CEE 7111
PD# 9: Runoff, Unit Hydrograph Theory
Intro:
Data Collection
-Stream flow records at a point
-Usually continuous measurement of river stage
-Stage-hydrograph  Rating Curve  “Discharge
Hydrograph”
Typical Discharge Hydrograph
tp= time to peak
tr= recession time > tp
Hydrograph Component Flows
Total flow hydrograph = baseflow + D.R.H.
Note: Shape and timing of Direct Runoff Hydrograph are
integrated effects of duration and intensity of rainfall after
interaction with the geological/physical features of the
watershed.
Base Flow Separation:
-Methods are approximate, but for major storms this is not
critical
-Objective: to determine the time at which the DFH ends.
1. Constant Baseflow
2. Storm Time-base Concept
DEFINE UNIT HYDROGRAPH: the hydrograph
produced by 1-inch of runoff from rainfall excess over a
specified time duration and for a specified stream site.
Thus, the area under the unit hydrograph MUST represent
EXACTLY 1.0” of runoff over the known drainage area or
interest.
Assumptions of the Unit Hydrograph:
a. Rainfall is distributed the same (time & space)
for all storms.
b. Linear system:
c. Superposition applies:
d. “Time Invariant”:
Uses of the Unit Hydrograph:
1. Reconstruct flow records from
precipitation
2. Transfer unit hydrograph to ungaged
basins
3. Flood forecasting
Unit Hydrograph Derivation – Isolated Strom Method
Steps:
1.
2.
3.
4.
separate baseflow
determine volume of direct runoff
check duration of effective rainfall
reduce ordinates of direct runoff
hydrograph
Qs/Vs=Q/1.0
5. adjusted ordinates should be a unit
hydrograph- Check runoff volume
Example: Develop Unit Hydrograph and  index:
Given:
Drainage area= 300 acres
P(ave)= 2.6 inches
1 hr
P(ave)
250 cfs
Q(cfs)
50
0
2
t (hours)
Solution:
6
How to apply a known unit hydrograph to a given design
storm:
i (design storm hydrograph) total design rain
1.
2.
3.
4.
subtract losses
get Pe by tr intervals
Synthesize direct runoff- composite graphs
add expected baseflow
Note: sequence is opposite of unit hydrograph derivation
Suggestions for the ‘Isolated Storm Method”:
1. Better to average several ( ~ 5) hydrographs
from storms of same duration
2. Compute average or peak flows (not concurrent
average)
3. Compute average time to peak
4. Fine adjustments in shape are interpreted (by
eye) to give Direct Runoff = 1.00”
Summary: The Unit Hydrograph represents the hydrograph
of one-inch direct runoff from a storm of a specified
duration.
*For a storm of the same duration but different amount of
runoff, the unit hydrograph of direct runoff is assumed to
have the same time base as the unit hydrograph and
ordinates of flow proportional to the runoff volume.
Example: Complex Storm Synthesis
Given: 3 separate 1-hour storms
2”
3”
1
0
2
1.5”
2
4
6
3
8
10
12
-Add storm 1,2, and 3 for each hour (tabulate) to generate
one DRH
-Add in expected baseflow
Complex Strom Synthesis- Spreadsheet format
Time UH
0
1
2
3
4
5
6
7
8
9
10
11
0
50
100
75
50
25
0
-
Pe=2”
H#1
0
100
200
150
100
50
0
-
Pe=3” Pe=1.5”
H#2 H#3
0
150
300
225
150
75
0
-
*Qb- Assume constant
0
75
150
112
75
38
0
Qb
Qt
10
10
10
10
10
10
10
10
10
10
10
10
10
110
210
160
260
360
310
310
197
85
48
10
Unit Hydrograph Manipulations
1. To increase Unit Hydrograph duration
2. To develop an S-curve
3. SCS Dimensionless Method
Example: Lets say we have a 100-year design storm for our
300-acre watershed:
3.6
2.6
2.1

Note: The hydrograph is the total design rainfall
To apply this design storm to the U.H.:
1. Subtract losses  from the total (0.60 in/hr)
2. Calculated Pe for each tr interval:
Ex:
hour 1 (0-1) : Pe = 2.0 inches
hour 2 (1-2): Pe= 3.0 inches
hour 3 (2-3): Pe= 1.5 inches
3. Synthesize DRO-Composite graphs
i.e. apply linearity = superposition
4. Add expected baseflow
Note: this sequence is opposite the UH derivation.
Example: Complex Design Storm Synthesis
We actually have 3 separate 1-hour storms
1 2
3
3
1
2
We would now add 1+2+3 at each hour to generate a DRO
hydrograph.
Add base-flow
Complex Strom Synthesis- Spreadsheet format
Time UH
0
1
2
3
4
5
6
7
8
9
10
0
50
100
75
50
25
0
-
Pe=2”
H#1
0
100
200
150
100
50
0
-
Pe=3” Pe=1.5”
H#2 H#3
0
150
300
225
150
75
0
-
*Qb- Assume constant
0
75
150
112
75
38
0
-
Qb
Qt
10
10
10
10
10
10
10
10
10
10
10
10
110
360
535
485
322
160
48
10
10
10