11.4 Tsunami and coastal hazard assessment

Tsunami Generation and Propagation

Tsunamis are powerful ocean waves triggered by sudden, large-scale displacements of water. They can cross entire ocean basins at jet-aircraft speeds, then pile up into devastating walls of water as they reach the coast. Assessing where, when, and how badly they'll strike is one of the most consequential problems in geophysical hazard analysis.

This section covers the physics of tsunami generation and propagation, methods for reconstructing past events, numerical modeling techniques for hazard mapping, and the design of early warning systems and community preparedness strategies.

Mechanisms of Tsunami Generation

Most tsunamis originate from large, sudden vertical displacements of the seafloor. The three primary generation mechanisms are:

• Subduction zone earthquakes — The most common cause. When the overriding plate snaps upward during fault rupture, it displaces the entire water column above it. The 2011 Tohoku earthquake ($M_w$ 9.1) displaced the seafloor by up to ~5 m over a rupture area roughly 500 km × 200 km.
• Submarine or coastal landslides — A large mass of sediment or rock slides into or beneath the ocean, displacing water. These can generate locally extreme wave heights (the 1958 Lituya Bay landslide produced a run-up of 524 m in the confined bay) but tend to attenuate more rapidly than earthquake-generated tsunamis.
• Volcanic eruptions — Underwater explosions, caldera collapses, or flank collapses can displace water suddenly. The 2022 Hunga Tonga-Hunga Ha'apai eruption generated a tsunami detected across the Pacific.

The initial wave height scales with the amount of vertical seafloor displacement, while the wavelength is controlled by the spatial extent of the source area. A larger rupture area produces a longer-wavelength wave that carries more energy across the open ocean.

Other factors that influence generation efficiency include:

• Water depth at the source (shallower water means less volume to displace, but the coupling between seafloor and surface is more direct)
• How efficiently energy transfers from the solid earth to the water column
• Source directivity, which controls how wave energy is distributed azimuthally

Characteristics of Tsunami Propagation

Tsunamis behave as shallow-water waves because their wavelengths (often 100–500 km in the open ocean) are far greater than the ocean depth (~4 km average). This means the entire water column moves, and the wave speed is governed by:

$c = \sqrt{g \cdot h}$

where $g$ is gravitational acceleration and $h$ is water depth. In 4 km of open ocean, this gives $c \approx 200 \text{ m/s}$ (~720 km/h), comparable to a commercial jet. Despite these speeds, open-ocean tsunami amplitudes are typically less than 1 m, making them nearly undetectable at sea.

As a tsunami enters shallower coastal water, wave shoaling occurs:

1. The wave slows down as $h$ decreases.
2. Conservation of energy flux forces the wave amplitude to increase.
3. The wavelength compresses, concentrating energy into a shorter, taller wave.

Several bathymetric effects shape how energy arrives at the coast:

• Refraction — Wave fronts bend toward shallower regions, focusing energy on headlands and spreading it across bays.
• Diffraction — Wave energy spreads around islands and into shadowed areas behind obstacles.
• Resonance — Bays, harbors, and continental shelves can trap and amplify wave energy at their natural oscillation periods. Crescent City, California, is notoriously vulnerable to this effect; during the 1964 Alaska tsunami, harbor resonance amplified waves well beyond what the open-coast signal would suggest.

Paleotsunamis and Historical Records for Hazard Assessment

Because large tsunamis are infrequent at any given location, the instrumental record (roughly the last century) is far too short to capture the full range of possible events. Extending the record backward through paleotsunami research and historical documentation is essential for estimating recurrence intervals and worst-case scenarios.

Paleotsunami Evidence and Analysis Techniques

Paleotsunami deposits are the physical traces left behind when a tsunami floods a coastal area. Common deposit types include:

• Sand sheets — Thin layers of marine sand found inland within fine-grained coastal sediments (marshes, lagoons). Their landward extent provides a minimum estimate of inundation distance.
• Boulder accumulations — Large coral or rock boulders transported onshore by extreme wave energy.
• Erosional unconformities — Surfaces where pre-existing sediment was stripped away by high-velocity flow.

Identifying these deposits and distinguishing them from storm deposits relies on several techniques:

• Sedimentological analysis — Grain size distributions, sorting characteristics, and internal sedimentary structures (e.g., normal grading, rip-up clasts) that are diagnostic of tsunami flow.
• Geochemical markers — Elevated salinity, marine-sourced trace elements, or other saltwater indicators within otherwise freshwater sediments.
• Microfossil assemblages — The presence of marine diatoms, foraminifera, or other organisms in terrestrial or brackish sediment sequences confirms a marine incursion.

Dating methods pin these deposits in time:

• Radiocarbon ($^{14}C$) dating of organic material above and below the deposit brackets the event age.
• Optically stimulated luminescence (OSL) dates the last time quartz or feldspar grains were exposed to sunlight, useful when organic material is absent.

By mapping multiple paleotsunami deposits along a coastline and dating them, researchers can reconstruct recurrence intervals. The Cascadia Subduction Zone, for example, has a paleotsunami record showing roughly 19 major events over the past 10,000 years, yielding an average recurrence interval of ~500 years.

Integration of Historical Records and Modern Modeling

Historical records fill the gap between the paleotsunami record and the instrumental era. Sources include:

• Written eyewitness accounts (the 1755 Lisbon tsunami is documented extensively in European archives)
• Photographs and newspaper reports from more recent events
• Tide gauge records, which provide quantitative wave arrival times and amplitudes (the 1960 Chile tsunami was recorded on tide gauges across the Pacific)

Combining paleotsunami data, historical records, and modern source characterization enables probabilistic tsunami hazard assessment (PTHA). PTHA estimates the probability of exceeding a given wave height at a specific location over a defined time period, analogous to probabilistic seismic hazard analysis. The outputs are hazard curves and maps that inform risk management decisions, land-use planning, and building code requirements.

Numerical Modeling for Tsunami Inundation and Hazard Mapping

Numerical Models and Governing Equations

Numerical models simulate the full lifecycle of a tsunami: generation, open-ocean propagation, and coastal inundation. The workflow generally follows these steps:

1. Define the source — Specify earthquake fault parameters (location, geometry, slip distribution) or landslide volume and geometry.
2. Compute initial sea-surface displacement — For earthquakes, this is typically done using elastic dislocation models (e.g., Okada, 1985).
3. Propagate the wave — Solve the governing equations on a computational grid that covers the ocean basin.
4. Resolve coastal inundation — Use high-resolution grids near the coast to capture shoaling, run-up, and flooding.

The most commonly used governing equations are:

• Nonlinear shallow-water equations (NLSWE) — These capture the essential physics of long-wave propagation and are computationally efficient. Most operational tsunami models (e.g., MOST, ComMIT, GeoClaw) are based on NLSWE.
• Boussinesq equations — These add dispersive terms that become important for shorter-wavelength tsunamis (e.g., landslide-generated waves) where frequency dispersion affects wave shape during propagation.

Key model inputs include high-resolution bathymetry (seafloor topography) and coastal topography (elevation data for inundation modeling).

Model Outputs and Applications

Model outputs include:

• Maximum wave heights at each grid point
• Flow velocities and inundation depths on land
• Arrival times at coastal locations

These outputs feed directly into hazard mapping and risk assessment:

• Nested grid approaches balance computational cost and resolution. A coarse grid covers the open ocean (perhaps 1–4 km resolution), intermediate grids cover the regional shelf (~100–500 m), and fine grids resolve harbors and coastal communities (~10–30 m).
• Hazard maps delineate zones of expected inundation for scenario events or probabilistic return periods. These maps guide evacuation zone boundaries, land-use planning, building codes, and insurance rates.

Model validation is critical. Modelers benchmark their codes against:

• Analytical solutions for idealized problems
• Laboratory wave-tank experiments
• Observed data from historical tsunamis (tide gauge records, field survey measurements of run-up and inundation)

Without rigorous validation, hazard maps derived from models cannot be trusted for life-safety decisions.

Tsunami Early Warning Systems and Community Preparedness

Components and Effectiveness of Early Warning Systems

Tsunami early warning systems aim to detect a tsunami-generating event, estimate the threat, and deliver actionable warnings before the waves arrive. The basic chain of operations is:

1. Seismic detection — Seismometers detect the earthquake and rapidly estimate its location, depth, and magnitude. For tsunamigenesis, the key parameters are whether the earthquake is shallow, submarine, and large enough (generally $M_w \geq 7.0$ for significant tsunamis).
2. Sea-level monitoring — Deep-ocean pressure sensors (DART buoys, maintained by NOAA and partner agencies) detect the passage of the tsunami wave in the open ocean. Coastal tide gauges confirm wave arrivals and amplitudes.
3. Threat assessment — Pre-computed model databases are queried in real time. The observed DART data constrain which scenario best matches the actual event, allowing rapid refinement of wave height forecasts.
4. Warning dissemination — Alerts are issued through national warning centers (e.g., PTWC, JMA) to emergency management agencies, which activate sirens, broadcast alerts, and initiate evacuations.

The effectiveness of the system depends on:

• Station density and distribution — Gaps in the monitoring network create blind spots.
• Processing speed — For near-field tsunamis (source close to the coast), warning times may be only minutes. The 2018 Sulawesi tsunami struck Palu within ~10 minutes of the earthquake, leaving almost no time for a formal warning.
• Communication reliability — Warnings must reach the public through multiple redundant channels (sirens, cell alerts, radio, TV).
• False alarm management — Too many false alarms erode public trust and reduce compliance. Too few warnings risk missing real events. Robust detection algorithms and clear communication protocols are essential.

Community Preparedness and Mitigation Strategies

Even the best warning system is useless if communities don't know how to respond. Preparedness has several components:

• Public education — Residents and visitors in tsunami-prone areas need to know the natural warning signs (strong earthquake shaking, unusual ocean withdrawal) and the correct response (move to high ground immediately without waiting for an official alert).
• Evacuation planning — Hazard maps define evacuation zones. Evacuation routes should be clearly signed, lead to high ground or designated assembly areas, and be designed to handle the expected population flow.
• Regular drills — Practicing evacuations maintains awareness and reveals logistical problems before a real event. Japan conducts annual tsunami drills on the anniversary of past disasters, and participation rates directly correlate with evacuation compliance during actual events.
• Vertical evacuation structures — In flat coastal areas where high ground is too far away, reinforced concrete buildings or purpose-built evacuation towers provide refuge above expected inundation levels. These structures must be engineered to withstand both the hydrodynamic forces and debris impact of a tsunami.
• Resilient infrastructure — Seawalls, breakwaters, and coastal forests can reduce (but not eliminate) tsunami energy. The 2011 Tohoku tsunami overtopped many seawalls designed for smaller events, demonstrating that structural defenses alone are insufficient.

Post-event assessment after every significant tsunami provides feedback for improving the entire system. Field surveys measure actual run-up and inundation, which are compared against model predictions. Interviews with survivors reveal how warnings were received and how evacuations unfolded. Lessons from the 2011 Tohoku tsunami, for example, led to major revisions in Japan's hazard maps, seawall design standards, and evacuation protocols.