Question $3.(30$ points$)$

For a rain duration of $2$ hours, streamflow was observed in a creek as reported below. The baseflow of the stream before the event was $10$ cfs and it will be taken as constant throughout the event. Drainage area of the creek is $2\mathrm{.}5k{m}^2.$

$\backslash$table$[[$Time $($h$),1,2,3,4,5,6,7,8,9,10],[$Rainfall $($in$),1\mathrm{.}5,1\mathrm{.}5,,,,,,,,],[$Streamflow $($cfs$),60,280,340,284,204,128,68,36,16,10]]$

a$)$ Calculate the surface runoff generated by the storm in $[$mm and inch$]$ and estimate the ordinates of a $2$ h unit hydrograph of this catchment $[$cfs$/$inch$].$ Start with time $=0$ and $Q=10cfs($baseflow$).$

b$)$ Estimate the maximum soil retention parameter S of the SCS Curve number method based on the rainfall and runoff observations above and find the Curve Number value of this watershed based on S$.$ You are using the experimental evidence here not a CN table. This is often done at project site where flow data is collected. Given runoff, think about how you can estimate $S.$

c$)$ Calculate the runoff from a storm depth of $4$ inches that lasts for $4$ hours using this SCS maximum retention parameter you estimated above. Plot the $4-$hour runoff hydrograph for this event assuming an initial baseflow of $18$ cfs in the creek.