Flood estimation
Every bridge, culvert, spillway, embankment and urban drain must pass a design flood. Underestimating it risks failure and loss of life; overestimating wastes money. Engineers choose a method according to the data available and the importance of the structure.
Empirical formulas, such as Dickens' and Ryves' formulas, relate peak flood to catchment area with a regional coefficient. They are quick but crude. The rational method, Q = C i A, suits small catchments, usually under a few square kilometres, such as urban drains and culverts: the design intensity is taken for a duration equal to the time of concentration. Unit hydrograph methods, with design storm rainfall, suit medium catchments and are widely used in India through regional flood estimation reports. Flood frequency analysis fits a statistical distribution (Gumbel, log-Pearson Type III and others) to the annual maximum floods recorded at a gauge, giving the flood for a chosen return period.
Return period T is the average interval between floods equal to or larger than a given size. A 100-year flood has a 1 percent chance of being exceeded in any one year, and a significant chance during a structure's life. Major dams use the probable maximum flood, from probable maximum precipitation, because failure would be catastrophic. Climate change and land-use change mean historical records may not represent the future, so sensitivity checks are increasingly expected.
Rational: Q = C i A / 3.6 (Q m³/s, i mm/h, A km²)Dickens: Q = C_D A^(3/4)Gumbel: Q_T = Q̄ + K_T σ; K_T = −(√6/π)[0.5772 + ln ln(T/(T − 1))]Risk over n years: R = 1 − (1 − 1/T)ⁿ
Problem. Annual maximum floods at a site have mean 1 450 m³/s and standard deviation 520 m³/s over a long record. Estimate the 100-year flood by Gumbel (large-sample K_T) and the risk of exceeding it in 50 years.
- K₁₀₀ = −0.7797 × [0.5772 + ln ln(100/99)] = −0.7797 × [0.5772 + ln(0.01005)] = −0.7797 × (0.5772 − 4.600) = 3.137.
- Q₁₀₀ = 1 450 + 3.137 × 520 = 3 081 m³/s.
- Risk in 50 years = 1 − 0.99⁵⁰ = 0.395.
Answer. About 3 080 m³/s; about 40 percent risk in 50 years
Quick quiz
1When is the rational method suitable?
For small catchments such as urban drains and culverts.
2What does a 100-year flood mean?
A flood with a 1 percent chance of being exceeded in any year.
3What design flood is used for major dams?
The probable maximum flood.
Clauses and documents to read
- IRC:SP:13-2004 (guidelines for design of small bridges and culverts)
- IRC:5-2015 (standard specifications, road bridges, general features)
- CWC flood estimation reports (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
Found an error? Write to indiacongroupofengineers [at] gmail [dot] com. For corrections and feedback. We never ask for payment or personal details.