# Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan
## 4 Discussion  
A unified computational grid for tsunami simulation is currently not available, so professionals have to apply many alternative solutions. For transoceanic events, the step size is usually comparable to 2 arc minutes (that is, nearly 3.6 km at the latitude of Japan). For inundation mapping, one can use a 5-10 m grid step. In other words, the choice of grid step should be correlated with the goals of the numerical modeling. In our case, we studied the distribution of tsunami maximal heights along the coastline for near-field events. So, we calculated wave propagation in a water area within an approximately \(1000\times 2000\) km rectangle. The simulation was carried on up to a depth of 10 m. We considered grid step sizes of 0.003 arc degrees in the east-west direction (nearly 280.6 m) and 0.002 degrees in the north-south direction (about 223 m), suitable for our purposes. The mesh points were matched with geographic coordinates. In particular, this means that the length of the east-west direction grid step slightly changes from the southern to northern edges of the considered water  
Figure 11: Distributions of tsunami wave maxima along the shore generated by the sources _S0-a,b,c_ (**A**), _S1-a,b,c_ (**B**), _S2-a,b,c_ (**C**), and _S3-a,b,c_ (**D**). Wave height maxima by the _Si-a_ sources (\(i=0\), 1, 2, 3) are drawn as yellow lines, those by _Si-b_ sources as pink lines, and those by _Si-c_ sources as blue lines. The horizontal axis shows the longitudinal coastline point position on the computational grid (see the lower part of Figure 3 for numbering). area. The Japanese bathymmetric data produced by the Japan Oceanographic Data Center (JODC) and distributed by the Data On-line Service System (see [16][[http://jdoss1.jodc.go.jp/cgi-bin/1997/depth500_file](http://jdoss1.jodc.go.jp/cgi-bin/1997/depth500_file)]([http://jdoss1.jodc.go.jp/cgi-bin/1997/depth500_file](http://jdoss1.jodc.go.jp/cgi-bin/1997/depth500_file))) were used for the grid development. The main goal of our study was to provide fast and accurate evaluation of tsunami wave maximal heights along the coastline. We neglected fine analysis of the processes at depths less than 10 m, even though such analysis is very important for mapping possible flooding areas. To our understanding, the computed distribution of the wave heights provides the basis for such research, and we will arrange the corresponding studies in the future. Note also that, according to [18; 19], it is possible to use formulae for recalculating the obtained tsunami wave height at the vertical wall at a depth of 10-20 m for rough determination of the long wave run-up height. Such a coefficient is predetermined for each coast point and is obtained by tsunami numerical modeling using more accurate (in some cases, three-dimensional) hydrodynamic models. We note that there is no information for fine-resolution (compared to 10 m) grids in the global bathymetry databases. In case one would like to refine the resolution by interpolation, fine details of the real depths could just be missed. This may lead to the divergence of numerical simulation results from reality. The nested grid approach, where the mesh step depends on the distance from the shore, is able to resolve this problem--provided that the distribution of depths is known with the required precision. Hardware code execution acceleration (with the help of \"graphics cards\"--GPUs) for a nested grid was previously used by the authors for modeling tsunami in the Tohoku/Fukushima area of Japan [20]. Pictures A, B, C, and D of Figure 11 present the tsunami height distribution according to the alongshore variation of the model source position. The longitude position of the coastal grid points in these distributions is counted along the horizontal axis from 1 at the left boundary up to 3000 on the right (see the scale at the bottom of Figure 3). Analysis of the distribution of wave height maxima along the coast leads to the following conclusions.