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Real-time Prediction Method of Tsunami Inundation for Railway Line

To evaluate the influence of tsunami inundations on railway lines and implement measures for evacuation, it is necessary to predict the depth of tsunami inundations at sites of railway facilities. The author therefore developed a real-time prediction method of tsunami inundations for railway lines, immediately after large earthquakes occur at sea. This method first predicts tsunami water levels in the coastal areas, using tsunami water levels at sea and the tsunami propagation functions. Secondly, the method predicts the depth of tsunami inundations for the target railway line, using a database of tsunami inundations for scenario earthquakes, created in advance.


Introduction
To evaluate the influence of tsunami inundations on railway lines and rapidly implement measures for evacuation, it is necessary to predict the depth of tsunami inundations at sites of railway facilities immediately after the occurrence of an earthquake. The author developed a real-time prediction method of tsunami inundations for railway lines, using tsunami data observed at sea and tsunami simulation results prepared in advance. Since the 2011 off the Pacific coast of Tohoku earthquake, water-pressure gauges have been installed on the ocean floor off the Pacific coast of the Tohoku region [1]. Real-time tsunami prediction methods which apply the assimilation theory to tsunami data [2] and interpolate into tsunami simulation results [3] have been developed. These methods however, do not satisfy both the immediacy and stability for tsunami warning. This study therefore uses tsunami data at one observation point to improve the immediacy of tsunami warning. A database of tsunami propagation functions and tsunami inundation maps were compiled in advance to improve the stability of tsunami warning. Based on these results, the real-time prediction method, which in-tegrates the prepared tsunami simulation results with the observed tsunami data, was developed. This paper also presents an example of this method being applied to predict the depth of tsunami inundations along an actual railway line.

Outline of the method
The real-time prediction method of tsunami inundations for railway lines proposed in this study consists of two steps: first, a real-time prediction of tsunami water levels in the coastal areas, and second, a real-time prediction of the tsunami inundation areas. Figure 1 shows an overview of this method. Tsunami water levels in the coastal areas, for the first step in this method, are predicted by multiplying the tsunami data recorded at one observation point at sea with the tsunami propagation function prepared using the 2-D tsunami simulation in advance. In the second step, the tsunami inundation areas that are expected by the predicted tsunami water levels in the coastal areas, are extracted from the inland tsunami inundation maps due to possible scenario earthquakes stored in the database.

Scenario earthquakes and target area
This section describes the compilation of the database used in the second step. For the fault model, 96 earthquake source faults with a magnitude of more than 8, according to the combination of segments (Fig. 2), were set at the plate boundary of the Japan Trench, from off Tokachi to off the Boso Peninsula. In this fault model, the inhomogeneity of the slip amount is characterized. Twice slip amount as large as the average slip amount is arranged in the large slip region and four times slip amount as large as the average slip amount is arranged in the super large slip region, according to the scale of magnitude [4]. Figure 3 shows examples of the scenario earthquake fault models (No. 1: single segment rupture, No. 22: 4 segments-linked rupture including a large slip region).
Tsunami inundation simulations of the scenario earthquakes at the plate boundary of the Japan Trench were performed for Ishinomaki City. Figure 4 shows the detailed seafloor topographical model around Ishinomaki City (for an area with a grid size of 15 m).

Database of tsunami inundations for the target area
The linear long-wave theory was applied to the 2-D tsunami simulation from the deep sea area to the coastal area, and the shallow water long-wave theory [5] was applied to the 2-D tsunami inundation simulation from the coast area to the inland with the boundary condition of run-up [6]. The various conditions for the 2-D tsunami inundation simulation were set as shown in Table 1. Figure  5 shows examples of the results of the tsunami inundation simulations for Ishinomaki City by scenario earthquake fault models (No. 1 and No. 22) at the plate boundary of the Japan Trench. The scenario earthquake fault model of No. 1 has a small tsunami inundation area, because the slip region is located far from Ishinomaki City (Fig. 3 left). On the other hand, the fault model of No. 22 has a large tsunami inundation area, because the slip region is located near Ishinomaki City (Fig. 3 right). In this way, a database of tsunami inundation maps in Ishinomaki City, which stores inundation areas for various types of tsunamis, was created for 96 scenario earthquakes at the plate boundary of the Japan Trench.

Real-time prediction of tsunami water levels in a coastal area
As shown in the first step of Fig. 1, the tsunami water levels in the coastal areas were predicted in real-time, using the tsunami water levels observed at sea and the tsunami propagation functions depending on the seafloor topography [8]. The following shows the specific procedure

Real-time Prediction of Tsunami Inundations for an inland area
As shown in the second step of Fig. 1, the tsunami inundation area was predicted in the real-time, using the predicted tsunami water levels in the coastal area and the tsunami inundation maps based on scenario earthquakes. The specific procedure of this method is described below, and was verified using data from the tsunami of the 2011 off the Pacific coast of Tohoku earthquake that occurred at the plate boundary of the Japan Trench. -A scenario earthquake was selected, by a matching method on the similarity between the predicted tsunami water level at the evaluation point in the coastal area obtained from the first step, and the tsunami water level at the same evaluation point based on scenario earthquakes [2]. -The tsunami inundation area in the target area based on the selected scenario earthquake is extracted from the database. Figure 9 shows a scenario earthquake (amount of slip in the large slip region: 8.74 m, amount of slip in the background slip region of the scenario earthquake: 5.35 m) selected from the tsunami water level at the evaluation point in the coastal area shown in Fig. 8 and the Cabinet Office model as the correct answer. Although the fault area of the selected scenario earthquake was consistent with the Cabinet Office model, the fault area of the selected scenario earthquake was located in slightly south of the Cabinet Office model, and the detailed slip distribution was different. A comparison of the tsunami inundation area in Ishinomaki City obtained through the selected scenario earthquake and the tsunami inundation area by the Cabinet Office model are shown in Fig. 10. The inundation area (76 km 2 ) based on the selected scenario earthquake, matched the inundation area (81 km 2 ) in the Cabinet Office model by more than 90% with a good agreement.
Furthermore, the arrival time of tsunami in Ishinomaki City after the occurrence of the selected scenario earthquake is shown in Fig. 11. It is found that extra time of more than one hour could have been secured in Ishinomaki City after the 2011 off the Pacific coast of Tohoku earthquake, against a computation time within one minute for extracting the tsunami inundation area from the database.

Real-time prediction of tsunami inundation for a railway line
As an example of the application of this method to railways, Fig. 12 shows a real-time prediction of the depth of tsunami inundations along the railway line (Fig. 10) for the 2011 off the Pacific coast of Tohoku earthquake. As a result, some sections have depths of tsunami inundation more than 5 m. On the other hand, there are sections where the tsunami does not arrive because of the higher altitude. Therefore, evacuating a moving train towards such a section ensures the tsunami resistance of the railway. This method is expected to be able to transmit sections identified for evacuation to the moving train before the tsunami arrives, by presenting the prediction result for the depth of tsunami inundation along the railway line immediately after the tsunami was observed at sea. As described above, this method can predict immediately and stably tsunami inundation depth along railway lines at an early stage.

Conclusions
To reduce tsunami damage of railways, the author developed the real-time prediction method of tsunami inundation, which integrates the prepared tsunami simulation results with the observed tsunami data, for railway lines. This method has the unique features of improving the immediacy of tsunami warning by using tsunami data at one observation point and improving the stability of tsunami warning by compiling a database of tsunami propagation functions and tsunami inundation maps prepared in advance. The proposed method was applied to the tsunami of the 2011 off the Pacific coast of Tohoku earthquake, and its performance was verified with the tsunami inundation area in the Cabinet Office model. As a result, it was confirmed that tsunami inundation area by the proposed method matched over 90% of the tsunami inundation area in the Cabinet Office model. Immediately after the tsunami observation at sea, this method can present the prediction results for the depth of tsunami inundations along railway lines.