$12.(20$ points$)$ The initial infiltration capacity of a watershed is $\backslash (1\mathrm{.}4\backslash$mathrm$\{$in$\}/\backslash$mathrm$\{$hr$\}\backslash ).$ The time constant is $\backslash (0\mathrm{.}4\backslash$mathrm$\{$hr$\}^\{-1\}\backslash ).$ The final infiltration capacity is $\backslash (0\mathrm{.}2\backslash$mathrm$\{$in$\}/\backslash$mathrm$\{$hr$\}\backslash ).$ A watershed experiences a rainfall event, expressed in rainfall hyetograph as below.

a$)(10$ points$)$ Use the Horton Infiltration method to calculate the excess rainfall hyetograph.

b$)(10$ points$)$ Based on the excess rainfall estimated from Problem $12($a$)$ and the $\backslash (1-\backslash$mathrm$\{$hr$\}\backslash )$ Unit Hydrograph in the table above, and with baseflow of $40$ cfs $,$ calculate the resulting storm hydrograph for the watershed.