Fast Screening of Dispersion-Sensitive Tsunami Waves: For Early Warning and Hazard Mapping

Tsunamis generated by impulsive sources such as submarine landslides and earthquakes commonly exhibit N-wave structures, including Leading Depression (LDN), Leading Elevation (LEN), and symmetric/isosceles forms. As these waves propagate offshore, their evolution may endure nonlinear effects, which can produce trailing dispersive tails. During propagation across variable bathymetry, these long waves may remain well described by non-dispersive shallow-water equations (SWE), or they may undergo dispersive spreading that reshapes the leading wave packet before coastal impact. Identifying the onset of dispersion for realistic N-wave families is therefore critical for near-field warning, where lead times are short and offshore transformation strongly conditions shoreline amplification and inundation.

We develop a controlled workflow to predict the onset of dispersion for tsunami-like N-waves using a Korteweg–de Vries (KdV) solver as the propagation model. Approximately two-hundred tsunami-like N-wave cases are initialized following Tadepalli and Synolakis’ idealized leading-wave model. These initial conditions span wave type, amplitude, and crest–trough separation. Dispersion onset (tdisp) is labeled by a physically grounded criterion: dispersion begins when the tallest trailing ripple exceeds 5% of the initial leading-crest amplitude. For each simulation we extract dimensional and dimensionless descriptors, including an effective wavelength, dispersive strength, and nonlinearity.

We then train an interpretable, two-stage machine-learning framework using XGBoost: (i) a classifier for whether dispersion is detected within the simulation horizon, and (ii) a regressor predicting tdisp for detected cases. The resulting surrogate enables accelerated prediction by eliminating the need for full numerical simulation when estimating dispersion onset time, supporting rapid estimates that can be integrated into real-time forecasting workflows. It also provides parameter sensitivity, revealing which wave characteristics (e.g., steepness, amplitude, and length-scale measures) most strongly control dispersion timing and thereby improving physical understanding of N-wave evolution. Once trained, the framework offers generalizability to unseen wave configurations, supporting analysis and hazard assessment. Finally, we include analytical benchmarking by comparing ML-predicted onset behavior against both the simulation outputs and analytical dispersion scaling (e.g., Glimsdal et al., 2013), testing robustness across the full parameter space and strengthening confidence in the resulting dimensionless dispersion-onset screening parameter. This parameter enables faster and more defensible model-selection triage in early warning (SWE vs. dispersive (e.g., Boussinesq)), more targeted inclusion of dispersive physics in hazard-map scenario libraries, and clearer communication of “dispersion-sensitive” conditions for coastal communities and critical infrastructure planning, including future-condition scenarios under sea-level rise and evolving bathymetry.

By creating a high-fidelity dataset and ML framework, this research not only advances fundamental tsunami science but also delivers practical tools for agencies, researchers, and modelers worldwide to improve early-warning systems and better understand dispersive wave phenomena.