Understanding the Simple Model of Tsunami Propagation by SiTProS - PDF document

Understanding the Simple Model of Tsunami Propagation by SiTProS Model Wattana Kanbua 1* , Somporn Chuai-Aree 2 1 Marine Meteorological Center, Thai Meteorological Department, Bagkok 10260, Thailand 2 Faculty of Science and Technology, Prince of Songkla University, Pattani 94000, Thailand E-mail: watt_kan@hotmail.com * ABSTRACT In this paper, we use the approximation of shallow water waves to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth. Our procedure also includes a new mathematical model for tsunami generation, propagation, real-time simulation and visualization. The model is so called SiTProS (Siam Tsunami Propagation Simulator). The model can run for any given regional or global grid with a prescribed topographic dataset as ETOPO2. The grid resolution can be arbitrary in space and time. The propagation can be done on a latitudinal – longitudinal or on a cartesian grid. The finite differences method is used to solve the equation. A tsunami struck the shores of southern Thailand and along the Andaman coast on the December 26, 2004. The hardest-hit area of affected provinces is given based on the shoaling, refraction, diffraction and reflection phenomenon. The SiTProS can run for any given regional or global grid with a prescribed topographic dataset as Etopo2. The finite difference method is used to solve the equation. The SiTProS provides five different computing regions, which are Asia, Europe, Arab (Iran-Kenya), Africa, and Andaman. The SiTProS is designed for interactive simulation and user friendly. This paper has introduced the tsunami propagation simulator model which calculated trends to check the model could predict the tsunami arrival times. We have already compared the result of model with observation time in the case of the December 26, 2004. In general, it was found that the model can predict quite well the timing. The SiTProS as tsunami propagation simulator model has therefore been developed by ourselves, using a fast algorithm for a quick estimate of the tsunami front propagation. We have applied this model to the 26 th December event. It shows a very satisfied prediction of the time of the main events. The software is available at http://www.schuai.net/SiTProS. 1. INTRODUCTION On December 26, 2004 at 07:59 am (UTC 00:59 am, JST 09:59 am), a giant earthquake occurred off the west coast of northern Sumatra, Indonesia. Its epicenter is shown in Figure 1. Figure 2 shows that the seismic activity in this region is very high as the Pacific Rim. Its magnitude was reported by some institutes as shown in Table 1. The West Coast Alaska Tsunami Warning Center and the Pacific Tsunami Warning Center issued magnitude 8.0 warnings within fifteen minutes of the earthquake. The magnitude 9.0 which is well- known nowadays was reported nineteen hours later. These revised magnitudes, however, do not mean the centers made mistakes, but indicate the difficulty in analyzing such a giant earthquake in such a short time, even for leading seismologists. This was the fourth largest earthquake in the world since 1900, see Figure 3 and Table 2. Another earthquake which occurred in this region three months later was the seventh largest event. The giant earthquake generated a huge tsunami which was the third largest since 1900, as shown in Table 3. This tsunami hit many countries in the Indian Ocean. With the exception of Indonesia, the Andaman Islands and Nicobar Islands, the tsunami, not the earthquake, caused all of the extensive damage (see Figure 4.). This was the greatest tsunami disaster in history. The tsunami hit the southeast coast of Thailand, which was about 500 km from the epicenter. Because the area has world famous resorts like Phuket Island and the tsunami hit the coast at around high tide (Figure 5), there was a dreadful tragedy. 5,400 people were killed and 3,100 people reported missing due to the tsunami in Thailand. To study this disaster, a field survey was carried out from December 30, 2004 to January 3, 2005 along the southeast coast of Thailand. Further, a numerical simulation was conducted to investigate the source mechanism of the tsunami. In this chapter, those results are reported.

Figure 1. The epicenter of the 2004 Sumatra Earthquake. Figure 2. Seismic activity in the world from 1978 to 2000 [4]. Table 1. A history of reported magnitude of the earthquake [3]. *1 "M" means that the type of magnitude was not shown in the e-mail. *2 Where no issued time was shown in the e-mail, the posted time informed by the institute's SMTP server is used. *3 The origin time of the earthquake is assumed to be 12/26/2004 00:59 UTC by USGS. Table 2. Largest earthquakes in the world since 1900 [3] Table 3. Largest tsunamis in the world since 1900 [1]

Figure 3. Bathymetry. Figure 4. The tidal change and the tsunami arrival time at Phuket [5]. 2. FIELD SURVEY AND DATA FOR THE EVENT The general objective of the field survey on the disaster is to determine the damage caused and to study the factors involved. The magnitude of the damage is a result of a balance between factors on the side of the disaster and factors on the human side. In a tsunami disaster, the former factors imply tsunami height, velocity, hydraulic power, etc. and the latter factors imply preparedness, countermeasures, education, evacuation, etc. Many field surveys are desired to investigate factors on both sides. Because of the difference in tide levels between when the tsunami arrived and when our measurements were made, the measured tsunami heights were corrected by the method shown in Figure 5. The tsunami arrival times were assumed to be a uniform 10:00 am local time. Figure 5. The method of tide level correction [5]. In order to evaluate the various calculations an analysis of the arrival times of the waves on the various locations has been performed. Three sources of information have been used such as news reports, radar images from the NASA/NOA satellites and surveys data. 3. THE SITPROS MODEL The SiTProS model stands for “Siam Tsunami Propagation Simulator” model which is Tsunami Propagation Model. The SiTProS has simulated and animated tsunami generation and propagation in a given arbitrary shaped bathymetry. The module for wave equation, describe each variable and parameter. We calculate from tsunami behavior, shallow water equation by defining wave propagation speed.

The model for Tsunami propagation is based on wave equation. The code is programmed by Pascal Programming language. This software is designed for fast computing in Real-Time Simulation and Visualization in 2D domain based on graphical user friendly interface. This model and all simulated results cannot be used for any commercial purposes, but training, warning systems and education are available. 4. NUMERICAL SIMULATION 4.1. Model Equation The numerical code is based on wave equation in Grid computing, we have rectangle grid, 2D grid and coordinate system in Figure 6(a), (b). We calculate from tsunami behavior, shallow water equation by defining wave propagation speed. The wave equation can be written as ∂ ⎛ ∂ ∂ ⎞ 2 2 2 U U U = + 2 ⎜ ⎟ a (1) ∂ ∂ ∂ 2 2 2 ⎝ ⎠ t x y where U is wave height, x is spatial grid in x-direction, y is spatial grid in y-direction, a is wave propagation speed, d is water depth. The shallow water equation can be written as = × a g d (2) (a) (b) Figure 6. 2D grid system.