Hydrology: Precipitation, Losses and Runoff

Hydrology estimates how much water a catchment gives and when. It feeds the design of dams, bridges, drains and irrigation systems.

Precipitation

• Rain gauges: non-recording (Symons) and recording (tipping bucket, weighing, float).
• Average rainfall over a catchment:
• Arithmetic mean (flat areas, even gauges).
• Thiessen polygon: each gauge weighted by its area of influence: P = Σ PᵢAᵢ/ΣAᵢ.
• Isohyetal: areas between lines of equal rainfall; the most accurate.
• Missing data (normal ratio method): P_x = (N_x/n) Σ(Pᵢ/Nᵢ), used when normal rainfalls differ by more than 10%.
• Double mass curve: checks the consistency of a gauge record; a break in slope means a change in the gauge site or exposure.
• Optimum number of gauges: N = (C_v/ε)², with C_v the coefficient of variation of rainfall and ε the allowable error (%).

Losses

• Evaporation: measured with pans (Class A pan coefficient about 0.7).
• Infiltration: Horton's equation f = f_c + (f₀ − f_c) e^(−kt).
• φ-index: the constant loss rate such that rainfall above it equals the runoff volume. W-index excludes initial losses.

Runoff

• Rational method (small catchments): Q = C i A/3.6 (Q in m³/s, i in mm/h, A in km²), with i for a duration equal to the time of concentration t_c.
• t_c from Kirpich's formula.
• Runoff coefficient C is about 0.7–0.95 for paved areas and 0.1–0.3 for grassland.

Hydrographs

A hydrograph plots discharge against time at a point: rising limb, crest, recession limb. Base flow is separated out to get the direct runoff hydrograph (DRH).

Worked example

A catchment of 2 km² has C = 0.5 and design intensity 72 mm/h.

• Q = 0.5 × 72 × 2/3.6 = 20 m³/s.

Practice