Runoff

Introduction to Runoff

Runoff is the portion of precipitation that flows over the land surface and eventually reaches streams, rivers, or oceans. It is the output of the catchment system.

Components of Runoff:

1. Overland Flow: Water flowing over the land surface before reaching a channel.
2. Interflow: Water moving laterally in the upper soil layers.
3. Baseflow: Groundwater contribution to streamflow.

Catchment Characteristics

The Catchment Area (Watershed or Drainage Basin) is the area of land where precipitation collects and drains off into a common outlet.

• Area: Total surface area ($A$).
• Slope: Steeper slopes produce faster and higher peak runoff.
• Shape:
  • Fan-shaped: Runoff from different points reaches outlet simultaneously $\to$ High Peak.
  • Fern-shaped (Elongated): Runoff reaches outlet at different times $\to$ Low Peak.
• Land Use: Urbanization (impervious surfaces) increases runoff volume and peak flow.

Rainfall-Runoff Relationships

The Rational Method

A simple empirical method used for estimating peak discharge ($Q_p$) for small catchments ($< 50$ km$^2$), primarily in urban drainage design.

Where:

• $Q_p$ = Peak discharge (m$^3$/s)
• $C$ = Runoff coefficient (0 to 1, dimensionless). Represents the fraction of rain that becomes runoff.
• $I$ = Rainfall intensity (mm/hr) for a duration equal to the Time of Concentration ($t_c$).
• $A$ = Catchment area (km$^2$).

Note: The constant 0.278 converts units. If $A$ is in hectares and result in L/s, the formula is roughly $Q = CIA / 360$.

Time of Concentration ($t_c$)

The time required for water to flow from the most remote point of the catchment to the outlet. Kirpich's Formula is commonly used:

Where:

• $t_c$ = Time of concentration (minutes)
• $L$ = Length of main channel (m)
• $S$ = Average slope (m/m)

Flow Duration Curve

A cumulative frequency curve that shows the percentage of time specified discharges were equaled or exceeded during a given period.

• Q50: Median flow.
• Q90: Low flow (available 90% of the time).