The seawall protects the city while the still-water level plus wave run-up rises. Overtopping occurs whenever the instantaneous crest height exceeds the wall's freeboard.
crest(t) = SWL + A·sin(ωt + kx)
freeboard = wall_height − SWL
overtop if crest > wall_height
dFlood/dt = Q_in(overtop) − Q_pump(drain)
- Wall height — raises the defensive freeboard against surge and waves.
- Storm surge / sea level — the still-water level (SWL) driven by tide and storm surge.
- Wave energy — scales wave amplitude A, increasing crest height and run-up.
- Pump drainage rate — how fast floodwater is pumped out from behind the wall once it overtops.
Real-world application: coastal engineers size seawalls, levees and pump stations using exactly this balance of freeboard vs. surge-plus-wave run-up, informing designs like the Thames Barrier or Rotterdam's Maeslantkering.