Coastal delta flood resilience

What is modelled

A river delta 560 m wide with four branching distributary channels, a protected town behind a seawall, mangrove belts on both flanks, and villages inland. Sea-level rise, a storm surge, the seawall crest and the mangrove belt width are the controls. The page works out where the water goes, how many buildings get wet and a simple damage index. Terrain height is real-scale (about 7.5 m of relief); the horizontal scale is 1 unit = 1 m.

Equations and rules

• Water surface at the open coast: H = SLR + tide + surge. Tide is a sine of amplitude 0.35 m when animated.
• Mangrove belt: a surge that crosses a belt of length x is reduced as S(x) = S0 e-x/L with an assumed decay length L = 380 m, so 500 m removes about 73 %. Real attenuation depends on density, species, depth and wave period (published values vary by a factor of several); L is an illustrative choice. Cells in front of the town do not cross the belt and get the full surge.
• Seawall: while H ≤ crest the polder behind the wall is pumped dry. When the surge tops the wall, the polder fills to a surface of H - crest (a quasi-steady shortcut, no overtopping discharge or time).
• Flooding is hydraulically connected: a grid cell floods only if its ground is below the local water surface and it touches an already flooded cell, starting from the sea. A low inland hollow that is not connected stays dry. The "bathtub" figure (no connection test) is shown for comparison and is always at least as large.
• Damage index: each building has a relative value (house 1, stilt house 1.2, tower 6) and takes damage min(depth / 3 m, 1), where depth is water above the ground at the building. Stilt houses are lifted 1.75 m. The linear curve is illustrative; real depth-damage curves depend on building type and are measured from claims data.

Checks run in the page

• Belt attenuation by explicit Euler integration of dS/dx = -S/L against the closed form.
• An independent recount of the bathtub flooded fraction with a different loop order, connected ≤ bathtub, and monotone in sea level.
• With the wall holding, no polder cell floods; with a larger surge the wall is overtopped.
• The half-value belt width L ln 2.
• The damage curve is monotone in [0, 1] and the reported index equals a fresh value-weighted sum.

Honest simplifications

• This is a static, steady-water-level model. Real floods depend on storm duration, wave run-up, rainfall and river discharge, and flow speed, none of which are modelled; there is no time stepping of the water.
• The terrain is an invented delta shaped like real ones, not a survey of a particular place. Subsidence, sediment supply and erosion are ignored.
• Buildings are placed by a fixed random seed. The seawall is a single straight wall with no gates, drains or failure.

What to try

• Pick "Severe storm, no mangroves" then "Severe storm, wide mangroves": compare the flooded flanks and the damage index.
• Raise the sea level until the unconnected bathtub figure and the connected figure separate.
• Raise the wall above sea level plus surge to see the town stay dry, then lower it by 10 cm to see it overtop.