MODULE 1
_______________________________________________
RAINFALL - RUNOFF
Introduction
In order to understand and design erosion control BMPs and structures a
background in applied hydrology is needed. Knowing how to compute or determine
volumes and peak rates of runoff in the context of the recurrence interval or return period
are important skills. Conceptually, the precipitation - runoff process can be visualized as
shown in Figure 1-1. At the start of a runoff producing precipitation event, the surface
runoff is zero. As the rain continues, the areas located nearest the point-of-interest or the
stream will slowly begin to yield some runoff water, causing runoff to begin at a low rate at
the point-of-interest, see time t1. As the rain continues, larger and more remote areas of
the watershed begin to contribute runoff, see time t2. When rain has occurred long
enough for the total watershed to be contributing runoff, the time of concentration, tc, the
peak rate of runoff occurs. The peak rate of runoff is the parameter needed for the design
of most water carrying structures, such as channels, culverts, slope drains, temporary
diversions, etc. In the cases where water storage structures, such as silt and skimmer
basins, it is necessary to have a measure of the total volume of runoff. This is the area
under the runoff rate versus time plot (called a hydrograph).
Figure 1-1. Conceptualization of the hydrologic processes.
Rain, in addition to causing or driving the runoff process, also drives the erosion
process. The commonly used RUSLE erosion model is based on the rainfall energy
needed to detach soil particles.
In order to properly plan and correctly size most erosion control structures, it is
necessary to predict peak rates and/or volumes of surface runoff as a function of the
probability that the design storm will be exceeded during the life of the structure. The
ability to predict runoff characteristics requires a great deal of information about time of
the year, geographic location, size of contributing watershed, duration of the storm, time
required for all areas of the watershed to contribute runoff water to the outlet, rainfall
intensity, soil moisture conditions, and the degree or magnitude of flooding being
considered.
The purpose of this module is to explain how to quantify the runoff volume and the
peak rate of runoff expected from small watersheds (<1000 acres). The following two
sections on Risk Analysis and Time of Concentration are common to both of the
hydrologic analysis methods presented later in this module--the Soil-Cover-Complex
Method of determining peak runoff rates and volumes of runoff and the Rational Method
of predicting peak runoff rates.
Exceedance Interval, Return Period and Risk Analysis
By studying natural events, rainfall and runoff in particular, in a given location over a
long period of time it is possible to determine that large events occur less often than small
events and to relate the probability, Pr, of a given sized event occurring in any year to a
parameter known as the exceedance interval or return period, T, as
T=
1
Pr
(1)
For instance, a storm that has a 5% probability of occurring in a given year has a
20-year return period (1/0.05 = 20). Therefore, a 2-year return period storm has a 50%
chance of occurring each year. Similarly a 100-year storm has a 1% probability of
occurring each year. If an erosion control structure is expected to function without risk of
failure (failure being defined as being asked to carry more water than it was sized, or
designed, to carry) for a period greater than one year, the risk of failure, R, is related to
the return period, T, and the life of the structure, n in years as (Viessman et al., 1972)
1
R = 1 − ⎛⎜1 − ⎞⎟
⎝ T⎠
n
(2)
Commonly used return periods and structure lives have been substituted into
equation 2 and plotted in Figure 1-2. For instance, if a channel on a 3-year construction
project was sized to carry the 10-year return period peak runoff rate, there would be 27%
chance that a runoff event would occur during the 3-year project that would have a peak
rate of runoff larger than the 10-year design storm. Note that Figure 1-2 provides risk
Risk of Failure During Structure Life (%)
assessment for projects having durations of l to 20 years. Most erosion control structures
are designed for a 2-,10-, or 25-year return period and are usually assumed to have a life
at least as long as the construction project.
90
80
2-yr
70
5-yr
60
10-yr
50
25-yr
40
30
50-yr
20
100-yr
10
0
0
5
10
Life of Structire (yrs)
15
20
Figure 1-2. Risk of failure as a function of structure life.
The return period used to design an erosion control facility should be chosen
because of the need to (1) limit economic damage due to flooding or (2) protect human
life. If failure of a structure is expected to cause loss-of-life or serious property damage, a
return period of at least 100 years should be chosen. If loss-of-life is not a reasonable
expectation, one should select the design return period based on "how often replacement
or repair the structure can be afforded". For example a diversion ditch used to divert
runoff away from a construction site is relatively easy and inexpensive to replace; such
structures are usually designed to carry the runoff from a 5- or 10-year event.
Precipitation Data
Most models developed to evaluate or predict either runoff volume or peak runoff rate
require reliable rainfall data as input. The rainfall input data required for proper use within
the models discussed herein are available on the web at
http://hdsc.nws.noaa.gov/hdsc/pfds/orb/nc_pfds.html and summarized in the appendix to
this module.
Time of Concentration
The time of concentration is defined by USDA-SCS (1986), as the time required for
surface runoff water to travel from the watershed's most remote point to the
point-of-interest. Many methods have been developed to estimate the time of
concentration for specific watersheds (Kirpich, 1940; Izzard, 1946; Aron and Egborge,
1973; Bedient and Huber, 1992; USDA-SCS, 1972b; USDA-SCS, 1975b; USDA-SCS,
1986). Presented below are two relatively simple and widely used methods of estimating
the time of concentration--the Kirpich Method (Kirpich, 1940), and the Segmental Method
taken from the 1986 (2nd) release of TR-55 (USDA-SCS, 1986).
These two methods do not, and are not expected to, yield the same estimated
values for time of concentration. Each method is different because each was developed
by a different scientist for a different group of watersheds. The answer to the question of
‘which method is better?’ or ‘which method should be used?’ is not easy or
straightforward. The method chosen is usually based on one of two lines of reasoning; (1)
the method specified by an ordinance, code or set of regulations, or (2) the method for
which you have the necessary data. Neither of these selection processes is satisfactory.
The first selection method is often a practical reality dictated by local and/or state officials
who like a certain method. The second way of selecting a time of concentration method
often results from lacking sufficient field data to use one or another of the available
methods. These time-of-concentration methods are presented below. Finally, it is
convenient to know that as long as a watershed’s area is less than 4.6S, where S is the
slope in percent, the time of concentration can be taken to be 5 minutes.
What role do E&SC BMPs have on a watershed’s time of concentration? Though
little research is available to answer this question, there are several observations that are
rather obvious. First, all BMPs require that something be done to the flowing water,
therefore, the action by the BMP on the flowing water will definitely slow the water process
over the watershed. BMPs that are designed to control erosion, will slow the water and
provide some detention, so these BMPs will increase the time of concentration; how much
is difficult to determine. Finally, sediment control BMPs require that the flowing water be
captured and held for a period of time so the soil can settle from the water. Though it is
hard to determine exactly how to implement this information in runoff calculations, the
detention times used in the design of stilling and sediment basins can, in theory, be added
to the watershed’s time of concentration.
Kirpich Method
Kirpich (1940) developed a formula for predicting time of concentration from seven
rural watersheds in Tennessee. The watersheds had well defined channels and steep (3
to 10%) slopes. The Kirpich formula is
0.385
⎡ L3 ⎤
⎢H ⎥
tc = ⎣ ⎦
128
(3)
where tc is the time of concentration in minutes, L is the length of the longest flow path
from the most remote point in the watershed to the point-of-interest, in feet and H is the
elevation difference between the most remote point and the point of interest in feet. The
Kirpich Method yields very conservative or short times of concentration that result in high
peak runoff rates, especially from the Rational Method. The Kirpich Method has, more
than any other method, become associated with the Rational Method.
Example 1. The watershed supplying runoff to a culvert has an area of 3
acres, a longest flow path of 400 ft, and a slope of 5% (H = 0.05(400) = 20
ft). Use the Kirpich Method to estimate this watershed’s time of
concentration.
Solution: To apply equation 3, we need to know; L = 400 ft and H = 20 ft.
Therefore, tc can be computed as
⎡ 4003 ⎤
⎢ 20 ⎥
⎦
tc = ⎣
128
0.385
= 2.5 min
SCS (NRCS) Segmental Method
In 1986, SCS released an updated version of TR-55 (USDA-SCS, 1986), which
presented a very different approach to computing a watershed's time of concentration.
The method, known today as the SCS Segmental Method, is based on the premise that
runoff flowing from any watershed's most remote point will begin in the upper reaches as
sheet flow, become shallow concentrated flow as it travels over the majority of the longest
path, and finally enter a channel, where Manning's equation best describes the flow
hydraulics. The SCS Segmental Method has become, to some degree, associated with
SCS (NRCS)’s Soil Cover Complex Method of determining runoff depth (volume) and
peak runoff rate. In the SCS Segmental Method, the longest flow path for a watershed is
classified into three types of flow; sheet flow, shallow concentrated flow and open
channel. The travel times computed for each type of flow are then added to yield the time
of concentration for the watershed. It should be noted that a large majority of the
watershed flow path is best classified as shallow concentrated flow. Only in special cases,
where sheet flow or channel flow are obviously present, should these two types of flow be
considered as part of the time of concentration computation.
Sheet Flow is flow over smooth, plane surfaces. It usually occurs near the headwaters of
watersheds where the overland flow is shallow and very uniform. Sheet flow also requires
flow over a rather smooth surface. Sheet flow may not occur on many watersheds,
especially in the upper reaches. The velocity of sheet flow is dependent upon the friction
value, which can be estimated from Manning's n, from Table 1-1.
Manning's n includes the effect of raindrop impact; drag over the plane surface; obstacles
such as litter, crop ridges, and rocks; and erosion and transportation of sediment. These
n values are for very shallow flow depths of about 0.1 foot or so. Table 1-1 gives sheet
flow Manning's n values for various surface conditions.
Manning's kinematic flow equation solution (Overton and Meadows 1976) is used to
compute the time of travel Tt for sheet flow segment (limited to a maximum of 300 feet at
the upper-most part of the watershed, which is usually considered to be excessive), as
Table 1-1. Manning's Roughness coefficients n for sheet flow. (Taken from
USDA-SCS, 1986).
Surface Description
n1
Smooth surfaces (concrete, asphalt, gravel, or bare soil)
0.011
Fallow (no residue)
0.05
Cultivated soils
Residue cover < 20%
0.06
Residue cover >20%
0.17
Grass:
Short grass prairie
0.15
Dense grasses2
0.24
Bermuda grass
0.41
Range (natural)
0.13
3
Woods:
Light underbrush
0.40
Dense undergrowth
0.80
1
The n values are a composite of information compiled by
Engman (1986).
2
Includes species such as weeping lovegrass, bluegrass, buffalo
grass, blue grama grass, and native grass mixtures.
3
When selecting n, consider cover to a height of about 0.1 ft.
This is the only part of the plant cover that will obstruct sheet
flow.
0.42(nL) 0.8
Tt s =
P20.5 S 0.4
(4)
where Tt is the sheet flow travel time in minutes, n is Manning's roughness coefficient
(Table 1-1), P2 is the 2-year, 24-hour rainfall depth in inches, S is the slope of the
hydraulic grade line, usually taken to be the land slope in ft/ft, and L is the sheet flow
length in feet. This simplified form of the kinematic flow equation is based on the following:
(1) shallow steady uniform flow, (2) constant intensity of rainfall excess (that part of a rain
available for runoff), (3) rainfall duration of 24 hours, and (4) minor effects of infiltration on
travel time.
Average Velovity, V (Ft/Min)
1000
100
Paved
Unpaved
10
0.001
0.01
0.1
1
Slope, S (Ft/Ft)
Figure 1-3. Average shallow concentrated flow velocities for paved and unpaved conditions.
The appropriate or correct length of sheet flow has been debated since this method
was published. The USDA-SCS (1986) publication states that sheet flow shall not exceed
300 feet. Many users of this time of concentration method have discovered that for typical
watersheds, the time of travel for sheet flow is often 50 to 80 percent of the total
watershed's time of concentration. Viewing this as unreasonable, many users have begun
shortening the length of sheet flow, trying not to use sheet-flow lengths in excess of 50 to
150 feet. Some hydrologists have suggested that sheet flow is rare on natural
watersheds and should only be considered part of the time of concentration when there is
documentable evidence that sheet flow exists. Some municipalities have begun to ask
that engineers not consider sheet flow at all. Here is a place where good engineering
judgment is needed.
Table 1-2. Shallow concentrated flow velocity
equations. Slope is in units of ft/ft.
Velocity in ft/min.
Land Use
Paved Areas
Unpaved Areas
Velocity Equation
V = 1302S0.53
V = 972S0.53
Shallow Concentrated Flow is how runoff usually flows over the land surface area
upland of entering a defined channel. The average velocity for this flow can be determined
from Figure 1-3 or computed using the equations in Table 1-2, in which average overland
flow velocity is a function of water flow area’s slope and type of land cover (paved or
unpaved).
One weakness in this method is that the overland flow velocities shown in Figure 1-3
assume the average overland flow velocity for unpaved land uses are the same. The time
for water to travel over an area as shallow concentrated flow, Tto is then computed as
Tto =
L
V
(5)
where L is the shallow concentrated flow path length in feet, and V is the shallow
concentrated flow velocity in ft/min.
Channel Flow is assumed to begin where surveyed cross section information has
been obtained, where channels are visible on aerial photographs, or where blue lines
(indicating streams) appear on United States Geological Survey (USGS) quadrangle
sheets. Manning's equation can be used to estimate the average flow velocity in these
channels. Average flow velocity is usually determined for the bankfull depth. Manning's
equation is used to estimate open channel flow velocities. This equation will be discussed
in detail in Module 2 as
2
1.486 R 3 S
V=
n
1
2
(6)
Where V is the channel velocity in feet/sec. When the channel velocity is used with the
channel length as in equation 6, the time of travel in the channel can be computed in
ft/min as
Ln
(7)
Ttc =
2
1
89.4 R 3 S 2
where V is the average velocity in ft/min, R is the hydraulic radius in feet, and R is equal to
A/Wp, where A is the cross sectional flow area in square feet, Wp is the wetted perimeter
in feet, S is the slope of the hydraulic grade line, taken to be the channel slope, ft/ft, and n
is Manning's roughness coefficient for open channel flow. Manning's n values for open
channel flow can be obtained from Module 2.
After the sheet, shallow concentrated, and channel time of travels have been
computed using equations 4, 5,and 7, they should be summed to yield the total time of
concentration for the watershed as
t c = Tt s + Tto + Ttc
Example 2. The watershed supplying runoff to a culvert has an area of 3
acres, a longest flow path of 400 ft, and a slope of 5% (H = 0.05(400) = 20
ft). Use the Segmental Method to estimate this watershed’s time of
concentration. Assume the entire flow length is shallow concentrated flow.
Solution: From Fig. 1-3 or by using the equation in Table 1-2, the overland
flow velocity can be obtained as:
a. From Fig. 1-3, V = 220 ft/min.
(8)
b. By the equation: V = 972(0.05)0.53 = 200 ft/min
Therefore, the time of concentration for this watershed is
tc =
L
400 ft
=
= 2 min
V 200 ft / min
Note that all flow was assumed to be shallow concentrated flow.
Estimating Runoff Volume and Peak Rates of Runoff
Estimating the volume of runoff or the peak runoff rate expected to occur from a
specific watershed in response to a specific rainfall event is a very difficult challenge.
Hydrologists have struggled to define the many critical relationships that define the
processes and the interrelationships between these processes for years. One of the first
successful attempts to quantify a watershed’s runoff response was developed by the
USDA-SCS (1972) when they published what we know today as the SCS or Soil-CoverComplex Method. A second early method was known as the Rational Method.
Both the Soil-Cover-Complex and Rational Methods will be discussed in this
module. Both have also been developed far beyond the scope of this module to include
the ability to determine not only runoff volumes and peak runoff rates (discussed herein),
but to determine excellent estimates of the complete runoff hydrograph expected from
each rainfall event.
Before either of these models is discussed in detail, it may be helpful to define the
capabilities of each model. Rainfall-runoff analyses usually seek to determine either (1)
the volume of runoff or (2) the peak rate of runoff or both from a specific watershed in
response to a specific rainfall event. The Soil-Cover-Complex Method was originally
developed to calculate the volume of runoff only. In recent years, this method has been
further developed to yield the peak rate of runoff as well. The Rational Method is a simple
equation that is only able to estimate the peak runoff rate. The limitations of these two
models are summarized in Table 1-3.
Lastly, it is important to mention that you should NEVER mix these two methods. It
is not appropriate to use the Soil-Cover-Complex Method to determine the volume of
runoff and the Rational Method to determine the peak rate of runoff. Pick the method that
yields the information you need and use it throughout the design.
Table 1-3. Summary of hydrology models and their capabilities.
Runoff Model
Soil-Cover-Complex
Rational
Runoff Parameters
Runoff Volume
X
Peak Rate of Runoff
X
X
Rational Method
The Rational Method (Water Pollution Control Federation, 1969) of predicting a
watershed's hydrologic response yields only the peak runoff rate. The Rational Method is
an appropriate method of runoff analysis when only the peak runoff rate is needed,
especially for applications such as the design of channels, culverts, slope drains,
temporary diversions, etc. If the volume of runoff is required for a particular application,
the Soil-Cover-Complex Method should be used to determine both design parameters.
The Rational Method is an old method of estimating the peak runoff rate expected
from a watershed. This method has several desirable characteristics including being
simple and conceptually more understandable that the Soil-Cover-Complex Method
discussed in the next section. Many political units prescribe the Rational Method for
erosion and stormwater calculations. The Rational Method is a simple formula often
referred to as the Rational formula:
Q p = CiA
(9)
where Qp is the peak runoff rate in cubic feet per second (cfs), C is the runoff coefficient, i
is the design rainfall intensity in inches per hour (iph), and A is the watershed area in
acres.
Rainfall Intensity. The rainfall intensity, i in the Rational Method is often referred
to as the design rainfall intensity. The design rainfall intensity is more properly defined as
the uniform rainfall intensity that has a duration equal to the watershed’s response time (or
time of concentration). This design rainfall intensity is a function of three parameters; (1)
the watershed's time of concentration, (2) the watershed's location and (3) the return
period for which the peak runoff rate is desired.
To determine the design rainfall intensity for use in the Rational Method, first
determine the watershed's time of concentration, tc using one of the methods discussed in
the time of concentration section of this chapter. In some cases the time of concentration
method may be specified, in other cases you will have the freedom to select the method
you feel most comfortable with or have the data to use. One of the important assumptions
upon which the Rational Method is based is that the rainfall duration is assumed to be
equal to the watershed's time of concentration. Second, determine the return period that
will limit the risk of a larger event to an acceptable level. Third, read the design rainfall
intensity from the best available Intensity-Duration-Frequency (IDF) information to
determine the design rainfall intensity for the rainfall duration and return period. IDF
curves are available at http://hdsc.nws.noaa.gov/hdsc/pfds/orb/nc_pfds.html. The
following example will demonstrate this procedure.
Example 3: Determine the 10-year return period design rainfall intensity for
a roadway construction site in Greensboro, NC having a 15-minute time of
concentration.
Solution: The design rainfall intensity for a 15-minutes storm with a 10-year
return period in Greenboro is 4.62 in/hr
(http://hdsc.nws.noaa.gov/hdsc/pfds/orb/nc_pfds.html).
Table 1-4. Rational Method Runoff Coefficients for Agricultural Areas.
(Taken from Schwab et al., 1971).
Vegetation
Slope
Runoff Coefficient, C
Sandy
Clay and Silt Tight Clay3
1
Loam
Loam2
Forest
0.10
0.30
0.40
0-5% slope
0.25
0.35
0.50
5-10% slope
0.30
0.50
0.60
10-30% slope
Pasture
0.10
0.30
0.40
0-5% slope
0.16
0.36
0.55
5-10% slope
0.22
0.42
0.60
10-30% slope
Cultivated
0.30
0.50
0.60
0-5% slope
0.40
0.60
0.70
5-10% slope
0.52
0.72
0.82
10-30% slope
1
Equivalent to Soil-Cover-Complex Hydrologic Soil Group A.
2
Equivalent to Soil-Cover-Complex Hydrologic Soil Group B and C.
3
Equivalent to Soil-Cover-Complex Hydrologic Soil Group D.
Runoff Coefficient. The watershed characteristics that contribute to the
attenuation of the precipitation to produce the peak runoff rate, are summarized in a single
parameter known, in the Rational Method, as the runoff coefficient. The runoff coefficient,
C is a dimensionless parameter between 0.0 and 1.0 depending on the watershed soil's
infiltration rate, the land use and the land slope. Soils with rapid infiltration rates, such as
sands, have low runoff coefficients (eg. 0.0 to 0.30), while soils with slow infiltration rates,
such as clays have much higher runoff coefficients. Impermeable areas such as roofs
and parking lots have runoff coefficients of 1.00 or nearly 1.00. The influence of
vegetation on infiltration rate is two-fold. First, the denser and larger the vegetative cover,
the more rain will be intercepted and not reach the soil surface. Second, the presence of
deep-rooted vegetation tends to improve soil structure and increase infiltration.
The combined interaction of the soil's infiltration (expressed as soil texture), land
use, and slope on the runoff coefficient for the Rational Method is summarized in Tables
1-4, 1-5, and 1-6. The runoff coefficient, C, is technically defined as the ratio of the peak
runoff rate to the rainfall intensity. From a practical standpoint, C can be viewed as the
fraction of rain that becomes runoff.
Table 1-5. Rational Method Runoff Coefficients for Urban Areas.
(Taken from Chow, 1962).
Land Use
Business areas
Downtown
Neighborhoods
Residential areas
Single-family homes
Multi-units; detached
Multi-units; attached
Suburban
Apartment buildings
Industrial
Light industry
Heavy industry
Parks, Cemeteries
Playgrounds, grassed
Playgrounds, paved
Railroad yards
Unimproved areas
Streets (including rights-of-way)
Brick drives and walks
Roofs
100% Impervious Surface
Runoff Coefficient,
C
0.83
0.60
0.40
0.50
0.68
0.33
0.60
0.65
0.75
0.18
0.28
0.80
0.30
0.20
0.83
0.80
0.85
1.00
It should be noted that selecting appropriate C-values for construction or
development activities is very difficult. This is because the Rational Method was
developed for use by “agricultural” related agencies. Thus all of the original (published) Cvalues were for agricultural land uses. In the late 1960s and early 1970s when engineers
began to be asked to develop erosion control and stormwater plans for construction
activities in the ag-urban interface, they found few, if any, appropriate C-values to use.
Most of the C-values beyond those shown in Table 1-5 were “made up” with a great deal
of professional judgment, by those needing to predict peak runoff rates. There is
essentially no research to back any of the C-values taken from Chow (1962) or ASCE in
Tables 1-5 and 1-6. As engineers using this method, engineering judgment is critical here.
Because most watersheds contain more than one soil type with multiple land uses
and slopes, it is necessary to determine the single runoff coefficient that represents this
total variability by determining the watershed’s weighted average runoff coefficient. The
weighted average runoff coefficient, C for an entire watershed can be computed as
follows:
Table 1-6. Rational Method Runoff Coefficients (Taken from ASCE)
Land Use
Business:
Downtown areas
Neighborhood areas
Residential:
Single-family areas
Multi units, detached
Multi units, attached
Suburban
Industrial:
Light areas
Heavy areas
Parks, cemeteries
Playgrounds
Railroad yard areas
Unimproved areas
Streets:
Asphalt
Concrete
Brick
Drives and walks
Roofs
C=
Runoff
Coefficient,
C
Land Use
Lawns:
0.70-0.95
Sandy soil, flat, 2%
0.50-0.70
Sandy soil, ave., 2-7%
Sandy soil, steep, 7%
0.30-0.50
Heavy soil, flat, 2%
0.40-0.60
Heavy soil, ave., 2-7%
0.60-0.75
Heavy soil, steep, 7%
0.20-0.40 Agricultural land:
Bare packed soil
0.50-0.80
Smooth
0.60-0.90
Rough
0.10-0.25
Cultivated rows
0.20-0.35
Heavy soil no crop
0.20-0.40
Heavy soil with crop
0.10-0.30
Sandy soil no crop
Sandy soil with crop
0.70-0.95
Pasture
0.80-0.95
Heavy soil
0.70-0.85
Sandy soil
0.75-0.85
Woodlands
0.75-0.85
Runoff
Coefficient,
C
0.05-0.10
0.10-0.15
0.15-0.20
0.13-0.17
0.18-0.22
0.25-0.35
0.30-0.60
0.20-0.50
0.30-0.60
0.20-0.50
0.20-0.40
0.10-0.25
0.15-0.45
0.05-0.25
0.05-0.25
A1C1 + A2C 2 + A3C3 + ... + An Cn ΣAC
=
A1 + A2 + A3 + ... + An
ΣA
(10)
where Ci is the runoff coefficient for watershed subarea Ai. This equation can be applied
in a tabular form as shown in the following example.
Example 4: Determine the weighted average runoff coefficient, C, for a
4-acre watershed, part of which will have a highway constructed on it, that
contains the following land uses, soils and slopes:
1. 1 Ac of woodland on 7% sloping silt loam soil.
2. 2 Ac of bare soil, construction site on 2% sloping sandy loam soil.
3. 1 Ac of riparian corridor on 2% sloping clay soil.
Solution: The weighted average runoff coefficient can most easily be
determined using the following tabular approach:
Part
1
2
3
Area, A (ac)
1
2
1
∑A = 4 ac.
Runoff Coefficient, C =
C
0.35
0.30
0.10
CA
0.35
0.60
0.10
∑CA = 1.05
ΣCA 1.05
=
= 0.26
ΣA
4
The "CA" column is obtained by multiplying the area, A column by the runoff
coefficient, C column as shown for each watershed subarea, ex. Part 1 is 1
x 0.35 = 0.35.
Final Note: The runoff coefficient, C, is unique to the Rational Method. Many
attempts have been made to harmonize the Rational Method's runoff coefficient with the
Soil-Cover-Complex Method's Curve Number. It would seem that they should be the
same with one simply expressed as a fraction instead of a percentage. This is an incorrect
assumption and the two coefficients are not equivalent and should never be interchanged
or considered equivalent. The notes at the end of Table 1-4 are an attempt to equate the
soil textures (not the C and CN values) in Table 1-7 with the Hydrologic Soil Groups
presented later in this module. This correlation should only be used as a last resort.
Peak Runoff Rates. Each of the factors in the Rational Method has been
discussed in previous sections. The parameters needed to determine the peak runoff rate
using the Rational Formula are the runoff coefficient, C, the design rainfall intensity, i in
inches per hour (iph) and the total watershed area, A in acres. The units in the Rational
Formula peak runoff rate, Qp in cubic feet per second (cfs) are correct as shown here
Q p = CiA
ft
hr
ft 3 in ac
43,560 ft 2
=
= 1.008cfs
x
x
x
x
ac
sec hr 1 3,600 sec
12in
The conversions to change the units of ac-in/hr to ft3/sec (cfs) are approximately
equal to 1.0 (1.008). This unit conversion factor of 1.008 is never used or shown when
applying the Rational Formula. Since the number of significant figures in the factors within
the Rational Formula is rarely more than two, this conversion is unnecessary. The
following example will illustrate the procedure for determining the peak runoff rate using
the Rational Method.
Example 5: Determine the 10-year return period peak runoff rate, in cfs,
expected from a 5-acre watershed located near Asheville, NC, and has the
following subareas, found on the watershed in order from the headwaters to
point-of-interest, with land uses, soil series, hydraulic lengths, and slopes
shown in the table below. The watershed has no defined channels and the
upland forest does not support sheet flow. The watershed’s hydraulic
length, = 600 ft and the average slope, S = 6%. Use the Segmental Method
to determine the watershed's time of concentration and the Rational Method
to estimate the peak runoff rate.
Subarea
Area
(acres)
1
2
3
4
1
1
2
1
Land Use
Forest
Row crops
Bare Soil
Pavement
Soil
Texture
Hydraulic Slope
Length
(%)
(feet)
Sandy loam
100
11
Silt loam
150
9
Tight clay
300
4
-50
2
Solution:
1. The return period is given as 10 years.
2. The time of concentration should be computed as shallow concentrated
flow for the slope given as 6% and the length given as 600 ft. The overland
flow velocity, form Fig. 1-3 is about 230 ft/min assuming all of the path is
unpaved. Therefore, the time of concentration is (600/230 = ) 2.6 min; so we
will use 5 minutes.
3. The 5-minute rainfall intensity for a 10-year storm in Asheville, NC, taken
from the charts in the appendix is 6.96 in/hr.
4. The runoff coefficient for the land uses, soils, and slopes given is
computed below.
Soil
Texture
Sandy loam
Silt loam
Tight clay
--
Land Use
Forest
Row Crops
Bare soil
Pavement
C=
Slope
(%)
11
9
4
2
Area, A
(acres)
1
1
2
1
∑A = 5 ac
C
0.30
0.60
0.60
1.00
CA
0.30
0.60
1.20
1.00
∑CA = 3.10
ΣCA 3.1
=
= 0.62
ΣA
5
5. The peak runoff rate, Qp is
Q p = CiA = 0.62 × 6.96
in
× 5acres = 21.6cfs ; Use 22 cfs.
hr
Soil-Cover-Complex Method (SCS, NRCS, TR-55, Curve Number)
The Soil-Cover-Complex (SCC) Method (USDA-SCS, 1972, 1875, 1986) of
predicting a watershed's hydrologic response will yield both the volume of runoff and the
peak rate of runoff. These estimates are reliable for the return period used in the analysis.
The Soil-Cover-Complex Method (sometimes referred to as the SCS or NRSC or
Curve Number, TR-55 Method) is based on the following equation
Q=
(P − I a )2
(P − Ia ) + S
(11)
which is the rainfall-runoff relationship with the initial abstraction taken into account. The
maximum retention S has been related to the initial abstraction Ia as Ia = 0.2S. By making
this substitution into equation 11 the final runoff relationship used in the Soil-CoverComplex Method is
Q=
( P − 0.2 S ) 2
.
P + 0.8S
(12)
The runoff coefficient, here called the Curve Number, CN is related to the maximum
retention S as
1000
1000
or S =
− 10
(13)
CN
S + 10
The CN integrates the effects of soil texture and ground cover into an average runoff
response parameter that represents the whole watershed.
CN =
Precipitation Input. The input rainfall data required for the Soil-Cover-Complex
Method is the 24-hour rainfall depth, in inches, expected for the return period specified or
selected from the risk analysis. The 24-hour rainfall data are available at
http://hdsc.nws.noaa.gov/hdsc/pfds/orb/nc_pfds.html.
Runoff Curve Number. In the Soil-Cover-Complex Method, the attenuation of the
rainfall by the watershed is summarized into a single parameter called the Curve Number,
CN. The curve number integrates the impact of land use, the hydrologic condition and the
infiltration capacity of the soils reflected in the Hydrologic Soil Group (HSG). SCS
subdivided all soils into one of four HSG, A, B, C, and D. The HSG designation is based
almost entirely on the soil’s infiltration capacity. Soils in the A HSG are sandy with very
rapid infiltration rates (think of beach sand). Soils in the D HSG are clayey with very low
infiltration rates (think of compacted clay skinned baseball field). The B and C HSGs are
indicative of most agricultural soils. Your NRCS County Soil Survey can provide
information on each soil’s HSG.
As discussed in the Runoff Coefficient discussion earlier, the SCC’s CNs were
developed by SCS (now NRCS) back in the 40s and 50s when the only land uses of
interest were agricultural. Not until SCS released the original version of TR-55 for urban
runoff was the original agricultural list of CNs enlarged. No experimental background or
data were ever presented to substantiate these new CNs. The CN's for each land use,
hydrologic condition and the four hydrologic soil groups given in Table 1-7 have been
selected from the larger agricultural list. The Curve Number (CN) varies from 0 for areas
expected to produce no runoff regardless of storm size to 100 for areas expected to
convey 100% of the rain to runoff.
A few agricultural land uses are included in Table 1-7, but the majority of the land
uses listed in Table 1-7 are for development or construction land uses. The hydrologic
condition (Good, Fair, or Poor) refers to the degree of soil cover and the condition of the
surface soil relative to its ability to infiltrate water. A "Good" hydrologic condition is
expected to yield less runoff than a "Fair" or "Poor" condition.
Because few watersheds have only one soil type or land use, it is necessary to be
able to determine a "weighted average" CN that represents the hydrologic response
expected for the entire watershed. This average CN is weighted according to the relative
portions or areas of the watershed in each hydrologic soil group and land use. The
weighted average CN can be determined using the following formula:
Often it is more convenient to compute the weighted average CN by placing the land use,
soils and hydrologic condition data into a table as shown in the following example. The
result of this tabular computation yields exactly the same answer for the weighted average
CN as equation 14.
CN =
A1CN 1 + A2 CN 2 + ... + An CN n
A1 + A2 + ... + An
(14)
Table 1-7 Runoff Curve Numbers for hydrologic Soil-Cover-Complexes (Taken from USDA-SCS,
1986).
Hydrologic Soil
Group
Land Use and Hydrologic Condition
Fallow, bare tilled soil
Row Crops, straight rows (field strips), good
Row crops, contoured
Continuous grazing, pasture, range, poor
Continuous grazing, pasture, range, fair
Impervious
(%)
A
B
C
D
0
0
0
0
0
77
67
62
68
49
86
78
71
79
69
91
85
78
86
79
94
89
81
89
84
Continuous grazing, pasture, range, good
Forage for hay
Brush w/weeds & grass, poor
Brush w/weeds & grass, fair
Brush w/weeds & grass, good
Orchard, Tree farm, w/ grass, poor
Orchard, Tree farm, w/ grass, fair
Orchard, Tree farm, w/ grass, good
Wooded, heavy grazing or burned, poor
Wooded, grazed but not burned, fair
Wooded, brush under story, litter, good
Farmsteads, buildings and lanes
Lawns, parks, golf courses, cemeteries
Poor condition (< 50% grass cover)
Fair condition (50-75% grass cover)
Good condition (>75% grass cover)
Paved parking lot, roof, driveway (no right-of-way)
Streets and roads (including right-of-way):
Paved; w/open ditches
Gravel
Dirt
Urban districts:
Commercial and business
Industrial
Residential subdivisions by avg. lot size
1/8-ac or less (townhouses & condos)
1/4-ac.
1/3-ac.
½-ac.
1-ac.
2-ac.
Newly graded, pervious area, no vegetation
0
0
0
0
0
0
0
0
0
0
0
-
39
30
48
35
25
57
43
32
45
36
25
59
61
58
67
56
48
73
65
58
66
60
55
74
74
71
77
70
65
82
76
72
77
73
70
82
80
78
83
77
73
86
82
79
83
79
77
86
0
0
0
100
68
49
39
98
79
69
61
98
86
79
74
98
89
84
80
98
83
76
72
89
85
82
92
89
87
93
91
89
85
72
89
81
92
88
94
91
95
93
65
38
30
25
20
12
77
61
57
54
51
46
77
85
75
72
70
68
65
86
90
83
81
80
79
77
91
92
87
86
85
84
82
94
Example 6: Determine the weighted average CN for a 4.5-acre watershed that has
the following soils, land uses, and hydrologic conditions:
Watershed
sub-unit
1
2
3
4
Area
0.5 acres
1.0 acres
2.5 acres
0.5 acres
Land Use
(Condition)
Wooded (good)
Row Crops (good)
Newly graded
½-ac Residential
HSG
B
A
C
C
Solution: The weighted average CN for this watershed can be computed using
equation 14 or by summarizing the data into the following tabular format for easy
computation.
Weighted Average Curve Number tabular computation.
Hydrologic
Land Use
Soil Group
(Condition)
CN
Area CNxArea
B
Wooded (good)
55
0.5
27.5
A
Row Crop (good)
67
1.0
67.0
C
Newly graded
91
2.5
227.5
C
½-ac Residential
80
0.5
40.0
Totals =
4.5
362
CN =
ΣCN ( A) 362
=
= 80
ΣA
4.5
Runoff Volume. Once the watershed's CN and 24-hour precipitation depth, P24
have been determined, the average runoff depth Q is determined from Figure 1-4. Figure
1-4 is the solution to equation 12 for the conditions where P ≥ 0.2S. The value of runoff,
Q obtained from Figure 1-4 is the average runoff depth, in inches, occurring over the
entire watershed under consideration. This average runoff depth is often referred to as
the volume of runoff even though it is not a true volume. In order to convert the average
runoff depth, Q into a true runoff volume, it is necessary to multiplying this runoff depth
times the watershed area, thus yielding a true volume in "acre-inch" units. This true
volume is the area under the runoff hydrograph. It is often convenient to express Q in
other volume units such as acre-feet, ft3, and even gallons. The following example will
demonstrate the process of determining the volume of runoff using the Soil-CoverComplex Method.
Example 7: Determine the volume of runoff expected from a 4.5-acre
watershed near Fayetteville, NC for a 10-year return period storm? The
watershed has a CN of 80.
Solution: First, the 24-hour, 10-year return period rainfall, P expected in
Fayetteville was determined for the website
(http://hdsc.nws.noaa.gov/hdsc/pfds/orb/nc_pfds.html) or from the appendix
at the end of this module as 5.47 inches.
Second, from Figure 1-4, the runoff depth, Q expected from this 5.47-inch
24-hour rainfall event on a watershed with a CN of 80, is 3.3 inches. Note
that until this point of the discussion the watershed area has not entered into
this determination. We used the rainfall depth of 5.47 inches with the CN =
80 to determine the average runoff depth (volume) of 3.3 inches. It may
now be convenient or even necessary, to convert the 3.3 inches of runoff
from this 4.5-acre watershed into true volume units. Using unit conversions
the 3.3-inch runoff depth can be shown to be equivalent to 15 ac-in, 1.2 acft, 54,000 ft3 or 400,000 gal of runoff from this storm.
8
7
Runoff, Q (inches)
6
5
100
4
90
95
85
3
80
75
65
70
2
60
55
50
45
1
40
35
30
0
0
1
2
3
4
5
6
7
8
Rainfall, P (inches)
Figure 1-4. Soil-Cover-Complex method of predicting runoff depth from rainfall depth. Curve
Numbers are shown below the lines. (Redrawn from USDA-SCS, 1986).
Peak Runoff Rate. To determine the peak runoff rate expected from a particular
storm using the Soil-Cover-Complex Method we must correctly distribute the average
runoff depth computed above, over the duration of the runoff event. The timing parameter
most often used to distribute the runoff is the watershed's time of concentration. Three
methods of estimating a watershed's time of concentration were discussed earlier in this
module.
The peak runoff rate, determined using the Soil-Cover-Complex Method, is a
function of the watershed's time of concentration, the runoff depth, Q and the watershed
area. The procedure for determining the peak runoff rate is to first determine the ratio Ia/P.
Remember Ia is the initial abstraction and is defined as Ia = 0.2S, where S is a function of
the CN defined by equation 14. Thus, the ratio Ia/P can be shown to be
I a 2(100 − CN )
.
=
P
P(CN )
(15)
The second step in determining the peak runoff rate is to determine the watershed's time
of concentration, tc. The most commonly used method of computing the time of
concentration for a watershed being evaluated for peak runoff rate using the Soil-CoverComplex Method is the Sequential Method. It is, however, not unusual for hydrologists to
use one of the other time-of-concentration methods to determine the time of
concentration.
Lastly, with Ia/P and tc known, either Figure 1-5 (for Type II rains) or 1-6 (for Type
III rains) are used to determine the unit peak runoff rate, qu, in units of csm/in, which is
equivalent to cfs/mi2-inch. Here it is easy to see how the unit peak runoff rate, qu is a
function of both the time of concentration, tc, shown on the x-axis, and the Ia/P ratio,
shown as lines within Figures 1-5 and 1-6. If the Ia/P ratio is outside of the limits shown in
Figures 1-5 or 1-6, use the limiting value. If the Ia/P ratio is between two lines in Figure1-5
or 1-6, interpolate to get the best value.
The unit peak runoff rate, qu read from either Figure 1-5 or 1-6, is then multiplied by
the watershed area, Am, in square miles (mi2) and the average runoff depth, Q, in inches
to obtain the peak runoff rate, Qp as
Q p = qu Am QFp .
(16)
Where Fp is a pond or swamp
adjustment factor that adjusts
the peak runoff rate based on
the portion of the watershed in
question that is under water,
see Table 1-8.
Rainfall Types. NRCS has identified four rainfall
distributions common to rains in the United States.
These are plotted in Figure 1-7. As shown in
Figure 1-8, North Carolina contains portions of
both the Type II and Type III rain distributions.
Thus those areas near the coast or within the
coastal plain should use the Type III rain
distribution, or the unit peak runoff rates from
Figure 1-6. The rest of North Carolina is within the
Type II region and thus the unit peak runoff rate
should be determined from Figure 1-5.
Figure 1-5. Unit Peak Runoff Rate for the Soil-Cover-Complex Method
for Type II rainfall distribution. (Redrawn from USDA-SCS,
1986)
Figure 1-6. Unit Peak Runoff Rate for the Soil-Cover-Complex Method
for Type III rainfall distribution. (Redrawn from USDA-SCS,
1986)
1.0
0.9
0.8
P/P24
0.7
0.6
0.5
I
IA
II
III
0.4
0.3
0.2
0.1
0.0
0
4
8
12
16
20
Time (hr)
Figure 1-7. SCS (1986) type distribution curves for 24-hour rainfall.
Figure 1-8. Regions of application for the various SCS (1986) type curves for rain distribution.
24
Table 1-8. Pond and swamp adjustment factor.
Portion of Watershed
that is pond or swamp
(%)
0
0.2
1.0
3.0
5.0
Pond Adjustment
Factor
Fp
1.00
0.97
0.87
0.75
0.72
When equation 16 is properly used to compute the peak runoff rate, the units of the
watershed area (mi2) [Note: 1 mi2 = 640 acres] and the units of the average runoff depth
(inches) cancel with the mi2 and inches in the denominator of the unit peak runoff rate to
yield units of cubic feet per second or cfs.
The following example will illustrate the procedure for determining the runoff
volume and peak runoff rate using the Soil-Cover-Complex Method.
Example 8: Use the Soil-Cover-Complex Method to determine the volume
of runoff, in inches of depth, and the peak rate of runoff, in cfs expected
once every 10 years, for a 4.5-acre watershed located near Fayetteville,
NC. Use the Kirpich Method to estimate this watershed's time of
concentration. The maximum length of flow is 800 ft and average slope is
6.7%. There are no ponds or swamps in this watershed.
Solution:
1. The design return period is 10 years.
2. From the web site or the appendix at the end of this module, the 10year, 24-hour rainfall, P24 in Fayetteville, NC is 5.47 inches
3. The runoff CN for the 4.5-acre watershed evaluated in Example 6 was
80.
4. From Figure 1-4, using a P24 of 5.47 inches and a CN of 80, the runoff
depth, Q = 3.3 inches. This is the runoff volume expressed as a depth.
[NOTE: to this point we have repeated Example 7.]
5. Use equation 3 to determine the time of concentration using the Kirpich
Method with the length, L = 800 ft, the slope, S = 6.7% (H = 0.067(800)
= 54 ft) as
0.385
⎡ L3 ⎤
⎢H ⎥
tc = ⎣ ⎦
128
⎡ 8003 ⎤
⎢ 54 ⎥
⎦
=⎣
128
0.385
= 3.8 min = 0.06hrs
6. The Ia/P ratio can be determined from equation 15 as
I a 2(100 − CN ) 2(100 − 80)
=
=
= 0.09
P
P(CN )
5.47(80)
7. Assuming Fayetteville is in the Type II region (Figs. 1-7 and 1-8) and
using the time of concentration of 0.06 hours and the Ia/P ratio of 0.09,
yields a unit peak runoff rate, qu = 1000 csm/in or cfs/mi2-inch, Figure 18.
8. Finally, with a Pond factor, Fp = 1.0 and data from this problem, the peak
runoff rate is
Qp = quAmQFp = 1000 cfs/mi2-inch(4.5 acres/640)(3.3 inches)(1.0) = 23 cfs.
The runoff response from this 4.5-acre watershed that has a 10-year return
period is a runoff volume of 3.3 inches and a peak runoff rate of 23 cfs.
Watershed Area
Determining the area of a watershed requires a topographic map. This implies that
a map is available that has an appropriate horizontal and vertical scale. The horizontal
scale is usually represented as either; (a) 1 unit on the map equals xxx units on the
ground, such as 1 inch = 400 feet, or (b) the units on the map and in the field are given as
a ratio, such as 1:24000. When the ratio is used the units on both sides of the colon are
the same. The vertical scale of a map is the contour interval. Enough contours must be
shown to adequately describe the watershed boundary.
Before the area of a watershed can be determined, one must first delineate the
boundaries of the watershed. This means that for a specified ‘Point-of-Interest’ (POI), a
watershed boundary line must be drawn such that all rain falling within the boundary will
runoff past the POI. All rain falling outside of the boundary flows some place else.
Once the watershed boundary has been delineated, some method must be
employed to determine the number of square inches enclosed within the watershed
boundary. Now by using the size (in in2) on the map and the map’s horizontal scale, the
area of the watershed can be determined.
Appendix A
Rainfall Intensity Data for North Carolina
for the Rational Method
Table A-1. Rainfall intensity data for Murphy, NC 35.0961N, 84.0239W.
T (Yrs) 5 min
10 min 15 min 30 min 1 hr
2 hrs
3 hrs
2
4.29
3.51
2.94
2.03
1.28
0.77
0.55
10
6.40
5.12
4.32
3.13
2.04
1.22
0.87
25
7.41
5.90
4.99
3.69
2.46
1.47
1.05
100
9.13
7.26
6.12
4.69
3.23
1.94
1.41
6 hrs
0.34
0.52
0.63
0.84
12 hrs
0.22
0.33
0.39
0.49
24 hrs
0.13
0.21
0.25
0.32
Table A-2. Rainfall intensity data for Asheville, NC 35.4358N, 82.5392W.
T (Yrs)
5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
4.80
3.83
3.21
2.22
1.39
0.81
0.57
10
6.96
5.57
4.70
3.40
2.22
1.29
0.90
25
8.03
6.40
5.41
4.00
2.67
1.55
1.10
100
9.60
7.63
6.43
4.93
3.39
1.98
1.42
6 hrs
0.35
0.55
0.66
0.86
12 hrs
0.22
0.34
0.40
0.50
24 hrs
0.13
0.20
0.24
0.30
Table A-3. Rainfall intensity data for Boone, NC 36.2167N, 81.6667W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
5.26
4.20
3.52
2.43
1.53
0.92
0.67
10
7.34
5.87
4.95
3.59
2.34
1.43
1.04
25
8.43
6.72
5.68
4.20
2.80
1.74
1.26
100
10.12
8.04
6.78
5.19
3.58
2.28
1.67
6 hrs
0.44
0.67
0.81
1.05
12 hrs
0.29
0.43
0.51
0.63
24 hrs
0.17
0.27
0.33
0.44
Table A-4. Rainfall intensity data for Charlotte, NC 35.2333N, 80.8500W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
5.22
4.17
3.50
2.41
1.51
0.88
0.62
10
7.19
5.74
4.85
3.51
2.29
1.35
0.97
25
8.00
6.37
5.38
3.99
2.65
1.58
1.15
100
9.00
7.15
6.02
4.61
3.18
1.93
1.42
6 hrs
0.38
0.59
0.70
0.87
12 hrs
0.22
0.35
0.42
0.53
24 hrs
0.13
0.20
0.24
0.30
Table A-5. Rainfall intensity data for Greensboro, NC 36.09750N, 79.9436W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
4.98
3.98
3.34
2.30
1.45
0.85
0.60
0.36
10
6.80
5.44
4.59
3.32
2.16
1.29
0.92
0.56
25
7.46
5.94
5.02
3.72
2.48
1.50
1.07
0.66
100
8.14
6.47
5.45
4.17
2.87
1.79
1.28
0.80
12 hrs
0.21
0.33
0.40
0.49
24 hrs
0.13
0.20
0.23
0.29
Table A-6. Rainfall intensity data for Raleigh, NC 35.8706N, 78.7864W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
5.09
4.07
3.41
2.36
1.48
0.86
0.61
10
6.97
5.58
4.70
3.41
2.22
1.31
0.93
25
7.72
6.16
5.20
3.85
2.56
1.53
1.11
100
8.68
6.90
5.81
4.45
3.07
1.87
1.38
6 hrs
0.37
0.57
0.67
0.85
12 hrs
0.22
0.34
0.40
0.51
24 hrs
0.13
0.20
0.24
0.30
Table A-7. Rainfall intensity data for Fayetteville, NC 35.0583N, 78.8583W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
5.62
4.49
3.76
2.60
1.63
0.96
0.68
10
7.84
6.27
5.29
3.83
2.49
1.52
1.08
25
8.86
7.05
5.96
4.41
2.94
1.81
1.31
100
10.25
8.15
6.86
5.26
3.62
2.28
1.68
6 hrs
0.41
0.65
0.79
1.02
12 hrs
0.24
0.38
0.47
0.61
24 hrs
0.14
0.23
0.28
0.36
Table A-8. Rainfall intensity data for Wilmington, NC 34.2683N, 77.9061W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
6.83
5.46
4.58
3.16
1.98
1.18
0.84
10
9.60
7.68
6.48
4.69
3.05
1.91
1.37
25
10.91
8.70
7.35
5.44
3.62
2.35
1.72
100
12.84
10.20
8.59
6.58
4.53
3.14
2.34
6 hrs
0.52
0.86
1.07
1.47
12 hrs
0.30
0.50
0.64
0.88
24 hrs
0.18
0.30
0.38
0.52
Table A-9. Rainfall intensity data for Washington, NC 35.5333N, 77.0167W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
5.77
4.61
3.86
2.67
1.67
0.99
0.71
0.42
10
8.04
6.43
5.43
3.93
2.56
1.57
1.14
0.68
25
9.13
7.28
6.15
4.56
3.03
1.91
1.39
0.84
100
10.86
8.64
7.27
5.57
3.84
2.51
1.87
1.14
12 hrs
0.25
0.40
0.50
0.68
24 hrs
0.15
0.25
0.31
0.41
Table A-10. Rainfall intensity data for Manteo Airport, NC 35.9167N, 75.7000W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
5.89
4.71
3.94
2.72
1.71
0.98
0.72
0.44
10
8.23
6.59
5.55
4.02
2.62
1.57
1.16
0.71
25
9.35
7.45
6.29
4.66
3.10
1.90
1.42
0.87
100
11.10
8.82
7.43
5.69
3.92
2.48
1.90
1.18
12 hrs
0.26
0.42
0.52
0.71
24 hrs
0.16
0.26
0.33
0.44
Table A-11. Rainfall intensity data for Cape Hatteras, NC 35.2322N, 75.6225W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
6.60
5.28
4.42
3.05
1.92
1.18
0.86
.053
10
9.26
7.40
6.24
4.52
2.94
1.89
1.40
0.87
25
10.49
8.36
7.06
5.23
3.48
2.30
1.73
1.08
100
12.36
9.82
8.27
6.34
4.36
2.99
2.29
1.44
12 hrs
0.31
0.52
0.64
0.87
24 hrs
0.18
0.30
0.38
0.51
Appendix B
Rainfall Depth Data for North Carolina
for the Soil-Cover-Complex Method
Table B-1. Rainfall depth data for Murphy, NC 35.0961N, 84.0239W.
T (Yrs)
5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.37
0.59
0.74
1.02
1.28
1.53
1.66
10
0.53
0.85
1.08
1.56
2.04
2.43
2.61
25
0.62
0.98
1.25
1.85
2.46
2.94
3.16
100
0.76
1.21
1.53
2.34
3.23
3.89
4.22
6 hrs
2.06
3.13
3.78
5.03
12 hrs
2.62
3.92
4.65
5.96
24 hrs
3.21
4.97
6.00
7.74
Table B-2. Rainfall depth data for Asheville, NC 35.4358N, 82.5392W.
T (Yrs)
5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.40
0.64
0.80
1.11
1.39
1.62
1.73
10
0.58
0.93
1.17
1.70
2.22
2.57
2.72
25
0.67
1.07
1.35
2.00
2.67
3.11
3.30
100
0.80
1.27
1.61
2.46
3.39
2.97
4.28
6 hrs
2.12
3.27
3.95
5.13
12 hrs
2.68
4.06
4.82
6.03
24 hrs
3.19
4.86
5.77
7.21
Table B-3. Rainfall depth data for Boone, NC 36.2167N, 81.6667W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.44
0.70
0.88
1.22
1.53
1.84
2.00
10
0.61
0.98
1.24
1.79
2.34
2.87
3.12
25
0.70
1.12
1.42
2.10
2.80
3.48
3.80
100
0.84
1.34
1.70
2.60
3.58
4.56
5.00
6 hrs
2.62
4.01
4.84
6.28
12 hrs
3.46
5.18
6.11
7.63
24 hrs
4.04
6.54
8.02
10.58
Table B-4. Rainfall depth data for Charlotte, NC 35.2333N, 80.8500W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.43
0.70
0.87
1.21
1.51
1.76
1.87
10
0.60
0.96
1.21
1.76
2.29
2.70
2.90
25
0.67
1.06
1.35
1.99
2.65
3.17
3.44
100
0.75
1.19
1.51
2.31
3.18
3.85
4.27
6 hrs
2.26
3.51
4.18
5.22
12 hrs
2.68
4.19
5.02
6.34
24 hrs
3.10
4.84
5.78
7.25
Table B-5. Rainfall depth data for Greensboro, NC 36.09750N, 79.9436W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.42
0.66
0.83
1.15
1.45
1.70
1.81
10
0.57
0.91
1.15
1.66
2.16
2.58
2.76
25
0.62
0.99
1.25
1.86
2.48
3.00
3.21
100
0.68
1.08
1.36
2.09
2.87
3.58
3.83
6 hrs
2.18
3.34
3.94
4.80
12 hrs
2.57
4.00
4.76
5.96
24 hrs
3.04
4.72
5.63
7.04
Table B-6. Rainfall depth data for Raleigh, NC 35.8706N, 78.7864W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.42
0.68
0.85
1.18
1.48
1.72
1.82
10
0.58
0.93
1.18
1.70
2.22
2.62
2.81
25
0.64
1.03
1.30
1.93
2.56
3.07
3.32
100
0.72
1.15
1.45
2.23
3.07
3.74
4.13
6 hrs
2.20
3.40
4.04
5.07
12 hrs
2.61
4.07
4.88
6.20
24 hrs
3.15
4.89
5.81
7.23
Table B-7. Rainfall depth data for Fayetteville, NC 35.0583N, 78.8583W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.47
0.75
0.94
1.30
1.63
1.92
2.03
10
0.65
1.04
1.32
1.92
2.49
3.03
3.25
25
0.74
1.18
1.49
2.21
2.94
3.62
3.94
100
0.85
1.36
1.72
2.63
3.62
4.56
5.06
6 hrs
2.43
3.89
4.73
6.11
12 hrs
2.86
4.63
5.67
7.41
24 hrs
3.37
5.47
6.67
8.63
Table B-8. Rainfall depth data for Wilmington, NC 34.2683N, 77.9061W.
T (Yrs)
2
10
25
100
5 min
0.57
0.80
0.91
1.07
10 min
0.91
1.28
1.45
1.70
15 min
1.14
1.62
1.84
2.15
30 min
1.58
2.35
2.72
3.29
1 hr
1.98
3.05
3.62
4.53
2 hrs
2.36
3.82
4.71
6.27
3 hrs
2.51
4.13
5.15
7.02
6 hrs
3.11
5.13
6.43
8.80
12 hrs
3.65
6.08
7.66
10.63
24 hrs
4.28
7.15
9.04
12.56
6 hrs
2.54
4.09
5.04
6.83
12 hrs
2.98
4.84
5.99
8.23
24 hrs
3.57
5.92
7.38
9.94
Table B-10. Rainfall depth data for Manteo Airport, NC 35.9167N, 75.7000W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
0.49
0.78
0.99
1.36
1.71
1.97
2.16
2.63
10
0.69
1.10
1.39
2.01
2.62
3.14
3.48
4.25
25
0.78
1.24
1.57
2.33
3.10
3.80
4.26
5.23
100
0.93
1.47
1.86
2.85
3.92
4.97
5.70
7.04
12 hrs
3.13
5.10
6.31
8.61
24 hrs
3.82
6.31
7.86
10.57
Table B-11. Rainfall depth data for Cape Hatteras, NC 35.2322N, 75.6225W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
6 hrs
2
0.55
0.88
1.10
1.53
1.92
2.36
2.59
3.20
10
0.68
1.09
1.38
1.95
2.51
3.17
3.50
4.33
25
0.87
1.39
1.77
2.62
3.48
4.60
5.18
6.44
100
1.03
1.64
2.07
3.17
4.36
5.98
6.89
8.61
12 hrs
3.79
5.14
7.76
10.51
24 hrs
4.38
6.02
9.03
12.15
Table B-9. Rainfall depth data for Washington, NC 35.5333N, 77.0167W.
T (Yrs) 5 min 10 min 15 min 30 min
1 hr
2 hrs
3 hrs
2
0.48
0.77
0.97
1.33
1.67
1.98
2.12
10
0.67
1.07
1.36
1.97
2.56
3.15
3.41
25
0.76
1.21
1.54
2.28
3.03
3.82
4.18
100
0.91
1.44
1.82
2.79
3.84
5.03
5.63