5. EXISTING MODELS  Next Chapter

5.1 A Review of Models

To construct a model to predict the effects of an inundation, data on a variety of topographies and environments must be combined, extending from the earthquake epicenter through to the houses themselves. The closer to the land one focuses their attention, the more localised the predictive models need to become. In order to arrive at predictions of any accuracy, one must operate models within models, and take into account the following series of events and environments, Earthquake, Tsunami, Bathymetry, Coastline, Topography, Landuse (population, buildings and roads). The Center for Tsunami Inundation Mapping Efforts (TIME) is a good example of state of the art mapping and topographical modelling efforts. It was created to assist the Pacific States in the development, maintenance, and upgrading of maps which identify areas of potential tsunami flooding. Their system is to first create earthquake event models and then map the wave propagation of these events in order to create a set of Tsunami Hazard Maps pertaining to specific areas. These are then made commercially available.

Earthquake models are generally simple and large scale, they exhibit similar figures worldwide, as it is a standard geological occurrence, though of course there are variations inherent, such as magnitude, depth, and fault type. For the purposes of this project, modelling an earthquake is not necessary. The approach will simply be to arbitrarily, though not unrealistically choose an epicentre and a variety of magnitudes from which a tsunami and destructiveness model will be created.

Tsunami models gain an extra complexity from sea floor topography, and position within the lunar tide period. There are two major factors that contribute to the amplitude of a tsunami; magnitude of triggering earthquake, and sea-floor topography. Depth is also a large contributing factor, the highest incidence of tsunamis occur from earthquakes at depths of 50 - 100km, though larger quakes at greater depth will have similar effect. Other contributing factors such as Coriolis force, linear and non-linear inertia force, bottom friction, frequency dispersion should be considered but play more or less importance depending upon wave travel distance. The 1960 Chilean tsunami that travelled 17,000kms and caused fatalities in Japan would have Coriolis force playing a larger part in calculations than would a locally triggered tsunami, while bottom friction and non-linear inertia force are insignificant. (Liu P.L.F et al., 1993)

Professor Nobuo Shuto of the Disaster Control Research Center, Tohoku University, Japan (www.geophys.washington.edu 1998) has created a computer generated animation of the 1960 Chilean tsunami. Logarithmic models were created using known data recorded at the event, as well as applying standard laws of wave motion theory.
Quicktime for Windows needed to play this movie

The US Geological Survey has also produced a number of computer generated animations of the July 17, 1998 tsunami, using separate data collected from seismic stations of the NEIC, Harvard University, and the Earthquake Research Institute
http://walrus.wr.usgs.gov/docs/tsunami/low_res_agif.html

There are two approaches to creating a predictive model; statistical, or mathematical. Statistical models are constructed solely from measured event data for a particular region, within a set of parameters and are somewhat limiting. In other words, they are estimations of wave heights based upon experience in a given area. Mathematical models are formulae constructed to describe in mathematical terms the physics of any given event, based upon measured data from given areas, but attempting to be applied to all possible areas. These are somewhat limited by the complexity of the variables, and their inaccuracy. The ideal method is to combine these two, first using existing data to create mathematical models, which are then tuned or modified by real-time events to create realistic and accurate models. (Abe, 1995).

Abe found when matching these equations against real-time events, there seems to be an uncertainty factor of about 1.5, particularly with a certain type of tsunamigenic earthquake known as a "tsunami earthquake", one which produces unusually large tsunamis for their relatively low magnitude. These comprise of about 10% of tsunamigenic earthquakes. He felt that these type of earthquakes should fit outside this mathematical model in order for it to be more accurate, and states that research needs to be done on tsunami earthquakes.

Bathymetry (click to view Bathymetry map of South China Sea) see also Bathymetry map analysis

Modelling for bathymetry has usually been included within tsunami modelling, in order to increase the accuracy of localised predictive models. The Pacific Ocean has a mostly flat sea bottom, averaging 6000 - 7000m, with continental shelves to 200m encircling all continental land masses at roughly 200kms distance from the coaust, with some exception, particularly countries lying adjacent to marine trenches. Tsunamis at sea are practically unnoticeable at sea level, they are a ripple barely a centimetre or two in height. Compression of the amplitude wave due to decreasing depth will proportionately increase wave height and speed, so by the time the wave makes it's land fall, it is travelling up to 650km/h and is as high as 10-30m. The shape of the sea floor and its cross section to the coastline will greatly determine the nature of the wave. Islands and sea mounts will cause drag on the shape of the wave with some dissipation of energy, but as can be seen in the 1960 Chilean event, (Liu et al, 1993) this did not appear to apply here. The continental rise is the first major obstruction that a wave will experience, and actually acts as a buffer to dissipate a large amount of inertia, and no doubt protects coastlines from much worse waves. However the simple transferral of energy becomes reflective, ie. the initial long waves of the tsunami bounce off the continental shelf, and reflect back to sea, into the radiating wave, hence getting bounced back in shore. This is the cause of multiple waves in tsunami events.

The recent PNG tsunami was particularly large due to several factors. The sea floor off the coast of Aitape drops away very quickly, to a depth of 3000m, and has an even slope from the epicentre that was 12 kms off shore.

Coastlines (click to view Bathymetry map of Zhujiang estuarine coastline) see also Coastline map analysis

Intimately related to bathymetry, modeling of coastlines becomes more localised than the previous factors in tsunami's. Adams & Lewis (1979) made a fair attempt to categorise coastlines into nine distinguishable types, including offshore type and coastline proper. The point at which the transferance of energy travelling through the water reaches the coastline and causes the water to physically move into a breaking wave is of crucial concern, because the shape of the offshore coast immediately before tideline will determine the focus of the wave as it breaks on land. For example, if the offshore coastline is convex, the force of the wave will be dissipated out to the sides as the wave breaks, and if the offshore coastline is concave, it will focus the breaking wave into the centre of the point of landfall. Adams & Lewis chose 3 simple shapes, linear, concave, and convex for both the offshore coastline and the shoreline, creating 9 possible combinations. An interesting issue was raised by Adams & Lewis in that a model for a complicated surface can be synthesised, with some decomposition, from a model for a linear surface. This means that the basic wave properties of a simple, clean coastline will remain the same for a coastline with small islands and rough sea-floor, with some extra distortion and minor reflecting waves. This is important in studying the Zhujiang region, as the mouth of the estuary is dotted with various islands that will possibly modify the tsunami properties as it makes it's landfall further up stream.

Topography

The action of the tsunami on land, and the destruction it causes, becomes specific to the immediate topography of the area experiencing the tsunami. Detailed topographical data for any part of China is difficult to obtain, for military reasons etc, but there are in other parts of the world, particularly those prone to tsunami, systems in place to model coastlines and topographies of various communities, on a council level. To achieve this, land surveying and mapping with the specific purpose of estimating wave actions upon land in mind must be carried out.

There is quite a large body of data in the form of historical accounts and eyewitness reports that can be drawn upon in the construction of wave destruction models. Earthquake scientists have paid a lot of attention to eyewitness reports, and have generally found that such reports have later been confirmed by breakthroughs in understanding from a scientific basis. In other words, people have tended to give pretty accurate reports of events, however much out of the ordinary they may have initially appeared to be.

For the Guangzhou region we have no topographic and land data more detailed than contained in the maps of this paper, so construction of a model will be largely speculative, manual and one based upon observational abilities. The basis of the physical model is very general, which is less than ideal, being unable to use hard data relating in detail to the area.

To assist in this, comparison of the maps in the Interactive Map Presentation section is required to intuit the possible threat from a given tsunami on the Delta region. Using information and reports from the July 17, 1998 PNG tsunami, and other well documented events, it is hoped to present here a scenario with enough details for it to have some value.

Land Use/Buildings

In terms of constructing a model to predict destructiveness upon land and built environment, detailed and specific localised information is required on the nature of built structures and roads as these house and service the populations. Construction materials and design of buildings is important to how a structure will resist or give way to the destructive force of a tsunami. Of secondary importance is the road system and communications, as these will determine the emergency response times and effectivenss in clean-up procedures.

Next Chapter