## 6 Example of Application of the Proposed Approach--The Chehalis Lake Landside-Generated Wave  
The landslide-induced wave in Chehalis Lake on 4 December 2007 (Figure 10, see Section 1) [6,7] is chosen as a test case of the proposed methodology for several reasons. It involves a representative mountain basin, and both the landslide [6] and lake characteristics [7] are well documented. In addition, multiple numerical modeling studies [6, 42, 43, 44] provide insights into open-water hydrodynamics necessary to reproduce documented impacts. Bathymetric data acquired through a SONAR survey [7] are used in QGIS v3.16 to estimate the lake's characteristics (see Section 2). The volume of the initial rockslide is estimated to be about 3 Mm\({}^{3}\). The rock mass rapidly fragmented, transforming into a rock avalanche as it approached the shoreline. Approximately 2.2 Mm\({}^{3}\) of rock debris entered the lake and triggered the wave [6,7,44]. Although this volume is larger than the one employed in hydrodynamics models (see Section 4), the maximum impact speeds are similar (about 60 ms\({}^{-1}\)[42,45], Figure 10), making the case study suitable for testing the method. The case study data are first used as inputs in the empirical equations provided by [PERSON] 2019 [46] (ETH-Zurich, 3D approach--Overland flow) to estimate flow depths at the Chehalis Lake shoreline. As this approach cannot be applied to the entire area of the lake, and because the lake is also divided into two sub-basins by a shallow subaqueous ridge,  
Figure 9: Hyperbolic relation between _WDPP_ and flow depth at the shoreline (mean—blue data; maximum—orange data; minimum—green data). Flow depth values for the Chehalis Lake event (blue) are obtained using the 2019 ETH Zurich equations. the test is limited to the north sub-basin (yellow rectangle in Figure 10). The sub-basins characteristics and landslide properties are summarized in Figure 10.  
Flow depths are calculated at shoreline locations corresponding to wave propagation angles in 10\({}^{\circ}\) increments and ranging from \(-30^{\circ}\) to +80\({}^{\circ}\) on both sides of the landslide midline (Figure 10). Calculations yield an open-water amplitude of the initial impulse wave of 37 m a.l.l., and shoreline flow depths ranging from 3.3 to 13.5 m, with a maximum opposite the slide source and a mean shoreline flow depth of 9.2 m (Figure 10). A _ShpP_ value of 139.34 m\({}^{2/3}\) and a _WDPP_ value of 2.495 (Equation (5) in Table 2 and Figure 8a) are calculated for the north sub-basin. Appling the latter value in Equations (6)-(8) yields estimates of maximum, mean, and minimum flow depths of 15.5, 8.8, and 4.9 m, respectively. The maximum and minimum values obtained with Equations (6)-(8) are higher than the ones obtained with the ETH equations, but a close match is found for the mean flow depth (Figure 9). However, the ratio of the maximum wave amplitude (37 m a.l.l.) and the _WDPP_ of 2.49 is 14.8 m, which is very close to the maximum flow depth calculated using the ETH equations. These results pertain only to the north sub-basin of the Chehalis Lake. Considering the whole lake, the _ShpP_-value is 196 m\({}^{2/3}\) and the _WDPP_ value is 3.36, yielding a slightly lower estimate of maximum, mean, and minimum flow depths at the shoreline of 12.63, 6.95, and 4.12 m, respectively. These results show the applicability of the proposed method and use of equations in Table 3, with specific values of _WDPP_, for a preliminary evaluation of potential landslide  
Figure 10: Chehalis Lake overview. Lake and landslide properties are shown (data from [6,7]). The distance and angle of wave propagation from the landslide impact point, which are useful inputs for the 2019 ETH-Zurich equations [46], are also shown. Flow depths at the shoreline in different locations are shown in white. Topographical background taken from Microsoft Bing Maps—2021 Microsoft Corporation Earthstar Geographics Bio (Accessed on 22 July 2021).