Indiacon Civil

Subjects › Hydrology › Intermediate

Unit hydrograph

Intermediate Hydrology Reviewed 24 Oct 2026 2 min read

The unit hydrograph is a simple but powerful tool for turning rainfall into a flood hydrograph. Proposed by Sherman, it is defined as the direct runoff hydrograph produced by one unit (1 cm or 1 mm) of rainfall excess falling uniformly over the catchment at a uniform rate for a specified duration D. It captures how a particular catchment responds.

Two assumptions make it work. Linearity: a storm of the same duration with twice the excess gives a hydrograph with twice the ordinates. Time invariance: the response does not depend on when the storm occurs. So the flood from a complex storm can be built by breaking the storm into blocks of duration D, multiplying the unit hydrograph by each block's excess, lagging each by its start time and adding them up (convolution).

Diagram: Indiacon original, not to scale.

A unit hydrograph is derived from observed storms on gauged catchments: separate base flow, compute the runoff depth, and divide the direct runoff ordinates by that depth. Several storms are averaged. Changing duration is done by superposition for multiples of D or by the S-curve method for any duration. For ungauged catchments, synthetic unit hydrographs relate peak, time to peak and widths to catchment area, length, slope and other characteristics; Indian practice uses regional relations published for hydro-meteorological subzones. The method is used for spillway, bridge and culvert design floods.

Tip

Check that the area under your unit hydrograph equals exactly one unit of depth over the catchment.

Key formulas
  • UH ordinate = DRH ordinate / runoff depth
  • Storm DRH: Q(t) = Σ Pₑ,ᵢ × U(t − (i − 1)D)
  • S-curve: S(t) = Σ U lagged by D; new UH of duration D′: [S(t) − S(t − D′)] × D/D′
Common mistake

Applying a unit hydrograph derived for one duration directly to excess blocks of a different duration.

Solved example

Problem. A 3-hour unit hydrograph (1 cm) has ordinates 0, 15, 40, 28, 14, 5, 0 m³/s at 3-hour intervals. Find the DRH for two successive 3-hour blocks of excess, 2 cm then 1 cm.

  1. First block × 2: 0, 30, 80, 56, 28, 10, 0.
  2. Second block × 1, lagged 3 h: 0, 0, 15, 40, 28, 14, 5, 0.
  3. Add: 0, 30, 95, 96, 56, 24, 5, 0 m³/s.
  4. Peak ≈ 96 m³/s at 9 hours.

Answer. Peak about 96 m³/s

Quick quiz

1Define a unit hydrograph.

The DRH from one unit of rainfall excess of duration D over the catchment.

2Name the two key assumptions.

Linearity and time invariance.

3Which method changes UH duration to any value?

The S-curve method.

Code note

    Clauses and documents to read

    • CWC flood estimation reports (regional synthetic unit hydrograph relations, cited by name)

    Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.

    References and further reading

    Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.

    • K. Subramanya, Engineering Hydrology, McGraw Hill Education (India), latest edition.
    • V. T. Chow, D. R. Maidment, L. W. Mays, Applied Hydrology, McGraw Hill, 1988.

    Free and official sources

    All references for this subject →

    Found an error? Write to indiacongroupofengineers [at] gmail [dot] com. For corrections and feedback. We never ask for payment or personal details.