## 2 Materials and Methods
### Model Setup  
The model was simulated for 39 days, from 1 September to 9 October in 2011; this period included the typhoon season and was chosen for the sake of constructing a robust model during extreme atmospheric conditions. The time step for the model was set to 80 s, while the outputs were stored every 12 min. All information about time stated in this paper is based on the local time, Japan Standard Time (JST). The maximum resolution of the horizontal grid was approximately 30 m around Hiroshima Bay, one of the main study areas of the model. The spatial grid resolution of the model varied flexibly to describe all islands and straits in the SIS (Figure 1b) as long as the number of nodes and cells maintained a reasonable level in terms of the computation time. For Hiroshima City and Osaka City, the complex coastlines with coastal infrastructures were described in great detail (Figure 1c). The maximum size of the mesh was approximately 9800 m near the main open boundary in the Pacific. The resolution of the grid near the Nankai Trough was determined by considering the gradient of bathymetry, as shown in Figure 11, to reduce the pressure gradient force errors in terrain-following (\(\sigma\)) coordinates by describing the steep bathymetric gradients near troughs in great detail. Thus, the total number of nodes and cells became 210,505 and 390,461, respectively, covering the domain with lengths of 500 km \(\times\) 420 km. Thirty sigma levels were used for the vertical grid. As a result, in terms of the computation time, it took approximately 30 min of real time to simulate one day of model time with ninety-six CPUs. The short simulation time will allow us to apply the near real-time feedback system between reality (physical space) and the model (virtual space). The Shapiro filter was adopted to suppress spurious velocity or temperature modes by increasing the stability of the model during the simulations. However, the momentum of fluids can be excessively dissipated if a meaninglessly high filter parameter is set, resulting in the unrealistic depression of surface elevations and velocities (the maximum filter value allowed by the model developer is 0.5). The horizontal resolution of our model was high, focusing on the target areas, river mouths, and narrow channels, as explained above. A small uniform value for the parameter such as 0.2 could not prevent the occurrence of spurious modes, resulting in unrealistic velocity patterns along the unstable mesh areas. When the value of 0.5 was applied uniformly, the spurious modes were successfully suppressed, but the momentum that should have been calculated was also suppressed. Applying the parameter uniformly across the entire model domain could not solve this problem. Therefore, we tried to generate a spatially varying parameter field considering instability factors, such as the maximum velocity, mesh resolution, and heavy river discharge, at each node. To obtain the maximum velocity field, we simulated the model with fewer vertical layers than the thirty layers used in this study. Then, the relatively high filter parameter values were calculated at the nodes with high velocities and high resolutions. Additionally, we set relatively high values for the river areas with freshwater discharges. Finally, we created a field for the parameter \(\gamma\) (Figure 2), after which the model simulation could perform much more stably and accurately without spurious modes or excessive energy dissipation. Careful attention was also paid to creating high-resolution bathymetric information for the numerical simulations. As the base bathymetry data, electronic charts of the M7000 series from the Japan Hydrographic Association were used. This dataset is based on bathymetric contours. It has strengths, especially near narrow and steep sea areas, because the contour intervals are more finely subdivided near these areas. However, the contour interval of the M7000 series is sometimes quite coarse in coastal areas, especially near Osaka Bay.