Semi-empirical predictive equations for the initial amplitude of submarine landslide-generated waves: applications to 1994 Skagway and 1998 Papua New Guinea tsunamis

Accurate predictions of maximum initial wave amplitude are essential for coastal impact assessment of tsunami waves generated by submarine landslides. Here, we analyse the existing predictive equations for the maximum initial amplitude (ηmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta_{\text{max} } $$\end{document}) of submarine landslide-generated waves and study their performance in reproducing real-world landslide incidents. Existing equations include various landslide parameters such as specific gravity (γs), initial submergence (d), slide length (B), width (w), thickness (T) and slope angle (θ). To determine how landslide parameters affect wave amplitude, we conduct a systematic sensitivity analysis. Results indicate that the slide volume (V = B × w × T) and d are among the most sensitive parameters. The data from the 1994 Skagway (observed ηmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta_{\text{max} } $$\end{document}: 1.0–2.0 m) and 1998 Papua New Guinea (PNG) (observed ηmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta_{\text{max} } $$\end{document}: 10–16 m) incidents provided valuable benchmarks for evaluating the performance of the existing equations. The predicted maximum initial amplitudes of 0.03–686.5 m and 3.7–6746.0 m were obtained for the 1994 and 1998 events, respectively, indicating a wide range for wave amplitudes. The predicted estimates for the smaller-sized event, i.e. the 1994 Skagway, appear to be more accurate than those made for the larger event, i.e. the 1998 PNG case. We develop a new predictive equation by fitting an equation to actual submarine landslide tsunamis: ηmax=50.67Vd0.34\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta_{ \text{max} } = 50.67 \left( {\frac{V}{d}} \right)^{0.34} $$\end{document}, where V is the slide volume (km3), d is initial submergence depth (m), and ηmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \eta_{\text{max} } $$\end{document} is in metres. Our new equation gives wave amplitudes of 1.6 m and 7.8 m for the 1994 and 1998 landslide tsunamis, respectively, which are fairly consistent with real observations.