Interpretation Analysis of Influential Variables Dominating Impulse Waves Generated by Landslides

Landslide impacts into water generate impulse waves that, in confined basins and along steep coasts, escalate swiftly into hazardous near-shore surges. In this study, we present a scenario-aware workflow using gradient boosting and <i>k</i>-means clustering, and explain them using Shapley additive explanations (SHAPs). Two cases are addressed: forecasting at water entry (Scenario I) with predictors Froude number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>r</mi></mrow></semantics></math></inline-formula>, relative effective mass <i>M</i>, and relative thickness <i>S</i>; and pre-event assessment (Scenario II) with predictors Bingham number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>i</mi></mrow></semantics></math></inline-formula>, relative moving length <i>L</i>, and relative initial mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>i</mi></mrow></semantics></math></inline-formula>. Using 270 controlled physical-model experiments, we benchmark six learning algorithms under 5-fold cross-validation. Gradient boosting delivers the best overall accuracy and cross-scenario robustness, with XGBoost close behind. Scenario I attains a coefficient of determination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> of 0.941, while Scenario II achieves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>=</mo><mn>0.865</mn></mrow></semantics></math></inline-formula>. Residual analyses indicate narrower spreads and lighter tails for the top models. SHAP reveals physics-consistent controls: <i>M</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>r</mi></mrow></semantics></math></inline-formula> dominate Scenario I, whereas initial mass and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>i</mi></mrow></semantics></math></inline-formula> dominate Scenario II; interactions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>r</mi><mo>×</mo><mi>S</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>i</mi><mo>×</mo><mi>B</mi><mi>i</mi></mrow></semantics></math></inline-formula> clarify non-linear amplification of wave amplitude and height. The cluster–predict–explain framework couples predictive skill with physical transparency and is directly applicable to coastal hazard screening and integration into shoreline early-warning workflows.