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 1 m range, while over 93% within a 2 m range.

中文翻译：

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基于能量守恒的快速简化确定海啸淹没范围的方法

本文开发了一种海啸淹没模型，填补了当前行业应用的简化方法（浴盆法和衰减法）与综合数值模拟之间的空白。所提出的模型利用根据液压原理（能量守恒和摩擦损失）建立的二维方程来生成有限差分二维模型。虽然深度平均数值模型的复杂性尚未完全复制，但通过伯努利能量方程将水力粗糙度和重力效应（斜率）结合起来，并辅以适当的假设，与简化的浴缸和衰减方法相比，显着提高了性能。这种改进不仅保留了出色的效率（在 100 秒内完成案例研究），而且还产生了与传统数值模型相当的淹没结果，而传统数值模型通常需要数小时到数天的时间。这是此类方程首次应用于二维海啸淹没模型，并在新西兰吉斯伯恩和基督城进行了模拟，以针对数值模型 COMCOT 进行验证。淹没范围比较得出的 F1 分数高达 84% 以上。1 m 范围内的淹没深度差异为 77%，而 2 m 范围内的淹没深度差异超过 93%。