THE NEED FOR A PARADIGM SHIFT IN SUBAERIAL LANDSLIDE-TSUNAMI RESEARCH

INTRODUCTION Subaerial landslide-tsunamis (SLTs) are caused by mass movements such as landslides, rock falls or glacier calving. Research into SLTs is ongoing for many decades, however, the advancement in the physical understanding and reliability of hazard assessment methods is not reflecting the number of articles published per year. It appears that a paradigm shift in SLT research is required for a genuine advancement. This article critically reviews the state-of-the-art of SLT research, highlights current limitations and introduces potential candidates to perform this needed paradigm shift.


INTRODUCTION
Subaerial landslide-tsunamis (SLTs) are caused by mass movements such as landslides, rock falls or glacier calving. Research into SLTs is ongoing for many decades, however, the advancement in the physical understanding and reliability of hazard assessment methods is not reflecting the number of articles published per year. It appears that a paradigm shift in SLT research is required for a genuine advancement. This article critically reviews the state-of-the-art of SLT research, highlights current limitations and introduces potential candidates to perform this needed paradigm shift.
CURRENT RESEARCH APPROACHES Catastrophes such as the 1958 Lituya Bay SLT, running up 524 m (Figure 1a), and the 1963 Vajont disaster, with nearly 2000 fatalities, triggered an increased research interest in SLTs in the 1960/70ties. The number of publications further increased once numerical models were able to complement or even replace laboratory studies. Despite of this large number of studies, reliable hazard assessments of SLTs is still lacking and to reliable predict SLT cases, such as the recent Lake Askja or Eqip Sermia cases shown in Figure 1, remains challenging. Currently, the most promising approaches to deal with SLTs are (I) prototype-specific physical and (II) numerical model tests and (III) generic empirical equations from experimental and numerical tests. Generally speaking, the approach (I) is most reliable, but time-consuming and expensive if the scale is sufficient large to avoid scale effects. Approach (II) requires less resources, but highquality calibration and validation data. In approach (III) the governing parameters (slide velocity, volume, geometry, hill slope, water depth, etc.) are systematically varied under idealised conditions in flumes (2D) (e.g. Heller and Hager, 2010) or basins (3D) (e.g. Heller and Spinneken, 2015; Figure 2) and the wave parameters are then expressed through generic empirical equations as a function of these governing parameters. The application of such equations is very inexpensive and efficient, but provides preliminary estimates only, with increased uncertainty for complex water body shapes.
Most ongoing research into SLTs aims to reproduce individual SLT laboratory or nature cases numerically (approach II) or to create new empirical equations to add to (III). However, wave parameters predicted with empirical equations based on (III) vary by factors (Heller and Spinneken, 2013) such that the focus should be on the understanding of the reasons for these discrepancies rather than on additional parameter variations. Further, SLTs are composed of several components affected by frequency dispersion, which is ignored in approach (III) where the superimposed wave parameters are investigated.

CANDIDATES FOR A PARADIGM SHIFT
Candidates for a SLT research paradigm shift are: Generic empirical equation method: Until new methods including the two suggested hereafter are fully exploited, holistic approaches combining various empirical concepts from approach (III) including SLT generation, propagation and their effects on the shore, such as , deliver preliminary wave parameter estimates, particularly for simple water body geometries and bathymetries. Machine learning, e.g. via Artificial Neural Networks (e.g. Ruffini et al., 2020), may be very instrumental to improve such holistic approaches.
Generic numerical code: Numerical models, in contrast to generic empirical equations, are able to consider complex slide scenarios, water body geometries and topographies. The development of a user-friendly and reliable numerical code which is able to provide realistic results over a wide range of SLT scenarios would be valuable. This would likely involve the coupling of different methods for slide propagation (e.g. the Discrete Element Method (DEM)), wave generation (e.g. the Reynoldaveraged Navier-Stokes (RANS) equations) and wave propagation and runup (e.g. the non-hydrostatic nonlinear shallow-water equations (NLSWEs)). Further, such a code involves challenges such as extensive computational cost, calibration and validation for a wide range of SLT scenarios, importing and handling topographic and bathymetric data and a user-friendly interface for users who are not highly trained in numerical modelling.
Korteweg-deVries (KdV) and Kadomtsev-Petviashvili (KP) equations: The KdV (for 2D wave propagation) and the KP (3D) partial differential equations describe the full theoretical wave type range from sines, Stokes, cnoidal to solitary waves. These partial differential equations can be used in combination with the (inverse) non-linear Fourier transform (NLFT) to describe and decompose data sequences such as the free water surfaces of SLTs ( Figure 3). Further, the KdV/KP equations also explicitly consider nonlinear wave-wave interactions (Brühl and Becker, 2018). The superposition of these components and their interactions results in the original wave profile and, crucially, it has the potential to reliable predict wave profiles at any desired point in the far-field.