Runoff Hydrographs

1
Runoff Hydrographs

• The Unit Hydrograph Approach

2
Storm Water Hydrographs

• Graphically represent runoff rates vs. time
• Peak runoff rates
• Volume of runoff
• Measured hydrographs are best
• But not often available
• Methods are available to develop a synthetic
  hydrograph
• Use a unit hydrograph (UHG)

3
Development of RO Hydrographs

• Most often interested in hydrographs at the
  watershed outlet (and possibly some selected
  points in the watershed).
• We modify the rainfall hyetograph to reflect
  watershed characteristics.
• The volume under the effective rainfall
  hyetograph is equal to the volume of surface
  runoff.

4
Hydrograph components

• qp is the maximum flow rate on the hydrograph
• tp (time to peak) is the time from the start of
  they hydrograph to qp.
• tb (base time) is the total time duration of the
  hydrograph.

5
Hydrograph Components

• tc (time of concentration) time it takes water to
  flow from the hydraulically most remote point in
  a watershed to the watershed outlet
• tL (lag time) is the average of the flow times
  from all locations in the watershed and can be
  estimated as the length of time from the center
  of mass of the first effective rainfall block, to
  the peak of the runoff hydrograph.
• If each block of effective rainfall has a
  duration of D

6
Unit Hydrograph

• Hydrograph of runoff resulting from a unit of
  rainfall excess occurring at a uniform rate,
  uniformly distributed over a watershed in a
  specified duration of time.

7
Unit Hydrographs

• Assumptions
• Rainfall intensity is not considered
• Linear relationship between stormwater runoff and
  rainfall
• UHG is independent of antecedent conditions
• Uniform rainfall distribution

8
Duration of the Unit Hydrograph

• Each unit hydrograph has a duration that is the
  same as the duration of the rainfall excess that
  produced it.
• Conceptually can have an infinite of
  hydrographs corresponding to different durations.
• Practically, a unit hydrograph is applied to
  rainfall excesses of duration as much as 25
  different than the duration of the unit
  hydrograph.

9
How is the unit hydrograph used?

• For a unit hydrograph of duration, D, the volume
  underneath the hydrograph is always 1, produced
  by 1 unit of excess rainfall.
• A hydrograph for a block of rainfall excess of
  any depth is obtained by multiplying the
  ordinates of the unit hydrograph by the depth of
  the rainfall excess block.
• The result is the ordinates of the runoff
  hydrograph.

10
How is the unit hydrograph used?

• Rainfall excess is divided into blocks, each of a
  uniform duration, D.
• A component hydrograph for each block of rainfall
  is calculated.
• The starting time for each hydrograph coincides
  to the starting time of the appropriate block of
  rainfall excess.
• All the component hydrographs are added
  vertically to obtain the total runoff hydrograph
  for the storm.

11
Checking the volume under a unit hydrograph.

• Where
• Dt is the duration time increment of the
  hydrograph (min)
• Sqi is the sum of the ordinates of the runoff
  hydrograph (cfs)
• A is the area (acres)

12
Deriving unit hydrographs

• Unit hydrographs can be derived from records of
  observed rainfall and streamflow
• BUT
• For small watersheds, synthetic unit hydrographs
  are generally used.
• Synthetic unit hydrographs provide ordinates of
  the unit hydrograph as a function of tp, qp and a
  mathematical or empirical shape description.

13
Estimating the time parameters

• Time of concentration (tc)
• For some areas, we can sum the time for various
  flow segments as the water flows toward the
  watershed outlet.
• Segments
• Overland flow
• Shallow channel flow
• Flow in open channels.

14
Lag time, tL

• SCS Equation to calculate time lag
• L hydraulic length of watershed (feet)
• S curve number parameter (inches)
• Y average land slope of the watershed ()
• tl time lag (hours)

15
Time to Peak and Duration

• Duration of rainfall excess should be 1/5 to 1/3
  tp.
• Base time, tb
• tb2.67 tp.
• Some use tb 5tp
• Some use tb 8

16
Estimation of peak flow parameters

• General form
• For a triangular unit hydrograph with tb2.67 tp
• Where
• tp is the time to peak (hrs)
• qp is peak flow (cfs)
• A is watershed area (square miles)

17
Shapes of unit hydrographs

• SCS uses a dimensionless unit hydrograph (Figure
  3.34).
• Also have a triangular unit hydrograph derived to
  have the same tp and qp as the dimensionless
  hydrograph.
• If either of these are used the qp and tp are
  related through

18
Triangular hydrographs

• Good approximation for peak and duration.
• Find the qp and tp of the unit hydrograph.
• Multiply qp by the depth of the rainfall excess
  block.
• Use the tb approximation to find the duration of
  the hydrograph.

19
Example 5.10 in Text (modified)

• Solution
• HSG D / Commercial ? T. 5.1 ? CN 95
• S 0.53 in.
• Assume AMC II ? Q 1.96 in. of runoff
• Find points to develop the unit hydrograph
• tl 0.75 hr (45 min)
• tp 1.25 hr (75 min)
• tb 3.33 hr (200 min)
• qp 302 cfs / 1 in. of runoff
• Plot unit hydrograph
• Check area under the triangle ? 1 in.

20
Q (cfs)
21
Volume under triangle (302.5 cfs x 4,500 sec) /
2 (302.5 x (12,000 4,500 sec) / 2
1,812,000 ft3
Surface runoff depth 1,812,000 ft3 / 21,780,000
ft2 0.08 ft 1.0 in. ? ok
22
Example 5.10 in Text

• Solution
• qp 2.5 rain 302.5 cfs x 1.96 in. of SRO
• qp 2.5 rain 592.9 cfs
• Plot storm hydrograph
• Check area under the triangle ? 1.96 in.

23
Q (cfs)
Surface runoff depth 1.96 in. ? ok
T(min)
24
AGSM 335

• Homework 6

25
SCS dimensionless unit hydrograph

• Haan equation

• Where
• qp is peak flow (in/hr)
• To convert from cfs to in/hr divide by A (acres)
  and 1.008.
• tp is time to peak (hrs)
• V is volume under the hydrograph (V1 for unit
  hydrograph)
• For a unit hydrograph K should be close to 3.77

26
Example 5.11 in text Using SCS UHG

• Rainfall excess for each time block of duration
  15 minutes 0.17, 1.10, 0.84
• tp 52.5 minutes qp 432 cfs
• Convert qp to in/hr.
• Calculate K

27
Coordinates of the UHG

• For each time block of duration D, calculate q(t)
  using
• These are the ordinates of the UHG.
• For each excess rainfall block multiply the depth
  of the excess rainfall by all the ordinates of
  the unit hydrograph.
• Each hydrograph should begin at the time the
  rainfall excess block begins. i.e. If the
  rainfall excess block occurred at 30 minutes, the
  hydrograph should start at 30 minutes.

28
Creating the Total Runoff Hydrograph

• Add the contents of each row (not including the
  UH ordinates) to get the total runoff at each
  time t.
• Plot t vs. Q.

29
Unit and Runoff Hydrograph calculations
Example of a Unit Hydrograph Example of a Unit Hydrograph Example of a Unit Hydrograph

qp 432 cfs
K 3.76
tp 0.875 hr
Excess Runoff (in) Excess Runoff (in) Excess Runoff (in) Excess Runoff (in)
t q(t) 0.17 0.84 0.71 0.24 Runoff (cfs)
0.00 0.00 0.00 0.00
0.25 57.04 9.70 0.00 9.70
0.50 263.93 44.87 47.91 0.00 92.78
0.75 414.04 70.39 221.70 40.50 0.00 332.59
1.00 417.11 70.91 347.79 187.39 13.69 619.79
1.25 329.67 56.04 350.38 293.97 63.34 763.73
1.50 223.48 37.99 276.92 296.15 99.37 710.44
1.75 136.27 23.17 187.73 234.07 100.11 545.07
2.00 76.90 13.07 114.47 158.67 79.12 365.34
2.25 40.90 6.95 64.59 96.75 53.64 221.93
2.50 20.76 3.53 34.35 54.60 32.71 125.18
2.75 10.14 1.72 17.44 29.04 18.45 66.65
3.00 4.81 0.82 8.52 14.74 9.82 33.89
3.25 2.22 0.38 4.04 7.20 4.98 16.60
3.50 1.00 0.17 1.86 3.41 2.43 7.88
3.75 0.44 0.08 0.84 1.57 1.15 3.64
4.00 0.19 0.03 0.37 0.71 0.53 1.65
4.25 0.08 0.01 0.16 0.31 0.24 0.73
4.50 0.04 0.01 0.07 0.14 0.11 0.32
4.75 0.01 0.00 0.03 0.06 0.05 0.14
5.00 0.01 0.00 0.01 0.02 0.02 0.06
1.00 0.01 0.01 0.01 0.02
1.25 0.00 0.00 0.01
0.00 0.00
0.00
30
Plots of Unit and Runoff Hydrographs
31
BAEN 460

• Homework 6