There are two components to this study: the tsunami simulation model and the economic losses model, as shown in
Figure 2. First, a tsunami hazard map is generated based on earthquake scenarios around the study area and computed by a mathematic model (TUNAMI-N2). We perform the simulation based on 6 earthquake scenarios along the Ryukyu Trench and the Okinawa Trough around Okinawa Island. TUNAMI-N2. The resulting hazard map is overlaid with a land use and topography map to identify vulnerable regions for computing economic losses. The economic model of this study area follows the MRIO model, where industrial sectors are scaled to correlate with the economic land use type and topography type (coastal area and inland area) by the Chenery–Moses-type. The relationship between the hazard map and the economic values is used to estimate the direct and indirect disaster losses. Direct losses can be directly estimated from the total income of the MRIO table, while the indirect losses can be computed by the direct losses and the interaction parameter of the MRIO table. The interaction parameter is formed in linear programming and is calculated using the Leontief methodology.
2.3. Multi-Regional-Input-Output Table
A single-regional input-output (SRIO) table, as a conventional input-output (IO) table, can generally be used to estimate direct and indirect economic effects by examining the economic linkages between sectors and regions [
42]. The SRIO table is explained in a monetary matrix (row and column) format containing inter-industry transactions. The rows of the matrix describe the distribution of outputs (product sale structure). The columns display inputs (purchase structure), the sum of raw materials and the value-added expenses (for details, see [
43,
44]). The equation used in the SRIO model with the mixed variables has been derived as follows. First, the vector of output is the sum of the intermediate transactions and the final demand (1); then, Equation (1) is transformed into a matrix as shown in Equation (3), as illustrated by the basic equation for IO tables with the Leontief inverse matrix.
where,
is the vector of output,
is the vector of final demand,
is the matrix of input coefficient,
is the identity matrix, and
is the Leontief inverse matrix
as
. When three sectors are assumed for the IO table, Equation (4) is as follows:
However, the conventional IO table as an SRIO table only demonstrates these processes in one region, thus, the impacts of domestic trade cannot be presented.
For estimating indirect losses, is the direct losses at sector 1 on while and are 0. In the Leontief inverse matrix, the coefficient of sector 1 is also changed for estimating the indirect losses of this sector as . The other indirect losses, and , affected by are investigated in Equation (5).
The SRIO table provided by the government has a limited ability to evaluate disaster areas because the disaster has an effect on other regions with economic linkages [
27]. In the case of Japan, there is mainly an economic network in 9 regions with 81 networks, and the economic value of the 81 networks is presented in
Figure 4. The network economic links of the 9 regions, which have been provided by METI, can be identified as the IRIO table [
30]. The METI IRIO table of Japan contains 53, 29, and 12 sector classifications.
The use of the IRIO table estimates the indirect losses from disaster, and the estimation has a limitation because the disaster does not occur in the whole country or regional area [
23]. The implementation of IRIO for estimating disaster economic losses requires a downscaling of the industrial sector specific to the disaster area. The method for downscaling the IRIO of the region of interest specific to the disaster area is shown in
Figure 5. First, selecting a value in the IRIO to assess the study area results in an SRIO with trade value. The industrial sector in the selected SRIO table has a relationship with the land use type, but the disaster area is related to characteristics of geography. For tsunamis, the disaster area occurs in a coastal area where the selected SRIO table must point to the coastal zone. Downscaling the selected SRIO table to the expected area of tsunami disaster, which is original to this research, can be done based on the characteristics of geography, e.g., the coastal and inland areas. In this study, we hypothesize that the coastal area, as the disaster zone, is the high-vulnerability area for tsunami effects. The coastal areas are identified based on the vulnerability class of tsunami hazards proposed by Sambah and Miura [
45]. That study proposed vulnerability classes of tsunami hazards from low to high based on the 2011 large tsunami event in Japan. We used the topography characteristics of the medium class from the previous study to classify the coastal areas in this study on Okinawa Island. The criteria of the 3 characteristics of geography used to identify the coastal area are shown in
Table 2. The criteria used to divide the coastal area include the 3 characteristics of geography: altitude, gradient and distance from the sea, as determined by the disaster zone map (see
Figure 6a). The distance from the sea is the measurement length from the coastal line, and we hypothesize that the coastal area is closed to the coastal line. Based on the tsunami wave runup processes, we classified the high vulnerability of tsunami runup area and the low vulnerability of tsunami runup area using 2 variables, gradient, and altitude. The tsunami wave is easy to runup in a low gradient, while the high gradient is difficult. In addition, tsunami runup is difficult for high elevations but easy for low elevations.
In the modification of the selected SRIO table, the ratio of land use (see
Figure 6b) in the coastal area and inland area is used to separate the economic value in each sector into different zones because of the relationship between land use and sector in the SRIO table. For the estimated effect in other regions, the modified IRIO table is combined with the IRIO table of other regions by the Chenery–Moses estimation method (for details, see [
46,
47]) to establish the MRIO table. The MRIO table can be used to calculate the indirect loss by the Leontief method, as mentioned above. The table contains the economic link from the micro scale (disaster area) to the global scale. This paper uses the model based on Equation (5) to complete the MRIO table to calculate the indirect economic loss of tsunami flood disasters on industrial sector production.