$8\mathrm{.}2\mathrm{.}6$ Consider a watershed with drainage area of $1k{m}^2,$ For a given storm event, the recorded average rainfall intensity and total instantaneous discharge at the outlet of the watershed are listed in the following table. Assume that the baseflow is $1\frac{m^3}{s}$ and rainfall amount in the first $30$min is the initial loss.

$($a$)$ Determine the total amount of rainfall.

$($b$)$ Determine the volume of direct runoff.

$($c$)$ Determine the average infiltration rate, i$.$e$.,$ index

$($d$)$ Determine the rainfall excess intensity hyetograph corresponding to the $$ index obtained in $($c$).$ Also, what is the duration of rainfall excess hyetograph?