$4.$ The $4-$hour unit hydrograph $($UH$)$ for a watershed is presented below in Table $7,$

Table $7$

$($a$)$ Derive the $2-$hour unit hydrograph for the same watershed using the S$-$curve method from Table $7.($Note: Fill in the blanks in the next page's working sheet and include a rough plot of both unit hydrographs for comparison.$)(8$ points$)$

$($b$)$ The loss rate $(-$index$)$ for the catchment is estimated as $\backslash (0\mathrm{.}25\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$h$\}\backslash ).$ Table $8$ shows the recorded total rainfall amount $($unit: cm $)$ for each $4$ hours. Calculate the effective rainfall amount $($ cm $)$ for every $4$ hrs during the entire storm event shows below: $(3$ points$)$

Table $8$

$($c$)$ The baseflow can be assumed to be $\backslash (15\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ derive the total stream hydrograph in the watershed due to the storm event given above using the $2-$hour UH $($Note: Fill in the blanks in the next page's working sheet$).(7$ points$)$