Status: this discussion paper is a preprint. It has been under review for the journal Natural Hazards and Earth System Sciences (NHESS). The manuscript was not accepted for further review after discussion.
A mathematical formulation for estimating maximum run-up height of 2018 Palu tsunami
Ikha Magdalena,Antonio Hugo Respati Dewabrata,Alvedian Mauditra Aulia Matin,Adeline Clarissa,and Muhammad Alif Aqsha
Abstract. Run-up is defined as sea wave up-rush on a beach. Run-up height is affected by many factors, including the shape of the bay. As an archipelagic country, Indonesia consists of thousands of islands with bays of diverse profiles, including Palu Bay, which is a well-known example of a bay with a drastically-increasing wave run-up height. In the case of the 2018 Palu tsunami, scientists found that the incident wave was amplified by the shape of the bay. The amplifying wave played a large role in the significant increase of run-up height. The run-up in question caused severe inundation, which led to a high number of casualties and damages. Therefore a mathematical model will be constructed to investigate the wave run-up. The bay's geometry will be approximated using three linearly-inclined channel types: one of parabolic cross-section, one of triangular cross-section, and a plane beach. We use the generalized nonlinear shallow water equations, which is then solved analytically using a hodograph-type transformation. As a result, the nonlinear shallow water equation system can be reduced to a one-dimensional linear equation system. Assuming the incident wave is sinusoidal, we can obtain a simple formula for calculating maximum run-up height on the shoreline.
How to cite. Magdalena, I., Respati Dewabrata, A. H., Mauditra Aulia Matin, A., Clarissa, A., and Aqsha, M. A.: A mathematical formulation for estimating maximum run-up height of 2018 Palu tsunami, Nat. Hazards Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/nhess-2020-223, 2020.
Our research presents a method that allows one to calculate an estimate for the maximum upward surge of a wave from the 2018 Palu tsunami as it touches the beach. The method involves using ideal geometric shapes to approach the shape of the real bay, yielding one estimate that equals the recorded tsunami wave height of 4.89 m. The direct formulae derived using three idealized bay shapes can be used to gain instant wave run-up estimates for emergency disaster response purposes.
Our research presents a method that allows one to calculate an estimate for the maximum upward...