Chapter 12
Disaster Simulation
Field of expertise: Computational Mechanics and Computational Disaster Science

Kenjiro Terada
Translated by Catherine Sachi Kikuchi

Summary
One of the essential words to describe the Great East Japan Earthquake is "unexpected” and there
is nothing more vulnerable to this unexpectedness than numerical simulations. In this chapter, I will
review the role and challenges of disaster simulations, which consist of setting conditions such as
the type and scale of disaster, calculation tools, prediction (output) results, and how to improvethem.
Keywords: numerical simulation, earthquake/tsunami, destructive phenomena, surrogate modelIntroduction
Numerical simulations are expected to provide useful preliminary information for disaster
preparedness within a set of assumed conditions. On the other hand, an essential word to describe
the Great East Japan Earthquake is "unexpected”. In this chapter, I reaffirm the utmost importanceof assumptions in disaster simulation, and present my personal views on the current issues anddevelopments.

1: Problems Revealed by the Great East Japan Earthquake
What happened?
Simulation is a means of predicting what will happen in the event of a disaster, but it is notpossible to predict what has not been anticipated. This obvious fact was exposed and theenormous damage that occurred could not have been foreseen. From the standpoint of a specialistin numerical simulations, this is all I can say, but it is necessary to consider what role simulations
played or should have played in the Great East Japan Earthquake, and what lessons we can learn
for the future.
The reality is still unclear1

I will leave the figures on the various types of damage to other chapters, but I will mention
that the energy of the earthquake far exceeded the performance ability of structures, regions andcities. This resulted in destruction over a wide area and over a long period of time. It was so severethat it made us think that our prior countermeasures were meaningless. However, there must havebeen some meaning to our precautionary measures. In fact, thanks to the measures taken after theGreat Hanshin-Awaji Earthquake, the damage to buildings caused by the Great East Japan
Earthquake was within expectations, except for the problem of them interacting with the ground. Itis also true that the structural measures taken in advance did not provide complete protection
against the tremendous destructive power of the tsunami, but they must have contributed in somesmall way to mitigating the damage by absorbing the energy. However, as will be explained later,
the actual situation cannot be clarified because the current simulation technology is unable toproperly reproduce this type of destruction. Here, I focus mainly on the predictive function ofdisaster simulations, although the scientific verification function of the effectiveness of theseproactive measures is also important, and we hope for the advancement of this technology.

2: Recognizing Unchanging Common Sense
In general, a simulation has an object for that simulation and tools are designed specificallyfor that object. A tool is a box, so to speak. When certain conditions (data) are put into the box, theresult (prediction) is the output. Therefore, for a simulation, the assumptions are the input, and they
are in one-to-one correspondence with the prediction results. However, even if the conditions are
not prepared, it is possible to foresee possible events within the range of accuracy, as long as therange of conditions is determined. In other words, if multiple predictions are made in advancewithin the assumed range of conditions, interpolation will provide useful advance information fordisaster preparedness. This is the conventional wisdom and it will continue to be.
While we naturally conclude that if the input to the assumed box is different from the actual
situation, the predictions will not match reality. This does not mean that everything is OK if theinput is correct. Whether the box works as expected and whether it provides reliable predictions isalways in question. The simulation tool (i.e., the box) is a computational program, but it is also amathematical model (i.e., an equation) that is designed to simulate a certain type of disaster. In
fact, we should not forget that there are assumptions here as well. We must verify whether themodel is trustworthy, whether it can adequately represent the phenomenon to be predicted, andwhether the input information, such as physical properties, is reliable.

3: Requirements for Improvement and Delineation
If the simulation is limited to the prediction and reproduction of physical phenomena suchas natural disasters, our purpose is to derive useful information that contributes to disasterprevention and mitigation through expressing physical phenomena in the language ofmathematics, then replacing it with a language that computers can understand, and thenreproducing it. Figure 12-1 summarizes numerical simulations of earthquake and tsunami disasters
and the changes in hardware and software. As time passes, the high performance of hardware(represented by supercomputers) and the sophistication of software have progressed in step witheach other, but with these changes, demands for more complex and large-scale (i.e., in the actualtarget area) disaster reproduction and predictions have increased as well. In parallel with thereview of design standards and legal systems triggered by major disasters, computational disasterscience has also been required to improve accuracy and adapt to new calculation targets.

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In particular, after the Great Hanshin-Awaji Earthquake, it became necessary to reproduce
phenomena that were not taken into account in the design calculations, such as the destruction
and collapse of buildings, and this is still one of the important research topics in the field ofcomputational science. On the other hand, even if the huge tsunami that occurred at the time of theGreat East Japan Earthquake could be predicted, the damage to cities and structures caused by
the fluid force was far beyond the complexity and scale that the simulation technology of the timecould handle. In fact, the phenomenon of tsunamis destroying structures, engulfing debris, andhitting people and buildings cannot be reproduced even today, and many researchers are working
hard to improve numerical simulations. Thus, the problems of destruction and the interaction
between the ground, structures, and liquids should be continuously challenged.

Figure 12-1. Disaster simulation and the changes in hardware and software

4: Demands for Efficiency and Certainty
There are several simulation tools that have a good track record and are currently usedwith a certain degree of reliability. These include tsunami arrival time and inundation predictions.
The method of estimating the generation and size of a tsunami at the same time as an earthquake
occurs, and making the most reliable prediction based on the results of calculations for many
scenarios (cases) in advance, has proven to be sufficiently accurate for practical use (although
there is no limit to what we can ask for). Once the tool is complete, the issues to be addressed are
to reduce the computational cost by introducing model reduction and surrogate models, to pursue
real-time performance, and to establish probabilistic risk assessment.
Figure 12-2 shows an example of calculating the tsunami that would hit Sendai Bay, Miyagi
Prefecture, by changing the fault slip angle (rake) and the amount of slip (explanatory variables) of
the fault. By expressing the maximum wave height as a function of the explanatory variables, as
shown in Figure 12-3, we can estimate the real-time damage. We can also show the probability ofother scenarios using the results of the most likely scenario as the expected value (Figure 12-4)(Kotani et al., 2020). Results of each scenario show the probability of occurrence for each.
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Figure 12-2. Variation in the maximum wave height of a tsunami reaching Sendai Bay resulting
from a simulation assuming variation in the slip amount and slip angle of the fault that generates
the tsunami

Figure 12-3. Expression of the maximum wave height as a function of the amount of fault slip andslip angle (rake) as explanatory variables

Figure 12-4 Density distribution of probable tsunamis with the maximum wave height in theassumed scenario
4It is essential to conduct research so that we can solve problems that have so far been
unsolvable, and continue practical research to improve efficiency and certainty of these solvableproblems.

Conclusion - from the authors
We would like to develop numerical simulations as a disaster prevention technology that
can answer with certainty the questions of whether or not a region, city, or structure has the mostimportant function of protecting human lives from disasters, and if not, what measures should betaken.

References
Kotani, T., Tozato, K., Takase, S., Moriguchi, S., Terada, K., Fukutani, Y., Otake, Y., Nojima, K.,
Sakuraba, M., & Choe, Y. (2020). Probabilistic tsunami hazard assessment with simulation-based
response surfaces. Coastal Engineering, 160, [103719].
https://doi.org/10.1016/j.coastaleng.2020.103719

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