Floods — Estimation & Flood Routing — Hydrology & Irrigation Engineering Notes

Last reviewed 16 Sept 2026 · 8 min read

Floods and design floods

A flood is an unusually high stage in a river, normally when it overflows its banks. Hydraulic structures must be designed to pass a chosen design flood safely.

Design flood	Meaning
Probable maximum flood (PMF)	Extreme flood from the most severe combination of meteorological and hydrological conditions reasonably possible in the region (derived from PMP)
Standard project flood (SPF)	Flood from the most severe combination considered reasonably characteristic of the region, excluding extremely rare combinations; typically a fraction of the PMF
T-year flood	Flood with return period T years, found by frequency analysis

Indian guidelines for dam spillways (IS 11223)

Dams are classified by the more severe of gross storage and hydraulic head:

Class	Gross storage	Hydraulic head	Inflow design flood
Small	0.5 – 10 million m³	7.5 – 12 m	100-year flood
Intermediate	10 – 60 million m³	12 – 30 m	Standard project flood
Large	> 60 million m³	> 30 m	Probable maximum flood

Smaller structures such as culverts, cross-drainage works and barrages use return periods chosen by their importance and the consequences of failure.

Methods of flood estimation

Physical indications of past floods (flood marks, local enquiry) + slope–area method.
Envelope curves — maximum observed flood peaks plotted against catchment area for a hydrologically similar region.
Empirical formulas.
Rational method — small catchments.
Unit hydrograph method — design storm applied to the UH.
Flood frequency analysis — statistical.

Empirical formulas

FormulaEmpirical flood formulas (

Q_{p}

in m³/s,

A

in km²)

Dickens' formula (central and northern India):

Q_{p} = C_{D} A^{3/4}

$C_{D}$ ≈ 6 (north Indian plains), 11–14 (north Indian hilly regions), 14–28 (central India), 22–28 (coastal Andhra and Odisha).

Ryves' formula (Tamil Nadu and parts of Karnataka, Andhra Pradesh):

Q_{p} = C_{R} A^{2/3}

$C_{R}$ = 6.8 (within 80 km of the east coast), 8.5 (80–160 km from the coast), 10.2 (limited areas near hills).

Inglis' formula (fan-shaped catchments of old Bombay State):

Q_{p} = \frac{124 A}{A + 10.4}

Empirical formulas give no return period and are only rough estimates for regions where they were developed.

Rational method

FormulaRational formula

Q_{p} = \frac{C i A}{3.6} (i in mm/h, A in km^{2}, Q_{p} in m^{3} / s)

$C$ = runoff coefficient; $i$ = rainfall intensity for a duration equal to the time of concentration $t_{c}$ and the design return period.

Kirpich formula for time of concentration:

t_{c} = 0.01947 L^{0.77} S^{- 0.385}

( $t_{c}$ in minutes, $L$ = maximum length of travel in m, $S$ = slope $H / L$ .)

Assumes the peak occurs when the whole catchment contributes (rainfall duration ≥ $t_{c}$ ) and that rainfall is uniform in space and time.
Suited to small catchments (commonly below about 50 km²) — urban storm drains, culverts and airports.
For a composite catchment: $Q_{p} = \frac{i \sum C _{j} A _{j}}{3.6}$ .

Flood frequency analysis

The annual maximum flood series is fitted to a probability distribution. The general equation (Chow):

x_{T} = \overset{x}{ˉ} + K σ_{n - 1}

Gumbel's extreme value distribution

FormulaGumbel's method

Reduced variate: $y_{T} = - ln [ln \frac{T}{T - 1}]$

Frequency factor: $K = \frac{y _{T} - y ˉ _{n}}{S _{n}}$ ( $\overset{y}{ˉ}_{n}$ , $S_{n}$ from tables for sample size $N$ )

For very large samples ( $\overset{y}{ˉ}_{n} \to 0.5772$ , $S_{n} \to 1.2825$ ):

K = - \frac{6}{π} [0.5772 + ln ln \frac{T}{T - 1}]

Confidence limits: $x_{T} \pm f (c) S_{e}$ , where $S_{e}$ is the probable error.

Gumbel plots as a straight line on Gumbel probability paper.
The mean annual flood has a return period of about 2.33 years in the Gumbel distribution.

Log-Pearson Type III

The logarithms of floods are fitted: $z_{T} = \overset{z}{ˉ} + K_{z} σ_{z}$ , where $K_{z}$ depends on the return period and the coefficient of skew of the log series; $x_{T} = 1 0^{z_{T}}$ . It is the standard method in USA practice (with regional skew weighting).

Risk, reliability and safety factor

FormulaRisk and reliability

Risk of a T-year event being exceeded at least once in $n$ years (design life): $R = 1 - (1 - \frac{1}{T})^{n}$
Reliability $= 1 - R$
Safety factor $= \frac{actual value adopted in design}{hydrological estimate}$ ; safety margin = difference.

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Floods — Estimation & Flood Routing