Unit Hydrograph

Q (t) = i \sum P_{e, i} U H (t - t_{i})

A unit hydrograph (UH) is the direct-runoff hydrograph from 1 unit of excess rainfall over the basin in a specified duration. Storm runoff is the convolution of excess-rainfall pulses with the UH. Peak and ordinates scale linearly with excess depth. Duration of the UH must match the pulse length (or be converted).

$U H$ (cfs/in or m³/s per mm): Unit hydrograph ordinate
$P_{e}$ (in): Excess rainfall pulse
$Q$ (cfs): Direct runoff

Step-by-step solved example

1-h UH peaks at 200 cfs/in. A 1-h excess of 0.40 in. Peak direct runoff?

UH is the catchment response to 1 unit of excess rain.

1. Linearity
Q_peak = 0.40 × 200 = 80 cfs.
$Q_{p} = 80 cfs$
2. Timing
Peak stays at the same UH lag (linear system).

Answer: 80 cfs

10 practice questions

0/10 correct

1.A 1-cm UH is the DRH from

2.Ordinates scale

3.Convolution is needed when

4.Baseflow is

5.A longer-duration UH is obtained by

6.Time to peak of the UH depends on

7.If excess doubles, the UH peak discharge

8.The area under the DRH equals

9.Snyder / SCS synthetic UH methods estimate

10.UH assumes excess is