$($a$)$ During a rainstorm, after $1\mathrm{.}5$ hours, the infiltration rate decreased to $25\mathrm{.}0m\frac{m}{h}r$ and

a total of $39\mathrm{.}0mm$ rain water infiltrated into the soil. Compute the soil sorptivity and

the final infiltration rate. Assume continuously ponded conditions.

$(8$ marks$)$

$($b$)$ The following table lists annual peak discharges recorded at a stream gauge station:

$(1)$ Use the Gumbel distribution function to determine the probability that an annual

flood peak of $35\frac{m^3}{s}$ will not be exceeded, and to evaluate the return period of the

annual peak discharge $50\frac{m^3}{s}.(2)$ Using the Gumbel distribution function and the

plotting position method $(P_m=\frac{m}{n}),$ determine the annual peak discharges for $2-$year

and $10-$year return periods. $(3)$ Comment on the results from both methods.

$(12$ marks$)$