S-curve 3-h UH and flood from two storms

Part 1: 3-h UH from the 2-h UH by the S-curve method

$S(t)=U_2(t)+S(t-2)$, and $U_3(t)=\dfrac{2}{3}\left[S(t)-S(t-3)\right]$ with $S(t-3)$ interpolated linearly.

The S-curve reaches equilibrium (896 m$^3$/s) at 22 h.

Part 2: Flood hydrograph

Effective rainfall ($\phi$ = 0.3 cm/h, assumed consecutive storms: 3 h of 8 cm, then 2 h of 7 cm):

• 3-h storm: $8 - 0.3\times3 = 7.1$ cm
• 2-h storm: $7 - 0.3\times2 = 6.4$ cm, starting at t = 3 h.

$$Q(t)=10+7.1\,U_3(t)+6.4\,U_2(t-3)$$

$U_3$ and $U_2$ are read at hourly intervals (linear interpolation of the S-curve; $U_2(t)=S(t)-S(t-2)$).

Answer: The 3-h UH ordinates are 0, 16.7, 75, 140, 180, 176.7, 130, 83.3, 43.3, 23.3, 16.7, 9, 2 m$^3$/s at 0, 2, ..., 24 h. The flood hydrograph peaks at about 2384 m$^3$/s at 10 h and returns to the base flow of 10 m$^3$/s by about 27 h.