The sea rises at the coast for three separate reasons: the tide, the low pressure of the storm, and wind pushing water onto a shallow shelf. Waves ride on top. Change the storm and see when the wall is overtopped, and why timing against high tide matters.
-peak total water level (above mean sea level)
-smallest freeboard (crest minus water)
-wind setup at the peak
-inverse barometer at the peak
-wave height at the wall (Hs, depth-limited)
-peak overtopping (litres per second per metre)
-water over the wall in 36 h (m3 per metre)
-flood depth behind the wall (basin model, capped by sea level)
The science
Four ingredients. Total water level at the wall = astronomical tide + inverse barometer + wind setup + wave setup. The tide is a cosine with the M2 period of 12.42 h. The inverse barometer is the sea rising where air pressure falls: eta = dP / (rho g), about 1 cm per hPa.
Wind setup. Wind drags the surface with stress tau = rho_air Cd U^2 (Cd from the Wu form, capped at 2.8e-3). In steady state, with the coast closed, the water surface tilts until the slope balances the stress: d eta/dx = tau / (rho g (h + eta)). We integrate this along a linear shelf with fourth-order Runge-Kutta. On a flat shelf it has the closed form eta = sqrt(h^2 + 2 tau L / (rho g)) - h: setup grows with fetch L, with wind speed squared, and is larger where the water is shallow (the 1/h factor).
Waves. Deep-water significant wave height comes from a fetch-limited fit, Hs = 0.0016 U sqrt(F/g). At the wall, Hs is limited by depth to about 0.55 of the local depth because bigger waves break, and the wave setup is taken as 10 % of Hs.
Overtopping. With freeboard Rc (crest minus still water) the mean discharge per metre is q = 0.2 sqrt(g Hs^3) exp(-2.6 Rc / Hs), an envelope form of the EurOtop manual for a smooth sloping wall; if the still water is above the crest a broad-crested weir term 0.54 sqrt(g) |Rc|^1.5 is added. Flooding depth assumes all the water collects in a flat basin of the length you choose, with no drainage and no return flow.
Why timing matters. Overtopping depends exponentially on freeboard, so the same surge on top of low tide is nearly harmless and on top of high water is not. The experiment shifts the surge peak through half a tidal cycle on either side of high water.
Honest limits. The model is one-dimensional and quasi-steady (valid when the storm lasts longer than the shelf adjustment time L / sqrt(g h), shown above). It leaves out the Coriolis force, Ekman transport and trapped coastal waves, tide-surge interaction, bottom friction, and the shape of real coastlines (bays and estuaries can double a surge). Coefficients are typical values; check them against the literature before quoting a number. The 3D scene is a stylised diorama: horizontal distances are compressed and the sea depth drawn is not your shelf depth. Wave motion is a visual sum of sine waves whose height follows Hs. This is an educational model, not a forecast.