Alternative to non-linear model for simulating tsunami inundation in real-time

Unlike in the deep ocean, simulating the propagation of tsunamis in the coastal zone requires a non-linear model with a fine resolution bathymetry/topography to cope with the non-linearity and complex coastal morphology. Consequently, it raises considerable computational burdens that may not be suitable for a real-time tsunami forecasting. To overcome the issue, we utilize a precomputed tsunami database comprised of pairs of low- and high-resolution maximum tsunami elevations and flow depths originating from various hypothetical earthquake scenarios. In the actual tsunami event, our algorithm requires only a low-resolution simulation result from a linear model as the input to generate the corresponding high-resolution inundation map. Therefore, the use of the non-linear model in the real-time computation can be circumvented. A dimensionality reduction or a projection to an optimal subspace is necessary to speed up the computation and possibly improve the accuracy. To that end, we construct a projection matrix based on a principal component analysis, commonly used in the computer vision field for pattern recognitions. We apply the proposed method to the 2011 Tohoku tsunami event and select the Rikuzentakata bay and Otsuchi bay as the study sites. The proposed algorithm produces the high-resolution inundation map within seconds using the low-resolution linear simulation result obtained in similar to 5 min, whereas a comparable inundation forecast accuracy by the direct non-linear forward model using a nested grid system takes similar to 40 min.