Time‐Dependent Probabilistic Tsunami Inundation Assessment Using Mode Decomposition to Assess Uncertainty for an Earthquake Scenario

This study presents an innovative probabilistic tsunami inundation assessment for an earthquake scenario to randomly generate tsunami inundation depth distributions by quantitatively evaluating the spatial correlation of tsunami inundation depths using singular value decomposition (SVD) derived from proper orthogonal decomposition and to evaluate the tsunami inundation depths considering the imminent occurrence of an earthquake. We found a good agreement between the evaluation results of the proposed surrogate model and the numerical results of the nonlinear long wave equations for the tsunami inundation depth distribution in Kamakura city, Japan, due to the Sagami Trough megathrust earthquake. Evaluating the spatial correlation using SVD has the advantage that the covariance matrix does not need to be defined in advance but can be defined from the data itself. We also achieved a significant reduction in the number of required tsunami propagation simulations for the probabilistic assessment and attained higher computational efficiency by extracting spatial correlations with SVD. Furthermore, we conducted a probabilistic tsunami inundation assessment focusing on a relatively short period (i.e., 50 years) considering the time‐dependent occurrence probability of the target earthquake. The proposed probabilistic assessment method with mode decomposition is applicable to the general probabilistic tsunami hazard assessment by integrating it with physical stochastic slip models.