A 4-hours rainfall in a catchment of 250 km² produces rainfall depths of 6.2 cm and 5.0 cm in successive 2-hour unit periods. Assuming the φ index of the soil to be 1.2 cm/hour, the runoff volume in ha-m will be

Concept:

Role of ϕ-index in rainfall

If rainfall is less than ϕ-index then, the infiltration rate is given as

Infiltration rate = Rainfall rate

If rainfall is greater than ϕ-index then, the infiltration rate is given as

Infiltration rate = ϕ-index

That means, above the infiltration rate

Excess rainfall = Runoff

Calculation:

Given,

Catchment area = 250 km²

Rainfall depths are 6.2 cm and 5.0 cm in successive 2 hr periods

∴ Rainfall depths in 1 hr period are 6.2/2 = 3.1 cm/hr and 5/2 = 2.5 cm/hr

ϕ-index = 1.2 cm/hour

Runoff depth = (3.1 - 1.2) × 2 + (2.5 - 1.2) × 2 = 3.8 + 2.6 = 6.4 cm

Runoff volume = Runoff Dept × Area of catchment

Runoff volume = 6.4 × 10^-2 × 250 × 10⁶ = 1600 × 10⁴ = 1600 ha.m

Hence the runoff volume in ha-m is 1600 ha.m

Alternate MethodTo find Runoff

We know ϕ - Index = P - R/t

Where,

P is the rainfall (cm), R is the Runoff (cm), and t is the duration (hr)

⇒ 1.2 = [(6.2 + 5.0) - R[/(4)

⇒ R = 6.4 cm.