Vary the moment magnitude Mw, epicenter distance, offshore wave height, coastal slope, shoreline geometry and vegetation cover to see the tsunami run-up height R, inundation distance, arrival time and damage class update in real time. Built on the Synolakis planar-beach run-up formula and Green's-law shoaling, it covers up to 3.11-class mega-tsunamis.
Parameters
Moment magnitude Mw
Subduction-zone quake size. 8.5+ is destructive, 9.0+ mega-tsunami
Focal depth
km
Shallower events deform the seabed more and excite larger tsunamis
Epicenter distance
km
Offshore wave height H0
m
Deep-ocean (≈1000 m) amplitude; overrides the Mw-derived value if larger
Coastal slope β
°
Gentler slopes inundate further; steeper slopes reflect more
Coastal geometry
Geometry factor from bay focusing, estuary run-up or harbor resonance
Coastal vegetation cover
%
Pine belt / mangrove coverage (up to 30% attenuation)
Results
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Offshore height (m)
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Shoaling factor (×)
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Geometry factor (×)
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Run-up R (m)
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Inundation distance (m)
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Arrival time (min)
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Coastal section & tsunami run-up animation
The offshore wave amplifies via shoaling and climbs the beach. Tree icons mark the vegetation belt; the dashed red line is the maximum run-up R.
Source amplitude (Abe 1995) is 10^(0.5Mw−3.3); Green's law applies spherical-spread decay √(50/D). The user-input offshore wave overrides the Mw-derived value when larger.
News reports say things like "maximum run-up 38 m". Is that the same as how high the wave is offshore?
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No — they are different things. The offshore wave height H_0 is how tall the wave is in deep water, usually only a few metres up to about 10 m. Once it reaches shallow water, Green's law h ∝ d^(−1/4) kicks in and the wave shoals, then it runs up the beach. The final elevation it reaches on land is the run-up R. In 2011, an offshore wave of 6-8 m ran up the slope at Aneyoshi (Miyako, Iwate) to R = 38.9 m. It is perfectly normal for R to be 4-6× the offshore amplitude.
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Why does it grow that much? Ordinary waves don't behave like that.
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Three reasons. First, shoaling: the wave's energy is trapped in shallow water so the height scales with depth to the −1/4 power. A 5-m tsunami at 4000 m depth becomes about 15 m at 50 m depth. Second, coastal focusing: V-shaped bays and ria coasts funnel the wave to 2-3× the open value. Third, slope run-up: the kinetic energy converts to potential energy and the gentler the beach, the higher it climbs. The Synolakis (1987) experimental relation R/H = 2.831√cot β captures this — drop the slope slider from 5° to 2° and R jumps.
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How much does Mw (magnitude) actually change the run-up? People say Mw 8.5 and 9.0 are completely different.
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Quake energy (Hanks & Kanamori) is 10^(1.5Mw+4.8), so each unit of Mw is 32× more energy. Even Mw 8.5 → 9.0 is roughly 5-6× different. The source amplitude scales as 10^(0.5Mw−3.3) — almost linear — but once that's amplified by shoaling, the final R differs by a factor of 2 or more. The 2011 Tohoku event (Mw 9.0) gave R = 10-40 m along Miyagi, Iwate and Fukushima. Sumatra 2004 (Mw 9.1) and the postulated Cascadia (Mw 9.0+) are similar. Even Mw 8-class events can hit 5-10 m locally, so anything Mw 8+ on a subduction zone is a red alert.
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I've heard pine belts and mangroves help against tsunamis — is that really true?
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Conditionally yes. Tanaka et al. (2007) studied the Sumatra event and found dense mangrove belts attenuated the rear-side fluid force by 30-70%. But the moment a wave exceeds the canopy height, the trees are stripped out and become projectiles. In 2011 the iconic Takata-Matsubara pine forest was wiped clean by an 8-m wave. This tool models a first-order linear attenuation up to 30% — useful for L1 tsunamis of a few metres. For L2 mega-tsunamis (over 10 m) the rule is evacuation plus multi-layered defence: seawall + vertical-evacuation building + relocation to high ground.
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It also shows "arrival time". Can I use that as my evacuation window?
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It's a rough first-wave estimate. Long-wave speed c = √(gd) — at d = 4000 m, that's 198 m/s ≈ 720 km/h, so a 200-km epicenter is about 17 min away. But the first wave is not always the largest: in 2011 the 3rd or 4th wave was the maximum at many sites. The rule of thumb is "if you feel the shake, expect the first wave within 30 min and stay alert for 2-3 hours". Treat this tool as a back-of-the-envelope check; for actual evacuation decisions follow the JMA tsunami warning and your local hazard map.
Frequently Asked Questions
Offshore wave height H_0 is the tsunami amplitude (sea-surface rise) measured in deep water. As the wave approaches the coast and the water becomes shallower, Green's law h ∝ d^(−1/4) amplifies it. The maximum elevation reached on the land after running up the beach slope is the run-up height R. Synolakis (1987) planar-beach experiments give R/H_0 = 2.831·√cot β, so gentle slopes climb higher. In the 2011 Tohoku event, an offshore tsunami of 5-10 m ran up to R = 30-40 m in the V-shaped bays of the Sanriku coast.
Subduction-zone quakes of Mw 7.0 can already trigger tens-of-cm to several-m tsunamis, but widespread damage typically requires Mw 8 and a near-certain mega-tsunami requires Mw 9. The energy formula (Hanks & Kanamori 1979) is 10^(1.5Mw+4.8): a unit of Mw is 32× more energy, so Mw 8 → 9 differs by roughly 30×. This tool lets you vary Mw, distance and offshore height independently — pushing Mw from 8.5 to 9.0 sharply raises the run-up. The JMA aims to issue major tsunami warnings within 3 minutes for Mw 8+ subduction events.
Taking a straight, open coast as the baseline (f_geom = 1.0), V-shaped (ria) bays focus the wave by 2-3×, river estuaries push it 3× through up-river run-up, and harbors resonate at about 1.8×. The effect is strongest when the tsunami wavelength matches the bay dimensions (Helmholtz resonance). In the Tohoku event, Ryori Bay in Iwate recorded R = 38 m and the Aneyoshi district of Miyako recorded R = 38.9 m. By switching the shoreline preset in this tool, the same Mw and distance produce very different R values.
Tanaka et al. (2007) surveys after the 2004 Sumatra event reported that dense mangrove or pine belts attenuated the rear-side fluid force by 30-70%. This tool models a first-order linear attenuation of up to 30% with vegetation cover. However, once the tsunami exceeds the canopy height (R > 5-7 m) the vegetation itself is uprooted and the attenuation rapidly disappears. In 2011 the famous Takata-Matsubara pine belt was completely washed away by an 8-m tsunami. Vegetation belts work against L1 tsunamis (a few m) but for L2 mega-tsunamis (10 m+) evacuation plus multi-layered defence is mandatory.
Real-World Applications
Coastal hazard mapping: The Japan Meteorological Agency, Cabinet Office and prefectural governments publish tsunami inundation maps for postulated subduction sources (Nankai Trough M9, Japan Trench M9, Kuril Trench M9). Simplified formulas like this tool are used upstream of detailed CFD codes (TUNAMI-N2, COMCOT, GeoClaw) to screen which districts fall inside the L2 inundation footprint. The detailed work is carried out by Tohoku University IRIDeS, JAMSTEC and NIED.
Nuclear plant and LNG terminal siting: Japan's nuclear safety regulator requires explicit site-specific run-up evaluation. The lesson of Fukushima Daiichi — where a 5.7-m design wave was overtopped by 14-15 m — pushed practice toward Probabilistic Tsunami Hazard Analysis (PTHA) at the 10^(−4)/year exceedance level, combined with the Earthquake Research Committee's long-term forecasts. This tool is convenient for the up-front sensitivity sweep across Mw, distance and shoreline geometry.
Evacuation planning and early-warning systems: JMA issues tsunami warnings within 3 minutes of a quake; the Pacific Tsunami Warning Center (PTWC, Hawaii) targets 1 hour for distant tsunamis. The arrival time c = √(gd) is the most basic check: near-source coasts must follow "if it shakes, run", while distant tsunamis can wait for the warning. This tool shows arrival time together with Mw and distance, making evacuation-time estimation immediate.
Seawall overtopping and coastal structures: When the run-up R exceeds the seawall crest T_d the wave overtops, scours and may collapse the structure. The Japan Society of Civil Engineers (JSCE) tsunami load guidelines design at two levels — L1 (design tsunami) and L2 (worst case). This tool gives a first-cut check whether existing seawalls are adequate against L2. Detailed loads are usually computed with OpenFOAM interFoam, Fluent VOF or SPH solvers such as DualSPHysics.
Common Misconceptions and Pitfalls
The biggest pitfall is confusing Mw with the Japan Meteorological Agency magnitude Mj. JMA first reports Mj, computed from ~5-s-period surface-wave amplitude, which saturates above Mw 8. The first 3.11 announcement was Mj 7.9 before being revised to Mw 9.0. Tsunami scaling absolutely requires Mw (long-period, moment-based); plugging Mj directly into a tsunami formula can under-predict mega-tsunamis by 1-2 orders of magnitude. This tool expects Mw input.
Next, assuming the first wave is the largest. A tsunami is a wave train lasting tens of minutes to hours; in 2011, the 2nd to 4th wave was the maximum at Ishinomaki, Miyako and several other stations. Bay-resonance modes, multi-segment fault rupture and reflections all stack constructively at different times. "The first wave receded, so it's safe" is a deadly misconception — stay on high ground for at least 2-3 hours after the warning is lifted. This tool only outputs the peak run-up; it does not represent the wave-train structure.
Finally, over-trusting the Synolakis formula as a direct predictor of real coastlines. R/H = 2.831√cot β is a 2-D, monochromatic-wave, planar-beach idealisation; it ignores 3-D bathymetry, breaking, scour, debris and the focusing or attenuation by buildings and infrastructure. This tool further uses a simplified stable form, and the error can easily be ±50%. Real design uses 2-D shallow-water solvers (TUNAMI-N2, COMCOT, GeoClaw) or 3-D CFD (OpenFOAM, ANSYS Fluent VOF). Treat this tool as an educational sensitivity calculator, not a substitute for an engineering hazard study.