SimuVeda

Environment · Simulator 087

Watershed Runoff

When rain falls on a catchment, some soaks in and some runs off into streams. Change the size of the storm and what covers the land, from forest to car parks. Compare how much water runs off and how high and how fast the stream peaks, and see why building over fields raises flood risk.

How the model works

The SCS curve number method (USDA) sums up land cover and soil in one number CN from 0 to 100. It sets the maximum retention S = 25400/CN − 254 mm and an initial abstraction I_a = 0.2 S (rain caught by leaves, puddles and the first soaking). Runoff depth for a storm of P mm is

Q = (P − I_a)² / (P − I_a + S) for P > I_a, otherwise 0

The left chart shows this runoff curve for both land covers: forest soaks up most storms, while paving sheds almost everything.

To turn runoff depth into stream flow, the model spreads each tenth of an hour's runoff over a triangular unit hydrograph. It peaks at t_p = Δt/2 + 0.6 T_c, where T_c is the time of concentration (how long water takes to travel from the far edge of the catchment), with peak flow q_p = 0.208 A / t_p m³/s per mm of runoff (A in km², t_p in hours). Smooth paved surfaces and drains shorten T_c, so the same runoff arrives faster and peaks higher.

Simplified: uniform rain over the storm duration, one soil type (hydrologic group B), no baseflow, channel storage or snowmelt, and curve numbers taken from standard tables. The curve number method is meant for design storms, not detailed forecasts.

Guided experiments

  1. Forest versus pasture. A 50 mm storm over 2 hours on a 5 km² catchment. Prediction: forest (CN 55) holds back almost everything: only about 0.3 mm runs off. Grassland (CN 69) sheds about 5.2 mm, with a peak of about 3.8 m³/s.
  2. Urbanization. Replace the pasture with commercial land (CN 92) and drains that halve T_c to 1 hour. Prediction: runoff rises about six-fold to 30.7 mm and the peak about seven-fold to 27 m³/s, arriving almost an hour earlier.
  3. Bigger storm. 100 mm in 6 hours on grassland vs commercial. Prediction: grassland now sheds about 31 mm because the soil is saturating; the gap between land covers narrows as storms grow.

Challenge

A 30 mm storm falls on land with CN = 80. Will there be any runoff? How large a storm is needed before any runoff starts?

Reveal the explanation

S = 25400/80 − 254 = 63.5 mm and I_a = 0.2 × 63.5 = 12.7 mm. Since 30 > 12.7, Q = (17.3)² / (17.3 + 63.5) ≈ 3.7 mm runs off. Runoff starts once the storm exceeds I_a = 12.7 mm.

References

  • USDA Natural Resources Conservation Service (1986), Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55).
  • USDA NRCS, National Engineering Handbook, Part 630 Hydrology, ch. 9–10 and 16.
  • Chow, V. T., Maidment, D. R. and Mays, L. W., Applied Hydrology (1988), ch. 5 and 7.