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Course EN-3011

Estimating Stormwater Runoff

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ESTIMATING STORMWATER RUNOFF 1 Introduction Stormwater runoff occurs when snowmelt or rain flow over the ground. Impervious surfaces like roofs, driveways, sidewalks, parking lots and streets prevent the rain or snowmelt from soaking into the ground. Some rain and snowmelt will soak into the ground, some will evaporate, some will be absorbed by plants, some will be retained in ponds but the rest becomes runoff. Evaporation is not typically considered important. Stormwater runoff ends in streams, rivers, lakes and oceans. Stormwater may cause flooding due to the volume and timing of the runoff. Stormwater may cause pollution due to the contaminants carried by the stormwater. Engineers design storm sewers, culverts, ditches and ponds to help solve some of these problems. Rainfall data is very important in determining the amount of runoff. The depth or volume of rainfall during a specific time interval should be known. The total runoff volume is equal to the runoff depth multiplied by the watershed area. The current NWS precipitation-frequency documents by state can be found in the Hydrometeorological Design Studies Center of NOAAs National Weather Service. It looks something like this:

As you can see from the table, for different durations, HYDRO-35, Technical Paper 40 and 49 are used in some states. Some states use Atlas 14 and Atlas 2 while other states use other documents.

The area of the watershed should be known as well as its shape and orientation. The watershed is the area of land that contributes runoff to a single point (culvert, inlet, or outfall). It is delineated and the area is determined from a contour map. Only a portion of the total rainfall will contribute to the runoff in the watershed or drainage area. In the United States, records have shown this to be from 30-50% of the precipitation depth. The total precipitation depth is equal to sum of the depth due to evaporation, the depth of runoff, the depth of depression storage, the depth of interception by plants and the depth of infiltration. The type of soil, land use and ground cover should be known. There are three methods that use this data to derive total runoff volumes. Horton equation Runoff coefficients NRCS (SCS) Curve number

The slopes of the drainage paths and channels should be known to calculate the time of concentration. The intensity (in/hr) over a time period should be know. The frequency of the storm should be known. The duration of the storm should be known. This type of data is often found in a rainfall intensity-duration-frequency (IDF) curve. Use the IDF curve for the area in question, which may be within a city or county IDF curve. 2 Methods of runoff estimation There are a number of empirical methods used to estimate stormwater runoff: Rational Method NRCS (SCS) Peak Flow Method USGS Regression Equations

The Rational method is good for determining peak discharge for an area of up to about 200 acres or 0.31 mi2. The USGS method is good from about 25 acres to 25 mi2. The NRCS method is good for up to 2000 acres or 3.1 mi2. These limits vary depending on your source. Some say the Rational method is good for up to 25 acres. Peak flows are usually adequate for the designing of storm drains and open channels.

3 Rational Method This is one of the most commonly used methods used to calculate peak flow.

, 1.008 .00278 , , , ,
Notice if we leave off k, the units of flow would be in acre-in/hr. Now, to convert to ft3/s, we multiply by 1.008 but most engineers just use 1.0. Some of the assumptions for the rational method are: Rainfall intensity is the same over the entire drainage area Rainfall intensity is uniform over the duration time which is equal to the time of concentration, tc. The time of concentration is the time required for water to travel from the most remote point of the drainage area to the point of interest. The frequency of rainfall intensity is assumed to produce the same frequency of peak flow The coefficient of runoff is the same for all storms Peak flow occurs when the entire drainage area is contributing to the flow

The runoff coefficient is a function land use, ground cover and many other factors. If the drainage area has varying amounts of land use and ground cover, a composite runoff coefficient should be calculated and used. Typical values are listed in the following table: In the Rational equation, Q=CAI, the runoff coefficient is good for storms 10 years frequency and less. The equation for other storm frequencies, should be: Q=CfCIA Storm (yr) Cf

<=10 1 25 1.1 50 1.2 100 1.25 Table 3a

Runoff Coefficients Type of Drainage area Business: Downtown areas Neighborhood area Residential: Single-family areas Multi-unit, detached Multi-unit, attached Suburban Apartment dwelling areas Industrial: Light Heavy Parks, cemeteries Playgrounds Railroad yards Unimproved areas Lawns: Sandy soil, flat, <2% Sandy soil, average, 2-7% Sandy soil, steep, >7% Heavy soil, flat, <2% Heavy soil, average, 2-7% Heavy soil, steep, >7% Streets: Asphalt Concrete Brick Drives and sidewalks Roofs Table 3b As you can see, there is a range of values for the runoff coefficient for different types of drainage areas.. Runoff Coefficient, C

0.70-0.95 0.50-0.70

0.30-0.50 0.40-0.60 0.60-0.75 0.25-0.40 0.50-0.70

0.50-0.80 0.60-0.90 0.10-0.25 0.20-0.40 0.20-0.40 0.10-0.30

0.05-0.10 0.10-0.15 0.15-0.20 0.13-0.17 0.18-0.22 0.25-0.35

0.70-0.95 0.80-0.95 0.70-0.85 0.75-0.85 0.75-0.95

You might like this table better:

Table 3c 3.1 Hydrologic Soil Group Descriptions The soil groups used in table 3c: A -- Well-drained sand and gravel; high permeability. B -- Moderate to well-drained; moderately fine to moderately coarse texture; moderate permeability. C -- Poor to moderately well-drained; moderately fine to fine texture; slow permeability. D -- Poorly drained, clay soils with high swelling potential, permanent high water table, claypan, or shallow soils over nearly impervious layer(s).

3.1.1 Example A 10 acre development has a Rational C value of 0.75 and the intensity is 0.63 in/hr. Given: C=0.75 I=0.63 in/hr A=10 acres Assume k=1.0 instead of 1.008 to convert from acre-in/hr to cfs

Q=kCIA= 1.0 x 0.75 x 0.63 in/hr x 10 acres = 4.7 ft3/s

3.1.2 Example We have a 32 acres site. About 9 acres are impervious and the runoff coefficient is 0.88. About 23 acres are pervious and have a runoff coefficient of 0.26. The rainfall intensity is .72 in/hr. C Area (A) acre 9 23 32 CA

0.88 0.26 Sums

7.92 5.98 13.9 0.43 0.72 9.9 ft3/s

Composite C= I= CIA=

0.88 9 0.26 23 0.43 32

To determine the intensity, we need to design for a certain year storm like the 2, 5 10, 25, 50 or 100 year storm. We would use and IDF curve like the one for Chattanooga, TN (Chart 3d).

Chart 3d If we are designing for a 2 year storm with duration of 2 hours, using Chart 3d, the intensity would be 0.8 in/hr.

3.2 Time of Concentration The time of concentration is the total time it takes water to travel from the most remote point in the watershed to the point of interest. The time of concentration may be from: Overland flow o Sheet flow o Shallow Flow Channel flow Pipe flow Combinations of flow

When the time of concentration is from a combination of flows, we determine the individual travel times and add them all up to determine the total time of concentration.

tc=tt1+tt2+tt3+ +ttn
3.2.1 Overland flow Overland flow travel time usually consists of the travel time from sheet flow and the travel time from shallow concentrated flow.

tt(overland flow)=tt(sheet flow)+tt(shallow concentrated flow)

3.2.1.1 Sheet flow Sheet flow is usually at a very shallow depth of 0.1 feet (1.2 inches) or less. It is usually less than or equal to 300 ft. The travel time can be computed using the Kinematic Wave Equation:

tt=sheet flow travel time (min) C=0.938 n=Manning roughness coefficient L=length of flow (ft), <=300 ft i=rainfall intensity (in/hr) S=slope of ground (ft/ft)

. . . .

Manning n values for overland flow

Table 3e Solving the Kinematic Wave Equation requires the designer to go through an interactive process since both the travel time and rainfall intensity are unknowns at this point. You start by assuming a travel time and determine the rainfall intensity and then insert the rainfall intensity into the equation. When the assumed time equals the calculated time from the equation, the designer would use the solution for the sheet flow travel time.

Another method for calculating the travel time for sheet flow is the NRCS Runoff method.

0.007. . .
tt=sheet flow travel time (hr) n=Manning roughness coefficient L=length of flow (ft), usually <=300 ft P2-24=2 year, 24 hour rainfall (in) from your State your County in Atlas 14 S=slope of ground (ft/ft) Part of 2 year, 24 hour table for Tennessee

Table 3f Note: Some states use Technical Paper 47, HYDRO 35 or something else for the 2 year, 24 hour depth.

3.2.1.2 Shallow concentrated flow After sheet flow, the flow usually becomes shallow concentrated flow. After shallow concentrated flow, the flow usually becomes ditch, gutter or channel flow. To calculate the velocity over an unpaved surface we use:

16.1345.
The assumptions for this equation are that n=0.05 and the hydraulic radius is 0.4 ft. To calculate the velocity over a paved surface we use:

20.3282.
The assumptions for this equation are that n=0.025 and the hydraulic radius is 0.2 feet.

V=velocity (ft/s) S= slope of ground (ft/ft) Once the velocity is know, the travel time can be computed from the following equation:

tt=travel time (min) L=length of flow (ft) V=average velocity (ft/s)

60

60=conversion factor from seconds to minutes

3.2.2 Pipe, gutter and channel flow The velocity of flow in a pipe, gutter or channel can be computed using the Manning equation:

V=velocity (ft/s) R=hydraulic radius=A/P (ft) A=area of flow (ft2) P=wetted perimeter (ft) S=friction slope (ft/ft)

1.49 . .

n=Manning roughness coefficient

Manning coefficient for channels and pipes

Table 3g

3.1.3 Example Given: The drainage area consists of 39.6 acres in Dyer county Tennessee. There are 30.4 acres that is single family residential and 9.2 acres that is sandy soil with a slope of 5%. The drainage path is broken into three sections of sheet flow, shallow flow and channel flow. The sheet flow section is covered with dense grass, its length is 104 feet and the slope is 0.01 ft/ft. The shallow flow section is unpaved, its length is 1320 feet and the slope is 0.02 ft/ft. The channel flow section is 3590 feet and has a slope of 0.005 ft/ft. The Manning coefficient is 0.05. The cross-sectional area of flow is 29 ft2 and the hydraulic radius is 25 ft Find: Find the time of concentration and the peak runoff for a 25 year and 100 year design storm. Solution: To calculate the travel time for sheet flow, we need the Manning coefficient and the 2 year, 24 hour depth. In the table 3e for Manning n values for overland flow, n=0.24 for dense grass. In partial table 3f, for 2 year, 24 hour depths in Tennessee for Dyer county, P2-24=3.88 inches.

0.007. 0.0070.24 104 . 0.294 . 3.88 . 0.01 /. .

To calculate the velocity for shallow flow over unpaved ground, we use:

16.1345. 16.13450.02 . 2.28

To calculate the travel time for shallow flow we use:

1320 9.64 0.161 60 60 2.28 /

To calculate the hydraulic radius for channel flow, we use:

29 1.16 25

To calculate the velocity for channel flow, we use:

1.49 . . 1.49 1.16 . 0.005 . 2.33 0.05

To calculate the travel time for channel flow we use:

3590 25.7 0.428 60 60 2.33

To calculate the time of concentration, we use:

0.294 0.161 0.428 0.883 52.9

To calculate the peak runoff for the 25 year and the 100 year design storm, we will need the rainfall intensities for those storms and the composite C for the drainage area. For this example, lets use the rainfall-intensity-duration curve for Chattanooga, Tennessee (chart 3d). We should use the one for Dyer County. Using the chart, for 53 min duration, we find:

I25=2.7 in/hr I100=3.4 in/hr

To calculate the composite C we use Table 3b for runoff coefficients for different types of drainage areas:

Land use residential single family sandy soil, 5% slope

A (acres)

CA

0.35 0.15 Sums

30.4 9.2 39.6

10.64 1.38 12.02 0.30

Composite C=

To calculate the peak flows for the 25 year and the 100 year design storms we use:

1.1 0.30 2.7 39.6 35.3 / 1.25 0.03 3.4 39.6 50.5 /
Note , C25 and C100 came from Table 3a. 4 NRCS (SCS) Peak Flow Method This method is sometimes called the Runoff Curve Number (CN) method or the Hydrologic method. It is described in the National Engineering Handbook, part 630, Chapter 10 and Urban Hydrology for Small Watersheds, Technical Release 55 (TR55). It is really the combination of two methods. The first determine the depth of rainfall and the second determines the peak flow. With this method you can generate a hydrograph based on a dimensionless unit hydrograph. This method is widely used to design culverts, detention ponds, stream relocation and large drainage ditches. We will only cover peak flow and not how to generate a hydrograph. This method should be used for areas less than 2000 acres. We will cover how to determine peak flow with charts and tables. This method is now done using a program (WinTR-55). Designers should become familiar with this program and start using it. Several parameters will be needed: Determine the design storm; 2, 5, 10, 25, 50, 100 year storm Delineate the drainage area and determine size Determine the location o Four rainfall types; I, IA, II and III o 24 hour rainfall amount from Atlas 14 Cover characteristics o Soil type and cover CN number Ia Antecedent Moisture Condition (AMC) Time of concentration o Sheet flow length <=100 feet instead of 300 feet

4.1 Location Once you determine the location of the site, you determine the rainfall distribution type from the following map:

Map 4a As you can see, most of the United States is Type II.

The 24 hour rainfall amount for the location comes from Atlas 14. It is online now. You enter your state, design storm and 24 hour duration.

Fig. 4b

I have zoomed in on Chattanooga so it will look something like this:

Map 4c As you can see from the map, the 24 hour rainfall the 10 year storm is between 5.0 and 5.5 inches. Since it looks to be in the middle, maybe we should use P=5.25 inches. 4.2 Cover characteristics Cover characteristics are soil type and land use. There are four soil groups used in this method. A. B. C. D. Sand, loamy sand, or sandy loam Silt loam or loam Sandy clay loam Clay loam, silty clay loam, sandy clay, silty clay, or clay

This is done by using an NRCS Soil Survey from your region office. It shows soils by name. TR-55 shows the soil name and group and it looks something like this: Soil name Soil group

ALBUS...........................B ALCALDE ........................D ALCAN...........................D ALCESTER .......................B ALCOA ..........................B ALCONA..........................B ALCOT...........................A ALCOVA .........................B ALCOVY .........................C ALDA, Saline....................B/D ALDA ...........................C ALDAPE .........................D

Once we have the soil group, we can determine the CN number from the cover using the following table:

Table 4d

Table 4e 4.3 Antecedent Moisture Condition (AMC) There are three classes of antecedent moisture conditions. The CN number we determined from the above tables is for normal moisture conditions and corresponds to AMC-II. AMC-I corresponds to a drier condition and AMC-III to a wetter condition. To compute the CN number for AMC-I, and round it to the nearest whole number use:

4.2 10 0.058

To compute the CN number for AMC-III, and round it to the nearest whole number use:

23 10 0.13

Once the CN number is determined, we can determine the Ia value from the following table:

Table 4f 4.4 Time of concentration We calculate the time of concentration for sheet flow the same as we did in the Rational method except the maximum length is 100 feet instead of 300 feet. Shallow and channel or pipe flow are calculated in the same way as the Rational method.

4.5 Depth of Runoff We use the following equation to calculate the depth of runoff in inches:

Q=depth of runoff (in) P=rainfall (in)

S=potential maximum retention after rainfall begins (in) Ia=initial abstraction or initial losses (in) Initial abstraction is all loses before runoff begins. It includes water retained in surface depressions, water intercepted by vegetation, evaporation, and infiltration. It is highly variable but generally depends on the soil type and cover. Many studies have shown that Ia = 0.2S. By substitution, we get a new equation:

0.2 0.8

S is related to the soil type and cover by the Runoff Curve Number (CN). CN has a range of 0 to 100. S is related to CN by the following equation:

1000 10

If we know P and CN, we can find S and Q.

Since we have the CN number and P, the depth of runoff can be calculated. We should use the following chart to check our answer. Engineers should always check their answer.

Chart 4g 4.6 Peak Runoff Next we would determine the peak runoff. The drainage basin should have a fairly homogeneous CN. The composite CN should be at least 40. The drainage basin should have one main channel. The peak runoff is computed by:

qp=peak runoff, ft3/s qu=unit peak discharge, cfs/mi2/in or csm/in Am= drainage area, mi2 Q=depth of runoff, in Fp=pond and swamp adjustment factor

Table 4h The unit peak discharge, qu, is estimated using:

qu=10K
where

K=C0 + C1 log10(tc) + C2 (log10(tc))2

The coefficients, C0, C1, and C2, can be found in the following table using Ia/P and rainfall type:

Table 4i The value of Ia/P should be rounded to two places after the decimal. It should be no lower than 0.10 and no higher than 0.50.

The unit peak discharge (qu) can be estimated from the following chart and is bases on the soil type, so since most of the United States is type II, the type II chart looks like this:

Chart 4j You need the time of concentration and Ia/P to determine an estimate of the unit peak discharge (flow). 4.6.1 Example The site is 50 acres. It consists of 15 acres of acre lots on type B soil, 20 acres of acre lots on Type C soil and 15 acres of open space in good condition on type C soil. The 24 hour, type II, 25 year depth of rainfall, P=6.7 inches. The time of concentration is 0.73 hours. There is negligible ponding and swamp land. The antecedent moisture condition is normal.

Calculate the composite CN (CN values are from Table 4d):

Area acres 15 20 15 50

CN

70 80 74

1050 1600 1110 3760 75

Composit CN=
Ia is obtained from a table 4f and Ia=0.667

Calculate S, the potential maximum retention after rainfall begins:

1000 1000 10 10 3.333 75

Calculate Q, the depth of runoff:

6.7 0.667 3.89 6.7 .667 3.333

Use the other equation to check your answer.

0.2 6.7 0.2 3.333 3.89 0.8 6.7 0.8 3.333

Use chart 4g to check you answer. From the chart, it looks like Q=3.9 in. Calculate Ia/P:

0.667 0.10 6.7

Use the table 4i to determine the coefficients, with Ia/P=0.10 for type II. If Ia/P were 0.12, you would need to interpolate the coefficients from the table. C0=2.55323 C1=-0.61512 C2=-0.16403 tc=0.73 hr

2.55323 0.61512 0.73 0.16403 0.73 2.638 10. 434

Use the chart 4j to check qu, with Ia/P=0.10 and a time of concentration of 0.73 hours. It looks like qu=440 csm/in (cfs/mi2/in). Calculate the peak flow or discharge:

434 0.0781 3.89 132

Note: 50 acres = 0.0781 mi2 Now if we were going to design a culvert, we would use the 132 cfs to size the pipe. The last equation for Qp, is supposed to be the simple procedure by NRCS for estimating peak flow. You have to go through a lot to get to the equation. That is why designers should become familiar with and learn to use the program, WinTR-55. 5 USGS Regression Equations This method is used to determine peak flow and develop a hydrograph for urban and rural drainage basins. We will only look at peak flow and not how to construct the hydrograph. This method is used on drainage areas up to 25 mi2. Regression equations were developed for most states for the 2, 5, 10, 25, 50, 100, 200 and 500 year floods. This information can be used to design storage facilities (detention ponds), outlet structures, storm drain systems, culverts, channels and energy dissipaters. Each state may be divided into regions.

Georgia Regions

Map 5a

Equations were usually developed for unban drainage basins and rural drainage basins.

Georgia Urban Regression Equations Frequency Region 1 Equations Region 2

2 year 5 year 10 year 25 year 50 year 100 year 200 year 500 year

Q2=167A0.73TIA0.31 Q5=301A0.71TIA0.26 Q10=405A0.70TIA0.21 Q25=527A0.70TIA0.20 Q50=643A0.69TIA0.18 Q100=762A0.69TIA0.17 Q200=892A0.68TIA0.16 Q500=1063A0.68TIA0.14

Q2=145A0.70TIA0.31 Q5=258A0.69TIA0.26 Q10=351A0.70TIA0.21 Q25=452A0.70TIA0.20 Q50=548A0.70TIA0.18 Q100=644A0.70TIA0.17 Q200=747A0.70TIA0.16 Q500=888A0.70TIA0.14

Region 3

Region 4

2 year 5 year 10 year 25 year 50 year 100 year 200 year 500 year

Q2=54.6A0.69TIA0.31 Q5=99.7A0.69TIA0.26 Q10=164A0.71TIA0.21 Q25=226A0.71TIA0.20 Q50=288A0.72TIA0.18 Q100=355A0.72TIA0.17 Q200=428A0.72TIA0.16 Q500=531A0.72TIA0.14

Table 5b

Q2=110A0.66TIA0.31 Q5=237A0.66TIA0.26 Q10=350A0.68TIA0.21 Q25=478A0.69TIA0.20 Q50=596A0.70TIA0.18 Q100=717A0.70TIA0.17 Q200=843A0.70TIA0.16 Q500=1017A0.71TIA0.14

Georgia Rural Regression Equations

Q Region 1 Region 2

Q2 Q5 Q10 Q25 Q50 Q100 Q200 Q500

207A0.654 357A0.632 482A0.619 666A0.605 827A0.595 1010A0.584 1220A0.575 1530A0.563

182A0.622 311A0.616 411A0.613 552A0.610 669A0.607 794A0.605 931A0.603 1130A0.601

Region 3

Region 4

Q2 Q5 Q10 Q25 Q50 Q100 Q200 Q500

76A0.620 133A0.620 176A0.621 237A0.623 287A0.625 340A0.627 396A0.629 474A0.632

Table 5c

142A0.591 288A0.589 410A0.591 591A0.595 748A0.599 926A0.602 1120A0.606 1420A0.611

5.1 Example Design storm is for 100 year flood. The drainage basin is in region 1. The drainage area is 175 acres = 0.273 mi2. The total impervious area (TIA) =32%. Determine the rural and urban peak discharge (flow). 100 year rural peak flow: 1010. 1010 0.273. 473 100 year urban (developed) peak flow: 762. . 762 0.273. 32. 561 USGS developed a computer program, NFF, which you can download and install for free. Version 3 has over 2,000 flood-flow equations for over 289 regions of the Nation, Puerto Rico, Tutuilla, and American Samoa. I ran the program with the same information in our example:

Figure 5d As you can see, we got the same results, 473 cfs for rural and 561 cfs for urban.

The 100 year urban hydrograph with a time lag of 0.53 hours looks something like this:

Figure 5e

The Flood Frequency Plot looks something like this:

Figure 5f The report looks something like this: National Flood Frequency Program Version 3.0 Based on Water-Resources Investigations Report 02-4168 Equations from database C:\NFF\NFFv3.2_2004-12-14.mdb Updated by kries 9/22/2004 at 4:03:24 PM fixed decimal place in constant Equations for Georgia developed using English units

Site: Site #22, Georgia User: Robert Date: Saturday, January 30, 2010 03:42 PM

Rural Estimate: Rural 1 Basin Drainage Area: 0.27 mi2 1 Region Region: Region_1 Drainage_Area = 0.27 mi2 Crippen & Bue Region 5

Urban Estimate: Urban 1 Basin Drainage Area: 0.27 mi2 1 Region Region: Region_1_Urban Drainage_Area = 0.27 mi2 Total_Impervious_Area = 32 percent Crippen & Bue Region 5

Flood Peak Discharges, in cubic feet per second

Recurrence Estimate Interval, yrs

Peak, cfs _____

Standard Error, % ________

Equivalent Years __________

____________________ _____________

Rural 1

2 5 10 25 50 100 200 500

88.6 157 216 304 382 473 578 737

31 29 29 29 30 31 33 36

3 4 5 12 14 16 17 18

maximum: 4030 (for C&B region 5)

Urban 1

2 5 10 25 50 100 200 500

190 295 338 425 490 561 642 714

34 31 31 29 28 28 28 28

maximum: 4030 (for C&B region 5)

6 Summary The Rational method and the USGS method seem very easy compared to the NRCS method. Remember, there is a program, WinTR-55, that can perform the NRCS method. Always check your answer. There is also a program, NFF, that can perform the USGS method. The WinTR-55 program is a much more complicated program to use than NFF program. Engineers should learn how to use both programs. The determination of which method to use may depend on State requirements, size of drainage area, or even the preference of the engineer. The Rational method is for relatively small drainage areas while the USGS method can be used on very large drainage areas.