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

Abstract

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 (max) 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 (γ s), 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 max : 1.0-2.0 m) and 1998 Papua New Guinea (PNG) (observed max : 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: max = 50.67 V d 0.34 , where V is the slide volume (km 3), d is initial submergence depth (m), and max 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.

A new empirical equation for predicting the maximum initial amplitude of submarine landslide-generated waves

“…Based on Sabeti and Heidarzadeh (2020), the slide volume ( V , initial submergence depth (d) and slope angle (θ) are among the most important parameters for predicting the initial wave amplitude. Hence, we define the non-dimensional maximum initial tsunami amplitude ( max,n d ) as a function of nondimensional forms of these most important parameters ( sin ; V d 3 ; V Bd 2 ; d B ; d h and m b w Bd 2 ) as previously adapted by Watts (1997), Watts et al (2005) and Najafi-Jilani and Ataie-Ashtiani (2008).…”

“…Gómez et al 2016). Due to the complexities associated with two-phase flows including water and solid involved in the evolution of landslide-generated waves, empirical equations proved beneficial for predicting the initial maximum amplitudes of the waves (Synolakis 2003;Watts et al 2005;Sabeti and Heidarzadeh 2020). A large body of research on the subject is associated with physical modelling of the phenomenon through two-dimensional solid blocks sliding down a plane slope (e.g.…”

“…2). Table 1 presents a few such predictive equations while the full list is given in Sabeti and Heidarzadeh (2020). There are six main landslide parameters that affect max,n : the slide specific gravity ( s ), initial submergence depth ( d ), slide length ( B ), width ( w ), thickness ( T ) and slope angle ( ) (Fig.…”

“…equation requires only three of these initial landslide parameters, whereas those equations of Watts et al (2005) and Harbitz and Pedersen (1992) require four/ five input parameters. The performance of the existing predictive equations was assessed by Sabeti and Heidarzadeh (2020). It was shown that the max,n predictions made by different equations are divided by a few orders of magnitude (10 −1 -10 4 m); therefore, it is essential to conduct further studies on this topic.…”

“…We use available experimental and field data from the literature along with some new laboratory data generated by our physical experiments to derive the new equation. In comparison to a previous study by Sabeti and Heidarzadeh (2020), in which they solely used field data from past landslide tsunamis, in the current study, we conduct new laboratory experiments Landslides to add to the existing data, use a more comprehensive dataset comprising a mix of field and laboratory data, employ non-dimensional forms of landslide parameters and apply a sophisticated regression tool. Moreover, the slope angle ( ), which is an important parameter contributing to landslide-generated waves, is added to our new equation.…”