Pre-Tsunami Evacuation Scenario

Updated 7 January 2026

Pre-tsunami evacuation scenarios are defined as systems integrating real-time hazard detection, Bayesian forecasting, and probabilistic risk assessments for effective emergency mapping.
They employ high-resolution numerical models and agent-based behavioral analysis to create precise inundation maps and optimize routing and zone delineation.
Robust communication infrastructures and risk-aware control strategies are implemented to mitigate network disruptions and manage urban evacuation congestion.

A pre-tsunami evacuation scenario refers to the planned sequence of real-time sensemaking, risk assessment, decision-support, population movement, and information dissemination operations that must be executed within the short interval between tsunami warning generation (often triggered by seismic detection) and the expected arrival of the first hazardous wave at a vulnerable coastal or port community. The scenario covers the technical frameworks for rapid hazard recognition, probabilistic scenario assessment, evacuation zone delineation, operational logistics, and communications, all of which must balance the statistical and physical uncertainties intrinsic to tsunami source characterization, near-shore wave transformation, networked evacuation dynamics, and communication disruptions.

1. Real-Time Tsunami Scenario Detection and Probabilistic Forecasting

Central to contemporary pre-tsunami evacuation strategy is the sequential Bayesian scenario-detection framework developed for highly diverse synthetic rupture databases. The method operates on low-dimensional features projected onto bases obtained by Proper Orthogonal Decomposition (POD) of precomputed tsunami gauges and inundation outputs (Nomura et al., 2024).

For $N_s$ tsunami scenarios and $N_g$ gauges, wave records organized as $X \in \mathbb{R}^{N_g \times (N_t N_s)}$ are approximated:

$X \approx \Phi_r A,$

where $\Phi_r$ contains $r$ leading POD modes and $A$ the coefficients per scenario. Incoming real-time gauge data $\eta_\chi^{(t_m)}$ are projected:

$\tilde{\alpha}_\chi^{(t_m)} = \Phi_r^\dagger \eta_\chi^{(t_m)},$

and Mahalanobis distances $\Delta_j^{(t_m)}$ computed to evaluate likelihoods:

$L_j^{(t_m)} = (2\pi)^{-r/2} |P^{(t_m)}|^{-1/2} \exp\left(-\frac{1}{2} [\Delta_j^{(t_m)}]^2\right).$

Sequential Bayes updating yields $P(E_j^{(t_m)} | \epsilon^{(t_m)})$ for all scenarios.

Two inference modes are then available:

Most-likely scenario detection: select $j^* = \arg\max_j P(E_j^{(t_obs)} | \epsilon^{(t_obs)})$ .
Scenario superposition (weighted mean): compute ensemble-risk indices such as

$h_{max}^\chi(x,y) = \sum_{j=1}^{N_s} P(E_j^{(t_{obs})}| \epsilon^{(t_{obs})})\, h_{max}^j(x,y),$

where $h_{max}^j(x, y)$ is 2D maximum inundation for scenario $j$ .

This Bayesian approach outperforms dynamic time warping (DTW) matching in both maximum offshore wave height and inundation classification after $t_{obs}\geq4$ min, with median absolute error $\leq10\%$ at $t_{obs} \geq 3$ min and true-positive inundation classification rates of $0.6$–$0.8$ (Nomura et al., 2024). In practice, 3–4 min of near-shore gauge data suffice for actionable evacuation mapping.

2. Numerical Tsunami Propagation and Inundation Modelling

Operationally validated inundation and hazard maps rely on solving nonlinear shallow water equations (NSWE) via high-resolution solvers such as Volna-OP2 (Giles et al., 2020), NAMI-DANCE (Peresan et al., 2023), and MOST (Arcas et al., 2023). These codes are distinguished by their treatment of unstructured meshes, frictional terms, and wet–dry interface:

NSWE (Volna-OP2/MOST/NAMI-DANCE):

$\frac{\partial H}{\partial t} + \nabla\cdot(H \mathbf{u}) = 0, \qquad \frac{\partial (H\mathbf{u})}{\partial t} + \nabla\cdot\left(H\mathbf{u}\otimes \mathbf{u} + \frac{g}{2}H^2\mathbf{I}\right) = -g H \nabla h(x, y)$

Ensembles spanning earthquake source parameter uncertainties (location, slip, magnitude) are forward-simulated to propagate both mean and worst-case hazard. In the Irish pilot scenario for the 1755 Lisbon tsunami, run-up heights of $\approx3.4$ m and inundation depths up to 2 m are mapped at 10-m grid scale, informing zone prescriptions and shelter placements (Giles et al., 2020).

3. Empirical Evacuation Behavior and Response Dynamics

Empirical agent-based or statistical evacuation models parameterize departure and return-time distributions using large-scale high-frequency geolocation data (Makinoshima et al., 2024). Observations from the 2024 Noto Peninsula earthquake and tsunami show:

Median evacuation departure time $\tau^50$ scales inversely with $\log_{10}$ (PGA), with $\tau^50 \approx 4.9$ min at PGA $=1000$ gal.
A sharp exponential decay in evacuation intensity with epicentral distance, $p_i \approx p_0 e^{-k R_i}$ .
Family unification and holiday effects reduced mill time, boosting rapid egress.
Population return begins as early as 20 min post-event, with $\sim$ 90% return by 100 min, well ahead of official warning cancellation.

Such quantitative hazard and behavioral kernels (e.g., Weibull-distributed departure times, empirical hazard-rate functions) enable fine-grained evacuation scenario simulation and calibration (Makinoshima et al., 2024).

4. Evacuation Zone Delineation, Routing, and Operational Protocols

Inundation scenarios translate directly into multi-band evacuation zoning. For example, in Sigatoka–Cuvu (Fiji), three distinct risk zones are defined by modeled flow depths and distances inland (Arcas et al., 2023):

Zone	Range from Shore	Modeled Flow Depth
Zone A	0–200 m	Up to 1 m
Zone B	200–400 m	1–2 m
Zone C	>400 m	≤ 0.5 m

Key evacuation actions—trigger by strong local earthquake or warning, immediate outbound movement to assembly points, ascent on prescribed inland routes, closure of last-mile access roads—are all sequenced explicitly by modeled tsunami arrival windows (e.g., first wave T+1 h 25 min, max inundation T+1 h 55 min) (Arcas et al., 2023). Similar protocols are constructed for Northern Adriatic localities, where safe elevations and zoning buffers (e.g., $>5$ m a.s.l., $300$ m inland) are tied to NSWE-computed wave amplitudes and arrival times (Peresan et al., 2023).

5. Communication Infrastructure and Information Dissemination Under Disruption

Earthquake-induced infrastructure loss necessitates redundant, opportunistic communication overlays. Analysis of the Hachijojima case shows (Kawano et al., 31 Dec 2025):

Epidemic (flooding) DTN routing achieves $\sim$ 33% delivery ratio of critical messages to shelters within the 30 min pre-arrival window; encounter-based selective protocols such as PROPHET are less reliable at short time scales.
Epidemic routing incurs extreme overhead (replica count per delivery $> 4000$ ), making resource constraints and buffer overflows a limiting operational factor.
Hybrid protocols and prioritized relay via emergency vehicles mitigates the trade-off between delivery robustness and resource exhaustion.
DTN design must account for transmission range ( $r \geq 25-30$ m), buffer allocations ( $\geq$ 5 MB personal devices, $100$ MB shelters), and TTL tuning aligned with the hazard arrival window.

Robust pre-tsunami evacuation scenarios thus require explicit modeling of message dissemination dynamics under network partition, including stochastic delivery and latency distributions (Kawano et al., 31 Dec 2025).

6. Optimal Control of Large-Scale Urban Evacuations

For urban regions where vehicular evacuation dominates, the Generalized Bathtub Model and risk-aware Model Predictive Control (MPC) achieve tractable coordination under load and hazard uncertainty (Hammerl et al., 9 Aug 2025):

The evacuation queue $\delta(t, x)$ (trips with $\geq x$ distance left) evolves with controlled origin-gating $u(t, x)$ and network state $v(t) = V(\rho(t))$ .
MPC objectives blend total delay, hazard-weighted delay (e.g., time spent in high-inundation cells), and tail-risk penalties (AVaR). Tsunami-specific risk fields $h(x)$ are encoded from hydrodynamic hazard models (e.g., $h(\xi) = 1/t_f(\xi)$ or $h(\xi) \propto H(\xi)$ ).
Analytical results prove that the optimal release schedule is a bang–bang profile (early saturating release, then throttling), provided the remaining trip-length hazard rate is non-decreasing—a common property with spatially uniform demand.
Numerical results show expected queue/delay reductions of $25$– $27\%$ relative to uncontrolled first-come/all-at-once release, with additional improvements in high-risk exposure times under hazard-weighted MPC (Hammerl et al., 9 Aug 2025).

7. Synthesis, Method Selection, and Open Directions

Pre-tsunami evacuation scenario planning integrates Bayesian scenario detection, high-performance shallow-water modeling, data-driven behavioral calibration, robust communications, and risk-aware traffic-control. Method selection is determined by operational objective:

Rapid, quantitative maxima (wave height or inundation value): most-likely scenario Bayesian output offers smallest spread.
Zone mapping where missed inundation is intolerable: weighted mean superposition ensures higher true-positive capture at minor false-positive cost (Nomura et al., 2024).
Urban network optimization: traffic MPC with hazard-weighting and tail risk management is effective for staged release and congestion minimization (Hammerl et al., 9 Aug 2025).
Communication-constrained environments: prioritize high-redundancy message flooding for emergency lifeline delivery to shelters, balanced with resource constraints (Kawano et al., 31 Dec 2025).

Ongoing challenges include robust fusion of behavioral, physical, and network uncertainties; explicit coupling between communication-layer and evacuation-layer dynamics; incorporation of real-time sensor data into Bayesian/MPC pipelines; and rapid model updating for compound hazard evolution.

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