$($a$)$ The table below lists annual maximum rainfall depth for the $20-$minute duration. The

annual maximum rainfall depth for that duration follows the Extreme Value Type I

distribution. For the rainfall duration of $20-$minute, calculate $($i$)$ the $100-$year, $500-$

year, and $1000-$year rainfall intensities in the units of $m\frac{m}{h}r,$ and $($ii$)$ the return

period for a rainfall intensity of $158m\frac{m}{h}r.$

$(12$ marks$)$

$($b$)$ The table below gives a recorded rainfall data. Philip's infiltration equation is

applicable, and $i_c=16m\frac{m}{h}r,$ and $S=12m\frac{m}{h}{r}^{\frac{1}{2}}.$

Determine the excess rainfall hyetograph and the cumulative infiltration. What is

the total depth of excess rainfall?

$(8$ marks$)$The table below lists annual maximum rainfall depth for the $20-$minute duration. The

annual maximum rainfall depth for that duration follows the Extreme Value Type I

distribution. For the rainfall duration of $20-$minute, calculate $($i$)$ the $100-$year, $500-$

year, and $1000-$year rainfall intensities in the units of mm$/$hr$,$ and $($ii$)$ the return

period for a rainfall intensity of $158$ mm$/$hr$.$