Basin area from 4-h unit hydrograph ordinates

A unit hydrograph represents 1 cm of direct runoff from the whole basin. So the volume under the UH equals area × 1 cm.

Step 1: Volume under the UH

The ordinates are at 1 h intervals, so the volume is the sum of the ordinates × 1 h (3600 s).

$$\sum Q = 4+25+44+60+70+61+52+45+38+32+27+22+18+14+11+8+6+4+2+1 = 544 \text{ m}^3/\text{s}$$ $$V = 544 \times 3600 = 1,958,400 \text{ m}^3$$

Step 2: Area

$$A = \frac{V}{\text{runoff depth}} = \frac{1,958,400}{0.01} = 195,840,000 \text{ m}^2 = 195.8 \text{ km}^2$$

Answer: Area of basin ≈ 195.8 km² (the hourly ordinates are summed directly; the first and last ordinates are small, so a trapezoidal correction would change the result by less than 1 %).