2-hr UH and flood hydrograph from storm

Part 1: 2-h UH from the 4-h UH (S-curve method)

$S(t)=U_4(t)+S(t-4)$, and $U_2(t)=\dfrac{4}{2}\left[S(t)-S(t-2)\right]$ (the S-curve lagged by the new duration, 2 h, and scaled by $4/2$).

The raw S-curve points zig-zag because the ordinates of the given 4-h UH are irregular. A smooth S-curve is drawn through them (3-point smoothing of the ordinates, ending at the mean equilibrium value 149 m$^3$/s). Differences are taken from the smooth curve.

(The sum of the $U_2$ ordinates is 298, equal to the sum of the $U_4$ ordinates, so the volume of 1 cm is conserved.)

Part 2: Effective rainfall ($\phi=0.15$ cm/h)

Part 3: Flood hydrograph

$Q(t)=40+\sum_j P_j\,U_2(t-2j)$ with $P=(2.2,3.7,3.7,2.7,2.7,2.7)$.

Answer: The 2-h UH ordinates (0, 2, ..., 24 h) are 0, 15, 20, 34, 46, 50.5, 42.5, 32.5, 24.5, 16.5, 11.5, 5, 0 m$^3$/s. The flood hydrograph, including base flow of 40 m$^3$/s, peaks at about 726 m$^3$/s at 14 h.