Total rainfall, net runoff, W-index of 120-min storm

Each interval is 20 min = 1/3 h, so rain depth = rate $/3$.

Total rainfall

$$P = \frac{5+8+15+12+9+2}{3} = \frac{51}{3} = 17.0\ \text{mm}$$

Net runoff

Excess rainfall above $\phi$ $= 0.833+1.833+4.167+3.167+2.167 = 12.167$ mm. The initial loss (0.5 mm) is taken from the start of the storm, so:

$$R = 12.167 - 0.5 = 11.67\ \text{mm}$$

W-index

The W-index is the average infiltration rate during the time $t$ when the rain intensity exceeds the infiltration capacity. The rain rate is above $\phi = 2.5$ mm/h only in the first five intervals, so

$$t = 5\times20 = 100\ \text{min} = 1.667\ \text{h}$$ $$W = \frac{P - R - I_a}{t} = \frac{17.0 - 11.67 - 0.5}{1.667} = 2.90\ \text{mm/h}$$

The last interval (rain 2 mm/h, less than $\phi$) is not counted in $t$.

Answer: Total rainfall = 17.0 mm; net runoff = 11.67 mm; W-index = 2.9 mm/h.