Probabilistic tsunami forecasting for early warning

The study addresses the core challenge of tsunami early warning systems: producing rapid, accurate forecasts of tsunami impact under severe real-time uncertainty about earthquake source parameters. Existing operational methods are typically deterministic and rely on conservative heuristics (e.g., safety factors, decision matrices, envelopes, or best-matching scenarios) that do not quantify uncertainty and often yield high false-alarm rates while still risking missed alarms. The authors propose Probabilistic Tsunami Forecasting (PTF) to quantify and propagate real-time source and modelling uncertainties into probabilistic forecasts of tsunami intensity measures at coastal points. This enables a transparent, rule-based mapping of forecast uncertainty to alert levels that can match any desired level of conservatism and separates scientific forecasting from decision-making considerations. The goal is to demonstrate PTF’s feasibility for near-field warning timelines (10–15 minutes), its statistical accuracy across diverse events, and its usefulness for setting alert levels with explicit control over missed versus false alarm trade-offs.

The paper situates PTF within prior efforts on uncertainty handling and rapid tsunami forecasting: (i) ensemble and probabilistic approaches are standard in weather forecasting; (ii) for distant events, moment tensors and deep-sea sensors (e.g., DART) support inversions and data assimilation, but near-field timelines preclude such data early on; (iii) rapid source estimation techniques (e.g., W-phase inversion, GPS-based magnitude, P-wave methods) have improved but retain intrinsic uncertainties; (iv) current operational tsunami warning commonly uses deterministic Decision Matrices (DMs), Envelopes (ENVs), or Best-Matching Scenarios (BMS), sometimes with implicit conservatism (maximum credible magnitudes, safety factors). Attempts to characterize uncertainty have been made (e.g., Bayesian frameworks, scenario statistics), yet operational systems remain non-probabilistic, precluding quantitative calibration. The authors also draw parallels to hazard-risk separation and long-term PTHA practices, and note ongoing advances in sensors (GNSS, SMART cables) and high-performance computing that can reduce but not eliminate uncertainty.

PTF produces, at any time after an earthquake origin, a probability distribution (hazard curve) of a tsunami intensity measure (TIM; here, near-coast wave amplitude extrapolated to 1 m depth) at forecast points by combining two factors via the total probability theorem: (1) a source factor, quantifying P(s|E; t), the probability an earthquake scenario s is consistent with real-time estimates E at time t; and (2) a propagation factor, P(X > x|s; p), mapping source scenarios to coastal TIMs via precomputed tsunami simulations and a statistical treatment of modelling uncertainty. Implementation details: - Source ensemble: Scenarios drawn from a comprehensive PTHA database (NEAMTHM18 for the Mediterranean; extended to Chile for Maule) cover the full range of plausible sources (crustal background seismicity and subduction interfaces). For near-field warning (3–8 min: hypocenter and magnitude available; 10–15 min: alert issue), P(s|E; t) is factorized as P(o|M,c;E,t) P(c|M;E,t) P(M|E; t), where M is magnitude, c the fault center, and o other rupture parameters. Real-time magnitude and hypocenter uncertainties are modelled as normal distributions; fault center uncertainty is derived by convolving hypocenter uncertainty with nucleation location within fault (scaling relations set fault dimensions). The distribution of remaining parameters o (mechanism, rake, slip heterogeneity) is taken from long-term seismo-tectonic constraints in NEAMTHM18; for magnitudes ≥8 on subduction, heterogeneous stochastic slip with possible shallow slip amplification is used. Background (BS) versus predominant subduction (PS) seismicity are handled via a mixture model weighted by the probability that nucleation lies on a subduction interface; for very large magnitudes (M > 8.1 in Mediterranean), scenarios are forced to PS. - Propagation database and simulations: Precomputed NEAMTHM18 simulations use Tsunami-HySEA on 30 arc-sec bathymetry (SRTM30+) with initial conditions from filtered seafloor displacement and Gaussian elementary sources, storing outputs at 50 m isobaths around the Mediterranean coastline. For Chile/Maule, additional on-the-fly simulations were performed on 30 arc-sec Pacific grids with 3D SLAB2 geometry. Near-coast amplitudes are extrapolated from offshore via Green’s law. - Modelling uncertainty: Propagation/generation/inundation simplifications are represented by a log-normal variability factor on simulated near-coast amplitudes (median equal to model output, variance set to 1, zero bias for this study), capturing unmodelled source variability and local amplification effects. - Computational strategy: To meet operational timelines (<2 min for the PTF calculation), the scenario ensemble is trimmed by probabilistic cut-offs on magnitude and hypocentral probability (tested at 1.5–3 standard deviations). A 2σ cut-off balances stability with speed (<2 minutes CPU for the Mediterranean implementation) with minimal impact on the 5th–95th percentile hazard curves. - Outputs and alert mapping: PTF yields full distributions at each forecast point; hazard maps can show mean or percentiles (e.g., 5–95%). Alert levels (Information, Advisory, Watch) are set by rules comparing a selected PTF statistic (mean, median, or chosen percentile) against NEAMTWS near-coast amplitude thresholds (e.g., <10 cm; 10–50 cm; >50 cm). This directly encodes a chosen conservatism level. - Case studies and testing: Hindcasts include the 2003 Mw 6.8 Zemmouri-Boumerdes (Mediterranean crustal), the 2010 Mw 8.8 Maule (Chile subduction), a synthetic Mw 8.5 Hellenic Arc scenario, and a 13-event Mediterranean testing set comprising all events since 2015 that triggered CAT-INGV alerts (plus Zemmouri). Statistical hypothesis tests evaluate consistency of PTF source (focal mechanisms) and tsunami intensity predictions against observed data (tide gauges, DART, run-ups), accounting for spatial correlations and using stacked misfit tests. Code is available (matPTF, Matlab).

• Feasibility and timeliness: With a 2σ scenario cut-off, PTF runs in under ~2 minutes for the Mediterranean, compatible with a 10–15 minute alert issuance window. - Zemmouri-Boumerdes 2003 (Mw 6.8): PTF hazard distributions matched available observations; several Balearic sites fell in the upper tail, likely due to basin/harbour resonances not captured at coarse resolution. High-percentile PTF or conservative envelope methods better encompassed such local amplifications. Finite-fault synthetic simulations from literature mostly fell within PTF 5th–95th intervals, indicating the ensemble captures realistic source variability. - Maule 2010 (Mw 8.8): PTF 15th–85th percentile ranges encompassed all DART, tide-gauge, and halved run-up observations; a slight overall overestimation tendency remained within uncertainty bounds. - Comprehensive testing (13 events, post-2015 Mediterranean alerts plus 2003 event): Formal statistical tests did not reject PTF for either focal mechanism forecasts or tsunami intensity predictions (α = 0.05), across both events with detected tsunamis and those without (for the latter, PTF predicted negligible amplitudes <0.10 m at observation points). - Alert-level performance versus operational baselines: • Decision Matrix (DM) and Envelope (ENV): low missed alarms (~3%) but high false alarms (~55%). • Best-Matching Scenario (BMS): high correct assignments (~86%), lower false alarms, but higher missed alarms (~11%). • PTF percentiles span and exceed these behaviours: choosing higher percentiles increases conservatism (fewer missed, more false alarms). For example, moving from median to 99th percentile reduces missed alarms from ~14% to <1% but increases false alarms from <1% to ~53%. PTF median and mean perform comparably to BMS (median ~85% correct vs BMS 86%; mean yields slightly more correct and fewer missed but more false alarms). - Stability advantages: PTF avoids discontinuities inherent in DM magnitude thresholds (e.g., during the 2020 Samos-Izmir event, small magnitude fluctuations around Mw 7 drastically changed DM-assigned alerts, whereas PTF remained stable by explicitly incorporating magnitude uncertainty).

The results demonstrate that PTF addresses the central problem of uncertainty in near-real-time tsunami forecasting by providing calibrated probabilistic hazard curves at coastal forecast points. This enables explicit control of conservatism when setting alert levels, transparently trading missed versus false alarms based on pre-agreed rules. The method proved statistically consistent across a spectrum of events—from moderate crustal earthquakes with complex local amplification to giant subduction events—indicating robustness of the ensemble and uncertainty representations. Compared to deterministic operational tools, PTF offers: (i) quantitative uncertainty communication to decision-makers; (ii) the ability to tailor alert rules to risk tolerance and action cost; (iii) reduced sensitivity to threshold instabilities; and (iv) a principled path to progressive forecast refinement as additional real-time data (moment tensors, DART, GNSS) arrive. While coarse-grid modelling can under- or overestimate local extrema, incorporating these effects into the uncertainty model and using higher percentiles yields conservative coverage until higher-resolution or assimilative methods refine the forecast. Overall, PTF converts real-time uncertainty into actionable, testable forecasts, bridging scientific outputs and risk-management needs.

This work introduces a practical, operationally viable Probabilistic Tsunami Forecasting framework that quantifies and propagates real-time uncertainties from earthquake source estimation to coastal tsunami intensities, and maps them to alert levels with explicit conservatism. The implementation for the Mediterranean (and extension to Chile) shows sub–2-minute runtimes, statistical accuracy across diverse case studies, and performance flexibility that spans current deterministic methods from conservative (DM/ENV) to event-matching (BMS). PTF thereby separates scientific forecasting from policy choices, enabling authorities to set alert rules consistent with acceptable balances of missed and false alarms. Future directions include: global-scale testing and calibration using larger observation datasets; refined modelling of local coastal amplification and inundation using higher-resolution grids and data assimilation; incorporation of advanced real-time sensors (GNSS, ocean-bottom networks, SMART cables); extending PTF to non-seismic tsunami sources; and optimizing HPC workflows to further reduce latency and enhance ensemble fidelity.

• Coastal amplification and harbour/basin resonances are not fully resolved at 30 arc-sec resolution, leading to local underestimation for smaller, steeper-source events unless higher percentiles are used; similarly, slight overestimation may occur for large subduction events given conservative uncertainty settings. - The propagation uncertainty is simplified as a log-normal factor with fixed variance (set to 1) and zero bias; this may over/underestimate true variability and warrants calibration by region and magnitude range. - Early-time PTF relies on long-term seismo-tectonic priors for faulting geometry/mechanism, which may mischaracterize rare or unexpected source behaviours (e.g., tsunami earthquakes, outer-rise events) until richer real-time constraints arrive. - The approach presently focuses on seismic sources; non-seismic triggers (landslides, volcanic) are harder to parameterize in real-time and are not operationally included. - Ensemble truncation via probability cut-offs trades computational speed for potential loss of tail accuracy. - Alert-level conversion rules and the choice of percentile are external policy decisions; societal cost models and multi-action strategies are needed to fully exploit PTF in practice.