Hydrology is the science of water occurrence, distribution, movement, and properties at and below the earth's surface. For civil engineers, engineering hydrology provides the tools to estimate design flood discharges for culverts, bridges, dams, and drainage systems. IS 5477 (1969, revised 2002) provides flood estimation methods for Indian rivers.
The Hydrological Cycle
The continuous movement of water in the earth-atmosphere system:
Precipitation → Interception (vegetation) + Infiltration (soil) + Surface Runoff → Evaporation + Transpiration → Atmospheric moisture → Precipitation
Water balance equation: P = Q + E + ΔS
where P = precipitation, Q = streamflow, E = evapotranspiration, ΔS = change in storage (soil moisture, groundwater, reservoirs)
Precipitation Analysis
Rainfall Measurement
- Rain gauges: Non-recording (Symons gauge, manual reading) and self-recording (tipping bucket, float type)
- Radar rainfall: IMD Doppler weather radars provide spatial coverage
- Satellite rainfall: TRMM, GPM datasets — used for ungauged catchments
Average Rainfall Over a Catchment
Three methods:
- Arithmetic Mean: Simple average of all gauge readings — suitable for flat terrain, uniform density
- Thiessen Polygon: Weighted average based on area of influence of each gauge — more accurate
- Isohyetal Method: Draw lines of equal rainfall (isohyets); most accurate but laborious
Rainfall Intensity-Duration-Frequency (IDF) Curves
Design rainfall intensity for any duration and return period:
i = KT^x / (t + a)^n (Sherman formula)
or Talbot formula: i = a / (t + b)
IMD provides IDF data for major cities. For return period T and duration t (minutes):
From Gumbel extreme value distribution: x_T = x̄ + K_T × σ
where K_T = (y_T − ȳ_n) / S_n (reduced variate from Gumbel tables)
Runoff Estimation — Rational Method
Peak discharge from small catchments (< 50 km²):
Q_p = C × i × A / 360 (Q in m³/s, i in mm/hr, A in hectares)
or Q_p = C × i × A / 3.6 (A in km²)
- C = runoff coefficient (dimensionless, 0–1)
- i = rainfall intensity for duration = time of concentration (tc), for the design return period
- A = catchment area
Runoff Coefficients (C values)
| Land Use / Surface | C (10-year return period) |
|---|---|
| Paved roads and rooftops | 0.70–0.95 |
| Gravel roads | 0.35–0.70 |
| Cultivated land (row crops) | 0.20–0.40 |
| Meadows / pastures | 0.10–0.35 |
| Forest / woodland | 0.05–0.25 |
| Urban commercial/dense | 0.70–0.95 |
| Urban residential (low density) | 0.25–0.40 |
Time of Concentration (tc)
Time for runoff to travel from the farthest point of the catchment to the outlet:
Kirpich formula: tc = 0.00195 × L^0.77 / S^0.385 (minutes)
where L = length of longest watercourse (m), S = slope of watercourse (m/m)
SCS Curve Number (CN) Method
More accurate for larger catchments and variable soil/land use:
Q = (P − 0.2S)² / (P + 0.8S) for P > 0.2S; else Q = 0
where S = 25400/CN − 254 (mm), P = storm rainfall depth (mm)
CN values range from 30 (forests, sandy soils) to 98 (impervious paved areas).
Unit Hydrograph
A unit hydrograph (UH) is the hydrograph resulting from 1 mm (or 1 cm) of direct runoff from a specific catchment produced by a unit storm of specified duration.
Key properties:
- Linearity: 2× the rainfall produces 2× the runoff (same time base)
- Time invariance: Same UH for all storms of that duration
- Superposition: Convolution of rainfall excess with UH gives total runoff hydrograph
Snyder's Synthetic Unit Hydrograph
For ungauged catchments:
tp = Ct × (L × Lc)^0.3
Qp = 2.78 × Cp × A / tp
- tp = lag time (hours) from centroid of rainfall to peak of UH
- L = length of main stream (km); Lc = distance to centroid (km)
- Ct = 1.35–1.65 (catchment physiography coefficient); Cp = 0.56–0.69
IS 5477 Part 3 provides procedures for deriving UH from observed flood data.
Flood Frequency Analysis
Annual maximum flood series: rank floods in decreasing order; assign return periods
Weibull plotting position: T = (n+1)/m (m = rank, n = years of record)
Gumbel's Extreme Value Distribution (EV1):
x_T = x̄ + K × σ
K = −(√6/π) × [0.5772 + ln(ln(T/(T−1)))]
For T = 100: K ≈ 3.14; T = 50: K ≈ 2.59; T = 25: K ≈ 2.04
Used to estimate T-year flood (design flood) when long flow records are available.
IS 5477 — Flood Estimation in India
IS 5477 provides four methods based on available data and catchment characteristics:
- Part 1: Estimation from rainfall (for ungauged catchments; rational method + empirical formulae)
- Part 2: Estimation from rainstorm data (rainfall-runoff relationships)
- Part 3: Unit hydrograph method
- Part 4: Flood frequency analysis (for gauged catchments with ≥10 years data)
Dicken's formula (empirical, India): Q = C × A^(3/4), C = 11–22 for plains, 22–35 for hilly regions — used for quick estimates when detailed data is unavailable.
Design Flood Return Periods (India)
| Structure | Design Return Period (years) |
|---|---|
| Road culvert (minor) | 25 |
| Road culvert / bridge (NH) | 50 |
| Railway bridge | 100 |
| Small dam (<10 m) | 100 |
| Medium dam (10–30 m) | 1000 |
| Large dam / reservoir | PMF (Probable Maximum Flood) |
Frequently Asked Questions
What is the difference between rational method and unit hydrograph method?
The rational method gives only the peak discharge (Q_p) assuming a uniform catchment response — suitable for small catchments (<50 km²) and simple drainage design. The unit hydrograph method produces a complete flood hydrograph (Q vs time) accounting for the catchment's temporal response — essential for routing through reservoirs, designing spillways, and flood inundation mapping for larger catchments.
What is a Probable Maximum Flood (PMF) and when is it used?
PMF is the maximum flood that is physically possible from the most severe combination of critical meteorological conditions and runoff factors for the drainage basin. It is used for the design of spillways and freeboard of large dams and nuclear facilities — structures where failure would cause catastrophic loss of life. PMF is estimated from PMP (Probable Maximum Precipitation) derived by hydrometeorological methods per IMD guidelines.