The earthquake magnitude sets the size of the seabed source; the water depth sets the speed of the wave; the topography decides how the wave climbs ashore. Two models run in your browser: a linear shallow-water model for the ocean (2 km cells, 280 by 200 km) and a nonlinear shallow-water model for the coast (10 m cells, 1.5 by 0.9 km, every building is a solid obstacle). The ocean wave measured at a gauge off the city is scaled to the Wave Height you chose and used as the inflow of the coastal model. Buildings, trees, cars and people respond to the computed flow.

Seismic moment M0 = 10^(1.5 Mw + 9.1) N m; rupture length and width from Wells and Coppersmith (1994) regressions, mean slip s = M0 / (mu L W) with mu = 30 GPa, seabed uplift about 0.35 s (typical for a shallow-dipping thrust, illustrative). Long waves travel at c = sqrt(g h): 198 m/s (713 km/h) in 4000 m of water. A magnitude 9.0 rupture is about 560 km long, so this lab uses a smaller idealised source patch.

d eta/dt + div(h u) = 0, du/dt + g grad eta = 0 on a staggered grid, forward-backward time stepping, absorbing sponge on the open edges. Shoaling follows Green's law eta2 / eta1 = (h1/h2)^(1/4) (checked below). Dispersion, Earth curvature and the Coriolis force are ignored, which is fine for a basin this size.

h_t + (hu)_x + (hv)_y = 0, (hu)_t + (hu^2 + g h^2/2)_x + (huv)_y = -g h z_x - g n^2 u |u| / h^(1/3). Finite volumes with an HLL Riemann solver, hydrostatic reconstruction (so a lake at rest stays at rest over any bed) and wetting/drying. n is the Manning roughness: 0.02 sea, 0.025-0.04 open land, 0.045 built-up, 0.12 forest. Buildings are solid cells. The offshore boundary uses Riemann invariants fed by the gauge series. The leading bore is captured as a shock (no breaking-wave turbulence or air entrainment); the white water you see is a visual cue computed from Froude number and depth gradient, not a fluid simulation of spray.

Each building keeps the largest momentum flux M = h u^2 in its neighbouring cells and a depth term; demand ratio r = M / Mc + k h. Mc (a capacity in m^3/s^2) is typical-order but illustrative: wood house 90-100, masonry 140-260, reinforced concrete 1000-4000, steel tower 5000, each multiplied by a random strength factor. r >= 1 means collapse; 0.15 / 0.4 / 0.7 are minor / moderate / extensive damage. Loss ratios 5 / 25 / 60 / 100 % of an illustrative value. Residents leave on foot after the warning plus 1-4 minutes decision time, walking straight inland at the chosen speed; tall reinforced buildings are counted as vertical refuges. Dots stand for about 25 people each. These numbers show how lead time, wall height and forest change results; they are not a forecast.

• 2D depth-averaged flow: no vertical structure, no overturning wave, no real breaking, no sediment or scour.
• Buildings never fail partially: they are solid obstacles until the moment of collapse, then the cells open up as rubble (n = 0.07). Before that, a continuous row of buildings reflects the surge, which overestimates the water level in front of it.
• The city is generated procedurally; the topographies are idealised profiles, not a real place.
• The wave height slider is the height you want at the gauge (a 12 m wall stops a 6 m wave here, but a 15 m wave simply overtops it); a given magnitude usually implies a smaller one (see the chip in the options tab).
• Capacities, losses and walking behaviour are illustrative.