will have an impact on offshore engineering. The maximum surge of water on the Dongshan Island and Dawanshan is relatively significant, which is 11.95m and 4.87m respectively. Followed by the area near the Zhuhai Port and Jiazi, with the maximum surge of water reaching about 4m. The maximum surge of water reaches 3.76m near the Huizhou Port and 2.0m-2.5m in Haimen, Shanwei, Jing'an and Hong Kong, and the influence on the west of Guangzhou and Zhanjiang is relatively weak.
(4) Due to the lack of historical records and tsunamis and seismic data in the South China Sea, the source mechanism solution cannot be effectively and accurately calculated, so the time period cannot be accurately determined. Tsunami waves calculated from linear superimposed tides are slightly safer than that from coupled tides. Moreover, the narration of tidal effects on tsunamis is too long, and it's follow-up research work. There is no significant difference in the arrival time of tsunami waves, the main difference is mainly reflected in the maximum wave height. Time periods of the maximum and minimal tide difference in years and time periods of the maximum and minimal tide difference in different months of a year, and simulation under the influence of northeast and southwest monsoon, and even extreme weather, can be considered in the future, to build a corresponding tsunami source database, so as to establish a perfect coupling mathematical model of the South China Sea.
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