Objectives: To define ‘unit hydrogarph’To estimate flood hydrograph due to a known ERH

UNIT HYDROGRAPHS

Reference: Hydrology and Floodplain Analysis, 2nd Edition, Philip B. Bedient, and Wayne C. Huber, Addison-Wesley Publishing Company, Reading, Massachusetts, 1992.

"One of the central problems of engineering hydrology is to convert net rainfall into direct surface runoff. The unit hydrograph is still recognized as one of the most important contributions to hydrology related to surface runoff predictions. This theory, combined with infiltration methods and flood routing in stream channels and reservoirs, is sufficient to handle input rainfall variability and storage effects in small and large watersheds."

Definition of a Unit Hydrograph

A unit hydrograph represents the basin outflow resulting from 1 inch (cm) of direct runoff generated uniformly over the drainage area by a uniform rainfall rate during a specified period. The definition of a unit hydrograph implies the following:

1. The unit hydrograph represents the lumped response of the catchment to a unit rainfall excess of D-h duration to produce a direct runoff hydrograph. It relates only the direct runoff to the rainfall excess. Hence the volume of water contained in the unit hydrograph must be equal to the rainfall excess. As 1 cm depth of rainfall excess is considered the area of the unit hydrograph is equal to a volume given by 1 cm over the catchment.

2. The rainfall is considered to have an average intensity of excess rainfall (ER) of 1/D cm/h for the duration D-h of the storm.

3. The distribution of the storm is considered to be uniform all over the catchment.

By using a unit hydrograph to estimate basin runoff, one assumes that the system is linear and time-invariant. The unit hydrograph serves as a basis from which runoff hydrographs can be constructed.

The assumption of linear response in a unit hydrograph enables the method of superposition to be used to derive DRHs. Accordingly, if two rainfall excess of D-h duration each occur consecutively, their combined effect is obtained by superposing the respective DRHs with due care being taken to account for the proper sequence of events. These aspects resulting from the assumption of linear response are made clearer in the following example.

Example: The ordinates of a 2-h unit hydrograph for a catchment are given in Table 1. Calculate the total streamflow hydrograph that would be observed as a result of a storm whose effective rainfall is given in Table 2. Use the horizontal line method to separate the baseflow. From observation of the hydrograph data, the streamflow at the start of the rising limb of the hydrograph is 150 m3/s. Thus, use 150 m3/s as the baseflow.

Table 1. 

Time (h) Observed Hydrograph

(m3/s)

Direct Runoff Hydrograph

(DRH) (m3/s)

Unit Hydrograph (m3/s/cm)

0 160 10 --1 150 0 02 350 200 403 800 650 1304 1200 1050 2105 900 750 1506 750 600 1207 550 400 808 350 200 409 225 75 1510 150 0 011 140 0 0

   

Table 2.  Time(h)

Pm(cm)

0 - 2 2.02 - 4 3.04 - 6 1.56 - 8 0.5

 Table 3. Calculation of storm hydrograph by method of superposition 

  1 2 3 4 5 6 7

Time(h) UH (m3/s/cm)

P1*UH (m3/s)

P2*UH (m3/s)

P3*UH (m3/s)

P4*UH (m3/s)

DRH (m3/s)

Total (m3/s)

1 0.00 0.00       0.00 150.00

2 40.00 80.00       80.00 230.00

3 130.00 260.00 0.00     260.00 410.00

4 210.00 420.00 120.00     540.00 690.00

5 150.00 300.00 390.00 0.00   690.00 840.00

6 120.00 240.00 630.00 60.00   930.00 1080.00

7 80.00 160.00 450.00 195.00 0.00 805.00 955.008 40.00 80.00 360.00 315.00 20.00 775.00 925.009 15.00 30.00 240.00 225.00 65.00 560.00 710.0010 0.00 0.00 120.00 180.00 105.00 405.00 555.0011     45.00 120.00 75.00 240.00 390.00

12     0.00 60.00 60.00 120.00 270.00

13       22.50 40.00 62.50 212.50

14       0.00 20.00 20.00 170.00

15         7.50 7.50 157.50

16         0.00 0.00 150.00

 

Explanation is as follows:1. Columns 2 - 5: Apply the proportionality principle to scale the UH by the actual

volume of the corresponding rectangular pulse, Pm. Observe that the resulting hydrographs are lagged so that their origins coincide with the time of occurrence of the corresponding rainfall pulse.

2. Column 6: Apply the superposition principle to obtain the DRH by summing up Columns 2 - 5.

3. Column 7: Add back the baseflow in order to obtain the Total Streamflow Hydrograph.

Unit hydrograph theory

Surface runoff hydrographs for storm events of the same duration will have the same shape, and the ordinates of the hydrograph will proportional to the ordinates of the unit hydrograph. For example, the discharge from one-half cm of runoff will be half of that from the unit hydrograph.

General Rules for Gauged Watersheds

1. Storms should be selected with a simple structure with relatively uniform spatial and temporal distributions.

2. Watershed sizes should generally fall between 1000 acres and 1000 mi2. 3. Direct runoff (DRO) should range from 0.5 to 2.0 inches. 4. Duration of rainfall excess, D, should be approximately 25-30% of the lag time, tp.

5. A number of storms of similar duration should be analyzed to obtain an average unit hydrograph for that duration.

6. Step 5 should be repeated for several different durations.

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

0 5 10 15 20

Time (h)

Dis

char

ge

(m3/

s)

P1*UH

P2*UH

P3*UH

P4*UH

DRH

Total

Ungaged Watersheds

For ungauged watersheds, there is no streamflow data from which a unit hydrograph can be developed. In these situations, the engineer is faced with two choices: 1) use a unit hydrograph developed for a nearby gauged watershed that has similar basin characteristics; 2) develop a synthetic unit hydrograph.