## 5 Results  
### Numerical Simulations and Wave Decay Potential Parameter  
For each scenario, lake-surface elevations are estimated along with line probes (L.P), which are lines along which the free-water-surface in the 3D domain is monitored over time following impact (Figure 4d). LPs are used to document and analyze maximum wave crest elevations in open water and flow depths at the shoreline. A set of 12 LPs extend from the domain origin (Section 4) to equal space-distributed points along the shoreline, allowing to qualitatively and quantitatively analyze the propagation of the impulse wave and how lake geometry affects the wave. An example is provided in Figure 5, which shows that a decrease in water depth results in progressively higher wave dissipation and a lower flow depth at the shore (compare Figure 5a-c). These trends reflect the increase in water volume that is mobilized by the impacting volume and reduced interaction and friction with the lake floor as the water depth increases. Conversely, the longer travel distances facilitated by incrementally wider lakes result in greater wave dissipation and, consequently, lower flow depth at the shoreline. The slight increase of flow depth along with the LPs in the proximity of the shoreline (Figure 5a,d,e) shows the wave deformation due to the interaction with the lake floor while approaching the shoreline.  
Figure 5: Free-water-surface elevation computed along with the LPs (e.g., Figure 4d) for typical circular artificial lakes with different widths and maximum depths (**a–e**). Each lake configuration influences the landslide–water interaction and wave dissipation, thus causing different impulse wave propagation patterns.  
The same patterns are observed for all 69 scenarios. Generally, for the medium-size lakes, the maximum wave crest elevation ranges from 29 to 5.9 m a.l.l along with L.P. 1 (the midline representative of the landslide's travel direction). Considering all L.Ps, average wave crest elevations range from 15.4 to 27.5 m a.l.l. At the shoreline, the average flow depth is 4.1 to 19.7 m a.l.l. The highest values of flow depth (6 to 35.6 m a.l.l.) occur at the shoreline along L.P. 1. In the case of large-size lakes, maximum wave crest elevations range from 29.4 to 33.8 m a.l.l. along with L.P. 1, and the average for all LPs ranges from 15.4 to 24 m a.l.l. At the shoreline, the average flow depth is 4.1 to 7.4 m a.l.l., with the highest values on L.P. 1 (4.2 to 15.9 m a.l.l.).  
The numerical analyses provide insight into potential impulse-wave threats for particular mountain lake configurations. A possible indicator of the threat level is the \"dissipation power\" of an impulse wave in a lake, which is a measure of the degree to which the wave attenuates as it moves away from the impact location. This metric is determined for each L.P. by calculating the ratio of the maximum wave crest elevation and the flow depth at the shoreline. A new parameter, defined as a single weighted-average decay ratio value and representative for the entire lake is henceforth termed the \"wave decay potential parameter\" (_WDPP_) is given by Equation (1):  
\[WDPP=\frac{\sum_{i=1}^{n}(a_{mi})\left(\frac{a_{mi}}{f_{dd}}\right)}{\sum_{i=1 }^{n}a_{mi}}\ (-) \tag{1}\]  
where \(a_{m}\) and \(f_{dc}\) are, respectively, the maximum wave elevation and the flow depth at the shoreline location for each of the LPs. For medium-size lakes, values of _WDPP_ range from 1.09 to 4.87, and for large-size lakes from 2.61 to 6.6. When a higher value of _WDPP_ is obtained, a higher dissipation power of the lake is expected, and vice versa.