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RUNOFF AND STREAMFLOW
Introduction ................................................................................................. 2
Runoff Hydrographs ................................................................................. 3
Prediction of Watershed Runoff .............................................................. 4
Runoff Curves (CN) .......................................................................... 5
Time of concentration (tc) ................................................................... 5
Peak runoff rate (Qp) ........................................................................... 6
Total Runoff Volume (Qt) ................................................................. 6
Some Useful Conversions ......................................................................... 7
Example .................................................................................................... 8
Prairie Snowpack Runoff ...................................................................... 10
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RUNOFF and STREAMFLOW
INTRODUCTION
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Rainfall or melting snow that does infiltrate and which is not stored in surface
depressions is runoff. Runoff is also termed overland flow.
As precipitation intensity increases, as infiltration rate decreases, and with increased
distance travelled down a slope the runoff becomes increasingly greater in volume and
velocity:
Sheet flow  rills  runoff channels  stream channels  rivers.
Watershed: also known as the catchment or drainage basin, represents an area of land
that defined by topography, results in all runoff waters flowing into one exit channel
Streamflow (Qs) is the flow rate, or discharge¸ of water in cubic meters per second
(m3/s) or cubic feet per second (ft3/s), along a defined natural channel. Streamflow from
a catchment is generally that part of longterm precipitation not lost to evaporation and
transpiration:
Q = P - Et, where Q, P, and Et are in cm or inches depth of water
Streamflow is generally classifed as either direct runoff (Qd, also called stormflow and
quickflow) or baseflow (Qb, return flow, groundwater or delayed flow).
Qs = Qd + Qb
Perennial streams have continuous flow when there is no storm flow, this flow is
generally that of baseflow. Intermittent streams have no baseflow, except that
following a runoff event, the stream bed is dry.
Soil
Infiltration
Ove
Inte
Watertable
Subsoil
rflow
rlan
d
Channel
Precipitation
flow
streamflow
Groundwater discharge (baseflow)
Fig. 1. Runoff, soil, and groundwater routes involved in streamflow.
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Dept of Agricultural & Bioresource Engineering, U.ofS.
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RUNOFF HYDROGRAPHS
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A hydrograph is a graph of watershed streamflow versus time. Streamflow includes
runoff (overland flow), interflow, and groundwater flow. Fig. 2 shows a typical
hydrograph resulting from that of a storm over a small watershed. The storm began at
time 'zero'. At that point the flow in the stream was that of baseflow, water just
comprising that of groundwater contributions to the stream, no surface runoff. Runoff
might begin immediately on pieces of land near the stream that are already wet. The
streamflow starts to rise and gets larger as more and more land contributes to runoff. The
peak flow arrives at sometime after the storm begins. This lag time is due to the time it
takes for runoff to begin, especially if the soil was dry to begin with, and also to allow for
that of travel time from parts of the watershed that receive the rain. The recession limb
begins after the peak in the storm has finished. At some point all of the surface runoff
has finished and streamflow is made up of just groundwater flow, although now the
groundwater flow is augmented by that of stormwater which has infiltrated and raised the
level of the groundwater. Eventually this too will recede. The total amount of runoff
from the stormcan be found by integration (graphical or mathematical) of the area under
the hydrograph curve.
18
Peak runoff
16
12
10
Fa
lli
ng
lim
b
8
6
Ris
ing
Streamflow (m3/s)
14
4
lim
b
Area under curve
= total runoff
2
Delayed flow
0
0
2
Time to peak
4
6
8
10
Time since start of storm, hours
Fig. 2. A typical runoff hydrograph developing from a small watershed.
To control and predict floods, to plan for water storage reservoirs, surface drainage
systems; knowledge is required about the watershed. Planning entails knowledge of
storm and/or snowmelt properties and watershed properties.
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Storm properties: depth of precipitation, duration, distribution, and return period for a
given event. More intense storms produce greater peak runoff rates whereas longer
duration storms produce more total runoff.
Watershed properties: geologic and soil hydrologic properties, land use and/or framing
practice, and antecedent (before rainfall) soil water content; area of watershed, and
topographic features (area, slope length-steepness-shape, and watershed shape). Shorter
steeper watersheds will have greater peak runoff rates than longer flatter watersheds.
Urban development can produce more runoff than agricultural, than forested for similar
soils and storm events.
Each watershed develops its own particular style of hydrograph, due to the watershed
properties - that is modified by the storm properties. Analyses of hydrographs can tell
planners much about the hydrology of a watershed. There are numerous methods for
interpretation of hydrographs. These methods help to predict volumes and timing of
flows for larger storms and thus are crucial in planning. One method, developed and
used by the U.S. Soil Conservation Service, is presented here.
PREDICTION OF WATERSHED RUNOFF
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Runoff Curves
The NRCS method incorporates the effects of soil type (Table 1), surface vegetation, and
management practices, into known values of runoff that are represented by curve
numbers (CN). The curve numbers are approximate percentage of rainfall that becomes
runoff (Table 2). These curves have been developed from decades of data collection
from research plots and watersheds throughout the United States. They can be used for
general applications but for accurate use with local conditions representative curve
numbers should be obtained.
Table 1. SCS hydrologic Soil Groups
Description
Lowest runoff potential. Inlcudes deep sands with little silt
and clay and deep permeable loess
Moderately low runoff potential. Mostly sandy and loess
soils less deep than A, but above average infiltration
Moderately high runoff potential. Comprises shallow soils
and high clay soils with below average infiltration.
Highest runoff potential. High clay soils with high
shrink/swell potential and some shallow soils with
impermeable horizons
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Soil
Group
Final infiltration
Rate (in/hr)
A
0.3-0.5
B
0.15-0.3
C
0.04-0.15
D
0.0-0.04
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Table 2. Runoff Curve Numbers for Average Antecedent Rainfall Conditions
Land Use and Hydrologic Condition
Fallow
Row Crop
Poor
Good
Contoured - good
Contoured and terraced - good
Small grain
Poor
Good
Contoured and terraced - good
Meadowed - continuous grass, no grazing
Pasture
Poor
Good
Woods-grass combination (orchard)
Woodland
Poor
Good
Farmsteads
Roofs and paved areas
Source SCS (1990)
Runoff Curve Numbers (CN)
Hydrologic Soil Groups (Table 2)
A
B
C
D
77
86
91
94
72
67
65
62
81
78
75
71
88
85
82
78
91
89
86
81
65
63
60
30
76
75
72
58
84
83
80
71
88
87
83
78
68
39
35
79
61
56
86
74
70
89
80
77
45
30
59
-
66
55
74
-
77
70
82
-
83
77
86
90
For a watershed that can be typified by one land use and hydrologic condition would thus
be represented by the one CN as choosen by Tables 1 and 2. Complex watersheds made
of several land uses would use a weighted averaging:
Time of concentration (tc)
is the time it takes for a drop of rainwater to travel from the most hydraulically remote
point of a watershed to the outlet. It is approximately equal to the "time to peak" shown
on the hydrography in Fig. 2. Although there are many methods, one commonly used
one is that of a simplified NRCS method given below. This method is for storms of 24 hr
duration that occur within central United States:
L0.8
tc =
1000
-9
CN
1140 s0.5
(
0.7
)
where tc is the time of concentration in hours;
L is the watershed length in feet
CN is the curve number; and
s is the average percent slope of the watershed
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Dept of Agricultural & Bioresource Engineering, U.ofS.
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Peak runoff rate (Qp).
One method is to use the time of concentration:
log (Qp) = 2.51 - 0.7 log (tc) - 0.15 (log(tc))2 + 0.071 (log(tc))3
where log is that to the base 10
tc is concentration time in hours.
Qp is the peak discharge in cu. ft per sec per inch of precipitation per sq
mile of watershed; ft3 / (s in mi2)
Qp = 10log(Qp)
Qp can be converted to ft3/s by multiplying the above by the number of inches of
precipitation and the number of sq miles of watershed.
Total Runoff Volume (Qt)
Total runoff volume from storms or melt is of interest for flood control and for planning
of water storage for irrigation or drinking supply. The NRCS method estimates storm
runoff using the curve number of the watershed and the following relationship:
Qt =
(P - 0.2S)2
(P + 0.8S)
where Qt is total runoff from the watershed (inches depth)
P is precipitation in inches
S is precipitation surface storage in inches of water before onset of runoff using
the curve number:
S=
1000
- 10
CN
Qt can be converted to a volume of acre-ft by multiplying it by the number of acres and
dividing by 12.
SOME USEFUL CONVERSIONS
Length: 1 m = 39.37 in = 3.281 ft;
1km = 3281 ft = 0.6214 miles
2
2
Area: 1 m = 10.76 ft
1 ha = 104 m2 = 2.471 ac
1 km2 = 100 ha = 247.1 ac = 0.3861 m2
Volume: 1 m3 = 264.2 US gal = 35.31 ft3 = 220.0 imperial gal = 35.32 cu ft
1 acre-ft = 42636 cu ft = 318925 US gal = 1207.1 m3
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REFERENCES
Schwab, G.O., D.D. Fangmeier, and W.J. Elliot. 1996. Soil and Water Management
Systems 4th Edition. John Wiley & Sons, Inc.
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Dept of Agricultural & Bioresource Engineering, U.ofS.
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EXAMPLE
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For planning purposes of a small agricultural watershed (Fig. 3), it is necessary to know
peak flow and runoff volume resulting from a 1 in 25 year rain storm that produced 4.5
inches of precipitation.
The watershed contains four different land uses; small grain under good management
conditions in (Soil Group A); fallow (Soil Group A); pasture in poor condition (Soil
Group C); and bush and woodland (orchard, Soil Group B.
Land Use
Area, A
Curve No, CN
A x CN
Grain
Fallow
Pasture
Woodland
700
300
350
200
63
77
86
56
44100
23100
30100
11200
Total
1550
108500
Watershed divide
fallow
Elevation
983.2 m
C
woodland
A
B
grain
pasture
Elevation
962.5 m
Fig. 3. Watershed map for Example 1.
Watershed CN is then the weighted average found by division:
CN = 108,500 / 1550 acres = 70.0
Length of watershed:
Farthest distance that water must travel (ABC on Fig. 4) is: 10,400 ft (3169.9 m)
Average slope:
Elevation difference between A and C divided by length = 0.65%
Time of concentration (tc) calculated to be 5.7 hours
Peak flow rate (Qp) calculated to be 84.2 cu ft / (s in sq mi) or
918 cu ft/s or 26.0 m3/s
Total volume of runoff from storm flowing through stream exit (Qt): 1.7 inches or
216.2 acre feet or 2.17 x 105 m3.
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Dept of Agricultural & Bioresource Engineering, U.ofS.
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PRAIRIE SNOWPACK RUNOFF top
Spring snowmelt; daily runoff (Wascana Creek)
Gray et al., 1985, 1986
18
16
14
12
10
8
6
4
2
0
Daily
flow
mm/d
Simulated, fallow
Simulated, stubble
Measured
10
15
20
April, 1982
25
30
Average winter precipitation
(1960-90)
130
120
Grande Prairie
110
110
120
130
Edmonton
Prince Albert
100
Saskatoon
90
80
Calgary
70
Regina
0
100 200
Kilometers
90
Lethbridge
100 90
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Swift
Current
70
Winnipeg
Brandon
70
80 80
120
90 100
Dept of Agricultural & Bioresource Engineering, U.ofS.
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Average annual snowpack (SWE
in mm, 1960-90)) for normal cut
wheat stubble
75
70
85
80
65
60
60
55
50
60
45
45
75
55
70
65
50
0
80
100 200
Kilometers
50
Average annual snowmelt
infiltration (mm, 1960-90) for
normal cut wheat stubble
32
31
30 29
28
25
26
27
24
23
24
24
24
0
100 200
Kilometers
27
26
25
25
24
Average annual runoff (mm,
1960-90) for normal cut wheat
stubble
55
45
40
35
40
50
45
35
50
30
25
55
30
25
0
100 200
Kilometers
25
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Dept of Agricultural & Bioresource Engineering, U.ofS.