A rapid simplified method for determining tsunami inundation extent based on energy conservation

This paper develops a tsunami inundation model, filling the current void between industry applied simplified methods (bathtub and attenuation) and comprehensive numerical modeling. The proposed model utilizes two-dimensional equations established on hydraulic principles (energy conservation and friction loss) to produce the finite-difference, two-dimensional model. While the sophistication of depth-averaged numerical modeling has not been entirely replicated, the incorporation of hydraulic roughness and gravitational effects (slope) through the Bernoulli energy equation, accompanied by suitable assumptions, significantly improves performance over simplified bathtub and attenuation methods. This improvement not only retains excellent efficiency (completing case studies in under 100 s) but also yields inundation results comparable to traditional numerical modeling, which typically takes multiple hours to days. This is the first application of such equations to a two-dimensional tsunami inundation model, leading to simulations at Gisborne and Christchurch, New Zealand, for validation against the numerical model, COMCOT. F1 scores produced from inundation extent comparisons were upwards of 84%. Inundation depth discrepancies recorded 77% within a +/-$\pm$1 m range, while over 93% within a +/-$\pm$2 m range.