Why Shanghai’s Flooding Is So Severe: Rainfall Intensity vs Drainage Capacity

Typhoon “Bai Hai Dolphin” is expected to bring 150–180 mm of rain to Shanghai, locally 200–230 mm and possibly >250 mm, with peak hourly intensity 60–80 mm/h.

On 19 July, Shanghai recorded 212.8 mm total at Yangpu Wujiaochang, with a peak of 104.5 mm/h, causing noticeable waterlogging.

Rainfall rate vs total amount

When the same total depth falls slowly (e.g., 100 mm over 24 h → ~4 mm/h), the drainage system can discharge water continuously. If the same depth falls within one hour (100 mm/h), the inflow exceeds the outflow capacity, creating a bottleneck analogous to a highway toll plaza.

The decisive metric is the volume of water entering the drainage network per unit time.

Urban flood model

For a given district with surface area A (m²) and rainfall intensity I (mm/h), the raw inflow rate is I·A·10⁻³ m³/h (assuming 1 mm = 1 L/m²). A runoff coefficient C (0 ≤ C ≤ 1) accounts for infiltration and temporary retention, giving effective inflow Q_in = C·I·A·10⁻³.

The drainage capacity Q_out (m³/h) aggregates the discharge capability of underground pipes, pump stations, rivers, and outlets.

The water stored on the surface evolves as ΔS/Δt = Q_in – Q_out If Q_in ≤ Q_out, ΔS stays near zero and water is drained promptly. If Q_in > Q_out, excess water accumulates on roads, underground spaces, and low‑lying areas, producing urban flooding.

Buffer storage and delayed flooding

Cities possess temporary storage: pipe volume, green‑space infiltration, ponds, and detention facilities. Let S_max be the total buffer capacity (m³). While Q_in > Q_out, the buffer is depleted at rate Q_in – Q_out. The time until exhaustion is t_buffer = S_max / (Q_in – Q_out) When the buffer is exhausted, surface water level rises rapidly, turning streets into temporary rivers.

Why drainage cannot be made unlimited

Expanding pipe diameters and pump stations to handle the most extreme historical rainfall would require massive reconstruction of roads, utilities, and outlets, incurring prohibitive cost while remaining idle most of the time. Consequently, design targets protection of critical infrastructure (e.g., subway tunnels) during extreme events and rapid post‑storm drainage, rather than guaranteeing zero waterlogging for any conceivable storm.

Key quantitative questions for extreme rain

What is the instantaneous rainfall intensity ( I)?

What is the city’s instantaneous drainage capacity ( Q_out)?

Given Q_in > Q_out, how long can the buffer S_max sustain the excess before flooding occurs?

These three questions define the mathematical model of urban waterlogging.