An Analysis of Some 

Storm-Period Variables

Affecting Stream 

Sediment Transport

By H. P. GUY

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-E

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402
CONTENTS

Abstract_ _____________________________

Introduction. ___________________________

Scope of work and available information,...

Theory of sediment yield and transport__.

Fine sediment.______________________

Splash, sheet, and rill erosion____

Environmental factors__ _ _______

Coarse sediment.____________________

Effect of velocity.__---__________

Effect of particle size_____________

Storm characteristics.____________________

The runoff hydrograph.______________

Seasonal characteristics.______________

Precipitation. ___________________

Infiltration__ _ _________________

Runoff _ ________________________

A graphical search for variables__________

The storm event technique__________

Water-sediment discharge relationsCompilation of data____________

Surface runoff.______________________

Season.____________________________

Ground-water runoff_________________

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A graphical search for variables Continued

Peakedness. ________________-_____-------_----- E20

Rainfall. _________________________________

Trend. ______________________-_ .

Concentration as a dependent variable.__.__. 

Summary of graphical search _____________

The model and transformation of variables ___. 

Computation results.___________________--_---.

The means and standard deviations._________

Simple correlations_______________________

Multiple regression equations for Hazel River. 

Comparison of streams.___________-------_.

Effects of dependent variables.__________

Effects of independent variables_________

Variation among basins_________________

Examples of application.______________--_-.

Range of specific variables________--___.

Comparison of locations__-____--_--___.

Extrapolation to other streams____-____.

Summary. _________--___-_-_-_---_-__--------.

Recommendations- _____-__---__----_----------

References.___________-___---_-___-_---------.

Appendix multiple regression equations ______

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ILLUSTRATIONS

FIGURE

Page

1. Chart of the principal factors affecting erosion and transport of sediment from the land surface..---------- E4

2. Components of a streamflow hydrograph___________._______-___________--------_------------------ 7

3. Seasonal probability of an intense 6-hour rainfall for the central Atlantic coast area_-_-____-_------------ 9

4. Wischmeier's erosion index for the area of the United States east of 105° W.___________--_-_------------ 10

5. Seasonal distribution of erosion index values at four locations in the Atlantic coast area._____------------ 10

6. Seasonal distribution of surface and total runoff for Rock Creek at Sherrill Drive, Northwest Branch Anacostia

River near Colesville, Md., and precipitation for the Washington Metropolitan area____---_---_------ 11

7. Effect of hysteresis and progressive lag on water-sediment discharge relations..--____-_------_----------- 13

8. Daily mean water and sediment discharge for two storm events for Hazel River at Rixeyville, Va _______ 14

9. Relation of sediment to water discharge for storm events, Hazel River at Rixeyville, Va_____------------- 17

10, 11. Variation of sediment discharge.

10. With time of year._________________________________________ - 18

11. With mean air temperature for time of year of given storm events_-________---------------------- 18

12. Magnitude and recession of ground-water runoff for Hazel River at Rixeyville, Va_---_-_---------------- 19

13-16. Variation of sediment discharge with 

13. Ground-water runoff..____________-________________________-____-______-___-_--------------- 20

14. Peakedness index.__-______________________________________________-_--__-_---------------- 21

15. Rainfall quantity_________________________________________________-_-__---_--------------- 22

16. Rainfall intensity ______________________________________________ 23

17. Variation of unadjusted and seasonal adjusted departure ratios with time..________-----_--------------- 24

18. Relation of sediment concentration to water discharge for storm events, Hazel River at Rixeyville, Va___-_- 25 

19, 20. Test of selected models against observed data for 

19. Shenandoah River._____________________-____________-_____.___----------------- ----- 34

20. Potomac River..__________________________________________________-_------_---- 35

21, 22. Comparison of the modified formula for 

21. James River at Buchanan with the observed data for the Shenandoah and Potomac Rivers...------- 36

22. Brandywine Creek with the observed data for the Shenandoah and Potomac Rivers._________------ 37
IV CONTENTS

TABLES

TABLE 1. Daily suspended-sediment records to September 1960 for streams draining to the Atlantic Ocean from the

United States.__________________.__________________________________________ E2

2. Computation of storm surface runoff and sediment discharge._...--_------___-____-__-__--_-____-_------ 15

3. Water, sediment, and related factors for storm events of the Hazel River at Rixeyville, Va----_----------- 16

4. Sediment records used for correlation and multiple regression analysis.-_________________________________ 23

5. Means and standard deviations of variables used in multiple regression analysis, by streams.--______-_-_-_ 26

6. Simple correlation coefficients and their significance, by streams.______________________________________ 28

7. A matrix of variables showing the average direction and significance of simple correlations________-______- 29

8. Regression coefficients and standard error of estimate of principle regression equations, by streams._______ 30

9. The regression equations, by streams, for 1, 2, or 3 independent variables._____-____--_-___-_-_-_-____- 32

10. Measured data for extrapolation of models to other streams..__________________________________________ 33
SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

AN ANALYSIS OF SOME STORM-PERIOD VARIABLES AFFECTING STREAM

SEDIMENT TRANSPORT

By H. P. GUY

ABSTRACT

This study of the effect of some natural factors on storm-period 

fluvial-sediment transport is a part of the development of 

techniques for utilization of sediment reconnaissance data. In 

more general terms, this report presents a study of the time and 

space variation of sediment transport in streams.

A review of the theory of sediment yield and transport indicates 

that for most streams the bulk of the suspended sediment 

transport occurs during the relatively brief storm periods when 

the drainage basin collects and routes precipitation excess to a 

specific site. Therefore, a description of the quantity of sediment 

moved during the storm runoff periods at a stream location must 

be based principally on the active and passive forces of erosion.

The investigation of these forces was accomplished by using a 

combination of graphical and analytical multiple correlation 

techniques. Graphical correlation was employed on data for 

seven stream locations in the Atlantic coast area; first, to determine which climatic, hydrologic, and sedimentologic variables 

might be used; second, to determine the required transformation 

of data; and third, to note any unusual elements of data or wild 

points for specific variables. An analytical method using the 

general multiple regression model on the electronic computer 

was then employed to develop and indicate the accuracy of 

optimum equations for predicting sediment movement with 

surface runoff. Several combinations of variables for each 

stream location were used to show the effect of interdependence 

among the variables.

In regard to a choice of the dependent variable for defining 

sediment variation, the mean concentration of sediment in 

streamflow was found to be somewhat superior to sediment 

discharge due to the high degree of intercorrelation between 

water discharge and sediment discharge.

Some of the storm-to-storm variation of sediment concentration in streamflow was found to be associated with storm 

magnitude, the time during a period of record, the season of 

the year, the antecedent condition of the basin, and the storm 

intensity. The sediment moving in streams tends to increase 

with measures of storm magnitude such as surface runoff 

quantity or rainfall quantity. An apparent trend of decreasing 

sediment with time was indicated for the records of all seven 

locations, but was statistically significant only for the locations 

on the Brandy wine Creek and the James River basins. With 

respect to seasonal change, sediment concentration tends to 

increase as mean air temperature increases. With respect to 

antecedent condition, sediment concentration tends to decrease 

as ground-water runoff increases. Ground-water runoff is 

generally high during the cool season for the Atlantic coast

area; therefore, intercorrelation with mean air temperature 

reduces the importance of this variable. Sediment concentration 

was found to increase with storm intensity. The measures of 

storm intensity used were peakedness index, peak flow, and 

rainfall intensity; however, only peakedness index was tested 

for all streams.

The standard error of estimate of the dependent variable (the 

storm-period sediment concentration) ranged from 0.14 to 0.30 

log units for most combinations of the independent or causative 

variables mentioned above. The range of this error was greater 

among the different streams than among the different combinations of variables for a given stream. This is attributed to 

variance of hydrologic and environmental factors that are not 

evaluated by the data, or possibly by the effect of some measurement errors in the basic data.

Three of the regression formulas derived in the above analysis 

were tested for extrapolation to other areas using observed data 

from the Shenandoah and Potomac Rivers. The results showed 

that these formulas can and must be modified to give a satisfactory comparison with the observed data.

INTRODUCTION

The development of methods for more effective use, 

and understanding, of available and future fluvialsediment data is considered to be the principal objective 

of this study. Sediment stations on streams are widely 

scattered or nonexistent in many areas because of (1) 

the high cost of sediment-measuring programs, (2) 

inadequate interpretation of the data, and (3) rather 

poor recognition of the need for sediment knowledge. 

Knowledge of stream-sediment conditions is so meager 

in many places that effective fluvial-sediment measurement programs cannot be designed satisfactorily 

without first making some reconnaissance measurements. 

Kind and intensity of such required reconnaissance 

observations must be based on knowledge of sediment 

conditions in distant as well as nearby streams and of 

the applicable techniques for interpreting the data. 

The study should also advance progress toward development of a "universal equation" for computing the 

magnitude of stream sediment transport by application 

of observations to specific variables.

El
E2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Sediment transport in a stream depends on such a 

great variety of circumstances that it is not considered 

practical to define fixed laws that would indicate the 

rate and amount of such sediment transport in the 

stream at any specific location. More specifically, the 

effects of widely varying climate, vegetation, and soils 

cause sediment conditions in streams to vary widely in 

time and space. Therefore, the task of describing and 

interpreting the yield, character, transport, and deposition of fluvial sediment seems almost insurmountable. 

In the past the most common method for describing 

fluvial sediment has been to collect a body of seemingly 

basic data representing the conditions of the problem 

requiring solution. Nearly all these data have been 

interpreted only so far as required for solution of the 

problem at hand, leaving the broader implications 

untouched. These programs have resulted in the basic 

data being widely scattered or even nonexistent in 

most parts of the country. This widely scattered 

information, however, could be a reservoir of data that 

if properly interpreted would increase general knowledge 

of fluvial sediment characteristics.

Therefore, the purpose of the project was to develop 

principles and methods for better understanding and 

use of sediment data. Experience has shown that it 

is not practical to describe sediment conditions in 

time and space with a comprehensive sampling program 

involving vast quantities of basic-sediment data. It 

may be practical, however, to use a limited amount 

of basic data and a program of data analysis and 

interpretation based on knowledge from adjacent 

areas. It is expected that the principles and methods 

will indicate the kind of measurements of environmental factors that can reasonably be obtained for 

interpretation of the sediment data.

The author acknowledges with warm appreciation 

the helpful suggestions and criticisms from colleagues 

who assisted in the formulation of the project, provided technical guidance, and read an early draft of 

the manuscript. Particular thanks are extended to 

W. F. White, W. B. Langbein, R. B. Vice, P. C. 

Benedict, B. R. Colby, B. C. Colby, and D. W. Hubbell. 

Messrs. F. J. Keller and H. E. Reeder assisted in 

assembly of data and correlation of variables for the 

Scan tic and James River basins, respectively.

SCOPE OF WORK AND AVAILABLE INFORMATION

The scope of the work involved to meet the objective of developing principles and methods for 

better understanding and use of sediment data is 

limited to a considerable extent by the availability of 

sediment and environmental data. Hence, it is necessary to determine what correlative, mathematical, 

and "intuitive" techniques can be developed to give

substance and understanding to this limited supply 

of available data.

The analysis of the available data for this report is 

limited to the Atlantic coast area. The bulk of the 

sediment data consists of daily mean concentration and 

daily suspended-sediment discharge at 39 sites in 

several river basins as indicated by the records listed in 

table 1. These records of sediment data were determined from the results of depth-integi ated samples 

mostly taken at a single fixed stream vertical and 

adjusted, if necessary, by use of more complete definition of concentration in the stream cross section. 

Samples generally were taken once per day, except 

during periods of rapidly changing water discharge or 

sediment concentration. During these changing conditions the aim was to make several observations per 

day. When sufficient samples could not be obtained 

during the changing conditions to define the nature of 

concentration variation during the storm-runoff event, 

simple statistical methods were used to arrive at a 

computed or estimated value of the concentration.

TABLE 1. Daily suspended-sediment records to September 1960 

for streams draining to the Atlantic Ocean from the United 

States

[Dates marked with an asterisk indicate record still in progress September 1960]

Stream and location

Hazel River at Rixeyville Va

James River at Scottsville Va

Yadkin River at Yadkin College, N. C. ..................

Drainage 

area 

(sq mi)

98.4 

90 

3,456 

44.5 

3,076 

889 

6,780 

27.1 

133 

160 

355 

1,147 

69.4 

122 

279 

1,893 

314 

12.2 

10.2 

7,797 

265 

339 

44.1 

3,354 

15.0 

333 

1,638 

772 

286 

616 

465 

2,084 

4,571 

1,802 

3,000 

2,550 

2,140 

2,280 

313

Month 

and year 

of record

*ll/52 

3/53-7/55 

1/54-6/59 

*l/56 

2/57-9/58 

5/48-3/53 

*9/49 

2/49-6/51 

9/47-3/53 

9/47-6/51 

*9/47 

3/48-9/51 

4/50-4/53 

9/47-6/51 

4/48-3/53 

*10/47 

*12/46 

*5/54 

*5/54 

1/51-7/54 

12/55-3/58 

12/55-3/58 

11/55-3/58 

1/51 

*2/54 

*5/59 

4/53-9/56 

10/55-9/56 

10/51-9/55 

*4/51 

5/51-9/56 

5/51-9/56 

12/50-9/56 

2/53-9/56 

1/54-6/57 

1/54-6/57 

*l/58 

*1/51 

*l/58

The variation found in sediment conditions, among 

sites and with time, indicates that most records of less 

than 4 years do not define the sedimentologic conditions 

of the stream within acceptable limits. This is caused
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E3

by the highly variable meteorologic and cultural patterns acting on the drainage basin which affects the 

sediment transported in the surface runoff. Thus 

when sediment data are collected only for a few storms 

in one season, the results are considered to be reconnaissance information.

Table 1 shows that most of the data for the Atlantic 

coast area are from a few States; thus, further indicating 

the need for developing techniques to extend available 

sediment data. Furthermore, even though Pennsylvania has the greatest number of station-years of record, 

the data represents only a small percentage of the 

drainage area in this particular State. Also, the 

special sediment studies in the Schuylkill Kiver basin are 

demonstrative of the fact that stations on large drainage 

basins do not give information as to the various conditions in that particular basin. On the other hand, 

the small area stations represent only some of the 

environmental conditions. The overall result is that, 

although the 39 stations listed in table 1 seem to represent 

a lot of information, the deficiency of sediment knowledge is still very great.

The development of the principles and methods used 

in this report is based on aspects of hydrology and 

sedimentology discussed in the following sections, entitled "Theory of sediment yield and transport" and 

"Storm characteristics."

THEORY OF SEDIMENT YIELD AND TRANSPORT

The two principal components of natural streamflow 

for eroding and transporting sediment are the surface 

or overland flow resulting from precipitation excess and 

the base flow from springs and other ground-water 

seepage. The sedimentological aspects of these segments of hydrology stem from the erosion and transportation capacity of the overland flow as it makes its 

way to stream channels by way of sheet and rill flow 

and (or) from the transporting and bank-eroding power 

of high streamflow which may be derived from large 

quantities of ground-water flow.

Overland runoff, as determined from precipitation 

excess, is the most active agent causing erosion and 

sediment transport. Thus rainfall intensity and infiltration capacity at the land surface are important 

factors affecting the amount of sediment movement. 

Both these factors are known to vary greatly with time 

and location within a drainage basin. The precipitation generally ranges from a light drizzle during the 

cool season to a heavy downpour during the warm 

summer months. The infiltration ranges from zero 

through impermeable surfaces to several inches per 

hour through a forest floor with good duff and a very 

permeable subsoil.

FINE SEDIMENT

SPLASH, SHEET, AND RILL EROSION

On land surfaces of erodible sediment, the kinetic 

energy of the raindrops causes a large amount of 

splashing of the soil and water and, hence, transport of 

fine sediment hi two ways. First, is the net movement 

in a downslope direction by gravity and (or) hi the 

leeward direction by wind as it is briefly airborne. 

Second, is that the impact of rainfall and dispersion of 

soil particles cause a sealing of the soil surface thereby 

reducing the infiltration. The reduced infiltration 

increases the amount of precipitation excess that must 

make its way to stream channels carrying its load of 

eroded sediment. This movement of flow over the 

land before collecting hi the rills is called sheet flow. 

The reduced infiltration is effective in increasing the 

amount of flow in the rills and stream channels and 

thereby the erosive power in these channels is also 

increased.

The way in which sheet flow differs from rill and 

channel flow hi eroding and transporting sediment is 

considerable. Sheet flow moves rather slowly owing 

to the small amount of tractive force (small depth) 

and owing to the large amount of resistance (relative 

roughness) offered by the land surface. The rill and 

channel flow, on the other hand, is confined to a small 

area of resistance; and with its relatively great depths 

and hence large tractive force or gravity potential, 

the energy of flow concentrated in a small area can be 

sufficient to move sand, gravel, or even boulders. 

Sheet flow therefore erodes and transports fine-grained 

sediment, the silts and clays, whereas the rill and other 

types of concentrated channel flow will carry all the 

fine-grained load derived from this sheet flow in addition to both fine and coarse sediments that may be 

eroded from the bed and walls of the channels.

Thus, it is evident that the quantity of fine sediment 

moved by the stream at a given time is nearly equal to 

that released by the environmental factors causing 

erosion within the drainage basin; whereas, the quantity of the various coarser sizes in transport is closely 

related to the magnitude of the fluid forces. For 

coarse material, Lane (1955) reported that if the supply 

is not equal to the carrying capacity through a stream 

reach, the stream will aggrade or degrade to establish 

approximate equilibrium between capacity and discharge of coarse sediment within the reach.

ENVIRONMENTAL FACTORS

Only small and generally unrelated segments of the 

relation of environmental factors to fluvial sediment 

have been studied by hydrologists and sedimentologists 

because of the diversity of climatic conditions, geographic areas, and segmented problem-solving objec-
E4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

SUBJECT CLASS MAJOR FACTORS ELEMENTS INFLUENCE OF ELEMENTS ON SOIL EROSION

Pamdrop Splash Erosion. Breaks down aggregates, dislodges and disperses soil, 

thereby sealing the surface and increasing precipitation excess.

Flow Erosion. Physical force due to pressure difference and impact of water 

dislodges, disperses, and transports. Intensity and duration affect rate of 

runoff after infiltration capacity is reached.

Alternate Freezing and Thawing Expands soil, increases moisture content and 

decreases cohesion thus facilitating dislodgement, dispersion, and transport.

Pressure Difference and Impact Dislodges by force due to pressure difference 

and (or) impact.

Granulation. Affects force required for dislodgement and transport. 

Stratification. Stratum of lowest porosity and permeability controls infiltration

rate through overlying layers.

Porosity. Determines waterholding capacity. Affects infiltration and runoff rates. 

Permeability. Determines percolation rate. Affects infiltration and runoff rates. 

Volume Change and Dispersion Properties. Soil swelling loosens and disperses soil

thereby reducing cohesion and facilitating dislodgement and transport. 

Moisture Content Moisture reduces cohesion and lengthens erosion period by increasing

the period of precipitation excess. 

Frost Susceptibility. Determines intensity of ice formation and affects porosity,

moisture content, and reduction in strength.

Gram Size, Shape, and Specific Gravity. Determines force needed for dislodgement 

and transport.

Orientation. Determines effectiveness of climatic forces. 

Degree of Slope. Affects energy of flow.

Length of Slope Affects quantity or depth of flow. Depth and velocity affect 

turbulence. Both velocity and turbulence markedly affect erosion and transport.

Vegetative. Grasses, legumes, vines, shrubs and trees give protection of land 

surface in proportion to interception of raindrops by canopy and retardation of 

flow erosion through decreasing velocity of runoff, increasing soil porosity, and 

increasing soil moisture holding capacity (transpiration).

Nonvegetative. Open surfaces result in a minimum of surface protection and therefore 

maximum splash erosion, reduced infiltration, increased runoff, and maximum 

erosion. A paved surface affords maximum surface protection with zero erosion and 

highly efficient runoff and transport characteristics.

FIGURE 1. Chart of the principal factors affecting erosion and transport of sediment from the land surface. Modified from Johnson (1961).

tives. Interpretation of this relation, using limited 

data for some specific climatic and drainage basin 

characteristics are reported by Glymph (1954), Maner 

(1958), Langbein and Schumm (1958), and Stall and 

Bartelli (1959). The sum of these and other works 

compose a meager knowledge of the total relation of 

environment to fluvial sediment.

Sayre, Guy, and Chamberlain (1962) listed five 

factors affecting the supply of sediment moved into 

and through a stream channel and, most applicable, 

the fine material contributed from the drainage area. 

This list, which follows, expands on the broad terms of 

climate and physical characteristics:

1. The nature, amount, and intensity of precipitation.

2. The orientation, degree, and length of slopes.

3. The geology and soil types.

4. The land use.

5. The condition and density of the channel system.

They noted also that these factors can operate either, 

or both, to resist or to advance the rate of erosion and 

transport. Precipitation, for example, if occurring at 

a low intensity and at ideal intervals, may advance the 

growth of vegetation and thereby the resisting force. 

Precipitation, if intense and following a drought, or 

occurring on an area without vegetative cover, is likely 

to cause a large amount of erosion. Because of the 

large variance and interrelation associated with the 

preceding list of factors, the definition of erosion and 

transport in drainage areas is difficult to attain.

One important factor resulting from the integrated 

effect of the above five factors is that the sediment 

yield of a large basin is generally found to be less than 

the sum of its subbasins. For example, the yield from 

a drainage area of 5 square miles generally ranges from 

400 to 4,000 tons per square mile; whereas, for 500 

square miles the range is 100 to 2,000 tons per square 

mile (Glymph, 1951). Though the deviation of yield
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E5

for a given size of basin is very great, the trend implies 

that sediment yield decreases as drainage area increases. 

For streams in equilibrium and having a fixed base 

level at the mouth, this loss of sediment in a stream 

system may be temporary. On the other hand, if the 

oceans are gradually rising with respect to the stream 

system, or a system of manmade base levels is imposed, 

the loss of sediment may be accounted for by the 

aggradation of the streams. Such sediment loss or 

aggradation also occurs when accelerated erosion in a 

drainage basin supplies more sediment than can be 

transported by the channel system. An index of the 

phenomenon of decreasing sediment in the downstream 

direction may at some future time be evaluated through 

some index of the condition and density of the channel 

system.

The interrelations of the active and passive forces 

that influence erosion are summarized in figure 1, as 

modified from Johnson (1961). Climate is considered 

the important active force as determined by rainfall, 

temperature, and wind. The important passive forces 

are the soil character (properties of soil mass and 

constituents), the topography (orientation, degree of 

slope, and length of slope), and the soil cover (vegetative and nonvegetative). Each of the active and passive forces are further described by refined factors in 

the illustration. For example, rainfall has a double 

action first is that of falling raindrops as described 

in a preceding paragraph and second is that of flowing 

water, which in broad terms is of either laminar or 

turbulent flow. The type of flow is a function of the 

velocity and depth of the water and the roughness of 

the surface over which it flows. Erosion and transport 

of sediment are negligible under the condition of laminar 

flow but, as the water from such laminar flow collects 

in rivulets and larger channels, the resulting energy 

of flow with increased scale and intensity of turbulence 

can be sufficient to carry heavy loads of sediment, 

especially fine particles. The important passive forces, 

therefore, tend to alter the depth and velocity patterns 

of overland or surface flow by keeping the flow spread 

thinly or by increasing the resistance to flow.

COARSE SEDIMENT 

EFFECT OF VELOCITY

B. R. Colby (written communication) showed that 

the discharge of sand in a sand-bed stream is closely 

related to the mean velocity of flow for rivers of a wide 

range of sizes. Many investigators had previously 

used the supposedly logical parameter of stage or depth 

as the independent variable for determining sand 

transport. The fallacy of the depth-transport concept 

is that the relation between velocity and depth has 

been demonstrated by Dawdy (1961) to be poorly

716-824i

defined both for an individual stream and among 

streams. Colby (1961) illustrated the complexity of 

the depth-transport concept by showing that the transport decreases with increasing depth at low velocity 

(less than about 3 fps (feet per second) and increases 

with increasing depth at high velocity.

Einstein (1950) treated the beginning of movement 

and the pickup of the sand grains from the bed as a 

probability for the individual grains to move. Thus 

a specific critical velocity is probably arbitrary and 

inexact as a measure of bed movement because of the 

arrangement of the grains on the bed and on local 

variations of velocity. At a velocity greater than the 

so-called critical value, movement in a very thin 

layer occurs by rolling, sliding, or skipping along the 

bed.

Sand swept up from the bed of a natural stream or 

suspended in a stream may be supported and transported downstream a considerable distance by the 

vertical components of currents in turbulent flow. The 

magnitude of these currents is largely a function of the 

horizontal velocity, the bed roughness, and the distance 

above the streambed. Hence, the suspended load of 

sand in a stream vertical can be considered to be 

associated with the mean velocity of flow.

EFFECT OF PARTICLE SIZE

The settling rate of a particle is a measure of its 

resistance to transport. Fine sediment particles in 

a dispersed state having a slow settling rate are easily 

carried in complete suspension by the fluid forces in 

natural streams, and, hence, have a tendency to move 

out of the drainage basin with the flow in which they 

are suspended. In contrast, coarse sediment particles 

with a fast settling rate may move by suspension for 

only short distances, or more probably, by rolling and 

bounding along the streambed. The smaller of these 

coarse particles move at a faster mean velocity than do 

the larger particles. The largest particles in a given 

stream would be transported only a short distance in 

a given period of movement and then only when the 

stream is experiencing a great flood. The coarse sediments on or near a streambed are being continuously 

sorted by the selective transport capacities of the 

stream.

Equilibrium of the concentration gradient of suspended sediment at a stream vertical requires that 

particles settling through a plane be balanced with a 

net upward movement of particles through this plane 

from a zone of heavier concentration. Particle fall 

velocity is then considered to be an indication of the 

rate of change of sediment concentration with distance 

above the streambed for a given scale and intensity of 

turbulence. An increase in turbulence, considered to
E6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

mean an increase in the vertical movements of flow, 

causes more uniformity of concentration for a specific 

size of sediment with respect to distance above the bed. 

Therefore, high values of velocity and (or) low values of 

particle size tend toward a uniform vertical concentration of sediment. If mean velocity is an indication of 

the scale and intensity of turbulence and the vertical 

variation of sediment concentration, then the discharge 

of coarse sediment is related to both stream velocity 

and particle size.

Colby (1961) showed that for a given mean velocity 

and a roughly equal bed roughness, a stream at a section 

of shallow depth will result in greater turbulence and 

hence contain a higher concentration of suspended 

coarse particles in a vertical than will be found in a deep 

section of the stream. Averaged over a long period of 

time, the sediment transported at the two sections, 

even though several hundred feet apart, is likely to be 

equal. With a substantial change of flow characteristics, such as greater depth and velocity, the transport 

through the two sections may temporarily be different, 

causing aggradation or degradation of the streambed.

The laboratory studies by Simons, Richardson, and 

Haushild (1962) showed inconclusive results regarding 

the effect of increasing concentration of fine material 

on the transport of coarse sediment. The data support 

the conclusion, however, that if bed roughness were 

the same, increasing fine sediment concentration will 

increase the transport of coarse sediment because the 

mean velocity of flow may be increased and the fall 

velocity of sediment particles may be decreased due 

to changes in the apparent viscosity and density of the 

suspending fluid.

Water temperature is an important environmental 

factor affecting the transport of sediment through its 

effect on viscosity of the fluid and the resulting changes 

in the fall velocity of the particles and changes in the 

turbulence of the streamflow. The effect of change in 

water temperature on particle fall velocity is greatest 

for fine sediment because these sizes settle more nearly 

in accordance with Stokes' law. For example, particles 

in a size class of 0.016-0.062 mm have a fall velocity 

of about 0.0017 fps at 32 °F and 0.0038 fps at 90 °F; 

whereas, particles in a class of 1.00-2.00 mm have a fall 

velocity of 0.59 fps at 32 °F and 0.74 fps at 90 °F 

(Hubbell and Matejka, 1959). Temperature change, 

however, does not affect the transport of fine material 

(less than 0.062 mm) because it is limited by the 

amount supplied to the stream system; that is, the 

stream will readily carry all available fine sediment 

at either a high or a low temperature. The temperature 

effect is probably most important for fine and medium 

sizes of sand.

STORM CHARACTERISTICS

Precipitation is undoubtedly one of the most 

important and yet most complex factors associated with 

the erosion and transport of fluvial sediment. A 

wealth of data concerning precipitation characteristics 

has been obtained by the U.S. Weather Bureau since 

1891. The basic precipitation data, daily quantity 

for nonrecording gages and hourly quantity for recording 

gages, is published in "Climatological data" by the 

Bureau. This data has been recorded for 40 to 50 

years. The density of the gages in the Atlantic coast 

area averages about 2.5 per 1,000 square miles for the 

nonrecording gages and 0.9 per 1,000 square miles for 

the recording gages. This seemingly large number of 

gages gives a fair representation of precipitation over 

large river basins, especially for storms of large aereal 

extent but are very inadequate when correlation with 

small basins is necessary, especially for the small 

convection storms.

Wischmeier and Smith (1958), in a correlation of 

rainfall characteristics with erosion and soil loss data, 

showed that an index consisting of the product of 

rainfall energy and the maximum 30-minute intensity 

of the storm is the most important measurable precipitation variable to explain storm-to-storm variation of soil 

loss from field plots. This concept is based on the fact 

that large fast-falling raindrops with a large amount 

of kinetic energy will cause much splash erosion, thereby 

sealing the surface and increasing the amount of 

surface runoff. The maximum 30-minute intensity is 

also proportional to both the total quantity of rainfall 

and the average intensity.

THE RUNOFF HYDRO GRAPH

Storm runoff is defined as the part of total runoff 

derived from storm rainfall or rapid snowmelt which 

reaches an observation point within a relatively short 

period of time. The time of runoff depends on the 

drainage basin characteristics, especially that of area, 

and requires only a few minutes for areas of a few acres 

but 5-12 days for drainage areas of 10,000 square 

miles. The ground water runoff or base flow part of 

a streamflow hydrograph lags the causative precipitation by a distinguishably longer period of time than 

does the surface runoff. Oftentimes, storm runoff 

may include subsurface ground-water flow which has 

infiltrated the surface of the ground but causes an 

increase in ground-water flow to the surface channel 

sufficiently soon to be classed as storm runoff. Such 

rapid transit of the subsurface storm flow results from 

the relatively short underground path through perched 

water tables, through flowing saturated zones, or 

through semichannels beneath the surface. The true
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E7

o

UJ

<

Ground-water runoff

1_______I

TIME > 

FIGURE 2. Components of a streamflow hydrograph.

surface runoff, or that amount of precipitation in excess 

of infiltration and surface storage, reaches a surface 

channel with its path on and above the ground surface. 

Except for ephemeral streams and small plots or fields, 

the physical measurement of these separate components 

of flow is practically impossible.

Attempts to separate storm runoff into the components of surface and underground runoff are made 

primarily through empirical analysis of runoff hydrographs. The general concepts of such an analysis are 

illustrated by figure 2, showing a typical hydrograph 

where ABODE represents the total runoff, where 

AFDE represents the amount of ground-water runoff, 

and where AGO is the estimated division line between 

true surface runoff and subsurface runoff. The area 

between curves AGO and AFD represents the volume 

of subsurface flow effected by the storm. The division 

line AGO, separating the surface and underground 

runoff, is of greatest significance in this study since 

the amount of sediment erosion in the upland areas 

should logically be directly related to only the amount 

of surface runoff. The transport rate of the coarser 

sizes of sediment in the stream channels is affected by 

the total flow.

Since water discharge generally varies directly with 

gage height at a given stream site, it is feasible to use

the trace of the gage-height recorder instead of plotting 

the water discharge against time to separate the 

components of surface and underground runoff. In 

fact, more sensitive results are possible by use of the 

gage-height chart because the line represents nearly 

instantaneous conditions, whereas most discharge 

data are averages for discrete elements of time. The 

writer has not found it convenient, however, to obtain 

and use the gage-height records in most instances.

The most convenient hydrographic data source for 

investigating records of considerable length is the 

series of Water-Supply Papers, "Surface Water Supply 

of the U.S.," which give the mean flow for each day of 

all streams gaged. With the exception of the lowyield storms, the author has also found that a tabular 

system using these daily values is quite adequate to 

separate the components of surface and underground 

runoff. Fortunately, the errors involved in estimating 

the volume of underground runoff are generally small 

in comparison with the volume of total surface runoff. 

For low-yield storms, where the amount of underground 

flow is more significant relative to the total flow, the 

number of days involved in the hydrograph will be 

fewer and hence the chance of significant cumulative 

error will be less.
E8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

SEASONAL CHARACTERISTICS

PRECIPITATION

The air always contains some water vapor, but rain 

or snow occurs only a small part of the time. Precipitation requires, in addition to moist air, and atmospheric disturbance in the air mass through lifting of 

large volumes of warm moist air to higher altitudes 

where it is cooled to a temperature below the dew point. 

Although the lifting is the decisive factor, strong convergence is also necessary to produce heavy precipitation. On the basis of the meteorological phenomena 

that cause and accompany precipitation, the causative 

storms may be divided into three types, namely, 

cyclonic, convectional, and orographic.

The contrast of the large land and water masses of the 

earth causes differential heating from the sun and 

therefore a great impetus for circulation of air. For 

example, in the winter the landmass cools more rapidly 

and may be covered with snow which reflects much of 

the sun's heat rather than absorbing it. High pressure 

cells of cold then push the polar front toward the south 

in North America. Low pressure cells of warm air 

are formed over adjacent ocean areas at this time. In 

the summer this situation is reversed.

Cyclonic storms are atmospheric waves, formed along 

the polar front by the interaction of the cold and warm 

airmasses. The general circulation pattern caused by 

the earth's rotation, or the terrestrial winds, pushes 

these storms from west to east in the latitude of the 

United States. Such cyclonic storms are characterized 

by a warm moist air sector on the south side which, 

being lighter than the existing cool air it meets, rides 

up over the wedge of cool heavy air. This causes condensation and a broad belt of rather low-intensity and 

long-duration precipitation when a warm front is experienced and a belt of rather high-intensity and shortduration precipitation when a cold front is experienced. 

The cold front moves more rapidly and has a steeper 

gradient of cold air than does the warm front.

The convectional type of storm is caused by uneven 

heating over a relatively small area and occurs only in 

areas of the large low pressure cells of warm air. For 

example, convection may be triggered by excessive 

heating of the air over a city when the streets and roofs 

are warmer than the surrounding countryside. The 

ascending warm air expands and cools as it rises, and if 

sufficient moisture is present, precipitation is formed. 

Such storms affect a relatively small area and at times 

cause heavy downpours; however, when the conditions 

of high temperature and moisture are present, the result is generally one of numerous cells of precipitation. 

The multiplicity of such convection cells and their

movement with the larger patterns of circulation tend 

to cause precipitation over relatively large areas, 

although the amount at points within the area may be 

highly variable.

Orographic precipitation occurs wherever mountain 

ranges, highlands, or ridges rise above the surrounding 

country in the path of the moisture-bearing airmasses. 

An example of this is found on the southwesterly slope 

of the Appalachian Mountains to which the moistureladen air is brought by tropical maritime airmasses 

from the ocean. As a result of the way warm moist 

air moves from the Atlantic Ocean with the terrestrial 

air movements and due to the relatively small change 

in altitude of the terrain, the orographic precipitation 

is not an important factor in producing storm runoff in 

the rivers draining the Atlantic coast area States.

It is evident that most of the above types of storms 

would vary considerably with the months and seasons 

of the year by the general northward and southward 

migrations of the planetary wind systems and by variations in convectional activity. Although the annual 

distribution of precipitation, by months, is rather uniform in the Eastern United States, the winter precipitation is mainly of cyclonic origin resulting from the 

interaction of moist tropical air from the south and 

dry polar air from the north. In summer, precipitation 

is mainly of the convectional and frontal thunderstorm 

variety. The total quantity of precipitation on an 

annual basis tends to increase in a southerly direction.

The statistics of storm precipitation are summarized 

by the U.S. Weather Bureau's Technical Paper 40 

(1961). The maximum total amount of rainfall to be 

expected in a given length of time, at a given location, 

and for a given return period can be determined. The 

durations of rainfall are for J£, 1, 2, 3, 6, 12, and 24 

hours. The return periods are for 1, 2, 5, 10, 25, 50, 

and 100 years. The publication also gives the seasonal 

probability of intense 1-, 6-, and 24-hour rainfalls for 

eight subareas of the United States east of 105°W. 

Figure 3 shows a chart from this reference for the 

seasonal variation of the 6-hour storms in the central 

Atlantic coast area. This illustration shows, for 

example, that a storm of an intensity likely to occur 

on an annual basis has a probability of 1 percent of 

happening in January and 23 percent of happening in 

August. This and other charts show that storms of 

greater intensity and return period are also likely to 

occur in July and August.

INFTLTRATION

In addition to precipitation variation, seasonal 

variation in infiltration capacity is also an important 

cause of seasonal variation in stormrunoff. The effects
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E9

100

60

40

30

20

Q

0 10

cr

cr

i I i i i r I i i r

M O N D

FIGURE 3. Seasonal probability in percent of an intense 6-hour rainfall 

for the central Atlantic coast area. (After U.S. Dept. of Commerce, 

1961.)

of season and temperature on infiltration were discussed 

by the author (1951), as follows:

* * * While resembling the mean temperature curve, the 

season infiltration capacity curves have a more marked rise in 

the spring and a more rapid recession in the fall. With respect 

to actual water temperature, sprinkling from a height of about 

six feet with water ranging from 40° to 110°F showed no significant differences of infiltration rates. Free, Browning, and 

Musgrave (1940) found that the contribution of temperature * * * was not a dominant factor in a study of 68 soils. 

There must then be other factors which largely over-balance the 

effect of change in viscosity due to change of water temperature. 

Water at the higher temperatures may cause swelling in the soil 

which will oppose the effects of decreased viscosity.

 and 

Since changes in water temperature cannot account for seasonal 

infiltration changes, it is believed that biologic factors are the 

principal causes. These include soil fungae, earth worms, ants, 

and beetles. The activity of these biota is largely dependent 

upon proper moisture conditions which may account for some of 

the increased variability of infiltration capacity under mid-summer conditions as compared to other seasons of the year.

The rate of storm infiltration would be at a minimum 

if the soil were frozen. In drainage areas of the 

central Atlantic area States, soil freezing may occur in 

varying degrees during part of the year. Topsoil in a 

wooded area having a good layer of duff and snow

cover is protected against freezing at very cold temperatures. The areal extent, depth, and duration of 

freezing, however, do increase in a northerly direction. 

Seasonal variation in infiltration is also a product 

of several changes in land use during a year. Under 

agricultural use, the state of cultivation is likely to 

cause a high infiltration rate under a firmly aggregated 

soil with a cloddy surface condition and a low rate 

under a fine-textured soil with an easily dispersed 

surface condition. The varying condition of the 

vegetative cover during the season is a critical element 

in reducing the impact of the raindrop and hence 

splashing and sealing of the soil pores. Other activities 

of man and animals tend to compact the soil surface 

or disrupt vegetative cover in varying amounts during 

the season.

RUNOFF

The runoff characteristics of a storm depend on the 

integrated precipitation and infiltration characteristics 

over a drainage basin and the routing of the resulting 

precipitation excess to the site on the stream in question. 

Splash, sheet, and rill erosion, with subsequent transport of fine sediment, is dominant for storms having a 

great deal of surface or overland runoff. Channel 

erosion, with subsequent transport of the coarser 

material found lining the channels, is dominant for 

storms carrying a great deal of underground runoff. 

Movement of the coarse material is largely a function 

of stream hydraulic and roughness characteristics and 

is therefore more readily correlated with the stage of the 

stream. This is not so for the fine material since its 

movement at a stream site is determined largely by 

erosion of the land surface and the routing with 

waterflow.

A study of stream sediment movement then should 

have close correlation with the geographic and seasonal 

distribution of rainfall erosion potential as determined 

by Wischmeier (1962). For a specific storm, the most 

applicable erosion potential was found to be the product 

of two rainstorm parameters; the kinetic energy of the 

rainfall in hundreds of foot-tons per acre times the maximum 30-minute intensity in inches per hour. The 

average of these values for the storms during the year 

is called the annual erosion index where all factors contributing to soil erosion other than rainfall are held 

constant. The index is directly proportional toor closely approximates, the annual soil loss from open 

cultivated areas. Figure 4 shows a map of the mean 

annual erosion index for the area of the United States 

east of 105° W. The approximate seasonal values of 

the erosion index are shown in figure 5 for central 

Vermont, central Pennsylvania, central North Carolina, 

and central Georgia. The increase in magnitude and 

peakedness of the seasonal indexes from north to south
E10 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

FIGUEE 4. Mean annual values of Wischmeier's erosion index for the area of the United States east of 105° W.

O

COO 

 cc.

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC 

FIGUEE 5. Seasonal distribution of erosion index values at four locations in the Atlantic coast area.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT Ell

2.00 -

" 1.60 -

2 1.20 -

0.80 -

0.40 -

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

FIGURE 6. Seasonal distribution of surface and total runoff for Rock Creek at Sherrill Drive, Northwest Branch Anacostia River near Colesville,

Md., and precipitation for the Washington Metropolitan area.

in the Atlantic coast area indicates the need for giving 

greater attention to the passive forces in the south than 

in the north. The seasonal effect of the erosion index 

of the important active forces (rainfall parameters) 

must be integrated with the seasonal effect of the passive 

forces such as the changes in soil properties and cover if 

the relative amount of sediment transport in streams 

is to be evaluated.

Information in the literature on the seasonal variation 

of surface or overland runoff in streams is lacking. 

Therefore, the storm-by-storm surface runoff of Rock 

Creek at Washington, D.C., and the Northwest Branch 

Anacostia River near Colesville, Md., was computed for 

the years 1949-60. The land use in these basins, 

though adjacent to each other, is quite different in that 

the Anacostia is largely rural in character; whereas 

Rock Creek is about % rural, % urban, and % in various 

stages of becoming urban. Figure B shows the variation of the monthly average surface runoff as well as 

the total flow for this 12-year period of flow. The same

chart also shows the monthly average precipitation to 

1950 for a 60-year period.

As expected, the proportion of surface runoff to total 

runoff was somewhat greater for Rock Creek than for 

the Anacostia River due to the greater amount of 

impervious surface in the Rock Creek basin. The effect 

of impervious surface is also shown by the fact that 

Rock Creek has the greatest flow (both surface and 

total) during the warm season, whereas the Anacostia 

has the greatest total flow during the cool or low intensity precipitation season. Greater losses by evapotranspiration during the warm season are likely in the 

Anacostia basin. The seasonal effect of evapotranspiration is very evident when the decreasing total flow of 

May, June, and July is contrasted with increasing 

precipitation of these months. The reverse occurs in 

the fall when the mean flow (both surface and total) 

increases nearly 100 percent from October to November 

while precipitation decreases somewhat.
E12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

A GRAPHICAL SEARCH FOR VARIABLES 

THE STORM EVENT TECHNIQUE

The task of selecting useful correlative, mathematical, 

and "intuitive" techniques to explain the storm-tostorm variation of sediment moved by a stream is made 

difficult by the complexity of hydrologic and sedimentologic conditions resulting from the active and 

passive forces of erosion and from the streamflow characteristics which route the sediment through the channel 

system. Readily available hydrologic and sedimentologic data, however, will be assembled and tested by 

correlative techniques. The investigations are limited 

to the Atlantic coast area and to streams selected from 

those listed in table 1.

The graphical technique is used to search for suitable 

variables to explain the nature and cause of sediment 

discharge variation. Mathematical analysis was avoided 

at this searching stage because it is more cumbersome 

to use, and the variance of individual bits of data would 

be obscured. The graphical technique of multiple 

correlation using the method of deviations is most 

adaptable to the "trial and error" and "intuitive" 

methods for selecting optimum measures for reducing 

the data scatter and for determining the type of conversions necessary for normalization of the data. In 

other words, graphical regression is less restrictive than 

analytical regression in that the model need not be 

completely specified in advance.

WATER-SEDIMENT DISCHARGE RELATIONS

Of all the data available for streams in the Atlantic 

coast area, the principle bivariate system for a specific 

stream location is generally considered to be that of the 

relation of sediment discharge to water discharge. The 

sediment-water discharge relation has been used by 

several investigators to solve specific problems. Campbell and Bauder (1940) used it for comparing discharges 

in the Red River Basin of Oklahoma and Texas; Miller 

(1951) for extrapolation of records for the San Juan 

River of Utah using flow-duration curves, and Leopold 

and Maddock (1953) for describing the interrelations of 

measured sediment with other hydraulic variables. 

One of the most comprehensive reports summarizing the 

applications of the sediment-water discharge curves is 

that of Colby (1956).

The sediment-water curves used by these investigators were derived from instantaneous, mean daily, mean 

monthly, or mean yearly sediment and water discharge 

data. There are four severe limitations to the curves 

derived by the instantaneous approach: (1) The sample 

data may be biased with respect to either time or water 

discharge because generally measurements are made 

more frequently at times of high flow and high concentration of sediment, especially during the recession of

the runoff hydrograph, than at other times. (2) The 

sediment concentration of instantaneous samples for a 

given stream tends to fluctuate about a mean value due 

to variation in the amount of fine material eroded and 

transported from upstream tributaries and due to 

changes in suspension of coarse material at the sampling 

vertical. (3) The sediment load for small drainage 

areas is generally, and for large streams is often, mucji 

greater for a given water discharge during the rising leg 

of a storm hydrograph than for the falling leg. (4) 

Under conditions of relatively high base flow and sediment originating at a considerable distance upstream, 

it has repeatedly been found that the sediment movement lags behind the flood wave so that the peak sediment concentration may occur after the flood crest.

Figure 7 illustrates the third and fourth concepts. 

Data from Leopold and Maddock (1953) showed the 

hysteresis effect for the San Juan River and illustrated 

that the sediment load for a water discharge of 5,000 cfs 

(cubic feet per second) is 10 times greater on the rising 

leg than on the falling leg of the hydrograph. The 

effect of the progressive lag of sediment movement with 

respect to the downstream movement of the flood wave 

is demonstrated by data from Heidel (1956) for the Bighorn River at Manderson and Kane, Wyo.

Water-sediment discharge data plotted from mean 

daily data, although very convenient because most data 

are published in this form, have some of the shortcomings exhibited by the instantaneous data,; especially 

the previously mentioned concepts three and four. The 

small scale variations of concept two are averaged during the 24-hour period, but the 24-hour division of the 

hydrograph is random, causing undefinable scatter in 

the relation due to concepts three and four. If the 

instantaneous or mean daily data were used, the effects 

of rainfall and possibly other weather and hydrologic 

conditions would be difficult to evaluate for correlation 

with sediment discharge due to the complexity of routing their effects downstream to the measuring site.

Monthly and especially yearly plotting cannot be 

effectively used for lack of sufficient record; at least 

they would not be effective for making predictions due 

to the higher standard error of estimate resulting from 

the small number of points. Each monthly or yearly 

discharge would be a composite of several hydrologic 

events, the integrated effect of which would be difficult 

to ascertain.

On the basis of the above considerations, the storm 

event is the most logical unit of data to fulfill the objectives of this study. The storm event unit (1) will not 

bias the curve with untimely data, (2) will average out 

the instantaneous fluctuations, and (3) will integrate 

the overall variations of sediment-water conditions over 

the hydrograph. One important advantage of using
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E13

WATER DISCHARGE (SAN JUAN RIVER), IN CUBIC FEET PER SECOND 

1000 2000______5000 10,000 20,000 50,000 

10,000

- 500,000

500 1000 2000

WATER DISCHARGE (BIGHORN RIVER),

IN CUBIC FEET PER SECOND

5000

1000

FIGUEE 7. Illustration of variation in water-sediment discharge relations. Effect of hysteresis for the San Juan River. Effect of progressive

lag for the Bighorn River.

the storm event unit, especially when only surface 

runoff is used, is that adjacent storm events are less 

likely to be related serially than are adjacent instantaneous or daily sediment data. Another advantage 

is that certain weather and hydrologic conditions can 

be evaluated for correlation with the sediment-water 

discharge relation. The two principal disadvantages 

of the storm event technique are that (1) data are 

published on the instantaneous, daily, or monthly

716^824

basis and (2) the sequence of weather may be such that 

the discharge from different storms may overlap each 

other in some instances. In the Atlantic coast area, 

a 3- or 4-year record will generally yield a sufficient 

number of storm events to adequately define the 

necessary correlations; whereas, if daily or instantaneous 

values were used only a sampling of the total data 

would probably be used to avoid an unwieldy volume 

of data.
E14 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

1000

500

200

100

50

20

10

 Total water discharge, in cfs

 I- Estimated discharge from underground, in cfs

 Mean sediment concentration, in ppm 

A Sediment discharge, in tons

12 13 14 15 16 17 18 

MARCH 1953

19 20 21 22 12 13 14 15 

JUNE 1953

16 17

FIGURE 8. Graphs of daily mean water and sediment discharge for storm events of March 13-20 and June 13-15, 1953, Hazel River at

RixeyvUle, Va.

COMPILATION OF DATA

Any statistical evaluation of the variation of sediment 

concentration in streamflow should be conducted so 

that the principal cause of the variation will be considered first. A reasonably convenient measure of the 

important storm volume variable is that of the surface 

runoff past a stream site for a specific storm. Records 

from the Hazel River at Rixeyville, Va., will be used 

to illustrate how data are extracted for the storm event

technique. Table 2 shows the results for the two 

storms, March 13-20 and June 13-15, 1953. Graphs 

of the daily mean total water and estimated underground runoff, or the combined subsurface and groundwater runoff, are plotted with daily mean sediment 

concentration and daily sediment discharge in figure 8. 

Computations for the surface runoff and sediment 

discharge for other storm events were made directly on 

the tables of published data to eliminate the need for
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E15

copying the data to tables or plotting hydrographs. 

Estimated daily values of underground runoff were 

used that would result in a rounded figure of the net 

surface runoff for each day, see table 2. Also, as shown 

in table 2, the sediment discharge for the storm event 

is the rounded total of all days having net surface 

waterflow. Mention should be made of the fact that 

the standard procedures used to obtain the published 

data omit from consideration the sediment moving 

near the streambed.

TABLE 2. Computation of storm surface runoff and sediment

discharge

[Illustration from record of Hazel River at Rixeyville, Va.]

Date

196S

13 . 

14.... ........... .........

15.. ....... ... 

16- 

17. . ............. ......

18 

19 .. 

20 

21 

13 

14 

15 

16 

Total 

runoff 

(cfs)

397 

845 

712 

769 

1,060

769 

731 

845 

676 

578

178 

326 

382 

252 

210

Estimated underground 

runoff 

(cfs)

397 

405 

422 

439 

480

509 

531 

555 

566

578

178 

186 

192 

202 

210

Net 

surface 

runoff 

(cfs)

0 

4401 

290 

330

580

260 

200 

290 

110, 

0

0 

140 

190 

50 

0

2,500 

380

Sediment 

discharge 

(tons)

1 

130\ 

35 

207 

1,170

62 

57 

103 

24, 

12

4 

2961 

273 

15 

10

1,790

r580

The water, sediment, and related factors for 75 

storm events for the Hazel River from October 1951 

to September 1955 are listed in table 3. The basic 

data for each storm event are described by column 

numbers as follows:

1. The consecutive number of months during the 

period of record Mt, beginning with May 1951.

2. The net surface runoff Qw in cfs-days.

3. The sediment discharge Qs in tons.

4. The water-discharge-weighted storm event con370.4& centration of sediment, C=- 

(parts per million).

m ppm

5. The ground-water runoff at the beginning of the 

storm event, Qh in cfs.

6. The long-term mean air temperature for the 

given time of year, Ta in °F.

7. The peak rate of water discharge, less the base 

flow, Pn in cfs.

8. A peakedness index indicating a measure of storm

intensity, Pt=Q!L -

9. The aerial mean precipitation for the basin, RQ in 

inches, as computed by the Thiessen method.

10. The aerial mean precipitation intensity for the

basin, Rt in inches per hour, as computed by the 

Thiessen method using the hourly data given 

from recording gages in or near the basin and 

using only the periods of rainfall for which 0.05 

inch or more in a given hour was recorded.

SURFACE RUNOFF

In the search for an explanation of the variation of 

sediment discharge, the water and sediment discharge 

data for the Hazel River at Rixeyville, Va. (table 3, 

columns 2 and 3), were used to plot a sediment transport 

relation. The data were plotted (fig. 9) with separate 

symbols for the cool and warm seasons to determine if 

there is a difference in transport with change of season. 

The transport curve, which appears to be a straight 

line on a log-log graph, was drawn approximately 

through the means of groups of storm events subdivided 

on the basis of several approximately equal logarithmic 

intervals of the volumes of water discharge. The division of the data into the two seasons shows three things: 

first, that the warm season storms have a greater range 

of water discharge volume; second, that the number of 

warm season storms greatly exceeds the number of the 

cool season storms on the side of the higher sediment 

discharge, and vice versa; and third, at small volumes 

of water discharge the division is very pronounced, but 

at large volumes of water discharge the storms' for each 

season are dispersed on both sides of the line.

To visualize how the sediment concentration varies 

among the storm events, lines of equal concentration 

for 100, 200, 500, and 1,000 ppm were drawn on the 

graph. At a small volume of water discharge, for 

example 500 cfs-days, the concentration lines show that 

the data scatters from 100 ppm to nearly 1,000 ppm; 

but, at a large volume of water discharge, for example 

10,000 cfs-days, the scatter is less and ranges from about 

300 ppm to about 800 ppm.

SEASON

The previously mentioned implications regarding the 

variation of sediment discharge with season require 

further testing. The ratio of the observed sediment 

discharge to that indicated by the transport curve is 

shown in column 11 of table 3 for each storm. These 

ratios, when considered as a group, are a measure of the 

departures or deviations of sediment discharge about 

the transport curve independent of water discharge or 

storm size. A plotting of these ratios against their 

respective time of year (fig. 10) results in a mean curve 

that varies with time of year, ranging from about 0.50 

in February and March to about 1.75 in June and July. 

The plot also shows again the great diversity in sediment yield of the storms larger than 3,000 cfs-days and 

their occurrence with all seasons.
E16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS 

TABLE 3. Water, sediment, and related factors for storm events of the Hazel River at Rixeyville, Va.

Date of collection

Time in

months

Mt

(1)

Surface 

runoff

(2)

Sedimen 

discharge 

Q.

(3)

t Sediment 

concentration 

C

(4)

flow

(5)

Mean air 

temp.

Ta

(6)

water 

discharge

Pn

(7)

Peakedness index 

Pi

(8)

Mean

rainfall

quantity

R,

(9)

Mean

rainfall

intensity

Pi

(10)

1951 

Nov. 7-10._____...............

Dec. 5-9--._ ... ....

Dec. 21-25... .

1952

Jan. 5-8_____. __ . 

Jan. 10-12...-------------

Jan. 22-24 ................ .

Jan. 27-31.....................

Feb. 3-9

Feb. 17-19-. _ - .

Mar. 11-17. 

Mar. 19-22 

Mar. 23-29. 

Apr. 5-9-- 

Apr. 14-18... 

Apr. 24-May 4 .............

May 11-15.--. ___ ... 

May 25-27.__........ ....

May 30-June2______....

June 15-16... _ . 

June 22-26.... ..

June27-July 2______._. 

July 8-11..... .

July 17-18-. . 

Aug. 2-3.- -----------------

Aug. 6-11---- .

Aug. 16-17. .

Sept. 1-5 

Nov. 15-17 . 

Nov. 20-27 .

Dec. 11-14...--- --___....

1953 

Jan. 1-4 

Jan. 8-16 

Jan. 24-28 

Feb. 15-17.. . 

Feb. 21-24...... ....

Mar. 13-20. . 

Mar. 24-Apr. 1................

Apr. 12-17.- 

May 4-10.---.-------------.

May 14-19. 

May 20-24. .................

May 31-June 2_________ 

June 13-15.. . 

June 22-23... . 

Aug. 17-19 

Oct. 28-31 

Nov. 23-25 .

Dec. 7-9...------ ._------

Dec. 13-16--- .

1954 

Feb. 21-24. 

Mar. 1-8 

Apr. 16-21. 

Apr. 24-30-. .

May 3-6____________ 

May 28-31 .

June 10-13.- 

June 14-15.-_-______... 

June 16-21 

Aug. 20-22 .

Aug. 30-31 

Oct. 15-18 - 

Nov. 19-22. .

Dec. 14-17. .

1955 

Dec. 29-Jan. 2...._______

Feb. 6-10.. -- 

Mar. 5-13 .

Mar. 21-28 

May 22-24. - - __ 

June 8-10-....................

June 11-15 

June 19-21.-..-.. .._ 

July 9-12 - ----

Aug. 8-9 

Aug. 12-16 

Aug. 17-25 

810

2,230

2,420

960

750

600

1,010

5,250

730

7,630

1,920

800

1,100

I,640

II,060 

950 

370 

430 

140

1,090 

470

1,470 

250 

410

2,700 

90

2,360

300

14,650

1,430

570

4,090

2,110

670

930

2,500

8,720

1,870

800

3,720

1,310

510

380

360

510

290

290

490

1,080

580

5,240

1,750

1,750

700

980

470

380

680

100

190

3,210

1,030

1,690

1,590

1,220

4,480

2,530

220

750

1,110

260

260

460

5,610

34,460

510

2,820

1,810

160

300

170

360

7,270

220

14,500

1,640

270

360

1,470

6,520

450

180

140

180

2,330

860

1,620

360

630

2,700

60

4,430

40

20,880

1,560

130

3,470

1,880

83

450

1,790

6,580

1,350

700

7,540

650

520

580

840

510

133

77

280

1,200

155

9,250

450

4,090

1,630

2,200

750

570

530

20

100

10,400

420

1,130

1,230

550

3,290

1,080

55

300

550

150

140

920

7,900

41,010

233

469

277

62

148

105

132

512

111

704

316

125

121

332

218

175

180

120

476

792

677

408

533

569

370

246

694

49

528

403

84

314

329

46

179

265

279

267

324

853

183

377

565

863

370

81

98

211

333

652

95

866

861

830

590

555

288

74

195

1,200

151

247

286

167

264

158

93

148

184

214

199

740

522

441

75

75

190

270

320

235

380

425

325

300

490

580

465

430

430

440

330

325

150

115

140

110

110

60

90

135

90

80

115

330

300

360

440

270

375

390

500

400

380

310

370

280

175

150

30

30

45

105

100

100

150

160

260

240

165

105

120

130

10

14

110

150

110

220

255

150

72

145

140

57

35

65

225

520

2,000

1,250

380

520

530

700

3,500

520

4,400

950

300

450

600

3,500

600

250

270

160

700

190

610

280

450

2,100

110

1,900

220

6,200

1,000

300

1,400

1,100

430

500

800

2,300

800

300

2,200

750

350

240

370

510

180

180

370

700

490

2,000

720

600

400

600

200

320

280

120

200

2,900

670

1,100

1,100

800

1,400

990

200

430

560

160

220

540

4,400

28,700

0.64 

.90 

.52

.40

.67

.71

.59

.49

.38

.41

.37

.31

.63

.68

.63

1.14

.64

.40

.42

1.12

1.10

.78

1.22

.80

.73

.42

.70

.53

.34

.52

.64

.54

.32

.26

.43

.38

.59

.57

.69

.63

1.03

1.00

.62

.62

.76

.65

.84

.38

.41

.34

.57

.61

.43

.84

.41

1.20

1.05

.90

.65

.65

.66 

.31 

.39 

.91 

.57 

.50 

.62 

.85 

1.17 

.78 

.83

1.84

1.94

1.10

.67

.82

.75

.85

1.79

.99

1.66

.94

.86

.57

1.80

4.19

1.48

.90

.99

.29

1.44

2.44

2.58

.26

1.97

3.08

.77

4.39

.83

5.77

1.20

.37

1.78

1.04

.60

.45

1.64

2.77

1.20

1.40

1.96

.82

.96

.70

.44

2.00

2.29

1.34

1.50

1.38

2.88

1.83

1.59

.98

.56

.68

.92

.65

1.08

.98

6.35

1.65

1.52

1.24

1.06

2.34

1.15

.78

1.33

1.00

1.47

4.33

8.07

0.212

.270

.138

.091

.131

.075

.152

.099

.133

.088

.084

.102

.106

.077

.137

.166

.139

.050

.193

.432

.171

.143

.723

.226

.430

.259

.152

.168

.157

.100

.081

.119

.078

.103

.102

.189

.103

.251

.251

.113

.133

.176

.100

.253

.167

.231

.151

.104

.132

.256

.113

.137

.104

.370

.168

.625

.051

.063

.090

.374

.095

.074

.109

.074

.144

.095

.128

.144

.127

.120

.223

.278

.251

.248

The model for analytical computation requires that a 

numerical linear measure of the seasonal factor be 

obtained. Assignment of arbitrary numbers to months 

of the year is not adequate. Since seasonal variation is

a result of climate, some measure of climatic variation 

should logically be suitable. A seasonal curve of the 

mean monthly air temperature has been found to vary 

closely with the seasonal variation of sediment dis-
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E17

100.000

50,000

10,000

5000

2

o

Q 

LJ 

(S)

1000

500

100

50

10

\ r

STORM EVENTS

 Apr to Sept 

A Oct to Mar

50 100 500 1000 5000 10,000

WATER DISCHARGE (SURFACE RUNOFF), IN CFS-DAYS

50,000

FIGURE 9. Relation of mean sediment concentration and discharge to water discharge for cold and warm season storm events,

Hazel River at Rixeyville, Va.

charge. Figure 11 shows a plotting of the mean air 

temperature (column 6, table 3) for the date of the 

specific storms against the same departure ratios or 

measure of sediment discharge variation. The mean 

linear regression ranges from a ratio of 0.43 at 35° to 

1.45 at 75°. The extremes of the scatter in the plot 

tend to be parallel to the regression.

GROUND-WATER RUNOFF

Because the amount of runoff and erosion from a 

drainage basin probably depends on the length of time 

since the last storm and the condition of the basin with

respect to "wetness" and vegetative cover, it is necessary that some measure of the antecedent condition of 

the basin be used. A reliable determination of the 

traditional antecedent precipitation index is difficult to 

obtain for a complete drainage basin. The rate of 

ground-water runoff of a stream prior to a storm is 

assumed to be related to the time since the previous 

storm and the "wetness" of the basin. It has already 

been noted that the base flow increases during the 

course of a storm and decreases following the runoff 

event. Thus, the amount of the ground-water flow at 

any time will be a function of the length of time and
RATIO UNADJUSTED TO COMPUT

P P P P 

Kooj^oib

DEPARTURE RATIO (UNADJUSTED)

p p p t-1

GJ *> o> b

1 I I T

CT Wl

O O

of

O Q.

f:

 °
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E19

1000

500

£ 200

o

CO

0 100

cc

UJ

Q

Z

o 

cc

CJ

50

20

10

X REPRESENTS DAILY MEAN 

WATER DISCHARGE

TIME > 

FIGTJBE 12. Illustrations of the magnitude and recession of ground-water runoff tor Hazel River at Rixeyvllle, Va.

amount of flow immediately after passage of surface 

runoff. Figure 12 illustrates several ground-water 

recession curves for the Hazel River. The recession of 

flow tends to be steeper and of generally lower magnitude during the warm season than during the cool 

season, thus again reflecting the seasonal changes of 

evapotranspiration.

To determine if ground-water runoff, as a measure 

of antecedent conditions in the basin, is effective in 

explaining variation in sediment discharge, the departure ratios or measure of sediment discharge variation were plotted (fig. 13) against a logarithmic expression of the base flow (columns 11 and 5, table 3). 

Again, there are several factors other than groundwater runoff causing a wide variation in the departure 

ratios, but the trend of the data indicates decreasing 

sediment concentration with increasing ground-water 

runoff. As noted from figure 12, the high rate of 

ground-water runoff generally occurs during the cool 

season when other factors causing sediment erosion 

are at a minimum. Further study of ground-water 

runoff as a variable affecting sediment variation is 

indicated.
E20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

3.0

2.0

3 i.o

0.6

UJ

or

cr

0.4

0.3

0.2

0.1

 Storms >3000 cfs-days

10 20 50 100 200 

GROUND-WATER RUNOFF, IN CUBIC FEET PER SECOND

500 1000

FIGURE 13. Variation of unadjusted departure ratio or sediment discharge for a given storm size with ground-water runoff.

PEAKEDNESS

Measures of storm intensity should help to explain 

some of the storm-to-storm variation in the sediment 

transport relation of figure 9. The intensity of the 

storm is assumed to affect the rate of erosion and transport. One measure of storm intensity that can readily 

be obtained from the data at hand, other than rainfall 

intensity, is the peakedness of the runoff hydrograph. 

A peakedness index Pi} defined as a ratio of the peak 

rate of water discharge to the storm runoff volume for 

the event, is used in these analyses. The underground runoff was also subtracted from the peak 

flow because this underground runoff varies considerably with season and from storm to storm.

Figure 14 illustrates the relation of the unadjusted 

departure ratios to the peakedness indexes for the 

Hazel River data. The plotted data are from columns 

11 and 8 of table 3. The general increase of the departure ratio with increase of peakedness index indicates that further study of this factor is desirable.

RAINFALL

Measurement and publication of rainfall data on a 

daily and hourly basis for a network of stations make 

it possible to compute by the Thiessen method the

storm rainfall quantity and intensity on a particular 

drainage basin. See page E15 for further definition of 

the rainfall quantity and intensity factors. The results 

of such computations may, at times, poorly, represent 

the actual conditions over the basin due to the variation of the aerial distribution of the precipitation patterns with respect to the small sampling of the event. 

This is especially true for the thunderstorms that occur 

during the warm season. The applicability of such 

data also tends to decrease with decreasing size of 

drainage area. A small basin of 300 square miles, 

for example, may not contain a daily gage within 

its boundaries. There is even a much less chance of 

such a basin containing a recording rain gage.

In an attempt to use these precipitation data to help 

explain the variation of sediment discharge for the 

Hazel River, figures 15 and 16 were plotted to show the 

relation of the rainfall quantity (Rg) and rainfall 

intensity (Rt), respectively, to the first departure ratio. 

The apparent correlation of RQ with the departure 

ratios is poor, partly due to the error in measuring R9 , 

partly due to several factors affecting the variation in 

sediment discharge which cannot be observed, but 

mostly due to the fact that there is much intercorrelation between Rg and the quantity of runoff already
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E21

accounted for in deriving the departure ratio. The 

poor correlation of Rt with the departure ratios is due 

to the same factors, probably more so in regard to 

measurement error of Et and less so in regard to intercorrelation with quantity of runoff. The poor showing 

of the simple correlation of these precipitation factors 

with sediment data for the Hazel River does not preclude their application in a system of multiple regression 

analysis.

TREND

Several of the active and passive factors affecting 

soil erosion and transport indicated in figure 1 may 

sufficiently change during the course of a sediment 

record so that the average storm-to-storm sediment 

yield may gradually change. Such changes can be 

detected and evaluated by correlating time or the 

month Mt from the beginning of the record as an 

independent variable with the departure ratios. This 

would then show the variation of the storms and the 

general trend during the period of record. Data for 

the Hazel River are shown in figure 17 for both the 

unadjusted and the seasonally adjusted departure ratios. 

The unadjusted ratios, plotted on the upper part of 

the illustration, indicate a somewhat sinuous relation 

reflecting the seasonal variation as already shown by 

figures 10 and 11. Such scattering makes the definition 

of trend of sediment yield more difficult to determine.

The bottom part of figure 17 shows a more compact 

plotting of the sediment variation (nearer to 1.00) 

owing to the removal of the average seasonal variation. 

The scatter of the ratios throughout the period of 

record for the Hazel River for either type of plotting, 

however, is such that increasing or decreasing trend of 

sediment yield is not apparent.

CONCENTRATION AS A DEPENDENT VARIABLE

In a multiple regression equation, the regression 

coefficients are called partial regression coefficients. 

Each coefficient shows the effect on the dependent 

variable as a result of a unit change in the particular 

independent variable, while the other independent 

variables are held constant.

Sediment discharge, used as the dependent variable 

in the preceding discussions, is defined as the product 

of the sediment concentration in the stream, the quantity of water discharge, and a constant. This, then, 

makes sediment discharge highly interrelated with 

water discharge, and thus the true independent variable, 

or sediment concentration, cannot be evaluated in 

terms of a unit change of water discharge. In other 

words, sediment discharge will always correlate well 

with water discharge. For example, a log-log plot of 

water-sediment discharge data for 10 storms having a 

wide range of water discharge but each having identical

3.0

2.0

l.O

0.6

0.4

0.3

0.2

12

 Storms >3000 cfs-days numbered 

by order of occurrence

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

PEAKEDNESS INDEX (UNADJUSTED) 

FIGUEE 14. Variation of unadjusted departure ratio or sediment discharge for a given storm size with peakedness index.

1.1 1.2

716-824i
E22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

3.0

2.0

CO

3

s

<

CC.

CE

(£.

L0

0.6

0-4

0.3

0.2

0.1

0.20 0.40 0.60 1.00 2.00 4.00 10.00

RAINFALL QUANTITY (/?<?), IN INCHES 

FIGUEE 15 . Variation of unadjusted departure ratio or sediment discharge for a given storm size with rainfall quantity.

concentration will result in a perfect and, at first glance, 

an important correlation with a regression slope of 

one. On the other hand, if the concentration for these 

same storms were plotted against water discharge, the 

correlation and slope of regression would be zero.

Figure 18 shows the relation of mean storm sediment 

concentration to water discharge for the Hazel River 

data. The illustration can be compared directly with 

the sediment-water discharge plotting of figure 9. 

The apparent correlation between water discharge and 

concentration is not as good as that between water 

discharge and sediment discharge. The appraisal of 

concentration variation (fig. 18) as a dependent variable, 

however, for a given water discharge is readily visualized, whereas to obtain such an appraisal of concentration from the sediment discharge (fig. 9), it would 

be necessary to divide the sediment discharge by respective values of water discharge.

The impact of the nature of the storm-to-storm variation is also more apparent when concentration is used. 

This variation tends to be masked by the intercorrelation effect when sediment discharge is used. For

example in figure 18, it is much easier to visualize the 

need for and to delineate separate curves for the cool 

and warni seasons than it is in figure 9. It is further 

readily apparent from figure 18 that the transport 

curve of figure 9, transposed into concentration terms, 

was drawn too high at the lower values of water discharge.

SUMMARY OF GRAPHICAL SEARCH

Limitations on time for search of useful variables did 

not permit the investigation of many conceivable 

measures or to find the optimum mathematical expression of the variables used. For example, several 

measures of antecedent conditions may be determined, 

some based on precipitation quantity and time, some 

based on ground-water runoff and time, and some based 

on a measure of moisture deficiency in the basin. Also, 

measures of the seasonal variation may be tied to 

climatic factors other than air temperature such as 

precipitation quantity and intensity in some combination with air temperature, some measure of plant 

growth and residue, or to Wischmeier's erosion index.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E23

3.0

2.0

o

LU 

CO

I

z 

2,

o

1.0

0.6

cr

§ °-4 

o

0.3

0.2

0.02 0.05 0.10 0.20 0.50 1.00

RAINFALL INTENSITY FACTOR (R( )

FIGURE 16. Variation of unadjusted departure ratio or sediment discharge for a given storm size with rainfall intensity factor.

2.00

The graphical phase of the analysis for the sediment 

records of seven river basins in the Atlantic coast area 

as listed in table 4, involved plotting or correlating data 

for each of the 65-138 storm events on 10-25 graphs 

per basin. Much of this was done before the availability of the computer program and involved trial plots 

with variables that were noneffective, with other transformations of variables, and with checking on the 

effect of intercorrelation among the independent 

variables.

TABLE 4. Sediment records used for correlation and multiple 

regression

Stream and location

1. Scantic River at Broad Brook, 

Conn. 

2. Brandywine Creek at Wilmington. 

Del. 

3. Hazel River at Rixeyville, Va.... .. 

4. Rappahannock River at Remington, Va. 

5. Rapidan River near Culpepper, 

Va.

7. James River at ScottsvjUe, Va.. ...

Drainage area 

(sq mfi

98.4 

314

286 

616

465 

2,084

4,571

Period of record used

Dec. 1952-Sept. 1958 

Dec. 1946-Sept. 1956 

Oct. 1951-Sept. 1956 

May 1951-Sept. 1958 

May 1951-Sept. 1956 

.....do.................

.....do..... ............

Number 

of storm 

events

65 

138

75 

82

85 

65

67

This graphical search for variables that may be useful 

in explaining the variation of sediment discharge from 

storm to storm indicates that:

1. The month during the period of record (Mt) may be 

used to measure the trend of change with time.

2. The quantity of surface runoff per storm (Qw) may be 

used to indicate the magnitude and (or) intensity 

of erosion and transport. Precipitation quantity 

(Rq) , though difficult to evaluate, may also be used 

to indicate storm magnitude.

3. The long-term mean air temperature (Ta) for a given 

time of year can be used as a linear substitute for 

seasonal changes.

4. The ground-water runoff of the stream immediately 

prior to storm runoff ((?&) may be used as a measure 

of antecedent conditions.

5. The ratio of the peak rate of flow on the storm 

hydrograph to storm runoff volume (Pi) can be 

used as a measure of storm intensity which 

probably affects intensity of erosion and transport. 

Precipitation intensity (R*), though difficult to 

evaluate, may also be used for this purpose.
E24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

3.0

^ 2 '°

Q

LU 

&

ID

3 1.0

z

ID

CL

ID

cc

0.6

0.4

0.2

0.1

3.0

2 2.0

ID

Q 

<

O 1.0

0.6

0.4

0.1

/ .. \ .

' 'V \ /

\

V

/

FEBRUARY

10 20 30 40 50

TIME, IN MONTHS 

FIGURE 17. Variation of unadjusted and seasonal adjusted departure ratios with time.

60

THE MODEL AND TRANSFORMATION OF VARIABLES

Owing to the multiplicity and intercorrelative effects 

of the variables, it is apparent that the graphical 

approach to solution or evaluation of the cause of stormto-storm sediment variation would be difficult and to 

some degree indeterminate. Also, a rigorous definition 

of the significance of the regressions found by the 

graphical approach would not be attainable.

The total effect of all the advantages and disadvantages of the graphical and analytical methods listed by 

Riggs and others (written communication) is that a 

combination of the two methods must be used for this 

problem. Simple graphical correlation must be used 

to define the appropriate model, to determine the 

required transformation of the data, and to bring 

attention to wild points. The analytical method 

can then be used to obtain the best estimate of the
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E25

^ 2000 -

CO

cr

o

<

Iz

LLJ 

O

8

Q 

LU 

CO

1000

500

200

100

50

STORM EVENTS

 Apr to Sept 

A Oct to Mar

50 100 200 500 1000 2000 5000 10,000 20,000 50,000

WATER DISCHARGE (SURFACE RUNOFF), IN CFS-DAYS 

FIGUKE 18. Relation of mean sediment concentration to water discharge tor cold and warm season storm events for Hazel River at Rixeyville, Va.

equation coefficients and their significance and the 

standard error of estimate of the equation. The 

procedure for making the analytical computations are 

outlined in most textbooks on statistical methods, such 

as: Dixon and Massey (1957), Ezekiel and Fox (1959), 

and Snedecor (1956). The results of the analytical 

method are unique for the model and sample used and 

can be presented in a concise manner. Before completion of the multiple regression program for the 

electronic computer, the "hand" analytical procedure 

was found to be cumbersome and time-consuming even 

when as few as two or three independent variables were 

used. With use of the computer, up to 50 variables 

may be assimilated and multiple regressions computed 

from many combinations of the available variables.

Based on the generalized form of the regression model,

. . . +bnxn ,

the most frequently used models of the basic data for 

the computer program are as follows :

Log Qs=b0+bl log Qv+bsMt+biTa+b* log #6 +65P, 

Log #=& +&, log Qu+bzMt+bsTa+bi log #6 +65P, 

Log C=b0 +b1 logQv> +b2Mt+b3 Ta

+64 log Qb+b5 log RQ +bs log Bt 

Log (7=6,4-6! log Qw+b2Mt+bz Ta+bi log 

Log <7=60+61Mt+62 7;+63log Q^

Where Y is the dependent variable, Xi . . . xn are independent variables, b 0 . . . bn are constants, and the 

other symbols are defined on page El5. These combinations of variables are sufficient to define differences 

due to use of sediment discharge in place of concentration for the dependent variable, and more important to 

indicate the magnitude of the effects due to measurable 

factors for storm size, time trend, seasonal variation, 

antecedent conditions, and storm intensity.

Multiple regression analysis on the electronic computer is programmed so that all variables may either be 

converted to logarithms or left in the presented form. 

The above models show that nearly half are arithmetic 

and the remainder are logarithmic. Therefore, conversion must be done manually for the variables Qs, C, 

Qwj Q), Pn , RSj and Ri- Data for all variables had to 

be given for a specific observation or storm event. 

Therefore, some estimates of missing data were made, 

and in a few instances, the entire observation was 

omitted. To simplify the logarithmic expression of RQ 

and Rt, these data were multiplied by 10 and 100, 

respectively, before conversion.

COMPUTATION RESULTS

The electronic computer program for multiple regression analysis provided options for print-out of the 

many statistics normally found by longhand computation. The opportunity to check on the approximate
E26 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

for

Of

accuracy of the original data, some of the internal 

computations made by the computer, and the statistics 

summarizing the results and their significance is provided in the print-out of the following:

1. The original data.

2. The arithmetic mean and standard deviation for 

all variables.

3. The simple correlation coefficients between all 

pairs of original variables and the t-test 

significance.

4. The partial correlation coefficients and test 

significance.

5. The multiple regression coefficient and test of

significance. 

The regression weights, their standard error, and

test of significance.

The regression coefficients, 61, . . . , b n. 

The regression equation constant, b0 . 

The predicted values of the dependent variable 

and the residuals between the observed and computed dependent variable. 

10. The sums of squares of residuals and standard

error of estimate of the dependent variable. 

The first three of these items deal with the mass of 

original data or all variables and observations; whereas,

6.

9.

the remaining seven deal with only the variables chosen 

for a specific multiple regression analysis. Usually, 

analyses are made of several combinations of the total 

number of available variables.

The use of a specific variable that is not important or 

effective in a given multiple regression analysis may 

increase the standard error of estimate of the dependent 

variable for an equation. Therefore, one important 

option on the computer program allows the machine, 

after completing items 4-10, to automatically reject the 

variable having the least significant regression weight 

(item 6) and then to repeat items 4-10 using the new 

set of variables. This is repeated down to a single 

independent variable. For example, if seven independent variables were selected for analysis, then the first 

equation would contain all seven variables, the second 

equation would contain the six most significant variables 

of the first equation. The optimum regression equation 

from a given combination is one with a combination of 

variables yielding a minimum standard error of 

estimate.

THE MEANS AND STANDARD DEVIATIONS

The statistics for the mean and standard deviation 

are listed in table 5 for 10 variables and each of the 7

TABLE 5. Means and standard deviations of variables used in multiple regression analysis, by streams

Mean concentration 

dog O

Sediment 

discharge 

(log Q.)

Water discharge 

(log Q.)

Time trend 

(MO

Mean air 

temp. 

(To)

Groundwater runoff 

(log Q»)

Peakedness 

index 

(Pd

Peak flow 

dog Pn)

Rainfall 

quantity 

(log WRg)

Rainfall in 

tensity 

(log 100#<)

Scantic River near Broad Brook, Conn.

Mean. ______________________

Standard deviation ______________

2.203

.154

2.531

.385

34.02

21.88

39.40

13.03

2.156

.261

0.852

.052

1.142

.312

1.10

.18

Brandy wine Creek at Wilmington, Del.

O K1Q

.284

3 m.

.578

3.161

.376

KQ 7K

32.83

50.93

16.53

2.560

.232

1.383

.511

3.239

.382

1.160

.226

1.23

.31

Hazel River at Rixeyville, Va.

Mean _________ 

Standard deviation ______________

2.426

.335

9 JM27

.672

3.016

.501 14.07

55.63

15.50

2.190

.403

0.650

.239

2.807

.436

1.099

.297

1.16

.23

Rappahannock River at Remington, Va.

Mean__ _________ _ .

Standard deviation ......

2.543

.280

3.354

EAO

28.90

17.76

56.79

15.71

2 474

.394

0.691

.228

1.120

.273

1.17

.25

Rapidan River near Culpeper, Va.

Mean . _________ .

Standard deviation ___ .

2.540

.338

3

OQJ.

JQft

28.07

18.05

55.40

15.22

2.444

.351

0.636

.185

1.159

.271

1.17

.23

James River at Buchanan, Va.

Mean _ _ . 2.076

qoo

4.144 30.71

17.02

KQ JO

13.52

3 171

.286

0.415

.114

3.747

.463

James River near Scottsville, Va.

Mean. ___ ._..__.__. __

Standard deviation __ . _______ _

o Qfi7

OCR

4

070 OQ O7

IQ fl7

55.36

14.63

3.431

.309

0.399

.118

3.959

.472
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E27

streams used in the analysis. These statistics are useful 

for comparing the average characteristics among the 

streams used in the analysis. For example, the mean 

air temperature Ta for the time of the storms used is 

39.4° for the Scantic River compared with 50.9° for 

the Brandywine Creek, and 56.8° for the Rappahannock 

River. The standard deviation measures the central 

tendency of the data or the degree of scatter; for example, the deviation of log C (concentration) on the 

Scantic is 0.154 log units, or ± 14 ppm, from the mean of 

160 ppm compared to the deviation of 0.335 log units, 

or ±22 ppm, from the mean of 266 ppm for the Hazel 

River.

SIMPLE CORRELATIONS

The independent variables in a regression are generally related to each other as well as to the dependent 

variable. The interrelation of the independent variables causes the partial coefficients in a multiple 

regression equation to be different from the simple 

regression coefficients. In the section, "Summary of 

graphical search," it was shown that a great deal of 

this intercorrelation among the variables existed. The 

simple correlation coefficients among the variables for 

each of the streams are given in table 6. The significance of each coefficient is indicated where the t-test 

shows a confidence level of 90 percent or greater.

The data in table 6 shows that several general correlations may be listed:

1. That the mean concentration of sediment for a large 

number of storm runoff events tends to increase 

with water discharge, ah- temperature, peak flow, 

rainfall quantity, and rainfall intensity.

2. That the sediment discharge tends to increase with 

water discharge, peak flow, rainfall quantity, and 

rainfall intensity and decreases with the peakedness index.

3. That the volume of water discharge per storm event 

tends to increase with ground-water runoff, peak 

flow, and rainfall quantity and decrease with air 

temperature and peakedness index.

4. That the ground-water runoff tends to increase with 

peak flow and decrease with time during the period 

of record, air temperature, peakedness index, 

rainfall quantity, and rainfall intensity.

5. That peak flow tends to increase with rainfall 

quantity.

6. That rainfall quantity tends to increase with rainfall

intensity.

Several of these correlations among the variables may 

not hold for all records as indicated by table 6. A 

matrix of the variables is shown in table 7 summarizing 

the data of table 6. The relative values of the coefficients are not shown, but the signs and degree of significance substantiate and further evaluate the above 

generalizations.

On the two stations where sediment discharge was 

used in the analysis (Brandywine Creek and Hazel 

River), the simple correlation coefficients (table 6) are 

respectively +0.91 and +0.88 to the effect that sediment discharge will increase with water discharge. 

Concentration also increases for these stations with 

water discharge as shown by the highly significant 

coefficients of +0.53 and +0.32. The difference in 

magnitude of the correlation coefficients is due to the 

fact that the sediment discharge is the product of water 

discharge, concentration, and a constant. Water 

discharge correlates well with rainfall quantity, peakedness index, and peak flow; therefore, these elements 

correlate better with sediment discharge than with 

concentration due to the intercorrelation between water 

discharge and sediment discharge.

MULTIPLE REGRESSION EQUATIONS FOR HAZEL 

RIVER

Data for all 10 variables shown in table 3 were used 

for the multiple regression analysis for the Hazel River. 

A detailed comparison between the dependent variables 

C and Qs was considered important. For each of these 

dependent variables, the multiple regression equations 

for the following combinations of independent variables 

were determined:

1. Log Qw, Mt, Ta, log Q», P<, log WBQ

2. Log Qw, Mt, Ta, log Qb , log 10#ff , log 1005,

3. Mt, Ta, log Q», Ft, log WBg

4. Log Qw, Mt, Ta , log Qb, P,

5. Log Qw, Mt , Ta, log Qb , log Pn

6. Log Qw, Mt, Ta, log Qb, log 1005,

By use of the option to repeat the analysis on a given 

combination after rejection of the least significant 

variable, these 6 cohibinations resulted in a total of 

32 multiple regression equations for each dependent 

variable. The 64 equations for the Hazel River from 

these combinations are shown in the appendix in 

which each of the above combinations are listed by a 

separate roman numeral.

Numerals I-VI in the appendix are for the combinations using log C as the dependent variable and VII-XII 

are for combinations using log Qs. Evaluation of 

the relative merits of these dependent variables can 

be made by comparing the resulting regression coefficients, their significance, and most particularly, the 

standard error of estimate of the regression equations. 

Each equation for log C has a lower standard error of 

estimate than the corresponding equation for log Q,. 

The use of log C instead of log Qs results in a more 

uniform significance of the regression coefficients.
E28 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 6. Simple correlation coefficients and their significance, by streams

Mean concentration 

(log C)

Sediment 

discharge 

(log Q.)

Water discharge 

(log Q.)

Time trend 

(Mi)

Mean air 

temp. 

(TJ

Ground - 

water runoff 

(log Qt)

Peakedness 

index 

(Pi)

Peak flow 

(log P»)

Rainfall 

quantity 

(log WRt)

Rainfall intensity 

(loglOOfl,-)

Mean storm concentration, log C

Hazel 

2+0.832 

2 +.704

i +0. 202 

2 +.531 

2 +. 316 

> +. 190 

2 +.380 

s +.309 

2 +.647

-0. 116 

1-.142 

+.058 

-.052 

-.135 

-.187 

-.043

+0. 130 

+.118 

2 +. 378 

2 +.376 

3 +.273 

+.167 

-.143

2+0.384 

-.093 

-.077 

-.029 

-.020 

3 -.274 

+.190

3+0.258 

+.000 

+.078 

+.065 

-.006 

+.095 

-.078

2+0.258 

2+.400

2 +.361 

2 +.704

-0.038 

2 +.456 

2+.3S4

3 +.255 

2 +.294

-0.043 

2 +.261 

2 +.470 

2 +.349 

J+.204

Sediment discharge, log Q,

2+0.832 

2 +. 704

2+0.910 

2 +.880

-0.075 

+.009

-0.134 

-.056

+0. 016 

+.179

2-0.367 

2 -.354 2+0.818 

» +.881

2+0.706 

2 +.678

+0.045 

'+.256

Water discharge, log Qw

Hazel 

i +0. 202 

2 +.531 

2 +. 316 

i +. 190 

2 +.380 

3 +.309 

2 +.647

2+0.910 

2 +.880

-0. 176 

-.019 

-.030 

+.038 

-.113 

+.040 

+.065

+0.159

2-. 228 

2 -. 318 

2 -.294 

 -. 272 

2 -.540 

2 -. 521

+0. 745 

+.098 

2 +.338 

2 +.377 

1+.193 

2+.33S 

2 +.549

-0. 115 

-.559 

-.524 

-.560 

-.548 

-.468 

-.506

2+0.818 

3 +.949

2 +.973 

2 +.976

2+0.655 

2 +.744 

2+.665 

2 +.660 

2+.63S

3+0.292 

-.121 

+.025 

-.123 

-.118

Time trend, Mt

-0. 116 

1-.142 

+.053 

-.052

-.135 

-.187 

-.043

-0.075 

+.009

 

-0. 176 

-.019 

-.030 

+.038

-.113

+.040

+.065 ....... .... .

+0.064 

+.044 

3 +.256 

+.161 

+.146 

+.036 

+.001

3 -0. 249 

i-. 146 

2 -.437 

2-. 420 

2 -.499 

3 -. 251 

-.165

-0. 131

+.065 

+.106 

-.052 

+.117 

1-.215 

+.141

+0. 136 

-.011

-.015 

+.111

-0.160 

-.002

+.120 

+.180 

> +. 195

-0.034 

-.082 

+.053 

-.028 

-.010

Mean air temperature, Ta

fl&tel.......... ...............................

+0. 130 

+.118 

2 +.378 

2 +. 376 

s +.273 

+.167 

-.143

-0. 134 

-.056

+0. 159 

2 -.288 

2 -.318

2 -.294

3 -. 272 

2 -.540 

2 -. 521

+0.064 

+.445 

3 +.256 

+.161 

+.146 

+.036 

+.001

+0. 189 

2-. 230 

2 -.317 

2 -.311 

2 -.309 

2 -.436

2-. 466

+0.097 

2 +.337 

2 +.344 

2 +.292 

2 +.330 

1+.239 

2 +.426

3 -0. 170 

3 -.238

2 -.538 

2 -. 471

2+0.366 

+.134 

+.021 

+.130 

+.145

2+0.367 

2 +.597 

2 +.376 

2 +.518 

2 +.501

Ground water runoff at beginning of storm, log Qt

Hazel .-. ___ .......... _________ .

2+0.384 

-.093 

-.077 

-.029 

-.020 

3 -. 274

+.190

+0. 016 

+.179

+0.745 

+.098 

2+.33S 

2 +. 377 

1+.193 

2 +.338 

2 +.549

3-0. 249 

i -. 146 2 -.437 

2 -.420 

2 -.499 

s -.251 

-.165

+0.189 

-.230 

-.317 

 .311 

-.309 

-.436 

-.466

+0. 131

2-. 263 

2 -.576 

2 -.536

2 -.313

+.028 2 -. 367

-0.002 

+.182

2 +.376 

2 +.510

-0.108 2 -.256 

3 -.234 

3 -.223 

S-.335

3 -0. 280 

2 -. 256 

2 -.308 

2 -.362 

2 -. 412

Peakednesa index, Pi

Hazel. ......... ........... .......

3+0.258 

+.000 

+.078 

+.065 

-.006 

+.095 

-.078

2-6.367

2 -.354

-0. 115 2 -. 559

2 -. 524 

2 -.560 

2 -.548 

2 -.468 

2 -.506

-0. 131

+.065 

+.106 

-.052 

+.117 

1-.215 

+.141

+0.097 

2 +.337 

2 +.344 

2 +.292 

2 +.330 

+.239 

2 +.436

+0. 131 

2-. 263 

2 -.576 

2 -.536 

2 -. 313 

+.028 

2 -.367

3-0.192 

3 -.259

3 -.256

2 -.315

-0.048 

2 -.374 

-.171 

1-.197 

-.164

-0.072 

2+.3S9

3 +.246 

+.124 

+.164

Peakedness, log PB

Hazel 

2+0.581 

2+.400 

2 +.361 

2 +.704

2+0.818 

2 +.881

2+0.818 

2 +.949 

2 +.973 

2 +.976

2+0.136 

-.011 

-.015 

+.111

-0. 170 

3-. 238

2 -.538 

2 -. 471

-0.002

+.182 

2 +.386 

2 +. 510

3 -0. 192 

3 -.259 

3 -. 256 

2 -.315

2+0.609

2 +.714

8+0.008 

+.149

Rainfall quantity, log WR,

Scantic- _______ __ . .

Hazel . .....

-0.038

2 +.456 

2 +.334

2 +. 255 

2 +.294

2+0.706 

2 +. 678

2+0.655 

2 + .744 

2 + .665 

2 + .660 

2 + .63S

-0.160

I¥Y>

+.120 

+.180 

i +. 195

2+0.366 

+.134 

+.021 

+.130 

+.145

-0.108 

2 -.256 

3 -.234 

» -.223 

2 -.335

-0.048 

2 -.374

-.171 

» -. 197 

-.164

2+0.609

2 +.714

2+0.546 

i +.163 

> +.404 

3 +.284 

2 +.292

Rainfall intensity, log 100/2,-

Hazel ..- - ..

Rapidan ____________________

-0.043

2 +.261

2 +. 470

5 j q^n

J+.204

+0 045

3 +.256

............

3 i n OQO

-.121

+.025

100

-.118

-0.034

+.082

+.053

+.028

-.010

2+0.367

2 +.597

2 +. 376

2 +.518

2 +. 501

3 -0. 280

2 -.308

2 -. 362

2 -. 412

-0.072

2 +.339

3 +.246

+.124

+.164

+0.008

+.149

 

2 +0. 546

1+.163

2+.404

3+.2S4

2 +.292 

1 Poorly significant (90 percent level).

2 Highly significant (99 percent level).

3 Significant (95 percent leveD.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E29

TABLE 7. A matrix of variables showing the average direction and 

significance of simple correlations

[+ or is used when two-thirds or more of records show the respective sign. ± is 

used when more than one-third of records show both signs]

LogC

Log Q a ._ -...

T

Log Q b .. ........

Pi...............

Log P. ..........

Log 100Ri ~

Log

i i

2 +

3 i

i

1 i

2 i

2 -|-

Log 

Q.

1 i

±

i

1 _

j i

1 . i

3

Log

1 1

±1 _

3 i

1 _

! i

j i

«,

i

2 _

±

±

r.

1 _

i

1 _

1 i

1 

i

1 ;]_

Log

i

:±i _

2 _

3 i

3 _

1 _

P,

+

1 _

1 _

1 _

2 _

i

Log

P

1 +

1 1

j 1

1 

3 1

2 

1 i

i

Log

2 -|_

1 i

1 i

±

,t

_

1 i

2 -|_

Log

2 +

3 i

1 _

I

i

2 -|_

1 Highly significant (99 percent level).

2 Significant (95 percent level).

3 Poorly significant (90 percent level). Where no footnote is shown, correlation is 

not significant

The nonuniformity of significance for log Qs is caused 

by the very high degree of simple correlation between 

log Qs and log Qw which results in log Qw assuming 

more than its share of significance from the total 

regression.

In the instance when log 10Rff is used instead of log 

Qw (compare combinations III and IV with X and XI), 

the minimum standard error is found to be 0.295 and 

0.444, respectively, for log C and log Qs. In other 

words, if log Qs must be used, then it is essential that 

log Qw be included as one of the independent variables; 

whereas, if log C is used, then the more uniform degree 

of intercorrelation among the independent variables 

results in a stronger equation. The use of log C 

instead of log Qs also tends to increase the significance 

of Pi} log lORg, and log IQQR* and tends to somewhat 

decrease the significance of log Qb .

The usefulness of specific independent variables to 

predict sediment conditions in a stream is based on 

their statistical significance and numerical value in 

the equation. When log C is used as the dependent 

variable, the following observations from the appendix 

for the Hazel River data seem pertinent.

1. The measure of ground-water flow for antecedent 

conditions log Qb is not effective. Only some 

equations in II and III, for example, rate as high 

as very poorly significant.

2. The coefficients for Mt or time trend are all negative, indicating the possibility of decreasing sediment during the period of record; however, it is 

not significant for any equation.

3. Runoff volume or log Qw is a better measure of 

storm volume than is rainfall quantity or log 

IQRg (contrast 1-2 with III-l and the respective 

Se of 0.270 and 0.297).

4. Net peak flow log Pn is only a slightly better measure 

for a storm intensity factor'than is peakedness 

index Ff (contrast IV and V).

5. Due to a large amount of intercorrelation, use of 

log Pn makes log Qw insignificant (see V).

6. When only two independent variables are used, log 

Pn and Ta yield better results than log Qw and 

Ta (contrast V-^ and 1-5).

7. Log WORi is the best measure of storm intensity 

when contrasted with the measures of peakedness 

Pt and log Pn .

As a result of the characteristic intercorrelation 

among variables and their expected variation for different drainage basins, the conclusions noted above 

for the Hazel River cannot be rigorously applied to 

other streams. On the basis of hydrologic and sedimentologic theory, however, these conclusions are 

logical and should, within limits, find general application.

COMPARISON OF STREAMS

The two principal objectives of this analysis were 

to define the effect of specific measurable independent 

variables on the variation of sediment in streamflow 

for specific locations and to determine how these 

effects change from basin to basin. As in the above 

analysis of the Hazel River, the regression coefficients, 

their significance, and the standard error of estimate 

for the equations will be compared to show these 

effects for seven locations in the Atlantic coast area.

The regression equations and their standard error 

of estimate and the significance of coefficients for several combinations of variables for the seven locations 

are given in the appendix. The constants or regression 

coefficients and their significance for two or more combinations of variables for each of the seven locations 

are shown in table 8. Equations were chosen for this 

table which demonstrated a minimum standard error 

of estimate and yet used the principal combination 

of available and applicable variables.

EFFECTS OF DEPENDENT VARIABLES

The results of comparing the dependent variable 

log Qs (sediment discharge) with the dependent variable 

log C (concentration) for the Hazel River were not 

conclusive in some respects. Therefore, a similar 

comparison was made for the Brandywine Creek. 

The two most important conclusions determined from 

the Brandywine data, which are similar to those determined for the Hazel River, are (1) that the standard 

error of estimate is less for log C than for log Qs but not 

appreciably so, and (2) that the very high significance 

of log Qw (water discharge) when log Qs is used causes 

a tendency for the remaining independent variables to 

lose significance.
E30 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

TABLE 8. Regression coefficients and standard error of estimate of principal regression equations, by streams

Equation 

constant 1

Water 

discharge 

(log <? )

Time 

trend 

(Mi)

Mean air 

temperature 

(T.)

Groundwater 

runoff 

(log <?»)

Peakedness 

index 

(P^

Peak flow 

(log P»)

Rainfall 

quantity 

(log 10 U,)

Rainfall 

intensity 

Gog 100 Rd

Standard 

error of 

estimate 

(±S.in 

log units)

Scantic River at Broad Brook. Conn.

+1. 551 

+1.492

+.031 

+.034 

+.241

* +0. 143 

* +. 135

4 +.503 

4 +.423 

4 +.460

-0.00102 

+.00120 

» +. 00157

+0.00112

* +0. 117 

s+,196

*-.206

'-.148 

*-.239

* +0.037

4 +1. 205 

4 +1. 158

* -0. 113

» -. 148

» +. 121

+0.068

*+.290

0.138 

.143

.177 

.178 

.198

Brandy wine at Wilmington, Del.

Log C.. ........................ ...........

Los O.

+0.886 

+1. 039 

+.406

-1.634 

-1.494 

-2.095

4+0.644 

»+.325

4 +. 719

4 +1. 633 

* +1. 310 

4 +1. 705

5-0.00155 

4 -.00199 

8 -.00150

*-. 00142 

 -. 00187 

* -. 00137

» +0. 00385 

4 +.00554 

4 +.00484

*+. 00365 

4 +.00526 

s +.00462

» -0. 195 

-.183 

-.124

-.199 

-.185

-.131

4 +0. 196

4 +.189

4 +0. 333

4 +.336

* -0.365 

-.274 

-.232

-.345 

-.262 

-.225

s+0.338

8 +.328

0.215 

.211 

.208

.216 

.212 

.210

Hazel River at Rixeyville, Va.

Log C._. _.....__.._..__... ___________________

Log <_.____._ ..._....._....._.._._______._____

+0.642 

+.791 

+.586 

+.660

-1.644 

-1.401 

-1.464 

-1.456

* +0. 513 

-.098 

4 +. 397 

4 +.474

4+1.406 

* +1. 029 

* +1. 355 

4 +1. 363

-0. 00256 

-.00200 

-.00242 

-.00289

-.00254 

-.00269 

-.00308

-.00313

4 +0. 00970 

4 +.01083

4 +. 01101

4 +. 01153

4 +.00837 

4 +. 01005 

4 +. 01025 

4 +. 01030

' -0. 178 

-.021 

-.040 

-.105

'-.184 

-.119 

' -.144 

-.151

» +0. 278 

'+.258

+.143 

+.141

« +0.509

+.341

* -0. 421

-.252

4+0.533

+.149 

'+.493

-.016

0.255 

.269 

.270 

.270

.265 

.278 

.280 

.282

Rappahannock River at Remington, Va.

+1.328 

+1.395

» +0.323 

8 +. 325

'-0.00276 

'-.00278

4 +0. 00925 

< +.00804

-0.092 

-.117

+0.154 -0. 171

-.257 « +0.221

0.247 

.245

Rapidan River near Culpeper, Va.

+0.768 

+1. 141

4 +0. 529 

«+.449

'-0.00284 

-.00268

4 +0. 00959 

4 +.00947

-0. 121 

-.126

 +0.395 '-0.300 

'-.283 +0.113

0.280 

.287

James River at Buchanan

+0.960 

+1.783

s +0. 532 

«+.486

« -0. 00530 

8 -.00621

« +0. 00777 

8 +.00807

4 -0. 556 

4 -. 572

4 +1. 019

4+1.027 ............ 

0.230 

.229

James River at Scottsville

+0.211

+.832

4 +0. 560 

» -. 359 » -0. 00297 

2 -.00322

a +0. 00286 

'+.00290

2 -0. 196 

 -.184

s +o. 770

4 +0. 926

0.194 

.186

Equations of minimum S,

Brandywlne. ________________

Hazel.... ....................................

Rappahannock __ --.. .....

James, Buchanan __ .

+1. 551 

+.406 

+.642 

+1. 333 

+.355 

+.960 

+.211

2 +0. 143 

4 +. 719 

* +. 513 

 +. 187 

4 +. 524 

5 +. 532 

4 +.560

"'"-O.'OOISO" 

-.00256 

a -. 00211

"s" -."00530" 

2 -.00297

"4"+6"66484" 

4 +. 00970 

s +.00711 

4 +.00970 

8 +.00777 

'+.00286

2 +0. 177 

3 -. 124 

» -. 178

""V-rsee"

»-.!%

2+0.037 

4 +.196

*+.429 

4+1.019

s +. 770

............

» -0. 113 

'-.232

»-.421

 -.275

 .

4 +0. 533 

«+.204

0.138 

.208 

.255 

.244 

.281 

.203 

.194

1 The dependent variable is log C except where noted for Brandywine Creek and 

Hazel River.

2 Significant (95 percent level).

8 Very poorly significant (80 percent level).

4 Very highly significant (99.9 percent level). 

8 Highly significant (99 percent level). 

« Poorly significant (90 percent level).

EI'FECTS OF INDEPENDENT VARIABLES

The effects of selected independent variables on 

variation of sediment discharge can be determined by 

study of the coefficients and their relative significance 

as given in table 8 and the appendix. Again, it is 

noted that variation of coefficients for a specific v ariable 

at a specific stream location is largely due to the effect 

of intercorrelation among the independent variables.

An outstanding example of this is shown by the difference in the first two equations for the Brandywine 

Creek in table 8. The first equation used rainfall 

intensity and the second equation uses peak flow as a 

measure of storm intensity. The first equation has a 

highly significant coefficient for log Qw of +0.644, and 

the second equation has a less significant coefficient for 

this variable of +0.325. The difference is attributed
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E31

to a highly significant coefficient of +0.333 for log Pn 

in the second equation and to the fact that peak flow 

has a very strong simple correlation with the quantity 

of water discharge for a storm period.

The significant regression coefficients in table 8 are 

usually of the same variables that had significant 

simple correlation with sediment concentration. See 

the first section of table 6. Generally, the significance 

of a specific regression coefficient is improved over that 

of the simple correlation due to the effects of the 

multiple regression in isolating the effects of a single 

variable. For example, the simple correlation coefficients of concentration with time trend for the Brandywine Creek is poorly significant (table 6); whereas, the 

regression coefficients for time trend (table 8) are all 

highly significant. In other instances the simple 

correlation coefficients are not significant at the level 

tested, but the regression coefficients are significant.

The regression coefficients tend to have the same 

sign as the simple correlation coefficients, especially so 

if they are significant. Exception to this is noted for 

rainfall quantity on the Brandywine Creek in which 

the simple correlation coefficient is positive and highly 

significant; whereas, the regression coefficients are 

negative and less than highly significant. Intercorrelation among the independent variables is the cause of 

this change of sign and significance.

Based on data used in this analysis and the equations 

derived therefrom, water discharge proves to be the 

most important independent variable for describing 

variation of sediment transport in streams. The tendency is strong for the mean concentration of sediment 

(on a storm event basis) to increase with increasing 

volume of water discharge. The least important independent variable is rainfall quantity. The poor 

results obtained from using rainfall quantity may be 

attributed to the poor measure of this statistic to represent the true rainfall quantity on a storm-to-storm 

basis and to its high degree of intercorrelation with 

quantity of runoff.

The importance of other independent variables range 

between that of water discharge and rainfall quantity. 

The regression coefficient for time during the period of 

record is negative for nearly all equations and is significant for equations for the Brandywine Creek and James 

River Basins. Thus, there is an important sediment 

concentration reduction with time for the two basins 

and the possibility of decreasing concentration in other 

basins. Sediment concentration increases significantly 

with mean air temperature or time of year for all 

streams except for the Scantic River and the James 

River at Scottsville, Va. The range for a 50° change of 

temperature varies from about 0.5 log unit of concentration for the Hazel River down to about 0.2 log unit

for the Brandywine Creek. An increase in groundwater runoff tends to correlate with a decrease in sediment movement. The coefficients for ground-water 

runoff variable were not significant for the Hazel, 

Rappahannock, and Rapidan Rivers and generally not 

highly significant in other basins. Thus, the rate of 

ground-water flow as a measure of antecedent conditions is not as effective in explaining storm-to-storm 

sediment variation as expected.

The three measures of storm intensity: peakedness 

index, peak flow, and rainfall intensity, were not fully 

compared for all streams. Only peakedness index was 

determined for all streams. Sediment concentration 

of storm runoff in streams increases with each of these 

measures of storm intensity. Peakedness index resulted in a slightly lower standard error of estimate 

than peak flow for the Brandywine Creek, the Hazel 

River, and the two locations on the James River. 

Peakedness index is not considered significant for the 

Hazel River. Rainfall intensity was not significant for 

the Rapidan River. Measures of rainfall intensity 

were not available for testing in the James Basin. 

Comparison of rainfall intensity with the parameters 

based on peak flow, as a measure of the effect of storm 

intensity, shows that the relative standard error of 

estimate of the equations is not consistently higher or 

lower when rainfall intensity is used. The significance 

of the regression coefficients shown in table 8 indicate 

that either peakedness index or peak flow is a better 

measure of storm intensity than is rainfall intensity.

VARIATION AMONO BASINS

Differences in the regression coefficients for the 

independent variables among the several streams used 

in the analyses may indicate part of the difference in 

the characteristics of drainage basins to cause stormto-storm variation in sediment movement. Table 8 

shows that the standard error of estimate Se varies 

some for a given basin depending on the combination of 

independent variables used in the regression. The 

variation of Se for several combinations of variables at 

a given location, however, is small compared to that 

among basins.

The list of equations by basins for the single, double, 

and triple most significant independent variables 

(table 9) further demonstrates that even though Se 

decreases somewhat as the number of variables is 

increased, there is a range of Se among the basins. 

This is caused by either some error in the basic data or, 

more likely, the variance of hydrologic and environmental factors which cannot be evaluated at this time. 

Evidence from the list of equations of the effect of 

intercorrelation among the independent variables 

suggests that if one variable contained considerable
E32 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

error it would be replaced by another variable of 

greater significance. When this takes place, or when 

all variables except one or two remain, however, the 

error of estimate is not materially changed.

TABLE 9. The regression equation*, by streams, for 1, 2, or 3 

independent variables

James, Buchanan . 

James, Scottsville .

HazeL 

Rappahannock.. 

James, Buchanan. . . 

James, Scottsville. . .

Hazel. 

Rappahannock- - - _

James, Buchanan___ 

James, Scottsville..-

One independent variable

Log C -1.714+0.227 logQt

Log C-1.255+.400 log Qw

/Log C = 1.563+.308 log Pn

(.Log C=1.973+.0082 Ta 

Log C-2.193+.0054 Ta

Log C-1.702+.259 log Q«,

Log C =0.683+0.425 log Pn

Two independent variables

Log C-l.719+0.2106 log Qt+0.031 P,

Log C-.349+.582 log Q«,+.239 P,

| Log C=. 809+ .324 log Qra+.0115 Ta 

{Log C-. 704+ .399 log Pn+.0108 Ta

I Log C= 1.576+ .368 log 10fl,+.0080 T* 

Log C =1.280+ .233 log Q..+.0078 T, 

Log C=. 957+ .335 log Q«+.0091 Ta

Log C = 1.352+.203 log Q w -.0038 Mt 

Log C=1.129-.211 log QH--496 log P

Three independent variables

[Log C=.462+.391 log Q«,+.0106 Ta+.304 P, 

{Log C-.554+.291 log Q«,+.0086 T<,+.441 log 100.R,-

lLog C = . 719- .00 18 Af,+.0112 T0+.402 log Pn 

Log C=1.373+.232 log 0»-.0021 M«+.0079 T« 

Log C- 1.035+ .327 log Qw -. 0027 Af,+ .0094 Ta

Log C = .036+.373 log Q w -.0043 M(+.0117 Ta 

Log C = 1.271-.0029 Af«- .262 log Q t+.525 log Pn

Se =0.144

S.= .242

S,= .311

S.= .312 

S,= .267

Se= .315

S.= .204

S.=0.142

8.- .220

S.= .273 

S.= .265

8.= .296 

S.= .246 

S.= .289

S.= .308 

S.= .198

S.-0.139

ST.- .313

S,= .268 

S.- .260

S.= .266 

S.= .240 

S.- .286

S.= .278 

S.= .192

EXAMPLES OF APPLICATION

RANGE OF SPECIFIC VARIABLES

The multiple regression equations determined in this 

analysis consists of an equation constant and coefficients 

for each independent variable. Each independent 

variable may affect the dependent variable through its 

range of values depending on the magnitude of the 

coefficient. One of the equations determined for the 

James River at Buchanan, Va. (see table 8) will be used 

to demonstrate this effect. 

Log (7-0.960+0.532 log #M -0.0053 M.+0.00777 Ta

-0.556 log &+1.019P*

The following realistic minimum and maximum values 

of the variables are applied:

Qw= 1,000 and 100,000 cfs-days; log &=3.00 and 5.00 

Mt= 1 and 65 months 

T0=35° and 75°F

#6=316 and 3,160 cfs; log #6 =2.5 and 3.5 

P,=0.19 and 0.64 

Log C (max)= +0.960+2.659 0.344+0.583-1.943

+0.652 

= +2.567±0.230 or (7=369 ppm ranging

from 217 to 626 ppm. 

Log C (min) = +0.960+1.594-0.005+0.272-1.388

+0.194

= + 1.627 + 0.230 or (7=42 ppm ranging 

from 25 to 72 ppm.

The differences between the maximum and minimum 

factors for these equations are +1.065, 0.339, 

+ 0.311, -0.555, and +0.458 log units for QU) Mt, Ta , 

Qb , and Pi} respectively. These differences are all 

greater than Se or 0.230 log units, and therefore, further 

indicate that these factors all yield a significant change 

in the dependent variable.

COMPARISON OF LOCATIONS

For comparing the regression equations between 

locations, the mean values of the independent variables 

will be used (see table 5) to compute the value of the 

dependent variable. The simplest comparison can be 

made by use of the equations for one and three independent variables as given in table 9. 

For the single variable on the Brandywine Creek: 

Log (7=+ 1.255+0.400 log Qw

= + 1.255+0.400X3.161

= +2.520± 0.242

This is an average of 331 ppm or a range from 190 to 

578 ppm. 

For the Rapidan River:

Log (7=+ 1.702+0.259 log Qv

= +1.702+0.259X3.234

= +2.540+0.315

This is a mean of 347 ppm or a range from 168 to 716 

ppm. The regression slope of log Qw is 0.400 for the 

Brandywine and 0.259 for the Rapidan, yet the mean 

concentration is nearly the same, due somewhat to the 

higher mean of log Qw for the Rapidan, but mostly due 

to the greater equation constant for the Rapidan. 

For the three independent variables on the Brandywine 

Creek:

Log (7=0.122+0.606 log &+0.0038 T0 +0.208 Pt

=0.122+0.606X3.161+0.0038X50.93 

+0.208X1.383

=2.518+0.213

This is a mean of 329 ppm or a range from 202 to 538 

ppm. 

For the Hazel River:

Log (7=+0.462+0.391 log &+0.0106 Ta

+0.304 P,

= +0.462+0.391X3.016+0.0106

X55.63+0.304X0.650

= +2.426 + 0.268

This is a mean of 267 ppm or a range from 144 to 494 

ppm. Comparison of the latter more complicated 

equations with the single variable equations shows that 

the Brandywine has the greater Qw and Pt factors and 

that the Hazel has the greatest equation constant and 

Ta factors but the totals differ by less than 0.1 log unit. 

Note that the range defined by the limits of Se is 

considerably less when three variables instead of one 

are used.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E33

ESXTRAPOIjATION TO OTHER STREAMS

In order to demonstrate the feasibility of applying 

the computed regression formulas to other streams, 

testing with observed data from some other locations 

is necessary. Observed data are available for 15 storms 

on the Shenandoah River at Front Royal, Va., (1,638 

sq mi) and for 14 storms on the Potomac River at 

Point of Rocks, Md., (9,650 sq mi). The Shenandoah 

data were obtained during the same period, and the 

Potomac data were obtained 7 or 8 years later than the 

data from which the models were derived. The 

Potomac River data, in addition to a somewhat different time span, also represent a much larger and more 

diverse basin than that from which the models were 

derived. The data are listed in table 10. The following are equations from the appendix for testing these 

data:

1. III-3 from the Brandywine Creek, 

Log C= +0.181 +0.610 log QW -0.00139M,

+0.00390 Ta+QSllPr- (0.208)

2. JII-2 from the Rappahannock River, 

Log C= + 1.059+0.289 log QW -0.00190M,

+0.00760Tffl+0.199Pf (0.239)

3. IV from the James River at Buchanan, Va., 

Log (7=-0.649+0.454 log QW -0.00333M,

+0.01175 Tffl +0.769Pr-(0.269).

TABLE 10. Measured data for extrapolation of models to other

streams

Observation No. LogC LogQ* Mt Ta P,

Shenandoah River

1 _ ...........................

2..............................

3...... .............. .......

4..............................

5 ___ . __ ...... ............

6..............................

7....... .......................

8 _ ...........................

9...... .....................

10 ...... ....................

11... ..........................

12.............................

13- .._.. .-... .-

14.............................

15...... .......................

1.88 

2.81 

2.04 

2.39 

2.99

2.25 

2.35 

2.38 

2.66 

2.40

1.97 

2.05 

2.49 

2.58 

2.97

3.72 

4.53 

3.63

4.18 

4.49

4.39 

4.27 

4.21 

4.59 

4.1«

3.94 

3.68

4.45 

4.45 

5.16

34 

35 

35 

38 

42

43

44 

46

47 

47

48 

48 

50 

52 

52

38 

41 

49 

73

58

44 

37 

39 

46 

50

58 

59 

72

75 

74

0.65 

.59 

.90 

.25 

.52

.32 

.53 

.39 

.27

.47

.41 

.48 

.20 

.56 

.43

Potomac River

1.. ............................

2..............................

3 _ ...........................

4... ...........................

5 ..._.._.._..........__.___

6............. .................

7. _ ..........................

8...... .....................

9 . _...._ .............

10 ..........................

11 _ ...... ....................

12.............................

13.............................

14.............................

2.68 

2.23 

2.90 

2.61 

2.77

2.30 

2.92 

2.65 

2.29 

2.34

1.90 

2.11 

2.38 

2^2

4.65 

4.58 

5.41 

5.31 

5.29

4.87 

5.34 

5.24 

5.30 

5.10

4.13 

4.73 

3.99

4.28

102 

105 

107 

108 

109

109 

117 

117 

119 

119

120 

120 

121 

125

62 

37 

52 

53 

63

69 

41 

42

55 

57

63 

67 

72

55

0.59 

.71 

.38 

.51 

.64

.60 

.47 

.53 

.40 

.52

1.29 

.54 

1.08

.77

The computed sediment concentration derived for 

each storm and for each model was plotted against 

the observed concentration in figures 19 and 20 for the 

Shenandoah and Potomac Rivers, respectively. The 

results show that:

1. None of the applications are reasonably close to the 

line of agreement; and, therefore, it is extremely 

dangerous to extend specific formulas to other 

basins.

2. The size of the river basin determines the shift of the 

computed values from the observed values. The 

model from the smallest stream (Brandywine 

Creek) yields results that are about 0.6 log unit 

too large when the Shenandoah data are used and 

about 0.9 log unit too large when the Potomac 

data are used. Also, the data from the larger 

Potomac River basin yield computed values for 

the three formulas that average about 0.2 log 

unit greater than data from the Shenandoah.

3. The concentrations computed from the models do 

not increase as rapidly as the observed concentrations. The Brandywine formula is not as 

serious in this respect as are the Rappahannock 

and James River formulas.

Although a given formula apparently cannot be 

extrapolated to another stream, the hypothesis that 

the general model can be extrapolated is still open. 

Thus, assuming that the observed data for the Shenandoah and Potomac are statistically representative, 

trial and error modification of the James River and 

Brandywine Creek formulas was made to shift the 

computed concentration. Shifting the set of computed 

values up and down on the ordinate of figures 19 and 20 

is accomplished by adjusting the equation constant. 

Change in the slope and scatter of the set is accomplished by shifting the emphasis on Qw or Pt. Due to 

the proximity of the James River and Brandywine 

Creek basins to the Shenandoah and Potomac River basins, 

there is little justification for altering the factors for 

Mt and Ta.

To accommodate the conditions exhibited by the 

Shenandoah River data, the equation constant and the 

coefficients for log Qw and Pt in the James River formula 

were changed by trial and error to a modified formula,

Log C= -0.600+0.600 log Qw -0.00333 Mt

+0.01175 ZVfO.200 P«.

The James River formula was also changed to accommodate the Potomac River data to

Log C= -0.800+0.600 log #w -0.00333 Mt

+0.01175 Ta.
E34 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

1.8 2.0 2.2 2.4 2.6 2.8

OBSERVED SEDIMENT CONCENTRATION, IN LOG UNITS 

FIGURE 19. Test of selected models against observed data for Shenandoah River.

3.0
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E35

1.8 2.0 2.2 2.4 2.6 2.8 

OBSERVED SEDIMENT CONCENTRATION, IN LOG UNITS

3.0

FIGURE 20. Test of selected models against observed data for Fotomac Eiver.
E36 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

2.0 2.2 2.4 2.6 2.8 

OBSERVED SEDIMENT CONCENTRATION, IN LOG UNITS

3.0

FIGURE 21. Comparison of the modified formula for James River at Buchanan with the observed data for the Shenandoah and

Potomac Rivers.

Figure 21 compares the computed sediment concentration from each modified formula with their respective 

observed sediment concentrations. The results of the 

comparison are reasonable in that the computed values 

are sufficiently close to the line of agreement so that all 

but 4 out of 15 for the Shenandoah River and all but 

5 out of 14 points for the Potomac River are within the 

standard error of estimate (0.269 log units) defined by 

the original James River model.

In a like manner, the Brandywine Creek formula 

was changed to

Log C= -0.700+0.700 log #«,-0.00139 Mt

+0.00390 Ta

to accommodate the Shenandoah River data; and to

Log C= -0.970+0.700 log #«,-0.00139 Mt

+0.00390 Ta

to accommodate the Potomac River data. Comparison 

of the computed values from these modified formulas 

with the observed data (fig. 22) is within the standard 

error of estimate (0.208 log units) defined by the 

original Brandywine model.

The similarity of the two modified models is indicated 

by the similarity of the deviations from the line of 

agreement with respect to the individual storms. For 

example, in figures 21 and 22, note that observations 

2 and 5 for the Shenandoah and 1 and 13 for the 

Potomac plot below the limits of one Se.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E37

3.0

2.8

2.6

o 2.4

2 

O 

O

O

8

2.0

1.8

1.6

/Observation number

+ Shenandoah River Data 

 Potomac River Data

1.6 1.8 2.0 2.2 2.4 2.6 2.8 

OBSERVED SEDIMENT CONCENTRATION, IN LOG UNITS

3.0

FIGUBE 22. Comparison of the modified formula for Brandywine Creek with the observed data for the Shenandoah and Potomac

Rivers.

SUMMARY

The analysis of some storm period variables affecting 

stream sediment transport has involved a study of 

available sediment data to determine which hydrologic, 

physical, and biological factors cause sediment variation 

in time and space. The knowledge gained from this 

and other similar analyses can be used to interpret and 

extrapolate the small amount of information available 

from existing or reconnaissance sediment data.

A review of the theory of sediment yield and transport shows that most of the fine sediment (clay and 

silt sizes) eroded from a drainage basin is easily suspended by the stream turbulence and hence readily 

moved through the channel system; whereas, the 

coarser sediment (sands, gravels) are moved in accordance with the interaction of the stream energy on the 

particle and the settling rate of the particles. The 

amount of coarse sediment transported is generally 

much less than half the total sediment discharge. The 

coarse sediment discharge can be approximately determined by considering hydraulic factors; such considerations are beyond the scope of this report. The most 

important variables for consideration in the analysis 

involve the forces of erosion and transport as related 

to fine sediment.

These forces operate during or immediately following 

periods of substantial precipitation and runoff from the 

land surface, thus the adopted hydrologic unit for 

study in this report is the storm event. Subsurface 

and ground-water runoff are not important erodents
E38 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

of the land surface; therefore, only the surface runoff 

part of the hydrograph is used.

Analysis of data to determine the cause of sediment 

variation was accomplished by a combination of graphical and analytical multiple regression methods. Graphical correlation was necessary to determine which 

variable to consider, to determine the required transformation of the data, and to note unusual elements 

of the relationship. Using the general regression model

the analytical method was then used to obtain the 

best estimate of the equation coefficients and their 

significance and the standard error of the equation. 

The analysis was made using data for seven stream 

locations in the Atlantic coast area through a program 

developed for the Burroughs 220 computer.

The graphical search for variables useful to explain 

the variation of sediment concentration or discharge 

from storm to storm showed that:

1. The month during the period of record may be 

used to indicate the trend of change of time.

2. The quantity of surface runoff, expressed in log 

units, should be used as a measure of the magnitude and intensity of erosion and transport 

precipitation quantity, also in log units, is not 

as effective.

3. The long-term mean air temperature for the time 

of year of the given storm can be used as a measure 

of seasonal change.

4. Ground-water runoff of the stream prior to storm 

runoff, expressed in log units, is a convenient 

measure of antecedent conditions.

5. The peakedness of the storm hydrograph can be 

used as a measure of storm intensity. Precipitation intensity, expressed in log units, is sometimes 

too difficult to evaluate and too inaccurately 

determined for an effective measure of storm 

intensity.

The computer program is designed to print out 

simple correlation coefficients and then* significance. 

These indicate the degree of intercorrelation among 

the variables for a given set of storm-period data at a 

stream location. In general terms, the correlations 

show a tendency for:

1. The mean concentration of sediment in the storm 

runoff to increase with sediment discharge, 

water discharge, air temperature, peak flow, 

rainfall quantity, and rainfall intensity.

2. The quantity of sediment discharge to increase with 

water discharge, peak flow, rainfall quantity, and

rainfall intensity, and to decrease with peakedness 

index.

3. The quantity of water discharge per storm event to 

increase with ground-water runoff, peak flow, and 

rainfall quantity, and to decrease with air temperature and peakedenss index.

4. The ground-water runoff to increase with peak flow 

and to decrease with time during the period of 

record, air temperature, peakedness index, rainfall quantity, and rainfall intensity.

5. The peak flow to increase with rainfall quantity.

6. The rainfall quantity to increase with rainfall 

intensity.

Comparison of log Qs (sediment discharge) and log C 

(sediment concentration) for use as the dependent 

variable in the analytical computation of the multiple 

regression equation was completed for the Hazel River 

and Brandywine Creek. The two most important 

conclusions from this comparison are: (1) the standard 

error of estimate is less for log C than for log Qs but not 

appreciably so; (2) when log Qs is used, the very high 

degree of significance for log Qw causes a decrease of 

significance for the remaining independent variables.

It was noted from the regression equations that 

variation of coefficients for a specific variable at a 

specific stream location, when different sets of variables 

are used, is largely due to the effects of intercorrelation 

among the variables. In regard to a measure of storm 

size, water discharge proves to be the most important 

independent variable for describing sediment variation, 

and rainfall quantity is generally the least important. 

The poor significance of rainfall quantity is probably 

due to the poor quality of available data and its high 

degree of intercorrelation with quantity of runoff and 

other hydrologic factors.

The regression coefficients for time during the period 

of record show a reduction of sediment concentration 

with time for nearly all sets of variables. This reduction is statistically significant for the locations on the 

Brandywine Creek and the James River basins.

The equations show that sediment concentration 

increases significantly with mean air temperature 

or time of the year for all streams except the Scantic 

and the James River at Scottsville.

Although the regression coefficients for groundwater runoff were not significant for the Hazel, Rappahannock, and Rapidan Rivers and not highly significant in other basins, the sediment concentration tends 

to decrease as ground-water runoff increases.

Of the three measures of storm intensity, only 

peakedness index was determined for all streams. 

Sediment in streams tends to increase with each of 

measures of storm intensity.
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E39

The standard error of estimate for the equations 

varies much more among the different streams than 

among the different combinations of variables for a 

given stream. This is caused by the variance of hydrologic and environmental factors not evaluated by the 

data used, or possibly by some error in the basic data. 

The standard error of estimate ranges from 0.14 to 

0.30 of a log unit for most computed combinations of 

variables.

Three of the regression formulas were tested with 

observed data from 15 storm events on the Shenandoah 

Eiver at Front Royal, Va., and from 14 storm events 

on the Potomac River at Point of Rocks, Md. The 

results indicated four points of interest: (1) None of 

the computed concentration values were consistently 

close to agreement with the observed values. (2) The 

relative size of the river basin determines the shift of 

the computed values from the observed values. (3) 

The ratio of the computed to the measured values 

decreases as the observed values increase. (4) The 

formulas can be modified to yield computed values in 

good agreement with the observed values.

RECOMMENDATIONS

Although the analysis of data for seven stream 

locations in the Atlantic coast area using several combinations of variables yields formulas for predicting 

sediment transport, it is apparent that extrapolation 

to basins of different sizes and locations is not practical 

at this stage.

Four areas of further study are apparent:

1. Continue the search for suitable independent variables and their proper transformation. This would 

further explain the storm-to-storm variation for 

specific stream locations.

2. Determine the effect of the number of storm events 

on the equation and its significance for at least 

three stream locations.

3. Reduce to dimensionless terms the data that is 

affected by drainage basin size. This would include such variables used in this study as sediment 

discharge Qs, water discharge Qw, ground-water 

runoff Q6 , and peak flow Pn .

4. Extend the work to other stream locations to encompass environments of considerably different climate, soil characteristics, topography, vegetative 

cover, drainage density, and drainage basin size. 

Measures of these characteristics on a stream 

location basis must be developed. 

The results of such studies will help to advance

progress toward development of a "universal equation"

for computing stream sediment transport through 

application of specific observed variables.

REFERENCES

Campbell, F. B., and Bauder, H. A., 1940, A rating curve 

method for determining silt discharge of streams: Am. 

Geophys. Union Trans., part 2, p. 603-607.

Colby, B. R., 1956, Relationship of sediment discharge to 

streamflow: U.S. Geol. Survey open-file report, 170 p.

 1961, Effect of depth of flow on discharge of bed material: 

U.S. Geol. Survey Water-Supply Paper 1498-D.

Dawdy, D. R., 1961, Depth-discharge relations of alluvial 

streams discontinuous rating curves. U.S. Geol. Survey 

Water-Supply Paper 1498-C, 16 p.

Dixon, Wilfred J., and Massey, Frank J., 1957, Introduction to 

statistical analysis: New York, McGraw-Hill, 2d ed.

Einstein, H. A., 1950, The bed-load function for sediment 

transport in open channels: U.S. Dept. Agriculture Tech. 

Bull. 1026, 70 p.

Ezekiel, Mordecai, and Fox, Karl A., 1959, Methods of correlation and regression analysis: New York, John Wiley and 

Sons, 3d ed.

Glymph, L. M., Jr., 1951, Relation of sedimentation to accelerated erosion in the Missouri River Basin: U.S. Dept. 

Agriculture, SCS-TP-102, p. 6.

 1954, Studies of sediment yields from watersheds:

Assoc. Internac. d'Hydrol. Sci., U. Geophys. Internac.,

Assemblee Generate de Rome. 

Guy, H. P., 1951, Level terrace design as affected by hydrologic

factors: Unpublished thesis, Iowa State College, Ames,

Iowa, p. 23-24. 

Heidel, S. G., 1956, The progressive lag of sediment concentration

with flood waves: Arn. Geophys. Union Trans., v. 37, no. 1,

p. 56. 

Hubbell, D. W., and Matejka, D. Q., 1959, Investigations of

sediment transportation Middle Loup River at Dunning,

Nebraska: U.S. Geol. Survey Water-Supply Paper 1476,

p. 72. 

Johnson, A. W., 1961, Highway erosion control: Am. Soc.

Agricultural Engineers Trans., v. 4, no. 1, p. 144-152. 

Lane, E. W., 1955, The importance of fluvial morphology in

hydraulic engineering: Am. Soc. Civil Engineers Proc., Vol.

81, Paper No. 475. 

Langbein, W. B., and Schumm, S. A., 1958, Yield of sediment in

relation to mean annual precipitation: Am. Geophys. Union

Trans., 39, p. 1076-1084. 

Leopold, L. B., and Maddock, Thomas, Jr., 1953, The hydraulic

geometry of stream channels and some physiographic implications: U.S. Geol. Survey Prof. Paper 252, 57 p. 

Maner, S. B., 1958, Factors affecting sediment delivery rates in

the Red Hills physiographic area: Am. Geophys. Union

Trans., 39, p. 669-675. 

Miller, C. R., 1951, Analysis of flow-duration, sediment-rating

curve method of computing sediment yield: U.S. Bur. of

Reclamation Report, 15 p. 

Rouse, Hunter, 1950, Engineering hydraulics: New York, John

Wiley & Sons, p. 83-103. 

Sayre, W. W., Guy, H. P., and Chamberlain, A. R., 1963, Uptake

and transport of radionuclides by stream sediments: U.S.

Geol. Survey Prof. Paper 433-A.
E40 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

Simons, D. B., Richardson, E. V., and Haushild, W. L., 1962, 

Some properties of water-clay dispersions and their effects 

on flow: U.S. Geol. Survey Water-Supply Paper, 1498-G.

Snedecor, G. W., 1956, Statistical methods: Ames, Iowa, Iowa 

State College Press, 5th ed.

Stall, J. B., and Bartelli, L. J-, 1959, Correlation of reservoir 

sedimentation and watershed factors, Springfield Plain, 111.: 

Illinois State Water Survey, Report of Investigation 37.

U.S. Dept. of Commerce, 1961, Rainfall frequency atlas of the

United States: Technical Paper No. 40, p. 113. 

Wischmeier, W. H., 1962, Rainfall erosion potential: Agricultural

Engineering, v. 43, no. 4, p. 212. 

Wischmeier, W. H., and Smith, D. D., 1958, Rainfall energy and

its relationship to soil loss: Amer. Geophys. Union Trans.,

v. 39, no. 2, p. 285.
APPENDIX
E42 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

MULTIPLE REGRESSION EQUATIONS

This appendix contains regression equations for seven 

stream locations in the Atlantic coast area and for 

selected combinations of variables used in the analyses 

to show the effect of these variables in predicting 

sediment conditions on the basis of storm events. The 

relative value of each equation is indicated by the standard error of estimate of the dependent variable in terms 

of log units. This is shown in parentheses at the end of 

each equation. The significance of the regression 

coefficients is indicated by superscript as follows:

a. Very highly significant (99.9 percent level).

b. Highly significant (99 percent level).

c. Significant (95 percent level).

d. Poorly significant (90 percent level).

e. Very poorly significant (80 percent).

Where a superscript is not shown with a coefficient, 

the variable cannot be considered useful in explaining 

sediment variation. Such a variable, however, cannot 

be dropped from a specific equation without adjustment 

to coefficients of other variables.

SCANTIC RIVER NEAR BROAD BROOK, CONNECTICUT 

Surface runoff 65 storm events 

I. Log C la dependent variable

1. Log (7=1.548+0.151° log #w-0.00001 M, 

+0.00115 ra+0.163° log #6 +0.036° P«

-0.1386 log 10 Rg Se=O.UO

2. Log (7=1.547+0.151° log #w +0.00114 Ta

+0.163° log #6 +0.036° Pi-0.138d log 10 Rg

&=0.138

3. Log (7=1.551+0.143° log #w +0.177° log Qb

+0.037C Pi-0.1136 log 10 Rg £e=0.138

4. Log (7=1.532+0.082d log #«,

+0.200b log #6+0.035° Pt &=0.139

5. Log (7= 1.719+0.21 lb log #6

+ 0.0314d P, £e=0.142

6. Log (7=1.714+0.227b log #6 £e =0.144

ii

1. Log (7=1.516+0.135° log #«,-0.00021 Mt

+0.00121 ra+0.190°log #6 -0.153d log W Rq

+ 0.065 log 100 Rt &=0.144

2. Log (7= 1.492+0.135° log #«,+0.00112 Ta 

+0.196° log #6 -0.149e log 10 RQ

+0.068 log 100 Ri £e=Q.143

3. Log (7=1.567+0.135° log #«,+0.00138 Ta

+ 0.182° log #6 -0.132e log Rg Se =Q.U2

4. Log (7=1.572 + 0.125° log #«,+0.200b log #6

-0.1026 log 10 RQ Se=O.U2

5. Log (7=1.553+0.070e log #w +0.219b log #6

&=0.143

6. Log (7=1.714+0.227b log #6 &=0.144

Total runoff 65 storm events 

III

1. Log (7=0.033+0.502* log #w -0.00100Mt

+ 0.00019Ta -0.208d log #6+1.202*Pi £e=0.179

2. Log (7=0.031+0.503* log #w -0.00102Mt

-0.206° log #6+1.205*^ &=0.177

3. Log C= 0.134+0.487* log #w 0.216° log #6

4. Log (7=0.090+0.398* log #w + 1.387*Pi &=0.178

5. Log (7=1.259 + 1.155^ &=0.213

IV

1. Log (7=0.024+0.415* log #W +0.00131M, 

-0.00104Ta -0.127 log &+1.171aP, 

+ 1 0.142 114e log 105ff Se

2. Log (7= 0.034+0.423* log #W +0.00120M<

-0.148e log #6+1.159*P,+0.121 e log WRg

3. Log (7= 0.154+0.412* log #«,-0.166" log #6

+ 1.187Pr|-0.109 log 105ff £e=0.178

4. Log (7=0.134+0.488* log #w -0.216° log #6

+ 1.225*P< £e=0.178

5. Log (7=1.259 + 1.155*Pi

v

1. Log (7=0.267+0.404b log #«,+ 0.00181 e Mt

-0.00138 Ta -0.184e log #6

+0.105 log 10 5ff +0.0256e log 100 Rt

2. Log (7=0.31 l + 0.412b log #w +0.000165e Mt

-0.214d log #6+0.086 log 10 Rq

+ 0.2256 log 100 Rt £e=0.199

3. Log (7= 0.241+ 0.460* log #«,+0.00157e Mt

-0.239° log #6+0.290° log 100 Rt

£e =0.198

4. Log (7= 0.435+0.438* log #-0.263° log #6

+ 0.275d log 100 Rt Se=0.200

5. Log (7=0.768+0.481* log #w -0.341b log #6

^e=0.204

6. Log (7= 0.527+0.327* log #w &=0.217

Total runoff 136 storm events

[Rainfall data not available]

VI

1. Log (7=0.549+0.695* log #w +0.00128 Mt

+ 0.00147 Ta -0.318b log #6 +1.42* Pt

2. Log C= -0.480+0.683* log #w +0.00132 Mt

-0.311b log #6 +1.461* Pt ^e=0.239

3. Log C= -0.375+0.672* log #w -0.325b log #6

+ 1.472* P{ &=0.239

4. Log (7= -0.677+0.538* log #«,+1.56* P4 ^=0.:

5. Log (7=0.558+0.285* log Ow Se=0.:

C. -LAJg, ^J \J.\JI I ^\J.tJ<JfJ AV»g v^

>. Log (7=0.558+0.285* log Qw 279
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT

4.

E43

BRANDYWINE CREEK AT WILMINGTON, DELAWARE

Surface runoff 138 storm events

I

1. Log 0=0.886+0.644* log #«,-0.00155b Mt

+0. 00385eTa -0.195e log #6 -0.365e log 10 Rg

+0.338b log 100 Rt $=0.215

2. Log 0=0.450+0.559* log #«,-0.00137c Mt

+0.0038C T«-0.208e log 10 #9+0.368b log 100 Rt

$=0. 218

3. Log 0=0.611+0.452* log #«,-0.00136c Mt

+0.00241d T0 +0.353b log 100 Rt $=0.219

4. Log O=0.674+0.429* log #«,-0.00137M,

+0.463* log 100 Ri $=0.220

5. Log 0=0.610+0.430* log #«,+0.446* log 100 Ri

$,= 0.224

6. Log 0=1.255+0.400* log #. $=0.241

n

1. Log C=1.039+0.325e log #«,-0.00199* Mt 

+0.00554* T«-0.183e log #6 +0.333* log Pn

-0.274d log 10 Rg $=0.211

2. Log O=1.029+0.166d log #«,-0.00195* Mt

+0.00431* Ta -0.109e log #6 +0.352a log Pn

$,= 0.213

3. Log O=0.731+0.155d log #«,-0.00186b Mt

+0.00462* Ta+0.363* log Pn Se=0.2l3

4. Log O=0.859 0.00208* M.+0.00411* Ta

+0.486* log Pn $=0.215

5. Log O=1.163-0.00194b M4 +0.454* log Pn

$=0.224

6. Log 0=1.120+0.432* log Pn $=0.232

in

1.

2.

3.

4.

5.

6.

1.

2.

3.

Log 0=0.406+0.719* log #«,-0.00150bM, 

+0.00484*Ta -0.124e log Q6 +0.196*P!

= 0.232e log 10 Rq $,=0.208 

Log 0=0.958+0.674* log #«,-0.00139c Mt 

+ 0.00457* ra+0.212* P.-0.127 log 10 R,

$=0.208 

Log 0=0.181 + 0.610* log #«,-0.00139 c Mt

+ 0.00390* T«+0.214* P, $=0.208 

Log O=0.121+ 0.606* log #«,+0.00382b Ta

+ 0.208* P, $=0.213

Log 0=0.349 + 0.582* log #«,+0.239* Pt $=0.220 

Log 0=1.255+0.400* log #. $=0.241

IV

Log Qs=-1.634+1.633*log Q«,-0.00142C Mt 

+ 0.00365C Ta -0.199e log Q6 -0.354C

log 10 5,+0.3286 log 100 Rt $=0.216 

Log Qs= -2.079 + 1.546* log Q«,-0.00123 C Mt 

+ 0.00317d Ta -0.194e log 10 JR9 +0.359b

log 100 Rt $=0.219 

Log Q,= - 1.929 + 1.445* log QW -0.00123 C Mt

+0.002276 Ta+0.346b log 100 Rt $=0.220

5.

6.

Log Q=- 1.870+ 1.425* log #W -0.00123C Mt

+ 0.448* log 100 Rt $=0.221 

Log Q=- 1.928+ 1.426* log Qw+ 0.448* log 100 Rt

$=0.224 

Log ^=-1.320+1.397* log Qw $=0.240

Log &=-1.494+1.310a log Qw -0.00187b Mt 

+ 0.00526* Ta -0.185c log Q6+0.336* log Pn

-0.262" log 10 R9 $=0.21 2

Log Q,= - 1.504 + 1.1 58* log Qw -0.00183b Mt 

+0.00408* Ta - 0.144" log 4+0.355* log Pn

Log Qs=-1.817+1.147*log &,-0.00174b Mt

+0.00441* Ta +0.366* log Pn $=0.214 

Log Qs=- 1.884 +1.205* log Q«,+0.00438* Ta

+0.298* log Pn $=0.221 

Log Qs=- 1.744+ 1.459* log &,+0.0049* Ta

$=0.229

6. Log &=-1.302+1.397*log $=0.241

VI

Log Qs= -2.095+ 1.705* log &,-0.00137e Mt 

+ 0.00462b Ta -0.131 e log Qb+ 0.189* Pi

-0.2256 log 10 R, $=0.210 

Log Qs= -2.141 + 1.596* log &,-0.00131 c Mt 

+ 0.00358b Ta -0.667 log &+0.200* Pt $=0.211 

Log Qs= -2.345+ 1.600* log Q«,-0.00125 C Mt

+0.00374b Ta +0.208* Pt $=0.211

Log Qs= -2.399 + 1.597* log #«,-0.00366b Mt

+ 0.202* Pt $=0.214

Log #,= -2.180+1.574' log #.+ 0.232' P, $=0.221 

Log #,= -1.302+1.397' log #. $=0.241

HAZEL RIVER NEAR RIXEYVILLE, VA. 

Surface runoff 75 storm events

Log O= + 0.660 +0.474* log Qw- 0.00289 Mt 

+ 0.00153* Ta-O.lOSlog Qb 

+0.2586 Pi-0.149 log 10 R, $=0.271

Log O=0.586 +0.397* log #«,-0.00242 Mt 

+0.01101* Ta -0.040log #B +0.278e P, $=0.270

Log O=0.470 +0.396* log #. 0.00199 Mt

+ 0.01 104* Ta+ 0.31 ld Pi $=0.268

Log 0=0.462+0.391* log #«,+ 0.01057* Ta

+ 0.304d Pf $=0.268

Log 0=0.809 + 0.324* log #.

+ 0.01148* Ta $=0.273

Log 0=1.973+0.00815* Ta $=0.312
E44 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

II

1. Log C= +0.642+0.513*log # 0.00256 Mt 

+ 0.00970a Ta -0.178e log Q>

-0.421° log 10 fiff +0.533a log 100 Rt

£e =0.255

2. Log C= +0.524 + 0.482*log #«+0.00909a Ta

-0.124 log #6 -0.390c log 10 Rg

+ 0.554a log 100 Rt #e=0.255

3. Log C= +0.362+0.394* log #«+0.00918a Ta 

-0.2516 log 10 flff +0.551 a log 100 Rt

£e=0.256

4. Log <7=0.554+0.291 a log <?«+0.00864a Ta

+0.44P log 100 R- £e =0.259

5. Log <7= 0.809+ 0.324a log #«+0.01148a Ta

Se =0.273

6. Log <7=1.973 + 0.00815a Ta Se=QM2

in

1. Log C= + 0.963-0.0045 M,+0.00852a Ta 

+0.175e log &+0.188 Pt

+0.452a log 10 Rg Se =0.297

2. Log (7= + 0.930 + 0.00845a Ta +0.183e log Qb

+0.196 P,+ 0.453a log 10 Rq Se =0.295

3. Log C= + 1.236 + 0.00893* Ta+0.114 log Qb

+0.404a log 10 Rg Se =0.295

4. Log C= 1.576+0.00800* Ta

+0.368b log 10 Rg Se =0.296

5. Log (7= 1.973 + 0.00815* Ta £e =0.314

IV

1. Log (7=0.586+0.397* log ^-0.00242 Mt

+ 0.01101* T«-0.040 log #6 +0.278e Pt Se =0.270

2. Log <7= 0.470+0.396a log &-0.00199 Mt

+0.01104* Ta+0.311d Pf £e=0.268

3. Log C= 0.462+0.391* log Qw

+0.01057* Ta+0.304d P, Se =0.268

4. Log <7=0.809+0.324a log Qw

+0.01148* Ta &=0.273

5. Log (7=1.973 + 0.00815* Ta £e =0.312

v

1. Log C=+ 0.791-0.098 log Qw -0.00200 Mt 

+0.01083* Ta -0.0214 log Qb

+ 0.509d log Pn Se =0.269

2. Log (7=+0.745-0.125 log Qw -0.00176 Mt

+0.01085* Ta +0.535c log Pn £e =0.267

3. Log (7=0.719-0.00178 Mz +0.01125a Ta

+0.402a log Pn Se=0.

4. Log (7=0.704+0.01082* Ta +0.399* log Pn

Se=

5. Log (7=+ 1.563+0.308* log Pn Se=0.3ll

VI

1. Log (7=+0.645+0.303* log &,-0.00175 Mt 

+0.00902a Ta -0.034 log Qb

+0.419b log 100 R{ &=0.262

2. Log C= +0.568+0.294* log &-0.00136 Mt 

+0.00901* Ta +0.436b log 100 Rt

£e=0.260

3. Log C= +0.554+0.291* log &+0.00864* Ta

+0.441b log 100 Rf £e=0.259

4. Log C= 0.809 +0.324* log &+0.01148* Ta

5. Log (7=1.973+0.00815* Ta ^=0.312

vn

1. Log &=- 1.456 + 1.363* log Q«,-0.00313 Mt 

+0.01030* Ta -0.151 log Q6+0.141 Pt

-0.016 log 10 RQ Se=Q.282

2. Log Qs=- 1.464+ 1.355* log &-0.00308 Mt 

+0.01025a Ta -0.144e log Q6 +0.143 Pt

3. Log Qs=- 1.220+ 1.333* log &-0.003456 Mt

+0.01052a Ta -0.186d log Qb ^=0.279

4. Log Q,= -1.347+1.316Mog Q«,+0.00998* Ta

-0.133e logQ6 ^=0.280

5. Log Qs=- 1.597+ 1.288* log &+0.01078* Ta

Se= 0.283

6. Log &=-0.677+1.182* log Qv £e=0.324

VIII

1. Log Qs=- 1.644+1.406* log &-0.00254 Mt 

+0.00837* Ta -0.184e log Q6 -0.252 log 10 R,

+0.493b log 100 Rt £e=0.265

2. Log Qg =-1.761 + 1.375*log &,+0.00778b Ta 

-0.130 log Q6 -0.221 log 10 Rff

+0.514b log 100 Rt Se=Q.265

3. Log Qs=- 1.739 + 1.267* log &,+0.00752b Ta

-0.062 log Q6 +0.449b log 100 Rt Se=0.265

4. Log Qg =-1.873 + 1.252*log Q«,+0.00770b Ta

+0.478b log 100 Rt £e=0.265

5. LogQg =-1.597+1.288*logQ«,

+0.01078a Ta ^e =0.

6. Log Qg =-0.677+1.182*log Qw ^e =0.

IX

1. Log Q,= -0.584+ 0.00390 Mt+0.00166 Ta

+0.654b log Q6 -0.059 Pt+ 1.713* log 10 Rq

2. Log Qs= -0.686+0.00409 M.+0.00149 Ta

+0.678* log Qb + 1.727* log 10 Rg ^=0.447

3. Log Q,= -0.571 +0.00434 M«+0.662a log Qb

+ 1.723 log 10 Rg &=0.444

4. Log ^g =-0.317+0.597a log Q6 +1.726a log 10 Rg

Se= 0.445

5. Log &= + !. 198+1. 537a log Rg *Se=0.501
STORM-PERIOD VARIABLES AFFECTING STREAM SEDIMENT TRANSPORT E45

5. Log (7=1.448+0.184" log #w +0.00843aTa

6. Log (7=2.162+0.00671*ro #1=0.263

1. Log Qs=- 1.464+ 1.355* log Qw -0.00308 Mt 

+0.01025* T0 -0.144e log &+0.143 Pt

Se= 0.280

2. Log&=-1.220+1.333*logQw -0.00345e M,

+0.01052* T0 -0.186d log Q6 £e=0.279

3. Log &=-1.347+1.316*log (^+0.00998* Ta

-0.1336 log Qb £e =0.280

4. Log &=-1.597+1.288*log (^+0.01078* Ta

#e =0.283 

5. .= -0.677+1.182a logQw S=0.324

XI

1. Log Qs=- 1.401 + 1.029* log Qw -0.00269 Mt 

+0.01005* T0 -0.119 log &+0.431 log Pn

Se =0.27S

2. Log &=-1.528+0.961*log Qw+0.00957* Ta

-0.067 log &+0.4036 log Pn #e =0.278

3. Log &=-1.668+0.878a log Qw +0.00981a Ta

+0.485" log PB Se=0.277

4. Log &=-1.597+1.288a log Qw +0.01078a Ta

&= 0.283

5. Log&=-0.677+1.182a logQw &=0.324

xn

1. Log Qs=- 1.642+1.280* log QW -0.00205M,

+ 0.00797^-0.098 log Q& +0.425b 

log 100 Ri ^=0.266

2. Log Q=-1.739 + 1.267a log Qttl +0.00752b 7T0-0.062 

log Q6 +0.449b log 100 Ri Se=0.265

3. Log Q=- 1.873+1.252* log Qttl +0.00770b 7T0

+0.478" log 100 Ef ^=0.265

4. Log Q=-1.597+1.288a log Qw +0.01078aT0

Se=0.283

5. Log Q= -0.677+1.182* log Qw Se=0.324

RAPPAHANNOCK RIVER AT REMINGTON, VA.

Surface runoff 82 storm events

I

1. Log C= 1.328+0.323° log Qw -0.00276eM, 

+ 0.00925*?;-0.092 log Q6+0.154Pf

-0.171 log IORQ £e=0.247

2. Log <7=1.130+0.270b log Qw-O.OQ202Mt

+ 0.00890*7^+0.207^-0.0752 log WRS

&= 0.246

3. Log (7=1.202+0.235a log Qw -0.00215eMz

+0.00850a 7T0+0.190ePi ^=0.245

4. Log (7=1.462+0.191b log Qw 0.00229eM(

.00892a ro ^=0.246

1.

2.

3.

4.

5.

1.

2.

Log (7= 1.395+0.325" log Qw -0.00278eM< 

+0.00804aT0 -0.117 log Qb -0.257 log 1QR, 

+ 0.221d log IQQRi #e= 

Log C= 1.230+0.238" log QW -0.00189M< 

+0.00753aT0 -0.126 log IORQ

+ 0.240d log 100#i Se=0.245 

Log (7=1.333+0.187" log Qw -0.00211 eM,

+ 0.00711"ra +0.204d log 

Log <7=1.313+0.180b log Qw +

+0.215d log 

Log (7=1.448+0.184" log Qw +0.00843a Ta

Se=0.248 

Log (7=2.162+0.00671aT8 #e=0.263

Surface runoff 124 storm events

[Rainfall data not available]

III

Log (7=0.826 + 0.286* log Qw -0.00182" Mt

+ 0.00791* T0+0.0734 log Q6 +0.252d Pt #e=0.239

Log (7=1.059 + 0.289* log QW -0.00190C Mt

+ 0.00760* 7;+0.199e P< #e=0.239 

Log (7=1.373 + 0.232* log Qw- 0.00208" Mt

+ 0.00792* Ta Se=0.240 

Log (7+1.280+0.233* log Qw +0.00782* Ta

Se=0.246 

Log (7=2.193+0.00544* Ta Se=0.267

RAPIDAN RIVER NEAR CULPEPER, VA. 

Surface runoff 85 storm events

Log (7=0.768+0.529a log #w -0.00284e Mt 

+0.00958a ^-0.121 log Q6+0.395d Pf

-0.3006 log 10 Eq =0.280

Log (7=0.456+0.489a log Qw- 0.00209 Mt 

+0.00962a 7^+0.421^^ 0.208 log 10 Rg

#e=0.280

Log (7=0.355+0.524* log #w +0.00970* Ta

+0.429C P,-0.275d log 10 Rg Se =0.281

Log (7=0.566+0.400* log #w +0.00820* r.+O.SS^P,

5.

6.

Log (7=0.957+0.335d log Qw+0.00904* Ta

Log (7=1.702+0.259a log Qw ^=0.315
E46 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

1. Log (7=1.141+0.449*log Q«,-0.00268M,

+0.00947* ra -0.126 log Q6 -0.283e log 10 Rg

Se=0.287

2. Log (7=1.307+0.438*log &,-0.00313" M,

+0.01008* ra-0.149 log &-0.249 log 10 RQ

Se=0.286

3. Log (7=0.960+0.380*log Q1D -QW222 Mt

+0.01017* ra-0.130 log 10 Rg &=0.287

4. Log (7= 1.035+0.327* log Q«,-0.00268e M,

+0.00944* Ta Se=0.286

5. Log (7=0.9568+0.335* log &.+0.00904* Ta

&=0.287

6. Log (7=1.702+0.259* log Qa &=0.315

JAMES RIVER AT BUCHANAN, VA. 

Surface runoff 66 storm events

[Computer option to discard least significant variable or each combination was not

used]

I

Log C=+0.960+0.532b log Q«,-0.00530bMt

+0.00777b Ta -0.556* log Q6 +1.019* Pt &=0.230

n

Log C= + 1.783-0.486d log Q«,-0.00521b Mt

+0.00807b Ta -0.572* log Q6 +1.027* log Pn

&=0.229 

m

Log C=+ 1.625+0.418* log Q«,-0.00633b Mt

+0.00826° ra -0.482* log Q» &=0.252

IV

Log C=-0.649+0.454* log QK) -0.00333d Mt

+0.01175* Ta+0.769c Pt Se =0.269

Log C= +0.0359+0.373*log Q.

-0.00434CM, +0.01170* Ta Se=0.278

VI

Log C= + 1.352+0.203b log Qw

-0.00380d M4 &=0.308

JAMES RIVER AT SCOTTSVILLE, VA. 

Surface runoff 67 storm events

1. Log (7=+0.832-0.359e log Qw -0.00321 cMt 

+0.00290eTa -0.184d log Qb +0.926* log PB ^e=

2. Log (7= 1.245-0.446° log Q«,-0.00333CM,

-0.217C log &+0.989* log Pn ^e=0.188

3. Log (7=1.271-0.00293cMi-0.262b log

Q6 +0.525*logPB ^e=

4. Log (7=1.129-0.211° log Q6+0.496* log Pn

5. Log (7=0.683+0.425* log Pn

ii

1. Log (7=0.21 1+0.560* log Qw- 0.00297° Mt 

+0.002866 Ta-0.196c log &+0.770b Pf

2. Log (7= 0.554 +0.537* log &,-0.00309cMt 

-0.229C log Q6 +0.846* Pt

3. Log (7=0.489+0.504* log Qw-0.182d log Q6

+0.751b Pt

4. Log (7= +0.074+0.451* log Q«,+0.808b P«

5. Log (7= +0.806 +0.357* log Qw

Se= 0.204

Se 

Se

0.206

0.221

U.S. GOVERNMENT PRINTING OFFICE; 1963 O 716-824