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RUNOFF
Rainfall-Runoff Processes
Runoff is that fraction of the rainfall that moves over the surface or through the soil
toward surface water features (ponds, lakes, streams, rivers, etc.). For most purposes, runoff
refers to surface runoff only. Runoff occurs when the rainfall exceeds the demands of
interception, evaporation, infiltration, and surface storage.
A fraction of the rainfall will be intercepted by the foliage of plants. If the vegetation is
dense enough, a brief, light rain may not wet the soil beneath the plants. After the rain has
ended, the water stored on the leaves may slowly run down the stems, drop off the leaves, or
evaporate back into the atmosphere.
Runoff will occur after the intensity of the rain exceeds the rate at which water can
infiltrate the soil. Infiltration is the entry of water into the soil surface. The movement of water
downward through the soil profile is called percolation. When the intensity of the rainfall
exceeds the infiltration rate, the excess rainfall begins to pond on the soil surface. This water
fills the small depressions caused by irregularities in the soil surface. The volume of water that is
temporarily held in these depressions is called surface storage. When the rainfall ceases, the
water held in surface storage will either infiltrate into the soil or evaporate. The volume of water
that exceeds the volume of surface storage becomes surface runoff. Runoff may begin as a
relatively uniform layer of water moving over the soil surface called sheet flow. Gradually the
water begins to concentrate into small channels.
The economic design of water control structures requires knowledge of the probability of
occurrence of storms of various intensities and durations. It is cheaper to occasionally rebuild the
structure than to design it to handle the largest expected rainfall event. The U.S. Weather Bureau
has analyzed rainfall data and published maps depicting the depth of rainfall during given storm
durations expected to occur for various return periods. The return period, or reccurence interval,
is the period during which the depth of rainfall that occurs during a storm of specified duration
will be equaled or exceeded once on the average. If the 10-year, 24-hour rainfall for a location is
6.2 inches, then the depth of the rainfall expected during a storm lasting 24-hours will exceed 6.2
inches once every ten years. This does not mean that such a storm will occur only once every ten
years. A storm of at least that depth and duration may occur in consecutive years or even more
than once in the same year. However, over the long-term, such a storm would be expected to
occur, on average, only once every 10 years. Structural practices for erosion and sediment
control are generally designed to safely pass the runoff from a 10-year, 24-hour storm event
(Figure 1).
Factors that influence the rate and volume of runoff from a storm are related to
characteristics of the storm and characteristics of the watershed. Storm characteristics that
influence runoff are intensity, duration, and areal extent of the storm. Consider two storms, both
of which total 2 inches of rainfall. The first storm lasts for 1 hour and has an average intensity of
2 inches/hour. The second storm lasts for 20 hours and has an average intensity of 0.1 inches per
2
hour. The soil on which the rainfall occurred has a steady infiltration rate of 0.3 inches per hour.
Since the intensity of the first storm exceeds the infiltration capacity of the soil, a large portion of
the rain from the storm may become surface runoff. The intensity of the second storm is less
than the infiltration rate of the soil and, therefore, all of the rainfall will probably infiltrate and
there will not be any surface runoff. The runoff from a storm is dependent upon both the
intensity and duration of a storm. If a storm does not entirely cover the area of a watershed, the
runoff volume and peak runoff rate will be less than if the storm had covered the entire
watershed, because the parts of the watershed that are not receiving rainfall will not be
contributing to runoff at the watershed outlet.
Watershed characteristics that influence runoff include size, shape, and topography, soils,
and vegetation. As the size of a watershed increases, total runoff volumes and peak runoff rates
increase. Watersheds that are long and narrow will generally have reduced peak runoff rates
compared to more compact watersheds of the same size. Because it takes longer for runoff from
the most remote portions of a long watershed to reach the outlet. The time required for runoff
from the most remote point of the watershed to reach the watershed outlet is called the time of
concentration (Tc). If a storm has a duration less than the time of concentration of the watershed,
peak flows will be less than would occur for a storm of the same intensity with duration equaling
or exceeding the time of concentration because the storm will have ended and runoff from areas
near the outlet will have been reduced before the runoff from the remote area reaches the
watershed outlet. The topography of the watershed also influences runoff rates and volumes.
Watersheds with an extensive network of steep channels will produce greater runoff rates than a
watershed with few channels or one with channels having a mild slope. Watersheds with deep,
permeable soils will produce less runoff than watersheds with thin soils overlying less permeable
materials. More of the rainfall will infiltrate into deep soils. Rainfall that infiltrates into the
shallow soil profiles is likely to flow over the less permeable horizons in the shallow soils and
reappear as surface flow somewhere downslope (interflow). Vegetation influences the rate and
volume of runoff because it retards the flow of the runoff over the soil surface.
Design Investigations
An on-site investigation of the system site and tributary area is a prerequisite for
estimating runoff rates. Information regarding capacity, elevations, and condition of existing
runoff channels and/or conduits is needed, as well as topography, size and shape of drainage area,
and extent and type of areal development; profiles, cross sections, and roughness data on
pertinent existing streams and watercourses; and location of possible ponding areas. Adequate
information regarding soil conditions, including types, permeability or perviousness, vegetative
cover, depth to and movement of subsurface water, and depth of frost is also necessary. Outfall
and downstream flow conditions, including high-water occurrences and frequencies, also must be
determined. Effect of construction on local interests’ facilities and local interests’ requirements
that will affect the design of the system need to be evaluated. Where diversion of runoff is
proposed, particular effort will be made to avoid resultant downstream conditions leading to
unfavorable public relations, costly litigations, or damage claims. Any agreements needed to
obtain drainage easements and/or to avoid interference with water rights should be determined at
the time of design and consummated prior to initiation of construction. Possible adverse effects
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on water quality due to disposal of drainage in waterways involved in water-supply systems
should be evaluated.
Maps and charts showing necessary detailed topography and other essential features of
the areas to be drained and outlining the watershed area and subareas for determining runoff
quantities are necessary for design. Aerial photographs including stereoscopic pairs should be
used if available. Supplemental surveys may be required.
Hydrologic studies should include a careful appraisal of factors affecting storm runoff to
insure the development of structures capable of providing the required capacity. Ground
conditions affecting runoff should be selected to be consistent not only with existing and
anticipated areal development but with the characteristics and seasonal time of occurrence of
design rainfall. For drainage areas of up to about 1 square mile, and where only peak discharges
are required for design and extensive ponding is not involved, computation of runoff may be
accomplished by the so-called rational method, unless suitable unit-hydrograph data are
available. For drainage areas up to 2000 acres the SCS, USDA, Engineering Field Manual for
Conservation Practices, Chapter 2, (SCS, 1989) method may be used. Procedures based on the
SCS, USDA, TR-55, procedures may be used for basins up to 20 square miles (SCS, 1986). For
larger areas and where detailed consideration of ponding is required, computation should be by
unit-hydrograph and flow-routing procedures.
Appendix B: Computing Design Runoff
Design Storm
The design storm will normally be based on rainfall of at least a 10-year recurrence
interval. Where potential damage or functional operational requirements warrant a more severe
criterion a greater design recurrence interval should be used. Rainfall intensity should be
determined from the best available intensity-duration-frequency curves. Basic information of
this type may be obtained from such publications as:
US Weather Bureau, Rainfall Frequency Atlas of the United States. Technical Paper No.
40, Washington, DC, May 1961.
US Weather Bureau, Generalized Estimates of Probable Maximum Precipitation and
Rainfall-Frequency Data for Puerto Rico and Virgin Islands. Technical Paper No. 42,
Washington, DC, 1961.
US Weather Bureau, Rainfall-Frequency Atlas of the Hawaiian Islands. Technical Paper
No. 43, Washington, DC, 1962.
US Weather Bureau, Probable Maximum Precipitation and Rainfall-Frequency Data for
Alaska. Technical Paper No. 47, Washington, DC, August 1963.
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These publications may be supplemented as appropriate by more detailed weather bureau
publications and by studies of local rainfall records. For some areas, it might be reasonable to
assume that the ground would be covered with snow when the design rainfall occurs. If so, the
snowmelt would add to the runoff. Detailed procedures for estimating snowmelt runoff are given
in TM 5-785. It should be noted, however, that the rate of snowmelt under the range of
hydrometeorological conditions normally encountered would seldom exceed 0.2 inch per hour
and could be substantially less than that rate.
Principal factors entering into computation of runoff from rainfall comprise initial losses,
infiltration, transitory storage, and in some areas, percolation into natural streambeds. If
necessary basic data are available, an excellent indication of the magnitudes of these factors can
be derived from thorough analysis of past storms in the locality by the unit-hydrograph approach.
Generalized information derived from many such studies has been developed for guidance in
estimating design runoff for areas for which analytical data are not directly available. Usually, at
the onset of a storm, some rainfall is effectively retained in “wetting down” the vegetation, in
satisfying soil moisture deficiencies, and in filling surface depressions. Retention capacities for
different types of areas vary considerably. For high intensity design storms of the convective,
thunderstorm type, a maximum initial loss of up to 1 inch, depending on drainage area
characteristics, may be assumed to take place during the first hour of storm precipitation, but the
usual values are in the range of 0.25 and 0.50 inch per hour. If the design rainfall intensity is
expected to occur during a storm of long duration, after substantial amounts of antecedent
rainfall, the retention capacity would be satisfied by the antecedent rain and no further
assumption of loss would be made. Infiltration rates vary considerably, depending on types of
soils and vegetal cover, and on the use to which the areas are subjected. Also, the rates
commonly decrease as rainfall continues. Typical mean values of infiltration for generalized soil
classifications are shown in Table B1.
These infiltration rates are for uncompacted soils. Studies indicate that compacted soils
decrease infiltration values from 25 to 75 percent, the difference depending on the degree of
compaction and the types of soils encountered. The effect of vegetation is generally to decrease
the infiltration capacity of coarse soils and to increase that of clayey soils. The reduction in peak
rates of runoff due to transitory storage in the watercourses themselves and in minor ponds along
drainage routes is reflected in the C factor in the rational formula, in the CN in the SCS method,
and in the shape of the unit hydrograph. The effect of transitory storage, which varies widely,
depends on natural topography and on manmade developments in the area. Streambed
percolation losses to direct runoff need be considered only for sandy, alluvial watercourses, such
as those found in arid and semiarid regions. Rates of streambed percolation commonly range
from 0.15 to 0.5 cubic foot per second per acre of wetted area.
Table B1. Typical Values of Infiltration Rates
Infiltration,
Description
inches/hour
Sand and gravel mixture
0.8-1.0
Silty gravels and silty sands to
0.3-0.6
inorganic silt, and well-developed
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loams
Silty clay sand to sandy clay
Clays, inorganic and organic
Bare rock, not highly fractured
0.2-0.3
0.1-0.2
0.0-0.1
Rational Method
The rational method of predicting a design peak runoff rate is expressed by the
equation:
q = CiA
(B-1)
where
q = the design peak runoff rate in cfs,
C = the runoff coefficient,
i = rainfall intensity in inches/hour for the design return period and for a duration
equal to the “time of concentration” of the watershed, and
A = the watershed area in acres.
The time of concentration of a watershed is the time required for water to flow from the
most remote (in time of flow) point to the outlet once the soil has become saturated and minor
depressions filled. It is assumed that, when the duration of a storm equals the time of
concentration, all parts of the watershed are contributing simultaneously to the discharge at the
outlet. One of the formulas often used in the US for computing the time of concentration is:
Tc = 0.0078L0.77S-0.385
(B-2)
where
Tc = time of concentration in min,
L = maximum length of flow in ft, and
S = the watershed gradient in feet per foot (the difference in elevation between the
outlet and the most remote point divided by the length, L).
The runoff coefficient C is the ratio of the peak runoff rate to the rainfall intensity and is
dimensionless. Estimating the value of the runoff coefficient is difficult. The coefficient must
account for all factors affecting the relation of peak flow to average rainfall intensity other than
area and response time. Design values are normally obtained from tables of suggested values or
graphs (Table B2).
Table B2. Runoff Coefficients, C, for the Rational Formula
Type of Surface
Factor C
For all watertight roof surfaces
.75 to .95
For asphalt runway pavements
.80 to .95
For concrete runway pavements
.70 to .90
For gravel or macadam pavements
.35 to .70
*For impervious soils (heavy)
.40 to .65
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*For impervious soils, with turf
*For slightly pervious soils
*For slightly pervious soils, with turf
*For moderately pervious soils
*For moderately pervious soils, with turf
*For slopes from 1% to 2%
.30 to .55
.15 to .40
.10 to .30
.05 to .20
.00 to .10
The rational method is recognized to have a number of weaknesses in light of modern
knowledge of runoff mechanics. It is a great oversimplification of a complicated process.
However, the method is considered sufficiently accurate for runoff estimation in the design of
relatively inexpensive structures where the consequences of failure are limited.
The rational method is developed from the assumptions that: (1) rainfall occurs at
uniform intensity for a duration at least equal to the time of concentration of the watershed, and
(2) rainfall occurs at a uniform intensity over the entire area of the watershed.
Detailed description of the Rational Formula and applications of the Rational Formula
may be found in:
Maidment, D.R. (ed). Handbook of Hydrology. McGraw-Hill, Inc., NY. 1992.
American Iron and Steel Institute. Handbook of Steel Drainage & Highway Construction
Products. AISI, NY. 1971.
Chow, V.T. (ed). Handbook of Applied Hydrology. McGraw-Hill Book Co., NY. 1964.
Black, P.E. Watershed Hydrology. Prentice Hall, Englewood Cliffs, NJ. 1990.
Chow, V.T., Maidment, D.R., and Mays, L.W. Applied Hydrology. McGraw-Hill, Inc., NY
Schwab, G.O., Fangmeier, D.D., Elliot, W.J., and Frevert, R.K. Soil and Water Conservation
Engineering, Fourth Edition. John Wiley & Sons, Inc., NY. 1993.
SCS Method
The SCS Runoff Curve Number (CN) method is described in detail in NEH-4 (SCS
1985). The SCS runoff equation is:
Q
( P  Ia ) 2
( P  Ia )  S
where
Q = runoff (in),
P = rainfall (in),
(B-3)
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S = potential maximum retention after runoff begins (in), and
Ia = initial abstraction (in).
Initial abstraction (Ia) is all losses before runoff begins. It includes water retained in
surface depressions, water intercepted by vegetation, evaporation, and infiltration. Ia is highly
variable but generally is correlated with soil and cover parameters. Through studies of many
small agricultural watersheds, Ia was found to be approximated by the following empirical
equation:
Ia = 0.2S
(B-4)
By removing Ia as an independent parameter, this approximation allows use of a
combination of S and P to produce a unique runoff amount. Substituting equation (B-4) into
equation (B-3) gives:
Q
( P  0.2 S ) 2
( P  0.8S )
(B-5)
S is related to the soil and cover conditions of the watershed through the CN. CN has a
range of 0 to 100, and S is related to CN by:
S
1000
 10
CN
(B-6)
The major factors that determine CN are the hydrologic soil group, cover type, treatment,
hydrologic condition, and antecedent runoff condition. Another factor considered is whether
impervious areas outlet directly to the drainage system or whether the flow spreads over pervious
areas before entering the drainage system. The peak discharge in the SCS method is derived
from a triangular approximation to the hydrograph resulting from a rainfall excess of duration D.
This method described by SCS (1989) and included as Appendix B was originally
developed for uniform rainfall. The time to peak flow is:
Tp = D/2 + TL = D/2 + 0.6 Tc
(B-7)
where
Tp
D
TL
Tc
=
=
=
=
time to peak (T),
duration of excess rainfall (T),
time of lag (T),
time of concentration (T).
Time of concentration equal to TL/0.6 is the longest travel time and may be obtained from
the equation:
Tc = L0.8[(1000/N) - 9]0.7/[4407 (Sg)0.5]
where
(B-8)
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Tc
L
N
Sg
=
=
=
=
time of concentration in hours,
longest flow length in m,
runoff curve number,
average watershed gradient in m/m.
The time of peak is necessary to develop a design hydrograph for routing runoff through a
storage reservoir or for combining hydrographs from several subwatersheds. It is not required for
peak flow estimates. The peak flow rate is calculated from the equation:
q = quAQ
(B-9)
where
q
qu
A
Q
=
=
=
=
peak runoff rate (m3/s),
unit peak flow rate (m3/s per ha/mm of runoff),
watershed area in ha,
runoff depth in mm
The unit flow rate is obtained from graphs using the time of concentration and the ratio of
initial abstraction to 24-hour rainfall. This ratio represents the fraction of rainfall that occurs
before runoff begins. The initial abstraction is usually taken as 0.2S, where S is the maximum
difference between rainfall and runoff calculated from Eq. B-6.
The SCS method is the most widely used in the United States for estimating peak runoff
rates on small drainage basins. Application of the SCS method is simple and direct. Problems
are caused by different analysts obtaining different answers as a result of choice of different
procedures, especially for estimating Tc and in choosing the curve number CN.
For basins up to 20 square miles, SCS procedures developed from TR-55 (SCS, 1986)
may be used to predict peak runoff rates. Those procedures are described in the following
references:
SCS. Urban Hydrology for Small Watersheds. TR-55, Soil Conservation Service, USDA,
Washington, DC. 1986.
Maidment, D.R. (ed). Handbook of Hydrology. McGraw-Hill, Inc., NY. 1992.
Additionally, several computerized sources of the TR-55 method are available.
Unit Hydrograph Method
Where basic hydrologic data on rainfall and runoff are adequate to determine unit
hydrographs for a drainage area under consideration, the uncertainties inherent in applications of
the rational and SCS methods can be largely eliminated. Apparent loss rates determined from
unit-hydrograph analyses of recorded floods provide a good basis for estimating loss rates for
storms of design magnitude. Also, flow times and storage effects are accounted for in the shape
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of a unit hydrograph. Where basic data are inadequate for direct determination of unit
hydrographs, use may be made of empirical methods for synthesis, such as those outlined in EM
1110-2-1405. The methods involve lag relations and average or typical summation hydrographs
(S curves) that have been developed for regional streams. Use of the unit-hydrograph method is
particularly desirable where peak runoff from large tributary areas is involved in design and
where large-scale protective works are under consideration. The volume and duration of storm
runoff may be the principal design criteria in determining the functional dimensions of hydraulic
structures. These design computations as well as flow-routing procedures should be determined
by a competent engineer.