Appendix A Health and Safety Retrospective Appendix B - Acknowledgements. 7. References 47

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1 Contents Page No. 1. Introduction 2 2. Numerical Modelling of Tsunami 2.1. Submarine earthquake models Tsunami propagation models Boundary conditions COMCOT 8 3. Model Verification 3.1. Procedure Results /12/2004 Sumatra /09/2007 Sumatra /08/2007 Peru Analysis Model Implementation 4.1. Early warning systems Warning Potential Method Generation regions Potential buoy locations Population centres Simulations Design Results and Discussion 5.1. Optimal result with r = Influence of reaction time, r Conclusions and Further Work 6.1. Conclusions Further work References 47 Appendix A Health and Safety Retrospective Appendix B - Acknowledgements 1

2 1. Introduction Past tsunami, such as that on Boxing Day 2004 and, most recently, that hitting Japan in March 2011, have demonstrated how destructive a force large wavelength ocean waves can be, and the vast and lasting damage they can have on coastal villages, cities and even entire countries if caught unaware. Tsunami waves originate from the displacement of a huge quantity of water in the deep ocean. This usually results from an underwater, or submarine, earthquake occurring along a tectonic plate boundary, but can also be caused by submarine landslides or a volcanic eruption on the sea bed. The water displaced by this motion instantaneously [1] increases the height of the water surface, which then propagates away from the source in all directions as a large wavelength wave. In the deep ocean, this wave is small in amplitude, but as the water becomes shallower near the continental shelf, the wave length of the incident tsunami becomes shorter and the amplitude is increased. The tsunami then poses a much greater risk. Once at the coastline, the tsunami runup is exceptionally powerful. Water can travel for many kilometres inland, washing away all things in its path. As a result of the Japan tsunami in March of this year, almost 20,000 were killed and tens of thousands left homeless, as entire cities were swept away by the deluge [2]. Figure 1: Damage resulting from the Japan tsunami on 11 th March In order for the destruction caused by future events to be limited and to reduce the loss of life, it is essential that people in areas at risk are made aware of this danger and given the opportunity to prepare and evacuate to higher ground prior to inundation. Tsunami Early Warning Systems 2

3 (EWSs) are introduced for this purpose. These systems use buoys located offshore to measure the tsunami risk associated with an earthquake event and give an early indication to those regions at risk of the arrival time of the tsunami. A system of this nature has already been successfully implemented in the Pacific Ocean. The aim of this research project is to investigate the methods used to model tsunami propagations, and apply these methods to design a prototype for an EWS in the South China Sea. The South China Sea has been chosen due its current lack of comprehensive warning system, and its high risk status. The Manila subduction zone is formed where the Philippine oceanic plate overrides the Eurasian continental plate, along the western edge of the Philippines. The socalled Manila Trench runs for approximately 1000km. Here, a huge amount of pressure can build up due to friction and the brittle deformation of the earth s crust as the two plates move relative to each other at a speed of up to 70mm/year [3]. This results in frequent earthquake occurrence, and this region has been classified as the highest earthquake tsunami source region [4]. The Manila trench has not recently experienced any major earthquake, and many experts are now expecting a large earthquake to occur in the relatively near future. The potential for a catastrophic tsunami is therefore great, and the development of an EWS to protect the increasing population of the rapidly developing coastal regions around the South China Sea is critical. Figure 2: The South China Sea and Manila Trench 3

4 Whilst there has been much discussion with regards to collaborative EWS development in the Indian Ocean and the Caribbean Sea after the events of Boxing Day 2004, the risk associated with the South China Sea has been of less interest. Currently, China has two individual buoys stationed in the South China Sea to provide tsunami warning capabilities for its population alone, and it has proposed the installation of a further buoy. Malaysia also operates a single buoy. However, an EWS linking numerous countries around the South China Sea together, and allowing them to share information, costs and maintenance with each other, is yet to be commissioned. The development of an EWS in this paper makes use of the Warning Potential Method, as proposed by Braddock and Carmody [5], to optimise the location of detector buoys in the open ocean, so as to maximise the coastal population that can be warned of an impending tsunami and then evacuated to safety. Whilst the program must then be implemented locally to allow for the local environment and culture of the various coastal communities, it is integral that there is international and mutual collaboration amongst countries involved in the program, to ensure that it can be implemented for the benefit of many countries simultaneously. 4

5 2. Numerical Modelling of Tsunami 2.1. Submarine earthquake models In order for a tsunami to be effectively modelled, it is necessary to first identify and model the source of the original water displacement. This initial sea floor disturbance can be classified by the rate at which deformation takes place. If the duration of the sea floor motion is much shorter than the period of the tsunami wave being generated (which is usually between 10 minutes and 2 hours), as is the case for all tsunamigenic earthquakes, then it can be considered instantaneous, and the water surface can be assumed to exactly follow the uplift of the sea floor since water over this large rupture area cannot be drained out within such a short duration. This uplift can be determined through the use of closed analytical expressions, as derived by Okada [6] and Mansinha and Smylie [7], for the displacement fields at the surface of an isotropic, homogenous half space, as a result of an inclined, finite, rectangular, shear or tensile fault. The semi-infinite half plane is an idealised representation of the interface between two colliding tectonic plates, where violent relative motion occurs during an earthquake event. The dislocation (or slip motion) occurring on the fault place will then deform the surface of the semi-infinite medium, which is considered as the seafloor displacement during the earthquake event [1]. The assumption that the sea bed is isotropic and homogenous is sufficiently accurate as the source model used in the analysis is inherently non-unique and the quality of crustal movement data is generally poor. It is therefore meaningless to create a complex and highly accurate model for inherently less accurate fault data. The following parameters characterise an earthquake event, as given by Wang [1], and must be obtained in order for the fault motion to be analysed: Focus: The centre of the fault plane, where rupture starts. Epicentre: The projection of the focus on to the mean surface of the Earth. Focal depth, h: The vertical distance between the focus and the epicentre Strike, θ: The angle measured clockwise from the local north to the strike direction, defined as the facing direction when standing on the top edge of the fault plane with the fault plane on the right. Dip, δ: The angle measured down from the mean Earth surface to the fault plane. 5

6 Rake, λ: The angle measured counter-clockwise from the strike direction to the slip direction, defined as the direction the hanging block moves relative to the foot block on the fault plane. Length, L: The length of the top or bottom edge of the fault plane. Width, W: The length of one of the other two edges. Dislocation: The distance of motion of the hanging block relative to the foot block, along the slip direction. Figure 3: Sketch of a fault plane and parameter definition [1] 2.2. Tsunami propagation models Once initiated, the evolution of a tsunami is often modelled by the Shallow Water Equations (SWEs). These are derived from the Navier-Stokes equations. In many events, the wavelength of a tsunami is large compared to the depth of the water that it is propagating through. In this situation, the vertical velocity of the water is small and the vertical pressure gradients are almost hydrostatic. Depth-averaging the incompressible Navier-Stokes equations therefore give the following non-linear SWEs in spherical coordinates: (1) (2) 6

7 (3) Where η is the water surface elevation; P and Q denote the volume fluxes in the x- and y- directions respectively; φ and ψ denote the latitude and longitude of the Earth; R is the radius of the Earth; g is the gravitational acceleration; h is the still water depth and reflects the effect of transient seafloor motion; H is the total water depth, i.e. H = η + h; f represents the Coriolis force coefficient due to the rotation of the Earth, where f = Ωsinφ and Ω is the rotation rate of the Earth; F x and F y represent the bottom friction in the x- and y-directions respectively. The two roughness terms are given via Manning s formula: (4) (5) Where n is the Manning s roughness coefficient. In the deep ocean it is often reasonable to assume that the tsunami amplitude is much smaller than the water depth, meaning that the effects of friction on the sea bed and convective inertia can be considered negligible. In this case, it is appropriate to use the linear form of the SWEs, given below: (6) (7) (8) 7

8 Whilst this is accurate for describing tsunami propagation in deep water, it becomes inaccurate as the tsunami approaches the coastal zone and the neglected factors begin to affect the flow. Here, it is most accurate to use the full SWEs. A final consideration that must be noted is that of the physical frequency dispersion effect experienced by travelling tsunami waves, whereby waves of different wavelengths propagate with different phase velocities. Again, where the length scale of the tsunami is much greater than the depth of water in which it propagates, this effect can be neglected. Were this not the case, and the tsunami wavelength were not large enough, dispersion must be incorporated through the use of the Boussinesq equations, which include additional dispersive terms. The computational cost associated with using these equations for modelling tsunami propagations is great Boundary conditions There are a number of ways in which the boundaries of the geographic domain can be represented. A wall boundary can be specified whereby the wave flux across the boundary is zero, or a sponge boundary condition could be used whereby all incident waves are absorbed. Alternatively, an open (radiation) boundary can be chosen. This is obviously the most appropriate when modelling real tsunami propagations as it is a more realistic condition COMCOT The numerical model to be used for design purposes is termed COMCOT [8], and was developed by the Civil and Environmental Engineering group at Cornell University. It uses the SWEs in Cartesian or spherical coordinates to compute the propagation of a tsunami, for a given initial water surface profile and bathymetry data. Both linear and non-linear SWEs can be specified for the simulation. Two versions of the programme are available, version 1.6 and the newer version 1.7. Both are fundamentally the same, using the same governing equations and numerical methods, but the newer version has an improved user interface and affords more functions. Both versions have been trialled during the course of this research. COMCOT makes use of a grid system, whereby the geographic domain being considered is divided into grid squares of equal size, as specified by the user. The SWEs are then evaluated 8

9 to determine the water surface displacement at the centre, and the volume fluxes, P and Q, at the edge centres of each grid cell. The evaluation of these factors is also staggered in time as the computation of the volume flux components requires data on the free surface elevation from the previous time step, and vice versa. This explicit evaluation allows the full propagation of the tsunami waves over the whole domain over time to be determined. This method is known as a leap-frog finite difference scheme [1], and is used for both the linear and non-linear forms of the SWEs. Another notable aspect of the COMCOT programme is its nested grid configuration, whereby finer sub-levels of grids can be allocated to different regions of the main 1 st level grid. The linear or non-linear SWEs can be assigned to differing regions of grids. This is particularly beneficial where wave profiles are being resolved in shallow water regions and the wavelength of the tsunami is reduced. The modelling programme can itself simulate, given fault parameters, the displacement of the sea floor due to a submarine earthquake and the initial change in the water surface profile that results, using the solutions proposed by Okada [6] and Mansinha and Smylie [7]. In the case of an underwater landslide, details of the transient motion of the seafloor can be inputted to allow for the computation of the change in the free surface elevation. This initial change in elevation, from whatever source, initiates the tsunami propagation. Apart from the fault parameter or transient motion input data, it is also necessary to provide the COMCOT control file with the bathymetry data for the region in question. This information must be in ASCII format, and written in three columns of x-coordinates, y- coordinates and water depth, where the water depth information is positive for bathymetry data and negative for topographical data. The output data produced by COMCOT details the free surface elevations at all grid points at each time step. This time step is specified by the user in the control file, subject to one constraint (see 4.6). From these files, the surface elevation at a specific location can be extracted at each time step, and plotted to demonstrate the water level variation over time as the tsunami passes this point. The minimum and maximum water elevations at each grid point over the entire simulation can also be obtained in the newer version of the model, as well as the volume flux data at each time step if specified. 9

10 3. Model Verification 3.1. Procedure Initial experimentation was necessary to ensure that the COMCOT model was capable of reproducing the tsunami wave propagations to a sufficient accuracy. This experimentation involved modelling past tsunami events and comparing the predicted sea level variations over time with those measured at coastal sea level gauges. This was carried out for three past tsunami events: 15 th August 2007 off the coast of Peru, 12 th September 2007 and 26 th December 2004 both off the coast of Sumatra. For each of these events, the required bathymetry of the region was obtained from the ETOPO2v2 database [9] and the fault parameters for the past tsunamigenic earthquakes from the Global Centroid Moment-Tensor project [10]. The parameters obtained were inputted in to the COMCOT control files and used to run the simulation. For the first two simulations, the earlier version of COMCOT was used. For the 2004 Sumatra earthquake, the latest multifault version of COMCOT was used with six faults being instigated at the same time. The characteristics of the six faults were obtained from research by Hébert, Sladen and Schindelé [11]. For each tsunami event, the measured sea level variations were obtained for several coastal tidal gauge stations from national and international internet databases. In many cases, it was necessary to remove the background tidal fluctuations. This filtering was done by estimating graphically the sinusoidal frequency, phase and amplitude of the tide and deducting this from each point of the measured data. It should be noted at this point, that due to outputted results from the COMCOT simulation only being available at a discrete number of nodes (those corresponding to the corners of the grid cells), the location at which the predicted data is taken, and the location at which the measured data is taken are different. The degree to which this affects the results is discussed shortly. 10

11 3.2. Results /12/2004 Sumatra a) Figure 4: (a) Bathymetry of the Sumatra region. (b) Approximate locations of the earthquake epicentres and tidal gauge stations. a) b) c) d) Figure 5: Tsunami propagation at (a) t = 0 (b) t = 30 minutes (c) t = 1 hour and (d) t = 2 hours. 11

12 The measured gauge data was taken from the Survey of India and National Institute of Oceanography [12] database for three stations: Kochi, Chennai and Tuticorin. All three data series started at 00:00 on the 26 th December, approximately 1 hour before the main earthquake shock, and was therefore shifted when plotted to ensure the time series correlated correctly. In all the below figures the green line corresponds to the water level variation predicted by COMCOT, whilst the blue corresponds to that measured at the coastal gauge station. Figure 6: Kochi station (Lat: Long: Figure 7: Chennai station (Lat: Long: ) Figure 8: Tuticorin station (Lat: Long: ) 12

13 /09/2007 Sumatra Figure 9: Approximate locations of the earthquake epicentre and tidal gauge station/dart buoy. a) b) c) d) Figure 10: Tsunami propagation at (a) t = 0 (b) t = 30 minutes (c) t = 1 hour and (d) t = 2 hours. 13

14 The gauge station data in this case was obtained for two stations: Padang and DART buoy The latter was retrieved from the US National Oceanic and Atmospheric Administration (NOAA) database, whilst the former was provided by the Ocean Data and Information Network for Africa [13][14]. Figure 11: Padang station (Lat: Long: ) Figure 12: DART (Lat: Long: ) /08/2007 Peru a) Figure 13: (a) Bathymetry of Peru region. (b) Approximate location of the earthquake epicentre and tidal gauge stations/dart buoy. 14

15 a) b) c) d) Figure 14: Tsunami propagation at (a) t = 0 (b) t = 30 minutes (c) t = 1 hour and (d) t = 2 hours. The gauge data was again obtained from the NOAA database [15] for tide stations Arica, Caldera and Coquimbo and DART The data for the first three stations was collected at two minute intervals, starting around 18 minutes after the main earthquake shock. The obtained data for DART was given for every minute from the time at which the tsunami was initiated. Figure 15: Arica station (Lat: Long: ) Figure 16: Caldera station (Lat: Long: ) 15

16 Figure 17: Coquimbo station (Lat: Long: ) Figure 18: DART (Lat: Long: ) 3.3. Analysis The results above demonstrate that there is a definite correlation between the measured water level variation and that predicted by the COMCOT simulation in all three cases. The most important consideration when analysing these graphs in the context of this project is the predicted arrival time. The arrival time is defined as the time at which the first significant increase in water level at the specified location occurs. From the above graphs it is seen that COMCOT has been relatively successful at predicting the arrival time of the tsunami. For the last tsunami simulation, in the case of Arica, the approximate difference between predicted and measured is 6.0 minutes as shown in figure 15, whilst for Caldera (figure 16) and Coquimbo (figure 17) the difference is approximately 5.5 and 9.1 minutes respectively. For the former two scenarios, the maximum differences can be seen in figure 8 at Tuticorin (around 21 minutes) and figure 7 at Chennai (around 19 minutes), whereas the difference between predicted and observed is virtually zero for both DARTs (figure 12) and (figure 18), and no more than 2.0 minutes at Kochi gauge station (figure 6). There are a number of possible reasons for any discrepancies. Firstly, as mentioned previously, the location at which the predicted data is obtained does not match up exactly to the location of the measured costal tide gauge data. For example, the predicted data for Arica is taken from a location with a latitude difference of o and longitude difference of o from the actual station coordinates. Based on a water depth of 8000 m, the tsunami can be deemed to be travelling at a speed of: 16

17 At this propagation speed, and assuming an Earth radius of m [1], these inconsistencies could result in a maximum difference of 1 minute in the predicted arrival time, which would cover some portion of the discrepancy observed. Secondly, as discussed above, there are many methods of simulating tsunami wave propagation. COMCOT solves the linear SWEs for the initial and boundary conditions specified, meaning it ignores the non-linear friction term. As the tsunami approaches the continental shelf, the linear form of the equations may be inaccurate, as the water becomes shallower and the bottom friction and non-linear convective inertia terms become more important. This may result in inaccuracies in the predicted water surface variations. Finally, the COMCOT model used has operated with only one grid layer, which means that the simulation is likely to have been relatively crude and inaccuracies could have resulted. Whilst the time difference between the predicted and measured results may seem notable, when a tsunami EWS is designed, it is the reaction time of the population that is of the greatest significance to the accuracy of the analysis. Inaccuracies resulting from this uncertainty will often outweigh errors resulting from imprecise simulation, and whilst the arrival time must obviously be as accurate as possible to validate the investigation, the COMCOT predictions can be considered exact enough for the purpose of this research. The extent to which the reaction time affects the EWS design will be covered in depth later in this paper. Another factor of the above graphs that must be considered is the predicted amplitude of the first peak in water height. This amplitude would give some indication of the damage potential of the tsunami. It can be seen that in the case of Arica (figure 15) and Coquimbo (figure 17) stations, and both those analysed for the 2007 Sumatra tsunami, the predicted and measured values are relatively close. In figure 18, for DART 32401, the match is exceptionally good. On the other hand, for Caldera (figure 16) and all those stations used for the 2004 Sumatra earthquake and tsunami, the first peak is underestimated, in some cases quite severely, by the COMCOT simulation. The reason for this may again be due to those factors explained above, and this underestimation must be considered if future work is to be carried out which involves using this value to provide warning of the damage potential of the tsunami. In the case of the 2004 Sumatra earthquake, the discrepancies between the measured peak and the 17

18 predicted peak at all stations could be a result of inaccurate fault parameters, leading to a forecasted wave of lesser amplitude than that observed. Beyond the first peak, there are increasing inconsistencies between the two results for all of the stations shown. However, for the purpose of this research, these discrepancies are unimportant. It should be mentioned that, for each of the three tsunami modelled for verification purposes, the stations used to compare the predicted data with, are, for availability reasons, all fairly close together. This may mean that the full propagation of the tsunami in all directions cannot be verified, as errors may occur at far-field points which have not been checked for by the comparisons made. This error has been mitigated by using three different tsunami, and three different sets of stations for testing. 18

19 4. Model Implementation 4.1. Early warning systems The methods used for tsunami warning systems in the past have made use of only seismic data and coastal sea level data. However, both of these methods contain inherent and obvious limitations. Seismometers measure the occurrence of earthquakes, but not all such events generate tsunami. This can often lead to a high rate of false alarms, which is costly, not only in monetary terms, but also in terms of community reaction to warnings [16]. For example, prior to the implementation of an EWS for the US Pacific coast, 75% of those warnings issued were false [17]. Coastal sea level data is provided by tidal gauge stations usually located on piers or wharfs. While these gauges are capable of measuring an incident tsunami, they were not designed to do so and are often, therefore, not connected to a communication network. In addition, they are often located where they can be easily damaged by tsunami. These tide gauges are therefore frequently unable to detect and inform of the existence of a tsunami, let alone measure its characteristics [5]. Additional technology is therefore necessary to confirm the existence of a tsunami and form a more accurate EWS. Deep-ocean Assessment and Reporting of Tsunami (DART) buoys are increasingly being used for this purpose. Tsunami waves have long periods, and changes in hydrostatic pressure as a result of the passing of the tsunami can be detected on the sea floor by an anchored seafloor bottom pressure recorder (BPR) [18]. Despite the change in water level being only small, the relatively quiet environment on the sea floor in deep water means that this change in water pressure close to the sea bed is noticeable, and validates the use of pressure measuring systems. Wind generated surface waves are generally not felt by the water below half their wavelength (a few metres) in depth [19]. They therefore have no influence on the BPR measurements attained. The BPR collects data on both the pressure and temperature of the water at distinct intervals. The pressure value can then be corrected for temperature effects, and converted to an estimated water surface elevation by assuming a constant value of 670mm/psia. It is assumed that the errors associated with neglecting both acceleration and density effects are negligible and hence this constant value can be used [19]. The collated data is transmitted to a surface buoy via an acoustic link. Providing the surface buoy, or tsunameter, is within a 40 degree cone of the BPR, the system is capable of 19

20 incredible sensitivity; approximately 1mm in a 6km depth of water. Outside of this cone, the signal to noise ratio of the acoustic link deteriorates rapidly and the data integrity is compromised [19]. Real-time communication to tsunami warning centres is then materialised through the use of a commercial satellite network. From there, warnings can be issued as necessary. This forms a so-called end-to-end system [20]. The DART system operates in two discrete modes. Under normal operation, i.e. with no tsunami detected, the buoy will operate in standard mode whereby measurements are communicated to the shore every 15 minutes. An automatic detection algorithm is utilised to detect a tsunami wave over a threshold wave height value, which then triggers the DART system in to event mode. Once in this mode, readings are transmitted every 15 seconds during the initial few minutes, and then 1 minute averages are given for up to 4 hours after the event. The newest system, DART II, allows for two-way communication between the tsunami warning centres and the buoy, meaning that the buoy can be put in to event mode in anticipation of an incident tsunami. This two-way contact also allows for real time troubleshooting and diagnostics of the system [21]. Figure 19: Schematic of a DART buoy system [21] The most extensive DART buoy tsunami warning system in use is that in the Pacific Ocean. The first DART buoy was deployed here in 1995, and prior to the 2004 Boxing Day tsunami, 20

21 the USA operated 6 buoys. As a result of the 2004 disaster, however, a further 32 were announced, and as of March 2008, the USA operates 39 DART buoy stations in the Pacific and Atlantic Oceans and the Caribbean Sea. These buoys are proven to be both robust and reliable [17]. Between 1997 and 2003, the six buoys in operation gave a 91% cumulative data return ratio, meaning that of the data expected on shore, 91% of it was received in a complete and timely manner [19]. This is relatively high. In addition, field experimentation has shown that, indeed, the only loss of data associated with the system is in transmission to shore, and that surface wave noise and wave driven buoy motion play no adverse role in the performance of the acoustic link when properly installed [17]. Prior to 2006, DART systems had, on six occasions, contributed to operational decisions, avoiding false alarms and the resultant costs associated with them [22]. For example, on 17 th November 2003, a magnitude 7.5 earthquake originating in the Aleutian Islands triggered a tsunami watch in Hawaii and Alaska. Data from three tsunameters indicated that the tsunami generated was not significant, and no warning was issued, thus saving Hawaii an estimated $68 million in evacuation costs [19]. The reliability and efficiency of this system therefore validates its use in the design of further EWSs Warning Potential Method The Warning Potential Method (WPM) was first put forward by Braddock and Carmody [5], in the context of designing a fictional EWS for the Pacific Ocean. The objective of the method is to optimise the deployment of a limited number of detector buoys within a number of fixed locations so as to maximise the coastal population warned, and hence minimise the loss of life due to an incident tsunami. Braddock and Carmody illustrate that this optimisation can be formulated as an integer programming problem, and then solved, using MATLAB, to find the desired combination. This method is described below. For the sake of computational time and effort, it is obviously unrealistic to consider all potential tsunami generating faults and all the populations that are at risk from inundation by tsunami generated along the Manila Trench. When optimising the EWS, therefore, a small sample of representative population centres and a select number of potential generation faults have been selected. A more in depth solution could consider further sites, but it is considered unnecessary for this initial optimisation exercise. 21

22 The identified locations at which the detector buoys could be placed can be denoted: (9) For a particular number of buoys and potential buoy locations, there will be a set number of distinct alternative deployment combinations. Each alternative deployment of buoys can be represented by a vector, B, in which each element of B, b n, describes whether, for this particular deployment, there is a buoy present in location L n. (10) (11) The number of buoys that can be deployed is likely to be limited by capital or maintenance costs. Therefore an additional constraint applies such that: (12) Where X is the maximum number of buoys that can be afforded. The number of distinct combinations, K, is therefore: (13) The tsunami generating fault regions can be denoted: (14) And the major population centres under consideration can be represented by: 22 (15)

23 It is now necessary to consider the generation of a large tsunami at one of the V generation points. If a particular population centre is to be warned of the incident tsunami in sufficient time, the time taken for the tsunami to be detected and a warning issued must be compared to the time taken for the tsunami to reach that coastal population. The travel time of the tsunami from a generation point, G v, to the nearest and occupied buoy location can be found and given the symbol t v *. This can be calculated for each generation point for a given deployment of detectors, B k. The minimum time for a warning to be issued to the population centres on the coast of an imminent tsunami generated at fault G v is therefore: (16) Where s is the time required for processing and signalling the generation of the tsunami, and r is the reaction time required for the emergency services to pass on this warning, and evacuate the population. The reaction time is likely to be a function of the population centre in question as it will depend on the infrastructure in place and the smooth coordination of the operating authorities in each centre. However, for the purpose of this study, this time is to be taken constant across all population centres. For a warning to be sufficient, the population centre must be notified and moved to safety before the tsunami hits the coast. The time for a tsunami originating at generation point G v to travel to population centre P w, can be taken as t v,w. The population at w can therefore be considered safe if: (17) Let: (18) For all v and w, where p w is the population at population centre P w, and e v,w (B k ) is a function of the deployment B k. 23

24 The total population that can be warned effectively of a tsunami originating at generation point G v, is thus: (19) This can be summed over all the hypothetical generation points, and normalised, to give a total warning potential for each particular deployment. (20) The objective is therefore to maximise E with respect to deployment vector B k, whilst also subject to the additional constraint on availability given by (12). This optimisation will give the most effective combination of detectors for the population centres and generation points identified Generation regions To carry out the above analysis, representative generation points must be decided upon. Six hypothetical fault segments were postulated by Kirby et al. [23] through research in to the highest risk fault regions along the Manila Trench. The data provided gives the longitude, latitude, strike angle and dip angle of the six hypothetical fault lines. Liu [24] determined the length of these six faults by considering the major cracks along the Manila Trench. He also reconsiders the strike angles postulated by Kirby et al. and makes some alterations to the noted epicentres of the six faults. These alterations are to be upheld. The rake angle is assumed to be 90 o as this will result in a maximum displacement of the sea floor, and is therefore conservative, and a focal depth of 15km is to be utilised as is commonly observed in several major past earthquakes here [24]. Based on these characteristics, work carried out by Wells and Coppersmith [25] can be utilised to deduce further fault parameters. Here, Wells and Coppersmith carried out a study to develop empirical relationships between the moment magnitude, surface rupture length, subsurface rupture length, downdip rupture width, rupture area and maximum and average 24

25 displacement per event for various fault types. The study collated the parameters for 421 historical earthquakes from the published results of field investigations and seismological investigations. Of these, 244 were selected for the formation of empirical relationships. From the published research, the following formulae can be extracted for reverse faults: (21) (22) Here; M w is the moment magnitude of the earthquake; SRL is the surface rupture length; RW is the rupture width. Using (21), the moment magnitude of each of the six faults can be determined, and this can then be used in (22) to determine the predicted width of the fault, as shown below in table 1. Table 1: Rupture width, as estimated by Wells and Coppersmith [25] relationships. Fault Length (SRL) (km) M w Width (RW) (km) G G G G G G Average = For the purpose of simplicity, the average value for the width over the six faults (35km) is adopted for all six fault planes. Finally, it was necessary to establish the dislocation or slip of the hypothetical faults. This was done using the following equations [24] : (23) (24) 25

26 Where; M 0 is the scalar moment of the earthquake; μ is the rigidity of the Earth s mantle and is taken as 3.0 x N/m [24] ; D is the dislocation of the fault; L is the length of the fault plane; W is the width of the fault plane. The obtained parameters for the six hypothetical earthquakes are detailed in full below. Figure 20: Hypothetical fault segments Fault Longitude Epicentre Latitude Table 2: Fault parameters Length (km) Width (km) Strike ( o ) Dip ( o ) Rake ( o ) Dislocation (m) G G G G G G Potential buoy locations It was also necessary to identify suitable sites in the South China Sea basin where the DART buoys could be located and were certain to work effectively at all times. The number of potential locations was limited to six to minimise the computational effort of the method, i.e: 26

27 Beyond this, there were a number of considerations: The sensors have to be deployed in areas of flat, deep ocean to prevent incorrect data due to disturbances from complex geometry and coastal reflection [24]. The bathymetric data for the region could be plotted and used to identify deep regions with a relatively flat sea bed. In addition, they should be located far enough from the source region to prevent discrepancies as a result of the trembling of the source. However, they must be close enough to the source region to ensure that they are able to detect the tsunami as early as possible to allow sufficient time for warning and evacuation. Finally, these buoys must be located in regions outside of major shipping lanes or areas associated with piracy [18]. Shipping lane data was obtained [26] and gave an additional constraint on where the buoys could be positioned. The following figure therefore illustrates approximately the six possible locations identified as suitable for DART buoys. Their longitudes and latitudes are given in table 3. Figure 21: Potential buoy locations 27

28 Table 3: Potential buoy locations Buoy Location Grid Longitude Grid Latitude L L L L L L Population centres The representative population centres were determined through visual analysis of a map of the coastal regions around the South China Sea. Significant urban areas were identified, and their approximate populations obtained through official government statistics [27][28][29]. The details of the chosen centres are given below in table 4, and illustrated in figure 22. Figure 22: Population centres 28

29 Table 4: Population centres Population Centre City Country Population (millions) Actual Longitude Actual Latitude Grid Longitude Grid Latitude P1 Pingtung County Taiwan P2 Tainan Taiwan P3 Xiamen China P4 Shantou China P5 Shanwei China P6 Hong Kong China P7 Zhuhai China P8 Yangjiang China P9 Zhanjiang China P10 Shenzhen China P11 Quanzhou China P12 Haikou China P13 Da Nang Vietnam P14 Nha Trang Vietnam P15 Kota Kinabalu Malaysia P16 Kuching Malaysia Total population = No urban areas were selected along the Philippine coastline, as it was assumed that any tsunami initiated along the Manila Trench, which is located just off the coast of the Philippines, would propagate towards these coastal communities too quickly for an effective warning to be relayed. From analysis of the simulations produced, it is apparent that the time taken for the generated tsunamis to reach the Philippine coastline is only around 10 to 15 minutes. This is far less time than is required for processing, signalling and warning once the tsunami is detected, and this assumption is therefore justified. Furthermore, no population centres were included from the northern region of Vietnam, as it was assumed that these regions would be sheltered from tsunami inundation. From observing the propagation of the tsunami modelled, this can be seen to be a reasonable assumption. 29

30 4.6. Simulations In order to determine the arrival time of each potential tsunami at each of the buoy locations and population centres, COMCOT was used to model numerically the tsunami resulting from the six hypothetical faults. Bathymetry data for the region was downloaded from the ETOPO2v2 database [9] for the area of 1 o S to 33 o N latitude, and 99 o E to 133 o E in longitude, as shown below. Figure 23: Bathymetry The grid size of the downloaded bathymetry data was pre-defined in spherical geometry at Δx = Δy = 2 minutes. In real terms, this gave a distance between nodes of Δx = Δy = 3710m. The number of grid squares in both x- and y-directions was Only one grid level was to be used as this was initially deemed to be sufficiently accurate, and the increased computational effort required to implement further grid levels could not be justified. When creating the COMCOT control files for the simulations, a time step had to be decided upon at which the programme calculated the new water surface elevations across the domain. The time step chosen had to guarantee that the Courant condition [30], which is a necessary condition for convergence, was satisfied, i.e.: (25) 30

31 In COMCOT, the maximum time step allowable is half of this value [1]. From the downloaded bathymetry, the maximum water depth, h max of the South China Sea region modelled, is 10,026m. This gives a maximum time step in COMCOT of: A time step of Δt = 5s was therefore chosen. Each simulation was run for a total of 3 hours. Once simulated, the required data could be extracted from the water surface elevation output data files for the required points in the geographical domain (namely the six potential buoy locations and the sixteen population centres), and plotted over time. As with the preliminary model verification work, it was impossible to select data for the precise coordinates of the population centres, firstly, as they are located on land, and secondly, as water elevation data was only generated for specific nodes in the domain. A point near to the coastline of each population centre was therefore chosen. In some cases the chosen points had to be significantly off the coast in order to obtain a meaningful result. This, and the degree to which this would affect the results of the analysis, are discussed later. Where the tsunami did not clearly arrive at a population centre within the three hour simulation, it was assumed to arrive on the three hour mark so as to remain conservative. When extracting the arrival time from the output data files, the tsunami was assumed to arrive at a location when the water level rose to 0.01m above the still water level. This value was chosen as it gave distinct and significant results. When implementing the WPM, the reaction time, r, chosen for all population centres was initially taken as zero. Although this is obviously unrealistic, this value will allow analysis based on only tsunami travel time to be carried out, neglecting error due to uncertainties in the reaction time. The effect of altering this reaction time has been discussed. The time required for processing and signalling of the tsunami was taken to be 30 minutes [5]. Initially, the number of available buoys, X, was set to three. This was the optimal number obtained by Braddock and Carmody [5] in their research in to an EWS for the Pacific Ocean. Although the South China Sea is considerably smaller, they use a similar number of generation points and population centres in their research, and three seems a reasonable number to ensure all areas are covered. Three buoys in six possible locations give a total of 20 distinct deployments to be compared. 31

32 5. Design Results 5.1. Optimal result with r = 0 On carrying out the initial warning potential procedure with the choice of variables described above, a maximum warning potential of was obtained. This indicates that on average, over the six hypothetical faults, 99.7% of the representative coastal population of the South China Sea could be protected from tsunami inundation. Only the population at P 1 (Pingtung County, Taiwan) during a tsunami initiated at the first generation point, G 1, were not warned and evacuated in sufficient time. The warning potentials calculated for all 20 deployments are given below: Table 5: X = 3 results Deployment Warning Potential B B B B B B B B B B B B B B B B B B B B Mean Max Min Range

33 The results showed that four different deployments, B 1, B 2, B 3 and B 4 all gave this optimal warning potential of These deployments are shown graphically below: Figure 24: Deployment B 1, (1,1,1,0,0,0) Figure 25: Deployment B 2, (1,1,0,1,0,0) Figure 26: Deployment B 3, (1,1,0,0,1,0) Figure 27: Deployment B 4, (1,1,0,0,0,1) From figures 24 to 27 above, it is apparent that all four optimal deployments utilise a buoy in both locations L 1 and L 2, and that the third buoy could be located in any of the remaining positions. The third buoy is clearly of no significance to the maximum warning potential obtained. For all deployments, the populations at P 1 and P 2 (Pingtung County and Tainan, Taiwan) were the most at risk, and locating buoys in the top two locations therefore gave the maximum warning possible to these centres, and hence the maximum warning potential. All other population centres were sufficiently far from the generating regions so as to be warned and evacuated with sufficient time, regardless of the deployment used. Generation point G 1, 33

34 being the closest to centres P 1 and P 2, proved to be the greatest threat. Examining the maximum water surface elevations over the whole simulation for G 1 (shown in figure 28) it is clear that the path of the tsunami predominantly propagates through the points of L 1 and L 2. These detectors would obviously therefore prove the most effective at detecting the impending tsunami. Figure 28: Maximum water surface elevations for G 1 The small range of results above do show, however, that there is little variation in the warning potentials achieved, and the number of people saved is not very sensitive to the deployment utilised when the reaction time remains at 0. The result attained implies that the same maximum warning potential could be obtained if only two buoys were deployed, as long as they were located in positions L 1 and L 2. The WPM was therefore repeated with X = 2 so as to investigate this further. The number of possible deployments in this case was 15. The results of this experimentation showed that the maximum warning potential of could indeed be obtained through the inclusion of only two buoys in locations L 1 and L 2. This is a useful observation, as the deployment of two buoys instead of three would reduce the capital outlay and maintenance effort and costs associated with the system, whilst ensuring that the ability of the system was not compromised. Using only two buoys, did, however, result in a larger range of values and a lower mean value of warning potential than for the three buoy situation. This outcome further demonstrated 34

35 the criticality of the propagation of a tsunami from G 1 towards the population centres of P 1 and P 2, as with the two buoy constraint only one deployment could effectively warn these centres, whilst with three buoys, four deployments were capable of this. Table 6: X = 2 results Deployment Warning Potential B B B B B B B B B B B B B B B Mean Max Min Range Another notable aspect of these results is that, with three buoys, it is not possible to warn all the represented population of tsunami initiated at all generation faults. A small proportion of the population will always be unable to evacuate in sufficient time, and will therefore be at risk from inundation. It is therefore of interest to determine if increasing the number of available buoys would increase the population that could be warned to 100%. The warning potential calculations were therefore repeated with X = 4 to investigate this, and the results for the 15 possible deployments are shown below. 35

36 Table 7: X = 4 results Deployment Warning Potential B B B B B B B B B B B B B B B Mean Max Min Range These results show that the maximum warning potential that can be achieved with four buoys remains at This indicates that there is no arrangement of buoys for which the maximum warning potential increases beyond this value, and therefore, no matter the arrangement of buoys, 0.3% of the coastal population remains at risk. Increasing the number of available buoys from three to four does, however, reduce the range of warning potential values obtained over the different deployments. With X = 3, the warning potentials ranged from to , a difference of 3.1%. Arranging three buoys at random, without optimisation, could therefore result in a reduction of 3.1% or 1.6 million in the number of people warned effectively. With X = 4, however, the range of values is reduced to just or 0.89%, and the mean is increased to This offers a significant improvement. The WPM was further repeated with five available buoys (X = 5) and six available buoys (X = 6) and the results analysed. These computations showed that, as was expected, the maximum warning potential of could not be improved upon from that obtained by two buoys. Whilst the mean and range warning potentials continued to improve for the five and six 36

37 detector deployments, the use of more than two buoys would be unnecessary and entirely uneconomical. As Braddock and Carmody [5] state, any increase beyond two buoys follows the economic law of diminishing returns. Table 8: X = 5 results Deployment Warning Potential B B B B B B Mean Max Min Range Table 9: X = 6 results Deployment Warning Potential B Mean Max Min Range 0 The determined result has the most serious implications for Taiwan as the populations most at risk from incident tsunami are those on the Taiwanese coast. The design of an EWS is therefore critical if these populations are to be protected, and the Taiwanese government should consider implementing one as soon as viable. In order for a system to be designed to protect Taiwan effectively, it could be useful to carry out the WPM for the Taiwanese population only, with new, more numerous, potential buoy locations clustered around the north eastern region of the South China Sea. This optimisation could increase the coastal population of the country which are considered safe. 37

38 4.1. Influence of reaction time, r Another aspect which should be measured is the effect of increasing the reaction time of the population centres on the greatest warning potential and optimal buoy deployment. For the initial experimentation, the reaction time was set to zero. This is obviously unrealistic, as it will take a finite amount of time for the population to be warned by the emergency services and to move from the coastal regions, to places of relative safety. A non-zero reaction time must therefore be considered, and the WPM was repeated for the three buoy deployments (X = 3) with a non-zero value of r. Table 10: X = 3 results, with r = 60 minutes Deployment Warning Potential B B B B B B B B B B B B B B B B B B B B Mean Max Min Range

39 When r was increased to 60 minutes, the maximum warning potential that could be achieved reduced to 92.2%. Interestingly, the optimal deployment in this case was B 11, which is shown in figure 29 below. Figure 29: Deployment B 11, (1,0,1,1,0,0) It is clear, therefore, that increasing the reaction time reduces the reliance on buoys at locations L 1 and L 2, in favour of those protecting different areas of the South China Sea. This is likely to be because no single deployment is sufficiently effective to protect the population centres of P 1 and P 2 when the time taken for the population there to react is 60 minutes greater. The optimal deployment therefore ignores that region in order to concentrate on those population centres that are next closest and at risk, namely P 3, P 4, P 5, P 14 and P 15. The buoy located at position L 1 of deployment B 11 can detect tsunami propagating from the more northern faults of G 1 and G 2, towards centres P 3, P 4 and P 5, giving them sufficient time even with a 60 minute reaction period to evacuate, whilst the buoys at positions L 3 and L 4 ensure that tsunami originating at G 3, and G 4 and G 5 respectively are detected quickly. In this scenario, the tsunami initiated at G 2 is the most problematic as it is detected the least quickly, and not only hits P 1 and P 2 rapidly, but also inundates those population centres further around the coast relatively quickly. 39