CE322 Basic Hydrology
Jorge A. Ramírez
Unit Hydrographs - Example

A. Obtain a Unit Hydrograph for a basin of 315 km2 of area using the rainfall and streamflow data tabulated below.

Time

(h)

Observed Hydrograph (m3/s)

0

100

1

100

2

300

3

700

4

1000

5

800

6

600

7

400

8

300

9

200

10

100

11

100

Time

(h)

Gross Precipitation (GRH)

(cm/h)

0 - 1

0.5

1 - 2

2.5

2 - 3

2.5

3 - 4

0.5

Empirical Unit Hydrograph Derivation
  1. Separate the baseflow from the observed streamflow hydrograph in order to obtain the Direct Runoff Hydrograph (DRH).
    For this example, 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 100 m3/s.
  2. Compute the volume of Direct Runoff. This volume must be equal to the volume of the Effective Rainfall Hyetograph (ERH).
     

    Thus, for this example:

    VDRH = (200+600+900+700+500+300+200+100) m3/s (3600) s = 12'600,000 m3

  3. Express VDRH in equivalent units of depth:
    VDRH in equivalent units of depth = VDRH/Abasin = 12'600,000 m3/(315000000 m2) = 0.04 m = 4 cm.
  4. Obtain a Unit Hydrograph by normalizing the DRH. Normalizing implies dividing the ordinates of the DRH by the VDRH in equivalent units of depth.

    Time (h)

    Observed Hydrograph (m3/s)

    Direct Runoff Hydrograph (DRH) (m3/s)

    Unit Hydrograph (m3/s/cm)

    0

    100

    0

    0

    1

    100

    0

    0

    2

    300

    200

    50

    3

    700

    600

    150

    4

    1000

    900

    225

    5

    800

    700

    175

    6

    600

    500

    125

    7

    400

    300

    75

    8

    300

    200

    50

    9

    200

    100

    25

    10

    100

    0

    0

    11

    100

    0

    0


     



  5. Determine the duration D of the ERH associated with the UH obtained in 4. In order to do this:
  1. Determine the volume of losses, VLosses which is equal to the difference between the volume of gross rainfall, VGRH, and the volume of the direct runoff hydrograph, VDRH .


    VLosses = VGRH - VDRH = (0.5 + 2.5 + 2.5 +0.5) cm/h 1 h - 4 cm = 2 cm

  2. Compute the f-index equal to the ratio of the volume of losses to the rainfall duration, tr. Thus,


    f-index = VLosses/tr = 2 cm / 4 h = 0.5 cm/h

  3. Determine the ERH by subtracting the infiltration (e.g., f-index) from the GRH:

Time

(h)

Effective Precipitation (ERH)

(cm/h)

0 - 1

0.0

1 - 2

2.0

2 - 3

2.0

3 - 4

0.0

B. Using the UH obtained in A., predict the total streamflow that would be observed as a result of the following ERH:

Time

(h)

Effective Precipitation (ERH)

(cm/h)

0 - 2

0.5

2 - 4

1.5

4 - 6

2.0

6 - 8

1.0

As observed in the table, the ERH can be decomposed into a sequence of rectangular pulses, each of 2 hours duration. Thus, we can use the 2-hour UH obtained in A.
  1. Determine the volume of each ERH pulse, Pm, expressed in units of equivalent depth:

    Time

        (h)

    Pm

        (cm)

    0 - 2

    1.0

    2 - 4

    3.0

    4 - 6

    4.0

    6 - 8

    2.0

  2. Use superposition and proportionality principles:

 

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

0

     

0

100

2

50

50

     

50

150

3

150

150

0

   

150

250

4

225

225

150

   

375

475

5

175

175

450

0

 

625

725

6

125

125

675

200

 

1000

1100

7

75

75

525

600

0

1200

1300

8

50

50

375

900

100

1425

1525

9

25

25

225

700

300

1250

1350

10

0

0

150

500

450

1100

1200

11

   

75

300

350

725

825

12

   

0

200

250

450

550

13

     

100

150

250

350

14

     

0

100

100

200

15

       

50

50

150

16

       

0

0

100

  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.