Why does lower pressure raise sea level?

Lower atmospheric pressure presses less on the ocean surface. Hydrostatic balance gives Δη ≈ Δp/(ρg), so a 50 hPa pressure deficit raises water by roughly 0.5 m even without wind.

Why does shelf depth matter so much?

The wind setup estimate scales like 1/H. Over shallow shelves, a given wind stress has less water depth to accelerate and tilt, so coastal water level rises more for the same wind and fetch.

Is the tide part of storm surge?

Strictly, storm surge is the meteorological residual. Flood level is surge plus astronomical tide and wave runup. The tide slider is included because timing with high tide strongly affects coastal impact.

Storm track, coastline shape, Coriolis, bottom friction, wave setup, river flow, nonlinear shallow-water dynamics, and local topography are not modeled.

Storm Surge Bathtub + Wind Setup

Inverse barometer pressure setup plus wind stress τL/(ρgH) over a shelf; coastal water level and tide timing toy.

Live graphs

About this model

Storm surge is the abnormal coastal water level produced by storm pressure and wind forcing, often on top of the astronomical tide. This simulator uses a deliberately simple “bathtub” balance: the inverse barometer contribution is Δη_p = (p_ref − p_c)/(ρ_w g), about 1 cm per hPa pressure drop, and the wind setup over a shallow continental shelf is estimated as Δη_w ≈ τL/(ρ_w gH), where τ = ρ_air C_d U² is wind stress, L is shelf fetch, and H is shelf depth. A broad, shallow shelf lets the same wind stress pile up much more water than a steep deep coast. The canvas shows mean sea level, the pressure-induced offshore lift, the wind-driven ramp toward the coast, an optional tide offset, and component bars. This is a scale model for intuition, not a predictive coastal-flood model.

Who it's for: Students in oceanography, coastal engineering, meteorology, and environmental physics learning first-order storm-surge controls before numerical shallow-water models.

Key terms

Storm surge
Inverse barometer
Wind setup
Wind stress
Continental shelf
Coastal flooding
Astronomical tide
Shallow water

How it works

Storm surge bathtub model: pressure drop, wind stress over a continental shelf, shelf depth, and resulting coastal water level.

Key equations

Δη_pressure = (p_ref − p_c)/(ρ_w g)

Δη_wind ≈ τL/(ρ_w g H), τ = ρ_air C_d U²

Frequently asked questions

Why does lower pressure raise sea level?: Lower atmospheric pressure presses less on the ocean surface. Hydrostatic balance gives Δη ≈ Δp/(ρg), so a 50 hPa pressure deficit raises water by roughly 0.5 m even without wind.
Why does shelf depth matter so much?: The wind setup estimate scales like 1/H. Over shallow shelves, a given wind stress has less water depth to accelerate and tilt, so coastal water level rises more for the same wind and fetch.
Is the tide part of storm surge?: Strictly, storm surge is the meteorological residual. Flood level is surge plus astronomical tide and wave runup. The tide slider is included because timing with high tide strongly affects coastal impact.
What is left out?: Storm track, coastline shape, Coriolis, bottom friction, wave setup, river flow, nonlinear shallow-water dynamics, and local topography are not modeled.

Continue with similar topics in this category — or all 37 in Waves & Sound.

View category →

NewUniversity / research

Tsunami & Shallow Water (1D)

Launch Simulator

Linear η,u on H(x): c = √(gH) drops over shelf; Gaussian uplift impulse.

NewSchool

Water Wave Dispersion ω(k)

Launch Simulator

Shallow k√(gh), deep √(gk), full tanh(kh) — three curves.

NewSchool

Hearing & Loudness (sketch)

Launch Simulator

Qualitative threshold vs frequency; compare to equal-loudness ideas.

NewSchool

Larsen Effect (Feedback Loop)

Launch Simulator

Mic + speaker + delay: loop gain and saturation in a toy discrete feedback model.

NewSchool

Tide Constituents & Beats

Launch Simulator

M2/S2/K1/O1 harmonic superposition, spring-neap beat cycle, diurnal inequality, and an amphidromic phase cartoon.

NewSchool

Kelvin Ship Wake (Cusp Angle)

Launch Simulator

Deep-water wake V: arms at arcsin(1/3) ≈ 19.47° each side of the track (idealized).

Storm Surge Bathtub + Wind Setup

Live graphs

About this model

How it works

Key equations

Frequently asked questions

Related simulators

Tsunami & Shallow Water (1D)

Water Wave Dispersion ω(k)

Hearing & Loudness (sketch)

Larsen Effect (Feedback Loop)

Tide Constituents & Beats

Kelvin Ship Wake (Cusp Angle)

Storm Surge Bathtub + Wind Setup

Live graphs

About this model

How it works

Key equations

Frequently asked questions