Q$2.(40$ points$)$ Provide presentation quality plots separating baseflow and direct runoff hydrographs using the following methods:

$(1)$ Constant Slope Method $(10$ points$)$

$(2)$ Concave Method $(10$ points$)$

$(3)$ Varlable Slope Method $(10$ points$)$

The streamflow hydrograph is provided below in the chart and the table:

Streamflow Hydrograph:

$\backslash$table$[[$Time $($hri$),0,1,12,3,4,,,,,,,,],[$Q $($cifis$),102,100,98,220,5100,(2),6,12,8,9,10,11,12],[,,,,,(2),$ong,$409,,210,150,105,75,60]]$

For the three methods, assume that the point of inflection occurs at Time $=8$ hours. For the variable slope method, assume that the event ends at Time $=11$ hours $($hint: Use $t=11$ and $t=22$ to colculote the slope of the post$-$event recession cunvel.

$(4)$ If the watershed area is equal to $300$ acres, calculate the direct runoff depth $($in inches$)$ for the event using the baseflows obtained from the three methods. Which method has the highest runoff depth? Why is it the case? $(10$ points$)$

Hint: To calculate runoff depth, you will need to calculare the area under the cunes for calculating the streamfiow volume and baseflow volume $(f{t}^3).$ After that, you can subtract the two to get direct runoff volume $($ft$\text{'}).$ To get runoff depth, divide the direct runoff volume with the watershed orea. Assume that all the points can be connected with a straight line making the indivalual areas trapezovidal.