### University of Missouri Extension

G1518, Reviewed October 1993

# Estimating Peak Rates of Runoff from Small Watersheds

##### Robert W. SchottmanDepartment of Agricultural Engineering

Use the following equation to estimate the peak rates of runoff to be expected from watersheds smaller than 200 acres in Missouri:

Q = QT x L x I x T x S x V x C x P x F where

Q = Peak rate of runoff, cubic feet per second.

QT = Peak rate of runoff from a watershed with a specific set of watershed conditions (Table 1).

L = Watershed location factor.

I = Soil infiltration factor.

T = Topographic factor.

S = Watershed shape factor.

V = Vegetative cover factor.

C = Contouring factor.

P = Surface storage factor.

F = Runoff frequency factor.

Table 1
Peak rates of runoff, in cubic feet per second, to be expected from watersheds in Missouri under the following conditions.

1. Watersheds located along line 1.00, Figure 1
2. Soils with an average infiltration rate
3. Land slopes average 8 percent
4. A typical watershed shape
5. In row crops, with the crop rows planted across the slope without terraces
6. No appreciable surface storage
7. 10-year frequency runoff
Size of watershed Peak rate of runoff
5 acres 19 cubic feet per second
10 acres 36 cubic feet per second
15 acres 52 cubic feet per second
20 acres 67 cubic feet per second
25 acres 81 cubic feet per second
30 acres 94 cubic feet per second
35 acres 107 cubic feet per second
40 acres 120 cubic feet per second
45 acres 132 cubic feet per second
50 acres 144 cubic feet per second
55 acres 155 cubic feet per second
60 acres 166 cubic feet per second
65 acres 175 cubic feet per second
70 acres 185 cubic feet per second
75 acres 195 cubic feet per second
80 acres 205 cubic feet per second
85 acres 215 cubic feet per second
90 acres 225 cubic feet per second
95 acres 235 cubic feet per second
100 acres 245 cubic feet per second
110 acres 265 cubic feet per second
120 acres 285 cubic feet per second
130 acres 304 cubic feet per second
140 acres 322 cubic feet per second
150 acres 340 cubic feet per second
160 acres 356 cubic feet per second
170 acres 372 cubic feet per second
180 acres 388 cubic feet per second
190 acres 404 cubic feet per second
200 acres 420 cubic feet per second

Figure 1
Location factors, L

Table 1 gives peak rates of runoff to be expected from various sizes of watersheds:

• Located along line 1.00 in Figure 1
• A soil of average infiltration
• Average land slope of 8 percent
• A typical watershed shape
• Planted to row crops with the crop rows planted across the slope without terraces
• With no appreciable surface storage
• In an average 10-year period.

If the watershed for which the peak rate of runoff is being estimated has conditions different from those in Table 1, then multiply the values from Table 1 by the appropriate factor, which can be found in the following information.

## Watershed location

Values in Table 1 are for watersheds located along line 1.00, Figure 1. If the watershed is in another location, multiply the value from Table 1 by the appropriate factor obtained from the map in Figure 1.

## Soil infiltration

Values in Table 1 are peak rates of runoff to be expected from a soil with an average infiltration rate, such as a Summit silt loam or a Shelby loam. If soil conditions differ from this, multiply the value from Table 1 by an appropriate factor selected from the following:

Soil infiltration rate Soil infiltration factor, I
Very High (coarse textured soils throughout, such as Sarpy sand or Bruno sand) 0.8
Above average (soils with medium to moderately coarse textured surface, well drained as evidenced by bright or nonmottled subsoil colors, such as Marshall or Menfro silt loams) 0.9
Average (soils with medium textured surface and moderately-fine textured subsoils with restricted drainage as evidenced by having gray or mottled subsoil colors, such as Shelby loam or Summit silt loam) 1.0
Below average (soils with medium to moderately fine textured surface with a claypan or fragipan subsoil within 12 inches of the surface, such as Mexico or Lebanon silt loams) 1.1
Very low (soils with fine textured surface or soils eroded into claypan subsoils, such as Wabash clay or severely eroded Mexico silt loam) 1.2

## Shape of watershed

The peak rate of runoff will be affected by the maximum distance the runoff must travel in reaching the discharge point. In long, narrow watersheds, the runoff must travel a greater distance than in a compact watershed, hence a lower peak rate of runoff can be expected. If terraces or diversions drain away from the discharge point, the runoff must travel a greater distance and a lower peak rate of runoff can be expected.

Determine the maximum distance the runoff must travel in reaching the discharge point. Find this distance in Table 2 in the number of acres in the watershed and read the corresponding S factor in the right hand column of the table. Multiply the value from Table 1 by this S factor.

Table 2
Determining the maximum distance runoff must travel in reaching the discharge point

Size of watershed (acres) Shape factor, S
5 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200
Maximum distance in feet that runoff travels
600 800 1000 1100 1300 1400 1500 1700 1800 1900 2100 2300 2500 2700 1.25
550 700 900 1100 1200 1400 1600 1700 1800 1900 2100 2400 2600 2900 3100 1.20
550 800 1000 1200 1400 1600 1800 1900 2000 2200 2400 2700 3000 3300 3500 1.15
400 600 900 1200 1400 1600 1800 2000 2100 2300 2500 2800 3100 3400 3700 3900 1.10
500 700 1000 1400 1600 1800 2100 2300 2500 2700 2900 3200 3600 3800 4100 4300 1.05
600 800 1200 1600 1900 2100 2400 2700 2900 3100 3300 3600 4000 4300 4600 4800 1.00
700 950 1400 1900 2200 2400 2700 3100 3300 3600 3800 4100 4500 4800 5200 5500 0.95
800 1100 1600 2200 2600 2900 3200 3600 3800 4100 4400 4700 5100 5500 5900 6200 0.90
900 1300 1900 2600 3100 3400 3700 4100 4400 4600 5000 5400 5900 6300 6700 7000 0.85
1100 1600 2300 3100 3600 3900 4200 4600 5000 5400 5700 6200 6700 7100 7500 7900 0.80
1300 1900 2800 3600 4200 4600 5000 5400 5800 6200 6600 7100 7600 8000 8400 8800 0.75

## Topography

Values in Table 1 are peak rates of runoff to be expected from watersheds with an average land slope of 8 percent. If the average land slope on a watershed differs from this, multiply the value from Table 1 by the following factor:

Average land slope Topographic factor (T)
0.5 percent 0.50
1 percent 0.65
2 percent 0.72
3 percent 0.78
4 percent 0.83
5 percent 0.88
6 percent 0.92
7 percent 0.96
8 percent 1.00
9 percent 1.04
10 percent 1.07
12 percent 1.14
14 percent 1.20
16 percent 1.26
18 percent 1.32
20 percent 1.37

## Vegetation

Values in Table 1 are peak rates of runoff to be expected from watersheds with the entire watershed in row crops. If different crops are expected on a watershed, multiply the value from Table 1 by the following factor:

Type of cover Vegetative cover factor (V)
Row crop 1.0
Small grain, good quality 0.8
Small grain, poor quality 0.9
Pasture, good quality 0.6
Pasture, poor quality 0.8
Timer, good quality 0.5
Timer, poor quality 0.6

If several types of cover are present on a watershed, a weighted vegetation factor should be computed. For example, assume that a 160-acre watershed contains 80 acres of small grain, 40 acres of meadow and 40 acres of timber, all with good quality cover. The weighted vegetation factor would be computed as follows:

 80 acres small grain multiplied by factor 0.8 equals 64 40 acres meadow multiplied by factor 0.5 equals 20 40 acres timber multiplied by factor 0.5 equals 20 160 104

104 ÷ 160 = 0.65, the weighted vegetation factor.

## Contouring

Values in Table 1 are peak rates of runoff to be expected from watersheds with crop rows planted across the slope without terraces or without contour guide lines.

If the entire watershed is farmed parallel to contour guide lines or terraces, multiply the value in Table 1 by an appropriate factor selected from the following:

Acres in watershed Contour factor (C)
0 to 10 0.95
11 to -40 0.96
41 to 100 0.97
101 to 200 0.98

If the entire watershed is not farmed on the contour, make an appropriate adjustment in the contouring factor. For example, if only 20 acres of a 60-acre watershed are farmed on the contour, the contouring factor would be 0.99.

0.97 + [(60-20 ÷ 60) (1.0-0.97)] = 0.99, the weighted contouring factor.

## Storage

Any water detained or impounded on the watershed will reduce the peak rate of runoff from the watershed. Values in Table 1 are peak rates of runoff to be expected from a watershed with no appreciable surface storage. If water is impounded on the watershed, multiply the value from Table 1 by an appropriate factor. The storage factor may vary depending on the percent of the watershed that drains into the impoundment, the amount of storage provided and the location of the impoundment on the watershed.

Because of the wide variations in type of impoundments and the many possible locations on the watershed, it is impossible to give specific values for the storage factor that would be applicable for all situations. The following general principles may be helpful in evaluating the storage factor:

• Impoundments with only an emergency spillway will not reduce the peak rate of runoff an appreciable amount, particularly if they are expected to be full when the design storm occurs.
• Impoundments with a principal spillway at a lower elevation than the emergency spillway will reduce the peak rate of runoff. The amount of reduction will depend on the percent of the watershed that drains into the impoundment, the rate of flow through the principal spillway, the amount of storage provided between the principal and emergency spillways, and the capacity of the emergency spillway.
• Impoundments located in the upper part of a watershed give the greatest reduction in the peak rate of runoff; those located in the lower part give the least reduction while impoundments located throughout the watershed will have an intermediate effect.
• The effect of level terraces on the peak rate of runoff depends on the percent of the watershed terraced and the amount of storage provided.
• The effectiveness of natural storage such as lakes, swamps and sink holes will depend on their location on the watershed, the percent of the watershed draining into them and the amount of storage available when the design storm occurs.

To obtain the best estimate of the effect of storage on the peak rate of runoff, the design storm should be flood routed through the impoundments. If this is not feasible, the following procedure is suggested:

• Determine the peak rate of runoff to be expected from the area of the watershed below the impoundments.
• Determine the expected flow through the spillways of the impounding structures for the frequency of storm being considered.
• Add the spillway discharge to the discharge to be expected from the area below the impoundments to obtain the total peak rate of runoff.

Water in temporary storage in the channels of graded terraces will reduce the peak rate of runoff from the watershed.

If the entire watershed is terraced, the storage factor P can be selected from the following table:

Acres in watershed Storage factor P for graded terraces (average length of terraces)
500 feet 1,000 feet 1,600 feet
0 to 10 0.95 0.90 0.80
11 to 40 0.97 0.93 0.85
41 to 100 0.98 0.95 0.90
101 to 200 0.99 0.97 0.95

If the entire watershed is not terraced, make an appropriate adjustment in the storage factor. For example, if 40 acres of a 50-acre watershed were terraced and the terraces averaged 1,000 feet long, the storage factor would be 0.96.

0.95 + [(50 - 40 ÷ 50) (1.0-0.95)] = 0.96

## Runoff frequency

Values in Table 1 are the peak rates of runoff to be expected in an average 10-year period. If the peak rate of runoff for a different design frequency is desired, multiply the value from Table 1 by the following factor:

Runoff frequency Runoff frequency factor (F)
1/2 year 0.2
1 year 0.3
2 year 0.5
5 year 0.8
10 year 1.0
25 year 1.3
50 year 1.5

## Combination of several factors

For watersheds that have a number of factors differing from those specified for the watersheds in Table 1, determine the peak rate of runoff by multiplying the value from Table 1 by a succession of factors applicable to the watershed being considered.

For example, estimate the peak rate of runoff to be expected in a 10-year period from a 120-acre watershed located in Andrew County with the following characteristics:

• A Marshall silt loam soil.
• Land slopes average 10 percent.
• The runoff must travel a maximum distance of 4,700 feet in reaching the discharge point.
• Eighty acres of low cropland in the upper half of the watershed is terraced. The terraces average 1,300 feet in length. The crop rows are planted with the terraces.
• Forty acres of good quality pasture in the lower half of the watershed are not terraced.
• There are no impoundments, except terraces, on the watershed.
Condition Factor
Location, Andrew County 1.03
Marshall silt loam soil 0.9
Land slope, 10 percent 1.07
Maximum distance of water flow, 4,700 feet 0.90
Vegetation, 80 acres row crop (1.0); 40 acres pasture (0.6) 0.87
Contouring 0.99
10-year frequency runoff 1.0

The peak rate of runoff (Qt) for a 120-acre watershed from Table 1 is 285 cubic feet per second.

Substituting in the equation

Q = Qt x L x I x T x S x V x C x P x F

Q = 285 x 1.03 x 0.9 x 1.07 x 0.90 x 0.87 x 0.99 x 0.97 x 1.0

Q = 213 cfs

Compute the peak rate of runoff to be expected from the above watershed in a 25-year period. F = 1.3.

Q = 213 x 1.3 = 277 cfs

##### This publication was prepared jointly by state and field staffs of the College of Agriculture, MU, and the Natural Resources Conservation Service. Original MU author was the late R.P. Beasley.

G1518 Estimating Peak Rates of Runoff From Small Watersheds | University of Missouri Extension

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