## 4 Numerical Model Set-Up  
Numerical models are designed to reflect conditions typical of mountain lakes in alpine settings, albeit with some necessary simplifications. Alpine basins, whether small or large, commonly fill topographic depressions with adjacent steep slopes that in many cases are the product of glacial erosion or deposition [39]. Steep slopes are particularly common along valley sides, making subaerial landslides capable of generating impulse waves more likely along lakesed than ends (e.g., [6; 39; 40]). Consequently, impacting volumes initiated in these environments enter the lake along its sides in all modeled scenarios. Each numerical simulation considers that same impacting volume for triggering the wave. This lies initially on a sliding surface dipping 45\({}^{\circ}\) toward the lake and is represented by a 0.5 Mm\({}^{3}\) prismatic fluid body, 20 m thick, 208 m long, and 120 m wide, with a toe position directly above the lake surface (Figure 4). The volume is located mid-way along the side of each theoretical lake. A bulk material density of 1620 kg m\({}^{-3}\) is used for the landslide [38]. Additionally, an initial speed of 20 m s\({}^{-1}\) at simulation time 0, is arbitrarily set. This, together with volume deformation during the sliding process, results in a maximum speed of 60 m s\({}^{-1}\) for the center of mass at the impact in all models, regardless of lake geometry. For each simulation, the model domain includes the slide area, the entire water body, and the air above it to 40 m above lake level (m a.l.1). The origin of the system (_x,y,z_ equal to 0) is located midway along the long side of each artificial lake at the middle of the landslide toe (0 m a.l.1). The maximum depth \(D_{up}\) is located at the center of each theoretical lake (Figure 4e). A mesh block of 120 m \(\times\) 140 m \(\times\) 162 m, comprising 2 m \(\times\) 2 m \(\times\) 2 m mesh cells, includes the slope and the impacting volume (Figure 4a,e). To improve computational efficiency while also representing the complexity of nearfield landslide-water interaction, a finer mesh block within 500 m of the model origin and a coarser one beyond that is used. Medium-size lakes up to 500 m wide are modeled using uniform 2 m \(\times\) 2 m \(\times\) 2 m mesh cells in the nearfield and non-uniform 4 m \(\times\) 4 m \(\times\) 2 m cells beyond 500 m.  
Medium-size lakes wider than 500 m are modeled using uniform cells that increase beyond 500 m from 2 to 4 m. For all large-size lakes, uniform cells (5 m) and non-uniform cells (10 m \(\times\) 10 m \(\times\) 5 m) are used, respectively, within and beyond 500 m of the origin. In all models, the \"wall\" boundary condition of the mesh block at the lateral margins of the impacting volume is set in Flow-3D to simulate a continuous slope along the length of the lake, allowing wave reflection modeling. A \"symmetry\" boundary condition is set \begin{table}
\begin{tabular}{c c c c} \hline
**Lake Class** & \(d_{w}\)**–\(D_{w}\) (_m_)** & **W (_m_)** & **_L (m_)_** \\ \hline \multirow{4}{*}{Medium size lakes} & 10–20 & 250 & 500 \\  & 20–40 & 500 & 1000 \\  & 40–50 & 1000 & 1500 \\  & & 1500 & 2000 \\  & & 2500 \\ \hline \multirow{2}{*}{Large size lakes} & 40–70 & 1000 & 6000 \\  & 80–150 & 2000 & 12,000 \\ \cline{1-1}  & 100–200 & 3000 & \\ \hline \end{tabular}
\end{table} 
Table 1: Geometry parameters chosen for the theoretical lakes [lake width (W), length (_L_), and mean and maximum water depths (\(d_{w}\) and \(D_{w}\))]. Permutations of these three variables yield a total of 69 lake-basin configurations. to allow the impacting volume to leave the mesh of the sliding area and enter the mesh comprising the lake. \"Outflow\" boundary conditions, at the lake borders, on the other edges of the model domain allow the flow to exit the domain without reflection to avoid wave interference and, thus, simplify the computation process. This simplification was implemented because wave characteristics of the first front arrival at the shorelines are of principal interest (Figure 4a,e).