Abstract
Abstract. Tsunamis rarely occur in a specific area, and their occurrence is highly uncertain. Suddenly generated from their sources in deep water, they occasionally undergo tremendous amplification in shallow water to devastate low-lying coastal areas. Despite the advancement of computational power and simulation algorithms, there is a need for novel and rigorous approaches to efficiently predict coastal amplification of tsunamis during different disaster management phases, such as tsunami risk assessment and real-time forecast. This study presents convolution kernels that can instantly predict onshore waveforms of water surface elevation and flow velocity from observed/simulated wave data away from the shore. Kernel convolution involves isolating an incident-wave component from the offshore wave data and transforming it into the onshore waveform. Moreover, unlike previously derived ones, the present kernels are based on shallow-water equations with a damping term and can account for tsunami attenuation on its path to the shore with a damping parameter. Kernel convolution can be implemented at a low computational cost compared to conventional numerical models that discretise the spatial domain. The prediction capability of the kernel method was demonstrated through application to real-world tsunami cases.
Highlights
Tsunamis pose a major threat to low-lying coastal areas worldwide
The two steps can be combined by grid refinement algorithms, the coastal tsunami simulation still requires high computational costs; this may limit the range of uncertainty covered by the scenarios
Such methods will contribute to the realtime prediction of coastal tsunami impacts from a tsunami waveform that is observed or predicted in deep water
Summary
Tsunamis pose a major threat to low-lying coastal areas worldwide. They are initiated by the rapid displacement of seawater, which is often triggered by earthquakes and/or submarine landslides. The occurrence of a tsunami is highly uncertain; we need to prepare for potential tsunami hazards by considering many different source scenarios that are often based on scarce historical data This involves performing numerous tsunami simulations that are often implemented by a two-step approach, i.e. deep-water tsunami modelling and coastal tsunami modelling. The first step predicts tsunami propagation from the source to coastal shelves; the linear shallow-water equations are solved on a relatively coarse grid. Analytical solutions for non-breaking wave evolution over a uniform slope have been derived for incident transient waves in different forms, which allow us to predict tsunami run-up height on the shore by prototype inci-. A possible way to rapidly predict a real-world tsunami transformation is to use kernel representation of long wave propagation over a sloping coast. The practical kernel works when an onshore tsunami profile needs to be predicted directly from observed or simulated wave data away from the shore.
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