Modelling Tsunami Wave Propogation Along Kalutara, Sri-Lanka Coastline by Quickbird-1 Data Maged Marghany, Mazlan Hashim, Mohd Ibrahim Seeni Mohd and Samsudin bin Ahmad Faculty of Geoinformation Science and Engineering Department of Remote Sensing Email: magedupm@hotmail.com Abstract The aim of this investigation is to model the successive tsunami waves hit the Kalutara coastline and spelled out the pattern of the Arabic word for Allah. Two models have been used: (1) two Dimensional Fourier Transform and (2) linear Boussinesq model to extract the tsunami wave propagation from Quickbird-1 satellite. The combination of two models used to model 3-D of tsunami wave propagation along Kalutara. Introduction According to NOAA (2005), the earthquake off the Sumatra coast on December 26 2004 was powerful which was released energy of approximately 20X1017 Joules, or 475,000 kilotons (475 megatons), or the equivalent of 23,000 Hiroshima bombs. The December 26 2004 tsunami traveled 600 km in 75 minutes which means it reached speed of 480 km/hr. it is no wonder these walls of water are capable of inflicting massive damage along the coastal lands. The consequent tsunami devastated coastlines around the ocean and killed around 226,000 people, with millions left destitute. The tsunami traveled both east and west away from the fault line, which runs north-south. This is why nearby countries to the north, such as low-lying Bangladesh, escaped unscathed, while much more distant countries to the west, such as Somalia, suffered considerable damage. This earthquake occurred within three days of a magnitude 8.1 earthquake in the Macquarie Islands. An alternative to the hypothesis that the Macquarie Ridge and Sumatra/Andaman Islands earthquakes are causally related is that the occurrence of the two, widely separated, great earthquakes within three days was a probabilistic coincidence. It seems clear that long-term stress changes associated with one earthquake may trigger other earthquakes on the same fault or on nearby faults. In fact, the aftershocks that occur around the source of a large earthquake are triggered by such stress changes. But the long-term stress changes caused by an earthquake decrease rapidly with distance away from the earthquake source. The Macquarie Ridge earthquake was very far from the site of the yet-to-occur Sumatra-Andaman Islands earthquake, and occurred on a different plate boundary. The hypothesis that long-term stress changes associated with the Macquarie Ridge earthquake triggered the Sumatra-Andaman Islands earthquake therefore does not seem compelling (DigitalGloble, 2004). The occurrence of the December 26 tsunami has caused a redistribution of tectonic stresses along and near the boundary between the India plate and the Burma plate. In some areas, this redistribution of stresses will be such as to shorten the time to the next big earthquake compared to what would have been the case if the earthquake had not happened. In other areas, the redistribution of stresses will be such as to increase the time to the next big earthquake (USGS, 2004).. The main goal of utilizing remote sensing is to acquire information of tsunami phenomena for monitoring, assessment, management and/or planning. It has be used for monitoring of and for assessment of the damages caused by various types of hazards, including collapse of an engineering construction (buildings, bridges, etc), slope-sliding and landslides, geological (e.g. earthquakes and volcano, etc), and oceanic and atmospheric hazards (e.g. El Nino events and red tides), fire outbreaks, and so on. In fact, remote sensing is a potentially powerful tool for the monitoring of coastal hazards with high temporal resolution and at lower cost than using traditional methods. The tsunami impacts on the coastal water of Sri Lanka are readily distinguish at the resolution of Quickbird data (0.6 m). The area under investigation covers 22.5 km2 and represent Kalutara coast. The main objectives of this work is to simulate the tsunami wave propagation pattern along Kalutara coastal waters. Background of Extraction Wave Spectra from Optical Remote Sensing Data There are few studies have utilized optical remotely sensed data mainly aerial photography and SPOT data (Wadsworth and Plau, 1987 and Populus et al., 1990) for extracting ocean wave spectra information. The basic concept is to capture an image of the instantaneous wave propagation along the coastal water, assuming that grey level variation of the image contain the wave information. In fact, the optical sensor is captured the amount of the radiance have reflected from the objects. The radiance that is received at the sensor is dominated by the background sky radiance that is reflected from the ocean surface (Wadsworth and Plau, 1987). This radiance field is modulated spatially and temporally by the slopes of the waves as they propagate. Wave visibility is enhanced in sunny conditions looking close to the specular reflection direction. When the sea surface is modulated by sinusoidal movement, the specular vector is no longer unidirectional, but varies with the wave slope symmemetrically which remain small as wave slopes reach few degrees. Specular reflection is function of the sun elevation angle and the viewing incidence with respect to the vertical. Populus et al., (1990) reported that the sum value of viewing incidence and sun elevation must be above 60º for wave to be clearly visible in SPOT data. Another factor seem to influence the optical image quality is: angular dispersion, wavelength and wave height. In SPOT image above 2 m height the wave is easy to detect visually in due to the 10 m pixel resolution. Strong angular dispersion increase the signal to noise ratio which makes it easy to detect the onshore wave propagation. Methodology The two dimensional Fourier transform (2-DFFT) has been applied to a single Quickbird satellite image frame comprising of n x n image pixel which is extracted from Quickbird image. The image was taken by the DigitalGlobe Quickbird satellite on December 26 at 10:20 am local time, shortly after the moment of tsunami impact. It can be viewed at the website DigitalGloble (2004). The Gaussian algorithm has been applied to remove the noise from the image and smoothen the wave spectra into normal distribution curve. The wavelength has been estimated by using Autocorrelation algorithm. The autocorrelation algorithm has been implemented along the mid azimuth row and the mid-range column. In a two dimensional wavenumber spectrum, the spectral peak located at Cx, Cy of a N x N image spectrum which has the wavelength L and the wave direction q (Populus et al., 1990): 
According to Dean and Dalrymple, (1984) the elevation of sea surface may be related to one sides directional wavenumber spectra density by the following formula 
where A is wave amplitude, i is the unit imaginary number, and Kx, Ky are x- and y- components of wave number vector K, respectively. The wave velocity has been estimated by using the linear Boussinesq equations that is 
where w is wave frequency and h is the water depth (Goto and Ogawa, 1992 ) Results and Discussion The Quickbird data of the Kalutara coastline before and after the tsunami event are shown in Figures 1 and 2. Figure 2 indicates that the tsunami wave have diffracted around Srilanka island and then moved perpendicular to the Kalutara coast and spread inland, causing widespread flooding. Figure 2 shows that the water drained back into the ocean it built two barriers along Kalutara coastline. As successive tsunami passed the large barrier the wave spread along the crest behind the barrier. It was diffracted so that the barrier stopped part of the wave crest and rest it passed by generate a large eddy with radius of 150 m behind the barrier. This indicates that the successive tsunami waves hit the Kalutara coastline have change the coastal zone morphology pattern. As successive tsunami waves were induced strong sediment transport pattern along the Kalutara coastline. This scenario could be repeated along whole the coastal zones which hit by 26 tsunami.  Figure 1. Kalutara coastline before Tsunami  Figure 2. Kalutara Coastline After Tsunami Wave spectra of successive tsunami wave extracted by 2-DFFT is shown in Figure 3. It clear that wave spectra near the coastline of Kalutara have maximum wavelength of 50 m. The spectra density of the wave diffraction due to the barriers is 10 m2 /Hz within narrow wave number spectra band of 0.13 rad/m (Figure 4). This indicates highest amount of spectra energy have input along the coastline of Kalutara due to the wave diffraction around Srilanka. At point C there was a combination of refraction and diffraction which would induced a strong current tended to meander towards barrier B after it formed a closed eddy. Figure 5 shows 3-D dimensions for wave diffraction along Kalutara coastline. This indicates that turbulent water movement due to combination of wave diffraction, refraction and longshore current movement between the two barriers. Taken together, these were able to cause a pattern which spell out, approximately the pattern of the Arabic word for Allah.  Figure 3. 2-D FFT Tsunami Wave Spectra  Figure 4. 3-D of Wave Diffraction Pattern  Figure 5. 3-D of Wave Spectra Spilled out the pattern of Arabic Word for Allah Conclusion In this paper, we have demonstrated a new approach for extraction the successive tsunami wave spectra from the Quickbird-1 satellite along Kalutara coastline. The integration between 2-DFFT and the linear Boussinesq equations to model the tsunami wave propagation along Kalutara coastal water. The change of coastal geomorphology caused by tsunami had a great impact on coastal water movement. The spectra density of tsunami wave spectra is approximately 10 m2 /Hz which induced a large eddy with diameter of 300 m. It is also can be concluded that 3-D tsunami wave propagation can be extracted from Quickbird-1 satellite. References
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