Consider the following discrete triangular unit hydrograph $(u)$ representing the response of

a small watershed to a unit impulse of rainfall:

Assignment $2$

The watershed experiences a storm event with the following discrete hyetograph obtained

via the alternating block method $(p)$ :

The downstream hydrologic response $($discharge in $cfs)$ is given by the discrete convolution

of the unit hydrograph with the rainfall input:

$Q_n={\displaystyle \underset{m=1}{\overset{n}{}}}{p}_m{u}_{n-m+1}$

Where $Q_n$ is the discharge at time index $n,p_n$ is the precipitation at time index $n,$ and

$u_n$ is the unit hydrograph at time index $n.$ Compute the output $Q_n$ for each $10-$minute

time interval in the first $100$ minutes $($i$.$e$.$ compute $Q_1,Q_2,Q_3,$dots,$Q_{10}).$ Plot the resulting

discrete discharge hydrograph.