Effects of Water 

Temperature on the 

Discharge of Bed Material

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-G

Effects of Water 

Temperature on the 

Discharge of Bed Material

By B. R. COLBY and C. H. SCOTT

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 462-G

A study of the theoretical and observed effects 

of changes in water temperature on the 

transportation of bed material

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1965
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 - Price 25 cents (paper cover)
CONTENTS

Abstract _ ________________________________

Introduction _______________________________

Temperature effects through viscosity changes 

Effect on thickness of the laminar sublayer

Effect on vertical distribution of suspended sediTheoretical equation for vertical distribution. __ 

Relation of fall velocity to temperature _ _____

Computed temperature effects on bed-material 

dis charge ________________________________

Page 

Gl

1

2

2

3

3

5

Page

Temperature effects througn viscosity changes Con.

Effect on bed configuration___________--____-_-_- G7

Field streams_______--_-___------_-----__

Flume flows._______---_-_--_-------__----_-

Overall temperature effects on bed-material discharge 

Differences between flume flows and field streams. __ 

Roughly defined effect for field streams.___________

Effect of concentration of fine sediment._______________

Conclusions.________--_-__----_----_-__------------

References _______________-------____--_---_--------

ILLUSTRATIONS

TABLE

12

14

17

18

19

22

24

25

FIGURE 1-9. Graphs showing P»g«

1. Specific weight and kinematic viscosity of distilled water.-.-.---,-------------------------------- G2

2. Nomograph for ratio of mean velocity to V(^*S)m----------------------------------------------- 4

3. Effect of a change in water temperature from 40° to 80° F on the fall velocity of quartz spheres of several

sizes__--________-__________________-______-__-_-_-_----_-----_------------------------- 5

4. Size distributions of bed sediments for computing temperature effects.______________------.________ 6

5. Computed effect of water temperature on the relation of bed-material discharge to mean velocity. _ _ _ _ 8 

6-8. Computed sediment discharges by size ranges for a bed sediment:

6. Median diameter, 0.20 mm-___________--__-----_-----_-----------^--_----------------- 9

7. Median diameter, 0.40 mm__________________-____-_-____-_--------------------_------- 10

8. Median diameter, 0.60 mm. __________-__________________-____-----_-_---------__----_- 11

9. General variation of Manning's n with water temperature for Middle Loup River at Dunning, Nebr.,

section Cz_________________________________________.___----___-------__---------_------- 12

10. Longitudinal profiles of streambed at different water temperatures, Middle Loup River at Dunning, Nebr____ 13

11-19. Graphs showing 

11, 12. Variation of Manning's n with streamflow and water temperature:

11. Elkhorn River near Waterloo, Nebr_-____--__----------_,------------------------- 14

12. Mississippi River at St. Louis, Mo___________________________-____-__--------_--- 15

13. Ratios of observed values of n to values of n from average curve of figure 12 plotted against water

temperature__-_______-_______-___________-______---__-----___---_------------------ 15

14. Differences in resistance to flow for pairs of flume runs at high and low water temperatures. _____ 16

15. Differences in bed-material concentration for pairs of flume runs at high and low water temperatures- _____-_-____-__________-_--__-___-_________-_-_-_---_---_---------------------- 17

16. Relation of bed-material discharge to mean velocity for Niobrara River near Cody, Nebr._______ 20

17, 18. Approximate relative effect of water temperature on the relation between bed-material discharge 

and mean velocity:

17. Niobrara River near Cody, Nebr-_______-_-___----------_-_----_------------------ 20

18. Three rivers. _______________________ _ .1 21 

19. Approximate effect of water temperature and concentration of fine sediment on the relation of bedmaterial discharge to mean velocity-_--___---_---_-_----_------------------------------- 23

Page

TABLE 1. Measured and computed bed-material discharges for Middle Loup River at Dunning, Nebr.___________________ G21

m

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

EFFECTS OF WATER TEMPERATURE ON THE DISCHARGE OF BED MATERIAL

By B. E. COI.RY and C. H. SOOTT

ABSTRACT

Changes in water temperature and consequent changes in 

viscosity affect bed-material discharge (for this paper, the discharge of particles larger than 0.062 mm) in complex ways. 

These ways may be explained in terms of three separate effects. 

One effect is on the thickness of the laminar sublayer, and this 

effect is usually the smallest of the three. A second effect is 

on the vertical distribution of suspended bed material. It is a 

large effect that causes, according to several somewhat inexact 

computations, an approximate doubling of bed-material discharge if water temperatures are decreased from 80° to 40° F 

and if mean velocities, depths, and sizes of the bed sediments 

are the same for the two water temperatures. This second 

effect seems to "be the most consistent and predictable of the 

three. The third effect is on the bed configuration and, hence, 

on the resistance to flow. It is a seemingly erratic and somewhat indeterminate effect that is sometimes large and sometimes small.

Temperature effects on bed-material discharge may be of 

several kinds, and they require careful classification if their 

different possible meanings are to be understandable.

Experimentally defined temperature effects on bed-material 

discharge usually require classification in term® of the flow 

characteristics that were kept constant, the variables that were 

involved in the analysis of the data, and the way in which the 

data were analyzed. These effects for flume flows may seem 

to be considerably different from those for field flows. Part of 

the difference is due to the shallow flows, variable energy gradients, wide range of bed configuration, and relative lateral and 

longitudinal uniformity of the flume flows as compared with 

field flows. Part is due to differences in the kinds of temperature effects that are generally defined. That is, in flume flows, 

the bed-material discharges may be measured at constant flow, 

constant depth, variable energy gradient, and two or more different water temperatures. The bed-material discharges may 

then be plotted against shear, and a temperature effect may be 

determined on the relation between bed-material discharge and 

shear. For flows at a cross section of a natural stream, the 

bed-material discharges per foot of width at approximately 

constant energy gradient may be plotted against mean velocity 

to define an average relation. The individual departures of 

observed bed-material discharges from the average relation may 

be plotted against water temperature to show any general effect 

of temperature in causing 'bed-material discharge to depart from 

the average relation. Such a general effect might be much 

different from the temperature effect on the relation between 

bed-material discharge and shear in flume flows.

Experimental defined temperature effects on the relation of 

bed-material discharge to mean velocity for three rivers indicate

an average increase of about 75 percent in bed-material disicharge for a decrease of water temperature from 80° to 40° F. 

This average increase together with some other experimental 

data and theoretical computations is the basis of a graph that 

is given to show the approximate temperature effect on the relation between bed-material discharge and mean velocity. The 

graph shows an increase in the percentage of this temperature 

effect with increase in depth of flow.

High concentrations of fine sediment increase the apparent 

viscosity of a water-sediment mixture. The addition of 20,000 

parts per million of bentonite to distilled water has; an effect 

on viscosity that is about the same as the effect on distilled 

water of a reduction in water temperature from 60° to 34°F 

(Simons, Richardson, and Haushild, 1963, fig. 6). The equivalence of a particular concentration of fine sediment to a particular temperature change and some observed bed-material discharges for the Rio Puerco in New Mexico largely define the 

given graph of approximate effect of high concentration of fine 

sediment on the relation of bed-material discharge to mean 

velocity.

Of course, effects of temperature or of concentrations of fine 

sediment on the relation of bed-material discharge to mean velocity are not directly applicable to the relation of bed-material 

discharge to any factor or variable other than mean velocity.

INTRODUCTION

A general increase of bed-material discharge with 

decrease in water temperature has been reported for the 

Missouri Eiver (U.S. Congress, 1935, p. 1089-1092), the 

Colorado Eiver (Lane, Carlson, and Hanson, 1949), the 

Middle Loup Eiver (Hubbell and others, 1956, p. 54), 

and the Niobrara Eiver (Colby, 1956, p. 31-32). However, some flume experimenters have reported a decrease 

and some an increase of bed-material discharge with decrease in water temperature (Hubbell and Al-Shaikh 

Ali, 1961).

The purposes of this paper are (1) to explain at least 

qualitatively three different temperature effects that are 

due to changes in viscosity of the water, (2) to indicate 

reasons why temperature effects for flume flows may 

seem inconsistent or somewhat contradictory, whereas 

temperature effects for field streams seem to be relatively 

consistent, and (3) to give a rough idea of the temperature effect on the relation between bed-material discharge per foot of stream width and mean velocity. AlGl
G2 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

though changes in water temperature may affect somewhat the discharge of fine sediment (silt and clay), most 

streamflows can transport at any temperature their supplied amounts of fine sediments. Hence, this paper 

deals mainly with temperature effects on bed-material 

discharge, which for this paper is defined as the discharge of particles larger than 0.062 mm. The paper 

is based on some field and flume studies and on theoretical computations of the temperature effect. It is not 

comprehensive enough to be much more than a reconnaissance report on the whole field of temperature effects on bed-material discharge.

First, three temperature effects are explained individually, and some idea of the general magnitude of each 

is given; next, overall temperature effects as reported for 

flume and field studies are discussed; and finally, an 

approximate quantitative effect of water temperature 

on the relation between bed-material discharge and 

mean velocity is given.

TEMPERATURE EFFECTS THROUGH VISCOSITY 

CHANGES

Both the specific weight (or the density) and the viscosity of a liquid change as the temperature changes. 

The change in specific weight of water is small (fig. 1) 

for the usual range of temperature in natural streams. 

The change in viscosity of water (fig. 1) is much greater 

than the change in specific weight. The effect on sediment discharge of changes in the specific weight of 

water is so small that it generally can be disregarded, 

but the effect on sediment discharge of changes in viscosity may be large enough to be very significant, especially for some particle sizes.

Viscosity changes that result from changes in water 

temperature have three effects on sediment discharge. 

The first to be discussed is the effect on the thickness of 

the laminar sublayer; the second, the effect on the fall 

velocity of suspended sediment and hence on the vertical 

distribution of suspended sediment in turbulent flow; 

and the third, the effect on the bed configuration.

EFFECT ON THICKNESS OF THE LAMINAR 

SUBLAYER

Changes in thickness of the laminar sublayer because 

of temperature changes are generally small but should 

not be completely disregarded. Like other temperature 

effects, the effect on bed-material discharge of changes 

in this thickness depends not only on the flow and the 

bed sediment but on the factors, other than temperature, 

that also control bed-material discharge or are correlated with bed-material discharge. This effect is complex and difficult to evaluate except in terms of some 

selected relations that may not be generally accepted. 

(No one relation or set of relations is generally accepted 

as satisfactory for computing either bedload discharge

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i 62.40

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52 62.30

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62.20

$ 62.10

62.00

2.00

1.90

1.80

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Q 1.60

g 1-50

CL

1.40

1.30

§ 1-20

£

o 1AO

1.00

0.90

0.80

0.70

32

30 40 50 60 70 80 90 

TEMPERATURE, IN DEGREES FAHRENHEIT

100

FIGURE 1. Specific weight and kinematic viscosity of distilled water.

or bed-material discharge.) The effect is discussed here 

in terms of a particular relation of bedload discharge 

(the discharge of particles on or within a few particle 

diameters of the streambed) to mean velocity (Colby 

and Hubbell, 1961, pis. 1, 2). The relation involves 

, a quantity that has the physical dimensions of a
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G3

length and that is equal to the effective shear on the bed 

sediment divided by the specific weight of the watersediment mixture. This relation was used for this paper in computing bed-material discharge at the same 

mean velocities, depths, and size distributions of bed 

sediments, but at different water temperatures. Of 

course, other relations may be preferred by many persons, but the one used here should give at least a rough 

idea of the possible changes in bedload discharge and 

bed-material discharge when the thickness of the laminar sublayer varies as a result of changes in water 

temperature.

A change in thickness of the laminar sublayer 

affects the relation between mean velocity u and 

effective shear on the bed sediment yf(RS)m. This 

effective shear is the product of yf, the specific weight 

of water-sediment mixture, and (RS)m , a quantity 

that is computed from known mean velocity and a 

mean-velocity equation. The quantity yf is approximately constant, and (RS) m is roughly equivalent to 

R'S, the product of the hydraulic radius with respect 

to the grains as used by Einstein (1950) and the energy 

gradient. For a hydraulically rough boundary, the 

ratio of u to ^J(RS)m or to yf(RS)m does not change as 

water temperature changes. Also, if 1,000 ksu/(v-W5 ) 

is less than about 5, the relative effect of a change in 

water temperature is less at high ratios of u to ^(RS)m 

than at low ratios. (See fig. 2.) The amount and 

the direction of the temperature effect on the ratio 

are determined by the quantity 1,000 ksu/(v 105 ), in 

which ks is the diameter of bed sediment for which 65 

percent by weight is finer and v is the kinematic 

viscosity of water. Except for shallow depths and 

low mean velocities (the lower left corner on fig. 2), 

even an increase of temperature from 32° to 100°F 

changes the ratio of u to T/(RS) m by only 10 percent or 

less. Figure 2 is based on an evaluation of fixed 

boundary roughness by Keulegan (1938) and in particular on his equation 38 for a rectangular channel of 

infinite width and on his figure 3.

The method given by Colby and Hubbell (1961) for 

computing bed-material discharge from mean velocity 

is based mainly on the procedure formulated by Einstein (1950). The method implies the assumptions that 

the relation of bedload discharge to (RS) m is independent of water temperature and that the bed-material 

discharge is proportional to the bedload discharge if 

the depth of flow and the relative vertical distribution 

of suspended sediment remain constant. If these two 

assumptions are correct, changes in thickness of the 

laminar sublayer because of temperature changes 

should not affect the relation between bed-material discharge and effective shear on the bed sediment. The

changes should, however, affect somewhat the relation 

between bed-material discharge and mean velocity for 

a given depth unless the boundary is hydraulically 

rough. The effect of a particular temperature change 

on the relation between bed-material discharge and 

mean velocity should sometimes be in one direction and 

sometimes in the other. (See fig. 2.) Fortunately, it 

should be small enough to 'be insignificant in comparison to the larger effects of water temperature on the 

vertical distribution of suspended sediment and on the 

bed configuration.

EFFECT ON VERTICAL DISTRIBUTION OF 

SUSPENDED SEDIMENT

Basically, the vertical distribution of suspended sediment depends on a ratio between two quantities the 

fall velocity of the sediment particles in a turbulent 

water-sediment mixture and the effective turbulence 

of the flow for suspending sediment. Neither quantity 

has a well-defined effect that can be expressed in simple 

and exact mathematical terms.

THEORETICAL EQUATION FOR VERTICAL DISTRIBUTION

The usual equation for the vertical distribution of 

suspended sediment of a single fall velocity or a narrow 

range of fall velocities in turbulent flow between a water 

surface and a streambed that are plane and parallel was 

given by Rouse (1937):

By definition

^y a 

V d (1)

(2)

in which

d is the depth of flow;

a and y are distances above the streambed;

ca and cy are concentrations at distances a and y 

above the bed;

w is the fall velocity of sediment particles 

of one size or of a representative particle from a narrow range of sizes;

k is the turbulence constant; and __

u* is the shear velocity and equals -\fgRS, 

which is the square root of the product of the gravity constant, the hydraulic radius, and the energy gradient.

According to equation 2, 2 is inversely proportional 

to the product of &, a measure of the rate of change 

of velocity with depth and hence a measure of turbulence, and u*, a measure of shear on the streambed 

and hence, too, a measure of turbulence. Also, for 

a given turbulent flow, ku* is constant and z varies 

directly with fall velocity according to equation 2. 

Unfortunately, equation 2 is rather inaccurate.
G4 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

200

60

100,000 

80,000-

25

20

15

10

70 <

60

50

40

1000 ks .u

0.7 1.0 2.0 

y-10 5 , IN SQUARE 

FEET PER SECOND

FIGURE 2. Nomograph for ratio of mean velocity to

The quantity ku^ is an uncertain measure of turbulence. The turbulence constant k is commonly assumed to be about 0.40 for clear-water flow and to be 

somewhat lower for sediment-laden flows because of 

an effect of sediment on the vertical distribution of 

velocity (Einstein and Chien, 1954, fig. 12). For flow 

over dunes, the assumptions on which the turbulence 

constant k was originally based do not apply satisfactorily, and k as computed from a vertical-velocity curve 

varies widely as position of the vertical changes with 

respect to the crest of a dune. Hubbell and Matejka 

(1959, p. 71) found &'s much higher than 0.40 for flows 

over sand dunes. Besides the uncertainty and variation of k, the use of U* has also been questioned. Einstein (1950, p. 28, 59) used w*', which may be much 

less than u* for some flows, in the computation of z.
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G5

The numerator of the right-hand side of equation 2 

may 'be about as uncertain as the denominator. Experimentally determined 0's (often called sx 's) for 

different size ranges of sand within a given flow (Anderson, 1942) do not necessarily increase so rapidly 

as the 1.0 power of the fall velocity. Experimental 

0's for some streams increase as about the 0.7 power of 

fall velocities that are based on equations given by 

Rubey (1933, p. 332), according to Colby and Hembree 

(1955, p. 69-71) and Hubbell and Matejka (1959, 

p. 70-72). Of course, a defined relation between experimental 0's for different particle sizes and fall velocities depends not only on the #'s but also on the 

uncertain fall velocities that are assumed to apply. 

Particle sizes may be either sieve sizes or fall diameters. 

The effective fall velocities in a given turbulent flow 

are not known; the fall velocities used are based on 

laboratory experiments in relatively still water.

RELATION OP FALL, VELOCITY TO TEMPERATURE

The temperature effect on the fall velocities of sediment particles is different for different sizes. The resistance to fall of a particle through a fluid is due mainly 

to viscous forces for particles that are small and that 

fall slowly and is due mainly to turbulent forces for 

particles that are fairly large and that fall rather rapidly. The fall velocities of sands (particles whose 

diameters are from 0.062 to 2.0 mm) in water are affected by both viscous and turbulent forces, but to different relative degrees for different particle sizes. Fall 

velocities of sediment particles have been discussed at 

length by Schulz, Wilde, and Albertson (1954) and by 

the U.S. Inter-Agency Committee on Water Resources 

(1957).

The variable effect of water temperature on the fall 

velocities of quartz spheres of different sizes in water is 

indicated on figure 3. The percentage effect for the 

change in temperature from 40° to 80 °F is greatest for 

the quartz spheres in the size range of very fine sand 

and decreases progressively as the particle size and the 

fall velocity increase. The greatest absolute increase in 

fall velocity for the temperature change from 40° to 80° 

F is for quartz spheres whose median diameters are 

about 2 or 3 mm.

The percentage change in bed-material discharge that 

accompanies a particular temperature change is generally small for particles of 1 mm or larger. The fall of 

particles as large as 1 mm is resisted much more by the 

generation of turbulence, which does not vary appreciably with water temperature, than by viscous drag. 

The fall velocity of particles finer than sand is low no 

matter what the temperature may be, and a large percentage change in the low fall velocities may not affect

756-940 Q Q5 2

the carrying ability of the stream for these sizes to a 

significant degree.

0

0.4

n a

1.0

1.6 

an

70

30

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n

ii * 1

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1 Q

2.0

t 

<

< i

i

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0.088 0.177 0.353 0.707 1.414 2.830 5.660 

PARTICLE SIZE, IN MILLIMETERS

Explanation 

X, 80°F , 40°F

(mm)

0.088

.177

.353

.707

1.414

2.830

5.660

Geometric mean size

(ft)

0.00029 

.00058 

.00116 

.00232 

.00464

.01856

Size range of spheres

(mm)

0.062-0.125

.125- .250

.250- . 500

. 500-1.000

1.000-2.000

2.000-4.000

4.000-8.000

FIGURE 3. Effect of a change in water temperature from 40° to 80°F on the fall 

velocity of quartz spheres of several sizes (U.S. Inter-Agency Comm. on Water 

Resources, 1957, table 2).

COMPUTED TEMPERATURE EFFECTS ON BEDMATERIAL DISCHARGE

The effect on bed-material discharge of changes in 

vertical distribution of suspended sediment can be 

roughly evaluated at stream verticals from a few computations of bed-material discharge at different water 

temperatures. These computations are based partly on 

theoretical and partly on empirical relations. Even 

though the computed bed-material discharges are inaccurate, perhaps largely because of inaccurate 0's, the 

ratio between the computed bed-material discharge for 

one water temperature and that for another may be 

reasonably representative of actual temperature effects 

on bed-material discharges. The computed bed-material
G6 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

discharges should at least indicate the general way in 

which the temperature effect, mainly due to changes in 

vertical distribution of suspended sediment, varies with 

changes in particle sizes, depths of flow, and mean 

velocities.

Computations were made for three size distributions 

of bed material (fig. 4), at mean velocities of 2, 5, and 

10 feet per second, for depths of 1 (or 4) and 10 feet, 

and at water temperatures of 40°, 60°, and 80°F. In a 

general way, the computations were based on the procedure by Einstein (1950); however, the bedload 

discharge per foot of width, iBqB, was computed from a 

graph given by Colby and Hubbell (1961, pi. 2), and 

was taken from figure 2. The bed-material

discharges, which include both bedload and suspended 

sediment of the appropriate particle sizes, were computed from iBgB(P/1 H-/2 H-l); P is from figure 2, and 

/i and 72 , which is always a negative quantity, were 

taken from curves given by Einstein (1950, figs. 1 and 

2). For mean velocities of 10 feet per second, a depth 

of 4 feet rather than 1 foot was used to avoid Froude

numbers greater than 1.0. (The Froude number 

equals u/^gd.)

The computations of bed-material discharge included 

the effects of water temperature on both the thickness 

of the laminar sublayer, through the use of figure 2, 

and the vertical distribution of suspended sediment, 

through the use of the A and 72 curves. Because of 

the uncertainty of equation 2, the 2*$ that were used 

to determine A's and 72 's were computed from the simple and partly arbitrary equation

s=4.0 w°- 7 (3)

The equation was based on an examination of experimental s?s for the Niobrara River near Cody, Nebr., 

and for the Mississippi River near St. Louis, Mo.

The fall velocity w for equation 3 was based on a 

table given by the U.S. Inter-Agency Committee on 

Water Resources (1957, p. 26, table 2). Accurate fall 

velocities are not necessary for this equation because 

the computed temperature effect is based mainly on 

change in fall velocity rather than on absolute fall

99.9

99.8

99.5

99.0

98

LJ

3 95

Q

£ 90

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i= 80

Mississippi River at St. Louis, Mo (1958 water year)

South Loup River at St. Michael, Nebr

70

60

50

40

30

20

10

5

2

1.0 

0.5

^Kansas River at Wamego, Kans

0.2 

0.1

0.01 0.1 1.0 10

DIAMETER, IN MILLIMETERS 

FIGURE 4. Size distributions of bed sediments tor computing temperature effects.
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G7

velocity. Similarly, the accuracy of equation 3 is not 

particularly significant because the computations are 

intended to indicate mainly a relative temperature effect on the discharge of 'bed material instead of absolute 

discharges of bed material.

The ratio of computed total discharge of bed material at 40°F to the computed total discharge of bed 

material at 80°F averaged roughly 2:1 (fig. 5). The 

ratio always increased as the depth of flow increased. 

The ratio tended to decrease, at least slightly, as either 

mean velocity or median particle size increased. The 

decrease in ratio may not be significant, however, except 

for the change in median size from 0.40 to 0.60 mm.

The relations of computed total discharge of bed 

material to depth are not necessarily straight lines on 

log-log paper, but straight lines should be satisfactory 

approximations on figure 5 for connecting computed 

points.

Although the computed total discharges of bed material are inexact, they probably are realistic enough 

to make the computed temperature effects reasonable 

approximations of actual temperature effects on bedmaterial discharges at a stream vertical. However, a 

further check was made to see if a large change in 

computed a?s might give a much different indicated 

temperature effect.

The check was made by arbitrarily dividing the 0's 

from equation 3 by 2.0 and then recomputing the total 

bed-material discharges for a depth of 10 feet, a mean 

velocity of 10 feet per second, the bed sediment whose 

median diameter is 0.40 mm, and water temperatures 

of 40°, 60°, and 80°F. Although the recomputed bedmaterial discharges were about seven to nine times the 

original bed-material discharges (fig. 5), the indicated 

temperature effect was reduced only about 25 percent. 

Thus, the recomputations indicate that large absolute 

errors in computing total bed-material discharges may 

not change greatly the indicated temperature effect.

The relative consistency of the temperature effect 

(fig. 5) may be misleading unless the computed bedmaterial discharges are shown for individual size 

ranges and for the water temperatures of 40° and 80°F. 

(See figs. 6-8.) The percentage temperature effect 

indicated by the computed bed-material discharges is 

largest for the size range from 0.125 to 0.25 mm. The 

percentage effects for the two size ranges from 0.062 to 

0.125 mm and 0.25 to 0.50 mm are about equal, and 

they are next largest to the effect for the 0.125- to 

0.25-mm-size range. The percentage temperature effect 

on bed-material discharge decreases markedly as the 

particle size increases above 0.50 mm and would be 

small if all bed material transported by a flow were 

larger than 0.50 mm. Especially for the two finer 

bed sediments (figs. 6 and 7), nearly all the computed

bed-material discharges were of particles finer than 

0.50 mm. For any one depth, the percentage temperature effect is reasonably constant for all the flows and 

bed sediments for which computations were made, but 

this relation may be due partly to the use of equation 3 

for all flows. This effect generally increases as the 

depth of flow increases, particularly if the temperature 

effect is appreciable as it is for the fine sand.

The computed differences in bed-material discharge 

for different water temperatures were due mostly to 

changes in the vertical distribution of the suspended 

sediment rather than to changes in the thickness of the 

laminar sublayer. According to the computation procedure, only the bedload discharge is affected by 

changes in thickness of the laminar sublayer, and any 

percentage change in the bedload discharge will cause 

an equal percentage change in the bed-material discharge. The bedload discharge of all particle sizes for 

the 0.20-mm median diameter, at a depth of 1.0 foot 

and a mean velocity of 2.0 feet per second, was about 

11 percent more at 40° than at 80° F. For this size of 

bed sediment and this assumed flow, the bedload discharges for two of the individual size ranges were 

about 20 percent more at 40° than at 80°F. For all 

other computations, the differences in bedload discharge 

for individual size ranges or for total bedload discharge were never more than a few percent for the 

change in temperature from 40° to 80 °F. Some of 

these small changes in bedload discharge were plus and 

some were minus for the stated change in temperature. 

Minus changes in bed-material discharges, because of 

changes in the thickness of the laminar sublayer, exceeded the computed plus changes in vertical distribution of suspended sediment for the two coarsest size 

ranges of the 0.40-mm sand for a mean velocity of 

5 feet per second. That is, the computed bed-material 

discharg increased rather than decreased for a change 

in temperature from 40° to 80°F. (See fig. 7.)

EFFECT ON BED CONFIGURATION

The sand bed in a laboratory channel may have several distinctive kinds of bed configurations and widely 

different resistances to flow (Simons and Richardson, 

1961). The configurations are related to some measure 

of flow, and physical size of the bed sediment has a complex and sometimes large effect on bed configuration 

(Simons and Richardson, 1961, fig. 3; 1962, fig. 2). A 

change caused in the fall velocity of sediment of a given 

physical size by a change in viscosity probably affects 

bed configuration and resistance to flow in much the 

same way as a similar change in fall velocity caused 

by a change in physical size.

Because bed configuration is difficult to define quantitatively and to express mathematically especially for
G8 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

10,000

0.20

MEDIAN DIAMETER, IN MILLIMETERS 

0.40 0.60

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EXPLANATION 

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FIGURE 5. Computed effect of water temperature on the relation of bed-material discharge to mean velocity.
COMPUTED BED-MATERIAL DISCHARGE BY SIZE RANGE, IN TONS PER DAY PER FOOT OF WIDT

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FIGDRB 7.. Computed sediment discharges by size ranges lor a bed sediment whose median diameter is 0.40 mm.

Temperatures are on the Fahrenheit scale.
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE Gil

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EXPLANATION 

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DEPTH,IN FEET

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FIGURE 8. Computed sediment discharges by size ranges for a bed sediment whose median diameter is 0.60 mm.

Temperatures are on the Fahrenheit scale.
G12 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

field streams, resistance to flow generally is used in this 

paper as an indication of bed configuration. The use of 

resistance to flow should be fairly satisfactory because 

of the comparatively large effect of bed configuration 

on resistance to flow (Vanoni and Brooks, 1957, p. 93- 

94), though sediment in the flow tends to decrease the 

resistance to flow for a given bed roughness (Vanoni 

and Brooks, 1957, p. 93-94). Furthermore, if the 

streambed is fairly smooth, the resistance to flow seems 

to vary as the median diameter of the bed sediment 

changes (Dawdy, 1961, p. C14).

Persons who study mainly flows in laboratory flumes 

are likely to have concepts of bed configuration somewhat different from those of persons who study mainly 

field flows. Part of the difference is due to differences 

in the methods of study and observation and part to 

differences in behavior of the streambed in small flumes 

and in field streams.

A worker with laboratory flumes may define a dune 

in terms of the dune shapes and the particle movements 

that he can readily see. On the other hand, the shape 

of the dunes and the movements of sediment particles 

over the dunes are difficult to observe in field streams, 

but the characteristic softness of the dunes and the general irregularity of a dune-covered streambed are well 

known to a worker with field streams. Such a worker 

is likely to define the dunes in terms of the observations 

that he has made of the softness and irregularity of the 

bed. A flume worker usually thinks in terms of a wide 

range of bed configurations from a plane bed without 

sediment movement to violent antidunes at a high 

Froude number, perhaps as high as 2.0. The field 

worker realizes that neither the plane bed without sediment movement nor the antidunes at Froude numbers 

as high as 2.0 have much field significance; he concentrates his attention on bed configurations that range 

from ripples to perhaps a narrow band of antidunes 

down the middle of a field stream whose cross section 

seldom has a Froude number that even approaches 1.0.

A significant difference in bed configurations in laboratory flumes to those in field streams is that the bed 

configurations in flumes are usually about uniform over 

the bed during most runs, whereas the bed configurations in field streams may differ greatly both laterally 

and longitudinally. Even though the entire bed of a 

field stream may be covered with dunes, the size of the 

dunes is likely to vary from place to place. The nonuniformity of bed configurations in field streams results 

mainly from variations of depth, average velocity at a 

vertical, and particle size from place to place in a channel reach. A change of flow with time may cause a 

certain change in bed configuration at one place but a 

different change at another place in a field stream. In 

general, the changes in bed configuration and in resistance to flow in field streams tend to average out to some 

degree over even short reaches and to be more gradual 

and less distinct and extreme than those in laboratory 

flumes.

FIEIJ> STREAMS

The effects of temperature changes on bed configuration and on resistance to flow are difficult to determine 

for field streams. Flows usually fluctuate widely, sometimes during short periods of time, and changes in flow 

may cause changes in bed configuration. Large changes 

in water temperature usually occur gradually and over 

longe periods of time. Hence, the effects of such temperature changes are not so clearly indicated as they 

would be if the changes occurred rapidly and if variations in flow and possibly in size of the bed sediment 

were small during the temperature changes. Even 

fairly large changes in temperature probably sometimes 

cause little change in resistance to flow if, for example, 

the stream has ripples or sand dunes on the bed throughout the range of flow. Furthermore, many field sites 

where flow and resistance to flow are observed are a 

short distance upstream from a gravel bar or a riffle 

that is more effective than bed configuration in controlling depth and velocity of flow.

The Middle Loup River at Dunning, Nebr., which 

has unusually constant flow throughout most years, has 

generally lower Manning's n's when the water temperature is low than when the temperature is high (Hubbell and others, 1956, p. 54 and fig. 23). Although the 

computed n's scatter considerably from the average relation on figure 9, the trend is fairly clear. Hubbell and 

others (1956, p. 3, 5) also noted a general absence of 

sand dunes at some cross sections during the winter, 

when n's were commonly low.

Observations with an ultrasonic depth sounder confirm the change of bed roughness of the Middle Loup 

River at Dunning from summer to winter for approximately equal flows. (See fig. 10.) Three longitudinal

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WATER TEMPERATURE, IN DEGREES FAHRENHEIT

FIGURE 9. General variation of Manning's n with water temperature 

for Middle Loup River at Dunning, Nebr., section C2. Numbers beside 

points indicate flow, in cubic feet per second.
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G13

profiles were defined for a summer day and three for a 

winter day. Each profile was selected as at least roughly 

representative of the streambed for one-third of the 

width of the flow. Each profile for June 25 indicated 

dunes of about the same size as the dunes indicated by 

the other two profiles. The dunes extended throughout 

the lengths of the sounder runs. The bed on December 5 

was definitely smoothest at the left profile and roughest 

at the right profile, but even the right profile was 

smoother than any of the three profiles for June 25. 

The bed configurations of figure 10 indicate major decreases in Manning's n from summer to winter and are 

considered to be representative for the flows and temperatures at which they were defined.

The ultrasonic sounder was described by Richardson, 

Simons, and Posakony (1961). The field use of the 

sounder in the Middle Loup River at Dunning, Nebr., 

was explained by D. W. Hubbell, C. H. Scott, and J. V. 

Skinner (written commun., 1960).

Some other streams show less consistent decreases in 

Manning's n with decrease in water temperature. Manning's n's given by Beckman and Furness (1962, table 

2) for the Elkhorn River near Waterloo, Nebr. (fig. 11), 

show no clear-cut reduction in n as the temperature decreases at either low or high flows. However, the few 

n's for low temperatures average considerably lower 

than the n's for high temperatures at flows between 

2,500 and 5,000 cfs (cubic feet per second). Somewhat

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DISTANCE DOWNSTREAM FROM SOUNDER SECTION, IN FEET

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FIGURE 10. Longitudinal profiles of streambed at different water temperatures, Middle Loup River at Dunning, Nebr. Upper set of graphs 

shows variations in streambed for June 25, 1959 (flow, 350 cfs; temperature, 83°F). Lower set of graphs shows variations in streambed 

for December 5, 1959 (flow, 360 cfs ; temperature, 39°F).
G14

0.10

SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

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STREAMFLOW, IN THOUSANDS OF CUBIC FEET PER SECOND

10 20

-Variation of Manning's » with streamflow and water temperature for Blkhorn River near Waterloo, Nebr. X, 60°P and above; 

 , below 60°P. (Data from Beckman and Furness, 1962, table 2.)

similarly, the n's given by Jordan (1965, table 2) for 

the Mississippi River at St. Louis, Mo., generally decrease as the flow increases (fig. 12); but, except perhaps for flows of more than 400,000 cfs, n's do not seem 

to vary significantly with temperature (fig. 13).

The n's for the three rivers probably indicate that 

water temperature has an appreciable effect on the resistance to flow only within certain ranges of flow, and 

these ranges are different for different streams. The 

flow of the Middle Loup River seems to be generally in 

the range for which a decrease in temperature may 

cause an appreciable decrease in n.

FLUME FLOWS

For some experiments in laboratory flumes, water 

temperature may have no consistent effect on resistance 

to flow (fig. 14). The data on which figure 14 is based 

were reported by Hubbell and Al-Shaikh Ali (1961, 

fig. 301.1) for a bed sediment whose median standardfall diameter, as defined by the U.S. Inter-Agency Committee on Water Resources (1957, p. 13, 14), was 0.31 

mm. Probably the information on figure 14 is insufficient to justify many conclusions except that of apparent inconsistency. Perhaps a tendency should be noted 

for a particularly high or a particularly low resistance 

to flow at either high or low temperatures to change 

toward more moderate resistances whether the temperature is increased or decreased, but the tendency may 

not be significant.

A set of flume experiments by Straub, Anderson, and 

Flammer (1958) was made to determine a temperature 

effect on bed-material discharge for bed sediment from 

the Missouri River. The stated median sieve diameter 

of the bed sediment was 0.163 mm, and runs were made 

at the same water discharge and at six different water 

temperatures. Depth of flow apparently depended on 

the volume of water in the experimental equipment. 

A 9-percent reduction in depth as the temperature decreased from 86° to 34°F was, of course, accompanied 

by a 10-percent increase in mean velocity. The combined effect of the increased velocity and the decreased 

temperature was insufficient to change the bed configuration appreciably under the conditions of the experiments. The resistance to flow did increase somewhat 

as the temperature decreased. The energy gradient 

was permitted to adjust freely.
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G15

0.10

0.01

100 

STREAMFLOW, IN THOUSANDS OF CUBIC FEET PER SECOND

1000

FIGURE 12. Variation of Manning's n with streamflow and water temperature for Mississippi Kiver at St. Louis, Mo. X, 60°F and above;

 , below GOT. (Data from Jordan, 1965, table 2.)

LU

30 40 50 60 70 80 90 100 

TEMPERATURE, IN DEGREES FAHRENHEIT

FIGURE 13. Ratios of observed values of n to values of « from average 

curve of figure 12 plotted against water temperature.

In spite of the wide differences in resistance to flow 

(fig. 14), the observed changes in bed-material concentration reported by Hubbell and Al-Shaikh Ali 

(1961, fig. 301.1) were not particularly large (fig. 15). 

The greatest increase of concentration at low temperature over the concentration at high temperature was 

73 percent, and the greatest decrease was 29 percent. 

The changes were much less than those for the Middle 

Loup Eiver at Dunning, Nebr. (Hubbell and others, 

1956, fig. 23), or those for the Missouri River bed sediment (Straub, Anderson, and Flammer, 1958, p. 8).

Presumably a main purpose of flume experiments 

should be to obtain information that may be applied 

to the behavior of field streams. In such streams, the 

temperature effects that usually have the most meaning 

are those at a cross section or within a short reach of 

stream. If the cross section is representative of a 

fairly long reach of the stream, the energy gradient, 

at least at steady flow, does not change appreciably as 

the temperature changes. That is, the energy gradient 

of a long reach of stream channel is generally constant 

over long periods of time. Hence, if a temperature
G16 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

change could increase appreciably the energy gradient 

at one place along the reach, it would necessarily decrease the energy gradient at some other place. Therefore, flume studies of temperature effect on bed configuration and on bed-material discharge might be more 

meaningful for field streams if they were made at constant energy gradient.

If width and energy gradient are constant during a 

set of experiments with flume flows, the relations among 

other variables probably are more nearly restricted to 

the relations that exist in fairly uniform field channels. 

Any change in resistance to flow requires changes in 

both depth and mean velocity if the flow is constant. 

Any change in resistance to flow at either constant

depth or at constant mean velocity requires a change 

in flow. If the bed configuration varies when water 

temperature varies, the change in bed configuration 

generally depends on which of the variables flow, 

depth, or mean velocity is kept constant. Perhaps 

fairly consistent temperature effects on bed configuration could be defined regardless of which of these three 

variables was kept constant while the temperature 

changed.

If energy gradient is fairly constant, a progressive 

increase in depth and flow may cause successively a 

plane bed without sediment movement, ripples, dunes, 

a transition phase, plane bed with sediment movement, 

standing waves, and antidunes to form on a sand bed

10 11 12 13 

FLOW RESISTANCE, IN TERMS OF -%=

14 16

Bed, form and How regime

8

, ripples 

, dunes with ripples superposed 

©, dunes 

D, transition 

D3, plane

|, mild antidunes

A, antidunes

Long-dash line indicates lower regime

Short-dash line indicates transition

Solid line indicates upper regime

FIGURE 14. Differences in resistance to flow for pairs of flume runs at high and low water temperatures (after Hubbell and Al-Shaikh Ali,

1961, fig. 301.1).
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G17

90

UJ

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UJ

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60

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40 100 1000 

SEDIMENT CONCENTRATION, IN PARTS PER MILLION

Bed form and flow regime

10,000 30,000

8

, ripples 

, dunes with ripples superposed 

C, dunes 

D, transition 

E3, plane

|, mild antidunes

A, antidunes

Long-dash line indicates lower regime

Short-dash line indicates transition

Solid line indicates upper regime

FIGURE 15. Differences in bed-material concentration for pairs of flume runs at high and low water temperatures (after Hubbell and Al-Shaikh

All, 1961, flg. 301.1).

(Simons and Richardson, 1960, p. 77). However, the 

change in flow would have to be very large to produce 

all these kinds of streambed at constant energy gradient. A small change in flow may have a much larger 

effect on bed configuration at some ranges of the progressive increase than at other ranges.

Experiments at constant energy gradient should 

show a reasonably understandable temperature effect 

on the succession of bed configurations as the flow 

increases. In general, a decrease of fall velocity because of a decrease in temperature should have much 

the same effect on bed configuration as an appropriate 

increase in flow at constant energy gradient. In other 

words, the effect produced on the bed configuration by 

a particular temperature change should be about reproducible by the proper change in flow at constant 

temperature.

OVERALL TEMPERATURE EFFECTS ON BED-MATERIAL 

DISCHARGE

Iii the preceding discussions, three temperature effects that changes in viscosity cause on flow and on 

bed-material discharge have been considered. These 

effects on the thickness of the laminar sublayer, on 

the vertical distribution of suspended sediment, and on 

the bed configuration are the ones that might be included in a theoretical computation of bed-material discharge. Although theoretically computed bed-material 

discharges are generally inaccurate, a study of these 

three effects provides a background for evaluating and
G18 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

interpreting available field and laboratory information 

on the overall effect of water temperature on 'bedmaterial discharge.

Overall temperature effects, as the term is used here, 

are those that are based on experimentally determined 

bed-material discharges. They require careful classification mainly in relation to the other independent variables that were used as measures of bed-material discharge and to the manner in which the effects were determined rather than in relation to the theoretical temperature effects. Temperature, as compared to mean 

velocity or to shear, has a relatively minor effect on 

bed-material discharge, and the relation of bed-material 

discharge to factors that have major effects partly controls the residual temperature effect. For example, an 

experimentally defined temperature effect on bed-material discharge might be for a constant flow and mean 

velocity and a variable energy gradient, for a constant 

mean velocity and energy gradient and a variable flow, 

or for a constant flow and energy gradient and a variable mean velocity. A temperature effect might be obtained by a regression study that involved such other 

statistically independent variables as median particle 

size of the bed sediment, shear, and depth of flow. The 

effect on the relation between bed-material discharge 

and total shear might be considerably different from 

the effect on the relation between bed-material discharge 

and mean velocity; either of these effects usually is 

different for deep flows than for shallow flows, and for 

fine bed sediment than for coarse bed sediment. Briefly, 

any defined or definable overall temperature effect has 

little specific meaning unless it is carefully identified 

and clearly stated.

DIFFERENCES BETWEEN FLUME FLOWS AND 

FIELD STREAMS

Overall temperature effects for flows in laboratory 

flumes may appear to be considerably different from 

those for flows in field streams for at least five somewhat 

related reasons. These reasons are (1) the relative 

shallowness of flume flows, (2) the wide range of Froude 

number and of bed configuration for flume flows, (3) 

the general uniformity of bed configuration over the 

effective part of the flume bed at most times, (4) the 

variability of energy gradients for flume flows, and (5) 

the difference in types of data analysis for flume data 

and for field data. Because temperature effects are 

small as compared with some other effects on bed-material discharge, they usually are observed and defined 

for field streams at a cross section of a fairly uniform 

reach of channel in which the particle sizes of the bed 

sediment and the energy gradient remain fairly constant.

The relative shallowness of flume flows has considerable bearing on the observed temperature effects. In 

particular, the percentage effect, which is reasonably 

consistent, of water temperature on bed-material discharge because of changes in fall velocity and in vertical 

distribution of the suspended sediment is less in shallow 

flume flows than in deep field flows (fig. 5). In contrast, 

the highly variable effect of water temperature on bed 

configuration and on resistance to flow (fig. 14) is just 

as large and probably more noticeable in shallow flume 

flows than in deep field flows.

The wide range of Froude numbers and of bed configurations for flume flows leads to a strong emphasis 

on the variable effect of water temperature on bed configuration and on resistance to flow. In contrast, most 

canals and many large field streams that flow over beds 

of sand are in the dune range of flow nearly all the 

time. For example, the Mississippi River at St. Louis, 

Mo., seldom has a Froude number greater than about 

0.20 for a cross section and probably always has dunes 

on at least part of its bed even at the highest flows. 

(Of course, the Froude number for the whole cross 

section is only a very rough guide to bed configuration, 

but a low Froude number does indicate a narrow range 

of possible bed configurations.) Thus, the range of 

bed configuration of the Mississippi River at St. Louis 

may be only from dunes everywhere to dunes on part of 

the streambed and washed out dunes or perhaps a plane 

bed on other parts of the bed. For this range, a decrease of water temperature at a particular flow should 

always tend to reduce the resistance to flow, if it causes 

any appreciable effect.

The general uniformity of the bed configuration from 

place to place in a flume flow provides a better chance 

for observing the effect of water temperature for distinctly different bed configurations than does the usually 

less uniform bed configuration of natural streams. In 

field streams, most observations of temperature effect 

are made for a bed that is partly or wholly covered 

with dunes. Overall temperature effects on bed-material discharge have probably never been clearly defined 

for a natural stream that had one consistent bed configuration, other than dunes, throughout a reach at 

both high and low temperatures. (A natural stream 

does not include canals or artificially improved stream 

channels.) Many field streams may also have bars or 

riffles of coarse sand or of gravel. The surfaces of these 

bars or riffles may not change configuration or resistance 

to flow appreciably as the temperature changes.

The variability of energy gradients for flume flows 

introduces a complicating factor that is largely avoided 

for field flows by studying temperature effects at one 

cross section or within one short reach. The same sort 

of complicating factor might be included in studies of 

the temperature effect for field streams if these studies
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G19

were attempted by comparing bed-material discharges 

from cross sections of different streams whose energy 

gradients differed greatly. Because energy gradients 

usually are permitted to vary widely in flume experiments, flow is not closely related to either mean velocity 

or depth alone. In field streams on the other hand, 

streamflow, mean velocity, and depth are likely to be 

closely interrelated except, perhaps, for a narrow range 

of discontinuity (Dawdy, 1961) if the reach has relatively uniform lateral and longitudinal distributions of 

velocity, depth, and particle size. Because of the interrelations, the temperature effect at a constant flow has a 

more definite meaning for a field stream than for a 

flume flow, and fewer variables may need to be included 

in an analysis of the temperature effect in a field stream. 

Methods of analyzing temperature effects for flume 

studies may be much different from those for field 

studies. As noted above, somewhat different temperature effects are likely to be stressed and observed for 

flume flows than for field flows, and different data may 

be measured for the two types of flow. For example, 

energy gradient or at least water-surface slope is 

nearly always determined for flume flows, whereas it 

may not be determined at all or may be very inaccurate 

for field flows. On the other hand, mean velocity is 

nearly always known for field flows, but it is usually 

not determined directly for flume flows. Thus, workers 

with flume flows are inclined to base their analyses of 

data on such factors as shear or stream power that 

require a knowledge of energy gradient; workers with 

field flows are more likely to base their analyses on 

mean velocity or on discharge per foot of stream width. 

The use of mean velocity largely bypasses the rather 

indeterminate effect of water temperature on bed configuration. Flume workers, however, may reject mean 

velocity as a basic measure of bed-material discharge 

because it is a poor measure, according to A. A. Bishop 

(Sediment transport in alluvial channels: a critical 

examination of Einstein's theory: Colorado State Univ. 

Ph. D. thesis, 1961), at the high Froude numbers at 

which many flume experiments are run. Actually, few 

field streams have Froude numbers as high as 1.0 even 

for short periods of time.

Some difficulties in applying flume results to field 

streams are illustrated by the flume experiments for 

the Missouri River bed sediment ('Straub, Anderson, 

and Flammer, 1958). Because the depth of flow was 

permitted to decrease 9 percent as the temperature decreased, the mean velocity at constant flow per unit 

width increased 10 percent. If both the energy gradient and the flow had been kept constant, the indicated 

increase in resistance to flow with decrease in temperature from 86° to 34°F would liave required a decrease 

in mean velocity rather than an increase. Because bedmaterial discharge is likely to increase as perhaps the 

third power of the mean velocity at constant temperature, an appreciable part of the reported 200-percent 

increase in bed-material discharge may have been due 

to experimental conditions that were somewhat inconsistent with conditions at a representative cross section 

of a sand-bed stream.

The confirmation of the experimental temperature 

effect (Straub, Anderson, and Flammer, 1958, p. 10,11, 

and fig. 16) for the Missouri River sediment through 

computations of suspended sediment by the Einstein 

procedure (1950) was based on #'s somewhat inconsistent with observed z's for field streams. Generally, 

vertical distributions of suspended bed material in rivers (Einstein and Chien, 1954, fig. 1; Colby and Hembree, 1955, p. 69-77; Hubbell and Matejka, 1959, 

p. 70-72) show that z changes less rapidly than theoretical s's, which vary directly as the first power of 

the fall velocity. If Straub, Anderson, and Flammer 

had used 0's that changed less rapidly than the first 

power of the fall velocity, the differences between the 

computed bed-material discharges would have 'been 

smaller for each temperature change.

Briefly, the overall temperature effect observed on 

bed-material discharge in flumes is generally due 

largely to changes in bed configuration and resistance 

to flow. On the other hand, the overall temperature 

effect on the relation between bed-material discharge 

and mean velocity in deep field streams is due mainly 

to changes in vertical distribution of the suspended bed 

material.

ROUGHLY DEFINED EFFECT FOB FIELD STREAMS

Even though the effect of water temperature on bedmaterial discharge cannot be defined accurately, a 

rough idea of the amount of the effect on bed-material 

discharges in field streams should be generally helpful. 

A first step in determining the effect is to decide which 

other factors should be included as measures of bedmaterial discharge. As already indicated, the effect of 

change in water temperature on bed configuration and 

on resistance to flow is not well known but seems to be 

erratic and to depend on the antecedent bed configuration, whereas the effect of water temperature on the 

relation of bed-material discharge to mean velocity 

(fig. 5) may be fairly consistent. Hence, mean velocity 

may be a suitable major factor to use as a dominant 

measure of bed-material discharge, and a defined temperature effect on the relation of bed-material discharge 

to mean velocity may be meaningful and helpful.

An average relation between bed-material discharge 

(equivalent to discharge of sands for this site) per foot 

of stream width and mean velocity shows a rapid in-
G20 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

crease of bed-material discharge for the Niobrara River 

near Cody, Nebr., with increase in velocity. (See 

fig. 16.) The ratios of the individual bed-material discharges to the average bed-material discharges from 

the curve of figure 16 can be plotted against water 

temperature (fig. 17) to define a rough experimental 

effect of water temperature on the relation between 

bed-material discharge and mean velocity. Of course,

200

100

MEAN VELOCITY, IN FEET PER SECOND

FIGURE 16. Relation of bed-material discharge to mean velocity for 

Niobrara River near Cody, Nebr. (from Colby, 1964, fig. 7).

OBSERVED BED-MATERIAL DISCHARGE

 3.U 

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MATERIAL DISCHARGE FROM CURVE Fl OF5 p *- r> i- n oo c01 

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0.4

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X

.

. 

^

 . 

s

 N

 * *

 

,

 <

*

^

* ,

'

& .*-

X

*

sf

s

k

30 40 50 60 70 80 90 100 

TEMPERATURE, IN DEGREES FAHRENHEIT

FIGURE 17. Approximate relative effect of water temperature on the 

relation between bed-material discharge and mean velocity for Niobrara River near Cody, Nebr. (from Colby, 1964i, fig. 22).

scatter of points from the curve of figure 17 is due 

partly to experimental error and to factors whose effects 

have not been eliminated. Hence, the effect of water 

temperature should be more consistent than figure 17 

seems to indicate.

Temperature effects on the relation of bed-material 

discharge to mean velocity were similarly defined for 

the Middle Loup River at Dunning, Nebr., and for the 

Mississippi River at St. Louis, Mo. The three experimentally determined effects are surprisingly consistent 

(see the slopes of lines on fig. 18), perhaps partly by 

chance. They provide a rough idea of the probable 

temperature effect for field streams. The slopes of the 

lines on figure 18 indicate a change of bed-material 

discharge that is fairly consistent with the computed 

temperature effects of figure 5.

The relation of bed-material discharge to mean velocity for the Niobrara River (fig. 16) was based mainly 

on measurements that were made when the water was 

at least moderately warm. The streamflow and the 

depth generally increased as the mean velocity increased. The question might be raised whether the
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G21

relations shown by figures 16 and 17 can be applied to 

a stream such as the Middle Loup Eiver at Dunning, 

Nebr., in which the size of the bed sediment is about the 

same as that for the Niobrara River at Cody but in 

which the sediment discharge and the resistance to flow 

may change rather widely without much change in 

streamflow (Hubbell and others, 1956, fig. 23).

Bed-material discharges computed from figures 16 

and 17 (table 1) seem to explain adequately the increase 

of sediment discharge, mostly bed-material discharge, 

that accompanied a decrease in Manning's n, according 

to Hubbell and others (1956, fig. 23). The total bedmaterial discharges were computed from information 

given by Hubbell and others (1956, table 1) for section

0

;_.

NX

X

EXPLANATION

Niobrara River near Cody, Nebr

Middle Loup River at Dunning, Nebr 

Mississippi River at St. Louis, Mo

20 100

TEMPERATURE, IN DEGREES FAHRENHEIT

FIGURE 18. Approximate relative effect of water temperature on the 

relation between bed-material discharge and mean velocity for three 

rivers (after Colby, 1&64, fig. 23).

D at which substantially the total sediment discharge 

was measured. Water temperatures, mean velocities, 

and stream widths for computing bed-material discharges from figures 16 and 17 were also given by Hubbell and others (1956, tables 1 and 4).

TABLE 1. Measured and computed bed-material discharges for 

Middle Loup River at Dunning, Nebr.

[Basic data from Hubbell and others, 1956, tables 1 and 4]

Date

1955

Nov. 24... .............................

Nov.24. ............. ......

1956

Jan. 8

Mar.7 

Mar.8. - 

May8 

Section

Bi

C2

C2

Cz

C2

Bi

A

E

Temperature

38

35

32

32

39

32

55

64

Bed-material discharge (tons per day)

Measured

at section

DI

2,550

2,550

2,850

2,790

2,970

3,200

1,830

1,290

Computed 2

2,300

3,100

3,400

2,800

2,800

3,900

1,100

1,300

1 Practically the entire sediment discharge is in suspension and can be measured 

at section D.

2 Based on relations shown by figures 16 and 17 and on mean velocities, widths, and 

water temperatures for sections other than section D.

The generally satisfactory agreement (table 1) 'between bed-material discharges measured at section D 

and those computed for sections other than D from 

mean velocities, widths, water temperatures and figures 

16 and 17 implies some significant findings. (The agreement for section A, May 8,1956, is not good, but section 

A is more than a mile upstream from section D and is 

usually a poor section for either measuring or computing bed-material discharge.) One point is that figures 

16 and 17 may be applicable to streams other than the 

ones for which they were defined. Another point is 

that the increase in bed-material discharge that accompanies a decrease in resistance at almost constant flow 

is explainable in terms of the effect of the increased 

mean velocity on the bed-material discharge. A consequent point is that the erratic and difficult-to-define 

temperature effect on bed configuration and resistance 

to flow (figs. 11, 12, and 14) probably can be avoided 

by using mean velocity as a measure of tyed-material 

discharge.

If mean velocity is accepted as a logical major factor 

that correlates with bed-material discharge, an inexact 

but probably logical and practical graph can be defined 

for indicating the general effect of water temperature 

on the relation of bed-material discharge to mean velocity. The slopes of the curves of figure 18 can be used 

as experimental measures of the temperature effect for 

bed sediments whose median diameters are about 0.2 to 

0.3 mm. Unfortunately, these curves were based on 

data (fig. 17) that were not sufficiently exact to define
G22 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

a difference between the temperature effect at one depth 

and that at another. However, the probable relative effect of water temperature on the relation between bedmaterial discharge and mean velocity can be approximated for different depths from the curves of figure 5. 

Thus, information, partly theoretical and partly experimental, can be combined to define roughly the temperature effect that is indicated by the main graph of figure 

19, a figure that was given by Colby (1964, fig. 24). Of 

course, the relation is not well defined and gives only 

an approximate idea of the effect that might be expected 

for different depths and water temperatures. The effect 

is denned for, and is directly applicable to, only those 

bed sediments whose median diameters are about 0.2 

to 0.3 mm. The effect is on the relation between bedmaterial discharge and mean velocity. The temperature effect might be considerably different on, for example, the relation of bed-material discharge to total 

shear or to stream power. Hence, the temperature 

effect indicated on figure 19 should always be understood and designated as an effect of water temperature 

on the relation of bed-material discharge to mean 

velocity.

Of course, the temperature effect varies somewhat as 

the size distribution of the bed sediment changes even 

though the median diameter remains constant. It also 

varies as the depth or the mean velocity changes. A 

complete definition of the complex temperature effect 

on the relation of bed-material discharge to mean velocity obviously is not now possible. Even if a complete 

definition were possible, it probably would be very complicated, and its application for many flows might not 

appreciably improve the accuracy of computed bedmaterial discharge.

Because the effect of water temperature on the relation of bed-material discharge to mean velocity varies 

as the median particle size of the bed sediment changes, 

the effect indicated by the main graph of figure 19 

should be decreased as the bed sediment sizes become 

either much smaller than 0.2 mm or much larger than 

0.3 mm. (See figs. 5-8.) A very rough idea of the 

possible change in temperature effect with change in 

median diameter was given by Colby (1964, fig. 24) 

and is shown on the small graph of figure 19. The 

indicated decrease of the temperature effect as the 

median particle size of the bed sediment increases above 

0.3 mm may be too rapid. The decrease depends considerably on the size distribution as well as on the 

median diameter and has not yet been experimentally 

defined. Of course, an adjustment coefficient of 1.20 

from the main graph would become 1.16 (1.00+80 percent of 0.20) rather than 0.96 (80 percent of 1.20) for 

an 80-percent effect from the small graph. Thus, the 

effect on computed bed-material discharges of large

errors in the small graph generally will be small as 

compared to other possible errors in computing bedmaterial discharge, except for very high concentrations 

of fine sediment.

EFFECT OF CONCENTRATION OF FINE SEDIMENT

The effect of high concentrations of fine sediment, 

particularly of some clays, is discussed briefly here for 

two reasons. First, this effect, like the temperature 

effect, seems to be mainly through an increase in the 

apparent viscosity of the water-sediment mixture 

(Simons, Eichardson, and Haushild, 1963). Second, 

the effect of high concentrations of fine sediment may 

be much greater than the effect of water temperature 

and may obscure the effect of temperature in some 

field flows.

If the effect of the fine sediment on bed-material discharge is due almost wholly to the change that the fine 

sediment causes in the apparent viscosity of the watersediment mixture, the effect should be similar to a 

change in water temperature. According to Simons, 

Eichardson, and Haushild (1963), the addition to distilled water at 60°F of 2 percent or 20,000 ppm (parts 

per million) by weight of a commercial bentonite had 

the same effect on the apparent kinematic viscosity as 

a change in water temperature from 60° to 34° F. This 

general equivalence of concentration of 'bentonite to 

change in temperature was used by Colby (1964, fig. 24) 

as the basis for estimating the effect (fig. 19) of concentrations as high as 20,000 ppm of fine sediment that 

is mostly bentonite. Extensions of the effect to higher 

concentrations of fine sediment were based on rough 

proportioning from the lower concentrations and on 

some determinations of bed-material discharge, mostly 

determinations for the Bio Puerco near Bernardo, 

N. Mex. A given concentration of bentonite has a 

greater effect on apparent viscosity than the same concentration of kaolin (Simons, Eichardson, and Haushild, 1963).

Eecently, C. H. Scott (U.S. Geol. Survey unpub. 

data, 1964) measured the fall velocities of three small 

samples of sorted sands in distilled water and in dispersions of Wyoming bentonite in distilled water. The 

nominal diameters of the smallest and the largest of 

the sorted sands were 0.48 and 3.20 mm, and the maximum concentration of bentonite was 17,500 ppm. At 

this maximum concentration, the fall velocities of the 

0.48- and 3.20-mm sands were about 39 and 5 percent 

less, respectively, than in clear distilled water. The 

3.20-mm sand is large enough to have its fall controlled 

much more by turbulent forces than by viscous forces. 

The relatively small effect of the bentonite in suspension on the fall velocity of the coarse sand is consistent 

with the assumption that fine sediment probably af-
TEMPERATURE WATER FOR COEFFICIENT ADJUSTMENT 

SEDIMENT FINE OF CONCENTRATION AND 

I

f 

5

>- >- >- i-' i-' <G 00 -J CTi (Jl -t> GO W IO .(* .-_._. 

^ co ro - o o o o o o o oooooooooroo 

p p p p p Q Q Q Q Q b Q O 0 , Q O o o o o 

888888888§8§8§

FOR EFFECT PERCENTAGE 

SIZES PARTICLE MEDIAN DIFFERENT 

o >- 

o o 
G24 SEDIMENT TRANSPORT IN ALLUVIAL CHANNELS

fects fall velocity mainly by changing the apparent 

viscosity of the water-sediment mixture rather than by 

directly interfering with the settling of the course 

particles.

However, Scott found that the fall velocity of the 

0.48-mm sand decreased much more rapidly with increasing concentration of bentonite than the fall velocity of the 0.47-mm sand that was used by Simons, 

Richardson, and Haushild (1963). The reasons for the 

difference in effects are not clear, but the difference may 

be due, at least partly, to differences between the commercial bentonites that were used in the dispersions. 

J. C. Mundorff (written commun., 1960) has shown 

that both concentration and characteristics of the suspended material have a significant effect on the fall 

velocities of sands and that, in general, bentonite has 

the most pronounced effect.

Of course, care should be used in interpreting laboratory experiments on the effects of bentonite or other 

fine sediment on the fall velocities of sands. Differences in the kinds and concentrations of dissolved solids 

in the water-sediment mixture, in the exchangeable 

ions on the clay particles, and in turbulence all may 

have appreciable effects on the relation of the concentration of fine sediment to the fall velocities of the 

sands.

Presumably, the small graph of figure 19 can be used 

in a similar manner for adjustments for the effect of 

fine sediments and for the effect of water temperature. 

Of course, the indicated effect of the concentration of 

fine sediment is an effect on the relation of bed-material 

discharge to mean velocity and should not be used 

directly as an effect on any other relation of bedmaterial discharge to a factor that controls bed-material 

discharge.

CONCLUSIONS

Changes in water temperature have at least three 

effects on bed-material discharge as the result of 

changes in the viscosity of the water.

One effect is on the thickness of the laminar sublayer. 

A change in this thickness affects the relation between 

mean velocity at a given depth and the effective shear 

on the bed sediment. For most flows, the change in the 

relation is only a few percent for usual temperatures 

in natural streams.

A second effect is on the vertical distribution of sediment concentration because of changes in fall velocity. 

Several computations of bed-material discharge for different depths, average velocities, median particle sizes, 

and water temperatures of 40°, 60°, and 80°F gave reasonably consistent temperature effects on bed-material 

discharges for a stream vertical. The computed bedmaterial discharges were roughly twice as large for the

temperature of 40° as for the temperature of 80°. Effects of changes in the thickness of the laminar sublayer were included in the computations, but they were 

small as compared with the effects of changes in fall 

velocity. The computed temperature effect on bedmaterial discharge varied little as the velocity changed, 

but it did increase somewhat as the depth increased. 

The percentage effect differed widely from one size range 

to another and was small for particles coarser than 0.5 

mm.

A third effect is on bed configuration and resistance to 

flow. It seems to be rather erratic, at least for flume 

flows, and presumably affects field flows significantly 

when the bed configuration is close to a critical point of 

change to another configuration. This poorly defined 

temperature effect on bed-material discharge can be 

largely eliminated by using mean velocity as a dominant 

measure of bed-material discharge for field streams.

A temperature effect is rather meaningless unless it 

is carefully defined and clearly designated. Not only 

are there the three general types of temperature effect 

mentioned above, but each type of analytical study and 

each set of experiments may define a different sort of 

temperature effect because different variables are kept 

constant or different variables are included in the study.

Temperature effects observed in flumes may be considerably different from those defined at a cross section 

of a field stream. As compared with field streams, flume 

flows generally are shallow, have energy gradients that 

are frequently adjusted, and may cover a wide range 

of Froude numbers and bed configurations, but the bed 

configuration at any one time is likely to be relatively 

uniform laterally and longitudinally. Furthermore, the 

type of analysis used for flume data may be different 

from that used for field data.

A temperature effect was roughly defined for field 

streams whose bed sediments have median diameters of 

about 0.2 to 0.3 mm. For each of three rivers, an average curve was prepared of bed-material discharge per 

foot of stream width against mean velocity. The indicated scatter of each bed-material discharge from the 

average curve was then plotted against water temperature to define experimentally an average effect of water 

temperature on the relation of bed-material discharge 

to mean velocity for the river. The three resultant 

curves of temperature effect and the computed increase 

of percentage temperature effect as the depth increases 

(fig. 5) were used as the principal bases for a graph of 

approximate temperature effect on the relation between 

bed-material discharge and mean velocity.

High concentrations of fine sediment may have 

an effect on the apparent viscosity of a water-sediment 

mixture that is generally similar to and may obscure
EFFECTS OF WATER TEMPERATURE ON BED-MATERIAL DISCHARGE G25

the effect of water temperature. A graph of probable 

effect of concentrations of fine sediment that is mostly 

bentonite was based partly on the graph for the temperature effect and partly on some bed-material discharges 

for the Eio Puerco in New Mexico. Although the 

graph is inexact, it indicates a possibly very large effect 

of high concentrations of fine sediment on the relation 

of bed-material discharge to mean velocity.

Only a general idea is given in this paper of the different temperature effects and of the quantitative effect 

of water temperature on the relation of bed-material 

discharge to mean velocity. Much further study is required before the many different and complex temperature effects can be defined satisfactorily.

REFERENCES

Anderson, A. G., 1942, Distribution of suspended sediment in a 

natural stream: Am. Geophys. Union Trans., 23d ann. mtg., 

pt. 2, p. 678-683.

Beckman, E. W., and Furness, L. W., 1962, Flow Characteristics 

of Elkhorn River near Waterloo, Nebraska: U.S. Geol. Survey Water-Supply Paper 1498-B, 34 p.

Colby, B. R., 1956, Relationship of sediment discharge to streamflow : U.S. Geol. Survey open-file report.

 1964, Discharge of sands and mean-velocity relationships 

in sand-bed streams: U.S. Geol. Survey Prof. Paper 462-A, 

1964, 47 p.

Colby, B. R., and Hembree, C. H., 1955, Computations of total 

sediment discharge, Niobrara River near Cody, Nebraska: 

U.S. Geol. Survey Water-Supply Paper 1357, 187 p.

Colby, B. R. and Hubbell, D. W., 1961, Simplified methods for 

computing total sediment discharge with the modified Einstein procedure: U.S. Geol. Survey Water-Supply Paper 

1593,17 p.

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

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

Water-Supply Paper 1498-C, 16 p.

Einstein, H. A., 1950, The bed-load function for sediment transportation in open channel flows: U.S. Dept. Agriculture 

Tech. Bull. 1026, 70 p.

Einstein, H. A., and Chien, Ning, 1954, Second approximation 

to the solution of the suspended load theory: California 

Univ. Inst. Eng. Research, U.S. Army Corps of Engineers, 

Missouri River Div. Sediment Ser. 3, 30 p.

Hubbell, D. W., and Al-Shaikh Ali, K., 1961, Qualitative effects 

of temperature on flow phenomena in alluvial channels: 

U.S. Geol. Survey Prof. Paper 424-D, Art. 301, D21-D23.

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, 

123 p.

Hubbell, D. W., Jordan, P. R., Cul'bertson, D. M. } and Hembree, 

C. H., 1956, Progress report number 1, Investigations of 

some sedimentation characteristics of a sand-bed stream: 

U.S. Geol. Survey open-file report.

Jordan, P R,, 1965, Fluvial sediment of the Mississippi River 

at St. Louis, Missouri: U.S. Geol. Survey Water-Supply 

Paper 1802 (inpress).

Keulegan, G. H., 1938, Laws of turbulent flow in open channels: 

U.S. Natl. Bur. Standards Jour. Research, v. 21, p. 707-741.

Lane, E. W., Carlson, E. J., and Hanson, O. S., 1949, Low temperature increases sediment transportation in Colorado 

River: Civil Eng., v. 19, p. 619-620.

Richardson, E. V., Simons, D. B., and Posafcony, G. J., 1961, 

Sonic depth sounder for laboratory and field use: U.S. Geol. 

Survey Circ. 450, 7 p.

Rouse, Hunter, 1937, Modern conceptions of the mechanics of 

fluid turbulence: Am. Soc. Civil Engineers Trans., v. 102, 

p. 463-543.

Rubey, W. W., 1933, Settling velocities of gravel, sand, and silt 

particles: Am. Jour. Sci., 5th ser., v. 25, no. 148, p. 332.

Schulz, E. F., Wilde, R. H., and Albertson, M. L., 1954, Influence 

of shape on the fall velocity of sedimentary particles: 

Colorado Agr. and Mech. Coll., U.S. Army Corps of Engineers, Missouri River Div. Sediment Ser. 5, 161 p.

Simons, D. B., and Richardson, E. V., 1960, Resistance to flow 

in alluvial channels: Am. Soc. Civil Engineers Proc., v. 86, 

no. HY5. p. 73-99.

 1961, Forms of bed roughness in alluvial channels: Am. 

Soc. Civil Engineers Proc., v. 87, no. HY3, p. 87-105.

 1962, The effect of bed roughness on depth-discharge

relations in alluvial channels: U.S. Geol. Survey WaterSupply Paper 1498-E, 26 p.

Simons, D. B., Richardson, E. V., and Haushild, W. L., 1963, 

Some effects of fine sediment on flow phenomena : U.S. Geol. 

Survey Water-Supply Paper 1498-G, 47 p.

Straub, L. G., Anderson, A. G., and Flammer, G. H., 1958, Experiments on the influence of temperature on the sediment 

load: Minnesota Univ., U.S. Army Corps of Engineers, 

Missouri River Div. Sediment Ser. 10, 36 p.

U.S. Congress, 1935, Missouri River: U.S. 73d Cong., 2d sess., 

H. Doc. 238, p. 1089-1092.

U.S. Inter-Agency Committee on Water Resources, 1957, Some 

fundamentals of particle size analysis, in A study of methods 

used in measurement and analysis of sediment loads in 

streams: Rept. 12, 55 p., Washington, U.S. Govt. Printing 

Office.

Vanoni, V. A., and Brooks, N. H., 1957, Laboratory studies of 

the roughness and suspended load of alluvial, streams: 

California Inst. Technology [Pasadena, Calif.], Sedimentation Lab. Rept. E-68, 121 p.

US. GOVERNMENT PRINTING OFFICE: 1965 O 756-940