i

Relations Between Total-Sediment Load 

and Peak Discharge for Rainstorm Runoff 

on Five Ephemeral Streams in Wyoming

By James G. Rankl

U.S. Department of the Interior

U.S. Geological Survey

Water-Resources Investigations Report 02-4150
ii 

U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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 iii

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Description of study area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Sediment-load computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Relation between total-sediment load and peak discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Figures

1. Map showing location of data-collection sites on ephemeral streams used in the study. . . . . . . . . . . . 2

2. Graph showing discharge and total-sediment concentration for Dead Horse Creek 

near Buffalo, Wyo., storm of June 5, 1986 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3-8. Graphs showing relation between total-sediment load and peak discharge for rainfall runoff:

3. Dugout Creek tributary near Midwest, Wyo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

4. Fifteenmile Creek near Worland, Wyo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

5. Dead Horse Creek near Buffalo, Wyo.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

6. Coal Creek near Piney, Wyo.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

7. Belle Fourche River above Dry Creek near Piney, Wyo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

8. The five sites on ephemeral streams used in the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

9. Graph showing log Pearson type III probability distribution of annual total-sediment 

discharges for Dugout Creek tributary near Midwest, Wyo. and Dead Horse Creek 

near Buffalo, Wyo.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Tables

1. Streamflow-gaging stations used in the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2. Peak discharge and total-sediment load for rainstorm runoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

3. Results of regression analysis for relation between total-sediment load and peak discharge 

for rainstorm runoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Conversion Factors

Multiply By To obtain

cubic foot per second 0.02832 cubic meter per second 

inch 2.54 centimeter

square mile 2.590 square kilometer 

ton 0.9072 megagram

ton per year 0.9072 megagram per year

Relations Between Total-Sediment Load and Peak 

Discharge for Rainstorm Runoff on Five Ephemeral 

Streams in Wyoming

By James G. Rankl

Abstract

Total-sediment loads transported by ephemeral flows are a 

function of rainstorm energy and peak discharge. Rainstorm 

energy, estimated by rainfall intensity, is the primary mechanism for soil-particle detachment. Vegetation, soil cohesiveness, and land slope also are related to the amount of sediment 

detached, but these factors remain nearly constant, except for 

seasonal or human-induced changes in vegetation. Thus, the 

largest variability in total-sediment loads is the result of variability in rainstorm energy. The magnitude of the peak discharge in a stream from a runoff-producing rainstorm is a function of the intensity and volume of rainfall. The greater the 

rainfall intensity for the same volume of rainfall, the larger the 

peak discharge. Therefore, for each drainage area a relation 

exists between the total-sediment load for a rainstorm and the 

peak discharge for the rainstorm, because both are a function of 

rainstorm energy.

Total-sediment loads for runoff-producing rainstorms 

were computed from sample data collected at five ephemeral 

streams in semiarid areas of Wyoming. Regression analyses 

were used to develop equations relating total-sediment load to 

the peak discharge. Coefficients of determination ranged from 

89 to 97 percent. Average standard errors ranged from 35 to 94 

percent. The slopes of the lines defined by the equations were 

not different at the 95-percent level of significance, but the 

intercepts were significantly different for the five streams.

Introduction

Sediment-load data for semiarid basins drained by ephemeral streams are extremely difficult and expensive to collect. It 

is almost impossible for a hydrographer to collect depth-integrated samples because of the rapid nature of runoff from 

intense rainstorms. Automatic-pumping samplers activated by 

an increase in stage will sample one flow but might not sample 

the next because the hydrographer has not had a chance to 

remove the previous set of bottles and reset the sampler. The 

peak sediment concentration may occur before, at, or after the 

peak discharge of the rainstorm runoff (Rankl, 1987, p. 11). 

Frequently, the sediment concentration curve will have a double 

peak, whereas the runoff hydrograph will have a single peak. 

Because of the variability of sediment concentration in relation 

to discharge for ephemeral streams, the missing sediment-load 

data cannot be estimated accurately from sediment-transport 

curves (Rankl, 1987, p. 1l); therefore, the annual sediment discharge from rainstorms cannot be computed.

Annual runoff and sediment discharge for ephemeral 

streams is the sum of a series of discrete runoffs; therefore, an 

approach for computing annual sediment discharge needs to 

focus on runoff from individual storms. Woolhiser and Todorovic (1974) suggested that a linear relation exists between the 

logarithm of sediment load and the logarithm of peak discharge 

of the runoff from each rainstorm and that relation can be used 

to estimate annual sediment discharge for a basin. Singh and 

Chen (1982) developed a linear relation between the logarithms 

of sediment load and the logarithms of volume of direct runoff. 

Craig and Rankl (1978) used 105 hydrographs from 35 small 

basins to define a linear relation between the logarithms of volume of direct runoff and the logarithms of peak discharge. 

Rankl (1987, fig. 15) identified a linear relation between the 

logarithms of total-sediment load and the logarithms of peak 

discharge per rainstorm runoff. Parker and Troutman (1989) 

used a quadratic model to develop a relation between annual 

peak discharge and associated suspended-sediment load for 

large perennial rivers.

Rainstorm intensity is the primary mechanism for soil-particle detachment and has been used to estimate raindrop size 

(Mutchler and Young, 1975) and rainstorm energy (Wischmeier and Smith, 1958). Vegetation, infiltration rates of soil, 

soil cohesiveness, and land slope also are related to the amount 

of sediment detached, but these factors remain nearly constant, 

except for seasonal or human-induced changes in vegetation. 

Thus, the largest variability in sediment load is the result of 

variability in rainstorm energy. Hjelmfelt and others (1986) 

found that large rainstorm runoff, with an average occurrence of 

1 year or less, produced more than 50 percent of the soil loss and 

sediment yield from cultivated fields.
2 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

The magnitude of the peak discharge in a stream from runoff-producing rainstorms is a function of the intensity and volume of rainfall. The greater the rainfall intensity for the same 

volume of rainfall, the larger the peak discharge. Therefore, a 

relation should exist between the total-sediment load for a rainstorm and the peak discharge because both are a function of 

rainstorm energy.

This report documents the relations between totalsediment load and peak discharge for rainstorm runoff for five 

ephemeral streams in Wyoming. The relations were used to estimate total annual sediment discharge for two of the streams. 

Sediment and peak-discharge data for rainstorm runoff collected during 1977-87 formed the basis for the analysis. In addition, continuous streamflow data collected during 1971-90 were 

used. The amount of data available varied among the study 

sites. The data used in this study were collected in cooperation 

with the Wyoming State Engineer.

Description of Study Area

Five streams that originate in and drain areas of the Powder, Belle Fourche and Big Horn River basins in Wyoming are 

used in this study (fig. 1, table 1). The streams are ephemeral, 

except in places where ground water is intercepted by the channel, thus forming pools. Most of the water evaporates from the 

pools. Soils generally contain little organic material, are fine 

grained, and are alkaline. Sagebrush and native grasses predominate.

The land is semiarid to arid. The mean annual precipitation 

ranges from a low of 9 inches for Fifteenmile Creek near Worland to 13 inches for Dead Horse Creek near Buffalo (Lowham, 

1988). Most of the precipitation from October through March 

occurs as snow that sublimates. During April through September, precipitation occurs as rain showers and occasional intense 

thunderstorms.

Figure 1. Location of data-collection sites on ephemeral streams used in the study.

0 40 60 80 KILOMETERS 20

0

EXPLANATION

Streamflow-gaging station and

 site number

20 40 60 80 MILES

111 ̊ 110 ̊ 109 ̊ 108 ̊ 107 ̊ 106 ̊ 105 ̊ 104 ̊

41 ̊

42 ̊

41 ̊

44 ̊

45 ̊

BIGHORN

 

RIVER

BASIN

BIGHORN

 

RIVER

BASIN

POWDER RIVER

BASIN

POWDER RIVER

BASIN

BELLE

FOURCHE 

RIVER

BASIN

BELLE

FOURCHE 

RIVER

Jackson Jackson BASIN

Gillette

Buffalo

Sheridan

Worland

Cody

Thermopolis

Riverton

Rock

Springs

Rawlins

Laramie

Jackson

Cheyenne

Piney

Midwest

Casper

Belle

River

River

Bighorn

River River

Shoshone

Powder

River

River

River

River

Green

River

Sweetwater

Laramie

North

River

River

Wind

Snake

Platte

Cheyenne

Fourche

4

2

2

3

1

5

Base from U.S. Geological Survey

Digital Chart of the World digital data, 1995

Shaded relief map from 

National Elevation Dataset digital data, 1999

Albers Equal-area Conic projection

Standard parallels 41 ̊ and 45 ̊,

central meridian -107 ̊30'

U.S. Geological Survey

POWDER RIVER

BASIN

BELLE

FOURCHE 

RIVER

BASIN

BIGHORN

 

RIVER

BASIN

WYOMING
 3

Table 1. Streamflow-gaging stations used in the analysis

Site no.

(fig. 1)

Streamfowgaging station 

number Station name

Drainage area 

(square miles)

1 06268500 Fifteenmile Creek near Worland, Wyo. 518

2 06313180 Dugout Creek tributary near Midwest, Wyo. .81

3 06313700 Dead Horse Creek near Buffalo, Wyo. 151

4 06425750 Coal Creek near Piney, Wyo. 71.8

5 06425780 Belle Fourche River above Dry Creek near Piney, Wyo. 594

Runoff primarily occurs in response to rainstorms, but 

drainage basins within the Powder, Belle Fourche, and Big 

Horn River basins have some snowmelt runoff. Continuous 

streamflow records collected at Dugout Creek tributary near 

Midwest (site 2) during 1975-83 and Dead Horse Creek near 

Buffalo (site 3) during 1971-90) were analyzed to estimate the 

percentage of runoff attributed to rainstorms. Records for October through March were used to estimate snowmelt runoff, and 

records for April through September were used to estimate rainstorm runoff. Occasionally, runoff in October was from rainstorms, and some runoff in April was from snowmelt; however, 

records from the two 6-month periods generally are representative of the two types of runoff. About 74 percent of the annual 

runoff from Dugout Creek tributary (site 2) and about 81 percent of the annual runoff from Dead Horse Creek (site 3) were 

from rainstorms. The duration of runoff from rainstorms is measured in hours, whereas the duration of runoff from snowmelt, 

is measured in days and weeks.

Eight years (1979-86) of continuous streamflow and sediment records collected at Fifteenmile Creek near Worland 

(site 1) were analyzed to estimate the percentages of sediment 

discharge attributed to rainstorm runoff and to snowmelt runoff. 

The same time periods used for Dugout Creek tributary (site 2) 

and Dead Horse Creek (site 3), October through March and 

April through September, were used for Fifteenmile Creek. The 

analysis indicated that 88 percent of the runoff was from rainfall, and 12 percent of the runoff was from snowmelt. About 

95 percent of the annual sediment discharge occurred during the 

rainstorm-runoff period and 5 percent during the snowmeltrunoff period.

Sediment-Load Computations

Total-sediment loads for rainstorm runoff were computed 

from sediment-sample data collected at each of the five sites 

(table 1). Sediment samples were collected using automatic 

pumping samplers. Sediment concentrations in the pumped 

samples were verified by comparing them to concentrations in 

depth-integrated samples (Rankl, 1987, p. 8). Discharge and 

total sediment concentration data were collected at Dead Horse 

Creek near Buffalo (fig. 2) and Dugout Creek tributary near 

Midwest to define the total-sediment load for a rainstorm runoff. For the remaining three sites, total sediment loads for each 

rainfall-runoff storm were computed from sediment records 

used to compute the annual suspended-sediment discharge. 

Sediment loads for rainstorm runoff data were computed from 

sediment-concentration samples, not from sediment-concentration curves. Data were not included in this study unless sediment-sample data were available for more than 75 percent of the 

water volume of the rainstorm runoff.

Total-sediment loads, consisting of suspended sediment 

and bedload material, were accounted for at each of the streamflow-gaging stations used in the analysis. At Fifteenmile Creek 

near Worland, the unmeasured bedload was computed using a 

method developed by Colby (1957). At Dugout Creek tributary 

near Midwest and at Belle Fourche River above Dry Creek near 

Piney, samples were collected in the turbulent section of the 

control structure where all sediment particle sizes were in suspension. The channels at Dead Horse Creek near Buffalo and 

Coal Creek near Piney consist of clay and silt; therefore, the 

samples of suspended sediment are assumed to represent the 

entire sediment load (Guy and Norman, 1970, p. 54). The peak 

discharge and total-sediment load for each rainstorm runoff at 

each station used in this study are listed in table 2.

Relation Between Total-Sediment Load and 

Peak Discharge

Equation 1 is used to define the relation between totalsediment load and peak discharge for a rainstorm runoff:

log Ls = log a + b (log Qp), (1)

where Ls is the total-sediment load of the rainstorm runoff, 

in tons;

Qp is the peak discharge of the rainstorm runoff, in 

cubic feet per second;

a is the regression constant; and

b is the slope of the relation.
4 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

Figure 2. Discharge and total-sediment concentration for Dead Horse Creek near Buffalo, Wyo., storm of June 5, 1986.

Total-sediment concentration

Discharge

DISCHARGE, IN CUBIC FEET PER SECOND

CONCENTRATION, IN MILLIGRAMS PER LITER

TIME, IN HOURS

1 5 15 20 25 27 10

1,500 160,000

1,400

140,000

1,200

120,000

1,000

100,000

800

80,000

600

60,000

400

40,000

200 20,000

0 0

The annual total-sediment discharge from rainstorm runoff 

for a year can be computed using:

(2)

where Qsa is the annual rainstorm sediment discharge, in tons 

per year; and 

n is the number of rainstorm runoff peaks per year.

When regressions relating the logarithms of concentration 

and the logarithms of discharge are retransformed to the nonlinear form of the equation, a statistical bias occurs in computing the sediment load for each storm. Several investigators have 

explored the magnitude of statistical bias in computing sediment loads and have developed procedures to correct for the 

bias (DeLong, 1982; Ferguson, 1986; DeLong and Wells, 1987; 

and Cohn and others, 1989). The magnitude of the bias is a 

function of the number of samples and the value of the variance 

of the random error, σε

2

.

Cohn and others (1989) stated that the Quasi Maximum 

Likelihood Estimator, called the bias correction factor by Ferguson (1986), performs well for a large number of samples and 

for a σε

2

 less than 1.0. Although the number of samples for this 

study is small, the variance of the random error is considerably 

less than 1.0. The retransformed total-sediment discharges 

(equation 2) were corrected by the bias-correction factor developed by Ferguson (1986):

, (3)

where s

2 is an estimate of the variance of the random error of 

the population.

The log-Pearson type III probability distribution is useful 

to describe floodflow characteristics. Because the totalsediment load for a rainstorm runoff is a floodflow type of 

occurrence, the log-Pearson type III distribution was used to 

describe the distribution of the annual series of total-sediment 

discharge from rainstorm runoff. The median (0.50 probability) 

sediment discharge of the series also was computed.

Qsa aQpi

,

b

i 1 =

n

= ∑

Qsa aQpi

b 2.65s2

exp( )

i 1 =

n

= ∑
 5

Table 2. Peak discharge and total-sediment load for rainstorm runoff

Date of 

rainstorm 

runoff

Peak discharge

(cubic feet per 

second)

Total-sediment 

load

(tons)

Date of 

rainstorm 

runoff

Peak discharge

(cubic feet per 

second)

Total-sediment 

load

(tons)

Site 1. Fifteenmile Creek near Worland1

1Total sediment load for a rainstorm runoff computed from sediment record used to compute annual suspended-sediment discharge.

Site 3. Dead Horse Creek near Buffalo–continued3

5/17/81 443 42,900 9/02/86 43 1,220

5/22/81 1,110 208,000 9/10/86 61 684

5/27/81 718 46,400 7/17/87 401 17,550

6/01/81 175 7,320 8/25/87 288 6,910

8/10/82 995 94,400 Site 4. Coal Creek near Piney1

8/11/83 1,840 99,600 5/27/81 1,170 2,760

6/11/84 272 27,000 7/04/81 10 20

6/16/84 410 33,600 7/14/81 52 142

6/17/84 389 21,400 7/19/81 45 163

2 7/24/84

2

This rainstorm not used in regression analysis.

93 932 7/25/81 544 1,630

8/01/84 365 15,170 8/16/81 10 20

5/27/85 77 5,250 5/20/82 44 202

7/14/85 66 4,120 5/27/82 17 27

7/31/85 395 30,800 6/01/82 42 156

6/30/86 287 16,600 8/09/82 46 140

9/09/86 222 17,800 8/17/82 8.2 11

Site 2. Dugout Creek tributary near Midwest3

3

Total sediment load for a rainstorm runoff computed from sediment samples.

8/21/82 34 147

5/19/82 16 91 9/14/82 173 468

5/27/82 88 679 9/27/82 20 60

6/08/82 2.6 6.5 Site 5. Belle Fourche River above Dry Creek near Piney1

6/16/82 70 275 6/14/77 1,630 761

7/24/82 11 40 7/09/77 77 256

8/09/82 15 43 6/30/79 126 301

8/20/82 5.9 12 5/27/81 838 1,780

6/03/83 22 130 8/16/81 8.5 4.6

7/23/83 129 1,340 5/21/82 70 102

8/04/83 194 1,160 5/28/82 30 12

Site 3. Dead Horse Creek near Buffalo3 7/26/82 7.5 5.8

6/5/86 1,400 26,500 8/21/82 574 1,780

6/30/86 82 1,970 9/14/82 184 394
6 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

Discharge and sediment data compiled in table 2 for the five 

streamflow-gaging stations were analyzed to determine the 

regression constant and slope for the log-linear relation between 

total-sediment load and peak discharge for a rainstorm runoff. 

The distribution of the data for each of the stations is shown in 

figures 3 through 7. The data for Fifteenmile Creek near Worland 

included runoff from a localized rainstorm on July 24, 1984, that 

was not representative of runoff and total-sediment load from the 

basin. This rainstorm runoff with a total-sediment load of 932 

tons was not included in the regression analysis. Total-sediment 

load and peak discharge were available for only six rainstorms at 

Dead Horse Creek near Buffalo, but the analysis was included in 

the study because of the availability of the peak discharges for all 

rainstorm runoff for 14 years. The number of total-sediment load 

and peak-discharge rainstorms available for analysis, N, the computed parameters, the coefficient of determination, R2

, the sample standard deviation, s, and the standard error of estimate in percent are shown in table 3.

Residuals computed in the regression analysis were analyzed to determine if the data are approximately normally distributed. Skewness and kurtosis were computed for the residuals of 

each of the five data sets. For an approximately normal distribution, skewness is close to 0 and kurtosis should be close to 

3. Skewness values for the five data sets ranged from positive 

0.31 for Fifteenmile Creek to negative 0.67 for the Belle Fourche 

River. Kurtosis values ranged from 1.99 for Dugout Creek tributary to 3.75 for Dead Horse Creek. All of these values suggest 

that the data are approximately normally distributed.

The regression lines from figures 3 through 7 are plotted 

together on figure 8. The regression lines seem to indicate the 

relation is consistent for all five sites. To determine if that was the 

case, an analysis of covariance was made for slopes and intercepts summarized in table 3. Dummy variables were applied to a 

multiple-regression model (Kleinbaum and others, 1988) to 

determine if there was a significant difference in the slopes or 

intercepts at the 95-percent confidence level. The analysis indicated that the slopes are not significantly different and that the 

intercepts are significantly different. The parallel regression lines 

indicate that the relation is consistent for the five basins. However, field inspections of the basins indicated that the sediment 

availability and erodibility are different in each of the five basins, 

which may account for the significant difference in the intercepts 

of the five regression lines.

Figure 3. Relation between total-sediment load and peak discharge 

for rainstorm runoff, Dugout Creek tributary near Midwest, Wyo. 

(from Rankl, 1987, fig. 15). TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1 10 100 1,000

10,000

1,000

100

10

1
 7

Figure 4. Relation between total-sediment load and peak discharge 

for rainstorm runoff, Fifteenmile Creek near Worland, Wyo. TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

10 100 1,000 3,000

100,000

300,000

10,000

1,000

100

Not used in analysis

The limitations of the study are the upper limits of the 

total-sediment load and discharge relation defined by the data 

listed in table 2. Total-sediment load for runoff greater than 

bankfull stage was measured at two of the stations without an 

apparent deterioration in the relations. Extension of the relations beyond the data could result in errors. However, if the 

relations are to be useful for predicting annual total-sediment 

discharge resulting from rainstorm runoff, then the magnitude 

of these errors needs to be evaluated.

To explore the potential magnitude of error due to extension of the total-sediment load and peak-discharge relation 

beyond the limits of the data used in the regression models, a 

linear error was assumed, ranging from zero at the upper limit 

of the defined relation to a plus or minus 50 percent at the maximum peak discharge of record. The peak discharge of record 

was about 8 times the upper limit of the defined relation at Dugout Creek tributary near Midwest, and the peak discharge of 

record was about 2.5 times the upper limit of the defined relation at Dead Horse Creek near Buffalo. The magnitude of two 

errors was explored—the error in the arithmetic mean and the 

error in the geometric mean of the annual sediment load. For 

Dugout Creek tributary near Midwest, the error in the arithmetic 

mean was a plus or minus 15 percent, and the error in the geometric mean ranged from a positive 1.0 percent to a negative 1.1 

percent. For Dead Horse Creek near Buffalo, the error in the 

arithmetic mean was a plus or minus 14 percent, and the geometric mean ranged from a positive 0.4 percent to a negative 0.6 

percent. The small errors in the geometric mean indicate that the 

log- Pearson type III distribution could minimize the effects of 

the potential errors in median sediment discharge (0.50 probability) from the basins when records are extended beyond the 

defined regression equations.

To define the distribution of the annual total-sediment discharge from rainstorm runoff for Dugout Creek tributary near 

Midwest and Dead Horse Creek near Buffalo, values for the 

mean, standard deviation, and the coefficient of skewness were 

computed for the log-Pearson type III distribution. Equation 3 

was used to compute the estimated annual total-sediment discharge from the peak discharge for all rainstorm runoff compiled for the two stations. The fit of the log-Pearson type III distribution to the annual total-sediment discharge for the two sites 

is shown in figure 9. The median annual total-sediment discharge for Dead Horse Creek near Buffalo is about 10 times the 

median annual total-sediment discharge at Dugout Creek tributary near Midwest.
8 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

Figure 5. Relation between total-sediment load and peak discharge 

for rainstorm runoff, Dead Horse Creek near Buffalo, Wyo.

Figure 6. Relation between total-sediment load and peak discharge 

for rainstorm runoff, Coal Creek near Piney, Wyo. TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

10 100 1,000 10,000

100,000

10,000

1,000

100

TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

6 10 100 1,000 3,000

10,000

1,000

100

10

Two rainstorms
 9

Figure 7. Relation between total-sediment load and peak discharge 

for rainstorm runoff, Belle Fourche River above Dry Creek near 

Piney, Wyo.

Table 3. Results of regression analysis for relation between total-sediment load and peak discharge for rainstorm runoff

[N, number of runoff rainstorms; R2, coefficient of determination; s, sample standard deviation]

Site 

No. Station name N

Regression

constant Slope R2 s

Standard 

error of 

estimate 

(percent)

1 Fifteenmile Creek near 

Worland

15 33.88 1.13 0.89 0.164 39

2 Dugout Creek tributary 

near Midwest

10 1.78 1.29 .97 .146 35

3 Dead Horse Creek near 

Buffalo

6 16.59 1.07 .91 .219 54

4 Coal Creek near Piney 14 1.98 1.08 .96 .154 37

5 Belle Fourche River above 

Dry Creek near Piney

10 .62 1.16 .89 .348 94

TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1 10 100 1,000 4,000

1,000

4,000

100

10

1
10 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

Figure 8. Relation between total-sediment load and peak discharge 

for rainstorm runoff at the five sites on ephemeral streams used in 

the study. TOTAL-SEDIMENT LOAD, IN TONS

PEAK DISCHARGE, IN CUBIC FEET PER SECOND

6 10 100 1,000 3,000

100,000

200,000

10,000

1,000

100

10

Belle Fourche River

Coal Creek

Dugout Creek tributary

Dead Horse Creek

Fifteenmile Creek

6
 11

Figure 9. Log Pearson type III probability distribution of annual totalsediment discharges for Dugout Creek tributary near Midwest, Wyo. 

and Dead Horse Creek near Buffalo, Wyo.

PROBABILITY

0 0.2 0.4 0.6 0.8 1

1,000,000

100,000

10,000

1,000

100

TOTAL-SEDIMENT DISCHARGE, IN TONS PER YEAR

Dead Horse Creek

Dugout Creek tributary

Summary and Conclusions

Total-sediment load is related to peak discharge for rainstorm runoff in ephemeral streams. Regression equations were 

developed from data for five ephemeral streams in Wyoming. 

Coefficients of determination ranged from 89 to 97 percent. 

Standard errors ranged from 35 to 94 percent. The slopes of the 

equations for the five streams are not statistically different at the 

95-percent confidence limit, which may indicate that slopes are 

a function of rainstorm intensity for detaching the sediment particles. The intercepts are statistically different for the five 

basins, which may indicate that this difference is a function of 

sediment availability; that is, vegetation, soil erodibility, and 

land slope.

The annual sediment discharge primarily is a function of 

sediment availability, the number of rainstorms, and the magnitude of the rainstorms. The relative sediment availability is 

defined by the position of each of the relations for total-sediment load and peak discharge (fig. 8). Onsite reconnaissance of 

the five basins indicated that the relative positions (increasing 

sediment availability with increasing sediment loads for a given 

peak discharge) of the relations for total-sediment load and peak 

discharge are correct.

Peak discharges for all rainstorm runoff were compiled for 

Dugout Creek tributary near Midwest and for Dead Horse 

Creek near Buffalo. The peak discharges for each basin were 

applied to the total-sediment load and peak-discharge equation 

for that basin to determine the sediment load for each rainstorm 

runoff. The sediment loads for rainstorm runoff were summed 

to obtain the annual sediment discharge for rainstorms. The statistics for a log-Pearson type III distribution were computed 

from the annual total-sediment discharges to determine the 

median annual total-sediment discharge.

Total-sediment discharge from rainstorms at Dugout 

Creek tributary and Dead Horse Creek was estimated to be 

between 90 and 95 percent of the annual total-sediment discharge. This estimate takes into consideration that runoff from 

rainstorms accounts for 74 percent of the annual runoff at Dugout Creek tributary and 81 percent of the annual runoff at Dead 

Horse Creek. This estimate also takes into consideration the 

smaller suspended concentrations in snowmelt than in rainstorm runoff (Rankl, 1987, p. 15) and the relation between sediment discharge for snowmelt and rainfall runoff at Fifteenmile 

Creek near Worland.
12 Relations Between Total-Sediment Load and Peak Discharge, Five Ephemeral Streams

The relation between total-sediment load and peak discharge of rainstorm runoff has an application not explored in 

this study that could prove useful. A shift in the relations could 

be used to define changes in sediment loads as a result of an 

environmental change—either anthropogenic or natural. 

Because the slopes of the relations for the streams studied are 

not significantly different and the intercepts are significantly 

different, sediment availability possibly might be regionalized.

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