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Tsunami warning system
Tsunami warning system
Tsunami warning system
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Evacuation route sign in a low-lying coastal area on the West Coast of the United States

A tsunami warning system (TWS) is used to detect tsunamis in advance and issue the warnings to prevent loss of life and damage to property. It is made up of two equally important components: a network of sensors to detect tsunamis and a communications infrastructure to issue timely alarms to permit evacuation of the coastal areas. There are two distinct types of tsunami warning systems: international and regional. When operating, seismic alerts are used to instigate the watches and warnings; then, data from observed sea level height (either shore-based tide gauges or DART buoys) are used to verify the existence of a tsunami. Other systems have been proposed to augment the warning procedures; for example, it has been suggested that the duration and frequency content of t-wave energy (which is earthquake energy trapped in the ocean SOFAR channel) is indicative of an earthquake's tsunami potential.[1]

History and forecasting

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The first rudimentary system to alert communities of an impending tsunami was attempted in Hawaii in the 1920s. More advanced systems were developed in the wake of the April 1, 1946 (caused by the 1946 Aleutian Islands earthquake) and May 23, 1960 (caused by the 1960 Valdivia earthquake) tsunamis which caused massive devastation in Hilo, Hawaii.[2] While tsunamis travel at between 500 and 1,000 km/h (around 0.14 and 0.28 km/s) in open water, earthquakes can be detected almost at once as seismic waves travel with a typical speed of 4 km/s (around 14,400 km/h). This gives time for a possible tsunami forecast to be made and warnings to be issued to threatened areas, if warranted. Until a reliable model is able to predict which earthquakes will produce significant tsunamis, this approach will produce many more false alarms than verified warnings.[citation needed]

International systems (IS)

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Pacific Ocean

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Japanese Tsunami warning sign

Tsunami warnings (SAME code: TSW) for most of the Pacific Ocean are issued by the Pacific Tsunami Warning Center (PTWC), operated by the United States NOAA in Ewa Beach, Hawaii. NOAA's National Tsunami Warning Center (NTWC) in Palmer, Alaska issues warnings for North America, including Alaska, British Columbia, Oregon, California, the Gulf of Mexico, and the East coast. The PTWC was established in 1949, following the 1946 Aleutian Island earthquake and a tsunami that resulted in 165 casualties on Hawaii and in Alaska; NTWC was founded in 1967. International coordination is achieved through the International Coordination Group for the Tsunami Warning System in the Pacific, established by the Intergovernmental Oceanographic Commission of UNESCO.[3]

Chile

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In 2005, Chile started to implement the Integrated Plate boundary Observatory Chile (IPOC)[4] which in the following years become a network of 14 multiparameter stations for monitoring the 600-km seismic distance between Antofagasta and Arica. Each station was provided with broadband seismometer, accelerometer, GPS antenna. In four cases, it was installed a short-base tiltmeter (pendulum). Some stations were ubicated underground at a depth of 3–4 meters. The network completed the tidal gauge of the Hydrographic and Oceanographic Service of the Chilean Navy.[5]

The long-base tiltmeters (LBTs) and the STS2 seismometer of the IPOC recorded a series of long-period signals some days after the 2010 Maule earthquake. The same effect was registered by broadband seismometers of India and Japan some days after the 2004 Indian Ocean earthquake and tsunami. Simulations held in 2013 on historical data highlighted "tiltmeters and broadband seismometers are thus valuable instruments for monitoring tsunamis in complement with tide gauge arrays." In the case of the 2010 Maule earthquake, tilt-sensors observed a discriminating signal "starting 20 min before the arrival time of the tsunami at the nearest point on the coastline."[5]

Indian Ocean (ICG/IOTWMS)

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Main article: Indian Ocean Tsunami Warning System
Tsunami Early Warning Tower board in Hikkaduwa, Sri Lanka

After the 2004 Indian Ocean Tsunami which killed almost 250,000 people, a United Nations conference was held in January 2005 in Kobe, Japan, and decided that as an initial step towards an International Early Warning Programme, the UN should establish an Indian Ocean Tsunami Warning System. This resulted in a warning system for Indonesia and other affected areas. Indonesia's system fell out of service in 2012 because the detection buoys were no longer operational.[6] Tsunami prediction was then limited to detection of seismic activity, with no system to predict tsunamis based on volcanic eruptions.

Indonesia was hit by tsunamis in September and December 2018. The December 2018 tsunami was caused by a volcano.[7] Sea level sensors were then installed by the Indonesian government to fill the prediction gap.[8]

North Eastern Atlantic, the Mediterranean and Connected Seas (ICG/NEAMTWS)

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The First United Session of the Inter-governmental Coordination Group for the Tsunami Early Warning and Mitigation System in the North Eastern Atlantic, the Mediterranean and connected Seas (ICG/NEAMTWS), established by the Intergovernmental Oceanographic Commission of UNESCO Assembly during its 23rd Session in June 2005, through Resolution XXIII.14, took place in Rome on 21 and 22 November 2005.

The meeting, hosted by the Government of Italy (the Italian Ministry of Foreign Affairs and the Italian Ministry for the Environment and Protection of Land and Sea), was attended by more than 150 participants from 24 countries, 13 organizations and numerous observers.

Caribbean

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A Caribbean-wide tsunami warning system was planned to be instituted by the year 2010, by representatives of Caribbean nations who met in Panama City in March 2008. Panama's last major tsunami killed 4,500 people in 1882.[9] Barbados has said it will review or test its tsunami protocol in February 2010 as a regional pilot.[10][needs update]

Regional warning systems

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Tsunami warning system in East Timor

Regional (or local) warning system centers use seismic data about nearby recent earthquakes to determine if there is a possible local threat of a tsunami. Such systems are capable of issuing warnings to the general public (via public address systems and sirens) in less than 15 minutes. Although the epicenter and moment magnitude of an underwater quake and the probable tsunami arrival times can be quickly calculated, it is almost always impossible to know whether underwater ground shifts have occurred which will result in tsunami waves. As a result, false alarms can occur with these systems, but the disruption is small, which makes sense due to the highly localized nature of these extremely quick warnings, in combination with how difficult it would be for a false alarm to affect more than a small area of the system. Real tsunamis would affect more than just a small portion.[citation needed]

Japan

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Evacuation route sign on the pavement in Kamakura, Japan
See also: Tsunami Warning (Japan)

Japan has a nationwide tsunami warning system. The system usually issues the warning minutes after an Earthquake Early Warning (EEW) is issued, should there be expected waves.[11][12] The tsunami warning was issued within 3 minutes with the most serious rating on its warning scale during the 2011 Tōhoku earthquake and tsunami; it was rated as a "major tsunami", being at least 3 m (9.8 ft) high.[12][13] An improved system was unveiled on March 7, 2013, following the 2011 disaster to better assess imminent tsunamis.[14][15]

India

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India is one of the 5 countries to have the most advanced tsunami warning systems in the world.[16] In 2004, right after being hit by an earthquake in Sumatra, a massive tsunami devastated the coasts of India,[17] prompting the Government of India to set up the INCOIS (Indian National Centre for Ocean Information Services).[18] The center is an autonomous organization of the Government of India, under the Ministry of Earth Sciences, located in Pragathi Nagar, Hyderabad, India. This center offers ocean information and advisory services to society, industry, government bodies in areas like Tsunami warning, ocean state forecast, fishing zones and more.[19]

This center receives data from over 35 sea level tide gauges at intervals of 5 minutes.[20] Along with this it receives data from wave rider buoys, bottom pressure readers (BPRs) and a network of seismographs that have been installed at various locations in the IOR (Indian Ocean Region). The Indian Tsunami Buoy Type 1 System[21] consists of 2 units – a surface buoy and a bottom pressure reader (BPR). Communication between BPR and the surface buoy is through acoustic modems and the surface buoys use the INSAT satellite system to communicate readings back to shore stations. The Tsunami warning station collates information from 17 seismic stations of the Indian Meteorological Department (IMD), 10 stations of Wadia Institute of Himalayan Geology (WIHG)[22] and more than 300 international stations. INDOFOS (INDian Ocean FOrecasting System) is a service that forecasts the ocean state and is capable of predicting surface and sub surface features and states of the Indian Ocean.[23] These forecasts are made accessible through Information centers, Radio, local digital sign boards, websites, TV channels and subscription services. Oceansat 2 system is a collection of earth observation satellites operated by ISRO[24] in conjunction with Oceansat ground station that covers an area of 5000 km radius around India and is capable of monitoring sea flora and fauna along with oceanic features like meandering patterns, eddies, rings, upwelling and others. Oceansat-2 was successfully deployed to predict the landfall and mitigate the effects of Cyclone Phailin, in October 2013.[25]

Conveying the warning

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Mast with warning system, and sign detailing escape routes, on the coast of Okumatsushima, Miyagi prefecture, Japan (this coast was severely hit by the 2011 tsunami)

Detection and prediction of tsunamis is only half the work of the system. Of equal importance is the ability to warn the populations of the areas that will be affected. All tsunami warning systems feature multiple lines of communications (such as Cell Broadcast, SMS, e-mail, fax, radio, texting and telex, often using hardened dedicated systems)[citation needed] enabling emergency messages to be sent to the emergency services and armed forces, as well to population-alerting systems (e.g. sirens) and systems like the Emergency Alert System.[26]

Shortcomings

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With the speed at which tsunami waves travel through open water, no system can protect against a very sudden tsunami, where the coast in question is too close to the epicenter. A devastating tsunami occurred off the coast of Hokkaidō in Japan as a result of an earthquake on July 12, 1993. As a result, 165 people on the small island of Okushiri, Hokkaido lost their lives, and hundreds more were missing or injured. This tsunami struck just three to five minutes after the quake, and most victims were caught while fleeing for higher ground and secure places after surviving the earthquake.[27]

While there remains the potential for sudden devastation from a tsunami, warning systems can be effective. For example, if there were a very large subduction zone earthquake (moment magnitude 9.0) off the west coast of the United States, people in Japan, would therefore have more than 12 hours (and likely warnings from warning systems in Hawaii and elsewhere) before any tsunami arrived, giving them some time to evacuate areas likely to be affected.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Tsunami warning system

View on Grokipedia
from Grokipedia
A tsunami warning system is a coordinated network of monitoring, detection, , and communication technologies designed to identify potential tsunamis generated by earthquakes or other events and issue timely alerts to coastal communities, enabling evacuations that save lives and reduce damage. Globally, these systems operate through international cooperation led by organizations like 's Intergovernmental Oceanographic Commission (IOC), which coordinates efforts among 150 member states to build resilient early warning capabilities across regions such as the Pacific, , , Northeast Atlantic, and Mediterranean. Key components include seismic networks to detect earthquakes, deep-ocean buoys like the Deep-ocean Assessment and Reporting of (DART) systems for measuring wave disturbances in the open sea, and coastal tide gauges to track near-shore water levels, all feeding data into 24/7 warning centers that use forecast models to predict tsunami impacts. These systems emphasize rapid data transmission, public education, and community drills to ensure effective response, with milestones including the establishment of the Pacific Tsunami Warning System in 1965 following the 1960 Chilean tsunami and expansions after the 2004 disaster that killed over 230,000 people. In the United States, the (NOAA) manages two primary warning centers—the National Tsunami Warning Center in , and the in Honolulu, —which monitor events and issue alerts for U.S. coasts as well as international partners in the Pacific and . Alerts are categorized into four levels: Information Statement for distant events unlikely to affect areas, Watch for potential threats requiring preparation, Advisory for non-life-threatening inundation, and Warning for dangerous waves expected to strike soon, disseminated via radio, TV, wireless alerts, , and websites like tsunami.gov. Since 1900, 34 tsunamis have caused over 500 deaths and $1.7 billion in damages in the U.S., underscoring the systems' role in mitigation, such as avoiding $200 million in unnecessary evacuations in through improved forecasting. Programs like TsunamiReady, which has certified 200 communities as of March 2024, further enhance local preparedness by promoting education and readiness.

Overview

Definition and Purpose

A tsunami warning system is a coordinated network of detection, analysis, and alert mechanisms designed to identify promptly, forecast their potential impacts, and disseminate timely warnings to populations in coastal areas at risk. These systems integrate global and regional efforts to monitor seismic activity and ocean conditions, enabling rapid response to threats that can originate from distant sources. The primary purpose of tsunami warning systems is to minimize loss of life and property damage by providing critical lead time—often hours in advance—for evacuations, sheltering, and other protective actions. They address tsunamis triggered by earthquakes, which are the most common cause, as well as non-seismic events such as submarine landslides, volcanic eruptions, and meteorological phenomena like intense storms. The urgent need for these systems was underscored by the 2004 Indian Ocean tsunami, which resulted in approximately 227,000 fatalities across 14 countries due to the absence of effective warnings, prompting enhanced global coordination through the UNESCO-Intergovernmental Oceanographic Commission (IOC). Core elements of these systems operate at a high level through detection of initial events, forecasting of wave propagation and arrival times, and efficient dissemination of alerts via multiple channels to emergency managers and the public. International frameworks, such as the Pacific Tsunami Warning and Mitigation System (PTWS) coordinated by the UNESCO-IOC, facilitate this end-to-end process across regions.

Key Components

Tsunami warning systems rely on an integrated comprising detection networks, analysis centers, communication , and response coordination mechanisms to detect, assess, and mitigate tsunami threats effectively. Detection networks form the foundational layer, utilizing seismometers to identify earthquake-generated by monitoring seismic activity in real-time, and tide gauges or buoys to measure sea-level changes that confirm wave . Analysis centers serve as the decision-making hubs, where experts employ models to evaluate tsunami potential, estimate wave heights, arrival times, and inundation zones based on incoming data. These centers process information rapidly to issue timely warnings, often within minutes of an event's detection. Communication infrastructure ensures rapid dissemination of alerts to at-risk populations through diverse channels, including emergency sirens, television and radio broadcasts, mobile apps, and notifications, enabling widespread awareness and evacuation initiation. Response coordination integrates these elements with local evacuation plans, public programs, and inter-agency to facilitate organized evacuations and minimize casualties, emphasizing and preparedness. The interconnectivity of these components creates an end-to-end system, where data from global detection networks is shared instantaneously via international frameworks such as the (CTBTO)'s International Data Centre, which provides seismic and hydroacoustic data to national warning centers for collaborative analysis. Standardization efforts by the Intergovernmental Oceanographic Commission (IOC) of play a pivotal role in ensuring across systems, defining uniform components like detection thresholds and communication protocols, while establishing warning levels such as watches (for distant threats), advisories (for potential impacts), and warnings (for imminent danger) to harmonize global responses. A prominent example of an integrated system is the NOAA-led TsunamiReady program, which certifies communities that have implemented all key components—including detection linkages, analysis access, robust communication tools, and coordinated evacuation plans—to enhance local preparedness and response capabilities.

History

Early Developments

The devastating 1896 Meiji Sanriku in , which claimed over 22,000 lives with run-up heights reaching 38 meters, marked the beginning of systematic tsunami observations and research. In response, the Japanese Ministry of Education's Earthquake Prevention Commission published the first scientific article explicitly linking earthquakes to tsunamis, emphasizing the need for monitoring earthquake forerunners. Initial efforts relied on manual observations by coastal communities and rudimentary networks already in place; the 1896 event was instrumentally recorded at three regional stations, providing crucial data on long-period waves that confirmed its origin as a "." These early s, operational since the late , formed the foundation of Japan's nascent monitoring system, though warnings remained local and based on visual sightings of changes or post-earthquake watches. By the early , expanded its observational capabilities, incorporating seismic stations to detect potential tsunamigenic events more reliably. Seismic telegraphs—early devices that transmitted signals via wire to central observatories—enabled faster relay of data across regions, supplementing manual coastal observer reports. Scientists like Hugo Benioff played a pivotal role in advancing seismic detection; his 1932 invention of the Benioff seismograph, a sensitive vertical-component instrument, improved the recording of distant earthquakes, aiding in the identification of zone events prone to generating tsunamis. These tools were instrumental in events like the 1933 Showa Sanriku tsunami, where timely seismic alerts allowed partial evacuations despite the disaster's severity. The push for formalized international coordination intensified after the and tsunami, which killed 159 people in (and 6 in ) despite a five-hour from the earthquake. This event exposed the limitations of isolated national efforts, prompting the U.S. Coast and Geodetic Survey to lead the establishment of the Pacific Tsunami Warning System (PTWS) in 1949 under the auspices of UNESCO's Intergovernmental Oceanographic Commission (IOC). Headquartered in , the PTWS initially depended on a network of seismic stations and coastal tide gauges for detection, with telegraphic communication disseminating warnings to Pacific Rim nations. This marked the first global-scale effort, focusing on rapid assessment of distant tsunamis through international via the U.S. agency.

Evolution After Major Events

The devastating in , which generated a trans-Pacific that killed 61 people in , prompted significant expansions to the Pacific Tsunami Warning System (PTWS). In response, the coordinated the establishment of a formal Pacific-wide distant warning system in 1965, involving 26 member states to enhance coordination and alert dissemination across the region. This initiative built on earlier U.S.-led efforts by integrating seismic networks and tide gauges, marking a shift toward international collaboration for distant tsunami threats. During the 1960s to 1990s, further advancements included the development of deep-ocean assessment and reporting of tsunamis (DART) buoys to improve real-time detection. Initiated by NOAA's Pacific Marine Environmental Laboratory in 1987, the DART system deployed bottom pressure sensors in the open ocean to measure wave heights directly, addressing limitations in coastal tide gauge data for early warning. The first operational array of six buoys was completed in 2001, but its conceptual and prototype work in the 1980s and 1990s laid the groundwork for scalable ocean monitoring. The 2004 Indian Ocean tsunami, which claimed over 230,000 lives across 14 countries due to the absence of a regional warning system, catalyzed global reforms. This catastrophe led to the establishment of the Tsunami Warning and Mitigation System (IOTWMS) in 2005 under UNESCO's Intergovernmental Oceanographic Commission, with operational coordination formalized by 2006 to provide timely alerts to Indian Ocean rim nations. It spurred a broader push for multi-hazard early warning frameworks, influencing the UN's Framework for Disaster Risk Reduction in 2015, which emphasized integrated systems for tsunamis, earthquakes, and other perils. More recent events have continued to drive enhancements. The 2011 Tohoku earthquake and in , despite existing warnings, exposed gaps in near-field detection and led to seismic network upgrades worldwide, including faster magnitude estimation algorithms and denser sensor arrays for rapid alert issuance within minutes. Similarly, the July 29, 2025, M8.8 earthquake generated a Pacific-wide that tested transboundary alert mechanisms, highlighting the effectiveness of coordinated international bulletins that prompted evacuations in , , and U.S. territories with minimal casualties. These events have influenced key policy shifts toward comprehensive coverage. UNESCO's Tsunami Ready program, launched in 2022, aims to train 100% of at-risk coastal communities globally by 2030, supported by UN resolutions under the Early Warnings for All initiative to achieve universal early warning system access. Post-2010s integration of satellite data, particularly from Global Navigation Satellite Systems (GNSS), has enhanced detection by providing real-time ionospheric and displacement measurements to refine forecasts.

Detection and Monitoring

Seismic and Oceanographic Sensors

Seismic sensors form the foundational layer of tsunami detection by identifying undersea earthquakes that may generate , typically those with magnitudes exceeding 7.0 on the . Broadband seismometers, which capture ground motion across a wide range (0.01–50 Hz) and amplitude spectrum, are deployed globally to record both weak and strong seismic signals from distant events. These instruments enable rapid location and magnitude estimation, often within minutes of an earthquake's onset, providing initial alerts for potential tsunami generation. Complementing seismometers, (GPS) stations measure real-time ground deformation, including coseismic slip along fault planes during large earthquakes. By tracking millimeter-scale displacements, GPS data quantify the extent of seafloor uplift or that displaces ocean water, offering more accurate assessments of potential than seismic data alone. For instance, during major events, GPS observations have revealed slip distributions up to 20 meters, directly informing source models. Oceanographic sensors focus on direct measurement of disturbances following seismic triggers. Coastal tide gauges, originally designed for tidal monitoring, detect wave arrivals by recording sea-level anomalies at intervals as short as one minute, confirming wave heights and propagation speeds near shorelines. These fixed installations provide essential validation for warnings, particularly in regions with limited offshore coverage. In the open ocean, Deep-ocean Assessment and Reporting of Tsunamis (DART) buoys employ bottom pressure recorders (BPRs) anchored at depths up to 6,000 meters to sense seafloor pressure changes induced by passing waves. Each BPR detects variations as small as 1 cm in water height, transmitting acoustic signals to a surface for satellite relay, enabling early offshore detection hours before coastal impact. Key networks integrate these sensors for comprehensive coverage. The Global Seismographic Network (GSN), comprising approximately 150 broadband stations worldwide, delivers real-time seismic data critical for global tsunami monitoring and earthquake characterization. In the Pacific, where tsunami risk is highest, the U.S. operates 39 DART buoys as of 2025, strategically positioned to intercept waves from zones. Data from these sensors are transmitted in real time to warning centers via systems like , ensuring low-latency delivery essential for timely alerts. Seismic data from GSN stations reach centers with latencies under 2 minutes, while DART buoys forward pressure readings with delays less than 3 minutes, allowing integration into decision-making processes.

Advanced Detection Technologies

Satellite-based technologies are advancing tsunami detection by providing global coverage and rapid data acquisition potential, complementing ground-based seismic and ographic sensors. Global Navigation Satellite System Reflectometry (GNSS-R) utilizes reflected signals from GNSS satellites, such as GPS, to measure sea surface altimetry and detect subtle wave perturbations indicative of . Feasibility studies, including those from the German-Indonesian Tsunami Early Warning System (GITEWS), demonstrate that GNSS-R can achieve sea height measurements accurate to within a few centimeters, offering a promising approach for remote regions. Interferometric Synthetic Aperture Radar (InSAR), particularly using data from the European Space Agency's satellites, facilitates rapid mapping of earthquake-induced ground deformation, which is crucial for assessing generation potential. By generating interferograms shortly after seismic events, InSAR reveals fault slip and surface displacements with sub-centimeter precision, enabling quicker evaluation of tsunamigenic earthquakes compared to field surveys. For instance, data has been instrumental in post-event analyses, such as the 2018 Palu earthquake, where it mapped co-seismic ruptures in under 24 hours to inform risk. This technology addresses limitations in real-time coverage by providing wide-swath imaging unaffected by weather conditions. Emerging technologies further enhance detection speed and accuracy through innovative sensing of atmospheric and seismic precursors. NASA's Global Universal Alert and Response Detector for Ionospheric Anomalies from (GUARDIAN), deployed in 2025, leverages ionospheric disturbances caused by tsunami-generated to provide early warnings. The system analyzes (TEC) anomalies in the using ground-based GNSS receivers and satellite data, detecting tsunamis up to 1,200 kilometers away and issuing alerts 30 to 45 minutes before coastal impact. In a 2025 Pacific test following the magnitude 8.8 Kamchatka , GUARDIAN confirmed tsunami signals 20 minutes post-event, outperforming tide gauge detections by up to 45 minutes. TEC anomalies serve as reliable precursors, with studies showing perturbations detectable 10 to 30 minutes after onset, correlating strongly with wave propagation. Artificial intelligence and machine learning (AI/ML) algorithms are increasingly applied to recognize patterns in seismic data for distinguishing tsunami-generating s from non-tsunamigenic ones. These models, such as classifiers, process real-time seismograms to identify subtle characteristics, achieving detection accuracies above 90% in simulations of events like the 2011 Tohoku . By integrating multi-sensor inputs, AI/ML reduces false alarms and accelerates processing, with recent frameworks using to forecast heights from initial seismic signals in under 10 seconds. Integration of these advanced technologies into global networks exemplifies enhanced collaborative detection. The Comprehensive Nuclear-Test-Ban Treaty Organization's (CTBTO) International Monitoring System (IMS), comprising over 300 stations, shares real-time seismic and hydroacoustic data with 22 tsunami warning centers worldwide through bilateral agreements, providing lead times of up to three minutes for alerts. This integration incorporates ionospheric TEC data and AI-processed outputs, as seen in the 2025 Kamchatka event where IMS data validated GUARDIAN detections, improving coverage in data-scarce regions like the South Pacific. Such systems address key challenges, including sparse monitoring in remote oceanic areas, by enabling space-based and atmospheric sensing that extends detection beyond traditional coastal networks.

Forecasting and Modeling

Tsunami Propagation Models

Tsunami propagation models are computational tools that simulate the generation, travel, and transformation of tsunami waves from their to coastal areas. These models primarily rely on finite-difference methods to solve the nonlinear shallow-water equations, which approximate the of long waves in oceans of varying depth. The core equations include the , ∂η∂t+∂[(h+η)u]∂x+∂[(h+η)v]∂y=0,\frac{\partial \eta}{\partial t} + \frac{\partial [(h + \eta) u]}{\partial x} + \frac{\partial [(h + \eta) v]}{\partial y} = 0, and the momentum equations, ∂u∂t+u∂u∂x+v∂u∂y+g∂η∂x=0,∂v∂t+u∂v∂x+v∂v∂y+g∂η∂y=0,\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + g \frac{\partial \eta}{\partial x} = 0, \quad \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + g \frac{\partial \eta}{\partial y} = 0, where η\eta is the sea surface elevation, hh is the undisturbed water depth, uu and vv are the depth-averaged velocity components in the xx and yy directions, gg is gravitational acceleration, and tt is time. A prominent example is NOAA's Method of Splitting Tsunami (MOST) model, which divides the simulation into generation, propagation, and inundation phases, using these equations to propagate waves across deep ocean basins while accounting for nonlinear effects near shorelines. These models simulate wave from the —where initial seafloor deformation occurs due to an —through transoceanic travel to coastal run-up. Key factors influencing include , which governs wave speed via c=ghc = \sqrt{g h}
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