The magnitude 9.0 earthquake that struck Japan on 11 March 2011 caused the largest insured loss as an earthquake in history. The majority of economic and human losses were caused by the resulting tsunami rather than by ground shaking. However, tsunami has been a largely unmodeled risk in the insurance industry. In response to the latest Japan tsunami, Dr Toru Tamura says Swiss Re’s Nat CAT experts and underwriters have developed a probabilistic tsunami model for Japan – the first in the industry – to be used for the quantitative assessment of tsunami risks.
In order to estimate natural catastrophe risk, the insurance industry has employed probabilistic modelling.
A probabilistic catastrophe model normally consists of two major components; a hazard component which generates huge numbers – for instance, 100,000 – of potential catastrophic events such as earthquakes and tropical cyclones; and a vulnerability/financial component which translates the intensity of an event into economic loss.
As a result, based on the probability of occurrence of each event, the model can estimate the probability of a certain financial loss sustained from the natural catastrophe.
Shortcoming in CAT modelling
Even though we have been aware of tsunami as a significant secondary peril of earthquakes in Japan, especially after the Sumatra earthquake and tsunami in 2004, none of the probabilistic earthquake models in the insurance industry had integrated tsunami risk via probabilistic modelling, as described above.
Thus, the risk premiums of earthquake insurance in Japan were unable to adequately reflect the loss potential from tsunami. One of the obstacles in tsunami modelling was the intensive computational requirement to conduct a number of simulation runs with a high three-dimensional resolution covering the extensive domain of the country.
Modelling approach
For tsunami modelling, the first task was to create a hazard component that simulates tsunami events for all probabilistic earthquakes. In order to obtain an expected loss caused by tsunami, we need two sub-components:
• Offshore wave height (a model to simulate open water wave propagation triggered by deformation of the seabed)
• Onshore tsunami inundation (a model to simulate how far tsunami travels inland and how much it inundates onshore locations, once offshore tsunami hits the coastline)
Offshore wave height
It was necessary to come up with a computationally efficient approach applicable for probabilistic modelling.
Some scientific studies showed a candidate approach for probabilistic tsunami modelling, without having to simulate huge numbers of tsunami propagation according to each earthquake event.
These studies suggested that on the basis of linearity of tsunami dynamics, arbitrary tsunami propagation can be constructed from pre-computed individual tsunami scenarios. Therefore, tsunami propagation for any magnitude of earthquake can be synthesised by combining pre-computed tsunami propagations for a predefined magnitude.
We could successfully create a probabilistic tsunami event set by coupling our original probabilistic earthquake sources with pre-computed tsunami scenarios. By sorting according to tsunami height of the event and aggregating event probabilities, we can estimate what tsunami wave heights can be expected within a certain time frame.
Figure 1 shows that a significant tsunami hazard exists along the northeastern coast of Japan over 1,000 years, which would correspond to the latest tsunami event. More than 10 meters of tsunami is also expected along the coast facing the Nankai Trough. The Central Council of Disaster Prevention recently put its focus on the Nankai Trough as another threat of a magnitude 9.0 earthquake and tsunami triggered by cascading ruptures of the subduction zone.
Onshore inundation
While numerical modelling has been a major method for onshore inundation calculations, we used an analytic method based on static hydraulics, considering its computational advantage.
According to the Tsunami Risks Project 2000, the maximum inundation distance over relatively flat land can be solved from energy conservation between the potential energy of offshore tsunami at the coast and friction caused by surface roughness. By obtaining this maximum inundation distance, we can further estimate the inundation depth over an observation point according to its distance to the coast and elevation. Considering that most of insured values are located over relatively flat topography, we applied this method across Japan.
Figure 2 compares observed inundation areas with modelled tsunami inundation depths for the 11 March event in Japan. The simulated inundation area closely corresponds to the observation, and the modelled inundation depths closely replicate local surveys (The 2011 Tohoku Earthquake Tsunami Joint Survey Group). These facts validate that our inundation calculation is sufficient for probabilistic modelling.
Implications of the tsunami model
By integrating a vulnerability/financial component, we are now able to project insured losses caused by tsunami. We could validate the model’s capability by comparing simulated and reported losses of several insurance portfolios in the latest tsunami event. The Swiss Re tsunami model for Japan has been in practical use since the beginning of 2012.
Although recent scientific knowledge after the magnitude 9.0 event would affect our assumptions on probabilistic earthquake sources, the tsunami model can tell us how much we have underestimated annual expected losses of earthquakes. We found that when tsunami is included, the earthquake risk premium increases by roughly 10% in a typical insurance portfolio on a market-wide basis. It should be noted that the ratio of tsunami contribution is significantly dependent on the geographical distribution, insurance structure and occupancy class of a portfolio. For strongly coastal-exposed accounts, the increase in earthquake risk premium can be far more substantial.
The probabilistic tsunami model also helps to quantify tsunami risk for any place of interest – for instance in big cities close to the coast such as Tokyo, Nagoya and Osaka. Figure 3 shows the expected offshore tsunami height and its frequency for representative locations within the bays of these cities. Tsunami is obviously not a frequent event, but it could be a large loss driver in these concentrated cities over a long return period. It may suggest to policymakers that we have to consider not only physical mitigation but also financial risk transfer solutions for tsunami hazards as a cost-effective method in these cities.
Tsunami could cause devastating and extended loss in one event, but its risk significantly varies according to geographic location and local elevation. Our initial launch of the tsunami model for Japan is expected to contribute to better evaluation and management of earthquake risks, which would in turn lead to sustainable provision of earthquake protection by insurance companies.
Dr Toru Tamura is a Property Treaty Underwriter at Swiss Re.