## 1 Introduction  
Landslide-induced impulse waves in lakes are gaining interest in the scientific community due to the hazards they pose to people living or recreating along their shorelines and to dams and other infrastructure [1]. Additionally, climate change is driving rapid geomorphological changes in high mountains, which may increase the likelihood of landslides into mountain lakes. Rapid thinning and retreat of glaciers and an increase in heavy rainfall events can destabilize slopes adjacent to water bodies [2; 3; 4; 5]. In December 2007, a 3-Mm\({}^{3}\) rock avalanche entered the Chehalis Lake (Canada), generating an impulse wave that destroyed forest and campgrounds along the shoreline and achieved a maximum run-up of 37.8 m above average lake level [6; 7]. In July 2014, a 10-Mm\({}^{3}\) rockslide collapsed into Askja Lake (Iceland) from its rimming caldera and generated a wave that propagated \(>\)3 km across the lake with localized run-ups of up to 60-80 m [8]. In October 2015, a 50-Mm\({}^{3}\) landslide collapsed into Taan Fiord (Alaska), inducing one of the largest landslide-induced waves ever recorded, with a maximum run-up of 193 m on the slope facing the landslide; the wave traveled \(>\)17 km down the fiord, devastating forests and eroding soil and sediments along its path [5; 9]. In June 2017, an impulse wave generated by a 50-Mm\({}^{3}\) subaerial rockslide into Karrat Fiord on Greenland'swest coast killed four people and destroyed 11 buildings in the village of Nuugaatsiaq, 32 km from its source, and flooded other settlements along the coast [10]. These events are just a small subset of all the subaerial landslides known to have generated impulse waves around the world [1]. Different methods, including scaled physical tests, field investigations, and numerical models are used to investigate aspects of this phenomenon, including landslide behavior, landslide-water interaction, and wave formation, propagation, and inundation. The effect of basin geometry on wave propagation has been experimentally and numerically investigated [11; 12; 13]. Researchers have also analyzed wave dispersion and related wave decay. [PERSON] et al. [14] state that wave decay results from (i) frequency dispersion, (ii) bottom friction, (iii) lateral spreading of the water, and (iv) breaking of waves during generation and propagation. According to those authors, an increase in the lateral angle of the basin leads to a decay of solitary waves. The effect of lateral energy spread on wave amplitude is larger in a 3D basin-type geometry than the effect of frequency dispersion in a 2D flume-type geometry. To virtually reproduce wave dynamics generated by an impact, researchers have used several different numerical approaches, notably non-linear shallow water equations (NSWE), Reynolds-averaged Navier-Stokes equations (RANS), and smoothed particle hydrodynamic methods (SPH) [13]. These approaches have been used to retrospectively investigate specific landslide-induced impulse wave events, typically with much success. However, such modeling approaches, when used in assessments of possible future events, are compromised by cost, computational time, the considerable amount of data required for model calibration and validation, and the absence of run-up and inundation evidence typically used to fine-tune model parameters  
Other methods, such as generic empirical equations, can be used for preliminary assessment of the potential impact of landslide-generated waves and to guide decisions on the need for further investigations. Empirical relationships, commonly based on field-measured wave impacts of historical events or scaled physical experiments, are used to determine wave characteristics. The analytical equations of [PERSON] et al. [15], [PERSON] [16], and [PERSON] et al. [17] were developed to assess impulse waves in artificial water basins impounded by dams but are also applicable to natural lakes.