Hydrology

Hydrology quantifies water in the environment. Learn the hydrologic cycle, rainfall (intensity–duration–frequency, return periods and risk), infiltration and runoff (rational method, SCS-CN), time of concentration, hydrographs and unit hydrographs, and flood design.

Before you can size a culvert, a drain, a dam spillway or a flood wall, you need to know how much water will arrive and how fast. Hydrology turns rainfall into runoff estimates and design floods.

Because rainfall is random, hydrology is statistical: designs target events with a chosen return period (e.g. the 100-year flood) and accept a known risk.

An analogy

A catchment is like a funnel: rain falling anywhere drains to one outlet. The funnel's size, steepness and surface (grass vs concrete) decide how big and quick the outflow peak is.

The hydrologic cycle

Evaporation → condensation → precipitation → interception, infiltration and runoff → streams, groundwater and back to the sea. Urbanisation replaces soil and vegetation with impervious surfaces, increasing runoff volume and peaks.

Design rainfall and return periods

IDF curves give rainfall intensity for a duration and return period. A 100-year event has a 1 % chance each year — and a 39.5 % chance of occurring at least once in 50 years. Minor drains use 2–10 year events; major floodways and dams 100–10 000 years or PMF.

Peak runoff: rational method

For small catchments (< ~1–3 km²), peak flow Q = CiA, using rainfall intensity for a duration equal to the time of concentration (the time for water from the farthest point to reach the outlet). C ranges from 0.1–0.3 (parks) to 0.7–0.95 (roofs, roads).

Hydrographs and flood modelling

The unit hydrograph (response to 1 cm of effective rain) convolved with a rainfall series gives the flood hydrograph; SCS-CN estimates effective rain. Reservoir routing attenuates peaks. Continuous and event models (HEC-HMS, SWMM) and climate-change allowances are used for modern flood design.

Formulas

• Rational method: Q = 0.278 C i A (Q m³/s, i mm/h, A km²)
• Risk of exceedance in n years: R = 1 − (1 − 1/T)ⁿ
• Kirpich t_c: t_c = 0.0195 L^0.77 S^(−0.385) (min, L in m)
• SCS-CN runoff: Q = (P − 0.2S)²/(P + 0.8S), S = 25 400/CN − 254 (mm)
• Water balance: P = Q + ET + ΔS + G

Worked example: Rational method peak flow

Given: A = 2 km² residential, C = 0.7; i = 50 mm/h for t_c

Find: Peak runoff.

• Q = 0.278 × 0.7 × 50 × 2 = 19.5 m³/s

Answer: ≈ 19.5 m³/s

Worked example: SCS-CN runoff depth

Given: Storm P = 60 mm; CN = 80

Find: Runoff depth.

• S = 25 400/80 − 254 = 63.5 mm
• Q = (60 − 12.7)²/(60 + 50.8) = 20.2 mm

Answer: ≈ 20 mm of runoff (≈ 34 %)

Common mistakes

• Wrong: Using the rational method for large catchments. — Right: Use hydrograph methods beyond a few km².
• Wrong: Choosing rainfall duration arbitrarily. — Right: Use intensity for duration = time of concentration.

Applications

• Urban drainage: Storm sewers, detention ponds and sustainable drainage (SuDS).
• Dams & spillways: Design floods and reservoir routing.
• Bridges & culverts: Waterway opening and scour depth from design floods.

Key takeaways

• Q = 0.278 CiA for small catchments.
• Risk = 1 − (1 − 1/T)ⁿ.
• t_c sets the design storm duration.
• Use hydrographs and routing for larger systems.

Going further

• Frequency analysis: Gumbel, log-Pearson III and GEV distributions fit annual maxima for design floods.
• Climate change: Design rainfall uplifts (10–40 %) are now required in many codes.
• Groundwater hydrology: Aquifer tests, well hydraulics (Theis, Thiem) and recharge estimation.